# Spectral Switch Anomalies in Sagnac Interferometer with respect to Galilean
Frame

Shouvik Sadhukhan  Email<EMAIL_ADDRESS>Saikat Sadhukhan
Email<EMAIL_ADDRESS>Maruthi M Brundavanam  Email:
<EMAIL_ADDRESS>C S Narayanamurthy  Email:
<EMAIL_ADDRESS>
(Dated : )

###### Abstract

Sagnac interferometer experiments are used widely in many measurements. When
we use a white light source in this interferometer set-up we found the
rotational and radial changes resulting in a Doppler shift in white light
spectrum in terms of spectral switch amplitude shift. Detailed theoretical
analysis are shown to support our claims.

Keywords: Spectral anomalies, Temporal Coherence, Spectral switch, Sagnac
Interferometer, Gaussian polychromatic Beam, Galilean Frame

##  1 Introduction

Spectral switch is a special type of spectral anomalies that we get in
interferometric experiment with polychromatic source. It is a specific
characteristic of the spectral shift due to changing the optical path
difference. At a certain optical path difference between the reflected and
transmitted light in interferometer the spectrum peak starts to shift blue
side from red side, that means the red shifting starts blue shifting. This
point of change in spectral shift is called the spectral switch. In this
switch position we get an uncertainty to define the peak wavelength of the
spectrum as we get two peaks with equal intensity but for different wavelength
(for double peak around switch phenomena). The number of peak around switch is
dependent upon the path difference whether it is comparable to coherence
length of the given spectrum or not. If the path difference exceeds too much
in comparison to the coherence length we get more than two number of spectral
peak around the switch and we need to collect Data for spectral shifting by
considering the shift of the highest two peaks of the spectrum that are
situating nearest to the switch.[1, 2, 3, 4, 5, 6, 7, 8]

A number of researches has been done on such spectral anomalies from last few
years using different types of interferometric set-ups. We have discussed here
only the most simplified interferometer where the path difference has been
fixed between the two-perpendicular arm and the source light has been splitted
using cubic beam splitter.[1, 2, 3, 4, 5, 6]

The spectral switch and it’s shifting analysis has already done through
theoretical and experimental point of view for dispersion compensated
Michelson interferometer but almost nothing has been done for the same with
dispersion. In this research we have discussed the characteristics of the
spectral switch with dispersion and done the graphical analysis for the
same.[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]

Sagnac Interferometer is a square structured interferometric set up where
three reflecting mirror is used (figure 1). The position of source and
detector remains perpendicular to each other. The whole system base can be
provide gyroscopic motion. The rotation is non relativistic.

Here we shall provide an analysis of spectral switch with sagnac
interferometry set up including Non-relativistic angular velocity only. We
have tried to provide some calibration of spectral switch amplitude with
respect to the angular speed.

The paper has been proceeded accordingly, Section 2 we have given the
mathematical overviews of spectrum interferometry including relativistic and
non relativistic Sagnac interferometer. Section 3 contained with the phase
retrieve method that will be helpful to get the phases of our thought
experiment. In section 4 we have provided the details of our thought
experiment. The graphical results analysis have been given in section 5. paper
6 and 7 contains the principle result discussion and concluding remarks.

##  2 Methodology of this polychromatic spectrum interferometry

In this section we are providing the mathematical basis of our work that can
produce the results discussed in this paper. Primarily in this work we have
discussed the system with Gaussian optical beam source. In general we have
considered the Gaussian beam with central peak intensity $H_{0}$ and the
spectral domain intensity has been used as equation 1. (Spectral domain
intensity should be represented )

$I_{0}(\lambda)=H_{0}\exp{(-\frac{1}{2}(\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{2})}g(\lambda)$
(1)

The term $g(\lambda)$ brings the asymmetry in the wave form. we have taken
that function as in equation 2.

$\begin{split}g(\lambda)=1+\frac{A}{6}((\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{2}-3(\frac{\lambda-\lambda_{0}}{\Delta\lambda}))\\\
-\frac{C}{24}((\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{4}-6(\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{2}+3)\end{split}$
(2)

The constant $A$ is the asymmetry factor and $C$ is the excess. The wave form
should follow the following condition.

$g(\lambda)\rightarrow\begin{cases}=1&\text{for symmetric wave form
spectrum}(A=B=0)\\\ \neq 1&\text{for asymmetric wave form spectrum}(A\neq
B\neq 0)\end{cases}$

For our present work we have just used the symmetric and non-excess singlet
Gaussian Beam in spectral domain and hence for our work $A=B=0$.

Suppose the input spectral domain field is $\varepsilon_{0}(\lambda)$.
Therefore, the input intensity given in equation 1 can be rewritten as
follows.

$I_{0}(\lambda)=\varepsilon^{*}_{0}(\lambda)\varepsilon_{0}(\lambda)$ (3)

We have used the frequency domain of the spectrum in this present work. The
amplitude on the two arms of the interferometer can be taken as $a(\nu)$ and
$b(\nu)$ and both of them are dependent on the transmittance and reflectance
of the Beam splitter. We have considered the complex degree of coherence for
this system is 1. therefore, the wave field for the two arms of the
Interferometer can be taken as equation 3 and 4. ($a(\nu)=rt\exp{(ikL_{1})}$
and $b(\nu)=tr\exp{(ikL_{2})}$)

$\varepsilon_{1}(\lambda)=a(\lambda)\varepsilon_{0}(\lambda)$ (4)

And,

$\varepsilon_{2}(\lambda)=b(\lambda)\varepsilon_{0}(\lambda)$ (5)

The Field after interference will be as in equation 5.

$\varepsilon(\lambda)=\varepsilon_{1}(\lambda)+\varepsilon_{2}(\lambda)$ (6)

The intensity of the output can be found with
$I(\lambda)=\varepsilon^{*}(\lambda)\varepsilon(\lambda)$. Finally the
spectral domain intensity output with arbitrary phase $\theta$, can be written
as follows.[1, 2, 3, 23]

$I(\lambda)=H_{0}\exp{(-\frac{1}{2}(\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{2})}(1+\cos{(\theta)})$
(7)

Therefore, all those equation will be used to determine the interfered
intensity spectrum. This kind of Interferometer has same arm lengths for both
directions of the interfering lights. The phase difference comes only with the
rotation of the set up bench. Therefore in every cases we have considered
$L_{1}=L_{2}$.

##  3 Sagnac Interferometer and its phases due to rotation

Here in present calculation we shall only provide the results for Gaussian
beam. We can not introduce the geometrical path difference in Sagnac
Interferometer due to its structure. The rotation is the only process that can
provide optical path difference and thus we can get spectral shift due to
Gyroscopic motion of the interferometric set up. The mother equation for the
whole work is the equation 7.

###  3.1 Intensity Spectrum in Galilean Frame

Here also if we consider that the angular speed is under Non-relativistic
limit, we can consider $\frac{\omega R}{c}\rightarrow 0$. Thus we can proceed
the calculation as follows.

The non-relativistic phase shift can be written as follows.

$\theta=\frac{8\pi^{2}}{c}\frac{R^{2}\omega}{\lambda}$ (8)

Therefore,the intensity can be written as follows.

$I(\lambda)=H_{0}\exp{(-\frac{1}{2}(\frac{\lambda-\lambda_{0}}{\Delta\lambda})^{2})}(1+\cos{(\frac{8\pi^{2}}{c}\frac{R^{2}\omega}{\lambda})})$
(9)

This intensity function can provide the spectral switch and its shift with
different values of angular rotation for non-relativistic motion.

###  3.2 Overview of Phase retrieve method

In our present calculation we have used the predetermined phases induced in
the interferometer arms due to the dispersive medium. But in our thought
experiment we have to introduce the phase retrieve method to get the phases
with interpolation technique. Some necessary formulae have been given in the
following that will be useful in the phase retrieval technique.[4, 5, 6]

  * i

$I_{interference}(\lambda)=I(\lambda)(b(\lambda)+a(\lambda)+2\sqrt{b(\lambda)a(\lambda)}V(\lambda)\cos{(\theta)})$

  * ii

$VS(\lambda)=V(\lambda)\cos{(\theta)}$

  * iii

Interpolation $\rightarrow$
$\cos{(\theta)}=\frac{2VS(\lambda)-VS_{up}(\lambda)-VS_{down}(\lambda)}{VS_{up}(\lambda)-VS_{down}(\lambda)}$

The above process is to use to retrieve the phases to discuss the spectral
shift with our results.

Here this method has been used to find the optical phases due to the rotation
of the set up bench. For each speed of rotation we get the data for
intensities and fro those data we can use the above three points to derive the
phases.

##  4 The brief of our proposed thought experiment for both relativistic and
non relativistic motion

We are hereby providing the thought experimental set up and procedure to get
the spectral switch and its shift w.r.t. the Sagnac Interferometer. We
basically trying to interpret the idea of sagnac effect in the optical
sensitivity technique with broad band spectral switch. The figure of the
experiment is given in following figure 1.[23]

Figure 1: Sagnac Interferometer setup with the Gyroscopic table

The setup given in Fig. 1 consist of a dispersion-compensated Sagnac
Interferometer illuminated with a white-light source with central wave length
612 nm (fiber-coupled, collimated 50 W quartz tungsten-halogen lamp). A fiber-
coupled spectrometer (SD2000, Ocean Optics) is used at the output of the
interferometer to measure the spectral modifications due to varying temporal
correlation. A computer is used to control the gyroscopic table movement. The
set-up properties are suggested for only Non-Relativistic rotation. [1, 2, 3]

Here we shall provide different angular motion in the table to calibrate the
spectral switch with motion.

