# Survey of prognostics methods for condition-based maintenance in engineering
systems

Ehsan Taheri 111Research fellow, Department of Aerospace Engineering, 1320
Beal Avenue, Ann Arbor, MI 48109, USA<EMAIL_ADDRESS>Ilya Kolmanovsky
222Professor, Department of Aerospace Engineering, 1320 Beal Avenue, Ann
Arbor, MI 48109, USA Department of Aerospace Engineering, University of
Michigan, Ann Arbor, MI 48105, USA<EMAIL_ADDRESS>Oleg Gusikhin 333Advanced
Connected Services, Ford Research & Advanced Engineering, Dearborn, MI, 48124,
USA Ford Research & Advanced Engineering<EMAIL_ADDRESS>
###### Abstract

It is not surprising that the idea of efficient maintenance algorithms
(originally motivated by strict emission regulations, and now driven by safety
issues, logistics and customer satisfaction) has culminated in the so-called
condition-based maintenance program. Condition-based program/monitoring
consists of two major tasks, i.e., diagnostics and prognostics each of which
has provided the impetus and technical challenges to the scientists and
engineers in various fields of engineering. Prognostics deals with the
prediction of the remaining useful life, future condition, or probability of
reliable operation of an equipment based on the acquired condition monitoring
data. This approach to modern maintenance practice promises to reduce the
downtime, spares inventory, maintenance costs, and safety hazards. Given the
significance of prognostics capabilities and the maturity of condition
monitoring technology, there have been an increasing number of publications on
machinery prognostics in the past few years. These publications cover a wide
range of issues important to prognostics. Fortunately, improvement in
computational resources technology has come to the aid of engineers by
presenting more powerful onboard computational resources to make some aspects
of these new problems tractable. In addition, it is possible to even leverage
connected vehicle information through cloud-computing. Our goal is to provide
a report on the state of the art and to summarize some of the recent advances
in prognostics with the emphasis on models, algorithms and technologies used
for data processing and decision making.

###### keywords:

Prognostics and health management (PHM), Condition-based maintenance (CBM) ,
Remaining useful life (RUL) , Automotive, Aerospace and Marine engineering

††journal: arXiv

###### Contents

  1. 1 Introduction
  2. 2 Review of CBM, Modelings and Algorithms
    1. 2.1 Diagnostics and Prognostics: Key Differences
    2. 2.2 Critical component identification
    3. 2.3 Failure modes and Prognostic tasks
    4. 2.4 Confidence limits
    5. 2.5 Implementing prognostic models
  3. 3 Prognostic Models And Their Classification
  4. 4 Life expectancy models
    1. 4.1 Stochastic models
      1. 4.1.1 Aggregate reliability functions
      2. 4.1.2 Conditional probability models
      3. 4.1.3 RUL probability density function
      4. 4.1.4 Static Bayesian Networks
      5. 4.1.5 Dynamics Bayesian Networks
      6. 4.1.6 Bayesinan estimation with Kalman filters
      7. 4.1.7 Bayesian estimation with particle filters
    2. 4.2 Statistical models
      1. 4.2.1 Trend evaluation
      2. 4.2.2 Autoregressive models
      3. 4.2.3 Proportional hazards modelling
    3. 4.3 Physical models
  5. 5 P&HM Tool Selection Method
    1. 5.1 Visualization tools
  6. 6 Performance Metrics for Evaluating Prognostic Predictions
    1. 6.1 Applications
  7. 7 Automobile Applications
    1. 7.1 Peer-to-Peer Collaborative Vehicle Health Management
      1. 7.1.1 System Implementation
      2. 7.1.2 Experimental Results
      3. 7.1.3 Simulation Results
      4. 7.1.4 Preliminary penetration analysis
    2. 7.2 Automatic transmission: Wet-clutch system
    3. 7.3 Alternator
  8. 8 Challenges And Opportunities
  9. 9 Concluding remarks

##  1 Introduction

Mechanical and electrical systems, and in particular, their building
blocks/components, are subject to gradual tear and wear that will ultimately
disrupt their proper operation and make them faulty. However, the
deterioration procedure varies and depends on certain operating conditions
such as stress, load and environment, etc. Considering the vast application
and reliance of our daily life on machines, maintenance has a significant role
in assuring safe and proper operation of the existing systems.

Traditionally, maintenance activities have taken one of two approaches:
preventive and corrective [1]. The (time- or duty-based) preventive
maintenance also known as planned maintenance defines a periodic time interval
(or a certain duty), usually based on experience (or tests), to replace the
component irrespective of its actual health status [2]. For instance, the most
common application of such a strategy, in automotive engineering, is the
replacement of engine oil. These tasks are scheduled to occur after driving
for a certain number of months (or miles). Another example is the timing belt
on an automobile, which may be recommended to be replaced after five years (or
60,000 miles [3]).

Preventive maintenance leads to a costly maintenance strategy given the
expenses associate with the modern complex components. In addition, the
preventive maintenance does not provide any information about the health
status of a component, which is a major defect for safety-critical components,
which could lead to disasters, for instance, in the field of aerospace
engineering. On the other hand, the corrective maintenance strategy seeks to
replace a component once it is no longer operational and is not capable of
performing its assigned task. This maintenance strategy, which is the most
undesirable form of maintenance, has significant drawbacks. It is more labor
intensive, does not eliminate catastrophic failures and causes unnecessary
maintenance, which is costly by itself. In addition, there are costs
associated with maintenance labor and downtime as well as the safety concerns
and customer satisfaction. Considering a passenger vehicle, the impact on
customer satisfaction is a major driving factor simply because the component
failure might occur miles away from any repair shop. For other safety-critical
applications (e.g. in the aerospace engineering), the corrective maintenance
is avoided by adopting alternatives in which redundant components are
considered since the failure is not tolerated. Collectively, expenses due to
preventive and corrective maintenance constitute a significant portion of the
expenses of many industrial companies.

Between these two extreme maintenance strategies lies condition-based
maintenance (CBM), wherein maintenance actions are performed as needed based
on the condition of the equipment or component (see Fig. 1).

Figure 1: Schematic diagram for operational, maintenance and total cost;
colored regions denote different maintenance strategies.

CBM avoids any unnecessary maintenance task by scheduling maintenance actions
based on the conditions or observation of abnormal behaviours of a component.
The more effective a CBM program is implemented the less maintenance cost will
be. Within the aerospace community, and aside from the safety issue, this
corresponds to lowering the downtime, which directly translates into
significant amounts of money. With respect to the automotive industry, the
replacement prices as well as the repair costs when multiplied by the
population of vehicles is quite considerable. A CBM maintenance scheme can
directly affect the following aspects of a system: 1) to improve the ability
in detecting faults, 2) to improve the plant safety, 3) to better maintenance
plans and decision making, 4) to reduce the inspection time and associated
labor costs, 5) to increase the availability of assets.

CBM grants the ability to evaluate a system’s actual health/damage conditions
and provides the user with a prediction of failure, which is quite an
essential tool for industrial applications. The costs associated to
interruption of a business usually prove to be significantly higher than the
expenses due to the repairs to return a business back to service [4]. For the
electrical machines the average annual rate of failure is estimated to be at
least 3% and for motors that have to operate under hostile conditions and
environment, such as mining or pulp and paper industries, the annual failure
rate is even greater and could be as high as 12% [5]. Therefore, it is
inevitable to ensure the availability of assets if a business is interested in
profitable operation. This directly translates to an accurate estimation of
the remaining useful life (RUL) of a system and its constituents or
components. In other words, accurate RUL estimation can enable failure
prevention in a more controllable manner in that effective maintenance can be
executed in appropriate time to correct impending faults. There are two main
tasks in a successful CBM, i.e., diagnostics and prognostics, which will be
discussed in the next section. The overall life cycle cost of systems is
reducible by implementing prognostics health monitoring (PHM) [6, 7]. On the
other hand, developing a CBM is a significant technical challenge.

Presenting a survey for a field as diverse as CBM could be a daunting task.
Perhaps the most difficult issue is restricting the scope of the survey to
permit a meaningful discussion within a limited amount of space. To achieve
this goal, we made a conscious decision to focus on the most important aspect
of the CBM, i.e., prognostics. However, first we try to distinguish some of
the salient aspects of diagnostics and its relation to prognostics. We, then,
elaborate on the utmost objectives of CBM and highlight the significance of
each task necessary for realizing any CBM program. A brief discussion of the
methods, models and other important major steps of a CBM program are
presented, whereas the emphasis is to provide the reader with a review that
highlights and classifies the existing applications of prognostics in
engineering areas such as aerospace, marine and automotive. We then discuss a
few applications to prognostics of automotive engineering. Finally, we
describe some of the challenges and opportunities that belong to the ongoing
research. The authors’ intent is to provide the researchers in scientific
community, with the state-of-the-art in the aforementioned majors of
engineering over the recent few years.

##  2 Review of CBM, Modelings and Algorithms

In order to better understand the subject of CBM, it is necessary to
distinguish between its two main constituents, i.e., _diagnostics_ and
_prognostics_. In the following sections we explain briefly the fundamental
differences between these two tasks. We will also discuss the importance of
the confidence limit, which is a major factor in the decision making
procedure. Classification of the models used in prognostics is also provided.

###  2.1 Diagnostics and Prognostics: Key Differences

In principle, diagnostics is conducted to investigate the root cause of a
failure and analyze the nature of a problem, whereas prognostics is related to
predicting the future behaviour as a result of rational study and analysis of
available pertinent data. Diagnostics itself is broken into three subtasks: 1)
fault detection, 2) fault isolation, and 3) fault identification when it
occurs [1]. Fault detection is a task to indicate whether something is going
wrong in the monitored system; fault isolation deals with a task to locate the
faulty component; and the last step, fault identification, is a task to
determine the nature of the fault when it is detected. In terms of the
relationship between diagnostics and prognostics, the former is an in-depth
exploration of the failure mode to identify its leading cause after it has
occurred within a system/component, whereas the latter is the process of
generating a rational estimation of the RUL. Therefore, in its simplest form,
prognostics is to monitor and detect the initial indications of degradation in
a component, and be able to consistently make accurate predictions [8]. It is
important to realize that time is a critical variable in prognostics and it is
more or less trying to answer the question “when a component will fail?”,
distinguishing it from diagnostics, in which time plays a less important role,
and instead the emphasis being placed more on determining the parameters of an
already occurring fault or failure.

A diagnostics system consists of a series of steps each of which of its own
importance. These steps include 1) data collection, 2) feature extraction
(signal processing), and 3) a knowledge base of faults, which may be derived
from expert knowledge, physical models and historical data. Therefore, it is
highly reliant on the knowledge base as the final determination of what type
of failure has occurred, and why it is achieved by comparing the utilizing
feature extraction results with the knowledge base. A comprehensive review of
techniques and methods used in fault diagnostics in beyond the scope of this
work; however, the interested readers are referred to some of the excellent
reviews [1, 9, 10, 11]. The prognostics, on the other hand, shares some of the
tasks of the diagnostics and requires several other steps. It shares the same
tasks of feature extraction and a knowledge base of faults and further
conducts performance assessment, degradation models, analysis of the
degradation patterns and making judicious predictions. However, signals such
as fault indicators and degradation rates, that the prognostics relies on,
belong to the outputs of the diagnostics, which means that these two parts are
somewhat intertwined. When combined, performance assessment and degradation
models can describe a machine’s relative health status and indicate what kind
of degradation patterns may exist. The ultimate goal of most prognostic
systems is accurate prediction of the RUL of individual systems or components,
on the basis of their use and performance. This is important since it allows
advances scheduling of maintenance activities, proactive allocation of
replacement parts and enhances fleet deployment decision based on the
estimated progression of component life. Prediction algorithms, which could be
derived from classic time series theories, statistics or artificial
intelligence technologies, can forecast when machine performance will decrease
to an unacceptable level as defined by the failure analysis and health
management.

Engineering prognostics is used by industry to reduce business risks due to
unexpected failures of equipment. It still relies highly on the experience and
knowledge gained over years and its application is limited to systems for
which significant data base is available (e.g., rotary machines). On the other
hand, the models used in prognostics are application dependent, which requires
extensive analysis of the results and assumptions. Appropriate model selection
for successful practical implementation, requires both a mathematical
understanding of each model type, and also an appreciation of how a particular
business intends to utilize the models and their outputs. Unfortunately, there
is no general prognostic model to fit all business needs and not all of the
models are well proven mathematically. In addition, efficacy of models is
dependent upon the availability of required data, skilled personnel and
computing infrastructure.

