A hybrid support vector regression with multi-domain features for low-velocity impact localization on composite plate structure

https://doi.org/10.1016/j.ymssp.2020.107547Get rights and content

Highlights

  • A hybrid support vector regression with multi-domain features is proposed.

  • The empirical mode decomposition method is used to eliminate the trend component.

  • The multi-domain features with more comprehensive impact information are extracted.

  • The parameters of the support vector regression are optimized by using the bat algorithm.

  • Prove the satisfactory localization performance of the proposed method.

Abstract

The accurate localization of low-velocity impacts on the composite plate structure of the ship is still a great challenge. Current research mainly focuses on extracting single domain features from impact signals as the input of machine learning methods, whereas ignores multi-domain features with more comprehensive impact information. In this paper, a hybrid support vector regression with multi-domain features is proposed to increase the localization accuracy in determining the locations of low-velocity impacts on the composite plate structure. The proposed method consists of the signal preprocessing, the multi-domain feature extraction, and the impact localization. In the signal preprocessing, the trend component in the low-velocity impact signals is eliminated by adopting the empirical mode decomposition (EMD) method. Then, the multi-domain features, which include time domain features, frequency domain features, and time-frequency domain features, are extracted from the preprocessed impact signals. Finally, the optimized support vector regression based on the bat algorithm (BA-SVR) is designed to implement the localization of low-velocity impacts. The low-velocity impact localization system using four fiber Bragg grating (FBG) sensors is established on a carbon fiber reinforced plastic (CFRP) plate, and then five sets of experiments are executed. The statistical results in these experiments demonstrate the effectiveness and feasibility of BA-SVR that uses multi-domain features and four FBG sensors and the satisfactory localization performance of the proposed method in handling the low-velocity impact localization problem on the CFRP plate.

Introduction

Low-velocity impacts on the composite plate structure of the ship have attracted more attention since composite materials with high weight-to-strength ratio have been increasingly applied. These impacts caused by collisions with floating ice, stranding, and explosion can lead to barely visible impact damage (BVID). It is difficult to detect BVID on the composite plate structure by the visual inspection, but BVID can reduce the strength of the structure [1]. Therefore, to detect the locations of low-velocity impacts, it is crucial to develop structural health monitoring (SHM) for the composite plate structure of the ship. In the SHM system, low-velocity impact signals can be received by different types of sensors, such as piezoelectric (PZT) sensors [2], [3] and fiber optic sensors [4]. Among various available sensors, fiber Bragg grating (FBG) sensors are more suitable for SHM applications in large-scale structures. This is because FBG sensors have the advantages of flexibility, multiplexing capability, corrosion resistance, small sizes, and high sensitivity, and they can easily form a sensor network without causing damage to the composite plate structure. Additionally, FBG sensors are immune to the electromagnetic interference, which means that signals acquired by FBG sensors are not affected by the electromagnetic interference [5], [6], [7].

An increasing number of impact localization methods have been developed to locate the low-velocity impacts on the composite plate structure, which can be divided into active methods and passive methods. Different from active methods such as the time reversal method [8], passive methods are simpler and more effective when only the locations of low-velocity impacts need be determined. Passive methods mainly include geometric methods [9], machine learning methods [10], and reference database methods [11].

Since the low-velocity impact localization problem can be considered a classification problem or regression problem, machine learning methods such as the support vector machine (SVM) [12] and the back propagation neural network (BPNN) [13] have been widely utilized. Based on the frequency characteristics of impact signals which were achieved by the Fourier transform method, Jiang et al. [14] applied the extreme learning machine (ELM) to the identification of impact areas on a carbon fiber reinforced plastic (CFRP) plate. Yu et al. [15] achieved satisfactory impact localization results on a CFRP plate by using the short-time energy characterization extraction method and the SVM model whose parameters were optimized. For the impact localization on a CFRP plate, Lu et al. [16] combined the wavelet packet energy spectra of the low-velocity impact signals with the support vector regression (SVR) model to determine the locations of low-velocity impacts. Datta et al. [17] extracted the features, including the peak value, the mean value, the standard deviation, and the energy index, from time signals and strain signals and chose them as the input of the least squares support vector regression (LS-SVR) model. Moreover, Sai et al. [18] established the ELM model with the energy of frequency band signals which were obtained by the wavelet packet decomposition method. For the low-velocity impact localization system using FBG sensors, most of the current research focuses on using the single domain features to implement the localization or identification of low-velocity impacts on composite plate structures, which may lead to low localization accuracy.

