# A data-driven modular architecture with denoising autoencoders for health
indicator construction in a manufacturing process

Emil Blixt Hansen<EMAIL_ADDRESS>Helge Langseth  Nadeem Iftikhar  Simon Bøgh
Department of Materials and Production, Aalborg University, Denmark
Industrial Digital Transformation, University College of Northern Denmark,
Aalborg, Denmark  Department of Computer Science, Norwegian University of
Science and Technology, Trondheim, Norway

###### Abstract

Within the field of prognostics and health management (PHM), health indicators
(HI) can be used to aid the production and, e.g. schedule maintenance and
avoid failures. However, HI is often engineered to a specific process and
typically requires large amounts of historical data for set-up. This is
especially a challenge for SMEs, which often lack sufficient resources and
knowledge to benefit from PHM. In this paper, we propose ModularHI, a modular
approach in the construction of HI for a system without historical data. With
ModularHI, the operator chooses which sensor inputs are available, and then
ModularHI will compute a baseline model based on data collected during a burn-
in state. This baseline model will then be used to detect if the system starts
to degrade over time. We test the ModularHI on two open datasets, CMAPSS and
N-CMAPSS. Results from the former dataset showcase our system’s ability to
detect degradation, while results from the latter point to directions for
further research within the area. The results shows that our novel approach is
able to detect system degradation without historical data.

###### keywords:

prognostics and health management , health indicators , health index , machine
learning , manufacturing

††journal: arXiv

##  1 Introduction

The manufacturing industry has seen an increased interest in modern IT
technologies to enhance their production. These technologies are commonly
described as Industry 4.0. Nonetheless, many of the processes use old
equipment, which often lacks sensors and communication protocols to be used
with technologies of Industry 4.0, such as big data and analytics [1]. A study
also found that the use of old equipment negatively impacts the
competitiveness and innovation of a small and medium-sized enterprises (SME)
[2]. Prognostics and health management (PHM) concerns the topic of monitoring
and health indication of machinery. The health indicator (HI) part is
concerned with estimating the health of machinery. The HI can be constructed
differently depending on the equipment and setting, and an important design
choice is whether the HI is to be model-based, data-driven, or hybrid [3].
Model-based models takes the system’s underlying information into accounts
using mathematical models or other descriptions of the system behaviour. The
data-driven approach is where the HI score is not built on top of system
information, but rather learned from data. Lastly, the hybrid approach is a
combination of the other two. In this work we focus on the data-driven
approach. Within this category, there are different ways the HI can be
constructed, and examples include signal processing and statistical
techniques, including time series domains using time-domain or frequency-
domain feature [4, 5]. The continued development in deep learning has resulted
in several approaches to construct HI through deep learning. A variant of
autoencoders (AE) is for instance commonly used [6, 7]. Experiments from Zhao
et al. [7] showed that denoising autoencoders (DAE) outperformed other methods
for multivariate time series reconstruction problems, whereas [8] constructed
a convolutional neural network (CNN) to construct the HI directly.

Within the PHM domain, estimating the remaining useful life (RUL) of a given
machinery can be beneficial. RUL estimation is often based on the HI score,
but the RUL estimates will then typically rely on historical data of failures
to estimate the relationship between HI and RUL. Ensemble learning with time
dependant degradation weights has been shown to generate accurate RUL
predictions [9], while [10, 11] used an adaptive denoising algorithm to make
feature extraction and compute the RUL of aircraft engines. Moreover, it has
been shown that utilising semi-supervised learning can improve the performance
of RUL prediction [12]. A combination of ARIMA and LSTM models has been
proposed to increase performance in anomaly detection and forecasting [13].

The use of HI for PHM is often engineered to the specific machine/task, and
furthermore requires that sufficient data of the machine is available to
construct the HI. However, SMEs does not in general have this available to
them; when it comes to Industry 4.0, they are often behind larger enterprises
and do not have the knowledge to use technologies such as artificial
intelligence (AI) [14]. Previous work has focused on how to make these
technologies more available for SMEs, focusing on ease of use. For instance,
Hansen et al. [15] described a framework and conducted tests within image
classification problems.

To make HI scoring easy-to-use for SMEs, it is not feasible to assume that the
HI scoring system is particularly engineered to each specific machine used by
the SME. On the contrary, it should be possible for an operator to set up the
framework without understanding the underlying algorithms. Furthermore, since
a production process typically consists of multiple different machinery and
equipment, it could be beneficial for the SME not to be limited to a specific
engineering application. Therefore, ModularHI is not limited to specific
sensor input types. Instead it uses a modular divide-and-conquer strategy,
which is in-line with current thinking in AI. For instance, DeepMind [16]
presented PathNet, a scalable modular network suited for transfer learning
between different tasks in 2017. Here small neural network models together
form a larger network. The work was later extended by Stepwise PathNet [17].
These works demonstrate that modularity play a central role within deep
learning to enhance the overall performance.

In this paper we present ModularHI, a novel approach to construct an HI score
for an arbitrary machinery based on the available sensor inputs. ModularHI is
aimed at, but not limited to, use cases within the production sector. Our
working hypothesis is that while it is infeasible to engineer health
monitoring solutions for each machine, it is still beneficial to monitor a
machine’s health even if the employed system is less accurate than a tailor-
made solution would have been. The goal is thereby to provide a low-cost and
generally applicable HI monitoring system for SMEs, that can enable them to
start benefitting from Industry 4.0 technologies. The rest of the paper is
structured as follows. In section 2 the algorithm and components of ModularHI
is explained. In section 3 two different tests scenarios are described and in
section 4 the results are shown. Furthermore, in section 5 and section 6 the
discussion and conclusion is presented, respectively.

##  2 System architecture

ModularHI aims to support a broad set of use cases, and is not engineered for
specific tasks. We have therefore split the execution into three states:
setup, burn-in, and inference. The general execution flow of ModularHI’s three
states is shown in Figure 1. Besides the execution flow, the underlying system
comprises two main parts: the component models and the aggregator. The
execution flow and the two main parts are discussed next.

Figure 1: The execution flow of the three states: setup, burn-in, and
inference.

