# Application of supervised learning for classification of cracking and non-cracking major damage in TRMs based on AE features

Khan Junaid, Amir Si Larbi, Algourdin Nonna, Zyed Mesticou, Dimitrios Aggelis, Gaochuang Cai

► To cite this version:

Khan Junaid, Amir Si Larbi, Algourdin Nonna, Zyed Mesticou, Dimitrios Aggelis, et al. Application of supervised learning for classification of cracking and non-cracking major damage in TRMs based on AE features. Construction and Building Materials, 2024, 437, pp.137079. 10.1016/j.conbuildmat.2024.137079. hal-04845324

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# Application of supervised learning for classification of cracking and non-cracking major damage in TRMs based on AE features

Khan Junaid<sup>a, *</sup>, Amir Si Larbi<sup>a, c</sup>, Nonna Algourdin<sup>a</sup>, Zyed Mesticou<sup>a</sup>, Dimitrios Aggelis<sup>b</sup>, Gaochuang Cai<sup>c, a</sup>

## ARTICLE INFO

### Keywords:

* TRM
* Acoustic emissions
* AE
* ML
* SVM
* KNN
* Crack

## ABSTRACT

Textile reinforced mortar composites (TRMs) experience various types of damage. In this study, these damage mechanisms (such as cracking and non-cracking) were understood or distinguished with the help of acoustic emissions (AE). Four types of TRMs made of a single mortar matrix and two types of carbon textiles (coated and noncoated) were evaluated under uniaxial tension. Meanwhile, the acoustic emissions were monitored during the tensile test.

The study showed that AE features are sensitive to damage evolution but more importantly that TRMs are complex and various modes can coexist. Similarly, the evolution of improved b-value (Ib) also demonstrated sensitivity to the existence of damage. Finally, the supervised learning models (trained on AE data) demonstrated that information on the instant of cracking obtained through digital image correlation (DIC) can be successfully coupled with AE features to separate the cracking and non-cracking damage types with accuracy of above 80 %.

## 1. Introduction

Textile reinforced mortar (TRM) is a novel composite material of continuous fibers embedded in a mineral based matrix [1]. TRMs have found its use in the retrofitting applications due to its compatible nature with the concrete and masonry substrate [2]. Additionally, it is adopted for the construction of new building elements in lieu of the traditional reinforced concrete. Over RC elements, TRMs allow for corrosion resistance and light weight structural elements [3].

Considering the associated interest, the mechanical behavior of TRMs was extensively studied in the recent years [4]. However, due to the variety of matrices and fabric options and their implications on the performance of the interface, further understanding of the TRM's behavior is still required [5]. In addition to that, more experimental studies are required to comprehend the internal damage mechanisms of the TRMs due to the complexity of interaction between the different constituents of the TRM, the heterogeneity and anisotropy (initial and induced by the degradation process) of their respective mechanical and physicochemical properties.

Acoustic emission (AE) presents a suitable option for enhancing the understanding and identification of different damage mechanisms [6–10]. RILEMTC 212-ACD proposed recommendations to classify the type of tensile and shear cracking damage based on frequency and RA (Risetime/Amplitude) features of acoustic emissions [11]. Similarly, [12] used AEs for localization of damage and qualitative differentiation of micro and macro scale damage in steel elements, while [10] used AEs for a steel fiber reinforced concrete T-beam tests in four point bending to classify the damage zones as per load displacement curve. A support vector machine model was used for classification of various damages [10]. Additionally, the sensitivity of Ib (improved b-value) value was also analyzed by Ref. [10] in case of fiber reinforced concrete. Ib value is obtained as the slope of the cumulative frequency distribution of the amplitude around the mean of the distribution.

Various studies exist in literature on the AE monitoring of composites. For instance, AEs amplitude based Ib value analysis were used for qualitative damage characterization of micro and macro scale damage in carbon fiber reinforced polymers (FRPs) [13]. Similarly, [14] used AEs to study the behavior of ceramic composites and the associated failure

<footnote><sup>a</sup> Université de Lyon, Ecole Centrale de Lyon – ENISE, Laboratoire de Tribologie et Dynamique des Systèmes (LTDS) CNRS UMR 5513, 58 rue Jean Parot, Saint-Etienne 42100, France</footnote>

<footnote><sup>b</sup> Mechanics of Materials and Constructions, Faculty of Engineering, Vrije Universiteit Brussel, Brussels, Belgium</footnote>

<footnote><sup>c</sup> International Advanced Science and Technology Research Organization (IROAST), Kumamoto University, Kurokami, Kumamoto 8608555, Japan</footnote>

<footnote>* Corresponding author.
E-mail address: junaid.khan@enise.fr (K. Junaid).</footnote>
mode under tension. Dogbone specimen with two AE sensors were used. The study reported that matrix cracking was related to high energy signals.

The use of AE monitoring for textile reinforced mortar is so far limited. The scarcity of TRM studies on AE monitoring is common to structural and material scale. [15] and [16] used glass TRMs to understand the impact of TRM dimensions and travel distance on AE parameters. The studies showed that RA, duration and frequency were sensitive to the adopted width of the plate under flexural setup, and a proper approach was required for extrapolation of TRM coupon scale results to structural scale plates. Similarly, the evolution of AE parameters of curved textile reinforced mortar elements during flexure test was reported by Refs. [17,18].

In strengthening applications, the evolution of AE parameters for FRP strengthened RC members was reported by Refs. [6,8,19], while Ref. [19] also monitored the acoustic emissions of glass TRM strengthened RC beams. The AE monitoring allowed the detection and identification of delayed cracking for TRM strengthened beam as was verified with DIC. Additionally, shifts in average frequency (decrease) were recorded at the associated load drops (possibly due to debonding after cracking).

A few studies have reported the AE monitoring of TRMs under tension [20–23]. The first study on AE monitoring of coated glass textile TRMs under tension was performed in Ref. [22]. The study explored the strength of AEs in terms of localization (assisted with DIC), and phase/zone separation in the tensile response based on average frequency and RA values. Similarly, [21] comparatively studied the AE monitoring of 2D and 3D AR glass textile TRMs under tensile loading. The study found that 2D textile TRMs were associated with higher average frequencies and lower rise time compared to 3D textile TRMs. More recently, authors in Ref. [20] used AE monitoring coupled with DIC and optical fibers to explore the behavior of TRMs under tension. The influence of the number of 1–3 carbon textile layers was also explored in the same study. The study in Ref. [20] used unsupervised learning approach to classify the AE data in to different clusters. The clusters were assigned to different damage mechanisms (matrix cracking, mortar-textile interface damage, shear mechanisms and textile deformation) based on the observed frequency content.

However, as established in the studies on tensile response of TRMs that the behavior of TRMs is sensitive to the mortar textile combination and their relative properties [4]. Therefore, additional work is required to ameliorate the understanding of AE monitoring of TRMs in order to make it a more efficient damage characterization tool. For instance, the case of uncoated/noncoated vs. coated textile TRMs under AE monitoring needs to be addressed. Similarly, the sensitivity of Ib value in case of TRMs needs to be addressed. As per the authors knowledge no study has reported the evolution of Ib values for TRMs under tension.