In the experiments of relativistic sagnac effect we have used the broadband
polychromatic source of radio frequency ranges. The central wavelength of that
wave has been considered 6.12 m and bandwidth 2.38 m. The angular motions have
been taken of the range $10^{7}$ rps and the radius is in meter range.

##  5 Pictorial representations of the theoretical results under two frames

In the beginning of this work we have to fix the radius and the angular speed
of the gyroscopic table. After that we can make some changes into the angular
speed as well as the radius to find spectral shift in the spectral switch
representation of our white light interferometry. Here, we first show the
acceptable angular speed-radius doublets for getting first spectral switch in
both frames. For getting spectral switch from Galilean frame experimental set-
up, we must have to follow the following equalities.

$\frac{8\pi^{2}}{c}\frac{R^{2}\omega}{\lambda_{0}}=\pi$ (10)

Hence, using this relation we can plot the necessary radius-angular speed
doublets to get first spectral switch. Here, we considered a polychromatic
input with peak wavelengths for non-relativistic as 612 nm. The Bandwidths of
it has been taken as 238 nm .

Figure 2: Accepted Values for $\omega$ and $R$ for first order switch in Non-
Relativistic frame

Now, we are considering a radius of 0.3048 m of the gyroscopic stage with
angular speeds 58.52 rps (Green), 58.82 rps (Black) and 59.12 rps (Red). These
three angular velocities are providing different spectral switch. The radius-
angular speed doublet $=(0.3048,58.9)$ belongs to the trajectory with spectral
switch position.

Figure 3: $I(\lambda)$ and Shift with $R=0.3048m$ for different $\omega$ i.e.
$\omega=58.52rps$ (Green), $\omega=58.82rps$ (Black), $\omega=59.12rps$ (Red)
(Non-Relativistic Case). Here Figure a) is the total spectrum and b), c) and
d) are the zoomed parts of the spectrum.

we are also considering an angular speed of 58.82 rps of the gyroscopic stage
with radius values of 0.3028 m (Green), 0.3048 m (Black) and 0.3068 (Red).
These three radius valued systems are providing different spectral switch.
Here also the radius-angular speed doublet $=(0.3048,58.9)$ belongs to the
trajectory with spectral switch position.

Figure 4: $I(\lambda)$ and Shift with $\omega=58.82rps$ for different $R$ i.e.
$R=0.3028m$ (Green), $R=0.3048m$ (Black), $R=0.3068m$ (Red) (Non-Relativistic
Case). Here Figure a) is the total spectrum and b), c) and d) are the zoomed
parts of the spectrum.

Now we are showing the spectral shift with the graphs of normalized spectral
shift i.e. the NSS shift. We are showing two results of NSS in each following
figures. In first figure we have used the variation of $\omega$ from 0 rps to
300 rps with fixed radii of 0.83 m and 0.3048 m. Again in second figure we
have used variation of $R$ from 0.3 m to 2.5 m with fixed angular speeds
$\omega$ at 7.94 rps and 58.9 rps. The equation for getting NSS used in this
calculation is as follows. Here, we are also providing the peak values of the
spectral Intensity with path delay due to different $\omega$ and $R$.

$NSS=\frac{\lambda_{0}-\lambda}{\lambda_{0}}$ (11)

Now the figures are as follows. The first figure discussed above is numbered
as figure 7 and the second one as figure 8.

Figure 5: NSS vs $\omega$ with $\omega\in[0,300]rps$ and fixed radii $R=0.83m$
and $R=0.3048m$ (Non-Relativistic Case)

Figure 6: NSS vs $R$ with $R\in[0.3,2.5]m$ and fixed angular speed
$\omega=7.94rps$ and $\omega=58.9rps$ (Non-Relativistic Case)

Figure 7: Peak Spectral Intensity vs $\omega$ with $\omega\in[0,300]rps$ and
fixed radii $R=0.83m$ and $R=0.3048m$ (Non-Relativistic Case)

Figure 8: Peak Spectral Intensity vs $R$ with $R\in[0.3,2.5]m$ and fixed
angular speed $\omega=7.94rps$ and $\omega=58.9rps$ (Non-Relativistic Case)

Now we are showing the results discussed above in Lorentz frame with
relativistic angular speed.

###  5.1 Variation of Spectral switch amplitude (SSA) and Calibration

The spectral switch amplitude is determined with the difference between the
maximas and minimas of the NSS plots. This amplitude is the technique to get
differentiation of the experimental conditions w.r.t. the spectral switch
shift. The amplitude mainly assign the interferometry with its initial
conditions that separates one setup form another. Now we provide the Spectral
switch amplitude values from the NSS graphs given above. The SSA is calculated
according to the following formula.

$SSA=\frac{\lambda_{red}-\lambda_{blue}}{\lambda_{0}}$ (12)

The $\lambda_{red}$ and $\lambda_{blue}$ are the wavelengths of the red
shifted and blue shifted peaks across the spectral switch. The SSA figures can
be given as follows.

Figure 9: SSA vs $\Delta\omega$ with $\Delta\omega\in[0,20]rps$ and fixed
radii $R=0.83m$ and $R=0.3048m$ (Non-Relativistic Case)

Figure 10: NSS vs $\Delta R$ with $\Delta R\in[0.03,0.3]m$ and fixed angular
speed $\omega=7.94rps$ and $\omega=58.9rps$ (Non-Relativistic Case)

The above figures can be a calibration for the spectral switch amplitude
change with the change of angular speed and radius. Now we are showing the
peak spectral intensity figures by following the above said informations about
the angular speed and radius. We have provided the amplitude w.r.t. angular
velocity.

Figure 11: Spectral switch amplitude vs serial number of switch

This provides the conclusion that the change in frame can not change the
initial conditions of experimental setup and thus we can not get any change in
the properties of spectral switch. Although for large angular speed we may get
some shift in the switch position but the property will remain same. We are
providing the switch amplitude plot w.r.t. the serial number of switch to
bring the results of the two experiment setup together. The angular speeds can
not be included due to the magnitude difference.

##  6 Concluding Remarks

In this work we have tried to introduce the idea of spectral switch and its
shifting in Sagnac interferometric setup. The principle speciality of this
specific work is that we have established the spectral switch interferometric
optical sensing technique in presence of gyroscopic motion. The gyroscopic
motion is very much useful in observational astronomy and our work may
interpret the spectral switch optical sensing in it.

We have proceeded the whole work in two different thought experimental setup
where one works in Euclidean frame and another on in Lorentz frame. Normal
gaussian spectral domain white light broadband source was useful to discuss
the spectral switch in Sagnac interferometer in euclidean frame. The Lorentz
frame sagnac effect needed broadband gaussian spectral domain radio wave with
wavelength in meter scale.

We have also shown the Normalized spectral shift for both frame and provides
spectral switch amplitude w.r.t. the switch serial number. We have found that
the change of frame of experiment can not change the properties of spectral
switch. It can only provides some shift in the switch position due to having
large angular speed.

## Limitations of this work

We have established and proposed two experimental technique to reproduce the
spectral anomalies under sagnac effect. The Sagnac effect on frame
transformation can only be observed with the spectral switch shift.

## Future scope of this work

We can introduce the dispersing medium and modify the proposed technique to
reduce the noise effect due to external turbulence. This technique can be used
extensively to search gravitational wave strain and experimental analysis of
both perturbative and non-perturbative general relativity. All of those parts
are beyond the scope of this work.

## Acknowledgement

The authors are thankful to Indian Institute of Space Science and Technology,
Department of Physics and Adaptive optics and Indian Institute of Technology
Kharagpur, Department of physics for their help on this work. The authors also
thanks to DST for funding this project.

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# News Recommendation with
Category Description by a Large Language Model

Yuki Yada  Waseda UniversityTokyoJapan<EMAIL_ADDRESS>and
Hayato Yamana  Waseda UniversityTokyoJapan<EMAIL_ADDRESS>
(2018; 20 February 2007; 12 March 2009; 5 June 2009)

###### Abstract.

Personalized news recommendations are essential for online news platforms to
assist users in discovering news articles that match their interests from a
vast amount of online content. Appropriately encoded content features, such as
text, categories, and images, are essential for recommendations. Among these
features, news categories, such as tv-golden-globe, finance-real-estate, and
news-politics, play an important role in understanding news content, inspiring
us to enhance the categories’ descriptions. In this paper, we propose a novel
method that automatically generates informative category descriptions using a
large language model (LLM) without manual effort or domain-specific knowledge
and incorporates them into recommendation models as additional information. In
our comprehensive experimental evaluations using the MIND dataset, our method
successfully achieved 5.8% improvement at most in AUC compared with baseline
approaches without the LLM’s generated category descriptions for the state-of-
the-art content-based recommendation models including NAML, NRMS, and NPA.
These results validate the effectiveness of our approach. The code is
available at https://github.com/yamanalab/gpt-augmented-news-recommendation.