###  2.1 Execution flow

In the first state, setup state, the different models and their specific input
are configured. The models are called component models, and are further
described in section 2.2. Furthermore, the initial data collection also takes
place in this state. When enough data is collected, the execution goes to the
burn-in state.

The burn-in state is where the component models are fitted to the collected
datasets. We will assume that the data describes the monitored system in its
optimal performance state, preferably directly after machine maintenance. When
each component model has been sufficiently trained on their individual
datasets, the components model can calculate a real-time health indicator
(more on this in section 2.2). In the inference state the component model will
monitor its own status, and posts an alarm if the HI value is deemed to be
outside its acceptable region. First, however, the acceptable region must be
established. While several methods can be used to determine this acceptable
region, we use a simple strategy in this paper. We monitor the HI during the
burn-in state, calculate the standard deviation of the calculated HI during
this period, and define the acceptable region for the HI to between zero and
nine times the calculated standard deviation. Finally we define the HI at the
system level. This is done by the aggregator model, which collects and
combines the HI values from the component models. The combination is named the
joint HI ($\textrm{HI}^{j}$), represents the overall system’s HI score, and
has its own acceptable region. Again, the region is defined by nine standard
deviations calculated during the burn-in stage. The combinations of the
different component models is further described in section 2.3. Next, the
execution enters the third state, the inference state.

The inference state is where the ModularHI is executed on new data. Here a
continuous collection of data occurs, and every time a new data point is
collected, it is executed through the models. This includes calculating the
current HI score comparing the new datapoint to data collected during the
burn-in state. After that, $\textrm{HI}^{j}$ is calculated, and all of the
boundaries are checked. If at least one boundary is crossed, the system is
assumed to either be in a faulty state or sliding towards it, indicating that
maintenance or inspection is recommended. This therefore results in an alarm
state being published.

###  2.2 Component models

ModularHI has been designed with simplicity of use in mind. To handle
different sensor categories, with different data types and data dimensions, we
therefore designed specific models per sensor type. Hence, each sensor has its
own model, specifically designed for that measurement type. It follows that
component models are specifically trained for a certain type of measurement
(e.g., a specific model for temperature data).

As mentioned above, there are different ways of constructing a HI score. One
of the requirements for ModularHI is that it should be modular and handle a
different mixture of sensor inputs. Therefore, it is infeasible to train a
separate model to generate the system’s HI score for each possible scenario.
Instead, ModularHI consists of individual component models, each outputting a
HI score based on a single stream of data. To enable these HI scores to be
comparable to each other throughout the different sensor inputs, we have
chosen the DAE [7] as our go-to model type. Since the component models are
designed to only handle univariate time series, the model size is limited. In
the experiments reported in this paper, we have chosen to use a DAE with LSTM
layers to capture the time perspective in the data. The DAE architecture is
the same across all sensors and all experiments, and can be seen in Table 1.
We note that the same core modelling approach could be used to analyse other
streaming data like sound or video simply by adapting the DAE to handle that
data-type.

Table 1: The LSTM autoencoder. Layer type | Specification
---|---
Input | Shape (batch size, window size, 1)
LSTM | 8 units, returned sequence
Dropout | Probability 0.5
LSTM | 4 units
Repeat vector | 8 times
LSTM | 4 units, returned sequence
Dropout | Probability 0.5
LSTM | 8 units, returned sequence
Output | Time distributed of window size

Currently, this DAE architecture is used for all time series sensor input,
such as temperature, vibration, etc. Even though all models have the same
architecture, they are independently pre-trained on a relevant dataset. This
application of transfer-learning reduces the data-requirements during system
setup, reduces the compute required for training the model during burn-in, and
improves the model’s performance [18].

The HI score is based on the mean absolute error (MAE) during reconstruction
of the input-signal:

$\textrm{HI}^{m}_{k}=\frac{1}{n}\sum_{i=1}^{n}\left|x_{i}-\tilde{x}_{i}\right|.$
(1)

Here $\textrm{HI}^{m}_{k}$ refers to the HI score of the $k$’th component
model $m$ (out of the set of $M$ component models for a specific setup case),
$\bm{x}$ is a vector of measurements of window-size $n$ and $\bm{\tilde{x}}$
is the corresponding reconstructed measurements also of size $n$. As stated
earlier, each model has its own upper-bound calculated by taking the mean of
the HI of burn-in and finding standard deviation $\sigma$ from the sample
mean. Specifically, the upper boundary is specified by $9\,\sigma$ and the
lower is set to 0 (since MAE is a non-negative real number).

###  2.3 Aggregator

The objective of the aggregator is to combine the information from the
component models to give a system-wide HI, which we call the joint HI
($\textrm{HI}^{j}$). We note that $\textrm{HI}^{j}$ can be calculated in many
different ways, ranging from simple aggregations like maximum or sum to
increasingly complex combinations, e.g., represented by a deep neural network.
As ModularHI is designed for ease-of-use within a wide range of application
areas, to be data-driven, and to not require engineering input to define the
aggregation function, we choose to let each sensor contribute equally to
$\textrm{HI}^{j}$ by default. The joint health indicator is now simply the
average of the $N$ components’ HI scores:

$\textrm{HI}^{j}=\frac{1}{N}\sum_{i=1}^{N}\textrm{HI}^{m}_{i}$ (2)

Nevertheless, if an operator knows that some sensor is more critical to the
stability of a system, they can specify weights $\bm{w}$ for each sensor
input. An example of this could be that the operator knows that the system
starts to be unstable when the system temperature rises. The operator will
then give the temperature sensor input a higher weight the the others. Thus
the $\textrm{HI}^{j}$ will be more acceptable to changes from the temperature
sensor. The $\textrm{HI}^{j}$ is then calculated by a weighted average as seen
in Equation 3. By default all the weights are specified as 0.5, hence they are
all equal and the $\textrm{HI}^{j}$ will be calculated as Equation 2.

$\textrm{HI}^{j}=\frac{\sum_{i=1}^{N}w_{i}\cdot\textrm{HI}^{m}_{i}}{\sum_{i=1}^{N}{w_{i}}}$
(3)

ModularHI calculates the upper-bound for $\textrm{HI}^{j}$ at $9\,\sigma$
during the burn-in state. This is done when all component models have finished
their burn-in step. Then Equation 3 is calculated to find all of the
$\textrm{HI}^{j}$ from the burn-in period to calculate the sample mean and
thus the corresponding $\sigma$.

