Frequency response of impact echo were employed widely to detect defect area. In this approach, frequency domain and distinguished peak point of IE signals were used to classify IE signals in three classes: good, fair, and poor [
26]. The IE signals, which have a distinguished peak within the thickness resonance, were classified as good. In Fair condition, the principal concentration of energy was occurred in the thickness resonance band; however, a small part of the energy will be in the lower band of frequency. For poor or seriously deteriorated condition, higher frequency concentration can be seen in the lower thickness resonance band [
26]. In this study, the authors propose combining the peak frequency method with features extracted from IE signals for precise classification.
3.1. Statistical Result
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Data classification based on the length of the signals
The lengths of all preprocessed IE signals for two groups of data (defect and sound) were used to construct PDFs and their best fit distribution.
Figure 4a,b show the length dispersion of IE data for slab 2 defected and sound, respectively. After analyzing the length PDF graphs, it was made apparent that the IE can be classified into five types:
Type (1), IE signals in sound group concluded one distinguished peak point with signal’s length contained 200 points or less.
Type (2), IE signals in defect group concluded one or two distinguished peak points with the signal’s length contained 400 points or less than 400 points.
Type (3), IE signals concluded one or two distinguished peaks in different times, the length of signals contained more than 400 points, and less than 1000 points.
Type (4), IE signals concluded multiple distinguished peak points in different time intervals, the length of IE signals contained more than 1000 points, and less than 1800 points.
Type (5), Exceptional IE signals, this type of signal broke the common pattern that was obtained by frequency analyses for classification in previous research. For example, some IE signals in the sound set were not cut by the proposed processing method due to their unusual shape.
As seen in
Figure 4b, type (2), (3), and (4) were normally observed in IE data collected from defected areas. In contrast, as shown in
Figure 4a, most IE data extracted from sound regions were cut and classified into type (1) and (5).
Figure 5 shows the examples of IE signal in different types. The length of preprocessed IE signals showed to be a proper indicator for classification. The IE signals, which were categorized as type (2), (3), and (4), could be used to detect defect zone. Since the proposed classes have overlap, the authors investigated time interval corresponding to normalized peaks. In general, the energy of IE signals collected from the sound zones were more concentrated in short interval time (type (1)). Therefore, the length of preprocessed signals in sound zones was shorter than IE signals collected from the defect area. Some IE data from defect or sound did not follow this pattern. Thus, the time or frequency domain for normalized peak value and length of signals showed to be the good indicator (only one peak (type (1) and (2)). The results of the PDF analysis of IE data are summarized in
Table 1 and
Table 2, for defected and sound IE data, respectively. According to the result, roughly 90% of the preprocessed IE signals from the sound zones concluded 210 points, and these signals have not distinguished peaks in different time intervals. The energy of signals was more concentrated in special and short time range without shifting to other bands. For defected concrete, the length of only 25% of short IE signals was concluded 400 points with two or multiple peak points. In this research, the probability density function (f(x)) and histogram was used to classify IE data. The goodness of fit was obtained among forty common fits and it is mentioned for each slab, and the result shows that the statistical fit distribution cannot precisely predict all the observed data. However, it could be used to estimate the distribution of most preprocessed IE signals.
The best fitted distribution and statistical parameters for the length of all processed signals were extracted from the PDF plots and summarized in
Table 1 and
Table 2. According to the result, roughly 90% of the preprocessed IE signals from the sound zones concluded less than 411 points and these signals have not distinguished peaks in different time intervals. The energy of signals was more concentrated in special and short time range without shifting to other bands. The length of 90% of preprocessed IE signals was concluded less than 1062 points in the defect dataset, which showed that the energy of signals was not concentrated in a small interval time, also 25% of IE signals have two or multiple peak points in different time intervals.
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Data classification and statistical pattern recognition based on time interval and normalized peak values.
To increase the robustness of classification in this investigation, the values of absolute maximum and local peaks for all processed IE signals were obtained. Then, the local peaks were normalized with respect to the absolute maximum (see
Figure 2).