News Recommendation, Large Language Model, Deep Neural Network

††copyright: acmlicensed††journalyear: 2018††doi: XXXXXXX.XXXXXXX††conference:
Make sure to enter the correct conference title from your rights confirmation
emai; June 03–05, 2018; Woodstock, NY††isbn: 978-1-4503-XXXX-X/18/06

##  1\. Introduction

In recent years, online news platforms have gained widespread popularity,
making it commonplace for users to consume news articles on their mobile
devices. These platforms deliver a large amount of news content to users
daily, leading to an information overload problem, making it challenging to
discover articles that align with user’s interests. Therefore, personalized
news recommendations have become essential for online news platforms.

Figure 1. Neural News Recommendation Model

Many proposed news recommendation models use deep neural networks, which
achieve high performance (lstur, 2, 10, 19, 20, 21, 22). As shown in Figure 1,
most neural news recommendation models adopt a common approach that consists
of three core modules:

  1. (1)

News encoder: it generates a news vector that captures the semantic
information from the news content.

  2. (2)

User encoder: it generates a user vector that captures the user preferences
based on browsing history.

  3. (3)

Similarity calculator: it computes the similarity score between the news
vector and the user vector, estimating that news items with higher similarity
scores are more likely to match the user’s interests.

Previous studies have focused on investigating which neural network structures
to apply in the user and news encoder modules, resulting in various proposed
architectures for news recommendation models. Recent methods incorporate pre-
trained language models (PLMs) into the news encoder to learn news
representations. These PLM-based approaches have achieved high performance
(once, 7, 10, 15, 22, 23).

Simultaneously, a crucial source for understanding news content is the news
category. For example, the MIND (mind, 25) dataset, a well-known dataset in
the news recommendation field, contains news categories such as tv-golden-
globes. The naïve way to use categories in recommendation models is to adopt
predefined templates (e.g., The news category is {category}) followed by
combining them with original news recommendation models. However, these
templates are too generic to be applied to all news categories, resulting in
insufficient information. Constructing detailed descriptions for each news
category and using them as input can be beneficial for enabling recommendation
models to recognize news content accurately.

However, manually constructing detailed descriptions for each news category is
costly. To address this issue, we propose automatically generating descriptive
text for news categories using large language models (LLMs). Since LLMs are
pre-trained on vast amounts of text data and have extensive knowledge across
diverse topics, the LLM-generated detailed descriptions are expected to
enhance the recommendation performance. The contributions of this paper are as
follows:

  1. (1)

We first propose the adoptation of LLM-generated news category descriptions to
enhance news recommendations.

  2. (2)

Comprehensive experimental evaluations on the MIND dataset confirmed that our
proposed method consistently outperforms baseline approaches across multiple
recommendation models, achieving up to 5.8% improvement in AUC compared to
methods without category descriptions.

The rest of this paper is organized as follows. In Section 2, we reviews
state-of-the-art news recommendations and use of LLM-generated text. We
propose a new recommendation method enhanced by an LLM in Section 3, followed
by evaluations in Section 4. In Section 5, we discuss the limitations of the
proposed method. Finally, In Section 6, we conclude this paper.

##  2\. Related Work

In this section, we review related work on news recommendations and the use of
LLM-generated text.

###  2.1. News Recommendations

News recommendations have been extensively studied through various models
(nrecsurvey2023, 10, 22). Neural network-based models have achieved state-of-
the-art performance by encoding news content and user preferences to capture
the complex interactions between users and news items (lstur, 2, 17, 19, 20,
21). For instance, NRMS (nrms, 21) employs multi-head attention to acquire
news and user vectors, while LSTUR (lstur, 2) adopts GRU for to obtain user
vectors. Other models, such as MCCM (mccm, 17), NAML (naml, 19), and NPA (npa,
20), leverage CNN and attention mechanisms to generate user and news vectors.

Particularly, the models adopting PLMs, such as BERT (bert, 5) and RoBERTa
(roberta, 8), to obtain news vectors have achieved notably high performance
(once, 7, 10, 15, 22, 23, 24). For instance, Wu et al. (plmnr, 23) proposed a
framework incorporating PLMs into news recommendations, demonstrating 2.63%
improvement in the pageview rate through online experiments. In the ONCE
(once, 7), proposed by Liu et al., showed that using large-scale language
models such as LLaMa (llama, 16) can improve news recommendation performance.

Several neural recommendation models use different architectures from the
model shown in Figure 1. For instance, Zhang et al. introduced UNBERT (unbert,
27), which feeds a candidate news article and a list of previously viewed news
articles into a single language model to predict click-through rates. Another
notable work by Zhang et al. (prompt4nr, 28) is Prompt4NR, a news
recommendation approach using prompt learning with PLMs.

In summary, various methods with neural network-based models have been
proposed for news recommendation. The use of PLMs shows particularly high
performance; however, PLMs lack sufficient knowledge to interpret category
names. Thus, a space exists to enhance the performance of news recommendations
by adding detailed category information, which inspires us to adopt LLM-
generated category descriptions as additional features.

###  2.2. Use of LLM-Generated Texts

The use of text generated by LLMs, which have acquired extensive knowledge on
a wide range of topics through pre-training, has improved the performance in
various natural language processing tasks, such as text classification and
question answering (qagen, 6, 13, 26).

Yoo et al. (gpt3mix, 26) proposed GPT3Mix, which applies GPT-3-based (gpt3, 3)
data augmentation to text classification tasks by generating additional
training examples. For question answering tasks, Liu et al. (qagen, 6) used
knowledge expansion using GPT-3 to augment the context and improve the
performance of the question answering model. Pratt et al. (cupl, 13)
introduced CuPL, a method that leverages image captions generated by LLMs for
zero-shot image classification using CLIP (clip, 1). They automatically
generated image captions using LLMs and used them as text inputs for CLIP.

These studies demonstrated the effectiveness of utilizing texts generated by
LLMs in various tasks. Inspired by this, we aims to improve news
recommendation performance by generating news category descriptions using
LLMs.

Figure 2. Overview of our proposed method

##  3\. Proposed Method

Figure 2 shows our proposed novel news recommendation method enhanced by LLM-
generated category descriptions, consisting of two steps: 1) automatic
generation of news category descriptions, and 2) integration of the generated
category descriptions with the recommendation model as additional input
features.

###  3.1. Generation of Category Descriptions

In this step, we generate the descriptions for news categories using an LLM
without any manual effort. We employ GPT-4 (gpt4, 11) as the LLM for
generating category descriptions, as it has demonstrated high performance
across various domains and tasks (sparkGpt4, 4).

Figure 3 shows the prompts for the LLM to generate descriptions for news
categories. Although the prompts need to be prepared manually, they do not
require any manual effort once they have been prepared.

Figure 4 shows a specific example of the generated news category descriptions
for the tv-golden-globes category, one of the categories that appeared in the
MIND dataset (mind, 25). The average word count of the generated category
descriptions is 57.7 for all 270 news categories within the MIND dataset used
in our experiment.

[l]System Message You are a wonderful news writer. You assist readers by
providing more detailed and useful information about the articles. User inputs
the specific category for a news article using the format ’The news category
is category’. Please provide a detailed explanation, in about 50 words, **in
English**, on the category of the articles entered (such as politics,
economics, sports, etc.). Please avoid using symbols such as double quotes (”)
and single quotes (’), asterisks (*), and similar for emphasis as much as
possible. [l]User Message The news category is tv-golden-globes

Figure 3. Prompt to generate a category description for tv-golden-glove as an
example.

The TV-Golden Globes category focuses on news related to the Golden Globe
Awards specifically within the television industry. This includes nominations,
winners, notable moments from the ceremony, reactions, and any controversies
or highlights surrounding the event, which honors excellence in TV.

Figure 4. Category description for tv-golden-globes via GPT-4

###  3.2. Integration of Category Descriptions into News Recommendation Models

After generating the category descriptions, we train the news recommendation
model by leveraging the generated descriptions. Let $D_{title}$ denote the
news title text and $D_{desc}$ represent the generated category description.
During the inference phase of the recommendation model, we concatenate
$D_{title}$ and $D_{desc}$ using the special SEP token from BERT (bert, 5),
and feed the resulting text into the news encoder.

##  4\. Experiments and Results

In this section, we describe our experiments. First, we present the dataset,
evaluation metrics, baselines, and hyperparameters used in our experiments.
Second, we present the results and then discuss the effectiveness of the
proposed method.

###  4.1. Experimental Setting

We used the MIND (mind, 25) dataset, a widely used dataset for the news
recommendation field. The MIND dataset, whose statistics are shown in Table 1,
was constructed from the news click records of the Microsoft
News111https://news.microsoft.com service between October 12, 2019 and
November 22, 2019.