When the burn-in state is completed, the cycle of the inference state is
executed. For a new data point $x_{t}$ all component models will run a window
of the last $n$ samples including the new data point, such that
${\bm{x}=\\{x_{t-n+1},\ldots,x_{t}\\}}$. After that, all calculated
$\textrm{HI}^{m}$ values will be used to calculate the current
$\textrm{HI}^{j}$. With the new $\textrm{HI}^{j}$ all boundaries are checked
such that if any boundary is crossed in their respected HI, an alarm is
published. An illustration of the inference state of ModularHI can be seen in
Figure 2 where test 7 from section 3.1 is shown.

Figure 2: The combination of the different component models and the aggregator
from CMAPSS T7.

##  3 Experiments

To validate the use of ModularHI, we needed to test it on a relevant dataset.
This dataset should preferably contain multiple different sensors (to validate
the modularity), include recordings from a steady-state (to enable the initial
data collection), and have a continuous data steam eventually leading to a
faulty state. Finally, it would be beneficial if the dataset was relevant to
production applications, either being extracted from one or similar to a
process that could exist in one. The MIMII dataset, which contains various
recordings of failure of processes [19] is one potential candidate. However,
it does not contain continuous recording from steady-state to failure, and
does not include information such as vibration. A dataset collected from a
real production line containing various different sensors and faulty states
was presented in [20]. Unfortunately, this dataset consists mainly of
operations failures and not process failures. NASA published the jet engine
degradation dataset CMAPSS in 2008 [21]. This dataset contains simulated jet
engines monitored until failure, where each data point is an aggregated value
from one flight. More recently, they released an updated version, named
N-CMAPSS [22]. This dataset contains various sensor values from the same
setting. The main difference is that data in N-CMAPSS is collected throughout
the flights and includes both ascent and descent. Moreover, the initial states
of the flights are collected at actual flights, and only the run to failure is
simulated. Hence, N-CMAPSS is a larger and more complex dataset compared to
the original CMAPSS. We have chosen to test ModularHI against both CMAPSS and
N-CMAPSS. We chose both datasets because both of them have a continuous data
stream from steady-state until failure. Moreover, the two datasets symbolise
two different levels of complexity. The available datasets also show the lack
of available authentic production datasets which can be used in our case. Thus
the two CMAPSS datasets are the closest to an actual production dataset with
their continuous data stream of various sensors.

###  3.1 CMAPSS dataset test

The original CMAPSS dataset consists of multiple flights, which are commonly
used for RUL predictions [10, 11]. Here, however, we use ModularHI to generate
a HI and determine if the equipment/process is in steady operation. Therefore,
our test will only consist of a single jet engine (engine number 1 from the
dataset FD001). Besides which sensors to use, we also need to decide on two
hyperparameters: the duration of the burn-in period and the window size used
by the autoencoder. Since engine number 1 only has 220 recordings, a burn-in
period of 78 is chosen as it includes a stable amount of data. A window size
of 8 was chosen as it should capture enough of the temporal data. We remark
that the relatively small dataset used during burn-in is sufficient due to the
auto-encoder being pre-trained on a separate dataset. The component model
concerning temperature is pre-trained on historical weather
data111https://www.kaggle.com/budincsevity/szeged-weather and the component
models concerning generic time series data is pre-trained on accelerometer
data collected at Aalborg University. The general purpose of pre-training the
networks is to train them to reproduce the input; the underlying
characteristics of the individual sensor data will then be learned during the
burn-in state.

Table 2: The eight test setups for CMAPSS dataset. Each sensor has its own
model; if several sensors are mentioned together with only one model, then all
sensors have that type of model. The same is true with the assigned weights.
The model T is pre-trained temperature data and C is a generic model pre-
trained on accelerometer data.

Tests | Sensors | Models | Weights
---|---|---|---
CMAPSS - T1 | T50 | T | 0.5
CMAPSS - T2 | T30, T50 | T | 0.5
CMAPSS - T3 | T2, T30, T50 | T | 0.5
CMAPSS - T4 | T2, T30, T50 | T | 0.6, 0.2, 0.2
CMAPSS - T5 | P15 | C | 0.5
CMAPSS - T6 | P15, T2, T50 | C, T, T | 0.5, 0.5, 0.5
CMAPSS - T7 | P15, T2, T50 | C, T, T | 0.2, 0.2, 0.6
CMAPSS - T8 | P2, P15, epr, farB, Nf_dmd, PCNfR_dmd, T50 | T50: T, Rest: C | 0.5

We conducted eight tests on the data from Engine number 1, each with a
different combination of sensors and weights (refer to Equation 3). The test-
cases are described in Table 2. Moreover, the values for the sensors are
plotted in Figure 3. The eight tests are conducted to validate various aspects
of ModularHI. Tests 1 and 2 examine the usability of ModularHI with inputs
where degradation is present. Test 5 considers what happens when degradation
is not clearly present. Tests 3, 6 and 8 look at a combination of sensor with
“informative” and “uninformative” sensor values with equal weights. Finally,
Tests 4 and 7 (inference state visualised in Figure 2) highlight the same when
a larger weight has been applied to the “informative” measurements.

Figure 3: The nine used sensor from CMAPSS engine number 1 used, only in
sensor T30 and T50 is the degradation visible with an upward trend.

###  3.2 N-CMAPSS dataset test

Besides the original CMAPSS data, we also tested ModularHI on the more complex
N-CMAPSS dataset. Since N-CMAPSS consists of multiple flights of different
lengths, we chose flight number 2 from dataset DS01. These flights comprised
of data from flights over 3000 feet. All the flights include ascend from 3000
feet, cruise altitude and descending to 3000 feet. Flight number 2 describe
class three flights, meaning all flights is over 5 hours long [22]. The sensor
readings and flight settings are subject to high variance during a flight’s
ascend and descend. Since the focus of ModularHI is to be able to detect
deviations from stable operation, we have filtered out the ascending and
descending parts of the flights. Moreover, only cruise parts between 25,000
and 30,000 feet were included during the burn-in state. Furthermore, we only
included flights where the cruise part had a minimum of $1024$ observations
(as we used window-size $n=1024$ for the autoencoders). The cleaned file
consists of 4 sensors, and the first 105,876 readings are used for the burn-in
state.