Table 3a,b show the frequency of IE signals’ peaks for defect and sound concrete, respectively. All normalized values were plotted with respect to the corresponding time and probability density function as seen in
Figure 6 and
Figure 7 for slabs (2) and (6), respectively. In these figures, the relationship between time (0–9.99 ms) (X axis), normalized peak value of IE data (Y axis), and cumulative frequency of IE data (Z axis) are presented. According to 3D matrix and
Figure 6a for “defect set “, 98% IE of signals did not have a peak within the interval of 0 and 2 ms. The range of absolute maximum value of 79% of IE signals was between the range times of (2–4.5 ms). About 19% of IE signals showed small peaks (multiple peaks) in the time range of (4.5–10 ms), and the rest of 0.02% signals were not classified using this method, since they had an odd pattern.
Figure 7a shows 53% IE signals in “defect group”, which have distinguished peaks in the time interval of 0–2 and 6–10 ms. The data collected from the defect area were more distributed than the sound group, such that mathematical code was unable to classify them.
Figure 6c also shows some example of IE signals for defect regions, the IE signal (black signals) in type (3) has two or multiple distinguished peaks. The red signal had high magnitude between 2.5 ms < t < 4.5 ms, while the last one (in type (4)) had multiple peak points (green signals). In sum, 40% of signals were classified type (3) and (4) (defect set) because a small part of the energy was shifted to a lower-frequency domain (i.e., 4.5–10 ms or 0–2.5 ms). The remained signals were classified as type (2) (good set) because they had two distinguished peaks in the range time of (2.5 and 4.5 ms).
In contrast, according to
Figure 6b and
Figure 7b, 85% of IE signals were classified as type (1) (good) due to their distinct peak within the thickness resonance band (i.e., 2–3.5 ms) for “Sound” set. The result of defect signal in 3-D plot were more diverse compared to sound signals. Signals “sound set” in the time interval of 3.5–10 ms were more limited in range than the other types of signals in defect set (such as grey signal in type (1)).
Figure 6d also shows some abnormal IE signals collected from sound regions (blue signal in type (5)). It shows the fact that the mathematical code was unable to preprocess the type 5 IE signals.
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Normalized energy
The local normalized peak values of IE signals (Y axis) in 3D matrix can also be used for IE classification.
Figure 8 shows the frequency of signal’s peak values, which were normalized to 1 for slabs 4. The area under curve can be segmented to three areas:
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Area 1: normalized local peaks are between 0.005 and 0.4, with small local peaks compared to the absolute maximum.
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Area 2: normalized local peaks are between 0.4 and 0.6, with moderate local peaks compared to the absolute maximum.
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Area 3: normalized local peaks are between 0.6 and 0.95, with significant local peaks compared to the absolute maximum.
The area under each segment was calculated and summarized in
Table 4a,b for defect and sound data set, respectively. This approach revealed that the defected IE signals had higher value and more frequent local peak values compared to sound concrete. Moreover, one can observe more variability in the defected concrete as they were associated with four types of defects as opposed to sound IE data. These tables also show that the IE signals in each class of dataset, defect or sound, had similar statistical properties associated with their local peaks, while these properties were tangibly different from the other class. The result also showed that area (1) has the highest values compared to other domains. For example, most IE signals in both data set defect and sound had normalized local peaks lower than 0.4. However, these local peaks in sound set are concentrated in the small part of IE signal’s length near maximum points.
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Start and stop time
The start and end time of all processed IE signals were analyzed as another feature that can be used in Naïve Bayes for IE classification.
Figure 9 shows the box plot for two data sets (defect and sound concrete).
As seen, the sound concrete showed less variability compared to defected concrete in terms of start and stop time of processed IE signals. The center of each box in these figures indicates the median, while the top and bottom bounds of them were the 25th and 75th percentiles, respectively. The end time seems to provide a better mean for classification compared to the stop time.
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Defect type and histogram
The investigated slabs had four types of artificial defects, which were shown to affect the shape of the histogram and fitted distributions to the length of the processed IE as seen in
Figure 10. The proposed IE signals collected from deep delamination and sound group are slightly similar to each other in terms of signal length. Therefore, it cannot be used for proper classification of IE signals. On the other hand, the start and end time of the processed IE signals showed more promise for classification detection, especially for deep delamination.
The length of the 80% preprocessed IE signals was collected from shallow delamination and void ranging from 100 to 1000 points. It ranged from 0 to 600 points for most of the IE data collected from deep delamination and honeycombing, and the mathematical code did not truncate 16% of the IE data due to multiple peaks or their unusual shape. The length of the 75% of the preprocessed IE signals is between 100 to 455 and the mathematical code cannot split 30% IE signals due to multiple peaks.
