Non-destructive detection of highway hidden layer defects using a ground-penetrating radar and adaptive particle swarm support vector machine

Image filtering.

The objective of image filtering is to minimize the effects of noise and interference in raw images. The noise and interference are mainly attributed to the processes –image acquisition and image transmission. Gaussian filtering is typically used for image denoising, which can remove unnecessary interference and protect the edge of the image.

Image segmentation.

The objectives of image segmentation are to classify foreground and background pixels, and to determine the organization of foreground pixels (i.e., detect foreground objects) (Fengjun et al., 2018).

The Canny operator has been widely used for image segmentation of radar images, and its segmentation performance after Gaussian filtering is demonstrated in Fig. 2. Figure 2A is the original radar acquisition diagram. Figure 2B is the result after Gaussian transformation. It can be seen that the clutter in the original image is removed. Figure 2C is the disease characteristic waveform diagram extracted after Canny operator. To retain only the necessary information, the image was subjected to the morphological operations of expansion and corrosion; the results are shown in Fig. 3. Figure 3A is the image after Canny operator segmented the disease waveform. Figure 3B is an enhanced disease waveform diagram after the segmented waveform is processed by digital morphology, so as to facilitate the extraction of disease features in the following text. The processed image was segmented and objects were extracted using the vertical projection method, as shown in Fig. 4.

Feature extraction.

Feature extraction should satisfy the following requirements: (1) features should have strong anti-interference ability; (2) features should be insensitive to translation, rotation, and scale transformation of images; (3) features should be insensitive to geometric distortions; (4) distance between similar images should be as small as possible; and (5) distance between different images should be as large as possible. The algorithm for extracting feature vectors should be simple, and the dimensionality of the feature space should not be too high for ensuring the classification performance of the system (Xiao & Liu, 2017). To satisfy the above requirements, the following features were used: area, image complexity, image texture, and seven rectangular features.

In this study, three types of road hazards are studied, namely, road cracking, hollowing, and subsidence. Through simulation and actual images, combined with the classification of expert experience, three types of samples are collected to describe these conditions. Twentynine feature vectors were extracted for each sample, and the obtained set of features is shown in Tables 1, 2 and 3.

The dimensions of the different features are very different. Direct use of feature data not only reduces the system performance, but also affects the classification accuracy. To avoid this shortcoming, it is necessary to perform data normalization (Chowdhury et al., 2019). Let the eigenvector of a pattern vector be X = (x₁, x₂, …, x_m). Then the normalized eigenvector $x_i^{\prime }$ is (3)${\displaystyle x_{ij}^{\prime }=0.1+\frac{0.8\left(x_{ij}-x_{i,min}\right)}{x_{i,max}-x_{i,min}}\left(i=1,2,\dots ,m\right)}$ where, x_i,max, x_i,min are the maximum and minimum of {x_i(k)|k − 1, …, P}, and P is the overall number of samples in the training set.

Feature selection.

In this study, K − L transformation was used as the feature selection algorithm (Jun, 2016). K − L transformation can take into account different classification information and realize supervised feature extraction. Under the criterion of minimum mean square error, it can obtain an orthogonal transformation matrix A that can map the original feature X′ from high-dimensional space D to low-dimensional space vector y′. K − L transformation can retain the data component with the largest variance in the original data and highlight the data difference. Empirical knowledge was used for removing several highly correlated features, and K − L changes were used for reducing the dimensionality of the original feature space. A relatively simple class-center classifier was used for identifying the samples after the K − L dimensionality reduction transformation. The recognition rate is shown in Fig. 5 for the test set.

According to Fig. 5, when the dimensionality of the feature space reaches 12, the recognition rate saturates; thus, the optimal dimensionality of the feature space is 12. K − L transformation can take into account different classification information, realize supervised extraction of features with too high correlation, and then use K − L transformation to extract data information from them, thus achieving the purpose of compressing dimensions and improving recognition rate.