Table 3: The five test setups for N-CMAPSS dataset. Each sensor has its own model; if several sensors are mentioned together with only one model, then all sensors have that type of model. The same is true with the assigned weights. The model T is pre-trained temperature data and C is a generic model pre-trained on accelerometer data. Test | Sensors | Models | Weights
---|---|---|---
N-CMAPSS - T1 | T40 | T | 0.5
N-CMAPSS - T2 | SmLPC | C | 0.5
N-CMAPSS - T3 | T40, SmLPC, SmHPC | T, C, C | 0.5
N-CMAPSS - T4 | T2, SmLPC | T, C | 0.5
N-CMAPSS - T5 | T2, SmLPC, SmHPC | T, C, C | 0.6, 0.2, 0.2

We conducted five tests of the cleaned DS01 engine 2 data. All of them had a
sliding window size of 1024 and was tested in batches of 256. To combat the
abrupt changes in the values when going from a single cruise to another, we
only trained with mini-batches where one cruise was involved. The different
tests, along with their models and weights are reported in Table 3. A plot of
the used sensors after data cleaning can be seen in Figure 4. While some of
the sensors in Figure 4 show signs of degradation (see, in particular, SmLPC),
the apparently noisy variations in the readings dominate the signals. The
dataset is therefore particularly challenging for ModularHI, where we for
simplicity assume that all data during the burn-in period is from stable
operation of the equipment/process. From just plotting the dataset, one should
therefore expect that the monitoring system will be more challenged by this
dataset than from the previous one.

As with the CMAPSS dataset, the five tests were conducted to test different
aspects of ModularHI. Tests 1 and 2 was to see the effect of using only a
single sensor, where one of them (Test 2) had a clear degradation. Tests 3 and
4 use multiple sensor values, and Test 5 employs sensors with different
weights.

Figure 4: The 4 used sensor from N-CMAPSS engine number 2. Only in sensor
SmLPC is the degradation clearly visible with an downwards trend.

##  4 Results

The component models were learning until there was no improvement in the
validation loss for 25 consecutive epochs, and at that time the weights from
the epoch with the lowest validation loss was used.

###  4.1 CMAPSS dataset result

The first two tests, Tests 1 and 2, examined the system when degradation is
visually present in the sensor readings. Since T50 is included in both tests,
the results are almost identically. The result from Test 2 reported in Figure
5 show that $\textrm{HI}^{j}$ reacts at time-step 212. The two component
models first publish alarms at step 221 and 252 for sensor T50 and T30,
respectively.

(a) T30 sensor value and HI.

(b) T50 sensor value and HI.

(c) $\textrm{HI}^{j}$ for T30 and T50.

Figure 5: The result from Test 2. The green vertical line indicates the end of
the burn-in state. The horizontal red lines indicate the calculated
boundaries. The orange area in the $\textrm{HI}^{j}$ is when an alarm is
published.

In Test 7, we used sensors T50, T2, and P15. Sensor T50 displays a clear
degradation in the sensor values, while sensor P15 only has a small alteration
in the data, and T2 is static. The results can be seen in Figure 6, and show
that sensor T2 and P15 do not indicate any depredations, neither does their HI
score. However, since sensor T50 crosses its upper-bound an alarm is
published. We also note that $\textrm{HI}^{j}$ exceeds its upper bound even
though two sensors do not indicate a degradation.

(a) T2 sensor value and HI.

(b) T50 sensor value and HI.

(c) P15 sensor value and HI.

(d) $\textrm{HI}^{j}$ for T2, T50, and P15.

Figure 6: The result from Test 7. The green vertical line indicates the end of
the burn-in state. The horizontal red lines indicates the calculated
boundaries. The orange area in the $\textrm{HI}^{j}$ is when an alarm is
published. The HI score from 6(a) is below the upper boundary line.

Test 8 was conducted to see if a majority of non-contributing sensor values
will prevent $\textrm{HI}^{j}$ to detect that one sensor measures a
degradation. Therefore, this test includes one sensor with the degradation
evident (T50) and six without (P2, P15, epr, farB, Nfdmd, and PCNfRdmd). The
$\textrm{HI}^{j}$ results in Figure 7 show that an alarm is published before
$\textrm{HI}^{j}$ crosses its boundary. This is initiated by the sensor T50
crosses its upper-bound. Moreover, it can also be seen that $\textrm{HI}^{j}$
itself crossed its boundary at time 243.

Figure 7: The result from Test 8. The green vertical line indicates the end of
the burn-in state. The horizontal red lines indicates the calculated
boundaries. The orange area in the $\textrm{HI}^{j}$ is when an alarm is
published.

###  4.2 N-CMAPSS dataset result

We now focus on the more challenging N-CMAPSS dataset. Here, Test 3 was
designed to examine ModularHI with multiple sensors. We chose sensors T40,
SmLPC, and SmHPC, and gave them equal weight. The results in Figure 8 show
that the only component model that indicates a degradation is the SmLPC
sensor. After the burn-in state, $\textrm{HI}^{m}$ for this sensor is rising
and exceeds its upper bound in the end. The same trend is also present in the
aggregator where $\textrm{HI}^{j}$ is approaching the upper-bound. The two
alarms are published when SmLPC crosses its boundary.

(a) SmHPC sensor value and HI.

(b) SmLPC sensor value and HI.

(c) T40 sensor value and HI.

(d) $\textrm{HI}^{j}$ for SmHPC, SMLPC, and T40.

Figure 8: The result from test 3 of the N-CMAPSS dataset. The green vertical
line indicates the end of the burn-in state. The horizontal red lines
indicates the calculated boundaries. The orange area in the $\textrm{HI}^{j}$
is when an alarm is published.

Test 5 was conducted to test ModularHI when a higher weight is applied to one
measurement, and sensor T2 was given a higher weight than the other two
sensors (SmHPC and SmLPC) in this test. The T2 sensor values and its HI score
can be seen in Figure 9 along with the $\textrm{HI}^{j}$. Due to its higher
weight, T2 highly impacts $\textrm{HI}^{j}$, moreover, multiple alarms are
published.

