Digital image correlation-based structural state detection through deep learning

Abstract

This paper presents a new approach for automatical classification of structural state through deep learning. In this work, a Convolutional Neural Network (CNN) was designed to fuse both the feature extraction and classification blocks into an intelligent and compact learning system and detect the structural state of a steel frame; the input was a series of vibration signals, and the output was a structural state. The digital image correlation (DIC) technology was utilized to collect vibration information of an actual steel frame, and subsequently, the raw signals, without further pre-processing, were directly utilized as the CNN samples. The results show that CNN can achieve 99% classification accuracy for the research model. Besides, compared with the backpropagation neural network (BPNN), the CNN had an accuracy similar to that of the BPNN, but it only consumes 19% of the training time. The outputs of the convolution and pooling layers were visually displayed and discussed as well. It is demonstrated that: 1) the CNN can extract the structural state information from the vibration signals and classify them; 2) the detection and computational performance of the CNN for the incomplete data are better than that of the BPNN; 3) the CNN has better anti-noise ability.

Graphical abstract

Keywords

structural state detection / deep learning / digital image correlation / vibration signal / steel frame

1 Introduction

Structural damage detection (SDD) has been widely concerned in the field of structural health monitoring (SHM), which can detect possible structural defects in time. The traditional detection method is through visual observation, which is labor-intensive and can expose workers to an adverse environment [1]. As vibration signals can reflect the real structure state information [2], vibration-based SDD methods have been widely investigated to assess structural integrity. Vibration-based methods include the parametric and non-parametric methods. Some researchers have confirmed that the parametric-based method is effective as any local structural damage would change the mass, damping, and stiffness of a structure, resulting in changes in its natural frequencies and mode shapes [3–5]. More discussions on the modal parameters-based SDD methods can be seen in related literature [6,7]. The non-parametric SDD methods employ statistical means to identify damage directly from the measured vibration signals; these methods’ effectivenesshas also been demonstrated in relevant studies [8]. Nevertheless, the vibration-based SDD methods encounter several challenges [9,10]: 1) the frequencies change does not result into accurate damage information; 2) the derivatives of the modal parameters (e.g., flexibility-based [11–14], modal strain energy-based [15,16], and mode curvature-based [17], etc.) relied on the accurate modal identification; 3) nonparametric-based damage detection requires a lot of data processing, which is time-consuming and subjective. Consequently, a more advanced vibration-based detection tool is necessary.

The development of artificial neural networks (ANNs) provides a new tool in damage detection for SHM, and it is similar to a nonlinear function to establish the mapping between the input and output (e.g., the bending analysis of Kirchhoff plate [18], boundary value problems [19], and solution of partial differential equations in computational mechanics [20]). The traditional ANNs (e.g., the backpropagation neural network (BPNN)) have achieved promising results [21]. However, it is slow and time-consuming [22]. The CNN can automatically extract features from the original data [23]. The CNN has also been expanded to the applications of the vision-based SDD method; some researchers have proposed CNN models to detect and locate surface corrosion and cracks [24,25]. However, this vision-based SDD method cannot detect invisible damages (inner or/and inaccessible damages). Thus it is inevitable to develop the vision-based detection methods for invisible damages [26]. The latest research results indicate that the deep learning algorithm can automatically extract the feature information of structural states from acceleration signals, e.g., bolt loosening [27] and mass change [1] of structures. Our research team has also successfully applied the CNN to detect the damage of a steel frame and developed a strategy to generate training samples automatically [28]; in another research, the modal strain energy was combined with the CNN to detect damages in an experimental model [29]. The result of the vibration-based method was encouraging; nevertheless, it is usually laborious to arrange accelerometers for the large bridges, hence, the acquisition of vibration signals need to be improved.