Basic principle of the SVM

SVM is a binary classification algorithm that is trained using the supervised learning paradigm. The algorithm attempts to determine an optimal classification hyperplane, whereby the edge distance between two sample classes and the dividing hyperplane (decision boundary) is maximized. The larger the edge distance is, the more separated the two sample classes are, the stronger the classification robustness, and the better the method’s generalizability (Liu et al., 2018). The hyperplane equation is (4)${\displaystyle {\omega }^{T}x+b=0}$

where ω is the normal to the hyperplane, and x determines the angle with the hyperplane; b is the distance between the hyperplane and the origin. The hyperplane is denoted as (ω, b); then, the distance from a certain point (sample) to the hyperplane (ω, b) is denoted by r: (5)${\displaystyle r=\frac{\left|{\omega }^{T}x+b\right|}{∥\omega ∥}}$

Let the support vector be 1 and point away from the hyperplane, so that $\left|{\omega }^{T}x+b\right|=1$, and let the vectors in the two different classes be γ and point away from the hyperplane: (6)${\displaystyle \gamma =\frac{2}{\left|\right|\omega \left|\right|}}$

For optimal segmentation, we need to find the hyperplane with the largest interval; that is, we need to find the parameters ω and b that maximize γ. According to Eq. (6), only ${∥\omega ∥}^{-1}$ should be maximized.

Optimization of the SVM classifier parameters

We used MATLAB (Mathworks, Inc.) to validate the diagnostic accuracy of the SVM-based classifier with respect to the road conditions. We obtained a dataset comprising 100 examples of road cracking, hollowing, and subsidence conditions; 80% of these images were used for training the method, while the remaining 20% were used for testing the classifier.

The performance of any SVM classifier depends on the penalty factor and kernel function parameters. The optimal parameter values are typically determined using the grid search approach, which exhausts the set of possible parameter combinations to determine the optimal combination.

The penalty term c and the kernal function parameters g were considered to grow exponentially in the [2⁻¹⁴, 2¹⁴] range; at the same time, the step between each cell on the grid was set to 0.5, that is, the growth time-points were 2⁻¹⁴, 2^−13.5, …, 2¹⁴. As shown in Fig. 6, the best classification performance was obtained for log₂(c)=7.60, best log₂(g) = − 6.60.

As shown in the retrieval results above, the accuracy of log₂(c) between [2⁵, 2¹⁰] and log₂(g) between [2⁻¹⁰, 2⁻⁴] was relatively good; thus, the step was set to 0.2 in this range, and the parameters were further optimized. The results are shown in Fig. 7.

According to Fig. 7, the best classification was obtained for best = 7 and best= −5.2. These optimal values were used as the SVM classifier parameters for validating its classification performance; then, the accuracy of the classifier with these parameters was characterized. The validation results are shown in Fig. 8, and the final validation accuracy rate was 88.333%, the image recognition time is t = 0.630 s.

Adaptive mutation particle swarm

The results obtained using the grid search approach can meet the desired detection requirements, but because the grid search approach only considers discrete combinations of parameters, the optimal solution can be easily missed. At the same time, the grid search method is exhaustive, and needs to consider all the possible cases; thus, this optimization approach is time-consuming. To improve the accuracy and reduce the computation time, the PSO algorithm is proposed in this section.

The PSO approach.

PSO simulates a flock of birds, which are modeled as massless particles (Hsieh et al., 2018). Each particle has only two attributes: velocity v and position x. Velocity represents the speed of movement, and position represents the direction of movement. Each particle searches for the optimal solution separately in the search space, and records it as the current individual extreme value P; the individual extreme values are shared among all the particles in the entire swarm, and the optimal individual extreme value is determined as the current global optimal solution G of the entire swarm of particles. All of the particles in the particle swarm adjust their speeds and positions according to the current individual extremum P found by themselves and the current global optimal solution G shared by the entire particle swarm. The underlying PSO process is relatively simple, and can be divided into the following steps: (1) initializing the particle swarm; (2) evaluating the particles, that is, calculating the fitness values; (3) searching for individual extrema P; (4) searching for the global optimal solution G; (5) modifying the particles’ speeds and positions (Yang, Wang et al., 2019). The update equations are: (7)${\displaystyle \begin{array}{c}{v}_{id}^{k+1}=\omega v_{id}^k+c_1\cdot rand\left(0,1\right)\cdot \left(p_{id}^k-x_{id}^k\right)\hfill \\ +c_2\cdot rand\left(0,1\right)\cdot \left(p_{gd}^k-x_{id}^k\right)\hfill \\ x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}\hfill \end{array}}$ Where ω is the inertia factor, c₁ and c₂ are the acceleration constants, and rand (0,1) are random numbers in the interval (0,1). p_id denotes d the dimension of the individual extreme value of variable i.p_gd represents the dimensionality d of the global optimal solution. k represents the current number of iterations.