Prognostics is a relatively new research area and is not a well-developed
discipline compared to other areas of CBM. A number of literature reviews
covering CBM with emphasis on prognostic components including models and
approaches have already been presented in [12, 13, 14, 15, 16, 17, 18, 19,
20]. Table 1 summarizes some of the most important review papers to date where
AI, SA and ANN stand for Artificial Intelligence, Signal Analysis and
Artificial Neural Networks, respectively. In addition, Reference [21] reviews
the benefits and challenges of prognostics and Reference [22] reviews the
condition-based maintenance. Table 2 also shows highlights typical
applications for some of the more common predictive maintenance technologies
[23].

Table 1: Summary of the existing review papers and their focus on different prognostics methods. Reference | Year | Knowledge- | Experience- | Data- | Model- | Hybrid | Other methods
---|---|---|---|---|---|---|---
|  | based | based | Driven | based |  |
[24] | 2003 |  |  |  |  |  |
[3] | 2005 |  |  |  |  |  |
[1] | 2006 |  |  |  |  |  | AI
[25] | 2006 |  |  |  |  |  |
[26] | 2006 |  |  |  |  |  |
[27] | 2006 |  |  |  |  |  | Reliability, Stochastic
[28] | 2008 |  |  |  |  |  | Stress and effects-based
[17] | 2009 |  |  |  |  |  |
[29] | 2011 |  |  |  |  |  | Life Expectancy, ANN
[21] | 2011 |  |  |  |  |  |
[30] | 2014 |  |  |  |  |  |
[31] | 2014 |  |  |  |  |  | SA, Stochastic, ANN
[31] | 2015 |  |  |  |  |  |
Table 2: Common predictive technology applications. Technology |  Pumps |  Electric Motors |  Diesel Generators |  Condensers |  Heavy Equipment/Cranes |  Circuit Breakers |  Valves |  Heat Exchangers |  Electrical Systems |  Transformers |  Tanks, Piping
---|---|---|---|---|---|---|---|---|---|---|---
Vibration Monitoring/Analysis | $\times$ | $\times$ | $\times$ |  | $\times$ |  |  |  |  |  |
Lubricant, Fuel Analysis | $\times$ | $\times$ | $\times$ |  | $\times$ |  |  |  |  | $\times$ |
Wear Particle Analysis | $\times$ | $\times$ | $\times$ |  | $\times$ |  |  |  |  |  |
Bearing, Temperature/Analysis | $\times$ | $\times$ | $\times$ |  | $\times$ |  |  |  |  |  |
Performance Monitoring | $\times$ | $\times$ | $\times$ | $\times$ |  |  |  | $\times$ |  | $\times$ |
Ultrasonic Noise Detection | $\times$ | $\times$ | $\times$ | $\times$ |  |  | $\times$ | $\times$ |  | $\times$ |
Ultrasonic Flow | $\times$ |  |  | $\times$ |  |  | $\times$ | $\times$ |  |  |
Infrared Thermography | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ |
Non-destructive Testing (Thickness) |  |  |  | $\times$ |  |  |  | $\times$ |  |  | $\times$
Visual Inspection | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$
Insulation Resistance |  | $\times$ | $\times$ |  |  | $\times$ |  |  | $\times$ | $\times$ |
Motor Current Signature Analysis |  | $\times$ |  |  |  |  |  |  |  |  |
Motor Circuit Analysis |  | $\times$ |  |  |  | $\times$ |  |  | $\times$ |  |
Polarization Index |  | $\times$ | $\times$ |  |  |  |  |  | $\times$ |  |
Motor Circuit Analysis |  |  |  |  |  |  |  |  | $\times$ | $\times$ |

Although useful in appreciating the state of the art, we feel that there is a
need for a literature review that incorporated the salient aspects of a
reliable CBM that not only presents a review of models and their merits but
also focuses on specific practical implementations in specific engineering
fields. Reference [20] adopts a similar strategy while focusing on rotary
machine systems whereas the application of prognostics for other components is
growing. Knowledge of the prior work is a necessity for future research
efforts. To address this gap, this paper provides a review of the field of
PHM, which focuses on the practical applications on various components in the
fields of engineering such as automotive, aerospace and marine engineering.

###  2.2 Critical component identification

Identifying critical components is the first step in developing a prognostics
and health monitoring system. One approach in identifying the significance of
components on the overall performance and cost downtime of a system is to use
a quadrant chart as is shown in Fig. 2 (taken from [20]). A similar figure is
also shown in [32] for the selection of critical components.

Figure 2: Component fault Frequency-Downtime chart and four quadrants for
identifying critical components [20].

It displays the frequency of failure versus the average downtime associated
with failure for relevant components of 890 SW Robots. The effectiveness of
the current maintenance strategy can be seen when the data is graphed in this
way. The horizontal and vertical lines that divide the graph to four quadrants
are user-defined parameters based on their demands on production and/or
maintenance. The resulting quadrants are numbered 1-4 starting with the upper
right and moving counter clockwise. The first quadrant represents those
components that not only fail more frequently, but also result in extensive
downtime. Typically, there should not be any components in this quadrant
because such issues should have been noticed and fixed during the design
stage. However, there could be instances in which a manufacturing defect in,
or continued improper use of, a particular component could result in
repetitive failures and significant downtime. The second quadrant still
contains components with a high frequency of failure, but each component
causes a short downtime. The maintenance recommendation for such components is
to have an adequate number of spare parts on hand. The third quadrant contains
components with a low frequency of failure and low average downtime per
failure, which means that the current maintenance practices are working for
these components and no changes are required. In the fourth quadrant lie the
most critical components as their failures, though infrequent, cause the most
downtime per occurrence and could potentially incur significant costs. The
components of this last quadrant should be the focus of prognostics. For
instance, as is shown in Fig. 2, the filed of robotics prognostics should
focus on encoder, motor and gearbox as critical components. The existence of
similar data for the other engineering fields improves the return of
prognostics by developing frameworks for components that play a critical role
in the overall performance and cost. The reader is referred to [20] for
additional information on this matter.

###  2.3 Failure modes and Prognostic tasks

To understand the role of models in prognostics, it is important to identify
the various steps involved in obtaining an RUL estimate (which is the holy
grail of prognostics) and its confidence bounds. Figure. 3 shows the process a
component undergoes from a healthy state performance until its final failure.

Figure 3: Typical performance degradation for three different failure modes.

It depicts highly simplified degradation curves for three different and
independent failure modes, which could represent different types of failure of
the same component. There is a stable zone during which the performance of the
component is not affected. However, the component is eventually going to
degrade and fall into the degradation zone, which itself is divided into two
regions, i.e.,- low and high-degraded regions defined by their bounds
(levels), respectively. The selection of the performance levels is a critical
task in any prognostics approach. In addition, Fig. 3 shows the spread of the
time once a degradation curve hits a specific level. The confidence
(precision) in determining those probabilities is essential in decision making
and is discussed in the next section. Note also that there are factors that
effect the degradation patterns which triggers different failures. The
progression of any failure mode may be accelerated due to the changes in the
operating conditions, maintenance actions or even progression of the other
failure modes (e.g, a bearing fault causes high vibration that induces and
accelerates mechanical seal degradation). Therefore, an efficient procedure to
estimate RUL correctly needs to address the following questions (or know
preliminary information about them): 1) what is the current degradation rate?,
2) which failure mode (or modes) has (have) been triggered and contributes to
the degradation?, and 3) how much is known of the severity of the degradation?
(determines the position of the component of the particular curve).

If a systems-oriented approach to prognostic-based decision support is
desired, then RUL estimates should be further supplemented with forecasts
describing the impact of predicted failures on operational and maintenance
activities which can be considered at the business management level rather
than prognostics task [33, 34]. Based on the collective approaches, one could
conceptualize a diagnostic/prognostic framework that addresses prognostics
through three levels with varying degrees of complexity, i.e., existing
failure mode prognostics, future failure mode prognostics and post-action
prognostics [29]. The prognostics models discussed in this review keeps the
complexity to the simplest level, i.e., existing failure mode prognostics.
Almost all of the works in the literature belong to this category.

###  2.4 Confidence limits

The output of a prognostic algorithm has two components: 1) an estimate of
time to failure, which is also referred to as the RUL and 2) an associated
confidence limit [15]. Analysis of the confidence limit is important since the
prognostics intrinsically deals with estimating an uncertain variable
parameter, which is effected by several factors including the future operation
of the component, operating conditions and errors due to the fidelity of the
utilized diagnostics and prognostics models. Confidence limits are even more
important in prognostic modelling than for diagnostic prediction. This is due
to the fact that in diagnostics the failure and the extent of damage is known
and is an externally verifiable quantity (e.g., actual crack size) whereas
this is not the case in prognostics as it deals with failure. It is highly
important for business decisions to be made based on the bounds of the RUL
confidence interval rather than a specific value of the component expected
life [15].

###  2.5 Implementing prognostic models

There are certain aspects that have to be considered before implementing any
prognostics model. First of all, most of the prognostics program deal with
accurate prediction of URL of an identified failure mode. This strategy is
retained to keep the process simple and tractable. In addition, the existence
of certain type of data, level of complexity of the model and the underlying
assumptions will make the models better suited to certain applications. One
could pose a series of questions to assess the performance and suitability of
a particular model to a particular problem,

  * 1.

Prediction requirement: what does the RUL prediction need to achieve?

  * 2.

Model-process capability: can the model describe the reality?

  * 3.

Resource requirements: are the resources available to undertake the modelling?

  * 4.

Approach readiness: is the modelling approach sufficiently well proven to be
relied upon?

These four criteria do not include factor that should be considered before
prognostics are undertaken in the first place, which is beyond the scope of
this work. A good discussion of this topic is presented in [35].

##  3 Prognostic Models And Their Classification

With the discussion given on the overall task of prognostics and the
importance of the RUL estimation we focus on the existing models and their
capability in providing the necessary information to practitioners. Current
prognostic approaches can be categorized into four major classes:
experimental, data-driven, model-based and hybrid. Reviewing the literature it
is apparent that papers limit their discussions to data-riven or model-based
approaches and a few of them address the experience-based approach. A detailed
classification of models into four groups is given in [29] specifically
designed for RUL prediction. It is further divided into varying number of
subgroups (see Fig. 4). The material of this section is mainly taken from
[29].

Figure 4: Classification of models used for URL prediction.

  * 1.

Knowledge-based models [36, 37, 38, 36, 39]: these models assess the
similarity between an observed situation and a database of previously defined
failures and deduce the life expectancy from previous events. Sub-categories
include _expert systems_ and _Fuzzy systems_.

  * 2.

Life expectancy models: determine the life expectancy of individual machine
components with respect to the expected risk of deterioration under known
operating conditions. Sub-categories are separated into _statistical_ and
_stochastic_ models. Stochastic models are further divided into two models
i.e., aggregate reliability functions and conditional probability methods.
Statistical models include trend extrapolation, auto-regressive moving average
(ARMA) model and its variants, and proportional hazard modelling (PHM).

  * 3.

Artificial Neural Networks: These models compute an estimated output for the
RUL of a component, directly or indirectly, from a mathematical representation
of the component that has been derived from observation data rather than a
physical understanding of the failure processes. They are further grouped into
models used for direct URL forecasting and parameter estimation for other
models.

  * 4.

Physical models: These models compute an estimated output for the RUL of a
component from a mathematical representation of the physical behavior of the
degradation process. Types of physical models tend to be application (failure
mode) specific and are therefore not classified further.

It is a difficult task to strictly categorize a model into the presented
classes, particularly due to the fact that more recently the models in the
literature are a combination of two or more classical modelling approaches.
Model selection requires that the main advantages and disadvantages of each
model type be well understood. For a list of generic advantages and
disadvantages of the introduced models refer to [29]. A brief description of
each model is given in Table 3 to familiarize the reader with their basic
advantages and disadvantages. The advantages and disadvantages are mostly
associated with the simplicity of the method (either model and/or its of
implementation), capability to provide confidence limit, reliance on the
amount and accuracy of data, availability of tools and softwares, capability
to incorporate new data, ability to model previously unanticipated faults,
capability to manage incomplete data sets, being able to model multivariate
dynamic models and their level of computational efficacy. Table 4 summarizes
considerations for using or avoiding a particular type of model. These two
tables serve as an initial guideline for selecting a particular model to be
used in the later stages of a prognostic framework. In the next sections we
briefly discuss the underlying principles of each model.

