Journal of Sensors

Volume 2016 (2016), Article ID 6971952, 14 pages

http://dx.doi.org/10.1155/2016/6971952

## Gearbox Fault Diagnosis in a Wind Turbine Using Single Sensor Based Blind Source Separation

School of Instrument Science and Engineering, Southeast University, Nanjing, Jiangsu 210096, China

Received 28 January 2015; Accepted 19 March 2015

Academic Editor: Mehmet Karakose

Copyright © 2016 Yuning Qian and Ruqiang Yan. 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

This paper presents a single sensor based blind source separation approach, namely, the wavelet-assisted stationary subspace analysis (WSSA), for gearbox fault diagnosis in a wind turbine. Continuous wavelet transform (CWT) is used as a preprocessing tool to decompose a single sensor measurement data into a set of wavelet coefficients to meet the multidimensional requirement of the stationary subspace analysis (SSA). The SSA is a blind source separation technique that can separate the multidimensional signals into stationary and nonstationary source components without the need for independency and prior information of the source signals. After that, the separated nonstationary source component with the maximum kurtosis value is analyzed by the enveloping spectral analysis to identify potential fault-related characteristic frequencies. Case studies performed on a wind turbine gearbox test system verify the effectiveness of the WSSA approach and indicate that it outperforms independent component analysis (ICA) and empirical mode decomposition (EMD), as well as the spectral-kurtosis-based enveloping, for wind turbine gearbox fault diagnosis.

#### 1. Introduction

Wind energy is one of the renewable energy sources, which have received considerable attention around the world. As critical equipment for wind energy development, the wind turbine is being widely used due to its technological maturity and good infrastructure construction [1, 2]. However, with the high demand for energy efficiency, the size of the wind turbine is increasing over the years, leading to high operation costs and risk of failures. To avoid expensive maintenance costs and economic losses caused by wind turbine failures, researches on condition monitoring and fault diagnosis of the wind turbine have been carried out. For example, Kotzalas and Doll [3] investigated the failure principle of various wind turbines. Ciang et al. [1], García Márquez et al. [4], and Liu et al. [5] reviewed the existing condition-monitoring strategies and relative fault diagnosis methods for wind turbines. Chen et al. [6] summarized main failure modes of the wind turbines and corresponding signal characteristics. It is known that the wind turbine failures often occur in the generator, blade, gearbox, and electrical system. As a key component for wind turbines, the gearbox is vulnerable to damage and the gearbox failure has a severe influence on working status of the whole system. As a result, effective diagnosis of gearbox failures has become a focused research trend. Generally, the gear mesh signal is strong while the gearbox fault-related signal is often weak and transient, causing difficulty to separate such fault-related signatures from gear mesh signals.