Table 1. MIND dataset (mind, 25) #User | #News | #Impression | #Click
---|---|---|---
94,057 | 65,238 | 230,117 | 347,727
Table 2. Comparison of different methods on the MIND dataset Recommendation Model | PLM | Method | AUC | MRR | nDCG@5 | nDCG@10
---|---|---|---|---|---|---
NAML (naml, 19) | DistilBERT | title only | 0.675 | 0.292 | 0.317 | 0.384
title + template-based | 0.690 | 0.295 | 0.327 | 0.393
title + generate-description (ours) | 0.713 | 0.326 | 0.363 | 0.425
BERT | title only | 0.700 | 0.318 | 0.350 | 0.414
title + template-based | 0.696 | 0.308 | 0.340 | 0.405
title + generate-description (ours) | 0.707 | 0.322 | 0.357 | 0.420
NRMS (nrms, 21) | DistilBERT | title only | 0.674 | 0.297 | 0.322 | 0.387
title + template-based | 0.675 | 0.311 | 0.341 | 0.400
title + generate-description (ours) | 0.707 | 0.324 | 0.359 | 0.422
BERT | title only | 0.689 | 0.306 | 0.336 | 0.400
title + template-based | 0.667 | 0.301 | 0.329 | 0.389
title + generate-description (ours) | 0.706 | 0.320 | 0.355 | 0.418
NPA (npa, 20) | DistilBERT | title only | 0.700 | 0.311 | 0.344 | 0.408
title + template-based | 0.698 | 0.309 | 0.342 | 0.407
title + generate-description (ours) | 0.707 | 0.319 | 0.354 | 0.417
BERT | title only | 0.689 | 0.301 | 0.332 | 0.398
title + template-based | 0.694 | 0.314 | 0.345 | 0.410
title + generate-description (ours) | 0.710 | 0.324 | 0.360 | 0.422

We compared our proposed method with the following two baselines:

  1. (1)

title only: Input only the title text into the news encoder without any
category information.

  2. (2)

title + template-based: Input the concatenated text of the title and the
template-based sentence that follows the template: The news category is
{category} (e.g., The news category is tv-golden-globes), using the SEP token.

To evaluate the effectiveness of our proposed method, we adopted three state-
of-the-art content-based recommendation models: NAML (naml, 19), NRMS (nrms,
21), and NPA (npa, 20). We used the pre-trained models DistilBERT-base
(distilbert-base-uncased) (distilbert, 14) and BERT-base (bert-base-uncased)
(bert, 5) for the news encoder component. AdamW (adamw, 9) was used as the
optimization function with a learning rate of 1e-4, a batch size of 128, and 3
epochs. Following the previous studies (mccm, 17, 20, 23, 28), the maximum
number of recently viewed articles, which was used to capture user preference
information, was set to 50. We set the number of negative samples in the
training phase to 4. All experiments are conducted on a Tesla V100 GPU. For
implementation, we used PyTorch v2.1.0 (pytorch, 12) and Transformers v4.35.0
(transformers, 18) libraries. As performance metrics, we used the average AUC,
MRR, nDCG@5, and nDCG@10 for all impressions.

###  4.2. Results

Table 2 summarizes the comparison of our proposed recommendation method with
the baselines. The proposed method, title+generated-description, demonstrates
the highest performance compared with the baselines across all recommendation
models and achieved up to 5.6% and 5.8% improvements in AUC compared with the
title only and title+template-based baselines, respectively.

Furthermore, title + template-based shows insignificant improvement in
performance compared with the title only in most cases. This result suggests
that simply fitting the category name into a predefined template is
ineffective for representing the category information. The results also
indicate that for relatively small-scale language models like BERT, using only
the category names as input does not provide sufficient information for the
recommendation models to properly interpret the category information.

##  5\. Limitations

To explore the limitations, we performed a manual inspection of the category
descriptions. Although GPT-4 generally produces high-quality descriptions, it
occasionally fails to generate accurate descriptions.

Figure 5 shows an example in which the generated description for the tunedin
category focuses on entertainment, music, and television. However, the actual
article titles in Table 3 reflect a wider range of topics, including
technology and trends. A more accurate description would be that the tunedin
category casually provides news on various topics such as entertainment,
technology, and business, keeping readers updated on the latest trends. This
discrepancy highlights the model’s inability to accurately capture the
category’s broad scope.

This example, along with other similar instances, suggests that the model may
struggle to generate accurate category descriptions when the input lacks
sufficient background knowledge or context.

Table 3. News titles for the tunedin category News title
---
Coca-Cola released two limited-edition holiday flavored sodas
Google Maps and Waze may share certain features
Daylight saving time ends: Get ready to ’fall back’

The category ”tunedin” typically refers to news related to entertainment,
media, and television. It often includes updates on TV shows, interviews with
celebrities, insights into the music industry, and information on streaming
services. This category keeps readers engaged with the latest trends and
happenings in the world of entertainment.

Figure 5. Category description for the tunedin category

##  6\. Conclusion

In this study, we proposed a method to automatically generate news category
descriptions using LLMs and incorporate them into news recommendation models.
The experiments on the MIND dataset demonstrated that our method outperformed
the baselines across all metrics for multiple models. Our main contribution is
a novel approach to enhance news recommendation models’ understanding of
category information using LLMs. Our future work will include enhancing the
recommendation performance by improving the generated descriptions.

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Amit Sethi, Department of Electrical Engineering, Indian Institute of
Technology Bombay, Mumbai, 400076, Maharashtra, India.

# Classification of Various Types of Damages in Honeycomb Composite Sandwich
Structures using Guided Wave Structural Health Monitoring

Shruti Sawant11affiliationmark:  Jeslin Thalapil11affiliationmark:  Siddharth
Tallur11affiliationmark:  Sauvik Banerjee22affiliationmark:  and Amit
Sethi11affiliationmark:  11affiliationmark:  Department of Electrical
Engineering,Indian Institute of Technology
Bombay,Mumbai,400076,Maharashtra,India
22affiliationmark:  Department of Civil Engineering,Indian Institute of
Technology Bombay,Mumbai,400076,Maharashtra,India<EMAIL_ADDRESS>
###### Abstract

Classification of damages in honeycomb composite sandwich structure (HCSS) is
important to decide remedial actions. However, previous studies have only
detected damages using deviations of monitoring signal from healthy (baseline)
using a guided wave (GW) based structural health monitoring system.
Classification between various types of damages has not been reported for
challenging cases. We show that using careful feature engineering and machine
learning it is possible to classify between various types of damages such as
core crush (CC), high density core (HDC), lost film adhesive (LFA) and teflon
release film (TRF). We believe that we are the first to report numerical
models for four types of damages in HCSS, which is followed up with
experimental validation. We found that two out of four damages affect the GW
signal in a particularly similar manner. We extracted and evaluated multiple
features from time as well as frequency domains, and also experimented with
features relative to as baseline as well as those that were baseline-free.
Using Pearson’s correlation coefficient based filtering, redundant features
were eliminated. Finally, using an optimal feature set determined using
feature elimination, high accuracy was achieved with a random forest
classifier on held-out signals. For evaluating performance of the proposed
method for different damage sizes, we used simulated data obtained from
extensive parametric studies and got an accuracy of 77.89%. Interpretability
studies to determine importance of various features showed that features
computed using the baseline signal prove more effective as compared to
baseline-free features.

###### keywords:

Structural health monitoring (SHM), ultrasonic non-destructive testing (NDT),
honeycomb composite sandwich structure (HCSS), damage classification, feature
engineering

##  1 Introduction

Honeycomb composite sandwich structure (HCSS) consists of a lightweight
honeycomb core sandwiched between two composite skins. HCSS is utilized in a
variety of applications, including aerospace, because of their high strength-
to-weight ratio, high energy absorption, and outstanding thermal and acoustic
insulation. However, during manufacturing or operations HCSS can get damaged
in various ways which can jeopardize structural integrity Shipsha and Zenkert
(2005); Jollivet et al. (2013); Balasko et al. (2005); Sikdar and Banerjee
(2019). Damage classification is important because classifying the type of
damage occurring within a structure can allow the end user to assess what kind
of repairs, if any, that a component requires.

Ultrasonic guided wave-based structural health monitoring systems (GW-SHMs)
are popular for a variety of composite structures due to low cost of
instrumentation, sensitivity to small defects, and ability of guided waves
(GWs) to travel long distances on the structure without attenuation Yan et al.
(2010); Abbas and Shafiee (2018). Various types of damages affect GW signals
in multiple ways. Disbond in HCSS causes increase in amplitude of A0 mode,
while high density core (HDC) results in a decrease in amplitude Sikdar and
Banerjee (2016). However, due to a large variety of damages that may occur
throughout life-cycle of the material, different types of damages may result
in similar changes in amplitude and phase of GW signals. Perhaps due to this
challenge, damage classification has not been explored well enough.

Although damage classification in structures using GW-SHM has been attempted
before, these studies have various limitations with respect to the goals of
the current study, which is to classify damages in HCSS. For instance,
previously we reported high accuracy for damage classification for three types
of damages – rivet hole, notch, and added mass – using convolutional neural
networks (CNNs) under various temperatures but in a homogeneous aluminum panel
Sawant et al. (2022). We used simulated data for the three damages along with
experimental validation of binary classification for the notch damage.
Tibaduiza et al proposed hierarchical nonlinear principal component (PCA)
analysis approach for classifying delamination and cracking of the skin in a
carbon fibre reinforced polymer (CFRP) sandwich structure Tibaduiza et al.
(2018).