Table 3: Advantages and disadvantages of prognostic modelling options. Model |  Advantages |  Disadvantages
---|---|---
Knowledge based |  |
Expert systems |  1. Simple (albeit time consuming) to develop 2. Easy to understand |  1. Relies entirely on knowledge of subject matter experts 2. Significant number of rules required 3. Significant management overhead to keep knowledge base up to date 4. Precise inputs required 5. No confidence limits supplied 6. Not feasible to provide exact RUL output
Fuzzy systems |  1. Fewer rules required than for expert systems 2. Inputs can be imprecise, noisy or incomplete 3. confidence limits can be provided on the output with some types of models |  Domain experts required to develop rules
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Aggregate reliability functions |  1. Simple and well understood by reliability engineering community 2. Numerous software options available 3. Theoretically can be performed at all equipment hierarchy levels, especially whin a small number of failure modes dominate 4. Confidence limits are available for RUL predictions 5. Accuracy and precision increases as RUL decreases resulting in the ability to set useful warning limits |  1. Failures must be statistically independent and identically distributed 2. In most cases will require a statistically significant sample size pertaining to each failure mode for reliable RUL predictions 3. Warnings prior to actual failure are not readily available
RUL PDF |  1. Simple and easy adaptation of basic reliability approaches 2. Only requires that time at which failure has not occurred is monitored (i.e, no condition monitoring data) 3. Theoretically can be performed at all equipment hierarchy levels, especially when a small number of failure modes dominate 4. Confidence limits are available for RUL predictions 5. Accuracy and precision increases as RUL decreases resulting in the ability to set useful warning limits |  1. Available accuracy and precision is dependent on forecasting interval 2. In most cases will require a statistically significant sample size pertaining to each failure mode for reliable RUL predictions 3. Assumes that hazard is a function of operating time rather than external risk factors
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Static Bayesian Networks |  1. Can readily manage incomplete data sets 2. Allow/force user to learn about causal relationships 3. Captures and integrates expert knowledge 4. Algorithms available to avoid the over fitting of data 5. Computer software available for modelling 6. Confidence limits are intrinsically provided |  1. Cannot model previously unanticipated faults and/or root causes 2. Computational difficulty of exploring a previously unknown network 3. A Bayesian network is only as useful as the prior knowledge is reliable 4. Results may be sensitive to selection of prior distribution 5. Modelling experts required in addition to domain experts
Markov, Semi-Markov models |  1. Well established approach and able to model numerous system designs and failure scenarios 2. Can readily manage incomplete data sets |  1. Reasonably large volume of data required for training 2. Assumes a single monotonic, non temporal failure degradation pattern (i.e., different stages of failure cannot be accounted for) 3. Cannot model previously unanticipated faults and/or root causes 4. More complex semi-Markov models are required if failures or failur progression times are not exponentially distributed 5. Not appropriate for repairable systems that are only partially restored
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Hidden Markov, Semi-Markov models |  1. Can model different stages of degradation so failure trend does not need to be monotonic 2. Can model spatial and temporal data 3. Specific knowledge of failure mechanism progression is not required 4. Can readily manage incomplete data sets 5. Provide confidence limits as part of their RUL prediction |  1. Large volume of data required for training, proportional to the number of hidden states 2. Cannot model previously unanticipated faults and/or root causes 3. More complex Hidden semi-Markov models are required if failures or failure progression times are not exponentially distributed 4. Computationally intensive, particularly for a large number of hidden states
Bayesian techniques with Kalman Filters |  1. Can be used to model multivariate, dynamic processes 2. Basic KF is computationally efficient, particulary for systems with a large number of states 3. Can accommodate incomplete and noisy measurements 4. Variants available for non-linear processes 5. Other advantages on underlying Bayesian technique |  1. Process and measurement noise must be Gaussian 2. Some variants diverge easily 3. Variants for non-linear systems are more computationally intensive than basic Kalman filters 4. Measurement data required 5. Other disadvantages depend on underlying Bayesian technique
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Bayesian techniques with Particle Filters |  1. Can bes used to model multivariate, dynamic processes 2. Noise does not need to be either linear of Gaussian 3. More accurate than Kalman filter variants for non-linear systems 4. Other advantages depend on underlying Bayesian technique |  1. A large number of samples (or resampling) are required to avoid degeneracy problem 2. Can be more computationally intensive than basic Kalman filters 3. Measurement data required 4. Other disadvantages depend on the underlying Bayesian technique
Statistical |  |
Trend extrapolation |  1. Simplest technique to apply and explain 2. Easy to set alarms 3. Advanced software tools not required |  1. Few failures have a well-defined monotonic, single-parameter trend 2. Interpretability is affected by process/measurement noise and variations in operating conditions 3. Availability of confidence limits dependent on amount of data at the different states of failure development
ARMA Models & variants |  1. Advanced ARMA related techniques available for non-stationary data 2. Historical failure data is not required 3. Usually computationally efficient and therefore can be performed in real time 4. An understanding of detailed failure mechanisms not required 5. Provide accurate and reliable short term predictions of RUL |  1. Basic ARMA models assume stationarity of the process and noise 2. Does not integrate prior or expert knowledge 3. sensitive to noise and initial conditions 4. significant data required for model development and validation 5. Long-term predictions of RUL are less reliable
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Statistical |  |
PHM |  1. COTS software available 2. Accounts for age dependent and independent hazards 3. Models are simple to develop Confidence limits can be calculated |  1. All relevant covariates must be included in the model 2. Mixing different types of covariates in one model may be problematic 3. Strict (albeit implied) assumptions regarding nature of underlying process 4. Historical data required pertaining to individual failure modes 5. Multi-collinearity, monotonicity and large covariate values that can cause a failure of the model parameter estimation process 6. Parameter selection often manual and time consuming and the selection of parametric estimation technique is not straightforward 7. Traditional PHM equation assumes covariates describe a stationary process. Dynamic PHM is more involved 8. Can only be used to develop models for failures that have been experienced previously and for which associate covariate data is available 9. Too easy to develop a model that may be statistically adequate but does not represent any actual failure phenomenon (i.e. physically meaningless)
Table 3 (continued). Model |  Advantages |  Disadvantages
---|---|---
Artificial Neural Networks |  |
For Forecasting with ANNs |  1. Complex multi-dimensional, non-linear systems can be modelled 2. Physical understanding of the system behaviour not required 3. ANN variants facilitate the use of any type of input data 4. Computer software is available for modelling |  1. Requires a significant amount of data for training data that needs to be representative of true data range and its variability 2. Determining the most appropriate model is largely trial and error and therefore can be time consuming 3. Most networks cannot provide confidence limits on the output 4. Pre-processing is required to limit the number of data inputs and reduce model complexity 5. All published research is relatively recent 6. Outputs need to mapped to a physical representation
Parameter Estimation with ANNs |  1. As for RUL Forecasting with ANNs 2. Useful for incorporating with physics of failure models 3. Confidence limits available from underlying model (for which parameters are being estimated) |  1. Less data required for estimating parameters as models tend to be failure specific 2. Determining the most appropriate model is largely trial and error and therefore can be time consuming
Physical models |  |
Physical Models |  1. Provide most accurate and precise estimates of all modelling options 2. Confidence limits provided 3. Outputs can be easily understood |  1. Detailed and complete knowledge of system behaviour required 2. The accuracy and robustness are subject to the experimental conditions under which models were developed
Table 4: When to consider/avoid using particular models. Model |  When to consider |  When to avoid
---|---|---
Knowledge based |  |
Expert systems |  1. Well-understood, stable, narrow problem area 2. human experts are available to develop the knowledge base; and operating conditions are stable and predictable; and simple precise queries to define potential faults is impossible; and only an approximate RUL estimate is required |  1. No human experts are available to define comprehensive set of rules; or fault maintenance are not well understood; or operating conditions are highly variable; or highly accurate or precise RUL estimates are required
Fuzzy systems |  1. One or more variables are continuous; and a mathematical model is not available or not feasible to implement; and data contains high levels of noise or uncertainty; and difficult to define exact queries that identify specific faults |  No human experts are available to define fuzzy rules; or input data is discrete and limited to a small number of options
Stochastic |  |
Aggregate reliability functions |  1. Sample size is statistically significant and representative of individual sample; and 2. Small set of dominant failure modes; and 3. PDF is not exponential; and Reliability growth is not occurring; and 4. RUL prediction is predominantly used for overall maintenance management rather than tracking of a specific asset (e.g., when redundancy is available) so gradual escalation of warning levels are not required |  1. Only a small number of failures can be attributed to individual failure modes; or 2. Significant number of possible failure modes that cannot be easily differentiated, or historically have not been; or 3. Hazard rate is constant; or 4. Past operating conditions are not representative of current environment or usage; or 5. The specific asset is critical to plant safety or operations and warning is required prior to failure
Table 4 (continued). Model |  When to consider |  When to avoid
---|---|---
Stochastic |  |
RUL PDF |  1. Sample size is statistically significant and representative of individual sample; and Small set of dominant failure modes; and 2. PDF is not exponential; and 3. Reliability growth is not occurring 4. Condition monitoring data is not available; and 5. Operating age can be tracked to confirm absence of failure; and 6. Only final estimates need to be particularly accurate and precise |  1. Only a small number of failures can be attributed to individual failure modes; or 2. Significant number of possible failure modes that cannot be easily differentiated, or historically have not been; or 3. Hazard rate is constant; or 4. Past operating conditions are not representative of current environment or usage; or 5. Failure is hidden and no failure finding is being undertaken; or 6. High-level of accuracy and precision is required a long time into the future
Table 4 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Static Bayesian Networks |  1. Incomplete, multivariate data available; and 2. Root cause of failure known; and 3. process and plant configuration is relatively static or network is confirmed up to date; and 4. Modelling experts are available |  1. Root causes of failure unknown; or 2. Expert plant and modelling knowledge unavailable; or 3. Training data is unavailable
Markov, Semi-Markov models |  1. Simple to develop and implement; 2. Incomplete, multivariate data available; and Root causes of failure known; and 3. Process and plant configuration is relatively static or network is confirmed up to date; and 4. Relatively accurate and precise RUL estimate is required |  1. Repairable system; or 2. Temporal measurement data as model inputs; or 3. Sufficient data related to failure mode is not available for training; or 4. Failure being modelled has more than one discrete stage (e.g., crack initiation, growth , final failure, etc)
Hidden Markov, Semi-Markov models |  1. Repairable systems; and 2. Root causes of failure known; and 3. Failure being modelled has more than one discrete stage 4. Temporal data to be used as model inputs 5. Relatively accurate and precise RUL required |  1. Sufficient data related to failure mode is not available for training; or 2. Suitable hardware for computation is not available
Bayesian techniques with Kalman Filters |  1. Multivariate posterior distribution; and 2. Additive; and 3. Condition monitoring data is available; and 4. Relatively accurate and precise RUL estimate required |  1. Multiplicative noise; or 2. Single variable posterior distribution; or 3. Covariate data is not available for the failures of interest
Table 4 (continued). Model |  Advantages |  Disadvantages
---|---|---
Stochastic |  |
Bayesian techniques with Particle Filters |  1. Multi-variate or non-standard posterior distribution 2. Non-linear, non-Gaussian noise; and 3. Relatively accurate and precise RUL estimate required |  1. Typical deterministic posterior distribution; or 2. Linear, Gaussian; or 3. Multiplicative noise; or 4. Single variable posterior distribution; or 5. Covariate data is not available for the failures of interest
Statistical |  |
Trend extrapolation |  1. Single defined failure mode associated with a single monitored (or calculated) parameter that can be described with a monotonic trend; and operating conditions are stable or do not affect monitored parameter; and 2. Measurements are repeatable, reliable and not highly sensitive to measurement processes (e.g., online sensors) |  1. Incipient failure cannot be related to a simple measurable input; or 2. Varying operating conditions that affect the measured parameter but are not related to failure; or 3. Trend is not monotonic; or 4. Data highly dependent on measurement process; or Data is subject to high levels of process or measurement noise; or 5. Reliable confidence limits are required on the extrapolated RUL estimate
ARMA Models & variants |  1. Hazard rate is a linear relationship of covariates and noise; and 2. Short-term predictions required; and 3. Hazard rate is independent of age (i.e., exponential distribution); and 4. Measurement data is available for modelling and application but historical failure data is not |  1. Hazard rate is not a linear relationship of covariate and noise; or 2. When historical or expert data is available in addition to measurement data; or 3. Long-term predictions are required; or 4. Sufficiently large volume of data is not available for model construction and validation
Table 4 (continued). Model |  Advantages |  Disadvantages
---|---|---
Statistical |  |
PHM |  1. Times to failure are independent and identically distributed; 2. Covariate have a multiplicative effect on the baseline hazard rate; and 3. A number of covariates are available and required to describe change in risk; and 4. Process represented by covariates is stationary (unless using Dynamic PHM); and 5. Associated covariate data is available for the failure modes being modelled; and 6. Only the final RUL estimate and confidence limit is required (not an estimate of a precursor to failure) |  1. Failures have not occurred previously or have no associated covariate data 2. Hazard rate is not multiplicative; or 3. Failures cannot be segregated into individual (or dominating) failure modes; or 4. Covariates related to the failure modes being modelled cannot be measured; or 5. Process represented by the covariates is non-stationary; or 6. If a precursor to failure is to be predicted rather than final failure itself
Table 4 (continued) Model |  Advantages |  Disadvantages
---|---|---
Artificial Neural Networks |  |
For Forecasting with ANNs |  1. Large amount of noisy, numerical, temporal data; and 2. Physical, statistical or deterministic model is not known or impractical to apply; and 3. An exact optional answer for RUL is required |  1. Data is complex or symbolic; or 2. Justification or physical extrapolation not required; or 3. Temporal inputs are not available; or 4. Minimal data is available for training
Parameter Estimation with ANNs |  1. An RUL model (typically a physical model) is available but contains unkown parameters; and 2. Large amount of noisy, numerical temporal data; and 3. An exact optimal answer for RUL is required |  1. Data is complex or symbolic; or 2. Minimal data is available for training
Physical models |  |
Physical Models |  1. Failure modes are well understood and defined; and 2. A physical model for each failure mode is available; and 3. Operating conditions can be monitored and statistically represented; and 4. Process/condition data is available; and 5. High-accuracy and precision required in RUL prediction |  1. A physical model is not available

##  4 Life expectancy models

The basic idea in developing the life expectancy models is to determine the
RUL of a component with respect to the expected risk of deterioration. It is
also assumed that the operating conditions are known.