Additionally, the selection and application of machine learning methods also have a significant influence on the localization accuracy for low-velocity impacts. Many studies [19], [20], [21] have demonstrated the superior generalization performance of SVR compared with other nonlinear methods, whereas an inappropriate determination of hyperparameters in the SVR model can dramatically decrease the method’s performance on regression problems. In addition to the grid search (GS) method [22], metaheuristic algorithms are common optimization methods for strengthening the performance of SVR. For example, the particle swarm optimization (PSO) algorithm [23], the genetic algorithm (GA) [24], and the differential evolution (DE) [25] algorithm have been successfully applied to the parameter selection in the SVR model.

In this paper, we propose a hybrid support vector regression with multi-domain features for the low-velocity impact localization problem on the composite plate structure. To extract more effective features, the trend component in the low-velocity impact signals is eliminated by utilizing the empirical mode decomposition (EMD) method. Then, three feature extraction methods, which are the time-domain feature method, the frequency-domain feature method, and the short time Fourier transform method, are employed to obtain multi-domain features as the input of the SVR model. Moreover, the optimized v-SVR model (BA-SVR) is designed to enhance its regression capability, in which three parameters involving the kernel parameter γ, the penalty parameter C, and the parameter v are tuned by using the bat algorithm (BA). The low-velocity impact localization system using four FBG sensors is adopted to analyze and evaluate the performance of BA-SVR with multi-domain features.

The organization of this paper is given as follows. In Section 2, the relative theories of the FBG sensor and the proposed method are presented. The optimized v-SVR model is given in Section 3. Section 4 provides the details of the hybrid support vector regression with multi-domain features. Section 5 discusses the results obtained by the proposed method in five sets of experiments. Finally, the conclusion and the direction of future work are given in Section 6.

Section snippets

Principle of FBG sensor

The FBG sensor can reflect part of the spectrum of incident light, and its refractive index changes periodically along with the Bragg grating length [26]. Based on the effective refractive index nneff and the grating period Λ, the Bragg wavelength λ is calculated by Eq. (1).λ=2nneffΛ

The shift in the Bragg wavelength of the back-reflective light depends on the change of the refractive index and the grating period with the temperature and the strain. In the laboratory environment, the impact

Optimized v-SVR

The v-SVR model has three parameters which are the kernel parameter γ, the penalty parameter C, and the parameter v. The determination of these parameters commonly depends on the trial and error search method based on manual operation, which is time consuming and may have a negative influence on the regression performance of the v-SVR model. Generally, a larger penalty parameter C and a smaller kernel parameter γ indicate that the v-SVR model has a greater nonlinear fitting capability and

Hybrid support vector regression with multi-domain features

To increase the localization accuracy for low-velocity impacts on the composite plate structure, the hybrid support vector regression with multi-domain features is proposed. After acquiring low-velocity impact signals by the FBG sensing system, three steps, which are the signal preprocessing, the multi-domain feature extraction, and the impact localization, are executed. The procedures of the proposed method are illustrated in Fig. 1 and given in detail below.

Step 1: The trend component induced

Experiments and discussions

In this paper, a low-velocity impact localization system is utilized to monitor the low-velocity impacts on the composite plate structure. The contributions of the multi-domain features and influence of the number of FBG sensors and the number of optimal parameters are analyzed, and then the performance of the hybrid support vector regression with multi-domain features in solving the low-velocity impact localization problem is evaluated.

Conclusions

In this paper, a hybrid support vector regression with multi-domain features is proposed for the low-velocity impact localization problem on the composite plate structure. The proposed method has three steps including the signal preprocessing, the multi-domain feature extraction, and the impact localization. First, the low-velocity impact signals acquired by FBG sensors are preprocessed by the EMD method to remove the trend component. Second, the time domain features, the frequency domain

CRediT authorship contribution statement

Qi Liu: Conceptualization, Methodology, Validation, Investigation, Writing - original draft, Writing - review & editing. Fengde Wang: Software, Validation, Investigation, Writing - review & editing. Jindong Li: Validation, Visualization, Writing - review & editing. Wensheng Xiao: Validation, Resources, Data curation, Supervision, Project administration, Funding acquisition.

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.

Acknowledgement

The authors would like to acknowledge the High-tech Shipping Research Project from Ministry of Industry and Information Technology of China for supporting this study through the project “Research of full life-cycle reliability guarantee technology system for subsea oil and gas production system” with the grant number of 2018GXB01-02-003.

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      It indicates that the proposed impact localization method can provide greater localization performance than most of the comparative methods whether considering the number of FBG sensors or not. Additionally, the sampling frequency employed in the present work is lower than the sampling frequency employed in the previously published studies except [24,26], and [41]. However, the proposed impact localization method collects a larger number of impact samples than the comparative methods.

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