As seen in the established studies, the AE features are sensitive to damage in materials. This provides the opportunity for identifying various damage phenomenon in the material/system under consideration. For instance, the unsupervised learning approach adopted in Ref. [20] assigned the extracted clusters to various damage mechanisms based on different frequency ranges. However, the split based on the frequency content needs to be assessed further in case of TRMs due to coexistence of various damage modes and their influence on AE features/parameters in different TRM types. Additionally, because of challenges related to scale/damage mostly in civil engineering applications, clustering studies have not always been supported by microscopic observations to validate the proposed damage mechanism assigned to a cluster [24].

Although AE feature based clustering can provide initial guess on the triggering mechanism but the use of AE feature in maintenance/monitoring process can be taken a step further. For instance, identifying a particular damage type, with enhanced probability, can lead to robust maintenance operations by directing/aligning them more precisely. More importantly, this can enhance the understanding of AE features

related to particular class of damage in the context of TRMs. *Therefore, in this study, a step was taken towards differentiating cracking (surface damage) from internal/other damage mechanisms.*

The use of DIC allowed to effectively identify the cracking events due to their presence on the TRM's surface. To this end, this study used a supervised learning approach to separate cracking and non-cracking major/noticeable damage in TRMs based on AE features. The advantage of supervised learning approach is the associated enhanced certainty on classification/misclassification of the two classes, which can be cross checked with the training or test data. *As per the authors knowledge no study is so far reported on the use of supervised learning based on AE parameters to separate the cracking and non-cracking major damage classes in TRMs.* The present study was performed on coated and non-coated carbon TRMs. The influence of the number of coated layers and the hybrid usage of coated and noncoated layers was also addressed.

In summary, the associated novelty in this study can be categorized as follow:

a) Comparative evolution of trends in AE features in coated and non-coated textile TRMs

b) The evolution of Ib values in the context of TRMs under tension

c) A proposed supervised approach to separate cracking and non-cracking damage based on AE features

## 2. Material and methods

### 2.1. Textile

In this study, two variations of textile were used for TRMs as shown in Fig. 1. $T_{uncoated}$ was biaxial carbon textile without any coating. The mesh size was 5×5 mm. The value of tex was 12,000, and the filament diameter was 7 µm as per the manufacturer (see Table 1). Geometrically, the warp yarns in $T_{uncoated}$ were different than weft yarns due to the presence of in-plane crimp in the warp yarns. The 2nd textile (TCSBR) was the styrene butadiene coated version of $T_{uncoated}$. It is important to mention that the coating was industrially applied. The process of coating diminished the in-plane crimp of the warp yarns, which was present in $T_{uncoated}$. It is important to mention that although the textile was biaxial, however, warp yarns were used as the main load bearing components.

### 2.2. Mortar

A commercial hydraulic mortar designed for strengthening and rehabilitation purposes was adopted. The largest particle size of the fine aggregates was restricted to 1 mm to ensure enhanced mortar penetration in to the textile mesh.

The compressive and flexural strength of the mortar (given in Table 2) was obtained through 3 specimens of 40 × 40 × 160 mm, tested to the EU Norm EN-196-1 [25]. While the adherence/bond strength was supplied by the manufacturer.

### 2.3. Specimen configurations and preparation

In this study, four types of TRMs were tested (Table 3). The total length, thickness and width of the TRMs specimens along with their standard deviation (std) are given in Table 3. The adopted reinforcement ratio ($V_f$) for each TRM type is also mentioned.

$T1M$ and $TunM$ were made of a single layer of TCSBR and $T_{uncoated}$ textile respectively. Meanwhile, $T2M$ was formed with two layers of TCSBR textile. Lastly, a hybrid TRM, $ThM$ was prepared from one TCSBR layer sandwiched between two $T_{uncoated}$ layers (Fig. 2). For each type, three samples were subjected to tensile test to ensure repeatability.

Wet hand layup technique was used to manufacture a plate of 500 × 700 × (n+1) × t mm for each type of TRM [26]. Where “n” represents the number of textile layers and “t” is the thickness of a single mortar layer, which ranged between 2 and 3 mm. The plates were laminated in
<figure><img src="image_3.png" /><figcaption>Fig. 1. Representation of the styrene butadiene coated (TCSBR) and uncoated (Tuncoated) textile.</figcaption></figure>

<table><caption>**Table 1**

Properties of textile.</caption><thead><tr><th rowspan="2">Textile</th><th rowspan="2">Mesh (mm x mm)</th><th rowspan="2">Material</th><th rowspan="2">Coating</th><th rowspan="2">area weight (g/cm²)</th><th rowspan="2">No, filaments</th><th rowspan="2">Fil dia (μm)</th><th colspan="2">Warp</th></tr><tr><th>σ<sub>f</sub> (MPa)</th><th>E<sub>f</sub> (GPa)</th></tr></thead><tbody><tr><td>TCSBR</td><td>5×5</td><td>Carbon</td><td>Styrene butadiene</td><td>0.034</td><td>12,000</td><td>7</td><td>1400</td><td>120</td></tr><tr><td>T<sub>uncoated</sub></td><td>5×5</td><td>Carbon</td><td>non</td><td>0.025</td><td>12,000</td><td>7</td><td>1400</td><td>114</td></tr></tbody></table>

<table><caption>**Table 2**

Properties of mortar.</caption><thead><tr><th colspan="2">Mortar</th></tr></thead><tbody><tr><td>σ<sub>m,f</sub> [MPa] (CoV)</td><td>9 (0.14)</td></tr><tr><td>σ<sub>m,c</sub> [MPa] (CoV)</td><td>51 (0.10)</td></tr><tr><td>max grain size [mm]</td><td>1</td></tr><tr><td>Adherence [MPa]</td><td>2</td></tr></tbody></table>

<table><caption>**Table 3**

Description of the studied TRM configurations.</caption><thead><tr><th>TRM Type</th><th>Thickness/ std (mm)</th><th>Width/ std (mm)</th><th>Total Length (mm)</th><th>V<sub>f</sub> (%)</th><th>Textile orientation</th><th>Textile Layers</th></tr></thead><tbody><tr><td>T1M</td><td>5.71/ 0.045</td><td>70.23/ 0.20</td><td>650</td><td>1,2</td><td>Warp</td><td>1 TCSBR</td></tr><tr><td>T2M</td><td>9.66/0.53</td><td>70.29/ 0.16</td><td>650</td><td>1,6</td><td>Warp</td><td>2 TCSBR</td></tr><tr><td>TunM</td><td>5.93/0.22</td><td>69.84/ 0.40</td><td>650</td><td>1,2</td><td>Warp</td><td>1 T<sub>uncoated</sub></td></tr><tr><td>ThM</td><td>13.13/ 0.14</td><td>69.86/ 0.32</td><td>650</td><td>1,8</td><td>Warp</td><td>1 T<sub>uncoated</sub>- 1 TCSBR-1</td></tr></tbody></table>

molds made of plywood as shown in Fig. 3. The plywood molds were nailed with wooden strips for acquiring the desired thickness.

The plates were wet cured for 7 days, and afterwards, they were stored in relative humidity of approximately 50 % for 21 days. The 7 days of wet curing was adopted to reduce the associated shrinkage and curving of the TRMs. After 28 days, a wet saw was used to cut 3 samples each of 650×70 mm. All the edges of the plates were removed in width of 20 mm to eliminate any weaknesses generated from mold plate interaction during manual lamination process. Before finally tested, the

specimens were stored for 60 more days (90 days in total) at 25 C° and relative humidity of about 50 %.