Lee et al. Lee et al. (2022) demonstrated use of unsupervised deep auto
encoder (DAE). They use two different thresholds on reconstruction error
computed at output of DAE to distinguish between matrix cracking and
delamination however there is no report of performance parameters, size or
architecture of DAE. Deep learning-based methods reported for GW-SHM of
composite structure in supervised Rautela et al. (2021) as well as
unsupervised setups Rai and Mitra (2022) using public-domain Open Guided Waves
(OGW) dataset Moll et al. (2019). However, these studies model different
locations of the added mass damage on CFRP plate as different classes for the
classifier model. Therefore, these approaches actually solve damage
localization problem for the same damage type, instead of classifying
different damage types in composite structures. In addition to trying damage
classification, we wanted to avoid using deep learning based approaches in
order to rein in the number of trainable parameters towards implementation on
edge devices such as low-cost microcontrollers, field programmable gate arrays
(FPGAs), and low-cost graphics processing units (GPUs).

GW-based damage characterization requires interpreting damage features that
quantify deviation of monitoring signal from baseline signal. Conventional
algorithms first extract the wavemode of interest from time-series data using
group velocity, which requires knowledge of material properties, such as
Young’s modulus and density. Various statistical relations, such as sum of
differences in each sample for wave mode of interest, difference in the peak
amplitude of monitoring and baseline signal Sawant Shruti and Siddharth
(2021), correlation coefficient deviation (CCD) Zhao et al. (2007), are used
as features. Identifying effective damage features is crucial to the success
of damage characterization. Selection of suitable features usually requires
knowledge of material properties and varies for different structures and types
of damages. The utility of easy-to-compute statistical metrics obtained from
time-domain signals for machine fault diagnosis was shown by Bandyopadhyay et
al. Bandyopadhyay et al. (2018). Elhariri et al. proposed hybrid filter-
wrapper with multi-objective optimization feature selection method for crack
severity recognition for machine health monitoring Elhariri et al. (2020). A
low-cost corrosion sensing system based on pulsed eddy current detection to
detect the corrosion in steel reinforcing bars optimal feature selection and
dimensionality reduction was demonstrated using principal component analysis
Tamhane et al. (2021). For GW-SHM system, feature engineering (FE) is still in
nascent stages. Recently Liu et al. reported a feature selection method based
on binary particle swarm optimization with a new fitness function proposed in
combination with least-squares support-vector machine for damage
identification in variety of challenging practical scenarios for switch rail
damage Liu et al. (2021). FE approaches for GW-SHM of composite structures,
especially for in-situ monitoring with ligher ML model suitable for edge
implementation, remains to be explored.

In this work, we present a novel damage classification method using feature
engineering for classification of four different types of damages in HCSS –
core crush (CC), Teflon release film (TRF), lack of film adhesive (LFA), and
HDC. Two out of these damages (CC and LFA) cause increase in the amplitude
over the baseline signal, whereas the other two result in the opposite effect.
Choice and selection of the features was therefore important for this work.
Firstly, we conducted numerical study for four damages using models developed
in COMSOL. Secondly, we also conducted extensive parametric studies for
different damage sizes for each damage type. It is costly and, in some cases,
infeasible to generate experimental data for various sizes of damages.
Therefore, to evaluate performance for such test cases, we carried out
numerical simulations. Next, we collected data on HCSS using a pair of
detachable contact-type Nano-30 transducers which was observed to be in
accordance with numerical data. _To the best of our knowledge, this is the
first study to report numerical and experimental study for four different
damage types in HCSS._ Following noise augmentation of these experimental and
simulated dataset, we computed ten statistical features that do not require
knowledge of material properties, such as group velocity of various wavemodes
or dispersion curve of the material, and compared baseline-free features as
well as features computed using baseline in time and frequency domains. Using
Pearson’s correlation coefficient to filter redundant features we selected the
optimal subset representing the most relevant information. Finally, we
evaluated performance of five different classifiers using the optimal feature
subset and observed that random forest classifier shows perfect accuracy using
seven features on unseen experimental data. In the case of simulated data for
different damage sizes, we achieved an accuracy of 77.89% using random forest.
Our damage classification results are more accurate than those obtained using
baseline-free features reported by Liu et al. Liu et al. (2021).

Figure 1: Illustration of the proposed method using feature engineering for
damage classification in GW-SHM systems.

##  2 Feature engineering based damage classification method

The proposed method mainly consists of four steps as illustrated in Figure 1:

  * •

Data acquisition: GW-SHM system for HCSS panel considered in this study uses a
pair of detachable Nano-30 transducers to collect data non-invasively for
three sensor paths around different types of damages on the panel.
Preprocessing is essential as the experimental data contains offset.

  * •

Feature extraction: Features play crucial role in quantifying deviation of
monitoring data from the baseline data. We computed a total of $10$ features
in time as well as frequency domain for subsequent analysis. Along with these,
we also explored baseline-free features in this study.

  * •

Feature engineering: Primary feature identification involves selecting a
subset of features to enhance the accuracy of the models and reduce
generalization error introduced due to noise by irrelevant features. We used
Pearson’s correlation coefficient based filtering in this study using to
select optimal set of features.

  * •

Damage classification: Finally, to distinguish between four types of damage in
HCSS panel, we trained classifier models. Using one-hot encoding scheme labels
were generated for five classes (four damage types and baseline signal).
Performance of five different classifier models was evaluated using the
optimal feature subset.

Table 1: Features computed from time-domain GW signals. Glossary: $\bar{f}$: mean value of samples in time-series $f$, $T$: length of time-series, $f_{b}$: baseline signal, $A$: peak-to-peak amplitude of signal $f$, $A_{b}$: peak to peak amplitude of baseline signal $f_{b}$ Feature |  Expression
---|---
Correlation coefficient deviation (CCD) |  ${1-\sqrt{\frac{\\{\int^{T}f_{b}(t)f(t)dt\\}^{2}}{\\{\int^{T}{f_{b}(t)}^{2}dt\int^{T}{f(t)}^{2}dt\\}}}}$
Mean absolute deviation (MAD) |  $\frac{1}{T}\sum_{i=1}^{i=T}|f(i)-\bar{f}|$
Normalised difference of signal energy (NSED) |  ${\frac{\int^{T}{|f(t)|^{2}}dt-\int^{T}{|f_{b}(t)|^{2}}dt}{\int^{T}{|f_{b}(t)|^{2}}dt}}$
Peak to peak amplitude deviation (PPAD) |  ${A-A_{b}}$
Root mean square (RMS) |  $\sqrt{(1/T){\int^{T}{[f(t)]^{2}}dt}}$
Root mean square deviation (RMSD) |  $\sqrt{\frac{\int^{T}{[f(t)-f_{b}(t)]^{2}}dt}{\int^{T}{[f_{b}(t)]^{2}}dt}}$
Spectral difference deviation (SDD) |  $\sqrt{\frac{\\{\int^{F}|F_{b}(f)-F(f)df|\\}^{2}}{\int^{F}{F_{b}(f)}^{2}dt\int^{F}{F(f)}^{2}dt}}$
Ratio of signal energy (SER) |  ${\frac{\int^{T}{|f(t)|^{2}}dt}{\int^{T}{|f_{b}(t)|^{2}}dt}}$
Standard deviation ($\sigma$) |  $\sqrt{\frac{\sum_{i=1}^{i=T}{\left(f(i)-\bar{f}\right)^{2}}}{T}}$
Variance (VAR) |  $\frac{\sum_{i=1}^{i=T}{\left(f(i)-\bar{f}\right)^{2}}}{T}$
Table 2: Material properties (standard notations) of CFRP lamina used in
facesheet, adhesive, and honeycomb core in HCSS

Material |  $E_{11}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $E_{22}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $E_{33}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{12}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{23}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{13}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) | $\nu_{12}$ | $\nu_{13}$ | $\nu_{23}$ |  $\rho$ ($\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{m}^{3}$)
---|---|---|---|---|---|---|---|---|---|---
CFRP lamina | $135$ | 9 | 9 | 4.5 | 3.103 | 4.5 | 0.29 | 0.29 | 0.45 | 1780
Adhesive | 4.35 | 4.35 | 4.35 | 1.599 | 1.599 | 1.599 | 0.36 | 0.36 | 0.36 | 1100
Honeycomb core | 0.028 | 0.028 | 0.40 | 0.074 | 0.103 | 0.221 | 0.318 | $3.18\text{\times}{10}^{-5}\text{\,}$ | $3.18\text{\times}{10}^{-5}\text{\,}$ | 36.8

Table 3: Material properties (standard notations) of damages (CC, HDC and TRF)
considered for 2D numerical simulation of HCSS