Figure 10 also shows that the differences between the lengths of the IE signals collected from artificial defects could be related to the location, boundary conditions, or depth of the defect position.
Table 5 shows the effect of the type of artificial defects on the shape of the histogram and fitted distributions in terms of their type; mean, and standard deviation of the IE lengths. According to
Table 5, the IE signals collected from honeycombing and deep delamination had the least lengths in the prepressed signals.
This effect of type of delamination can be seen in the start and stop time as seen in
Figure 10. The time interval of the prepossessed IE signals can be obtained with using this figure.
About 50% preprocessed IE data collected from shallow delamination had distinguished points before 2.5 ms. However, preprocessed IE signals collected from sound area do not have distinguished peaks before 2.5 ms. In addition, 50% preprocessed IE signals collected from shallow delamination had distinguished points in time interval between 6 to 10 ms. For deep delamination, the start points of 50% prepossessed IE data collected from deep delamination was between 2.6 and 4.2 ms, which were different from those data collected from sound regions. The start points of preprocessed IE data collected from sound concrete were approximately 2.5 ms. There was an overlap between 50% preprocessed IE data collected from honey becoming and preprocessed IE data collected from sound area. The start and end time of 50% prepressed IE signals collected from honey becoming was between 2.5 and 5 ms. As
Figure 10 shows, there were overlaps between some part of prepressed IE data collected from void and preprocessed IE data collected from sound area in terms of sampling time interval.
3.2. Probability Classifier to Make Predicted Models Based on the Feature of IE Signals
Figure 11 shows the class of each data set, which was predicted using Naïve Bayes models and input layers. This model was able to predict the probability of present defects in the bridge using feature of signals, independently. Among all classifier approaches, Naïve Bayes models are applicable to IE data, since we can see the relationship between features and predicted surface, simultaneously.
The relationship between average of maximum local peak, length of signals, end and start time of preprocessed signals and output layers (defect or sound area) can be obtained by using this method. It demonstrates how these two-input variables (length of signals or maximum peak) could influence the output layers in all slabs.
Figure 12a,b demonstrate the probability of occurrence defect and sound regions based on nature of two independent variables.
It was made apparent that the length of the IE signals and normalized peak values influenced the results in the output layers of Naïve model (defect or sound) in all slabs. As
Figure 11a shows, the IE signals collected from defect area has more distinguished peak. Therefore, increasing the amount of peak in signals leads to increase the probability of defect surface, which means, it is more likely the IE signals collected from defect area. In contrast, if normalized peaks in IE signals was reduced, it would lead to an increase in the probability of detection in sound surface. The probability result over normalized peak values and average of maximum peak showed to be higher in signals associated with defects compared to the ones associated with sound regions. This can be explained by the fact that signals collected from sound regions returned to the surface after hitting the bottom of specimens (backwall reflection). Therefore, the echo is in sound regions propagated through a longer path compared to the IE signals collected from the defect area. This also results in more dissipation of energy in the structure; which led to smaller values of local peaks in the sound region. Moreover, the IE signal collected from defect areas has larger normalized peaks because the data signals have two or more peaks due to the seismic wave encounter with the defects. The length of IE signals collected from the sound region was lower than the defect region, and the energy of IE signals in the sound set was more concentrated in certain time ranges without shifting energy to other part of signals. So, the processed IE signals collected from defect part has higher end time.
Figure 11b shows the relationship between end time, start time, and the occurrence probability of defect or sound regions. The variation of defect surface is related to the end time of signals such that the variation of surface of defect was increased when the end time of IE signal was between 5 to 10 ms. However, the sound surface was more variable when the end time of IE signal is between 2 to 4 ms. Based on the investigation it can be said:
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The probability of the defect occurring ranges from 0.6–1 if the IE signal is truncated before 2 ms ().
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The probability of the defect occurring ranges from 0.6–1 if the IE signal is truncated before 5 ms.
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The probability that the defect occurs is between 0.8–1 if the average of maximum peak of IE signal are higher than 0.16
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The probability of the defect occurring ranges from 0.1–0.2 if the IE signal is truncated between 2 and 4 ms.
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The length of 90% of the preprocessed IE signals from the sound regions concluded 210 points within 2.5 and 3.5 ms. However, the length of 75% of preprocessed IE signals was concluded more than 400 points in the defect dataset, which is within 2.5 and 10 ms.