## 2.4. Tensile test setup and DIC

The tensile tests in this study were performed with a bolted clamp setup (shown in Fig. 4) as recommended in RILEM TC-232-TDT. Each clamp was 100×200 mm with 8 bolts for gripping the TRM. Rubber pads were placed between the clamps and the TRM surface to mitigate its susceptibility to bearing failure. The TRMs were carefully centered in the clamp's width. This was necessary to reduce any in-plane effects rooted in sample's misalignment.

The clamps were connected to the loading machine through spherical ball joints to reduce the transfer of parasitic moments. The adopted Wolpert tensile loading machine (having maximum capacity of 100 KN) was operated in displacement control. A displacement rate of 0.5 mm/min was used.

For consistency, the top surface of the composite (during lamination) was always adopted for DIC measurements while LVDT was attached on to the second face (always the one in contact with mold). This permitted to calculate average strains to cater for any deformation induced by out of plane bending, possibly caused by misalignment of the composite in the clamps and/or curvature in the TRMs due to shrinkage [27]. Stereo DIC was conducted using two cameras of 5 mega pixels. For measurement consistency, the process of DIC was supported by a light source of uniform luminosity. The images were acquired at frequency of 2 Hz.

The acquired images were postprocessed with a software MatchID. The gage length of the TRM was discretized into subsets of size 45 × 45 pixels at a step size of 15 pixels. This permitted a good tradeoff between the accuracy and the associated computation time. Both the subset shape and cross camera matching was represented by quadratic functions. The full field deformations from DIC were further processed with MATLAB. Lastly, it is important to mention that the outputs of the DIC were used to identify the evolution of cracking during the tensile test [28,29].
<figure><img src="image_4.png" /><figcaption>Fig. 2. Representation of the studied rectangular TRM samples.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Representation of the lamination approach for manufacturing one-layer TRMs.</figcaption></figure>

## 2.5. AE Setup

After mounting the sample in the clamps, two AE sensors of 150 kHz were attached on the TRM's surface one cm away from each clamp (Fig. 4). The use of 2 sensors at the ends of the gage length allowed to acquire, at the same time, the full field view of the rest of the TRM surface for DIC investigation. The sensors were maintained in place during the test with the help of elastic bands. Silicone gel was used between the surface of TRM and AE sensors to ameliorate the acoustic coupling. AEWIN (Mistras) was used for acquisition. A threshold of 35 dB and amplifier (ILxxS) gain of 40 dB was adopted. The threshold level was set such that no noise generated hit were recorded before the initiation of the test.

Pencil break approach was used to adjust the parameters of the test. This led to PDT, HDT and HLT 200, 400 and 1000 µsec respectively. The waveforms were recorded for 1500 µs. A wave velocity of 3500 m/s was adopted during the test.

# 3. Results and discussion

## 3.1. Stress-strain response

The tensile stress strain response of the tested TRMs is shown in Fig. 5 [29]. The three tested samples of each TRM type demonstrated good repeatability of the tensile behavior. The TRMs showed a triphasic response as observed in the literature [1]. The three phases/zones recorded were 1) pre-cracking, 2) cracking zone (strain hardening) and 3) the post cracking zone [1]. In accordance with the established literature [30], the first observation showed that the use of polymer coating significantly improved the ultimate strength of the TRMs. Similarly, 2 layers of TCSBR textile in T2M resulted in strength 1.43 times of T1M [31]. The ultimate strength of ThM was 1.24 and 0.63 times of the ultimate strength of TunM and T1M respectively. TunM demonstrated highest ultimate strains and longest cracking phase due to the presence of crimp in the textile parallel to load direction. The use of a TCSBR layer with Tunocated layer reduced the observed strains in ThM compared to TunM.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Description of the adopted test setup.</figcaption></figure>

## 3.2. Failure modes

The failure observed for the tested TRM configuration was classified in to the following three categories:

- Mode A: Textile breakage near clamp or in gage length

- Mode B: Textile breakage with noticeable textile slip

- Mode C: Textile breakage accompanied by slip and local delamination

The observed failure modes are illustrated in Fig. 6. The common failure mode among the tested TRMs was textile breakage. TIM and T2M failed due to brittle textile breakage (Mode A). Additionally, one sample of T2M showed minor local delamination. TunM was associated with limited telescopic slip followed by brittle partial textile rupture. On the other hand, ThM demonstrated lesser slip than TunM before failure by textile rupture. ThM also showed local delamination but more severe than T2M that is in accordance with the study of [32]. The delamination in ThM was observed at the TCSBR textile mortar interface.

## 3.3. DIC and crack identification

The cracks on the TRMs surfaces were identified with the help of DIC. A representation of the displacement fields (normalized by ultimate displacement) corresponding to 50 % of the ultimate load is given in Fig. 7 for the studied TRM configurations. The vertical jumps in the displacement fields demonstrate crack openings, while the distance between the jumps represents the crack spacing.

Following steps were adopted to precisely locate the cracks (in time) for the supervised learning process. Both the actual image of the TRM specimen and the corresponding displacement field were used to be precise about the instant of cracking event.

a) In the first step, all the cracks were identified in the TRM picture and/or displacement fields corresponding to the instant just before the peak load.

b) In the second step, each individual crack was tracked backwards (towards the initial stages of the test) to identify the instant of the crack formation.

Note that no automatic or threshold-based approach was suitable as the purpose of this identification was to develop accurate information about the cracking instant, which served the purpose of labelling the dataset for the supervised learning process.

## 3.4. Hit/Hit rate vs. Load time curve

The evolution of normalized load, cumulative hits and hit rate (1/s) with time is demonstrated in the Fig. 8. The load, cumulative hits and hit-rate were normalized by their corresponding maximum values to facilitate visualization. The presented data for hit and hit rates in Fig. 8 shows the average trend observed for these parameters.

Globally, the cumulative hit-time curve followed the evolution of the normalized load-time curve. This showed that the buildup of damage was closely represented by the cumulative number of hits.

The observation from Fig. 8 demonstrated the presence of observable hits and hit-rates in the pre-cracking phase, which goes in accordance with [22]. The existence of hits in the pre-cracking phase were contributed by the micro scale damage. After the micro scale damage, a peak in the hit rate was observed during the cracking phase/2nd phase, simultaneously with major load drops. This observation was identical among the studied TRMs. [21] demonstrated similar evolution of hit rate for 2D textile based TRMs. In the post cracking phase/3rd phase, the hits accumulated at a lower rate compared to the observed peak during the cracking phase. On average, the absence of the peak hit rates in post cracking might be related either to 1) the more severe/intensive nature of the cracking damage compared to fiber damage, local slip or debonding or 2) the gradual deterioration of transmission conditions in the post cracked/damaged composites. Lastly, the post cracking phase of T2M was populated in larger hit rates compared with the rest of the
<figure><img src="image_7.png" /><figcaption>Fig. 5. Stress-Strain response of the tested TRMs a) T1M, b) T2M, c) TunM and d) ThM.</figcaption></figure>

TRMs. This can be attributed to the comparatively strong debonding propensity between coated textile layers or the possible partial breakage of yarns.

* Frequency partial power: The frequency partial powers were defined as FREQPP1 (0–40 kHz), FREQPP2 (40–80 kHz), FREQPP3 (80–120 kHz) and FREQPP4 (120–200 kHz).