###  4.1 Stochastic models

Stochastic models provide reliability-related information, such as Mean Time
to Failure (MTTF) as probabilities of failure with respect to time. Stochastic
behaviour is at the heart of these methods and they are based on the
assumption that the times to failure of identical components can be
represented by statistically identical and independent random variables and
thus be described by a probability density function. One main driving factor
of these models is the existence of data, which in the case of sparse failures
leads to overly pessimistic estimates. It is shown that the accuracy of the
estimate of MTTF can be improved by utilizing censored (suspended data) (times
at which failure has not occurred or there is no evidence of failure) [40].
The ability to use censored data is important since most of the experimental
data is attained through accelerated tests using experimental rigs or bench
tests and most of the time the accelerated tests are terminated after a
certain period of time and consequently results in censoring. Using censored
data is not necessarily helpful especially in small data sets in which
censoring might occur early in life and this can introduce other errors [41].
In the simplest form of application, RUL is equated to the time remaining
before a critical number of failures (e.g., 5%) are expected to occur.

####  4.1.1 Aggregate reliability functions

This is the standard approach widely accepted and used in industry, especially
in certain problems for which reliable and considerable amount of data is
available. Detailed information on applying statistical distributions to
modelling and failure data can be found in various publications [41, 42, 43,
44, 45, 46, 47]. The overall task consists of determining a probability
density function and its related hazard function for a population of
components and analyzing the time to failure (TTF). Obviously, the density
function is the representative of the whole population and not a single fault
progression. In the simplest theoretical approximation, a fault progression
curve typically follows an exponential curve and provides information about
the expected time of failures. There are various mathematical relations to
approximate the probability distributions that best model the failure data
(e.g., Exponential, Gaussian, Normal, Lognormal and Weibull functions).
Gaussian distribution is the most famous and commonly used distribution in
reliability engineering due to its ability to describe many different failure
types. The classical well-known bathtub curve (see Fig 7 in [29]) is most
commonly described as a piece-wise function made up of three Weibull
distributions, each of which describes a different set of dominating failure
modes, i.e., early (infant failures), random failures and wear-out failures.

For more complex systems there exists another model for reliability estimation
assuming that load and material strength distributions are known. This model
is known as Overstress Reliability integral [44]. Failure data can be fitted
to a Weibull distribution using a variety of parameter estimation methods,
such as least squares, moments and maximum likelihood. These models make the
most famous distributions and are usually incorporated in commercially
available softwares. All of these models still depend on reliable large sample
sets of failure data points, which have to be collected and stored during
extensive (time consuming) tests or under real environmental conditions. In
addition, any situation where the failure distribution is exponential,
reliability analysis on its own is insufficient for estimating RUL. This is
due to the fact that the hazard rate of an exponential distribution is
constant over the life of a component and is independent of its service life.

On the other hand, what makes the reliability-based modelling approaches
appealing is that distributions are usually derived from observed statistical
data and are mathematically easy to construct. The required data can often be
extracted relatively easily from a company’s existing computerized maintenance
management systems. In addition, they provide confidence limits for the
results, which is an essential information for decision making. Consequently,
analysis of the results is also relatively straightforward and can be
performed by reliability engineers and avoids expertise on the subject under
study. From a theoretical standpoint, the reliability analysis can be extended
to include larger systems by combining the failure data appropriately. In
practice however, it is not advised to aggregate too many failure modes
together since the failure distributions of a system behaves similar to that
of an exponential distribution, which is problematic as discussed earlier.
More advanced prognostic models are required for estimating RUL of systems.

####  4.1.2 Conditional probability models

A number of stochastic models try to use conditional reliability functions in
conjunction with the Bayes’ theorem. In essence, a conditional reliability
function is used to describe the current state of the component. The future
behaviour/status of the component is estimated based on the recursive update
of the conditional function through direct or indirect utilization of Bayes’
theorem (thereby they could also be referred to as Bayesian models). Knowing
the current state of the asset, once a conditional reliability function is
determined, the RUL function is defined as the conditional expected time to
failure (which may or may not be time dependent) [48, 49, 50, 51]. Modelling
variants differ in the calculation procedure of the conditional probability
function as well as the kind of information used to define the current state.

####  4.1.3 RUL probability density function

The RUL probability density function is probably the simplest Bayesian
approach which is an extension of traditional aggregate reliability analysis.
It requires the probability density function of the relevant failure mode.
Information is then obtained to locate a specific item on this general
distribution (e.g., an age at which the item has not failed). This population
grows in size as the new data is appended and similarly the distribution is
amended to consider this information using Bayes’ theorem [52]. The process
repeated each time a new data point is available and this process is called
Bayesian ‘updating’. There are various names to the resulting distribution,
i.e., the predictive density function or the remaining RUL PDF. It is also
possible to derive a credibility interval (equivalent to a confidence
interval) [43, 53]. It is also possible to make improved predictions for the
new state (i.e., the condition probability, or posterior function) by
incorporating more advanced state estimation techniques such as Kalman
filtering, particle filtering methods. The rational behind selection of the
most appropriate method depends on both the system as well as the noise type.
In addition, predictions for the next state often involve evaluation of
integrals that do not possess closed-form solutions. Thus integration
approximation methods are often required, such as regression models [49] or
bootstrapping methods [51], to estimate the expected value and covariance of
these PDFs. The accuracy and precision of RUL estimation using this technique
improve as the end of life approaches. Besides, it is also relatively simple
to calculate and use these techniques.

####  4.1.4 Static Bayesian Networks

Bayesian Networks (BN)/Bayesian Belief Networks (BBF) are probabilistic
acyclic graphical models that represent a set of random variables and their
probabilistic interdependencies. Depending on the type of the information
used, these can also be considered as either knowledge-based, stochastic or
hybrid approaches. There are a number of nodes, which are connected by
directional arcs that represent a direct causal influence between nodes in a
mandatory acyclic pattern. The nodes themselves can take on distinct states or
levels and represent random variables. The strength of the causal influences
are quantified using conditional probabilities. Ultimately, each node has a
conditional probability table that defines probabilities for each state of the
node given the states of its parents [54]. Given a network design
configuration and nodal conditional probabilities, a BN can be used to
evaluate the likelihood of each possible cause being the actual cause of an
event. It could also represent probabilities associated with a particular
event occurring next if time series modelling is adopted. The output of the BN
is in the form of probabilities, which intrinsically contain information about
their confidence. This is a major advantage. A detailed mathematical
description of BN modelling in reliability and a list of modelling software
available can be found in [55].

####  4.1.5 Dynamics Bayesian Networks

Dynamics Bayesian networks are those in which the directed BN arc flow forward
in time and are therefore useful for modelling time series data [56].
Prognostic URL estimation is invariably undertaken using time series
forecasting as in [57]. The most common variants used in engineering
prognostics include Markov models, Kalman filters and Particle filters. For a
detailed review of Markov models see Ref. [29].

####  4.1.6 Bayesinan estimation with Kalman filters

Both Kalman and Particle filters (which is discussed in the next section) are
not different types of models, but rather different approaches to implementing
generic dynamic BNs. Howevver, they are widely used in engineering prognostics
and deserve particular attention, which requires a brief overview of the
underlying assumptions, limitations and strengths of these specific
approaches. The complexity of the dynamics and the type of noise are crucial
in assessing the domain of the application of these methods. The Kalman filter
is a computationally efficient recursive digital processing technique used to
estimate the state of a dynamic system from a series of incomplete and noisy
measurement in way that minimizes mean squared error. It is the most famous
estimation method within the control community. At any instant, it is defined
by its state estimate and error covariance. In five steps, it estimates
unknown states from only current observations and the most recent state and
these states need not be directly measurable [58]. Kalman filtering assumes
certain features for the process and measurement noise i.e, Gaussian, white,
independent of each other and additive. Traditionally, it was also assumed
that the dynamic being modelled needed to be linear, however, it has been
shown that this is not the case if the aforementioned assumptions on noise
holds [59, 60]. During the iterative procedure, it is necessary to solve a
number of integrals; but if the linearity assumptions are met, they have exact
solutions and it is not necessary to use approximation methods.

The Kalman filter requires an appropriate initial quantification of the
measurement noise covariance, which is relatively easy when observations are
stationary. However, determining the process noise covariance is more
challenging as it is often not possible to directly observe the process being
modelled. The performance of the filter improves when these parameters are
tuned separately to their proper values. The filter will reach steady-state
very quickly if both noise covariances are constant between iterations, i.e.,
process and observed data are stationary. There are several variants of Kalman
filter. For instance, Extended Kalman filter (EKF) is a modification of basic
Kalman filter free of the assumption regarding the linearity of either the
underlying process or of the relationship between the process and the
measurements. Instead, partial derivatives of the process and measurements
functions are calculated to linearize the estimation around the current state
prediction. Unfortunately, this also transforms the noise, which no linger
remains Gaussian, thereby invalidating one of the filter’s original
assumptions. This is a fundamental flaw in the EKF model, the effect of which
is that the state estimator only approximates the optimality of Bayes’ rule by
linearization [58]. It also requires a solution (albeit approximate) for a
Jacobian matrix, which is difficult to find. Computationally, it is less
efficient and process time increases as all covariance and model parameters
need to be recalculated in each iteration. Most importantly, there exists the
possibility of filter divergence. Traditionally, the EKF was the most popular
Kalman variant for state estimation of non-linear processes. However, due to
the issues mentioned, and improvement is computational resources alternatives
have recently been developed [59, 60]. The Gauss-Hermite quadrature Kalman
filter (GHKF), a modified version of the GHKF called the unscented Kalman
filter (UKF), and Monte-Carlo Kalamn filters (MCKF) are all variants of the
basic Kalman filter applied to non-linear processes; they differ in how
estimates for the Kalman filter integrals are calculated and consequently have
varying computational efficiencies. For all of the variants, assumptions about
Gaussian noise are still required [60]. In practice, if the system has a large
number of states, the UKF is the technique of interest for especially when the
non-linear functions are smooth [60, 61]. Specific examples of applying Kalman
filters to BN for the purposes of RUL estimation of engineering assets can be
found in [62, 63].

####  4.1.7 Bayesian estimation with particle filters

Particle filters are the candidate alternatives to Kalman filters as they are
not constrained by linearity or Gaussian noise assumptions. They are
particularly useful for situations in which the posterior distribution is
multivariate or non-standard. The principle different between Kalman filter
and Particle filter (with respect to how they calculate the posterior PDF) is
that the former relies on extrapolating from the prior state, whereas the
latter uses a sequential importance sampling scheme to simulate the entire
next state in every iteration of the filter. Particle filter does this by
generating a set of random samples (also known as particles) from a
theoretical density function and then adjusts the associated set of particle
weights at each iteration. Samples of dynamic noise are also generated with
each cycle. It is important to note that with sufficient samples, Particle
filters are more accurate than either the EKF or UKF. In addition, compared to
the classical Monte-Carlo integration, they require fewer samples to
adequately approximate the distribution, which results in a superior
computational performance. However, there are certain problems in real
applications. The first difficulty is that as the number of iterations
increases, the filter can degenerate and the posterior PDF approximation
becomes zero [60]. One possible method of avoiding this problem is obviously
to increase the number of samples and reduce the number of iterations.
Unfortunately, this is not always practical due to the increased computation
time. Alternatively, a re-sampling step can be introduced to each time
interval that replaces low probability particles with the same number of high
probability particles. A number of different re-sampling methods can be used
[64, 65], including the inverse transformation method [60] and the Bootstrap
Particle Filter [66, 67, 68, 69]. A detailed discussion on optimal sampling
(and re-sampling) is given in [70]. There are also a number of Particle filter
approximation techniques that do not involve re-sampling. These use Monte-
Carlo, Gauss–Hermite or Unscented Kalman filters to define an importance
density functions, from which particles are sampled. In the first two of these
methods the importance density is assumed to be Gaussian, based on the mean
and covariance output of the updated prior density. According to Haug, both
the Gauss–Hermite and Unscented Particle filters work well and are
implementable in real-time, while the Monte-Carlo Particle filter requires an
excessively large number of samples and outliers can result in numerical
instabilities that prevent convergence [60]. Although particle filters have
been used extensively in both econometrics and target trajectory forecasting,
there are only a few published example applications related to asset health
prognosis [71, 72]. [71] used sequential importance sampling Particle filters
to estimate the time progression of a fatigue crack, which was modelled with a
combined state dynamic model and a measurement model to predict the posterior
probability density function of the stage (the fatigue crack growth) [71].
Similarly, in [72] a combined Bayesian-behavioural model is used along with
Particle filters for prediction of fatigue crack growth progression.