Material |  $E_{11}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $E_{22}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $E_{33}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{12}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{23}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) |  $G_{13}$ ($\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$) | $\nu_{12}$ | $\nu_{13}$ | $\nu_{23}$ |  $\rho$ ($\text{\,}\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{m}^{3}$)
---|---|---|---|---|---|---|---|---|---|---
Teflon release film | 0.75 | 0.75 | 0.75 | 0.275 | 0.275 | 0.275 | 0.45 | 0.45 | 0.45 | 2200
Crushed core | 0.0214 | 0.0214 | 0.136 | 0.0507 | 0.071 | 0.152 | 0.318 | $3.18\text{\times}{10}^{-5}\text{\,}$ | $3.18\text{\times}{10}^{-5}\text{\,}$ | 92
High density core | 0.238 | 0.238 | 2.0 | 0.368 | 0.515 | 1.105 | 0.318 | $3.18\text{\times}{10}^{-5}\text{\,}$ | $3.18\text{\times}{10}^{-5}\text{\,}$ | 184

###  2.1 Feature extraction

Features computed from time-domain signals acquired using the embedded systems
are best suited for implementing ML models for damage inference at the edge.
For the damage classification model presented in this work, we utilized $10$
features computed from the time-domain signals, summarized in Table 1. Widely
used statistical features such as mean absolute deviation (MAD), variance
(VAR), standard deviation ($\sigma$) are computed using the monitoring signal
alone On the other hand, features such as root mean square energy (RMS), root
mean square deviation (RMSD) and peak to peak amplitude deviation (PPAD) of
signals Sawant Shruti and Siddharth (2021), signal energy ratio (SER)
Torkamani et al. (2014) etc. capture the deviation of monitoring signal from
baseline signal, and therefore the impact of damage on amplitude and phase of
the GW signals. Along with features easily computed from time domain signals,
we also computed spectral difference deviation (SDD) using Fourier domain
representation. SDD quantifies the difference in the Fourier spectra of
baseline ($S_{b}(f)$) and monitoring ($S_{m}(f)$) signals, normalized to their
respective energies Ren et al. (2019).

###  2.2 Filtering-based feature selection

Figure 2: Filtering-based feature selection approach

Filtering-based approaches are used as commonly used as preprocessing step in
ML-pipelines. These methods select features from the original feature set
irrespective of the use of which ML algorithm is finally used. In terms of
computation, these feature selection methods are fast and computationally
inexpensive ways to remove duplicated, correlated and redundant features.
Statistical measures used for feature selection in filtering-based methods
include Pearson’s correlation coefficient for continuous and Chi-square test
for discrete features. As shown in Figure2, in each iteration, we consider two
out of $10$ features and compute Pearson’s correlation coefficient as a
feature evaluation metric. We set the threshold on Pearson’s correlation
coefficient values for selecting the features. Considering subset of features
and applying threshold criteria if N features are correlated among themselves
then N-1 features are eliminated. The optimal feature subset thus obtained is
used to train and evaluate the performance of ML models.

###  2.3 Damage classification

Damage classification is modeled in this study as a supervised task using
optimal feature subset as input. In a classification problem, the target or
dependent variable, $y$, can take only discrete values for a given set of
features or independent variables, $X$. We evaluated the performance of five
different classifiers :

  * •

Logistic regression: Logistic regression is typically used for predicting
binary targets, it can be extended to multi-class classification problem using
heuristic method called ”one versus rest”, wherein, for $N-$class problem, $N$
different binary classifiers are trained to predict one class as positive and
other classes as negative. The coefficients in logistic regression are
estimated using maximum-likelihood estimation. Logistic regression is easier
to implement, efficient to train and can interpret model coefficients as
indicators of feature importance. The major limitation of Logistic regression
is the assumption of linearity between the targets and the features. It is
also sensitive to class imbalance problem and scaling of features and requires
careful tuning.

  * •

Support vector machine (SVM): For linearly separable classes, the SVM
algorithm learns the decision boundary as a hyperplane. Samples closest to the
hyperplane from both classes are called support vectors. Its learning
objective is to maximize the margin, i.e., the distance between the hyperplane
and the support vectors. SVM can be extended to a multi-class problem using
one versus one strategy. Here, for N-class problem, a total of
$N\times(N-1)/2$ binary classifiers are required, one for every possible pair
of classes. If the data is not linearly separable, kernel SVM technique
projects data in lower dimensions to higher dimensions in such a way that data
points belonging to different classes are allocated to different dimensions
and become linearly separable. Training SVMs and tuning its hyperparameters is
expensive and they are difficult to interpret compared to simple logistic
regression models.

  * •

Naive Bayes: It is a probabilistic classifier inspired by the Bayes theorem
under a simple assumption that features are conditionally independent. Despite
this oversimplified assumption, naive Bayes classifiers work very well in many
complex real-world problems. A big advantage of naive Bayes classifiers is
that they only require a relatively small number of training data samples to
perform classification efficiently, compared to other algorithms, such as
logistic regression, decision trees, and SVMs. For this study we use Gaussian
naive Bayes wherein values associated with each feature are assumed to be
distributed according to a Gaussian distribution. The drawback of calculating
model parameters of Gaussian distribution is that we cannot interpret feature
importance in this case.

  * •

Decision tree: It utilizes an if-then rule set which is mutually exclusive and
exhaustive for classification in the form of a tree structure. Decision tree
uses purity-based loss functions, such as Gini impurity and entropy, to
evaluate the split based on the class purity of the resulting node Myles et
al. (2004). Features in the top of the tree have more impact towards the
classification. Decision tree models have better interpretability. However,
decision trees are prone to overfitting. A single decision tree by itself
usually has subpar accuracy but the tree structure makes it easy to control
the bias-variance trade-off.

  * •

Random forest: A random forest consists of a large number of individual
decision trees that operate as an ensemble. Using bootstrap aggregation or
bagging technique, random bootstrapped samples are drawn from training set
Breiman (2001). Further, for each decision tree random subsets of features are
used, which often result in better predictive performance than a single
decision tree due to better variance-bias trade-offs Breiman (2001).

Figure 3: HCSS panel with lateral dimensions 1000x1200mm containing various
types of damages. Out of these, four types of damages, denoted as TRF, LFA,
HDC, CC of size 30x30mm were studied in this work. Figure 4: Experimental
layout of three Nano-30 sensor paths for the study of four types of damages
using guided wave propagation in HCSS panel

##  3 Numerical simulation of different types of damages in HCSS

To study the impact of different types of damages on GW propagation, we
carried out numerical simulation on the HCSS panel as shown in Figure 3, using
commercially available COMSOL Multiphysics 5.5 software using Structural
Mechanics module and analyzed it using Time Implicit study. The HCSS panel
consists of two halves. One half is of $14.97\text{\,}\mathrm{m}\mathrm{m}$
thickness comprising of $1.125\text{\,}\mathrm{m}\mathrm{m}$ thick $9-$layer
CFRP lamina skin on top and bottom surfaces, with
[0/+60/-60/-60/+60/0/0/+60/-60] layup bonded using
$0.01\text{\,}\mathrm{m}\mathrm{m}$ thick adhesive layer (HEXCEL-Redux 319L)
to a $12.7\text{\,}\mathrm{m}\mathrm{m}$ thick honeycomb core (HEXCEL-Al
$5056$ hexagonal aluminum Nomex core of cell size
$0.25\text{\,}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{h}$). The other half is of
$14.22\text{\,}\mathrm{m}\mathrm{m}$ thickness comprising of
$0.75\text{\,}\mathrm{m}\mathrm{m}$ thick $6-$layer CFRP lamina with
[0/+60/-60/-60/+60/0] layup bonded to the core. Table 2 provides the material
properties of the sandwich composite structure. A half-scale 3D model was used
to study the effect of four damages on a 100x150mm HCSS panel with a 15x15mm
damage as shown in Figure 5. GW paths 1-1* and 3-3* (Figure 4) were considered
to be baseline as the damage lies directly along path 2-2*. Out-of-plane load
(z-direction) was given as a point load to simulate the actuation produced by
the Nano-30 detachable miniature transducers, thus predominantly generating
$A0$ mode in the panel, and output out-of-plane displacement is measured at a
point $50\text{\,}\mathrm{m}\mathrm{m}$ apart. Accuracy of numerical
simulation depends on the mesh size and time-step increment in Time Implicit
study Leckey et al. (2018). As with previous studies on COMSOL based guided
wave numerical simulation, the largest mesh element size was restricted to
$1/6^{th}$ of the wavelength of the propagating mode Lei et al. (2019). The
time step was chosen to be $0.1\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{s}$
$(>1/60f)$. For excitation frequency $f=$
$100\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$, the wavelength of $A0$ mode in
the HCSS panel was approximately $12\text{\,}\mathrm{m}\mathrm{m}$. Thus, the
largest mesh size in the plate was set to $2\text{\,}\mathrm{m}\mathrm{m}$.
The time-domain profile of the out-of-plane point load was specified as a
$5-$cycle sine pulse shaped by a Hanning window, expressed as:

$V(t)=0.5\left[1-\cos\left(\frac{2\pi ft}{5}\right)\right]\sin(2\pi ft)$ (1)