## 3.5. AE parameters

The AE parameters based on the processed waveforms through AEWIN were obtained. The definition of the parameters is given in Fig. 9. More details on the AE parameters can be located in [33]. The parameters analyzed are further discussed:

* Rise time: The time required from first threshold crossing to the occurrence of amplitude (µs).

* Average frequency: The ratio of counts (number of threshold crossings) divided by duration (kHz).

* Energy (ENR/ENER): it's the scaled version of signal strength provided by AEWIN as output in µVolt-sec [33].

* Amplitude: The voltage of the highest cycle of a hit (V or dB).

### 3.5.1. Evolution of RA, ENR and AF

A derived parameter RA (rise time/amplitude) with average frequency (AF) has been used in the literature as a sensitive parameter for bifurcating tensile and shear damage in concrete ([11]). Smaller RA values with larger AF are more representative of tensile cracking. Meanwhile, larger RA values and lower average frequencies are dominant features during shear damage [34]. The trend of RA, AF, ENR and the corresponding load with time is shown in Fig. 10 for the tested TRMs.

The values of AF, RA and ENR showed fluctuations throughout the test which points towards the coexistence and the interaction of different damage modes in TRMs. Globally, a slightly increasing trend in the RA was observed with increasing time (especially compared to the
<figure><img src="image_8.png" /><figcaption>Fig. 6. Observed failure modes for TRMs; a) TunM, b) T1M, c) T2M and d) ThM.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Representation of normalized displacement fields corresponding to 50 % of the ultimate load for a) TunM, b) T1M, c) T2M and d) ThM.</figcaption></figure>

beginning/pre-cracking phase of the test). On the contrary, a decreasing tendency in the average frequency was recorded with the progression of the test. Both RA and ENR were associated with explicit peaks, while both upward and downward fluctuating shifts were observed in the average frequency. The global tendency of RA and AF followed the increasing propensity of TRMs towards slip especially in the cracking and post cracking regions [22].

The plotted vertical dashed line shows the time of first observable crack on the TRM as obtained from DIC. For T1M the identified crack

showed a peak in AF with a dip in RA. This was directly followed by a downward shift in the AF, which implicates the possibility of sudden slip after crack opening. Identical drops in frequency after cracking were commonly identifiable among the tested TRMs. [19] reported such dips in frequency for TRM strengthened reinforced concrete (RC) beam. For TunM and ThM the associated first crack RA peak was more explicit, which can be explained by the propensity of noncoated textile TRMs towards larger slips, rooted in the 1) weaker core to surficial filaments interaction and 2) the straightening of crimp. The existence of
<figure><img src="image_10.png" /><figcaption>Fig. 8. Evolution of normalized load, hit-rate and cumulative hits with time a) T1M, b) T2M, c) TunM and d) ThM.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Representation of the AE features [22].</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Evolution of AE features and normalized load with time for a) T1M, b) T2M, c) TunM and ThM.</figcaption></figure>

comparatively larger and multiple RA peaks in TunM and ThM compared to T1M and T2M further strengthened the proposition of larger susceptibility of noncoated textile based TRMs towards slips. It is important to mention that the slips can be exacerbated by the breakage of surficial filaments in case of the noncoated textile. Lastly, the presence of a RA peak at ultimate load and textile breakage, for instance, in T2M can point towards the slip of the textile through the mortar (for sure the interfilament slip is also a contributing factor).

Similar observations were made for the associated energy peaks (ENR). TunM and ThM showed multiple and larger energy peaks unlike T1M and T2M. The associated energy peaks are well aligned with the

observed load drops in Fig. 10. Qualitatively, the significance of energy peaks was associated with the overtness of load drops which may show that the effectiveness of redistribution of efforts determine the relative severity/scale of damage.

A common observation among the tested TRMs showed the existence of larger energy peak at the textile breakage (ultimate stage) Fig. 10. This explicit peak was present corresponding to the ultimate textile break of T1M and T2M. By this observation, one can argue that the existence of significant energy peaks throughout the test in TunM and ThM (unlike T1M and T2M) might correspond to the breakage of individual surficial filaments which is more likely due to the weaker
interaction of the core and outer filaments in noncoated textiles. However, it must be considered that various damage mode coexists in TRMs, and the energy peaks might be co-contributed by delamination or debonding. Yet, in the post failure observation no delamination was identified for TunM which showed identical energy peaks (before ultimate stage) to ThM (which had local delamination). Nonetheless the lower propensity of TunM to delamination compared to T2M and ThM makes it more probable that the abundant energy peaks corresponded to textile breakages. It is paramount to reiterate that slip and breakage may not be independent. Filament break can lead to further slips to ensure the required textile stretch and redistribution of efforts.

### 3.5.2. Ib-value analysis

The concept of Ib value analysis is a sophistication over the traditional Guttenberg ricter law, also known as b value-based analysis (in other engineering domains [12]). The “b value” in seismology is the slope of a straight line fitted to the earthquake magnitude and its cumulative exceedance relationship. In applications for assessment of structural damage, the magnitude is replaced with amplitude, which is sensitive to the fracture phenomenon. However, it should be noted that the linear fit is an approximation to the amplitude-cumulative hit relation, which might be nonlinear [12]. Therefore, a sophisticated Ib value was adopted that considers the stochastic parameters of the amplitude distribution. Previous studies have identified the sensitivity of Ib values in case of FRP, concrete and steel structures [10,12,13]. High Ib values have been associated with micro damage while lower Ib values have been considered representative of macro damage. The reduction in the slope of amplitude and cumulative hit exceedance relation (decrease in

Ib value) demonstrates the abundance of high amplitude hits compared to lower amplitude. This allows for assessing the presence of a macro damage phenomena. The exact definition of micro and macro might be relative and application dependent. However, as an example, macro scale matrix cracking and local fiber damage can be respectively considered as the representation of macro and micro damage [13].

In this study, the Ib values were computed over all the recorded hits, without any filtering based on frequency. Like the study of [13], frequency-based filtering before computing Ib values can provide a first guess on the expected damage source. However, as a first study on TRMs to assess global sensitivity of Ib value no frequency based filtering was adopted due to its extended scope. The observed hits were however filtered based on the recorded duration and the hits corresponding to zero duration were removed. Zero duration hits might be contributed by reflections, which are expected phenomena in thinner and cracked TRMs.

The Ib values were obtained as per the following relations also adopted in [12]. The calculation was performed for a group of 100 hits with a lag of 50 hits.

$$Ib = 20 \times \frac{\log(N_1) - \log(N_2)}{z_2 - z_1}$$

$$\text{where } z_1 = (\mu - \alpha \times \sigma), \text{ and } z_2 = (\mu + \alpha \times \sigma)$$

While $N_1$ and $N_2$ represents total number of hits with amplitude greater than or equal to $z_1$ and $z_2$ respectively. $\alpha$, which is the range parameter, was considered equal to 1 in this study. While $\mu$ and $\sigma$ are respectively the mean and standard deviation of the hit's group under consideration.