(a) T2 sensor value and HI.

(b) $\textrm{HI}^{j}$ for SmHPC, SmLPC, and T2.

Figure 9: The result from test 5 of the N-CMAPSS dataset. The green vertical
line indicates the end of the burn-in state. The horizontal red lines
indicates the calculated boundaries. The orange area in the $\textrm{HI}^{j}$
is when an alarm is published.

##  5 Discussion

The tests showed successful results on the original CMAPSS dataset. Each test
was able to detect the degradation within the dataset and successfully publish
an alarm at an appropriate time. ModularHI succeeded regardless of how many
non-degradation sensors were included to complicate the endeavour. This must
be partially attributed to the system design, as a single $\textrm{HI}^{m}$
crossing its boundary is sufficient to publish an alarm. The tests on the more
complex N-CMAPSS dataset were not as successful, as alarms only were published
when a single sensor value crossed its boundary. Furthermore, sensor T2
triggered an alarm during Test 5 even though no clear degradation trend can be
seen from that sensor.

The component models used in this paper are built around the idea that one
model should learn the underlying characteristics of a specific sensor. We
have pre-trained our models to speed up the training process, i.e., related to
the data collection and learning in the burn-in state. All the univariate
models are sharing the same DAE architecture (Table 1). A direction for future
research is to evaluate the performance of different architectures when
applied to univariate data, potentially reflecting what sensor the data
originates from. Some sensors output multivariate data streams, and while we
hypothesise that a DAE architecture similar to what is currently used for
univariate data could also work for multivariate streams, this is so far not
thoroughly tested. Similarly, specific DAE models should also be made for
images, videos, and sound to handle those types of sensor inputs. Another
issue is how to model correlated sensor values. Vibration can, for instance,
be measured by both a 3 degree of freedom (DoF) and 6 DoF accelerometers. To
detect increasing levels of vibration it could be beneficial to analyse
readings from both sensors together. The current version of ModularHI has
traded such fidelity in the model for simplicity, but the performance gains of
combining correlated signals into component-overarching models should be
investigated.

The aggregator handles all HI-values from the component models and decides
when an alarm should be published. One specific challenge is that the main
objective is that it should be data-driven. Therefore, the aggregator should
internally work out its optimal behaviour during the burn-in state. Currently,
the aggregator’s HI value is a weighted average of those from the component
models, and no computational work is done to find a better aggregation
formula. Nevertheless, since we can use a weighted average, it is possible to
get at least some expert knowledge into the system by tweaking the weights. If
doing so, we take a step away from an entirely data-driven approach, and move
towards a hybrid approach. Another idea is to find, e.g., a neural network
that uses the component models’ $\textrm{HI}^{m}$-values to generate
$\textrm{HI}^{j}$. This would enable the aggregator to learn the different
characteristics and dependency of all the components models and thus
understand the connection between sensor values, but would increase the data-
requirements to initialise the system.

Currently, the boundaries from both the component models and the aggregator
are calculated by the 9’th standard deviation from the HI mean during the
burn-in state. While this boundary was successful in the CMAPSS dataset as
described in section 4.1, it was less successful for the N-CMAPSS dataset.
This was partly because the DAE models used to calculate each component’s HI
value were not successful in faithfully reproducing the input-signal during
the burn-in state. As a consequence, we saw a larger variability in
$\textrm{HI}^{m}$, leading to rather large standard deviation during burn-in,
and therefore to a less responsive behaviour for our monitoring system. A
solution could be a locally adaptive boundary that is based on the historical
HI scores and changes as each new score is calculated. This would make the
boundaries dynamic, but potentially also prevent the detection of slowly
developing problem situations.

When working with time-series data in neural networks, the way data is
presented to the model is extremely important. We use a rolling window in our
implementation, and fix the window-size based on the available data and the
speed of the underlying dynamics. This choice, while difficult to make, can
influence the results dramatically. If the window-size is too small the model
cannot learn the temporal information, and if it is too-large the result can
be a prolonged training time and a reduction in available data batches
reducing the learning quality. We used a window size of 8 for the CMAPSS test,
and 1024 the N-CMAPSS dataset, as the dataset contained more data and high
variation throughout the dataset. To reduce the sensitivity wrt. this
parameter one could try to define the window size dynamically based on the
amount of data collected in the burn-in state along with other statistical
characteristics such as standard deviation, skewness, etc.

While other implementations of HI split them up into multiple zones compared
to the severity (see, e.g., [23]), we have chosen to have only one type of
alarm. This was done to avoid scenarios where a system would fail in, e.g.
warning state instead of in a critical state. Other researchers based their
zoning on historical data, which is not assumed to be present in our case.
Finally, it would be beneficial for the operators to have an RUL estimation,
but to the best of our knowledge there is still no method available to produce
reliable RUL estimates without historical data available.

To utilise ModularHI in practice, a few things are considered paramount to be
in place. Firstly, each component model is assumed to be already pretrained on
relevant datasets. The operator will then place and select the sensor inputs
through a GUI where he would define the stable period for the burn-in to
occur. When the burn-in period is finished, the system will atomically go into
the inference state. While we in this paper performed tests on the publicly
available datasets CMAPSS and N-CMAPSS, they are not the ideal use case.
ModularHI was designed with more generic manufacturing systems in mind, such
as punching machines, drill presses, CNC and bending machines. These types of
systems are more comparable to the CMAPSS dataset since the system is not as
complex as the data represented in the N-CMAPSS dataset. Nonetheless, as it is
now, ModularHI does not distinguish between different part numbers, e.i.
ModularHI has no way of knowing if the machine is currently producing a part
it was not present in the burn-in state.

##  6 Conclusion and future work

In this paper we presented ModularHI, a novel modular architecture for
constructing a HI in a production process. Our work does not require any
historical data, as the DAE is fitted during a stable process on-site.
Moreover, the operators choose the sensors available/required, and ModularHI
does not require any knowledge of the type of machinery. The system is data-
driven, easy-to-use and modular, and these design-choices make ModularHI
suitable for SMEs that do not have the resources to invest in PHM solutions
that large enterprises do.