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Probability classifier to make predicted models based on the estimated thickness and end time of preprocessed IE signals
In this section, the probability classifier approach, the IE data of sound regions, and Equation (1) were used to evaluate the frequency spectrum analysis method. The estimated thickness from each IE signal, which was obtained from frequency approach, was added to the other features to generate probability of detection as seen in
Figure 12 and
Figure 13. As it is clear in this figure, employing the data of the sound dataset can provide an appropriate prediction of the slab thickness amount, which ranges between 0.15–0.3 associated with a 100% detection rate with some exceptions (see S1, S2, S3 as examples). The thickness for defected signals were outside the range of 0.15–0.25. It is important to note that preprocessed IE signals with an end time less than 2 ms are not suitable to predict the slab thickness.
All eight slabs had identical condition during construction; however, the IE data collected from different slabs were not the same because the estimated thickness in not the same between slab (7) and slab (8). The time range of the prepossessed IE signals and the peak values of the IE signals are different for each slab. Based on previous research [
27], this difference could be due to the different mix design, moisture condition, and the operator’s preferences when collecting the data. As can be clearly seen in
Figure 12 and
Figure 14, the IE signals collected from slab (8) can estimate thickness more accurately. The estimated thickness is between for slab 8 was between 0.2 m and 0.25 m; however, this value was between 0.15 m and 0.3 for slab (7). This inconsistency shows the importance of investigating IE in the time domain to produce more accurate thickness estimation.
The purpose of this section was to obtain the 3-D surface as evidence to show how to detect defect area in IE signals in both time and frequency domains. Moreover, atypical IE signals collected from sound or the defect area can be obtained using the 3-D surfaces. For example, 10% of IE signals in sound data collected from slab (8) is not usable to estimate slab thickness.
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Pearson coefficient
Pearson coefficient was used to evaluate the correlation between two variables scaled from −1 to +1. A coefficient of 1 indicates that two datasets are significantly correlated, whereas -1 indicates that two datasets are in a strongly negative relationship [
28]. Pearson confidence coefficient is more common to evaluate the similarity between two objects in a large statistical dataset. So, the similarity between the slabs was determined based on the result of the frequency approach and the features of the raw IE signals in the time domain.
Table 6 summarizes the Pearson coefficient for all slabs obtained to examine the similarity between the IE signals in terms of frequency response among all slabs. According to
Table 6, slabs 1, 2, 3, and 4 are similar to each other, and slabs 5, 7, and 8 are more similar to each other. Finding similarity index between slabs can help a user of IE device to classify IE data more accurately.
Based on the result of statistical model, boxplots, probability classifier, and Pearson coefficient it was concluded that slabs (5), (7), and (8) were similar to each other and slabs (1), (2), (3), and (4) were more similar, which will be investigated in future studies. The proposed features in this study can be directly applied to IE collected by different data collection settings and devices as they were extracted from process IE signals.
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Comparison
In a different study, IE signals were used to build a prediction method without controlling the quality of IE signals or extracting atypical IE signals, which could lead to errors to predict defect area [
11,
20,
29,
30]. The result of the current study shows about 10% of IE signals do not have a normal shape in the IE dataset used in this study. Therefore, the authors suggested to extract atypical signals before creating the prediction method, which can reduce the estimation errors by 10%. The proposed method can be effectively used for IE signal quality control during inspections.
Using the proposed processing, IE signals can be used for more accurate estimation of concrete decks. In a previous study, the error of the estimated thickness was between 5 and 15% when using two datasets with 512 IE signals collected from slabs without defect area [
31]. In our study, all slabs contained four types of artificial defects including shallow delamination, deep delamination, honeycombing, and voids. The boundary conditions at the interface between the defect and surface of concrete leads to an increase in the error of the estimated thickness. This error is 10%, considering several of IE data used in this paper did not have the proper quality (unusual signals). Another merit of this investigation was to develop a method to find unusual IE signals in a large dataset with 2016 IE signals before estimating thickness.
In recent studies, the frequency approach and machine learning method were used to interpret IE signals, separately [
11,
20]. However, in this study, the Naive Bayes classifiers approach was used to detect defects for the first time by using IE signals in both time and frequency domains. The proposed pre-processing method reduced the classification error when applied on the IE raw data. Therefore, the result of classification using the proposed features in this study can be coupled with the conventional peak frequency method to consider both time domain and frequency domain characteristics.