Shock and Vibration

Volume 2019, Article ID 8239198, 16 pages

https://doi.org/10.1155/2019/8239198

## Fault Diagnosis of Piezoelectric Sensor Patches for Vibration Control Based on Multifeature Fusion and Improved SVM

^{1}College of Mechanical Engineering, Anhui University of Science and Technology, Anhui Huainan 232001, China^{2}Anhui Key Laboratory of Mine Intelligent Equipment and Technology, Anhui University of Science and Technology, Huainan 232001, China

Correspondence should be addressed to Tian-bing Ma; moc.361@btmfd

Received 27 May 2019; Revised 31 August 2019; Accepted 9 October 2019; Published 11 November 2019

Academic Editor: Mohammad A. Hariri-Ardebili

Copyright © 2019 Tian-bing Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The fault diagnosis of piezoelectric sensor patches is very important for the stability of the vibration control system and fault-tolerant control technology. In order to improve the accuracy of fault self-diagnosis of piezoelectric sensor patches, singular value decomposition (SVD) and Hilbert marginal spectrum method are proposed to extract multiple features of each IMF component and conduct feature fusion, and a support vector machine (SVM) based on particle swarm optimization (PSO) is designed for fault identification of different eigenvalues. In the experiment, the broken and degumming piezoelectric patches are simulated. Firstly, under the excitation of the square wave signal with no noise signal, when the SVD value and the maximum amplitude of Hilbert marginal spectrum are used as the fusion eigenvalue together, the diagnostic results show that the recognition accuracy can reach 95%, compared with the recognition accuracy of 70% and 80%, respectively, when the two are used as eigenvalues alone; the recognition result under fusion eigenvalue is obviously better than that of the latter. Secondly, in order to highlight the effectiveness of this method, the aforementioned experiment is conducted under the excitation of the square wave signal interfered by 0.5 dBW–1 dBW noise signal. The experimental results show that the fault recognition of the fused eigenvalue under different noise intensity signals is still superior to that of the single eigenvalue.

#### 1. Introduction

At present, the research on vibration fault diagnosis technology mostly focuses on the fault detection and diagnosis of vibration components themselves, such as bearings and rotors [1–3], although there are few studies on the fault diagnosis of vibration sensors. In fact, in the study of active vibration control, the failure of the vibration sensor has some influence on the results of closed-loop vibration controlling and the stability of the system. Piezoelectric patches are widely used in vibration active control systems because of their good positive and negative piezoelectric effects. However, in practical engineering applications, repeated deformation caused by the piezoelectric effect will lead to fracture damage of fragile piezoelectric patches, whereas excessively high working temperature or excessively long working time will lead to degumming damage of piezoelectric patches [4]. In order to ensure the effective operation of the active vibration control system, fault diagnosis of piezoelectric sensor patches is very important.

In the study of related fault diagnosis methods, Zhang et al. [5] proposed a bearing fault diagnosis method, and combined EMD and permutation entropy to extract the characteristics of bearing faults. Lu et al. [6] proposed a fault diagnosis method for rotating machinery based on a deep neural network, which had good robustness under various working noises and environments. For the research on sensor fault diagnosis, Gao and Ho. [7] proposed a new generalized estimation method for generalized systems with measured output noise, which applies the progressive estimator of the generalized nonlinear system state and output noise to sensor fault diagnosis. This method has a strong applicability, but it is less targeted. Yang et al. [8] used expert system technology to identify fault types, but the diagnosis results assisted operators in troubleshooting faults, and the accuracy of identification needs to be further studied. Yang et al. [9] proposed a method based on residual information for fault diagnosis of the automotive active suspension sensor. The residual information of this method is greatly disturbed by the surrounding environment, and its practicality needs to be further improved.

Although the fault diagnosis research of various sensors has reached a certain level, there are a few fault diagnosis research studies on the piezoelectric patch. At present, based on piezoelectric impedance technology, Sun et al. [10] studied the change of the virtual admittance value of the piezoelectric element and then detected the self-damage of the piezoelectric element. However, this method which had a heavy task needed to detect a large amount of piezoelectric element data. Because of the various fault types of the piezoelectric patch, such as degumming fault and fracture fault, it is difficult to obtain comprehensive fault information by using a single method to extract its characteristics. Therefore, EMD-SVD processing of signals and Hilbert marginal spectrum extraction are proposed, and both of them are taken as fusion features to achieve the purpose of feature extraction of piezoelectric patch fault information. At present, EMD-SVD technology has achieved some achievements in the field of rotating mechanism fault diagnosis. For example, Hou et al. [11] used approximate singular value decomposition to extract rolling bearing fault characteristics and designed experiments to verify the effectiveness of this method under the condition of strong noise and weak fault; using BEMD and Hilbert transform, Huang et al. [12] extracted amplitude-frequency characteristics of rotor faults and proved effective in such faults as oil film oscillation, oil film rotation, and rotor loosening.