We tested our contribution on two open datasets, CMAPSS and N-CMAPSS. All the
tests on the CMAPSS dataset successfully published an alarm and detected the
degradation in the underlying process. This indicates our novel approach of
using a combination multiple of individual trained DAEs aggregated together is
able to produce an HI score and degradation detection without any prior
historical data. This will benefit SMEs as it has been shown that they often
lack the resources and knowledge to invest in large PHM solutions.

The test of the N-CMAPSS was not as successful in detecting the degradation as
on the CMAPSS tests. This is because of the higher complexity within that
dataset since it contains different flights of different lengths and
altitudes; state changes that influence the data substantially. We tried to
overcome this problem by limiting the data to cruise flights above 10,000
feet, but found that this was not enough to make the data sufficiently stable.
One could try to limit this specific dataset to have different models for the
different stages of flights. Nonetheless, this is out of scope for ModularHI
since it is focused on a more “stable” system, which does not change
extensively throughout its execution.

For future work, ModularHI should be tested on real production data with
various sensors to validate it in its intended settings. Moreover, tests
should be carried out with both images and sound as the component models. More
research should be conducted on each component model to ensure the correct
architecture for each model. A more automatic system for choosing the window
size should also be researched to make the system more easy-to-use. Lastly,
more research within the aggregator should be conducted to see if it can learn
more from the component models instead of aggregating the results as it is
now.

## Acknowledgements

The work was conducted as a part of the Danish strategy for Industry 4.0 in
SMEs called Innovation Factory North.

## References

  * Gurkov [2007] I. Gurkov,  Dominant strategic archetype of the Russian industrial firm,  JEEMS Journal of East European Management Studies 12 (2007) 35–52.
  * Abrhám et al. [2015] J. Abrhám, W. Strielkowski, M. Vošta, J. Šlajs,  Factors that influence the competitiveness of Czech rural SMEs,  Agricultural Economics 61 (2015) 450–460.
  * Atamuradov et al. [2017] V. Atamuradov, K. Medjaher, P. Dersin, B. Lamoureux, N. Zerhouni,  Prognostics and health management for maintenance practitioners - review, implementation and tools evaluation,  International Journal of Prognostics and Health Management 8 (2017) 1–31.
  * Atamuradov et al. [2020] V. Atamuradov, K. Medjaher, F. Camci, N. Zerhouni, P. Dersin, B. Lamoureux,  Machine health indicator construction framework for failure diagnostics and prognostics,  Journal of Signal Processing Systems 92 (2020) 591–609.
  * Zhu et al. [2014] J. Zhu, T. Nostrand, C. Spiegel, B. Morton,  Survey of condition indicators for condition monitoring systems,  in: Annual Conference of the PHM Society, volume 6, 2014.
  * Luo et al. [2019] B. Luo, H. Wang, H. Liu, B. Li, F. Peng,  Early fault detection of machine tools based on deep learning and dynamic identification,  IEEE Transactions on Industrial Electronics 66 (2019) 509–518.
  * Zhao et al. [2019] R. Zhao, R. Yan, Z. Chen, K. Mao, P. Wang, R. X. Gao,  Deep learning and its applications to machine health monitoring,  Mechanical Systems and Signal Processing 115 (2019) 213–237.
  * Guo et al. [2018] L. Guo, Y. Lei, N. Li, T. Yan, N. Li,  Machinery health indicator construction based on convolutional neural networks considering trend burr,  Neurocomputing 292 (2018) 142–150.
  * Li et al. [2019] Z. Li, D. Wu, C. Hu, J. Terpenny,  An ensemble learning-based prognostic approach with degradation-dependent weights for remaining useful life prediction,  Reliability Engineering & System Safety 184 (2019) 110 – 122. Impact of Prognostics and Health Management in Systems Reliability and Maintenance Planning.
  * Berghout et al. [2020] T. Berghout, L. Mouss, O. Kadri, L. Saïdi, M. Benbouzid,  Aircraft engines remaining useful life prediction with an adaptive denoising online sequential extreme learning machine,  Engineering Applications of Artificial Intelligence 96 (2020) 103936\.
  * Saxena et al. [2008] A. Saxena, K. Goebel, D. Simon, N. Eklund,  Damage propagation modeling for aircraft engine run-to-failure simulation,  in: 2008 International Conference on Prognostics and Health Management, 2008, pp. 1–9. doi:10.1109/PHM.2008.4711414.
  * Ellefsen et al. [2019] A. L. Ellefsen, E. Bjørlykhaug, V. Æsøy, S. Ushakov, H. Zhang,  Remaining useful life predictions for turbofan engine degradation using semi-supervised deep architecture,  Reliability Engineering & System Safety 183 (2019) 240–251.
  * Hollingsworth et al. [2018] K. Hollingsworth, K. Rouse, J. Cho, A. Harris, M. Sartipi, S. Sozer, B. Enevoldson,  Energy anomaly detection with forecasting and deep learning,  in: 2018 IEEE International Conference on Big Data (Big Data), 2018, pp. 4921–4925. doi:10.1109/BigData.2018.8621948.
  * Hansen and Bøgh [2021] E. B. Hansen, S. Bøgh,  Artificial intelligence and internet of things in small and medium-sized enterprises: A survey,  Journal of Manufacturing Systems 58 (2021) 362–372. Digital Twin towards Smart Manufacturing and Industry 4.0.
  * Hansen et al. [2020] E. B. Hansen, N. Iftikhar, S. Bøgh,  Concept of easy-to-use versatile artificial intelligence in industrial small & medium-sized enterprises,  Procedia Manufacturing 51 (2020) 1146–1152. 30th International Conference on Flexible Automation and Intelligent Manufacturing (FAIM2021).
  * Fernando et al. [2017] C. Fernando, D. Banarse, C. Blundell, Y. Zwols, D. Ha, A. A. Rusu, A. Pritzel, D. Wierstra, PathNet: Evolution channels gradient descent in super neural networks, 2017. arXiv:1701.08734.
  * Imai et al. [2020] S. Imai, S. Kawai, H. Nobuhara,  Stepwise PathNet: a layer-by-layer knowledge-selection-based transfer learning algorithm,  Scientific Reports 10 (2020) 8132.
  * Zhuang et al. [2021] F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong, Q. He,  A comprehensive survey on transfer learning,  Proceedings of the IEEE 109 (2021) 43--76.
  * Purohit et al. [2019] H. Purohit, R. Tanabe, K. Ichige, T. Endo, Y. Nikaido, K. Suefusa, Y. Kawaguchi, MIMII Dataset: Sound Dataset for Malfunctioning Industrial Machine Investigation and Inspection, 2019\. doi:10.5281/zenodo.3384388.
  * Hansen et al. [2022] E. B. Hansen, E. R. van der Bijl, M. B. Nielsen, M. Svangren Bodilsen, S. V. Berg, J. Kristensen, N. Iftikhar, S. Bøgh,  A new authentic cloud dataset from a production facility for anomaly detection,  in: Towards Sustainable Customization: Bridging Smart Products and Manufacturing Systems, Springer International Publishing, Cham, 2022, pp. 415--422.
  * Saxena and Goebel [2008] A. Saxena, K. Goebel,  Turbofan engine degradation simulation data set,  NASA Ames Prognostics Data Repository (2008) 1551--3203.
  * Arias Chao et al. [2021] M. Arias Chao, C. Kulkarni, K. Goebel, O. Fink,  Aircraft engine run-to-failure dataset under real flight conditions for prognostics and diagnostics,  Data 6 (2021).
  * Velmurugan et al. [2021] K. Velmurugan, P. Venkumar, P. R. Sudhakara,  SME 4.0: Machine learning framework for real-time machine health monitoring system,  Journal of Physics: Conference Series 1911 (2021) 012026.