<figure><img src="image_13.png" /><figcaption>Fig. 11. The evolution of Ib value and normalized load with time for a) T1M, b) T2M, c) TunM and d) ThM.</figcaption></figure>
The evolution of the calculated Ib values for the studied TRMs along with the normalized load time curve is depicted in Fig. 11. The vertical dotted lines are used to provide identification of the three zones (in the stress strain behavior Section 3.1). Globally, the Ib values of TCSBR based TRMs (both T1M and T2M) maintained higher values compared to TunM and hybrid ThM. This might point towards the relative nature of the definition of the macro and micro scale damage. As obvious from the load drops in TunM and ThM, the effort redistribution was not as robust as T1M and T2M. Therefore, the Ib values of TunM and ThM were relatively lower. The lower Ib values of ThM and TunM suggested propensity towards a “relatively” macroscopic phenomena. It is important to reiterate that the terms microscopic and macroscopic are used in relative sense, not strictly referring to the scale of the damage, but to its influence of the TRM, for instance, in terms of efforts redistribution.

The starting Ib value in the linear phase was 0.9, 0.98, 0.83 and 1.01 respectively for T1M T2M, TunM and ThM. In relative sense, the lower Ib values in first zone of T1M and TunM implicates a macro phenomenon. This trend was well corelated with minor fluctuations in the load time curve of T1M and TunM, otherwise absent for T2M and ThM. The lowest Ib value of 0.58 and 0.73 was recorded in the cracking zone for TunM and ThM, respectively. While the smallest Ib value of 0.86 for T1M and 0.90 for T2M was located in the 3rd phase of the response.

A common observation among the tested TRMs showed a drop in Ib value in the second zone of the tensile response. For TunM and ThM, the fluctuation of Ib values suggested the relatively strong coexistence and interaction of micro and macro damage mechanism in the 2nd zone. A clear explanation was sought by closer observation of ThM Fig. 11d. At the first load flick (relatively smaller), just after 200 sec a drop in Ib value was noticed. The load flick was followed by increase in both the load and Ib value. The rise in the Ib value can be regarded as the accumulation of micro phenomena, which acted as a precursor of the macro damage. The 2nd load drop (the formation of another crack) showed a sudden dip in the Ib values. This observation explained the good sensitivity of Ib values to damage in TRMs.

After the second phase, Ib values of both T1M and T2M increased (accumulation of micro damage) before decreasing towards the end of the test. It is worth mentioning that for coated textile based TRMs the cracking process can well be resumed in to the early 3rd phase [27,35]. However, the 3rd phase cracking is kind of soft micro cracking (in between the established cracks) initiated by the mobilization of the transverse yarns. Additionally, the relative sense of the micro and macro damage needs to be considered, as the redistribution of efforts among textile and mortar is already established and robust compared to the 2nd phase. For ThM and TunM, the Ib values maintained the fluctuating behavior after the cracking phase. The fluctuation in Ib values in the 3rd phase of the response demonstrated the simultaneous coexistence of

dominating micro and macro processes. However, it should be noted that these macro processes might correspond to the breakage of textile, significant slips and debonding but not cracking (in TunM and ThM).

This study showed the different sensitivity of Ib value to the different types of TRMs. Further studies on micro scale are needed to bolster the relevant Ib patterns related to non-cracking type of damage. Additionally, its sensitivity can be assessed for the cases like fatigue, where it may prove a suitable differentiating parameter.

### 3.5.3. Zone identification

In Ref. [22] a single averaged value of (RA, AF) pair was used for the identification of the three zones of the TRMs in the tensile response. According to their study, progressive decrease of frequency (and increase of RA) was observed from zone 1(Z1) to zone 2 (Z2) and zone 2 to zone3 (Z3). In this study, a randomly selected group of at least 100 hits from each zone was averaged to identify the trends already observed by [22] for glass textile TRM. It is important to mention that the observed global trends were insensitive to the number of selected hits in a particular zone. The RA and AF values for the 4 types of TRMs and the three zones are plotted in Fig. 12a. The data showed an overlap of zone 2 with both zone 1 and zone 3. As the linear zone (Z1) is susceptible to micro cracking, shifts in frequencies are possible to occur. This led to overlap of the RA-AF pair of zone1 and zone2. The intersection of zone 2 and zone 3 can be explained by the coexistence of various damage mechanisms common to Z2 and Z3. Furthermore, it was observed that the largest average RA values for ThM and TunM were located in Z2. This behavior corresponds well with the sudden slip and larger initial crack opening of noncoated textile based TRMs due to its weaker inter-filament interaction. Unlike the study In Ref. [22], a consistent trend in the RA AF pair was not observed, especially, when different TRM configurations were observed. However, and although with limited margin, but an explicit separation between the RA- AF pair of Z1 and Z3 was identified. A line with a slope of 120 kHz/(µ.sec dB) in the RA-AF space was used to mark the separation among Z1 and Z3 as shown in Fig. 12b.

It can be noted that TRMs due to the complex damage modes and textile-mortar interaction does not always allow classification of various processes by a simple classifier.

### 3.6. Crack / non-cracking major damage and predictive modelling

Considering the sensitivity of AE features to damage process makes it an interesting tool for maintenance and operation of structures. Information obtained through AE monitoring can be used to identify the occurrence of damage in systems. Various approaches already exist to differentiate the type of damages based on AE features. For instance,

<figure><img src="image_14.png" /><figcaption>Fig. 12. AF and RA values for the 4 types of TRMs corresponding to a) the three zones b) for zone1 and zone3.</figcaption></figure>
RILEM proposed AF-RA pair to bifurcate the tensile crack and other types of cracking damage [11]. Similarly, unsupervised learning has been adopted to identify clusters in AE feature space, and associate them to damage types based on frequencies [20]. In TRMs various damage mode coexists and a more deterministic identification of a particular damage mode still requires further understanding of the complex interaction among damage modes and their influence on representative AE features. The use of a simpler linear classifier does not always permit the separation of different damage mechanisms.

Although the grouping obtained through clustering provides an initial guess on the type of the damage but without the certainty of the proposed type of deterioration. The increased probability of correct identification of a particular damage / deterioration type can lead to efficient and robust maintenance operations. The use of DIC coupled with AE provided an opportunity to take a step towards enhancing the prediction certainty. DIC permitted to identify cracking independently from the corresponding AE features. Therefore, to this end an effort was made to separate cracking and non-cracking major/significant damage in TRMs under tension with a supervised approach where the separation between the two mentioned classes is based on labeled data rather than assumed frequency range. Additionally, this study is a step towards (in TRMs) identifying surface damage with improved certainty by excluding the need for cameras, where they are used in zones not readily/routinely accessible (in the laboratory, and ultimately in-situ). The global approach adopted herein for dataset extraction and its use in the modelling is shown in Fig. 13.

### 3.6.1. Data extraction

In order to prevent the scenario of strongly imbalanced classes and also to reduce the computation time, only AE features corresponding to cracking events and major non-cracking events (these might have been 1) textile breaks, 2) significant slip or 3) significant debonding) were considered. For this purpose, the features corresponding to cracking were identified by correlating the DIC time for cracking (as mentioned in Section 3.3) with the corresponding AE time. Meanwhile, the non-cracking major damage was marked as distinctive peaks in RA values.