Altogether, the research of fault diagnosis technology has reached a certain level worldwide. The application of the technology is generally in the fault diagnosis of rotating mechanisms, such as gears, bearings and rotors, or the vibration parts themselves [13, 14]. The fault diagnosis of sensors is rarely studied, and the fault diagnosis of piezoelectric sensor patches is even less studied. Therefore, self-diagnosis of piezoelectric patches fault is still a relatively new research field. In this study, piezoelectric sensor patches in active vibration control of stiffened plate is taken as the research object. According to the common fault characteristics of piezoelectric patches, the multifeature fusion method is adopted to extract fault features, and the PSO-optimized SVM algorithm is used to identify fault types. Finally, the advantages of this method are compared and analyzed, and the fault diagnosis scheme with the best identification effect is determined.

#### 2. Theoretical Analysis of Piezoelectric Sensor Patch Fault Diagnosis

##### 2.1. Theoretical Analysis of EMD-SVD and Hilbert Marginal Spectrum

Empirical mode decomposition (EMD) is part of the Hilbert–Huang transformation algorithm. It can carry out adaptive decomposition according to the characteristics of the signal itself and obtain several intrinsic mode functions (IMF) [15, 16]. The specific process is as follows:(1)For signal *x* (*t*), select all local extremum points and use cubic spline function to interpolate the extremum points to fit the upper and lower envelops, and then take *m*_{1} (*t*), the mean of the upper and lower envelops:(2)If *h*_{1} is IMF, it is the first IMF component of *x* (*t*); otherwise, take it as the initial value and repeat step (1), and the result after *k* operations is as follows: Make *h*_{1k} meet IMF conditions.(3)Make

Subtract *c*_{1} from *x* (*t*), you get *r*_{1} (*t*) as follows:

Take *r*_{1} (*t*) as *x* (*t*) and repeat the previous steps to get the following results:

The iteration is stopped until *r*_{m} (*t*) becomes a monotone function that can no longer extract IMF components. At this time,

At this point, the signal is decomposed into m IMF components *c*_{m} (*t*) and residual *r*_{m} (*t*). Hilbert transformation is performed for each IMF component *c*_{m} (*t*) as given in the following expression:

Construct the analytic signal as follows:

Among them, *a*_{i} (*t*) is the instantaneous amplitude function and *φ*_{i} (*t*) is the instantaneous phase function. If the residual *r*_{m} (*t*) is ignored, we can get the following:

Instantaneous frequency is expressed as follows:

Therefore, the Hilbert spectrum can be obtained by expanding equation (9) as follows:

Hilbert marginal spectrum is the integral of Hilbert spectrum on the time axis, as shown in the following equation:

Singular value decomposition (SVD) is an algebraic feature extraction method [17]. Specifically, it is an orthogonal method. By multiplying the left and right sides of the original matrix by an orthogonal matrix, it is transformed into a diagonal matrix and the linearly dependent rows or columns of the matrix become linearly independent.

For any matrix , its rank is *r*. If there are two orthonormal moment **U** and **W** matrices and diagonal matrix **D** to make the following formula valid, then equation (13) is the singular decomposition of :Among them, **U** and **W** are orthogonal matrices and **D** is a diagonal matrix.

##### 2.2. Fault Recognition Principle Based on PSO-SVM

The support vector machine (SVM) is a method based on the statistical learning theory, whereas traditional statistical learning is difficult to achieve the ideal learning effect in the case of small samples. To address this problem, V.Vapnik and his research team proposed the SVM. The basic idea of SVM is to define the optimal hyperplane and transform the algorithm of finding the optimal linear hyperplane in space into an optimization problem [18, 19].

The actual signal data belong to the problem of linear inseparability. According to the constraint conditions,

Then, the hyperplane meets the following conditions:Among them, *ξ*_{i} is the penalty function of outlier and *C* is the penalty coefficient.

In the SVM train function, there are two important parameters *c* and ; *c* is the penalty parameter, and is the kernel parameter. Particle swarm optimization (PSO) is used to optimize the selection of these two parameters. The PSO algorithm seeks the global optimal solution by following the currently searched optimal value and evaluates the quality of solution by fitness.

The fault of different piezoelectric sensor patches is simulated, and the response signals under different excitation are collected in the experiment. The signal is decomposed by EMD, and the SVD value and Hilbert marginal spectrum of IMF components are obtained as the feature vectors. After normalization, those are, respectively, sent to the SVM for training and recognition. The cross-validation recognition accuracy of the SVM is taken as the fitness, and the *c* and parameters of the SVM are optimized by particle swarm optimization (PSO). Finally, the recognition accuracy of the SVM algorithm under optimal parameters of *c* and is obtained, so as to explore the influence of different feature value extraction on the fault recognition effect. The experimental flow chart is shown in Figure 1.