###  4.2 Statistical models

In this section we talk about the statistical branch of Fig. 4. Statistical
models use previous inspection results on similar components to estimate both
initiation and progression of a possible failure mode. They are most of the
time used in problems when suitable dynamic model is not available as an
alternative for ANN. The nominal (standard) behaviour of the component is used
as a reference and prediction of the RUL is achieved by comparing the current
behaviour to the nominal one. Statistical models are generally categorized
among the data-driven methods since they utilize temporal data such as
condition or process monitoring outputs.

####  4.2.1 Trend evaluation

Probably the simplest approach to RUL prediction is based on trend analysis.
It uses the trend of a single monotonic parameter which is believed to be
related to the remaining life of the component. The selection of the
appropriate “feature parameter”, which may represent a single sensor (feature)
or a number of sensor (features) is critical. This one feature parameter is
then plotted as a function of time and is used along with a pre-defined alarm
level. A warning end-of-life signal will be triggered when the feature
parameter reaches the alarm level. In fact, there could be several alarm
levels depending on the severity of the health deterioration of the component
and its capability to perform the assigned tasks. For instance, there could be
alarms for early-warning and ‘final failure’ (denoted by asterisk and red
circles in Fig. 3). Standard regression methods are used to calculate a
candidate trend e.g, polynomial fit using a least-square method. There are
situations in which there is no data for all parameter levels up to and
exceeding the alarm limits and requires trend extrapolation. However, in
engineering prognosis, often times failure mechanisms change with the progress
of failure and may alter the trends significantly. Therefore, interpolation is
always preferred over extrapolation. It is also important to chose alarm
limits with acceptable accuracy (through data records and personnel
knowledge). It is obvious that if a somewhat conservative limit is selected,
there is great possibility of premature replacement, and in contrast, if a
high value for alarm is used, it is highly probable that the algorithm will
miss a failure. With respect to the confidence limits, if only interpolated
data is being used, confidence levels on the prognosis can be calculated based
on the variance of the underlying trend. However, confidence limits cannot be
calculated for extrapolated regions. Implementation of this type of trend
evaluation is simple and easy but indications of impending failure are
typically noisy and often non-monotonic [15]. The failure situation gets even
more complicated when multiple failure modes exist. Consequently, simple
thresholds may not result in a reliable RUL prediction, particularly where
data needs to be extrapolated. On the other hand, as the failure is approached
damage conditions become clearer, which results in clearer trends. Note also
that parameters most appropriate for predicting RUL may not be the same as
those used for detecting the beginning of a fault mode. For example, in the
early stages of bearing’s failure, Kurtosis (4th statistical moment) of a
bearing’s vibration signal often increases but can then decrease as the
bearing approaches its end of life.

####  4.2.2 Autoregressive models

Forecasting of time series data are widely achieved through using
Autoregressive moving average (ARMA), Autoregressive integrated moving average
(ARIMA) and ARMAX models [73]. In all the variants, a linear function of past
observations (and random errors) is used to calculate the future value; a
comprehensive summary is presented in [74]. The three mentioned autoregressive
models are slightly different in the linear equation, which is used to relate
inputs, outputs, and noise. ARMA and ARMAX models should only be used for
stationary data since they can remove temporal trends. Note that a time series
is defined to be (weakly) stationary when its first two moments, i.e., mean
and variance, respectively, are time-invariant under translation [75]. The
autocorrelation also needs to be independent of time. Consequently, prior to
modelling it is essential to perform trend tests to ensure the validity of the
stationarity assumption. ARIMA models, that use the concept of integration
enforcement, are capable of describing systems with low frequency
disturbances. Autoregressive models are developed in three recursive steps:

  1. I.

Model identification: Initially, using a set of time series data, values for
the orders of the autoregressive and moving average parts of the ARMA/ARIMA
equations are hypothesized, as well as the regular-difference parts for the
ARIMA model. A suitable criterion of fit is also assumed.

  2. II.

Parameter estimation: Using non-linear optimization techniques (e.g., a least-
squares method), parameters of the ARMA/ARIMA equations are calculated to
minimize the overall error between the model output and observed input-output
data.

  3. III.

Model validation: A number of standard diagnostic checks are used to verify
the adequacy of models, utilizing unseen data. According to [76], options
include the following: examining standardized residuals, autocorrelation of
residuals, final prediction error, Akaike information criterion, and Bayesian
Information Criterion (BIC).

These three steps are repeated until a satisfactory model is obtained. Once
the model parameters are fixed, it can be used to forecast future values; if
the minimum mean squared error is used as the criterion these are simply the
conditional expectations of the model. However, note that, typical ARMA models
(and variants) are effective for short-term predictions, but less reliable
when used for long-term predictions. They are not reliable for the long-term
predictions due to dynamic noise, their sensitivity to initial system
conditions and an accumulation of systematic errors in the predictor [73]. An
extension of the basic ARIMA approach is proposed in [76] that uses bootstrap
forecasting for machine life prognostics. This variant avoids using previous
values predicted to forecast future values, and instead generates predictions
only based on true observations. As parameters were updated in realtime, the
model was able to adapt to dynamic changes in the operating process and did
not suffer from error accumulation. Predictions were superior to those based
on traditional ARIMA models. Another example utilizing ARMA modelling for
prognostic estimation is presented in [77]. Although few details are available
on the models themselves, ARMA techniques have also incorporated into the
prognostic and data fusion software developed by the NSF Center for
Intelligent Maintenance System as described in [25] (the system also uses
other types of modelling for residual life estimation including proportional
hazards and neural network approaches). One novel alternative to ARMA methods
for prediction of time-series data worthy of mention uses Dempster–Shafer
regression. Application of this technique to machinery prognostics is
presented in [78]. It offers significant potential for applications where
temporal trends of prognostic parameters (to be used for extrapolation) are
non-linear and/or chaotic and thus can not be modelled using ARMA techniques.
Reference [79] discusses the application of autoregressive to slowly degrading
systems subject to soft failure and condition monitoring at equidistant,
discrete time epochs.

####  4.2.3 Proportional hazards modelling

Proportional Hazards Modelling (PHM) was first proposed in [80] and models the
way explanatory or concomitant variables, also referred to as covariates,
affect the life of the equipment, and at the same time, is one of the most
extensively used models for prognostics. The basic difference between PHM and
the linear regression methods is that the former assumes a multiplicative
relationship for covariates, whereas that latter assumes an additive effect on
the overall hazard rate. PHM models deterioration as the product of a baseline
hazard rate, and a positive function. The multiplicative function reflects the
effect of the operating environment on the baseline hazard and is described by
a vector of covariates and an associated vector of unknown regression
parameters. RUL can be deduced from the associated survival function [81]. The
positive function is usually assumed to be exponential (primarily for
convenience) although other mathematical functions such as logarithmic,
inverse linear, linear or quadratic functions are also common [82, 83]. It is
possible for the elements of the covariate process vector to take positive
values implying that the covariate is actually improving the condition and
thus reducing the hazard rate when compared to the baseline. For instance,
increased corrosion inhibits (or concentration reduces) the rate of internal
corrosion [82]. For some mechanical as well as electrical components the
seasonal variation of temperature results in positive and negative
contributions. Covariates are often referred to as internal or external. In
the prognostics context, internal covariates refer to outputs generated by the
component being degraded and thus only exist as long as the degraded component
remains in service. An example of internal covariate is the vibration level at
the inner race bearing frequency that is used to predict bearing failure.
Internal covariates can also be considered ‘response covariates’ as they are
generated in direct response to the failure process. On the other hand,
external covariates refer to outputs generated by an independent process; they
can also be considered ‘risk factors’ and are usually not affected by
repairing or replacing the degraded component. An example for external
covariate is sulphur concentrations in crude oil that may be used to indicate
increased risk of process pipe corrosion. A more detailed discussion on
covariates is given in [84]. PHM works according to a number of assumptions:

  1. a)

Times to failure are independent and identically distributed, i.e., perfect
repair.

  2. b)

Covariates have a multiplicative effect on the baseline rate.

  3. c)

Individual covariates are independent (i.e., the value of the covariate
function for one item does not influence the time to failure of other items).

  4. d)

The effect of the covariates is assumed to be time independent.

  5. e)

All influential covariates should be included in the model.

  6. f)

The ratio of any two hazard rates is constant with respect to time (thus the
respective survival curves will not intersect).

It is possible to use graphical analytical goodness-of-fit tests to verify
whether these assumptions are valid for the system being modelled [82, 85].
Applying PHM requires the estimation of the parameters of the baseline hazard
function and the covariate process vector. Initially, the covariate vector
weightings are calculated irrespective of the form of the baseline hazard
function for which the maximum likelihood method is the most commonly applied
technique, but a variety of other approaches have also been used [86, 80, 82,
87, 88]. Higher weightings are given to the covariates that are good
indicators of failure, while those with little correlation to failure are
assigned much smaller weightings. The accuracy of the modelling is improved if
only relevant covariates are incorporated into the model. Consequently, a
backward step wise procedure is often implemented to exclude the least
significant covariates and re-estimates the model parameters; this procedure
is repeated until all remaining factors are significant. Alternatively, new
variables can be sequentially forced into the model during the search for
significant covariates. Once covariate parameters have been defined, variables
of the baseline hazard function can be estimated using either parametric or
non-parametric methods. The latter is generally preferred by statisticians as
the form can be estimated from the data [86, 80, 82, 89], which is then
compared with various standard distributions forms to identify the most
appropriate model. In practice, however, the baseline hazard function is often
assumed in advance to be a Weibull or exponential function to facilitate the
use of common parametric regression methods. Due to the confusing effects of
the covariates, these pre-assumed forms of the hazard function may not be
justified and may not be the best choice [86]. To ensure that the baseline
hazard function remains physically meaningful it is desired to configure
covariates in a manner that they equate zero for the ‘baseline’ operating
state (although this requirement is not a mathematical constraint). A critique
of early attempts to apply proportional hazards model to problems of
engineering reliability was provided by [86]. A more comprehensive review is
conducted in [82]. Nevertheless, the body of work on PHM clearly demonstrated
the advantages of PHM over standard regression techniques, including the
ability to manage nuisance variables (unrelated covariates), censored data
[89]. Over the past years, these basic techniques have been refined,
extrapolated and expanded, particularly for the purposes that include
optimizing maintenance decisions [90, 91, 92, 93, 94, 95, 96, 97, 82, 98],
analysing data obtained from accelerated life tests [83], and appliction to
model systems that are subject to partial repair [99, 100, 101]. Specific
examples of industry led research include [102, 103, 104, 105].

A variation of PHM that does not assume perfect repair, known as the
Proportional Intensity Model, exists and has also been applied by several
researchers [106]. Intuitively, the best models are expected to be based on a
mixture of diagnostic indicators, which seems to be problematic due to the
lack of published examples. To overcome the problem of insufficient failure
data, Ref [107] has applied an expert judgement approach (paired comparison),
in conjunction with a small amount of actual failure data to populate the PHM
parameters [107]. Collectively, this work to date on the application of PHM to
asset prognostics has been conducted using highly selective and well-
controlled data sets (albeit some of the data was collected from real
operating plants); in each case, only a small number of overlapping failure
modes was modelled. Thus, the ability of PHM to estimate RUL for prognosis of
varied faults in complex systems is uncertain and likely to be an ongoing
challenge. The extension of the PHM to complex repairable systems with a
number of sub-systems is a difficult task. A complex system has several
components with their associated failure modes and the assumption that
failures are independent and identically distributed is far from truth. In
addition, it is hard to find a comprehensive set of covariates to describe all
failure modes. However, as equipment becomes more reliable it is difficult,
from a practical standpoint, to obtain sufficient data pertaining to failures
and corresponding covariates to model all failures [108]. Furthermore, data
aggregation can obscure information about component failures thus making it
difficult to produce consistent and applicable histories [85]. All in all, it
is suggested to apply PHM at the failure mode level when appropriately refined
failure histories and physically relevant covariates are known. This is not a
straightforward task as it requires more data collection procedures in
addition to the knowledge of the physical root causes of failures (i.e., the
failure mode). In addition, associated working age and diagnostic information
must be recorded accurately [97] and in an accessible format.