Vision-based measurement technology has become a hot research topic. The relevant studies have proved its effectiveness (e.g., compared with accelerometers and strain gages) [30]. An early study was implemented on a suspension bridge near Los Angeles to determine the displacement of the actual structure [31], and its effectiveness was validated in a steel-plate girder bridge measured by the conventional sensors and the vision-based method. New researches demonstrated that the digital image correlation (DIC) technology was a promising method for vibration measurement [32–34], and the DIC-based modal analysis was used to identify the modal parameters of a steel frame [35], recently, combined with the unmanned aerial vehicle (UAV), the DIC technology was used to obtain accurate vibration signals of a bridge model [36]. Combining the DIC measurement technology with the CNN damage detection method is expected to promote the development of SDD.

This paper detects structural states using the CNN and vibration signals (collected by the DIC measurement). The samples with various damage states, obtained from the vibration experiments, are used to train the CNN and corresponding BPNN; the detection effects of both neural networks are compared.

2 Methods

The proposed method in this paper contains four parts: experimental descriptions, sample creation, deep learning architecture design, and structural state detection (Fig. 1). The CNN samples were obtained from the vibration experiments; the architecture of the CNN was designed by MATLAB (Mathworks Inc., Natick, MA, USA). After the training processes of the CNN and BPNN, the detection effects were assessed by the testing data.

2.1 Vibration experiment

The experimental model was a steel frame (Fig. 2(a)) with a length of 9.912 m, a width of 0.354 m, and a height of 0.354 m. It included 355 rods and 112 steel balls; for each rod, its external radius and thickness were 0.005 m and 0.002 m, respectively. The experimental instruments (Fig. 3) included: A Single-Lens-Reflex (SLR) camera (D5300, Nikon Inc., Tokyo, Japan) and an instrumented hammer. The hammer was used to excite the structure, and the SLR camera recorded the vibration information.

The vibration signal acquisition process was as follows.

1) Introduce damages at one or more locations or keep the structure undamaged.

2) The experimental model was excited by the hammer at the excitation points, and the SLR camera (sampling at 50 Hz) was used to record the structural vibration process.

3) The DIC technology processed the vibration signal, which was implemented by a MATLAB code. As illustrated in Fig. 4, the point P\left(x,y\right) moves to the point Q\left(x^{\prime },y^{\prime }\right), the displacement can be obtained by comparing the correlation of two subsets on the sequential images. The following formulas were employed to track the displacement of a point of interest:

(1)\begin{array}{rl}& C\left(\mathrm{\Delta }x,\mathrm{\Delta }y\right)=\\ & \frac{{\displaystyle {\iint }_S{I}_0\left(x,y\right)I_1\left(x+\mathrm{\Delta }x,y+\mathrm{\Delta }y\right)}\text{d}x\text{d}y}{\sqrt{{\displaystyle {\iint }_S{I}_0{}^2\left(x,y\right)}\text{d}x\text{d}y}\cdot \sqrt{{\displaystyle {\iint }_S{I}_1{}^2\left(x+\mathrm{\Delta }x,y+\mathrm{\Delta }y\right)}\text{d}x\text{d}y}},\end{array}

where I_0\left(x,y\right) and I_1\left(x\text{+}\mathrm{\Delta }x,y+\mathrm{\Delta }y\right) are the gray-scale distributions of two sequential images, and the real displacement \left(\mathrm{\Delta }x,\mathrm{\Delta }y\right) of the reference subset \left(S\right) maximizes the function C\left(\mathrm{\Delta }x,\mathrm{\Delta }y\right).

The steel frame was excited 3 times at the positions E1, E2, E3 in turn (Fig. 5), and 400 pictures were collected for each excitation (sampling frequency was 50 Hz, and sampling time was 8 s). Thus a total of 1200 pictures was collected throughout the process. The DIC technology tracked the 10 points of interest (POI, indicated by the red mark) from their vibration signals.

The damage was introduced by reducing the cross-section of the damaged rods (Fig. 6).

This paper investigated 6 states of the experimental model.

State 1: Intact structure.

State 2: Only damage on Rod 2.