Figure 5: Three-dimensional half-scale FE model of size 100x150mm with a
15x15mm damage which falls directly in the wave propagation path P2-2* Figure
6: Two-dimensional Core crush (CC) FE model with an ellipsoidal cavity of size
30x1mm with a crushed core Figure 7: Two-dimensional high density core (HDC)
FE model with a 30x12.7mm HD core zone Figure 8: GW signals for four types of
damages corresponding to three paths as per layout of the half-scale model
shown in Figure 5 Figure 9: Two-dimensional FE model of (a) size 300x14.22mm
comprising $0.75\text{\,}\mathrm{m}\mathrm{m}$ thick $6-$layer CFRP lamina
skin on top and bottom surfaces with [0/+60/-60/-60/+60/0] layup bonded using
$0.01\text{\,}\mathrm{m}\mathrm{m}$ thick adhesive layer (HEXCEL-Redux 319L)
to a $12.7\text{\,}\mathrm{m}\mathrm{m}$ thick honeycomb core & (b)300x14.97mm
comprising $1.25\text{\,}\mathrm{m}\mathrm{m}$ thick $9-$layer CFRP lamina
skin on top and bottom surfaces, with [0/+60/-60/-60/+60/0/+60/-60] layup
Figure 10: GW signal comparing baseline versus damaged HCSS panel with
increasing damage parameters for (a) LFA (b) TRF (c) HDC & (d) CC

To study the effect of damages present in the HCSS panel, signals for baseline
and the path containing the damage signal were compared for four types of
damages introduced in the model. LFA of length ”L” was modeled by removing the
adhesive layer between the CFRP skin and the honeycomb core, whereas TRF was
modeled as a $0.01\text{\,}\mathrm{m}\mathrm{m}$ thick Teflon film in between
the individual lamina. The material properties of Teflon considered in the
simulations are tabulated in Table 3. In the other half of the panel, CC was
modeled by creating a cavity with a crushed core region beneath the cavity at
the skin-core interface. The cavity and crushed core were modeled as a half-
ellipsoidal surface as shown in Figure 6. Previously reported experimental
investigations Raja B. et al. (2022) were analyzed to deduce the crushed core
material properties and are tabulated in Table 3. HDC zone of thickness
$12.7\text{\,}\mathrm{m}\mathrm{m}$ present in HCSS core as shown in Figure 7
was modeled in 2D FEM simulations with the material properties as listed in
Table 3.

Figure 8 shows that the time-series data for the path 2-2* containing the
damage has a significant effect on the amplitude with respect to the baseline
paths 1-1* and 3-3*. It is evident from the 3D simulations that CC and LFA
damage signals shows an increase in the peak amplitude when compared to the
baseline while HDC and TRF shows a decrease in amplitude.

###  3.1 Parametric study

Generating experimental data poses a significant challenge due to the high
costs and impracticality of creating different types of damages. To evaluate
the performance of the proposed algorithm for different damage sizes, we also
conducted extensive parametric study using two separate 2-D numerical
simulations, which were performed as follows:

  * •

A 300x14.22mm thick HCSS panel to study the effect of LFA and TRF as shown in
Figure9(a).

  * •

A 300x14.97mm thick HCSS panel to study the effect of CC and HDC as shown in
Figure9(b).

The studies carried out by varying parameters and GW signal data from
numerical simulation of baseline and damaged path were compared for the four
type of damages. Figure 10 shows that the time-series data for a damaged path
has a significant effect on the amplitude with respect to baseline signal. It
is evident from the various case studies presented that CC and LFA damage
signals show an increase in the peak amplitude when compared to the baseline,
while HDC and TRF show a decrease in amplitude. Due to the large computational
cost associated with 3D modeling, we used 2D COMSOL models for the parametric
study, a thorough analysis using 3D models is required to investigate effect
of damage size on amplitude and phase of the baseline signal.

Figure 11: Experimental setup showing HCSS panel instrumented with a pair of
Nano-30 detachable transducers used as actuator (transmitter) and receiver,
function generator for generation of actuation signal, and oscilloscope for
recording the receiver response. Figure 12: GW signals for four types of
damages corresponding to three paths as per layout shown in Figure 4. For
experimental study, we recorded $20\text{\,}$ such time-series data trials per
path for each of four damages. Figure 13: Trends in peak amplitude values of
four damages corresponding to twenty trials for each of the three paths
recorded using a pair of detachable Nano-30 transducers

##  4 Results and discussion

###  4.1 Experimental setup

Figure 14: Confusion matrices for the five classifiers on held out
experimental data Figure 15: Feature importance using permutation technique
for all classifiers for experimental data

To study the change in baseline signal due to different types of damages, we
analyzed a HCSS panel as shown in Figure 3. To perform non-destructive
ultrasonic GW testing of the HCSS panel with various damages, the experimental
setup shown in Figure 11 was used. We used a pair of Nano-30 transducers
(separated by $100\text{\,}\mathrm{m}\mathrm{m}$ distance) for GW transduction
using commercially available ultrasound gel as couplant. Compared to
conventionally used piezoelectric wafer transducers, these contact-type
transducers do not need to be permanently attached to the HCSS surface with an
adhesive, and are thus suitable for non-destructive testing. These transducers
generate predominantly anti-symmetric modes, and the interaction of the
fundamental anti-symmetric $(A0)$ mode with various damages depends on the
type of defect. A function generator (Tektronix AFG1022) was used to generate
$5-$cycle sine pulse shaped with Hanning window as actuation signal (equation
1). The signal frequency was $100\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ and
peak-to-peak voltage amplitude was $20\text{\,}\mathrm{V}$. A digital storage
oscilloscope (DSO, Tektronix MDO3024) was used to record the GW signal
acquired by the receiver Nano-30 at a sampling rate of
$100\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$. The amplitude of the recorded
signal is affected by various parameters, such as acoustic coupling,
mechanical impedance, position of the transducers, and pressure applied on the
transducers. The Nano-30 transducers were attached manually on the panel as
shown in Figure 11, that introduced variation in the amplitude. Therefore,
$20\text{\,}$ measurements were recorded for each of the three paths for each
damage with the transducers removed and attached again for each measurement.
The positions of the sensor paths relative to the defect are shown in Figure
4. Note that the region of the panel containing the damage falls directly
along the wave propagation paths P2-2*. GW response for path P1-1* and 3-3*
were considered as baseline signal, since it is sufficiently separated from
the damages.

Recorded time-series data contains an offset. Discrete wavelet transform
(DWT)-based approach was used to preprocess the GW signals prior to
computation of features. DWT yields step-wise decomposition of a signal in
different frequency bands centered at a specified frequency scale. For this
purpose, Daubechies mother wavelet of order $40$ was used to obtain a
$7-$level wavelet decomposition of each signal, and the $6^{th}$ coefficient
was used as the filtered version of the signal. Detailed discussion on the
DWT-based denoising method can be found in work by Rizzo et al. Rizzo et al.
(2005).

Representative time-series data for one of the $20\text{\,}$ trials thus
obtained for the three sensor paths for the four damage types is illustrated
in Figure 12. Experimental data was observed to be in accordance with
simulation data (Figure 5), which confirms that the experimental data was a
good representation of the underlying physical model. We observe that time-
series for sensor path P2-2*, containing the damage, shows significant change
in the amplitude with respect to sensor paths P1-1*, and P3-3*, which are
relatively away from the damage hence used as baseline data. It is important
to note that two damages, CC and LFA result in decrease in amplitude with
respect to baseline, whereas the remaining two damages HDC and TRF, show
decrease in amplitude with respect to baseline.

Trends in peaks of the $20\text{\,}$ trials recorded using detachable Nano-30
transducers in shown in Figure 13. These trends are consistent with the
variation of the signal containing the damage (P2-2*) with respect to baseline
data (P1-1* and P3-3*). The challenge here is to distinguish between damages
that cause similar change in the baseline signal.

To incorporate uncertainties due to environmental and operational conditions,
we added white noise to each time-series $s(t)$ :

$s_{n}(t)=s(t)+\beta_{n}\max(s(t))\left[w(t)\right]$ (2)

where $s_{n}(t)$ denotes the signal with added noise, $\max(s(t))$ is the peak
amplitude of signal $s(t)$, $\beta_{n}$ denotes the noise scaling factor, and
$w(n)$ is white noise generated using normal distribution with zero mean and
standard deviation of $1$. We studied the performance of the damage
classification method for signal to noise ratio (SNR) value of
$25\text{\,}\mathrm{d}\mathrm{B}$ using $\beta_{n}=0.01$. Each experimental GW
time-series obtained after wavelet-based preprocessing was used to generate
noise-augmented data by adding white noise as described in equation (2). For
feature computation and subsequent damage assessment, 10 noisy copies of each
time-series were generated randomly. After noise augmentation, there are total
200 time-series data for each of four damage types recorded for sensor path
P2-2*. For baseline data, we have data corresponding to P1-1* and P3-3* for
all four damages, i.e. total 80 time-series. We performed the study by
selecting 20 baseline time-series samples from different damage types and
creating 10 noisy copies of each time-series, it doesn’t affect the
classification accuracy. Here we have reported the study using 10 baseline
samples from CC damage and 10 samples from TRF damage, total 20 samples are
then noise augmented to get 200 samples with SNR of 25 dB.