Note that given current modelling limitations, when a subsequent
repair/replacement is made, suspension events need to be recorded against all
other potential failure modes that are affected by that repair/replacement, so
that working ages for these failure modes can be adjusted. (This is only
practicable if implemented as an autonomous process.) This is done to avoid
biases in estimates for the RUL, which may result in underestimations [97].
More information about data requirements for PHM is given in [108]. Since the
PHM relies on the data of particular failure modes, it is not capable of
estimating RUL of failure modes, which have not occurred previously.

The traditional PHM approach to non-stationary process (e.g., reliability
growth of repairable system) is performed by using a stratified approach [89,
109] in which data is grouped based on various failure times in the life cycle
for each component. Each step is then modelled individually, with required
failure histories for each step [82]. Dynamic PHM is an alternative to the
traditional PHM where a generalization of the basic PHM equation is used to
take into account time dependent covariates [92, 110, 88]. The dynamic model
is capable of predicting the future development of covariate and failure
times. In this work, the non-stationarity was accommodated by assuming that
the covariate vector was a multivariate non-homogenous Markov process with all
but failure state hidden. It was also assumed that covariates were only
observable at certain times (i.e., periodic inspection/monitoring) [88, 92].
Backward recursion algorithms and optimal stopping framework were then used to
determine optimal inspection intervals (based on minimizing expected cost) as
well as to calculate the expected RUL. It was assumed that the system was
renewed after replacement. In practice, only a few states are needed to
represent the failure process, such as those corresponding to periods of
‘wear-in’, ‘normal’ and ‘wear-out’. Some publications have reported the
results of this approach for analyzing real operating systems [94, 97, 111].

###  4.3 Physical models

Physical models (also known as physics of failure or behavioral models)
exploit physical laws to quantitatively characterize the behaviour of a
failure mode. Obviously, this requires a thorough/detailed understanding of
the system behavior in response to external loads such as stress, at both
macroscopic and microscopic levels. It is based on the fact that it is
possible to describe the behavior of a component accurately and analytically.
At the heart of the method is the estimation of an output for the RUL of a
component by solving a deterministic equation or set of equations derived from
extensive empirical data. Data includes common scientific and engineering
knowledge as well as those acquired through specific laboratory or filed
experimentation. The physical model entails physical properties, constant
parameters of the equations, corrosion rates, etc. In the end, the model is
described by using a series of ordinary or partial differential equations that
can then be solved in most cases with Lagrangian or Hamiltonian dynamics,
approximation methods applied to partial differential equations, distributed
models [18, 112]. A more comprehensive list of behavioral models is provided
in [17].

Once a model is developed and verified, sensor measurements of the actual
component are used against outputs of the developed model to calculate the
residuals (i.e., differences between reality and the model); The status of
fault is drawn if large residuals are observed while small residuals are
attributed to noise and modelling errors under normal operating conditions
[24]. A number of thresholds could be defined to identify the presence and/or
condition of faults. There are several methods to calculate the residuals
including parameter estimation, state-space methods or parity equations the
benefits of each are discussed in [113]. The projection of the degradation
behavior into the future is used for estimating RUL. One has to define
characteristics for a set of features and their associated levels of accuracy
in order to construct a physics of failure model:

  1. a)

Identify likely initiating failure modes for which behavioral models are
required.

  2. b)

Process behavior across possible/typical operating ranges.

  3. c)

Degradation behavior under aforementioned process conditions.

  4. d)

Relationship between process measurements and degradation behavior(s).

  5. e)

Process and measurement noise.

In practice and for many cases, the above parameters are inherently
probabilistic random variables thus demands the incorporation of their
statistical distributions into the model. This enables the estimation of
confidence limits. For the purposes of prognostics, failure mechanisms can be
broadly divided into two categories [114]. The first type of failure is
associated to over stress failures and they occur when incurred load exceeds
the strength of the material; this kind of stress is not destructive, i.e.,
they have no long-term effect once the load has been removed. Examples include
brittle fracture, yielding and buckling. Once the particular damage reaches
the allowed tolerance, normal operating loads exceed the remaining strength of
the material and an over-stress failure is said to have happened [46]. The
second type of failure is wear-out failures which are characterized by
accumulated damage that does not disappear when the load is removed (e.g.,
fatigue, wear in brake pads). A physical prognostic model for wear-out failure
modes needs to be able to track aggregated damage and its rate of progression
under any/all operation conditions.

Consequently, if available and when sufficiently complete, physics-based
models tend to significantly outperform other types of models [24].
Additionally, the outputs of physical models are easy to interpret. Their
obvious disadvantage is that the behavior of the system must be derivable from
first principles, which may not always be possible due to an imperfect
understanding of how the failure mechanisms behave under the range of relevant
operating conditions. Even if the mechanisms are fully understood, assigning
the appropriate parameters for all aspects of the model requires a significant
volume of accurate and reliable multivariate data that is rarely available.
Condition indicators specific to the failure mode being modelled must also be
identified and continually collected. Consequently, physics of failure models
tend to be used in isolated cases, for well-understood faults in simple
systems and/or by users with established diagnostic systems and predictive
maintenance programs. It seems that crack propagation failure modes are the
most commonly developed behavioral models for prognostics.

##  5 P&HM Tool Selection Method

In this section, a procedure is explained to facilitate the selection of the
most appropriate methods/algorithms for various steps involved in P&HM [20].
The available data is a steppingstone toward developing a systematic approach
to apply P&HM methodologies to traditional as well as novel areas. Prior to
examining the possibility of using certain algorithms, it is pivotal and
beneficial to understand the characteristics of the data and possible
causality between these characteristics, and the nature of the system in terms
of the operating condition, service intensity, system dynamics and all other
applicable attributes. Achieving an effective methodology with the appropriate
blend of algorithms that results in reliable accuracy is, more or less,
dominated by the characteristics of the data whether it is in the form of
vibration, acoustic emissions, environmental parameters, etc. The major tasks
in the field of PHM are already described and include signal processing,
feature extraction and reduction, fault diagnosis, health assessment,
performance prediction and so on. However, within each task there exist a
multitude of algorithms which have been developed and benchmarked to process
signals, classify them and using the results determine the current health
status and estimate the future condition of the component under study.
Practitioners and researchers usually have different algorithms preferences
which is dependent upon the application and available infrastructure. Table 3
presents a list of the most commonly used algorithms including their
applications, strengths and weaknesses in the field of P&HM. Algorithm
selection is a crucial step for developing an effective P&HM system, which
will ultimately affect the results and their confidence limit.

One way of selecting algorithms is to take a heuristic approach that relies on
researchers’ experience and expertise to meet users’ requirement. However,
such an approach is not ideal for situations in which there is a lack of
expert knowledge (and expert personnel), and could be time-consuming for
complex problems or systems. The goal is to achieve the following targets in
the most efficient way: 1) to provide quantified selection criteria, 2) to
enable automatic benchmarking, and 3) to recommend the appropriate tool(s) for
a particular application. It is therefore inevitable to devise a selection
scheme that compares and ranks the suitability of each algorithm by
considering the application attributes, proficiency and requirements of the
end user. A feasible solution can be a numerical comparison based on the
ranking of algorithm scores for each category so that the top algorithms can
be selected. A suitable ranking method for algorithm selection is Quality
Function Deployment (QFD) [115] and is best known as a tool for product
design, quality management, customer need analysis and decision making
purposes [116]. In traditional QFD, a House of Quality (HOQ) is constructed to
combine engineering attributes and customer needs (and their assigned
weights), and transform them into design specifications and controllable
parameters. This provides the quantification step of the aforementioned
targets. For algorithm selection, data characteristics, corresponding
algorithm suitability and user inputs are integrated to give a ranking of all
algorithm candidates in each category. The process of applying QFD for
algorithm selection can be summarized through the following main steps:

  1. 1)

According to the application and available knowledge of the data, all criteria
related to the application should be selected.

  2. 2)

The properties of each criterion should be identified in order to describe the
available data in a detailed manner. These criteria do not have to be binary
as long as ambiguity can be avoided, so users can classify the level of the
characteristic with high confidence. Furthermore, a quantified description is
recommended in this step, for example, low, medium and high stationarity can
be presented by ascending integers like 1, 3 and 5.

  3. 3)

Eligible algorithms for each characteristic are compared in a pair-wise way
based on algorithm applicability. Analytical Hierarchy Process (AHP) [117],
employed in this step, is a decision making tool, which is able to compare
every paired combination of algorithms and provide final applicability indices
for all algorithms for each specific characteristic.

  4. 4)

An HOQ can be established for each one of the algorithm categories to
aggregate all the indices from the previous step for all characteristics in
order to generate an overall weight, based on which a final rank of algorithms
can be decided for this category. Therefore, a procedure can be established
for the user to execute an effective, systematic P&HM approach with the top
ranked algorithms from each category.

As an example application, Figure 5 in Ref [20] illustrates the QFD algorithm
selection tool using the gears of a wind turbine. Rotary components of a wind
turbine system such as rotor blades, bearings, shafts and gears are working
under dynamic loads and are more susceptible to failure than other components.
The aforementioned systematic methodology can be referenced to explore and
develop fundamental techniques to aid in establishing a P&HM system for wind
turbines under varying environmental, operational and aging processes. In this
case, only vibration data is available, and the applicability of each relevant
algorithm is defined by assigning an importance to different characteristics
using a scale ranging from 1 to 5 (5 being the most important). The rankings
are structured so that in each catalog the algorithm with lowest ranking is
the most recommended one. The tool selection for each of the other critical
components can be performed in this fashion.

###  5.1 Visualization tools

After the selected algorithms have digested the data, prognostics information
is ready for further utilization to support the decision making process. One
valuable objective of PHM is to enable a support system to convey the right
information to right person so that judicious decisions can be made at the
right time. Therefore, visualization tools are essential parts of a PHM
methodology. Four frequently used visualization tools, Degradation Chart,
Performance Radar Chart, Problem Map and Risk Radar Chart, can be designed to
present prognostics information as shown in below Figure taken from [20] for
the sake of discussion.

Figure 5: Four visualization tools for P&HM [20].

The functionalities of the presented visualization tools are described as
follows [118]:

  * 1.

Degradation Chart-If the confidence value (0-unacceptable, 1-normal, between 0
and 1-degradation) of a component drops to a low level, a maintenance
practitioner can track the historical confidence value curve to find the
degradation trend. The confidence value curve shows the historical, current
and predicted confidence value of the equipment. An alarm will be triggered
when the confidence value drops under a preset threshold.

  * 2.

Performance Radar Chart-A maintenance practitioner can look at this chart to
get an overview of the performance status of each component. Each axis on the
chart corresponds to the confidence value of a specific component.

  * 3.

Classification and Fault Map-A Classification and Fault Map is used to
determine the root causes of degradation or failure. This map classifies
different failure modes of the monitored components by presenting different
failure modes in clusters, each indicated by a different color.

  * 4.

Risk Chart-A Risk Chart is a visualization tool for plant-level maintenance
information management that displays risk values, indicating equipment
maintenance priorities. The risk value of a machine (determined by the product
of the degradation rate and the value of the corresponding cost function)
indicates how important the machine is to the maintenance process. The higher
the risk value, the higher the priority given to that piece of equipment for
requiring maintenance.

##  6 Performance Metrics for Evaluating Prognostic Predictions

Performance criteria on metrics determine the adequacy of a prognostic
approach for a given application [119]. Extensive work has been reported to
define the appropriate performance metrics for a given application and health
management and conation monitoring approaches [120, 119, 28, 121]. As the
literature shows, there are three major performance indicators to determine
the efficiency and effectiveness of PHM applications: prognostic distance,
accuracy, and precision. The time between the predicted time of incipient
failure and actual component failure is called the prognostic distance. This
definition of prognostic distance has been derived from the application of
canaries [122]. Accuracy means the correctness of the remaining life
estimates. The correctness of the prediction of time determines the accuracy
of prediction. Precision accounts for the uncertainty estimates in remaining
life prediction. The width of the uncertainty band determines the precision of
the estimates. A shorter band has higher precision, and a wider band has lower
precision. The parameters that are of interest to risk-informed applications
include assessment of the reliability/safety margin for case or scenario being
evolved. Even though extensive work has been performed on the development of
performance metrics, there is need for further research on the development of
acceptance criteria for performance metrics [123].