It is important to mention that the peaks were identified based on RA 1) due to its established sensitivity as per the literature and 2) its sensitivity as noticed by the authors (for instance every identified crack on DIC demonstrated a corresponding RA peak). The peaks were distinguishable from the average of a particular group and were readily identified (See the shaded region in Fig. 14a along with examples of peaks corresponding to cracking and non-cracking events, which also included textile breakage). On average, values of RA above 5% of the peak RA values were identifiable as distinguished major damage peaks in the recorded RA data. The value of 5% and above permitted to include the observable peaks including all the AE peaks corresponding to the instant of cracking. Moreover, it established a balanced dataset for the separation/identification of cracking based on AE features, preventing the underrepresentation of the crack class". The features corresponding to each crack and non-cracking peaks were averaged over the corresponding second at which the peak was observed. This allowed to consider the hits just before and after the peaks and to avoid a very local measurement (which would have been the case if only the peak values corresponding to a microsecond was considered). This led to a dataset with 183 observations. It has been reported in [36] that the number of observations required for building machine learning model can be judged by comparing it to the features under consideration. The number of observations should be at least 3–5 times the number of features, which was the case in this study. However, as per [36] this rule is flexible depending upon the scenario/application under consideration. In Fig. 14b the plot of AF and RA is shown for the recorded cracking and non-cracking classes. The non-cracking classes may correspond to textile breakage, delamination or instantaneous large slips. The RA values of class non-crack were skewed as most of the RA values of non-crack class were below 15 µs/dB. The data were skewed towards larger RA values, which may influence the classifier's thresholds, however, preventing overlap with the RA values of cracking class. Additionally, the trained SVM model, for instance, can handle such outliers satisfactorily [37]. Therefore, because of the above-mentioned aspects and the satisfactory performance of the trained models this aspect was not addressed explicitly.

<figure><img src="image_15.png" /><figcaption>Fig. 13. Flowchart of data extraction and its use in modelling.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 14. An example of the peak identification from RA/number of cracks vs time (a). AF vs RA of the identified peaks for all the TRMs (b).</figcaption></figure>

### 3.6.2. Predictive models-workflow

In this study three types of models; decision trees, K-nearest neighbors (KNNs) and support vector machines (SVMs) [36] were evaluated for classification of the cracking and non-cracking major damage. Additionally, the tree models were primarily used for feature selection. The hyperparameters of the models were optimized using a built-in Bayesian optimization algorithm in MATLAB. The global modelling process consisted of splitting the data in to training and test set in a ratio of 80–20 % respectively [36]. The training data was used for training the model with 5-fold cross validation along with the optimization of the model’s hyperparameters. The adopted modelling workflow is demonstrated in Fig. 15.

### 3.6.3. Decision trees

Decision trees are hierarchical tree shaped algorithms. The structure of a decision tree is composed of root nodes, decision nodes and leaf

nodes [38]. The dataset is split at decision nodes using a statistical criterion to minimize the impurity at each node, for instance minimizing Gini diversity index. The final decisions are displayed at the leaf nodes.

In order to avoid overfitting, the fineness of the tree was controlled through the allowable number of maximum splits. Furthermore, coarse trees are simpler to explain compared to fine trees. The split criterion was part of the optimization process. The Gini diversity index ($Gi$) and the maximum deviance ($D_{ev}$) is given by [38]:

$$Gi = 1 - \sum_{i}^{nc} p_{i}^{2} \qquad (1)$$

$$D_{ev} = - \sum_{i}^{nc} p_{i} (\log_{2} p_{i}) \qquad (2)$$

Where $p_i$ is the probability of class “i” at the node under consideration.

<figure><img src="image_17.png" /><figcaption>Fig. 15. Workflow of the predictive modelling.</figcaption></figure>
The summation is over the total number of classes “nc”. Gi and D<sub>ev</sub> takes the value of 0 for a node with no impurity (only single class).

### 3.6.4. KNNs

In KNNs the classification is based on identification of the majority class among “K” nearest neighboring observations [39,40]. The distance metric to identify the nearest neighbors was part of the optimization process. The minimum number of neighbors were restricted to 11 to prevent against overfitting.

### 3.6.5. SVMs

SVM are suitable algorithm for multi feature based binary or multi class classification [40]. SVM defines a hyper plane through the feature space to categorize the different classes. The hyperplane is adjusted to maximize the boundary between the datapoint (support vectors) of the different classes. SVM allows for soft margins which permits certain non-separable data points to violate the margins. In order to obtain the desired hyperplane and allow for nonlinear boundaries, a kernel function was used to transform the feature domain. Kernel function was adopted as process of optimization. A classifier for feature space X and a binary class output “yi” can be written as [41].

$$Y = \text{sign}(\sum y_i \alpha K(X_i, X) + b_0) \qquad (3)$$

A polynomial kernel function is given by [42]:

$$K(X_i, X_j) = (r + \gamma X_i' X_j)^d, \text{ for } \gamma > 0; \qquad (4)$$

where r, γ and d are kernel's parameters.

### 3.6.6. Metrics

Different metrics were adopted to evaluate the performance of the models. Accuracy (Eq.5) which is the measure of correct predictions out of the total observation is not always a perfect evaluation metric for classification problems as it is sensitive to class imbalance [43]. Additionally, to assess the model's prediction capability for each respective class different metrics in combination with accuracy were adopted, in accordance with the established literature [40]. For a binary classification (as in this study), with equal importance placed on each class, true positive rates and false negative rates for each class was used as evaluation metric. Confusion chart in Fig. 16 is shown for representation of the discussed metrics. In this study, true positives (TPs) refer to accurate

predictions while false negatives (FNs) refer to wrong predictions on any of the two classes.

$$\text{Accuracy} = \frac{\sum_{i}^{nc}(TP_{s(i)})}{\sum_{i}^{nc}(TP_{s(i)} + FN_{s(i)})} \qquad (5)$$

While the summation in Eq. (5) is over the number of classes True positive rate (TPR):

$$TPR(i) = \frac{(TP_{s(i)})}{(TP_{s(i)} + FN_{s(i)})} = 1 - FNR(i) = \frac{\text{True cracks (or non cracks)}}{\text{all cracks (or non cracks)}} \qquad (6)$$

False negative rate (FNR):

$$FNR(i) = \frac{(FN_{s(i)})}{(TP_{s(i)} + FN_{s(i)})} = 1 - TPR(i) = \frac{\text{False cracks (or non cracks)}}{\text{all cracks (or non cracks)}} \qquad (7)$$

Where TPR (i) and FNR (i) is respectively the true positive rate and false negative rates of class “i”.

### 3.6.7. Data Set

In order to observe the multi feature space, a parallel coordinate plot was used as shown in Fig. 17. The definition of the features can be found in Fig. 9 and in [33]. Each line on the plot in Fig. 17 connects the feature values corresponding to the same observation. The units were not pasted on the plot to avoid obscuring the trends. The data in the plot was grouped by the type of damage. Qualitatively, it was observed from Fig. 17 that the cracking and non-cracking events demonstrated separate clustering in Rise time (RISE), Counts (COUN), energy (ENER/ENR), duration (Dur) and amplitude (Amp) features. While additional overlap between the frequency partial powers (FREQPP3, FREQPP4), frequency centroid (FRQ-C) and peak frequency (P-FRQ) features was observed among the 2 classes.

### 3.6.8. Feature space and feature selection

Combination of filtering and embedded approach was used to select the most important features for predictive modelling. Considering multiple number of features, the correlation among features was evaluated using spearman correlation coefficient [37,40]. This approach allowed for the identification of feature interdependence and the possibility of dimensionality reduction as the redundant features do not add independent value to the output (and might adversely influence the model's performance) [44]. The spearman coefficient, unlike Pearson correlation coefficient, permits the identification of both linear and nonlinear correlations [37]. The spearman correlation coefficient among feature “a” and feature “b” with distinct ranks is given by:

$$r(a, b) = 1 - \frac{6 \sum d^2}{n^3 - n} \qquad (8)$$

While d is the subtraction among ranked features for a particular observation, and “n” is the number of observations in the dataset.