State 3: Only damage on Rod 1.

State 4: Only damage on Rod 7.

State 5: Damages on Rods 1 and 7 (simultaneous damages on the two rods).

State 6: Damages on Rods 1, 7, and 11 (simultaneous damages on the three rods).

2.2 CNN samples

First, a MATLAB function (called mapminmax) was used to normalize the data, i.e., y = mapminmax(x, y_min, y_max), and the principle of the algorithm was as follows:

(2)y=y_{min}+\frac{x-x_{min}}{x_{max}-x_{min}}\left(y_{max}-y_{min}\right),

where x and y were the input and output of this function, respectively. In this paper, x was a time series of vibration signals; y_min and y_max were −1 and 1.

Then, the preparation of CNN samples was divided into two stages.

The first stage (Stage 1): for the intact structure, the vibration signal collected for two excitations (at E1 and E2) which was saved as an 800 × 10 matrix (Fig. 7). Sample 1 was 1−10 rows of the matrix (i.e., a 10 × 10 matrix, circled by the red box in Fig. 7), Sample 2 (i.e., the black dotted box in Fig. 7) was obtained by moving down the red box; this process was repeated to obtain all the 791 samples, 31 of which were randomly selected as the testing samples, and the remaining 760 were used in the training process (including training and validation samples). There were 6 structural states in this paper, so the total training and validation samples were 760 × 6 = 4560, and the testing samples were 31 × 6 = 186.

The second stage (Stage 2): e.g., for the intact structure, using the same method as in the first stage, the vibration signals (400 × 10 matrix) induced by the third excitation (at E3) was utilized to create 391 samples. The total samples of the 6 structural states were 391 × 6 = 2346, all of which were utilized as testing samples of the second stage.

The database of training samples, validation samples, and testing samples are listed in Table 1. As both Stage 1 and Stage 2 used the same CNN model, there were not training and validation samples for Stage 2.

The k-fold cross-validation can effectively evaluate the robustness of the network model. The specific implementation strategy is: the training samples and validation samples were divided into N parts (i.e., k = N), one of which was taken as the validation samples each time, and the other N-1 parts as the training samples. Therefore, a complete k-fold cross-validation process needs N experiments. In this paper, k = 10 (relevant studies have confirmed that 10 was widely used [37]).

2.3 Illustrations of the CNN and structural state detection

The designed CNN architecture and corresponding parameters are illustrated in Fig. 8 and Table 2. The original data goes through a series of functional layers, and finally outputs the corresponding classification (i.e., structural state). The proposed CNN model consists of two convolution layers (the sizes of convolution kernels were 5 × 5 and 2 × 2 respectively, the kernel number were 100 and 200, and their stride was 1), one pooling layer (size: 2 × 2, stride: 2), and one fully connected layer. A Leaky ReLU was used as the activation function after each convolution layer. Meanwhile, the learning rate, optimizer, maximum epoch, execution environment, and dropout rate of the network model were 0.001, adam, 90, GPU, and 0.5, respectively. The training was performed on a computer with NVIDIAGTX GeForce 1650 GPU, Intel Core i7-4790@3.60 GHz CPU, windows 10.

The CNN input was the vibration signals of various structural states. The CNN output was categorized into different labels, i.e., the intact structure was labeled 1, the damage on Rod 2 was labeled 2, the damage on Rod 1 was labeled 3, the damage on Rod 7 was labeled 4, the damage on Rod 1 and Rod 7 was labeled 5, and the damage on Rod 1, Rod 7, and Rod 11 was labeled 6.

The training process of the CNN involved the training and validation samples. The testing process of the CNN was divided into two stages, and the testing databases were illustrated in Section 2.2. The same data and detection processes were implemented in the BPNN.

This paper employed a multiple-layer BPNN as a controlled experiment, and its input size was 100, and the output size was 6. Therefore, the node number of the hidden layer was [38]:

(3)n_1=\sqrt{n+m}+a,

where n₁ was the number of the hidden neurons, n and m were the numbers of the input and output sizes, and a was a constant (1 to 10).

