Event identification in acoustic emission from wire breaks in pre-stressing/post-tensioning cables

Steel tendons commonly used in pre-stressed/post-tensioned concrete structural systems can lose cross-section due to corrosion, eventually leading to acoustic emission (AE) events when the stress exceeds the breaking strength of the wires that make up the tendons. Reliable differentiation of wire break AE events from traffic or grout crack events is critical for monitoring large structures, even where the distance between sensors may produce highly attenuated signals. In this paper, the Fuzzy c-means clustering algorithm was employed to differentiate AEs released from breaking wires of steel tendons from a database of 13464 AEs, including wire breaks, environmental and grout crack AEs. Wire breaks and grout crack AEs were collected from axial loading tests of grouted tendons in which the load increased until a wire broke. Environmental acoustic signals were collected from a bridge. Then all the collected AEs were gathered in a database and post-processed to simulate attenuation of up to 20 m from source to sensor. To optimize the speed and reliability of the Fuzzy c-means clustering algorithm, a non-dominated sorting genetic algorithm-II (NSGA-II) was used to find the minimum number of acoustic features needed. The NSGA-II algorithm started with 201 possible acoustic features and found 12 combinations of features that resulted in more than 80% wire break detection accuracy. In contrast, less than 3% of grout cracks and 0% of environmental signals were detected as wire breaks. The proposed method is suitable for deployment in a large sensor network and has sufficiently low-computational requirements for at-the-sensor processing, eliminating the need to send high-frequency sampled data outside the sensor node.


Introduction
Pre-stressed/post-tensioned concrete is one of the most widely used structural systems in bridge construction, and there are 150,000 pre-stressed concrete bridges in the USA alone [1].Unbonded or bonded steel tendons in combination with concrete or grout are the most commonly used reinforcing materials for pre-stressed concrete members.The composite system relies on tendons, which are pre-stressed or post-tensioned close (80%) to their ultimate strength [2,3].Steel, even encased in concrete, corrodes over time, and if the corrosion is sufficient, the stress within the tendons exceeds the breaking strength, and the wires that make up the tendon break [4][5][6][7].Moreover, some grouts used to encase tendons have been found to contain excessive levels of chloride that can increase the corrosion rate [8].Therefore, there is a critical need to detect wire breaks within pre-stressed/posttensioned concrete structures to ensure safety and optimize the maintenance of aging medium and long-span bridges.
There are various corrosion monitoring methods, including visual inspection, ultrasonic pulse velocity, electrochemical-based techniques, acoustic emission, strain monitoring, impact echo, and electromagneticbased methods in reinforced concrete structures [9][10][11].Among these methods, acoustic emission showed promising advantages like cost-effectiveness, high sensitivity, and real-time and continuous monitoring [6,[12][13][14][15][16]. Pre-stressed/post-tensioned tendons have considerable strain energy stored in them.When a wire in the processed to simulate attenuation of up to 20 m from source to sensor.A Non-dominated sorting Genetic Algorithm (NSGA-II) was used to select an optimized combination of acoustic features to feed into the clustering algorithm.This paper has been published as a chapter of the first author's PhD dissertation [38].

Tensile tests
To collect AEs from wire breaks and grout cracks, a static hydraulic testing machine (Instron 300DX) was used to apply a constant rate tensile load on 1.4 m 7-wire strands (bounded in grout) until at least one wire failed.To detect the AE signals, two piezoelectric transducers were attached to the chucks, and a laptop and a DT9816-S data acquisition system (Data Translation, model DT9816-S) with 750 kHz sampling frequency were used to record the AE signals.The transducers were developed by Durham et al [39] and had an approximately 63 kHz resonance frequency and a response range of 1 to 100 kHz.The transducer included two piezoelectric discs (STEMiNC, model SMD15T12S412) placed between two steel rods with a 12 mm radius and 20 mm length.To provide a better acoustic coupling between the chucks and transducers, a layer of couplant gel (Echo Ultrasonics, model Ultrasonix) was used.Figure 1 shows the schematic of the experimental apparatus.
A threshold-based algorithm, inspired by the work of Tsamtsakis et al [40] and Shateri et al [33], was used to extract AE hits from the recorded data.The first step of the algorithm was applying two levels of wavelet transform using Haar wavelet and then calculating the signal envelope using Hilbert Transform.After that, a threshold was applied to the envelope, and the first point that passed up the threshold was considered the start point of the hit.In a time (T) after the start point, the last point passed down the threshold was considered the hit's end.In this research, the threshold and T were found via trial-and-error and set to 0.12 and 200 ms, respectively.