11institutetext: Indian Institute of Science Education and Research (IISER)
Tirupati, India

# Production of pions, kaons, and (anti-)protons in Au+Au collisions at
$\sqrt{s_{NN}}$ = 54.4 GeV at RHIC

Krishan Gopal1<EMAIL_ADDRESS>for the STAR
collaboration

###### Abstract

We report systematic measurements of bulk properties of the system created in
Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV recorded by the STAR detector
at the Relativistic Heavy Ion Collider (RHIC). The transverse momentum spectra
of $\pi^{\pm}$, $K^{\pm}$, and $p$($\bar{p}$) are studied at mid-rapidity
$(|y|<0.1)$ for different centrality classes. We also present mid-rapidity
measurement of particle yields $(dN/dy)$ and particle ratios in Au+Au
collisions at $\sqrt{s_{NN}}$ = 54.4 GeV. The kinetic freeze-out parameters
($T_{kin}$ and $\^{a}\beta\^{a}$) are extracted from particle spectra using
the blast-wave model, and all the results are compared with previously
published experimental results.Â Â Â

##  1 Introduction

Quantum Chromodynamics (QCD) predicts that at very high energy density and/or
very high temperature, a new state of matter is formed where quarks and gluons
are deconfined, known as the Quark-Gluon Plasma (QGP) RefC . The study of
transverse momentum spectra of produced particles is important for
investigating the bulk properties of the QGP, such as integrated yields
$(dN/dy)$, average transverse momentum $\langle p_{T}\rangle$, particle
ratios, and freeze-out properties. This information is also useful for
understanding particle production mechanisms.

##  2 Analysis details

We have studied the transverse momentum spectra of $\pi^{\pm}$, $K^{\pm}$, and
$p$($\bar{p}$) at mid-rapidity $(|y|<0.1)$ for different centrality classes in
Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV, recorded by STAR star
experiment in the year 2017. In the STAR experiment, charged particle
identification is performed utilizing the Time Projection Chamber (TPC) and
Time of Flight (TOF) detectors depending on the momentum of the particle. For
low momentum particles, the TPC is used, while for particles with intermediate
or high momenta ($p_{T}$ > 1 GeV/c), the TOF is used. TPC works on the
principle of ionization energy loss of the charged particles passing through
TPC’s gas volume.
The TPC uses the ionization energy loss ($dE/dx$) for particle identification,
from which the variable $z$ is defined:

$\displaystyle z_{X}=ln(\frac{<dE/dx>}{<dE/dx>^{B}_{X}})$

where $<dE/dx>^{B}_{X}$ is the expected energy loss based on the Bichsel
function [3] and $X$ is the particle type ($e^{\pm}$, $\pi^{\pm}$, $K^{\pm}$,
$p$, or $\bar{p}$). A multi-Gaussian fit is carried out on $z_{X}$
distributions to extract raw yields.
For the TOF detector, we use mass square information,
$m^{2}=p^{2}(\frac{c^{2}T^{2}}{L^{2}}-1)$ where $m$, $p$, $L$, $T$ and $c$ are
mass of particle, momentum of the particle, path length, time of travel by the
particle and speed of light, respectively. From the above two methods we
obtain raw spectra from TPC and TOF. The TPC tracking efficiency and
acceptance, energy loss correction, pion and proton background subtraction are
applied to calculate corrected spectra. For the TOF analysis, TOF matching
efficiency correction is also applied.

##  3 Results and discussions

###  3.1 Transverse momentum spectra and particle yields

We calculate the $p_{T}$ spectra of $\pi^{\pm}$, $K^{\pm}$, and $p$($\bar{p}$)
in Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV. Figure 1 shows the $p_{T}$
spectra of $\pi^{+}$, $K^{+}$, and $p$ in different centrality classes from
central (0-5%) to peripheral (70-80%) collisions. The $p_{T}$ spectra of
identified hadrons show a clear centrality dependence. We fit the pion
($\pi^{\pm}$), kaon ($K^{\pm}$) spectra with the Levy function and
$p$($\bar{p}$) spectra with a double-exponential function, to calculate
particle yields ($dN/dy$).

Figure 1: $p_{T}$ spectra of $\pi^{+}$, $K^{+}$, and $p$ measured at mid-
rapidity ($|y|$ $<$ 0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV in
different collision centralities. The statistical and systematic uncertainties
are added in quadrature. Figure 2: Centrality dependence of $dN/dy$ normalized
by $\langle N_{\text{part}}\rangle/2$ for $\pi^{\pm}$, $K^{\pm}$, and
$p$($\bar{p}$) at mid-rapidity ($|y|<0.1$) in Au+Au collisions at
$\sqrt{s_{NN}}$ = 54.4 GeV. Errors shown are quadrature sums of statistical
and systematic uncertainties.