###  6.1 Applications

In this section, we present a list of works on the rotary machinery
prognostics as well as other critical components that are widely used in
engineering platforms, engines and mechanical systems. Table 5 gives an
introductory summary of tools for common critical components, regarding the
components’ issue and possible failure modes, characteristics, common
available data types, common features and algorithms applied for diagnostics
and prognostics. Note that the following abbreviations are used for Fourier
Transform (FT), Short Time Frequency Transform (STFT), Wavelet Transform (WT),
Empirical Mode Decomposition (EMD), Auto-regression (AR), Hilbert-Huang
Transform (HHT), Neural Network (NN), Hidden Markov Modeling (HMM), Support
Vector Machine (SVM), Genetic Algorithm (GA), Auto-regressive Moving Average
(ARMA), Principal Component Analysis (PCA),Wigner-Ville Transforms (WVT),
Support Vector Regression (SVR).

Table 5: Introductory summarization of tools of critical components. Item |  Issue & failure |  Characteristic |  Common measures |  Common features |  Used models
---|---|---|---|---|---
Bearing |  Outer-race, inner-race, roller, and cage failures |  Raw data does not contain insightful information; low amplitude; high noise |  Vibration, oil debris, acoustic emission |  Vibration characteristic frequency, time domain statistical characteristics, metallic debris shape, size, quantity, sharp pulses and rate of development of stress-waves propagatoin |  FT [124, 125], STFT [126], WT [127], EMD [128], Bispectrum [129], AR Frequency Spectra [130], NN [131, 132, 133], HMM [134, 135], Fuzzy logic [136], GA [137], ARMA [138], Stochastic Model [139, 140], PCA [141]
Gear |  Manufacturing error, tooth missing, tooth pitting/spall, gear crack, gear fatigue/wear |  High noise; high dynamics; signal modulated with other factors; gear specs need to be known |  Vibration, oil debris, acoustic emission |  Time domain statistical features, vibration signature frequencies, oil debris quantity and chemical analysis |  FT [142], STFT [143, 144], WT [145, 146], EMD [147, 148, 149], HHT [149, 150, 151], NN [152, 153, 154, 155], Fuzzy Logic [156], Neuro-Fuzzy Hybrid Model [157], Energy Index Analysis [157], Kalman Filter [158, 158, 159], SVM [160], Autoregressive Model [161, 162], Particle Filter [163]
Shaft |  Unbalance, bend, crack, misalignment, rub |  Vibration signal is relatively clean and harmonic frequency components of rotating speed can indicate the defects |  Vibration |  Vibration characteristic frequency, time domain statistical characteristics, system modal characteristics |  FT [164], WT [165], Wigner–Ville Transforms (WVT) [166], EMD [167, 168], Analytical or Numerical Models [169, 170], NN [171, 172, 173], Fuzzy Logic [174], Support Vector Regression (SVR) [175], GA [176, 177], ARMA [178, 179]
Pump |  Valve impact, score, fracture, piston slap, defective bearing and revolving crank, hydraulic problem |  Pump’s dynamic responses, generated by a wide range of possible impulsive sources, are very complex; nonlinear, time-varying behavior |  Vibration, pressure, acoustic emission |  Vibration characteristic frequency, pressure time domain statistical characteristics, sharp pulses and rate of development of stress-waves propagation |  FT [180], STFT [181, 182, 183], WT [184], Envelop Analysis [185], NN [186, 187, 188], Fuzzy Logic [189, 190], Neuro-Fuzzy Hybrid Model [191], Rough Set [192], PCA [193]
Table (continued). Item |  Issue & failure |  Characteristic |  Common measures |  Common features |  Used models
---|---|---|---|---|---
Alternator |  Stator faults, rotor electrical faults, rotor mechanical faults |  Currents and voltages are preferred for noninvasive and economical testing |  Stator currents and voltages, magnetic fields and frame vibrations |  Specific harmonic components, sideband components |  FT [194], WT [195, 196, 197], Instantaneous Power Fourier Transform [198], Bispectrum [199, 200], High Resolution Spectral Analysis [201, 202], Expert Systems [203, 204], NN [205, 206, 207], HMM [208], Fuzzy Logic [209, 210, 211], GA [211], Higher Order Statistics [212], Park’s Current Vector Pattern [213], Petri Net [214], Kalman Filter [215]

In addition, there are papers that discuss the prognostics on various
components/system including batteries [216, 217, 218, 219, 220, 221, 222, 223]
(prognostics for batteries appears to be at a more advanced stage than
prognostics for structures [3]), DC-motor [215, 224, 225], electric motors
[226, 227, 228] boiler tube [229], bearing [230, 134, 231], engine [232],
diesel engine [91], wind turbine [233], gearbox [234, 235], oil [236],
hydraulic system [237], pumps [238, 239], (automatic) transmission [105, 240]
and alternator [241].

In addition, there exist considerable literature on the application of
prognostics to aerospace engineering systems with a few of them listed here
due to their importance for further study [242, 243, 244, 207, 154, 245, 246,
247, 107, 248, 21, 249, 250]

##  7 Automobile Applications

In this section, we discuss the details of a few relevant applications of
prognostics. There are a few papers that worth attention. For instance, Ref
[251] determines a reliability index for the most failure parts and complex
systems of two brands of city buses for the period of time failures. The
analysis covered damages of the following systems: engine, electrical system,
pneumatic system, brake system, driving system, central heating and air-
conditioning and doors. Furthermore, the reliability was analyzed based on a
Weibull model. Ref [252] discusses the maintenance planning for a commercial
heavy vehicle. Reference [95] discusses work completed to improve the existing
oil analysis condition monitoring program being undertaken for wheel motors.
Oil analysis results from a fleet of 55 haul truck wheel motors were analyzed
along with their respective failures and repairs over a nine-year period.

###  7.1 Peer-to-Peer Collaborative Vehicle Health Management

This section reviews an advanced vehicle diagnostics and prognostics (D&P)
technology initiated by the General Motors company [253]. The proposed
framework which is called Collaborative Vehicle Health Management (CVHM) is
developed to automatically optimize the D&P algorithms on a host vehicle,
using the field data collected from peer vehicles encountered on the road. The
objective is to improve the D&P performance without incurring costs of human
intervention. The experimental results on battery RUL prediction show the
effectiveness of the proposed framework. This proposed framework has been
implemented in a small test fleet as a proof-of-concept prototype.

It is known that the failure modes of vehicles are diverse and vary from
vehicle to vehicle. As a result, it is very challenging to achieve accurate
and robust D&P performance for vehicle systems in the field. The traditional
approach to D&P is achieved by introduction of individual faults on bench
tests, test vehicles or through accelerated ageing tests and by collecting a
large amount of data. This requires a significant amount of algorithm tuning
to be done by the development engineers. The proposed CVHM framework is a
response to the above challenge, where filed data from peer vehicles are
aggregated to automatically optimize the D&P algorithms for the host vehicle.
This is an extension of the decade-long evolving research and development in
the area of remote vehicle diagnostics [254, 255, 256, 257, 258, 259], which
recently has been accelerated due to the advances made in the wireless
communication technology and the need for connected vehicle prognostics. The
necessary ingredients of a CVHM include

  1. 1)

An onboard CVHM architecture that facilitates efficient aggregation of peer
vehicle data, and host vehicle D&P algorithm adaptation.

  2. 2)

Intelligent data modelling and statistical decision making technologies that
allow the extraction of fault signature, failure precursor, trending
information, and other kinds of knowledge that enhances the performance of
D&P.

  3. 3)

A heterogeneous wireless communication solution that combines cellular
network, and opportunistic vehicle-to-vehicle (V2V) communication to allow the
exchange of large-volume data between vehicles in a cost-effective way.

The work in [253] addresses the first two items above, using battery RUL for
demonstration. A typical vehicle health management system architecture should
address the three main tasks associated with CBM, i.e., data collection,
feature extraction and decision making. Figure 6 (taken from [253])
illustrates a typical architecture. Sensor information regarding particular
vehicle subsystem is either directly collected by the VHM ECU that runs D&P
algorithms or is transferred from other ECUs through an in-vehicle
communication network. Note that, in real implementations, the VHM ECU may be
implemented as a functional module within an ECU, such as a body control
module (BCM), that executes control functions. The D&P module has various D&P
algorithms for different targeted vehicle components or subsystems, such as
battery, electrical power generation and storage (EPGS) system, fuel delivery
system, etc. The D&P module processes the sensor information, and generates
D&P results, including the detected anomalies, isolated faulty components, and
the predicted RUL of related components. The D&P algorithms are usually
developed, calibrated, and tested through a sophisticated vehicle development
process. Once the vehicle is released for production, the D&P algorithms and
the associated calibration values are usually fixed. If major updates on the
onboard algorithms are needed, an ECU reprogramming can be done after the
vehicle is usually called to a dealer service shop. Lately, the technology of
remote ECU refresh is maturing, which may allow the ECU reprogramming to be
done remotely through telematics connections.

Figure 6: A typical VHM system architecture in the state-of-the-art [253].

The CVHM system architecture proposed in [253] should address the tree main
ingredients of a realizable CBM system. Figure 7 demonstrates the proposed
CVHM system architecture.

Figure 7: CVHM system architecture proposed in [253].

The newly added V2X ECU provides the wireless communication interface in order
to exchange vehicle health related data between the host vehicle and peer
vehicles. V2X represents vehicle-to-vehicle or vehicle to infrastructure. The
V2X ECU stores the data in an onboard database. The VHM ECU has an algorithm
adaptation module and a learning algorithm library, in addition to the regular
D&P module. The algorithm adaptation module makes use of appropriate learning
algorithms to process the vehicle health related data stored in the onboard
database in order to tune and optimize the calibration values within the D&P
module.

The advantage of CVHM can be understood based on the following example. A
battery life prediction algorithm usually implements an ageing model that
specifies how the battery internal resistance grows given the number of
charge-discharge cycles. There are parameters in the ageing model that
specifies the growth rate of the battery internal resistance, which is
critical in battery life prediction. These parameters are typically calibrated
using accelerated ageing test during the vehicle development process, and
applied to across the board to all vehicles. However, it is difficult for a
pre-calibrated model to account for the intrinsic diversity of usage patterns
and environment impacts. The fact is that batteries for the same
battery/vehicle model may have different life span that ranges from 1 year to
10+ years. At the same time, with large enough vehicle population, for any
given vehicle, chance is high that there are peer vehicles with similar usage
profiles that have been used for longer time, and therefore have gone further
ahead in the ageing process. With CVHM, field data from these peer vehicles
can be used to fine tune the growth rate in the battery ageing model, and
consequently achieve higher prediction performance.

The general framework to develop model-based prognostics for RUL prediction
involves the following steps. First, one or more fault signatures are
identified to characterize target system’s state of health (SOH), $Z=f(SOH)$.
Depending on applications, these fault signatures may be assessed either
directly or indirectly. For example, in the application of Starting, Light,
Ignition (SLI) battery life prediction, multiple fault signatures have been
proposed. The second step is to establish the failure criteria for fault
signatures with respect to specific applications. That is, if $Z>Z_{0}$, a
system failure is declared, where $Z_{0}$ is a threshold. For example, one of
the main functions for SLI battery is to crank the engine. As battery ages,
its SOH deteriorates, and so does its cranking capability. One of the fault
signatures, cranking resistance, increases during the ageing process. When the
cranking resistance reaches certain level, the engine can hardly be started.
This is when a battery failure is declared. The failure criteria are highly
application specific, and usually require careful calibration. The third step
is to establish a system-ageing model that specifies how the fault signatures
evolve with respect to usage. That is,

$Z=Z(L;\theta),$

where $L$ is a set of variables that characterize the usage profile of the
target system, and $\theta$ is a set of parameters that specify the detailed
relationship between the usage and the fault signature evolution.