Acoustic emissions from environmental sources
Any AE-based wire break detection system will have to detect wire breaks in the presence of signals from environmental sources.Representative environmental signals were gathered for use in testing the wire break detection algorithm.A 6-lane city highway bridge with pre-stressed concrete girders was chosen.The bridge was located in Winnipeg, Canada, was a truck route and had an average 24-h weekday traffic volume of 78,700.To collect environmental signals, a piezoelectric transducer, an amplifier, and a microcontroller (Teensy 3.6) were used.The geometry of the transducer used in the previous section had variations in acoustic coupling to the concrete and due to rocking on uneven surfaces.The design was modified new to address this issue.The new transducer had a shorter length and also a flanged disk at its base to reduce the rocking problem (see figure 2 for its dimensions).The transducer had a piezoelectric disc (STEMiNC, model SMD15T12S412) bonded to a copper backing mass.Laboratory tests showed the transducer's resonance frequency was 55 kHz when it was not attached to any surface.When attached to a surface, the resonant behaviour of the transducer was heavily damped, and no resonance was observed below 100 kHz.The transducer was installed on pre-stressed girders near the expansion joints of the bridge.Similar to the tensile tests, a layer of couplant gel (Echo Ultrasonics, model Ultrasonix) was used to improve acoustic coupling between the copper disk and the concrete surface.An op-amp (Analog Devices Inc., model LT1124) was used to provide 100x amplification.Laboratory tests showed the circuit had 100 gain and a bandpass frequency of 1 to 100 kHz.The microcontroller analog-to-digital convertor sampled the incoming acoustic signals.When a threshold was exceeded, 77,000 samples were logged at a 920 kHz sampling frequency.The schematic of the experimental set-up is shown in figure 2. The performance of the circuit was validated by comparing logged sampled data with data acquired using an oscilloscope (Tetronix, model TPS 2024) with the circuit driven by a function generator (Tetronix, model AFG 3021).The logging system is low power and portable for field data logging and in the future will provide an edge processing system in future studies to sense, record and analyze AEs in the field.

Acoustic emission database
The database of collected AE signals included the acoustic signals collected from both the laboratory tensile test and the collected environmental signals.The database contained the AE examples of 123 grout cracks, 14 wire breaks, and 1087 environmental signal examples.In the end application of this method, the AEs will have varying distances to the sensor.Since the attenuation will vary with distance, the effect of attenuation was simulated to produce a more diverse data set.To model the effects of attenuation on the collected signals of wire breaks and grout cracks, the following equation was adopted: where W was a weight factor that simulated the effect of attenuation on the signal's amplitude, and attenuation was assumed 2 dB m −1 [41,42].The effects of attenuation were modelled using ten distances from 2 to 20 m in 2 m increments.With the effects of attenuation included, the number of AE signals of grout cracks and wire breaks increased to 1353 and 154, respectively.The environmental signals were assumed to have already come from sources of varying distances.However, to improve the robustness of the proposed method, we assumed the primary sources of signals have a 20 m distance to the sensor.So, by applying the same equation, we modelled new signals with fewer distances to the sensor.We employed ten distances from 18 to 0m in −2 m increments to increase the number of environmental signals to 11957.It should also be noted that attenuation is dependent on frequency as well [17].