Figure 2 shows the centrality dependence of $dN/dy$ normalized by half of the
average number of participating nucleons ($\langle N_{\text{part}}\rangle$/2)
for $\pi^{\pm}$, $K^{\pm}$, and $p$($\bar{p}$) in Au+Au collisions at
$\sqrt{s_{NN}}$ = 54.4 GeV, along with other RHIC’s Beam Energy Scan (BES)
energies.
The yields of $\pi^{\pm}$, $K^{\pm}$, and $\bar{p}$ decrease with decreasing
collision energy, whereas the proton yield is the highest for the lowest
energy of 7.7 GeV, which indicates the largest baryon stopping at mid-rapidity
at this energy.

###  3.2 Particle ratios

Figure 3: Variation of $\pi^{-}/\pi^{+}$, $K^{-}/K^{+}$, and $\bar{p}/p$
ratios as a function of $\langle N_{\text{part}}\rangle$ at mid-rapidity
($|y|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV.

Particle ratios of $\pi^{\pm}$, $K^{\pm}$, and $p$($\bar{p}$) in Au+Au
collisions at $\sqrt{s_{NN}}$ = 54.4 GeV are shown in Fig. 3. The
$\pi^{-}/\pi^{+}$ ratio is close to unity. The $K^{-}/K^{+}$ ratio shows a
mild centrality dependence. The $\bar{p}/p$ ratio decreases from peripheral to
central collisions. Figure 4 shows the centrality dependence of mixed ratios
($K^{-}/\pi^{-}$, $K^{+}/\pi^{+}$, $\bar{p}/\pi^{-}$, and $p/\pi^{+}$). With
increasing energy $K^{-}/\pi^{-}$ shows an increasing behavior. The
$K^{+}/\pi^{+}$ ratio has the maximum value at 7.7 GeV due to the associate
production of $K^{+}$ at low energy. Also $K^{+}/\pi^{+}$ increases from
peripheral to central collisions. The $\bar{p}/\pi^{-}$ ratio shows an
increasing trend with increasing collision energy and shows a mild centrality
dependence. The $p/\pi^{+}$ ratio decreases with increasing energy due to
reduced baryon stopping as we go to higher center-of-mass energies.

Figure 4: $K^{-}/\pi^{-}$, $K^{+}/\pi^{+}$, $\bar{p}/\pi^{-}$, Â and
$p/\pi^{+}$ ratios as a function of $\langle N_{\text{part}}\rangle$ at mid-
rapidity ($|y|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV. Figure
5: $\pi^{-}/\pi^{+}$, $K^{-}/K^{+}$, and $\bar{p}/p$ ratios at mid-rapidity
($|y|<0.1$) in 0â5% Au+Au collisions at $\sqrt{s_{NN}}$ from 7.7-200 GeV.

Figure 5 shows the collision energy dependence of the particle ratios
$\pi^{-}/\pi^{+}$, $K^{-}/K^{+}$, and $\bar{p}/p$ in most central collisions
at different energies. The latest result from 54.4 GeV follows the trend shown
from previous measurements of AGS, SPS, RHIC, and LHC RefJ  RefD . The
displayed uncertainties are statistical and systematic uncertainties added in
quadrature for each ratio plots (Fig. 3, Fig. 4, and Fig. 5).

###  3.3 Kinetic freeze-out parameters

The left panel of Fig. 6 shows the simultaneous fit to the $p_{T}$ spectra of
$\pi$, K, p and its anti-particle in 0-5% central collisions in
$\sqrt{s_{NN}}$ = 54.4 GeV collisions using the blast-wave model blastwave
blastwave2 . The right panel of Fig. 6 shows the variation of kinetic freeze-
out temperature ($T_{kin}$) with average transverse radial flow velocity
($\langle\beta\rangle$) for the different center-of-mass energies and
centralities. $\langle\beta\rangle$ decreases as we go from most central to
peripheral collisions, whereas $T_{kin}$ increases from central to peripheral
collisions due to the short-lived fireball formed in peripheral collisions.

Figure 6: Left panel: Simultaneous Blast-Wave model fits to the
$p_{T}$-spectra of $\pi^{\^{A}}$, $K^{\^{A}}$, $p$($\bar{p}$) in 0â5% central
Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV. Right panel: Variation of
$T_{kin}$ with $\langle\beta\rangle$ for different energies and collision
centralities.

##  4 Conclusions

We presented transverse momentum spectra for $\pi^{\pm}$, $K^{\pm}$, and
$p$($\bar{p}$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV. Particle
ratios from Au+Au collisions at $\sqrt{s_{NN}}$ = 54.4 GeV follow the trends
from measurements at lower and higher energies. The yields of $\pi^{\pm}$,
$K^{\pm}$ and $\bar{p}$ decrease with decreasing collision energy, whereas the
proton yield is the highest at 7.7 GeV. Also the $p/\pi^{+}$ ratio is the
largest at $\sqrt{s_{NN}}$ = 7.7 GeV and decreases with increasing energy due
to the reduced baryon stopping. The kinetic freeze-out temperature and
$\langle\beta\rangle$ show an anti-correlation. $T_{kin}$ decreases from
peripheral to central collisions indicating a short-lived fireball in
peripheral collisions and $\langle\beta\rangle$ increases from peripheral to
central collisions indicating a larger radial flow for central collisions.

## References

  * (1) K. Rajagopal and F. Wilczek, arXiv hep-ph/0011333 (2000).
  * (2) K. Ackermann et al. (STAR Collaboration), Nucl. Instrum. Meth. A 499, 624 (2003).
  * (3) H. Bichsel, Nucl. Instrum. Meth. A 562, 154 (2006).
  * (4) B. I. Abelev et al. (STAR Collaboration), Phys. Rev. C 79, 34909 (2009).
  * (5) B. I. Abelev et al. (STAR Collaboration), Phys. Rev. C 96, 044904 (2017).
  * (6) E. Schnedermann, J. Sollfrank, and U. Heinz, Phys. Rev. C 48, 2462 (1993).
  * (7) D. Teaney, J. Lauret, and E.V. Shuryak, arXiv:nucl- th/0110037.