Shock and Vibration

Volume 2018 (2018), Article ID 8218657, 7 pages

https://doi.org/10.1155/2018/8218657

## Research on Fault Diagnosis Based on Singular Value Decomposition and Fuzzy Neural Network

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, Heilongjiang 150001, China

Correspondence should be addressed to Yifan Hu; nc.ude.uebrh@g5027202102

Received 10 January 2018; Accepted 7 March 2018; Published 8 April 2018

Academic Editor: Giosuè Boscato

Copyright © 2018 Jingbo Gai and Yifan Hu. 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

A method based on singular value decomposition (SVD) and fuzzy neural network (FNN) was proposed to extract and diagnose the fault features of diesel engine crankshaft bearings efficiently and accurately. Firstly, vibration signals of crankshaft bearings in known state under the same working condition were decomposed by EMD to obtain the modal components containing fault-feature information. Then, the singular values of modal components which include the main fault features were used as the initial vector matrix, where the eigenvectors were decomposed to form a fault characteristic matrix. At last, the fault features matrix was trained by the fuzzy neural network, in order to realize the diagnosis and identification of the crankshaft bearings in different states in the form of numerical values. The experiment showed that the numerical identification of the fuzzy neural network based on the singular value had high fault diagnosis accuracy and stability. This method can also reflect the gradual change of the crankshaft bearings’ fault to some extent, so it has the desired reliability and value.

#### 1. Introduction

Crankshaft bearing is an important part of the diesel engine with a high failure and abrasion rate. If we can extract fault-feature information from the vibration signals effectively and identify the operating state of the crankshaft bearing and then repair or replace it in time, it will be of great significance for the safety and economy of the diesel engine [1].

If we want to classify different fault states exactly, it is necessary to extract accurate signal features and identify these features accurately. Many experts have done a great deal of research on this. Yang et al. [2] decomposed nonstationary vibration signals into a series of intrinsic mode functions with empirical mode decomposition and input their energy into the neural network for fault diagnosis, and this method achieved good results; Xia et al. [3] proposed a method of fault diagnosis based on the combination of empirical mode decomposition and AR spectroscopy; Si et al. [4] used wavelet packet to denoise the vibration signal, extracted the eigenvalue of the fault signal, and used the fuzzy neural network to diagnose and recognize the fault states. With reference to the modal aliasing of EMD, Zhang et al. [5] extracted engine crankshaft fault features by integrated empirical mode decomposition, which can identify different fault states efficiently. However, the above extraction methods of fault features still need to be further discussed in terms of accuracy and stability. Singular values are the inherent features of the matrix. When the matrix elements change slightly, the singular values of the matrix change very little. At the same time, singular values have scale invariance and rotation invariance. Therefore, based on empirical mode decomposition, singular value decomposition can effectively solve the above-mentioned problem. Guo et al. [6] constructed the time-frequency matrix of the vibration signal by Hilbert-Huang transform, and the singular value of the matrix was regarded as the feature vector, and then they used FCM to classify the fault states of the distribution switch. Zhou et al. [7] proposed a fault diagnosis method of rolling bearing based on EMD-SVD and FCM. Although the extraction of fault features was effectively improved by singular value decomposition, it is still worth a further discussion on the accuracy and stability of diagnosis and recognition. As an important intelligent information processing method, fuzzy neural network has strong self-learning and data direct processing ability, so it can express the structure of the result clearly. Therefore, the fuzzy neural network can be used to classify the features of different faults in the form of numerical value; this method can also reflect the gradient of fault to some extent.

This paper combined the advantages of the above-mentioned method in the extraction and recognition of fault features for the first time; a new fault diagnosis method based on EMD-SVD and fuzzy neural network was proposed. It was proved by experiment that this method can effectively compensate the shortage of previous research, and it had high accuracy and stability of fault diagnosis.

#### 2. The Introduction of EMD-SVD

##### 2.1. Empirical Mode Decomposition (EMD)

Empirical mode decomposition is a smoothing process, which can decompose a complex, nonstationary signal into a number of intrinsic mode functions, and we abbreviate it as IMF [8]. The instantaneous frequency of any point in the IMF is meaningful. At any given moment, the signal can contain several IMF components. Each IMF’s frequency and composition are different and the decomposition process is self-adaptive, so EMD is very suitable for dealing with nonstationary bearing vibration signals [9]. In the process of empirical mode decomposition, each IMF component must satisfy the following two conditions: firstly, the number of the extreme points and the zero points should be equal to or not more than one; secondly, the mean of the maximum and minimum of extreme points is zero at any point in the signal curve [10]. Since most of the nonstationary signals do not satisfy the IMF conditions directly, Huang made the following assumptions [11]: any complex signal is composed of IMFS which are independent of each other and each IMF component can be linear or nonlinear. For the signal , its empirical mode decomposition equation can be expressed as

In the equation, means the IMF components, means the residual component, and it represents the average trend of the signal.

However, vibration signals of diesel engine crankshaft bearings often contain noises or intermittent signals, and this makes empirical mode decomposition exhibit a shortage of modal aliasing, so the extraction of signal features becomes unstable and inaccurate [12]. Singular value decomposition can effectively reduce the interference of noise components and intermittent signals, so singular value decomposition based on empirical mode decomposition can effectively extract the stable fault features. In the process of solving practical problems, we often focus on the effective IMF components, which contain the main fault-feature information. Therefore, selecting the effective IMF components is also a key step of fault-feature extraction in this paper.

##### 2.2. Singular Value Decomposition (SVD)

Singular value decomposition (SVD) is an important orthogonalization method of matrix decomposition in linear algebra. For a linear correlation matrix of rows or columns, it can be transformed into a linearly independent one by multiplying an orthogonal matrix on its left and right side, respectively. For a real matrix, , whose rank is , if there exist two orthonormal matrices, and , and another diagonal matrix, , they satisfy the following equation:

Equation (2) is called the singular value decomposition of the real matrix .

In this equation, , , , , , and are the singular values of the real matrix . , , are the eigenvalues of . Under the restrictions of , the singular value of the matrix is unique [10]. The singular value has the following two features: (1) the singular values of matrices have a better stability and (2) the singular values also have both proportion invariance and rotation invariance. Therefore, singular values can reflect the features of eigenvectors very well. In the process of constructing the real matrix , the time delay embedding technique is usually used to reconstruct the phase space of one-dimensional time series. However, there is no clear theoretical guidance on how to determine the embedding dimension and the delay constant. For this problem, this paper combined EMD and SVD and formed the initial eigenvector matrix automatically by the IMF components with EMD. This combined EMD and SVD method can avoid the arbitrary choice of embedding dimensions and delay constants [10].

#### 3. Fuzzy Neural Network

Fuzzy neural network is an important intelligent information processing method, which combines the advantages of fuzzy logic and neural networks well. Therefore, the fuzzy neural network algorithm not only has a strong self-learning ability to deal with data directly but also has a strong ability of structural knowledge expression. Figure 1 shows the general structure of the fuzzy neural network.