The correlation coefficients are given in Fig. 18. It was observed that certain features were strongly corelated. For instance, RA values were strongly corelated to rise time, amplitude, counts and energy. The observation based on these correlations identified the prospect for reducing the feature space using informed decision.

Before the process of feature reduction, the feature space was populated with the labels for each TRM type to introduce features which explicitly relate to the difference contributed by the nature of TRM. This was achieved with the help of one-hot encoding approach [45,46]. As per this approach the use of a true value (1) for a TRM to which the observation belongs and a false value (0) for the rest of the three TRM labels was considered.

<figure><img src="image_18.png" /><figcaption>Fig. 16. Adopted confusion matrix in this study.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. 17. Parallel coordinate plot of the dataset separated by class.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 18. The observed correlation coefficient among the AE features.</figcaption></figure>

<table><caption>**Table 4**
The observed classification metrics for the cracking and non-cracking class.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Model</th><th rowspan="2">Model Feature</th><th rowspan="2">Acc</th><th colspan="2">Crack</th><th colspan="2">Non-Crack</th><th colspan="2">Crack</th><th colspan="2">Non-Crack</th></tr><tr><th>TPs</th><th>FNs</th><th>FNs</th><th>TPs</th><th>TPR</th><th>FNR</th><th>TPR</th><th>FNR</th></tr></thead><tbody><tr><td rowspan="6">Validation Set</td><td>Tree1</td><td>All</td><td>84,40 %</td><td>62</td><td>15</td><td>8</td><td>62</td><td>80,52 %</td><td>19,48 %</td><td>88,57 %</td><td>11,43 %</td></tr><tr><td>Tree2</td><td>Reduced</td><td>89,80 %</td><td>69</td><td>8</td><td>7</td><td>63</td><td>89,61 %</td><td>10,39 %</td><td>90,00 %</td><td>10,00 %</td></tr><tr><td>SVM1</td><td>Reduced</td><td>85,70 %</td><td>68</td><td>9</td><td>11</td><td>58</td><td>88,31 %</td><td>11,69 %</td><td>84,06 %</td><td>15,94 %</td></tr><tr><td>KNN1</td><td>Reduced</td><td>83 %</td><td>68</td><td>9</td><td>16</td><td>54</td><td>88,31 %</td><td>11,69 %</td><td>77,14 %</td><td>22,86 %</td></tr><tr><td>SVM2</td><td>All</td><td>84,40 %</td><td>67</td><td>10</td><td>13</td><td>57</td><td>87,01 %</td><td>12,99 %</td><td>81,43 %</td><td>18,57 %</td></tr><tr><td>KNN2</td><td>All</td><td>79,60 %</td><td>61</td><td>16</td><td>14</td><td>56</td><td>79,22 %</td><td>20,78 %</td><td>80,00 %</td><td>20,00 %</td></tr><tr><td rowspan="6">Test Set</td><td>Tree1</td><td>All</td><td>75 %</td><td>12</td><td>7</td><td>2</td><td>15</td><td>63,16 %</td><td>36,84 %</td><td>88,24 %</td><td>11,76 %</td></tr><tr><td>Tree2</td><td>Reduced</td><td>77,7 %</td><td>14</td><td>5</td><td>3</td><td>14</td><td>73,68 %</td><td>26,32 %</td><td>82,35 %</td><td>17,65 %</td></tr><tr><td>SVM1</td><td>Reduced</td><td>86,10 %</td><td>16</td><td>3</td><td>2</td><td>15</td><td>84,21 %</td><td>15,79 %</td><td>88,24 %</td><td>11,76 %</td></tr><tr><td>KNN1</td><td>Reduced</td><td>88,88 %</td><td>17</td><td>2</td><td>2</td><td>15</td><td>89,47 %</td><td>10,53 %</td><td>88,24 %</td><td>11,76 %</td></tr><tr><td>SVM2</td><td>All</td><td>86,11 %</td><td>17</td><td>2</td><td>3</td><td>14</td><td>89,47 %</td><td>10,53 %</td><td>82,35 %</td><td>17,65 %</td></tr><tr><td>KNN2</td><td>All</td><td>69,40 %</td><td>13</td><td>6</td><td>5</td><td>12</td><td>68,42 %</td><td>31,58 %</td><td>70,59 %</td><td>29,41 %</td></tr></tbody></table>
### 3.6.9. Feature importance

The feature selection was further made with the help of embedded approach. For this purpose, an optimized tree model was used to compute the score of each feature. All the models trained in this study with the obtained metrics are shown in Table 4. The Tree model for feature selection (Tree1) had accuracy of 84.4 %, FPR and FNR of 80.5 %, 19.5 % (for class crack) respectively (on validation set). Visualization of model Tree1 is given in Fig. 19. The model was simple to comprehend due to the coarse nature of the tree. The first split was made based on energy followed by amplitude before reaching the leaf nodes. On the second branch, the first split was followed by a decision based on frequency partial power 1 and risetime, respectively, before the leaf node.

Feature importance was computed by adding the modifications in the node risks (R) due to split based on each feature divided by the total number of the decision nodes (N<sub>d</sub>). The modification in the node risk was calculated as the difference in the risk between the parent node (A) and the accumulated risk of the children nodes (B and C). For a single split, by a feature, of a parent node to two children node the feature's score was augmented by:

$$ \Delta S = \frac{R_A - (R_B + R_c)}{N_d} \qquad (9) $$

Whereas,

$$ R_j = P_j \times G_{ij} \qquad (10) $$

While P<sub>j</sub> is the node's probability and G<sub>ij</sub> is the impurity at the node "j".

From the feature importance plot in Fig. 20, it was observed that Energy, Rise time, frequency partial power1 and amplitude (in that order) contributed to the model's prediction. It is worth noting that the labels included for the type of TRM did not demonstrate any relative importance. The absence of relative importance does not necessarily imply the absence of causality. However, the impact of TRM type might be more sensitively captured by the AE features, especially, for the non-cracking class. For the cracking class, the impact of TRM type might actually be insignificant due to similar mortar irrespective of the TRM type. Only the 4 important features were kept for further predictive modelling.

### 3.6.10. Model results

The metrics for validation and test set of the three types of models (Tree, SVM and KNN) are given in Table 4. For each case, a pair of models with only four selected features and all the features was

<figure><img src="image_21.png" /><figcaption>Fig. 20. Feature importance plot based on Tree1 model.</figcaption></figure>

evaluated. As observed from the given accuracies, the involvement of all the features did not lead to improvement in the model's performance. In fact, for tree models the validation set accuracy declined from 89 % to 80.5 % when all features were used (Tree1) instead of the selected features (Tree2). Similar observations were made for KNN1 (selected features) and KNN2, where KNN1 maintained 88.3 % accuracy compared to 79 % accuracy of KNN2. For SVMs, no significant change in the accuracy was noticed when reduced or all features were adopted.

The evaluation of Tree2, SVM1 and KNN2 (all with 4 features) is given in Fig. 21 in the form of confusion matrix. The confusion matrix for both the validation and test set is given in order to comparatively observe the performance of the models based on training and unseen test data.