Over the past, some filtering methods [7, 8], for example, spectral-kurtosis-based and autoregressive model-based methods, were used to extract the fault-related signal components, but the filtering results are highly related to the filter parameter selection and may be sensitive to noise. Li et al. [9] developed a noise-controlled technique based on stochastic resonance method to enhance the fault signal by adjusting the input signal and the noise level. Combet and Gelman [10] and Heyns et al. [11] both utilized the time synchronous averaging technique to remove the gear meshing frequency with the help of an independent encoder signal to resample the measured vibration signals. Different from the above methods, independent component analysis (ICA) is a blind source separation approach, which can separate the raw signal into several independent sources without any prior information or reference signal. For example, both He et al. [12] and Wang et al. [13] used the ICA to extract the fault-related features from gearbox vibration signals. However, the ICA approach needs to assume that each component to be separated is independent and does not take distribution changes of the signals into account. Compared with ICA, the recently developed stationary subspace analysis (SSA) [14] is also a blind source separation approach. The SSA can not only take the signal distribution into consideration [15], but also decompose a multidimensional time series into stationary and nonstationary source components without the independency assumption of these source signals. Since the gearbox fault-related signal often exhibits nonstationary behavior due to complex working condition of the wind turbines, it can be naturally characterized by the nonstationary components resulting from the SSA. Therefore, the SSA presents a good alternative for gearbox fault diagnosis. The applications of the SSA have been seen in change-point detection of the multidimensional time series [16], EEG signal processing [15, 17], geophysical data analysis [18], and image processing [19]. It should be noted that there is a multidimensional requirement when implementing the SSA algorithm. For real-time gearbox fault diagnosis of the wind turbine, although there are several sensors attached on the system, we often have only one sensor near the fault component to collect a single-dimensional signal that is highly related to the fault feature. To address such a problem, this paper presents a single sensor based blind source separation approach for gearbox fault diagnosis by integrating continuous wavelet transform with stationary subspace analysis, which is called the wavelet-assisted stationary subspace analysis (WSSA). The proposed approach first uses CWT to decompose a one-dimensional signal into multiscale wavelet coefficients, which can be considered as a multidimensional signal. Then, the SSA is applied to separating it into a set of stationary and nonstationary source components. It should be emphasized that the key of the proposed approach is to utilize the inherent multiscale analysis capability and the redundancy resulting from the CWT decomposition for dimension extension of a single sensor signal [20] and then select the SSA as a blind source separation approach for both the stationary and nonstationary signal components separation. Besides, this paper also proposes to use modified principal component analysis and runs test methods to select the number of wavelet scales and the number of nonstationary source components, respectively, for further improving the effectiveness of the WSSA approach.

The organization of the rest of the paper is as follows. Section 2 provides the theoretical background of the CWT and the SSA. The parameter selection methods for the SSA and the framework of the WSSA-based gearbox fault diagnosis approach are introduced in Section 3. Section 4 gives the experimental results, together with some discussions. Conclusions are finally stated in Section 5.

#### 2. Wavelet-Assisted Stationary Subspace Analysis

##### 2.1. Continuous Wavelet Transform

The CWT of a signal is defined as the inner product of the signal and a selected wavelet function, which is expressed aswhere is the scaled and translated wavelet function, is the scale factor, and denotes the time location. From this equation, the CWT at a certain scale can be considered as a continuous correlation operation between the original signal and the wavelet function by changing the time location . The result of the CWT is a series of wavelet coefficients with the same length as the original signal, which can express the similarity between the signal and the wavelet function at a given scale. It should be noted that the selection of the wavelet function significantly affects the performance of the CWT. Previous study for wavelet function selection using a quantitative measure (i.e., energy-to-Shannon entropy ratio) [22] has shown that the Morlet wavelet is effective for mechanical fault feature extraction and it has also been successfully applied in many cases [23–25]. Hence, the Morlet wavelet is chosen as the wavelet function in this study.

##### 2.2. Stationary Subspace Analysis (SSA)

The SSA [14] is a blind source separation technique that can separate the stationary source components from the nonstationary source components in a multidimensional signal. Neither independency nor prior information is required for these source components. In the SSA algorithm, the observed signal with -dimension is assumed to be generated by a linear mixture of stationary sources (-sources) and nonstationary (*n*-sources) sources , and can be expressed aswhere is an unknown invertible mixing matrix. The spaces spanned by the columns of and are called -space and -space, respectively. Particularly, different from the ICA algorithm, there is no independency assumption on the sources and . The aim of the SSA algorithm is to find a linear transformationthat can separate the stationary sources from nonstationary sources . This can be expressed aswhere and are the estimated stationary and nonstationary sources and and are called -projection and -projection. The SSA algorithm uses weak stationarity condition as an optimization criterion to recover the sources as stationary as possible [16]. The weak stationarity condition can be expressed as the mean and covariance of a time series are constant over time. Since the SSA employs an optimization criterion to recover the sources as stationary as possible, it can identify the true , not the true . The is often identified by maximizing the nonstationarity of the estimated nonstationary sources. The flowchart of the SSA is shown in Figure 1 and the specific procedures are illustrated as follows.