In actual engineering structures, the collected data may be incomplete [39]. In this paper, the influence of incomplete data on structural state detection was also studied. The data for each node of the testing data was removed in turn. In Fig. 9, Matrix A represented the complete data sample, while Matrix B represented the sample of missing data of Node 1, which was replaced by zeroes. Matrix C represented the sample of missing data of Node 2, etc. Totally 10 scenarios of incomplete data were included. The incomplete data set was used to assess the detection performance of neural networks. These data were employed to test the network model of Stage 1, thus clarifying the CNN’s detection effect on incomplete data.

As there inevitably existed noise in engineering practice, different intensities of Gaussian white noise were added to the testing data (displacement) and inputted into the CNN to compare the detection effect. The noise was generated using a MATLAB built-in function called wgn, and added to the normal data (non-noise). The signal-to-noise ratios of 1, 5, 10, 20, 30, 40, and 50 dB were used to illustrate the influence of noise intensity on the test results in this paper.

3 Results

The results included the following parts.

1) The measurement results of the DIC technology.

2) The results of structural state detection from the CNN and BPNN.

3) The results of structural state detection when the testing data were incomplete.

4) The results of structural state detection under the influence of noise.

3.1 Experimental results

Figure 10 illustrates some displacement-time history curves (for the intact structure) obtained by the DIC technology. The vibration amplitude was large at excitations and then attenuated over time. After three excitations, a total of 1200 data points were collected.

3.2 Detection results

To further clarify the robustness of the network model, the k-fold cross-validation experiment was implemented. Table 3 shows the cross-validation results when k = 10, and 10 validation results were named K1, K2, K3,…, K10. The results showed that the network model was not over-fitting and had ideal robustness, the average accuracy of the training and validation exceeded 99%.

For example, for the K1 network, the training process of the CNN is illustrated in Fig. 11); the network converged in about 35 epochs, and the time elapsed for 56 s; then the testing samples were inputted into the network. The accuracy (Tables 3 and 4) of the first and second stages was 100% and 99.3%, respectively; the average accuracy was 99.7%. For example, the first row of Table 4 represented that 31-testing samples of State 1 were correctly detected; the first row of Table 5 represented 391-testing samples of State 1, 381 of which were correctly detected, 4 of which were mistakenly detected as State 4, 6 of which were mistakenly detected as State 6. Then the BPNN [29] was used to implement a similar detection scenario; the accuracy (Table 6) was 99.5% and 98.9%, the average accuracy was 98.9%.

The high accuracy of the testing process confirmed the excellent detection performance of the CNN on the vibration signals. In this paper, the hammer excitation was arbitrary (implemented manually with a random amplitude), so the detection results of the second stage demonstrated that the CNN could extract structural state features from a new excitation.

The node number of the BPNN hidden layers has some influence on the detection results, and the accuracy ranged between 93% and 99%; when the node number was 17, the detection effect was optimal, which was 99.5% and 98.9% for the two stages, respectively.

The uptime of the CNN (56 s) was about 19% that of the BPNN (297 s), the BPNN and the CNN converged after 30 and 35 epochs of training, respectively, so the time of each epoch of the BPNN was 6 times that of the CNN. Generally, the CNN has a faster convergence speed without losing accuracy.

3.3 Testing results for the incomplete data

This subsection illustrated the detection results for the incomplete data in different locations. The accuracy of the CNN was about 44%–81%, with an average of 59.9%, and that of the BPNN was about 31%–64%, with an average of 48.7%. The detailed testing results are shown in Tables 7 and 8.

The results confirmed that the CNN still had some detection ability for the incomplete data and performed better than the BPNN for the structural state detection. This also confirmed the superiority of CNN’s sparse connection.