Extensive previous research has been conducted, and multiple SLI battery fault
signatures have been identified, including minimum cranking voltage, delta V,
cranking power, voltage residual, and cranking resistance. For instance, the
cranking resistance increases in an accelerated ageing experiment. In [253], a
few static parametric models are adopted, including polynomial curve fitting.
The algorithm development is based on a 3rd order polynomial model due to its
structural simplicity. Each fault signature is modeled by the following
equation

$\hat{y}(t)=p_{1}t^{3}+p_{2}t^{2}+p_{3}t+p_{4},$

where $\hat{y}$ is predicted fault signature value, $t$ is the battery age in
terms of service time, and $p_{1},p_{2},p_{3}$ and $p_{4}$ are model
parameters. Since both SOC and battery temperature can affect battery fault
signature, different models have to be learned for different SOC and
temperatures. The battery RUL is defined as

$RUL=arg\min_{t}[\hat{y}(t)=y_{0}]-t_{current},$

where $y_{0}$ is a predefined threshold, and $t_{current}$ is the current
battery age. The ageing model calibrated with accelerated ageing test may not
be able to characterize the ageing process in the field. In the proposed CVHM,
the ageing model is adapted using the data from peer vehicles that have gone
further in the ageing process. Let $y_{H}(t_{j})$ be the fault signature value
measured or estimated by the host vehicle at time instant $t_{i}$, where
$j=1\cdots J$ and $J$ is the current time index for the host vehicle. Let
$P_{H,1},P_{H,2},P_{H,3}$, and $P_{H,4}$ be the ageing model parameters
maintained by host vehicle, and $P_{P_{k},1},P_{P_{k},2},P_{P_{k},3}$, and
$P_{P_{k},4}$ be the ageing model parameters used by peer vehicle $P_{k}$,
where $k=1\cdots K$ and $K$ is the number of peer vehicles. The model
adaptation procedure is as follows,

  1. 1)

Estimate host vehicle fault signature values using peer vehicle’s ageing model
parameters, which yields,

$\hat{y}_{H,P_{k}}(t_{j})=p_{P_{k},1}t_{j}^{3}+p_{P_{k},2}t_{j}^{2}+p_{P_{k},3}t_{j}+p_{P_{k},4},$

where $\hat{y}_{H,P_{k}}(t_{j})$ indicates the estimate of host vehicle fault
signature using the ageing model from peer vehicle $P_{k}$.

  2. 2)

Calculate the corresponding estimation error for the ageing model from each
peer vehicle $P_{k}$ as,

$R_{H,P_{k}}=\sum_{j=1}^{J}[\hat{y}_{H,P_{k}}(t_{j})-y_{H}(t_{j})]^{2}.$

  3. 3)

Pick N models with the smallest error. Without loss of generality, the
corresponding peer vehicles can be represented as $P_{k_{1}}$, $P_{k_{2}}$,
$\cdots$, $P_{k_{N}}$. In the experiment presented in this paper, $N$ is set
to 3.

  4. 4)

Calculate the adjusted host vehicle fault signature values,
$\bar{y}_{H}(t_{j})$, by averaging the fault signature values based on the
selected peer vehicle’s ageing models,

$\bar{y}_{H}(t_{j})=\frac{1}{N}\sum_{n=1}^{N}\hat{y}_{H,P_{k_{n}}}(t_{j}).$

  5. 5)

Update the host vehicle ageing model, using the adjusted fault signature
values

${p_{H,1},\cdots,p_{H,4}}=arg\min_{p_{1},\cdots
p_{4}}\sum_{j=1}^{J}[\hat{y}_{H}(t_{j})-\hat{y}(t_{j})]^{2},$

where $\hat{y}(t_{j})=p_{1}t_{j}^{3}+p_{2}t_{j}^{2}+p_{3}t_{j}+p_{4}$.

The adjusted ageing model parameters $p_{H,1},\cdots,p_{H,4}$ are used for
future battery RUL prediction of the host vehicle.

####  7.1.1 System Implementation

The CVHM architecture proposed in [253] has been implemented in a three-
vehicle test fleet for the battery RUL prognosis application. To reduce the
development cycle and cost, the test fleet is constructed in a way that one
host vehicle implements the full CVHM architecture, and two peer vehicles
implement only the V2X module. Each of the two peer vehicles maintain a
database of battery D&P data from multiple batteries, which simulates the
situation where data from multiple peer vehicles can be transferred to the
host vehicle for D&P algorithm adaptation.

For the host vehicle prototype implementation, there are three major hardware
components. The first one is a dSpace® MicroAutoBox (MAB) that has direct
connection with the sensors on the battery. It employs the functions of data
acquisition, signal pre-processing, and fault signature generation. During
each vehicle cranking process, the MAB generates multiple battery-status
related parameters, including battery temperature, SOC, cranking resistance,
minimum cranking voltage, cranking powering, delta V, voltage residual. The
third major hardware component is a V2X communication laptop (an HP® Compaq
6910P with the OS of Linux Ubuntu 10) that communicates with the VHM laptop
through TCP/IP based connection. The V2X laptop implements the V2X module that
interacts with peer vehicles and infrastructure through a wireless
communication to exchange data. It maintains a MySQL® database server to
organize the data as well as manage the retrieval requests from the VHM
module. The V2X laptop also serves as the driver interface module to provide
battery health information to the end user.

####  7.1.2 Experimental Results

The CVHM system has been validated using the $JBI_{A}ging_{2}008$ data set. In
this data collection effort, 15 batteries from different suppliers were aged
from fresh to the end of life through an accelerated ageing process. The
battery age varies from 8 to 16 weeks. During the ageing process, weekly
cranking tests were conducted on a test vehicle for each battery after it was
conditioned to 100% state of charge (SOC) and the temperature of 25°C. Battery
current, battery voltage, and engine RPM were collected during cranking. After
data cleaning, there are totally 1710 cranking data files that have adequate
data for 14 batteries. Among these fault signatures, cranking resistance
appears to be better SOH indicators than others, due to its consistency and
monotonic correlation with the battery age. Therefore, we selected the
cranking resistance as the fault signature in the rest of the experiments. The
accuracy specifies the difference between predicted value and the actual
value. The precision specifies the spread of the predicted values.

####  7.1.3 Simulation Results

Figure 8 illustrates the battery RUL prediction results during one particular
ignition cycle. At this particular ignition cycle, the host vehicle battery
has been in service for 540 days, assuming each week of accelerated ageing
corresponding to about 90 days of real-world driving. The cranking resistance
has increased from the initial value, but is still significantly lower than
the end of life threshold indicated by the black horizontal line. The
initially calibrated ageing model, as shown by the blue line, predicts the RUL
is about 250 days, since the cranking resistance is predicted to pass the
threshold in about 250 days. This prediction is very different from the actual
cranking resistance data that are shown by the black cycles. At the same time,
the host vehicle has access to the data from peer vehicles’ batteries, of
which the data from nearest neighbors are shown by the green crosses.
Following the model adjustment procedure presented before, an updated battery
ageing model is obtained, and shown by the green line. The updated ageing
model traces the actual cranking resistance very well, and provides a fairly
accurate RUL prediction.

Figure 8: Comparison of battery RUL prediction with pre-calibrated model and
adaptive model [253].

####  7.1.4 Preliminary penetration analysis

A discussion is presented on how many peer vehicles are needed to achieve
specific RUL prediction performance. The performance of RUL prediction can be
measured by the accuracy and the precision. The relations indicate that under
the i.i.d. assumption, the RUL estimation will have zero expected error, which
is very desirable. And the error spread of the CVHM-based prediction is
reduced by a factor of $\frac{\sqrt{n+1}}{n}$ from the single vehicle battery
RUL prediction, which shows why the CVHM framework enhances the prediction
performance.

###  7.2 Automatic transmission: Wet-clutch system

Nowadays, automatic transmissions have become a popular choice in commercial
vehicles and been widely used in off-road/heavy-duty vehicles. As is obvious
from its name, an automatic transmission is a transmission that shifts power
or speed by itself. The key element that enables automatic powershifting or
speed-selection in automatic transmissions is a wet friction clutch. The power
transmission from the engine to the wheels through wet friction clutch is
based on the friction occurring in lubricated contacting surfaces. A wet
friction clutch (hereafter called wet clutch) is lubricated by an automatic
transmission fluid (ATF) having a function as a cooling lubricant cleaning the
contacting surfaces and giving smoother performance and longer life. For high-
power applications, the clutch is typically assembled with multiple friction
and separator discs. The friction disc is made of a steel-core-disc with
friction material bonded on both sides and the separator disc is made of plain
steel. An electromechanical hydraulic actuator is usually used for
engaging/disengaging a wet clutch. This actuator consists of some main
components, such as a piston, a return spring which is always under
compression and a hydraulic group consisting of a control valve, an oil pump,
etc. To engage the clutch, pressurized ATF is controlled by the valve to
generate a force acting on the piston.

A number of researchers have explored and developed model-based prognostics
techniques for wet clutches. Yang et al. (see [260, 261]) developed a physics-
based prognostics model by considering that the degradation occurring in a wet
clutch is due to thermal effect alone in the friction materials. To this end,
a dedicated invasive and destructive test, i.e., thermal gravimetric analysis,
is required for identifying some parameters for the prognostics model. Since
the degradation mechanism occurring in the clutch friction material is not
only due to thermal effect but also another major mechanism namely adhesive
wear (see [262, 263, 264]), the assumption made within the prognostics method
in [260, 261] is, therefore, too oversimplified. Moreover, this approach would
be difficult to implement by the end users when the complete design data of a
wet clutch system are not available. Prognostics algorithms for the ATF (i.e.,
lubricant) of wet clutches have been also developed and reported in the
literature. References [265] and [266] developed an empirical degradation
model for predicting the lifetime of ATF based on an SAE#2 modified plate
test, in which the energy per shift and bulk lubricant temperature are used as
input parameters. The degradation model applies only to a specific ATF under
certain operating conditions. Furthermore, Ref [267] developed a prognostics
methodology using extra lubricant sensor which is immersed in ATF. The sensor
provides an electrical signal indicating in real time the chemical condition
of the lubricant to be monitored. Three parameters, namely 1) total acid
number (TAN), 2) delta oxidation (OX), and 3) HPDSC induction time (MIN), can
be derived from the sensor readings. An empirical model was developed to
predict the RUL of ATF based on the three parameters. Because of its
robustness, hybrid prognostics approach under the Bayesian framework (e.g.,
Kalman filtering) has been attracting a number of researchers nowadays and
been successfully applied to various applications like bearings, batteries,
material crack growth, electrolytic capacitors, etc.

Demands of low-cost prognostics tool for automatic transmission clutches
(i.e., based on measurement data from sensors typically available) by industry
have increased since the last few years. In [240], a prognostics tool is
developed by fusing a newly developed degradation model with the measurable
pre-lockup feature under the extended Kalman filtering framework. As this
feature can be extracted from sensory data typically available in wet clutch
applications, the developed prognostics tool, hence, does not require extra
cost for any additional sensor. New history data of commercially available wet
clutches obtained from accelerated life tests using a fully instrumented SAE#2
test setup have been acquired and processed. The experimental results show
that the prognostics algorithm developed outperforms the early developed
prognostics algorithm, which is based on the weighted mean slope method (i.e.,
data-driven approach). It is shown that the clutch remaining useful life
estimations with the novel prognostics algorithm remain in the desired
accuracy region of 20% with relatively small uncertainty interval in
comparison .with the early developed prognostics algorithm. In this framework,
empirical or physics-based degradation models are fused with measurement data
(i.e., feature) in order to improve the RUL estimation.

###  7.3 Alternator

A vehicle alternator shares many similarities to AC generators and induction
motors, and studies have shown that bearing failure is responsible for 40% of
the failures for induction motors, making it the most common mechanical
failure [268]. The alternator is coupled to the engine by either a v-belt or a
serpentine belt pulley system and a higher than normal level of belt tension
can provide greater lateral loads on the bearing and reduce its life. There is
also a great deal of research in bearing health monitoring and prognostics,
which is likely not only due to bearings being an important component for
rotating machinery, but also due to the bearing geometry, there are specific
fault frequencies that are seen in the vibration spectrum [269].

A vehicle alternator’s overall function is to charge the vehicle battery as
well as power the electrical auxiliaries; an alternator that is degraded or
failed will ultimately result in the inability to use these additional
auxiliaries and an increased potential for a dead battery and stalled car.
Considering the importance of the alternator in the overall functioning of the
vehicle and perhaps in particular for military vehicles for which mission
success is dependent on the use of surveillance equipment or other features
that require a properly functioning vehicle electrical system; knowledge of
the health status of the alternator is useful information that can support
logistical, tactical and maintenance planning efforts.

The vehicle alternator is essentially a rotating machine that generates a
3-phase alternating current that is rectified by a set of diodes in order to
produce a DC current with low ripple content; the vehicle alternator shares
many similarities with a generator, and to some degree electrical motors, and
in turn some of the common health monitoring and prognostic techniques, as
well as common failure modes, for motors and generators are applicable.
Considering the similarity between vehicle alternators, electric motors and
generators, a general methodology for assessing the health of rotating
electro-mechanical components was developed and demonstrated for an automotive
alternator component.

The approach applies domain specific knowledge, along with processing the data
and extracting features from the time domain signal, as well as the order
spectrum, to train machine learning algorithms, such as statistical pattern
recognition, logistic regression, or a self-organizing map to assess the
health of the vehicle alternator.