The following parameter values were used: c₁ = 2, c₂ = 2, population size = 20, maximal number of iterations = 200, and cross-validation fold K = 5. The fitness curve for the optimized SVM classifier parameters is shown in Fig. 9.

After iteration 15, the fitness reached its optimal value. At this point, the classifier accuracy was 89.197%, the best c was 0.7596, and the best g was 0.7674. Although the basic PSO algorithm exhibits a good convergence speed and good optimization performance, it can prematurely converge onto a locally optimal solution; as a result, the population will easily stagnate without external pressure.

Variation improvement.

To deal with the premature convergence problem, we utilized the concept of mutations that is often used in genetic algorithms, and incorporated mutations into the PSO framework. For that, we defined a trigger to allow particles to escape locally optimal solutions, thus ensuring a global search (Tong et al., 2018). The population fitness variance σ² was used for determining whether a local maximum was reached in the iteration process. The population fitness variance σ² was defined as follows: (8)${\displaystyle {\sigma }^2=\sum _{i=1}^N{\left(\frac{f_i-f_{avg}}{f}\right)}^2}$

In the above equation, N is the number of particles, f is the normalized calibration factor, f_i is the fitness of the first particle, and f_avg is the average fitness. It can be seen that the larger the value of σ², the more divergent the particle swarm; conversely, the smaller the population fitness variance, the more convergent the particle swarm is. Values of σ² close to zero indicate that the particle swarm is approaching the globally optimal solution or is converging onto a locally optimal solution. To avoid premature trapping of the particle swarm in local optima, the swarm is subjected to mutations: (9)${\displaystyle x_i\left(k+1\right)=C\cdot rand\left(0,1\right)\cdot x_i\left(k\right)}$

In the above equation, C is a normally distributed random number in the $\left[0,1\right]$ interval and is the variation factor; rand(0, 1) is a random number in the $\left[0,1\right]$ range; k is the number of iterations. Mutations alter the particles’ positions and thus allow to escape local optima (Deng et al., 2019).

The fitness curve of the improved adaptive mutation PSO algorithm for SVM-based parameter optimization is shown in Fig. 10. Evidently, the best fitness converges to a local maximum after 17 generations. Mutations allow the particle swarm to escape this local maximum after 97 generations; after that, optimization parameters are determined with higher accuracy. The finally estimated parameter values are: c = 7.751, g = 5.754. The fitness at this global optimum is 91.698%.

Simulation results.

Based on the results in the previous section, the SVM model was constructed using the following parameter values: c = 0.7596 and g = 0.7674, which were determined using the PSO method. The results are shown in Fig. 11.

For these parameter values, the accuracy of the model was 86.667%, the image recognition time is t = 0.590s; however, the recognition accuracy had not improved. The main explanation was the trapping of the particle swarm in a local optimum during the process of parameter optimization. An SVM classifier was then constructed and validated using c = 7.751 and g = 5.754; these parameter values were determined using the adaptive mutation PSO algorithm. The validation results are shown in Fig. 12.

From Fig. 12, the classification accuracy of the SVM classification model with the parameter values determined by the adaptive mutation PSO was 91.667%, the image recognition time is t = 0.615s. This classification accuracy is significantly higher compared with that achieved by the SVM method that uses parameters optimized by the grid search approach.