3.4 Testing results under the influence of noise

Table 9 shows the influence of the noise with different signal-to-noise ratios on the BPNN and CNN. The results illustrated that: 1) the detection accuracy of the BPNN and CNN decreased with the increase of the signal-to-noise ratio; 2) the detection accuracy of the CNN was higher than that of the BPNN; 3) the BPNN was invalid when the signal-to-noise ratio was higher than 10 dB, while the CNN was still of about 90% accuracy when the signal-to-noise ratio reached 50 dB. This proved that the CNN had better anti-noise ability.

4 Visualization of features

A neural network was like a “black box”; the training process of the network was invisible; to get a more intuitive understanding of the process of extracting features from the vibration signals, this section visualized the features obtained from the convolution, pooling, and fully connected layers. In this paper, the “activation” function of MATLAB was used to visualize the signal features.

Two samples were randomly selected from the testing samples of State 1 and State 2, respectively. Figure 12 shows the 3-D images of the samples. Then two samples were inputted into the trained CNN, and a MATLAB code was used to get the features of convolution and pooling operations and then visualize the obtained features in Figs. 13 and 14.

The visualization of the features illustrates that the first convolution layer (Conv_1) primarily extracts the local features of the vibration signals; e.g., for the sample of State 1, each feature represents the local information of the raw data, and the combination of the feature images can describe the actual vibration curve.

Next, the data was inputted into the pooling layer (Max_pool), and the output features were visualized (Figs. 13 and 14), the features of the pooling layer were rougher than those of the previous layer (e.g., State 1, Fig. 13), and nevertheless, all the features (curves) combined can also describe the vibration signal of the structure.

Then the data was inputted into the second convolution layer (Conv_2), and 200 features (some of which were shown in Figs. 13 and 14) were obtained. These features (straight lines with different slopes) appeared to be more “elementary” and were the essential members of the raw data, i.e., the combination of these features was able to illustrate the raw data, i.e., the raw signal was divided into straight lines with different slopes.

Finally, all features were inputted to the fully connected layer, which outputted 6 feature values, the maximum output value was at Location 1 of the output map (Fig. 15(a)) for Sample 1, and at Location 2 of the output map (Fig. 15(b)) for Sample 2. These feature values were utilized as a vector to calculate the probability of belonging to categories using Softmax function [29]; the results demonstrated that the two samples were correctly detected. Hence, the fully connected layer was used to map the features of the previous layers to the structural state.

5 Discussions and conclusions

In this study, the CNN achieves the ideal effect of structural state detection by extracting the features from vibration signals, and the accuracy exceeded 99%. The CNN algorithm has better computational performance and faster convergence than the BPNN.

The method of vibration measurement based on DIC technology can avoid the arrangement of sensors and reduce the influence of the environment. In this paper, the magnitude of the excitation force is random, and the testing results from the second stage indicate that the deep learning algorithm can obtain the structural features and detect the structural state even for unstipulated excitations.

For the incomplete samples, the CNN still demonstrates some detection ability. The accuracy is about 11% higher than that of the BPNN, showing that CNN has a more robust feature extraction ability. Meanwhile, CNN has a better anti-noise ability than BPNN.

The features extracted by the CNN show the local information of the vibration signals. All the features were the essential members (straight lines with different slopes) of the vibration signals, i.e., the raw signal was dissected layer by layer, and the CNN extracted the features. Finally, as a feature combiner, the fully connected layer outputted a result (describing the structural state).

The conclusions are as follow.

1) As a classifier, the CNN can extract the dynamic features of the vibration signals and detect the structural state correctly.

2) The CNN has better computing speed than the BPNN with comparable accuracy.

3) The detection results of incomplete data confirm that the CNN still has some detection ability, and the accuracy is higher than that of the BPNN.

4) The CNN has better anti-noise performance than the BPNN.

5) The CNN obtains the dynamic features of the structure through feature extraction layer by layer and finally maps the features to the structural state.

6) The combination of the DIC technology and deep learning algorithm is effective for SDD.

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