Tree2 demonstrated accuracy of 89.6 % on the validation set while both SVM1 and KNN1 showed accuracy of 88.3 % on the training data. When tried on the test data the accuracy changed to 77.7 %, 86.1 % and 88.88 % respectively for Tree2, SVM1 and KNN1. This can be rooted in the less general compared to SVM1 and KNN1. This can be rooted in the discrete set of limited rules upon which the tree model was based. Maintaining accuracy (SVM1) or it's improvement (KNN1) on the test

<figure><img src="image_22.png" /><figcaption>Fig. 19. A view of the trained Tree1 Model.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Fig. 21. Confusion matrix for a) Tree2, b) SVM1 and c) KNN1 models.</figcaption></figure>

data does not necessarily implicate improvement of the model's performance for accurate prediction of both classes. Better accuracy on the test data might come from enhancement of the classifier for a single class, where it can mask the possible misclassification of the second class. Therefore, the classification capability for each individual class was compared.

Observation on the True positive rate (TPR) showed that from validation to test data the TPR for crack class changed from 89 % to 73 %,

88–84 % and 88–89 % respectively for Tree2, SVM1 and KNN1. Similarly, the FNR for crack class modified from 10.3 % to 26.3 % 11.6–15.7 %, 11.6–10.5 % for Tree2, SVM1 and KNN1, respectively.

For the non-crack class, Tree2 model had TPR of 82.3 % and FNR of 17.6 % on test data compared to TPR of 90 % and FNR of 10 % based on training data. For both SVM1 and KNN1, respectively, the TPR of non-crack class improved from 84 % and 77.1–88.2 % when test data was used in place of training data. Similarly, the FNR of non-crack class for
SVM1 and KNN1 reduced from 15.9% to 11.7% and 22.8–11.8% (respectively) from validation to test set.

Analysis of the TPR and FNR of both the classes showed that SVM and KNN models demonstrated superior performance or generality compared to the tree model. Based on TPR and FNR modification from training data to test data for crack and non-crack class, the lowest performance was observed for decision trees. The compromised performance of Tree2 can be attributed to the finite and discrete nature of rules adopted for classification.

### 3.6.10.1. Explainability- PDPs.
As observed from the classification metrics that the most stable classification performance was demonstrated by KNN and SVMs. Both models were further explored with partial dependence (PDPs) to assess the sensitivity of the models to feature perturbation. While constructing PDPs, only the features under consideration were perturbed and the remaining features were assumed to be stagnant. For PDPs no interaction or correlation among the features is considered [40]. The effect of all features, except the one under consideration, is averaged or marginalized for a particular class. PDPs due to the assumption of lack of correlation among features can lead to unrealistic or low probability instances. Therefore, its use beyond explanation purposes should be handled carefully. Moreover, in case of heterogenous relations among features and outputs, the PDPs can lead to misleading results. Heterogenous relations are the ones where part of a feature demonstrates direct relationship with the output, while some instances of that particular feature are inversely related to the output. For a classification model ($f_m$) the partial dependence (PD) is calculated based on the predicted scores of a class.

$$PD(X^i) = \frac{\sum_{j=1}^{N} f_m(X^i, X_i^C)}{N} \qquad (11)$$

In Eq. (11) $X^i$ is the feature space evaluated for partial dependence, and $X^C$ is the complement of $X^i$, which includes all the features except $X^i$. The scores are averaged over “N” observations of a particular class.

The PDPs for non-crack class based upon the two most significant features (rise time and energy) are given in Fig. 22. Both SVM1 and KNN1 demonstrated nonlinear evolution of cracking/non-cracking damage probability with Rise time and energy. As per the observed PDPs both SVM1 and KNN1 conveyed similar global meaning. Lower Rise time and Energy pairs were associated with low probability of non-cracking damage (or higher probability of cracking damage). Whereas high Rise time and energy pairs were related to higher probability of non-cracking damage (or low probability of cracking damage). The PDPs showed that the probability of non-cracking damage increased slowly

with increasing rise time and energy for SVM1. However, a rapid increase of non-cracking damage's probability was recorded by KNN1. This can be attributed to the nature of the classifier. As KNNs are based on nearest neighbors (min 11 in this study), which makes it more sensitive to capturing local trends, leading to the observed shape of PDPs. However, the global connotation based on PDPs for rise time and energy perturbation remained identical among SVM1 and KNN1.

The global observation from PDPs was in accordance with the general trends observed for rise time as the higher rise time was associated with non-cracking class. Similarly, larger values of energy, which may come from textile breakages, were also related to non-cracking classes. It is important to note that the observations obtained for classification through AE features needs to be tested further. The AE features are sensitive to experimental parameters, scale and distance effects. Lastly, the AE sensors are designed to be sensitive to the normal component of the vibration which means the AE features are susceptible to change even when obtained from same source and distance at sensors placed at different orientations [47].

## 4. Conclusion

This study evaluated the monitoring of acoustic emissions in TRMs. Various TRMs, made of noncoated, coated and hybrid textile layers were considered. The TRMs were subjected to tensile tests, which was supported with DIC to obtain information on the cracking evolution. The AE features corresponding to cracks were identified and distinguished from other peaks in RA values, which were contributed by major non-cracking damage. A supervised learning model was trained to predict cracks based on AE feature independently from DIC. Following were the main conclusions based on observations in this study.

* The normalized hit activity closely followed the evolution of the normalized load during the test. Higher hit rates were located during the cracking phase of the tensile response.

* The cumulative hit curve was sensitive to the occurrence of first damage in TRMs.

* The AE features was sensitive to damage during the test. RA showed a slightly increasing trend towards the end compared with the pre-cracking phase whereas decrease in the average frequency was recorded. The energy was populated with peaks for TunM and ThM, which may have been contributed by the textile damage.

* Ib values showed sensitivity to the occurrence of damage in TRMs. For instance, buildup of Ib value was noticed before crack formation followed by a drop.

<figure><img src="image_24.png" /><figcaption>Fig. 22. Partial dependence for non-crack class obtained from a) SVM1 and b) KNN1.</figcaption></figure>

<figure><img src="image_25.png" /></figure>
* The (AF,RA) pair identified for the three phases of the tensile response did not permit to separate the second zone from the other two zones. However, distinction between zone 1 and zone 3 was successfully made.

* The evolution of AE feature demonstrated that various damage modes and their interaction can coexist in the TRMs. The dominance of one mode (slip vs. textile damage) is dependent upon the textile, mortar and their combination.

* The SVM and KNN models provided satisfactory identification of cracking based on AE features independently from DIC. The feature selection process showed that no direct benefit was brought by introducing categorical features for the type of TRMs.

* In the reduced feature models, the TPR of crack class in the decision tree dropped from 89 % to 73 % when test data was used in place of training data. However, the SVM and KNN based models maintained their TPR of above 80 % when the validation data was replaced with test data.

The observations made in this study need to be further extended for different textile-mortar combinations. Additionally, the scale and distance sensitivity of AE features and its influence on the supervised learning approach needs to be evaluated further. A richer database on AE features of diverse configurations of TRMs can provide further insights in to developing surrogate thresholds for engineering purposes (for instance, energy parameter as seen in PDPs). Lastly, a richer database (with more data on cracking) will permit to analyze all the recorded AE observations without the peak based selection of the observations.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

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