Acoustic features
AE signals are often characterized using an often-used set of features [33,43,44].This study uses the commonly used features of Peak Amplitude, Duration, Rise Time, Counts, Energy, and Power.In addition, we have also used Entropy and the areas under the Fast Fourier Transform (FFT) curve in four bins, as they have proven useful for classifying AE signals (figure 3).The often-used characteristics have been described many times in the literature, but we include a brief description for completeness.The Peak Amplitude of an AE is the maximum measured amplitude of the voltage.Other features depend on an operator-defined threshold.Rise Time is the time difference between the Peak Amplitude and the first threshold crossing, and, Duration is the time interval between the first and last threshold crossings.Count is the number of times the signal rises through the threshold.To calculate Energy, Power, Entropy, and the areas under FFT, the part of the signal between the first and last threshold crossings is used.The Energy of a signal refers to the area under the squared signal, and, its Power is its Energy per unit of time.Shannon's Entropy, called Entropy in this paper, was proposed By Shannon [45] to calculate the uncertainty of probability distributions.The detailed calculation process of Entropy that is widely used as an index in damage detection [43,44,[46][47][48][49][50] is described in the literature.In this paper, Entropy was calculated in the time domain.As AE signals were discrete phenomena, the histogram of each signal was used to estimate the mass function in the calculation [43].The areas under FFT in four bins refer to the area under the signal's normalized FFT in 15 kHz intervals from 1 to 61 kHz.Each bin's area was divided into the total area of the four bins.To select the frequency interval, the authors examined 5, 10, 15, 20, 25, and 30 kHz intervals and found 15 kHz intervals provided less overlapping in the database.An explanation of the 15 kHz intervals is provided in section 3.

Fuzzy c-means clustering
In this work, the Fuzzy c-means algorithm (MATLAB's built-in function) was used to cluster the AEs autonomously based on their features.Clustering algorithms are unsupervised machine learning methods that group unlabeled data based on their similarity into clusters.Fuzzy c-means, proposed by Dunn [51] and Bezdek [52], is a low-cost and straightforward clustering algorithm that is widely used in structural health monitoring problems [33,[53][54][55][56][57][58].Fuzzy c-means minimizes Euclidean distance as a similarity measurement between clusters' centroids and data features to cluster data points [51,52].
In this work, the number of clusters, the number of iterations, and the minimum desired improvement in objective function were set to 3, 100, and 1e-5, respectively.The authors examined different numbers for theses parameters.It was found increasing the number of iterations and decreasing the minimum desired improvement in the objective function improved the results.However, using more than 100 iterations and smaller than 1e-5 minimum desired improvement had no visible effects.Three different criteria were used to evaluate the performance of the algorithm.First, what ratio of wire break signals were classified as wire breaks.
Second, what ratio of grout cracks were classified as wire breaks.Third, what fraction of environmental signals were classified as wire breaks.
2.6.Non-dominated sorting genetic algorithm-II (NSGA-II) Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to determine the optimal classification features.In this research, optimal classification features refer to the features that result in the maximum ratio of wire break AEs classified as wire break and minimize the ratios of grout cracks and environmental AEs classified as wire break.It also refers to the minimum number of features that lead to these results.It is important to optimize the choice of feature, as the potential feature set is impractically large.For example, the number of acoustic features can be made very large simply by choosing many different threshold levels.It is computationally costly and impossible to feed all possible combinations of acoustic features into the clustering algorithm.Multi-objective optimization methods can find one or a set of optimal solutions within the feasible space of an optimization problem.NSGA-II, proposed by Deb et al [59], is a well-known low-cost multiobjective evolutionary algorithm that is widely used in engineering problems [60][61][62][63][64][65].NSGA-II was employed in this study to address the issue of an optimal number of features for wire break detection.
Figure 4 shows the flowchart of the overall procedure used in the NSGA-II optimized feature selection.A detailed description of NSGA-II can be found in Deb et al [59].NSGA-II was programmed in MATLAB by the authors and validated with the examples from Deb et al [59].In figure 4, the procedure started with a feature matrix.The matrix contains 201 features.These include peak amplitude and calculating the following features when 20 thresholds (from 0.001 to 5V with 0.25 V increments) are applied to each signal (section 2.4).These threshold-dependent features are energy, power, count, Entropy, duration, rise time, Area under FFT from 1-16 kHz, Area under FFT from 16-31 kHz, Area under FFT from 31-46 kHz, Area under FFT from 46-61 kHz.
These features are calculated for each acquired signal in the AE database.This yields a matrix with 13464 rows and 201 columns, one row for each AE signal and 201 columns for each corresponding feature.In this algorithm, each individual represents a subset of the possible features.A one or zero is used to signify if a feature has been chosen for a particular individual.Therefore, each individual has 201 zeros and ones.The first step was started by randomly choosing 100 individuals as the Initial Parents Population, in which each individual has 201 zeros or ones elements.The number of these zeros and ones was equal to the number of features (columns of the features matrix).The zeros mean the individual does not use the corresponding features.Then the individuals were fed into Fuzzy c-means to calculate the three criteria explained in the previous section as the cost functions.
The individuals were evaluated and ranked in the next step by applying non-dominated sorting and calculating crowding distances [59].As shown in figure 4, crossover and mutation operations were used to produce offspring and mutants to feed them into the clustering algorithm and then evaluate and rank them.Binary tournament selection and simulated binary crossover [66] were used to select parents and generate offspring, and polynomial mutation [66] was used to create mutants.After that, parents, offspring, and mutants were merged into a population, and the best 100 individuals were selected for the subsequent iterations.This process was repeated until reaching the maximum number of iterations, then members with Rank 1 were exported as the final Pareto Front (final solutions).In this research, the number of parents, offspring, mutants, and the number of iterations were set to 100, 32, 30, and 200, respectively.