###  4.2 Feature engineering

As listed in Table1, we computed total 10 features for each noisy time-series.
For computation few of features such as RMSD, PPAD, SER etc., we used time-
series data corresponding to P3-3* as baseline $f_{b}(t)$. At the end of
feature extraction step, we obtained feature set with dimension $1000\times
10$. Next, out of the 10 features, the most relevant features were selected
using filtering approach with Pearson’s correlation coefficient as selection
criteria. Correlation is a measure of the linear relationship of two features.
The logic behind using correlation for feature selection criteria is that the
most relevant features are highly uncorrelated among themselves. If two
features are correlated, we can predict one from the other. Therefore, an ML
model only needs one of them, as the second one does not add additional
information. We set an absolute value of 0.95 as the threshold. Using
thresholding, if in the subset of N features are correlated among themselves
then N-1 features are eliminated.

###  4.3 Damage classification

For the damage classification problem, we used the optimal feature subset of
size $1000\times 7$ obtained in the previous step as our input and targets
were generated in one hot encoding scheme corresponding to five classes :
Baseline, CC, LFA, HDC and TRF. The dataset was randomly split in the
proportion $75\%:25\%$ for training and testing, respectively. We evaluated
performance of five different ML models for five class classification. We used
scikit-learn library for implementing the machine learning in python. The
codes are open sourced on GitHub. We repeated the experiment with 10 different
random splits i.e. randomly selecting $75\%:25\%$ for train:test dataset in
each trials. Accuracy as average of 10 trials for each of the five models is
listed in Table4. Logistic regressor and SVM have lower accuracy as these
models work better for linearly separable data. Gaussian naive Bayes performs
comparatively better for non-linear data due to its probabilistic approach.
Random forest performs better than decision tree by considering multiple
decision trees at a time. Confusion matrices are shown in Figure 14.

To understand the effect on each feature on the performance of the model we
used permutation importance metric. It shuffles the data corresponding to a
feature and computes the drop in accuracy (called as permutation importance)
using test data with a trained model. If a particular feature results in a
significant drop in the accuracy then that feature has more importance in the
prediction of the model. This metric is especially beneficial in case of
Gaussian naive Bayes model where we get model parameters for Gaussian
distribution and not weights of each feature. Permutation importance has also
been used for highly complex or non-parametric models such as support vector
machines. It addresses the issue where random forest models are biased towards
categorical variables with a large number of categories Altmann et al. (2010).
Figure 15 shows permutation importance of five classifiers for the seven
selected features. Here, RMSD plays crucial part in predicting test data with
higher accuracy. RMSD computes the change in the amplitude of monitoring
signal with respect to baseline. The next highest importance is observed for
Fourier domain features such as SDD and NSED. Frequency domain decomposition
such as Fourier spectrum are best suited to capture the non-stationary nature
of GW signals Torbol (2014). We also observe that the baseline-free features
have relatively lower importance compared the features computed using
baseline, which underlines the importance of signal normalization by using the
baseline information. Another important observation here is that the decision
tree has relatively higher range of importance values. This can be explained
based on the tendency of decision tree to have high variance. Random forest
using bagging technique fixes this issue and has a better bias-variance trade-
off.

Table 4: Classification accuracy for various classifiers using the six selected features Classifier | Accuracy (%)
---|---
Logistic regression | 59.2
SVM (Linear) | 58.8
Naive bayes (Gaussian) | 66.4
Decision trees | 98.4
Random forest | 100.0

####  4.3.1 Different damage sizes

Next, we evaluated feasibility of the proposed feature engineering based
damage classification framework for damage classification across different
damage sizes. We used simulated data obtained from parametric study reported
in section 3.1. From 2D numerical models, we generated one baseline signal and
nine timeseries corresponding to nine damage sizes between
$20\text{\,}\mathrm{m}\mathrm{m}$ to $90\text{\,}\mathrm{m}\mathrm{m}$. For
each damage and baseline, we obtained ten noise augmented copies for each
damage size, with feature set of size $450\times 10$. In this case, we
obtained accuracy of 77.89% indicating robustness of the proposed method for
nine damage sizes. This validates the use of simulation to assess the wider
utility of the proposed method. Optimal feature set used here consisted of the
same seven features as experimental study. Lower accuracy value compared to
experimental study can be explained using non-linear relationship between the
size of damages and their effect on amplitude and phase of baseline signal as
illustrated in Figure 9.

####  4.3.2 Baseline-free feature extraction

The baseline-free features reported by Liu et al Liu et al. (2021) are listed
in Table 5. We computed these 13 features using experimental data for all
damages. Noisy data corresponding to P2-2* was used to compute features for
four damages and baseline features for P3-3* for two damages CC and TRF. The
feature set of size $1000\times 13$ was filtered using Pearson’s correlation
coefficient with threshold of 95%. Features SF4, SF5, SF6, SF10, SF12 and SF13
were dropped and optimal feature set of dimension $1000\times 7$ was used for
damage classification. Random forest model gave the highest accuracy of 69.2%
among five classifiers. These features are computed using monitoring data
alone for pulse echo technique, which generally contains actuation signal
along with its reflection. GW data obtained from the network of transmitter
and receiver transducers instrumented on composite panels using pitch-catch
technique does not consist of an actuation signal. Therefore, for pitch catch
GW data, features that compute deviation from baseline work better.

##  5 Conclusion and future work

Damage classification using ML-based approaches reported in GW-SHM literature
consider different locations or intensities of the same damage as different
classes of ML model. Also, they use deep learning techniques for capturing
deviation in the amplitude of the data corresponding to the damaged path from
the baseline data, resulting in large model size. The challenge arises when we
have limited training data, which is usually the case in a a real world
scenario, and we try to distinguish between two or more types of damages in
HCSS that cause similar change from the baseline data. In this work, we
reported feature engineering-based damage classification using a total 10
statistical features that do not require knowledge of material properties,
such as group velocity, time of arrival of wavemode etc. Therefore, the
proposed features and method can be utilized for different materials without
knowledge of material properties. We classified four damages in HCSS, which
cause similar changes to baseline data. Optimal feature subset was obtained by
dropping four highly correlated features using Pearson’s correlation criteria.
If we plug more statistical features in the list, this feature engineering
approach will automatically filter out the redundant features without relying
on domain knowledge. Perfect accuracy of damage classification in experimental
test data was reported using seven selected features using a random forest
classifier. Also, the robustness of the proposed framework for nine damage
sizes is demonstrated using simulation data with an accuracy of 77.89%. To the
best of our knowledge, this is the first report on damage classification for
HCSS using GW-SHM domain. Interpretability of the model using feature
importance indicates that features capturing deviation of monitoring signal
from baseline signal are more effective compared to baseline-free features.

In the future we will explore edge-based deployment of these light-weight
models inspired by TinyML framework Sanchez-Iborra and Skarmeta (2020), that
could be directly embedded in the FPGA-based embedded system. This will pave
the way for designing truly portable, end-to-end smart SHM systems, which can
acquire the data and perform damage classification, specifically for efficient
in-situ monitoring of HCSS. In our more recent work, we explored damage
classification in the presence of data loss that may occur in wireless sensor
networks or IoT-based SHM systems Sawant Shruti and Siddharth (2021).
Furthermore, to make the method more robust to real world scenarios, we seek
to evaluate the performance of the algorithm for different materials under
varying environmental temperatures.

Table 5: Features computed from GW signals reported by Liu et al. (2021), where x is time domain signal and f is frequency domain representation.  Feature |  Expression
---|---
SF1 |  $\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{3}$
SF2 |  $\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{4}$
SF3 |  max(x) - min(x)
SF4 |  $\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{4}$ / ${(\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{4})^{2}}$
SF5 |  $\sqrt{\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{2}}$
SF6 |  $\sqrt{\frac{1}{M}\sum_{i=1}^{i=M}{(x(i)-\hat{x})}^{2}}$
SF7 |  max($|x|$) / $\sqrt{\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{2}}$
SF8 |  $\sqrt{\frac{1}{M}\sum_{i=1}^{i=M}{x(i)}^{2}}$ / $\frac{1}{M}\sum_{i=1}^{i=M}\sqrt{|x(i)|}$
SF9 |  max($|x|$) / $\frac{1}{M}\sum_{i=1}^{i=M}\sqrt{|x(i)|}$
SF10 |  max($|x|$) / ${\frac{1}{M}\sum_{i=1}^{i=M}\sqrt{|x(i)|}}^{2}$
SF11 |  $\frac{1}{M}\sum_{i=1}^{i=M}{f(i)}^{2}$
SF12 |  $\frac{1}{M}\sum_{i=1}^{i=M}{f(i)-\hat{f}}^{2}$
SF13 |  $\frac{1}{M}\sum_{i=1}^{i=M}{f(i)}$

The data that support the findings of this study are available upon reasonable
request from the authors. Codes developed for the proposed method are open-
sourced on GitHub

This work was partially supported by Indian Space Research Organization (ISRO)
[grant no. RD/0118-ISROC00-006]. The authors thank Mr.Ramana Raja, PhD
student, Department of Civil Engineering, IIT Bombay and Kajal Shivgan at
Wadhwani Electronics Laboratory (WEL), IIT Bombay for assistance with data
collection.

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