Results and discussions
The first sets of tests were used to develop the database and identify the AE features of wire breaks.Figure 5 shows a wire break signal taken using the procedure outlined in section 2.1 and its FFT.As shown in figure 5, the wire break AE signal has the most relative power for frequency content between one and 50 kHz.The Samples of grout cracks and environmental signal and their corresponding FFTs are also shown in figure 5.In comparison with the frequency distribution of the wire break, the grout crack and environmental signals tend to have more normalized magnitude at lower frequencies.The normalized ratio of areas under FFT curves in certain bands can be a useful feature for AE signal classification.The normalized areas under FFT curves for all the AE signals in the database, explained in section 2.4, utilizing increments of 15 kHz are shown in figure 6.As shown in figure 6, in the band between 31 to 46 kHz, wire break signals are well separated from environmental signals and have minimal overlap with grout cracks signals.This observation resulted in the bands with different widths being explored.However, bands with 15 kHz width showed fewer overlaps, so in the rest of this work, only this bandwidth was used.Figure 7 shows the variation of peak amplitudes for the database.In practice, acoustic signals are attenuated as they pass through materials.As the distance between the source of emission and the sensor increases, so will the attenuation.Therefore, signal amplitude alone is not a reliable indicator of the source of AE.In this work, the signals in the database have simulated attenuation for distances up to 20 m.As shown in figure 7, the peak amplitudes of wire breaks overlap with environmental and grout crack signals.Therefore, in this work, the focus is on methods of classification that are insensitive to attenuation.
The NSGA-II-based algorithm described in section 2.6 was used to find optimal sets of features by optimizing the three criteria of section 2.5; the ratio of wire breaks' signals classified as wire breaks and the ratios of grout cracks and environmental signals classified as wire breaks.The NSGA-II algorithm relies on random generation and selection operators to sample a large portion of the available solution space.Therefore, the NSGA-II-based algorithm will often produce different outcomes for each run.In many cases, the results will not be acceptable.After several runs, it was observed that it was possible to consistently find solutions with greater  than 80% wire break detection accuracy, that simultaneously had less than 3% of grout cracks and 0% of environmental signals detected as wire breaks.We ran the algorithm 20 times with the same number of parents, offspring, mutants, and the number of iterations (100, 32, 30, and 200, respectively).Three out of twenty cases produced the desired results of more than 80% wire break detection accuracy, while less than 3% of grout cracks and 0% of environmental signals were detected as wire breaks.
The NSGA-II-based algorithm produced 12 optimized feature sets to feed into Fuzzy c-means for wire break detection.By using these optimized feature sets, the Fuzzy c-means algorithm could detect wire breaks with an average 81.06% accuracy.Only an average of 2.69% of grout cracks were misclassified as wire breaks, and none of the environmental signals were classified as wire breaks.The number of features in the acceptable sets was between 10 to 15 features.To ensure the sets had the minimum number of possible features needed to achieve the same or better results, we eliminated features of each set one by one and fed the remaining features into Fuzzy c-means.During this elimination process, we removed the features that had no effect or negative effects on the Fuzzy c-means algorithm.The number of features could be further reduced by a maximum of two features for five feature sets.The final 12 feature sets and their features are listed in table 1.As shown in the table, all features found by the algorithm utilized FFTs with different thresholds and frequency bins.Table 2 shows the number of features, the number of thresholds used in the features, wire break detection accuracy, and false detection ratios for each set.As shown in table 1, several cases only require five calculations of FFT of signals, making this method suitable for deployment in at-the-sensor processing and eliminating the need to send high-frequency sampled data outside the sensor node.
In the previous section, a wire break detection rate of 80% was considered acceptable.This implies that there is a probability that several wires might break before a wire break is detected.If an AASHTO 36-in pre-stressed I girder with 16 seven-wire strands [67] loses 25% of its pre-stressing steel, its initial moment strength drops to Strength I of AASHTO LRFD Bridge Design Specification.In this case, the bridge is operational, but it should be repaired.Based on the limit states concept of AASHTO LRFD, Strength I is related to the load combination of the normal vehicular use of the bridge without wind.Losing 25% of pre-stressing steel for this girder is equivalent to losing 28 out of 112 wires.In the following, we assume that missed wire break detection is random.Considering the 81.06%rate of wire break detection, the probability that the proposed method misses all 28 wire breaks is 5.8 × 10 -21 .With the same detection rate, the probability that the proposed method misses 10, 15, and 20 wire breaks are 5.9 × 10 , 1.4 × 10 -11 , and 3.5 × 10 -15 , respectively.Therefore, a detection rate of 80.06% has a very high probability of detecting the majority of wire breaks before there is a significant loss of structural capacity.
The distribution of the final features selected was examined since the NSGA-II uses random starting feature sets, and only a small subset produced acceptable results.The features and the total number of using them in the 200th iteration of the 20 runs are shown in figures 8 and 9.The selected features in the last iteration include only FFTs in different bins, Count, and Entropy with different thresholds.Although the feature sets listed in table 1 only include FFT in different bins, the other sets that did not meet the suitable criteria also have FFTs with or without Count and Entropy.Some of the features (11 features) used in the optimal sets were used more than 200 times.The algorithm did not select features such as peak amplitude, Rise Time, Energy, and Power in the last iteration.Count is somewhat sensitive to attenuation and was chosen by the algorithm only 108 times (less than Table 1.The optimal sets of features.

Sets Features
1% of features made up the last individuals).More than 93% of features occurring in the last iteration are FFTs for different frequency bins.The NSGA-II algorithm can be a powerful tool for selecting optimal feature sets.

Conclusions
In this paper, we developed an automated method to detect wire breaks in pre-stressed/post-tensioned concrete girders using acoustic emission.To differentiate AE hits observed in pre-stressed/post-tensioned concrete girders, we employed the Fuzzy c-means.We collected AEs of wire breaks, grout cracks, and environmental signals present in an operating pre-stressed concrete bridge and post-processed them to simulate the effects of attenuation of up to 20 m from source to sensor.Then, we gathered them into a database of 13464 AEs.To   optimize the speed and reliability of the Fuzzy c-means clustering algorithm, we employed an NSGA-II algorithm to find the minimum number of acoustic features needed.The NSGA-II algorithm found 12 combinations of features that resulted in an average of 81.06% wire break detection accuracy.In contrast, an average of 2.69% of grout cracks and 0% of environmental signals were misclassified as wire breaks.For an AASHTO 36-in pre-stressed I girder with 16 seven-wire strands, the probability that the proposed method does not detect losing 25% of the girder's pre-stressing steel (dropping its initial moment strength to the Strength I of AASHTO LRFD Bridge Design Specification) is 5.8 × 10 -21 .Results show this method is reliable and suitable for deployment in an extensive sensor network and has sufficiently low-computational requirements for at-thesensor processing, eliminating the need to send high-frequency sampled data outside the sensor node.

Figure 1 .
Figure 1.The experimental set-up for the tensile test of a grouted strand.

Figure 2 .
Figure 2. The experimental set-up to record environmental noises.

Figure 3 .
Figure 3. Acoustic features used in this study.

Figure 4 .
Figure 4.The overall procedure used in the NSGA-II optimized feature selection.

Figure 5 .
Figure 5.The acoustic signal and FFT of a wire grout environmental AE.

Figure 6 .
Figure 6.The normalized areas under FFT curves for the database for 15 kHz bands.

Figure 7 .
Figure 7.The peak amplitudes for the database.

Figure 8 .
Figure 8.The features and the total number of using them in the 200th iteration of the 20 runs for thresholds (Tr.) from 0.001 to 2.251.

Figure 9 .
Figure 9.The features and the total number of using them in the 200th iteration of the 20 runs for thresholds (Tr.) from 2.051 to 5.001.

Table 2 .
The overall characteristics of the optimal feature sets.