Complexity

Volume 2018, Article ID 2896850, 13 pages

https://doi.org/10.1155/2018/2896850

## Research on Multidomain Fault Diagnosis of Large Wind Turbines under Complex Environment

^{1}Key Laboratory of Smart Energy in Xi’an, Xi’an University of Technology, Xi'an 710048, China^{2}GEIRI North America, 250 W Tasman Dr., San Jose, CA 95134, USA

Correspondence should be addressed to Fuqi Ma; moc.361@67174629381

Received 2 April 2018; Accepted 6 June 2018; Published 17 July 2018

Academic Editor: Changzhi Wu

Copyright © 2018 Rong Jia 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

Under the complicated environment of large wind turbines, the vibration signal of a wind turbine has the characteristics of coupling and nonlinearity. The traditional feature extraction method for the signal is hard to accurately extract fault information, and there is a serious problem of information redundancy in fault diagnosis. Therefore, this paper proposed a multidomain feature fault diagnosis method based on complex empirical mode decomposition (CEMD) and random forest theory (RF). Firstly, this paper proposes a novel method of complex empirical mode decomposition by using the correlation information between two-dimensional signals and utilizing the idea of ensemble empirical mode decomposition (EEMD) by adding white noise to suppress the problem mode mixing in empirical mode decomposition (EMD). Secondly, the collected vibration signals are decomposed into IMFs by CEMD. Then, calculate 11 time domain characteristic parameters and 13 frequency domain characteristic parameters of the vibration signal, and calculate the energy and energy entropy of each IMF components. Make all the characteristic parameters as the multidomain feature vectors of wind turbines. Finally, the redundant feature vectors are eliminated by the importance of each feature vector which has been calculated, and the feature vectors selected are input to the random forest classifier to achieve the fault diagnosis of large wind turbines. Simulation and experimental results show that this method can effectively extract the fault feature of the signal and achieve the fault diagnosis of wind turbines, which has a higher accuracy of fault diagnosis than the traditional classification methods.

#### 1. Introduction

As a kind of abundant, renewable, and efficient clean energy, wind energy has developed rapidly in recent years. Currently, wind power generation technology has become an important research area for countries to compete and has been promoted to the height of national strategy [1–3]. As the installed capacity of wind turbines becomes larger and larger, the structure of the turbines becomes more and more complicated, and they work under harsh conditions for a long period of time. Therefore, higher requirements are put on the fault diagnosis technology of the wind turbines [4, 5]. It is of great significance for wind turbine condition monitoring and fault diagnosis accurately and comprehensively to extract the fault feature of vibration signals [6–8].

Since the wind turbine fault vibration signals with the characteristics of nonlinear and nonstationary [9], at present, many scholars have done some research on the fault feature extraction of a wind turbine. The main method uses vibration sensors which acquire the vibration signal of wind turbine, utilize some methods with strong applicability for feature extraction, and then use fault diagnosis methods to diagnose the fault by utilizing fault information extracted for wind turbine. The methods for signal processing include wavelet transform (WT) [10, 11], Hilbert-Huang transform, empirical mode decomposition (EMD) [12, 13], and variational mode decomposition (VMD) [14, 15]. For instance, Gao et al. [16] utilize load mean decomposition (LMD) decomposing the vibration signal into multiple product functions. The characteristic parameters were achieved by the multiscale entropy method of processing the main product functions. The characteristic parameters were entered into the least square support vector machine (SVM) for fault diagnosis of the wind turbine.

Muralidharan and Sugumaran [17] compute the wavelet features by using discrete wavelet transform (DWT) from the vibration signals. And the rough sets are generated by wavelet features to classify using the fuzzy logic. Jiao et al. [18] use the EMD method to decompose the original vibration signals into finite intrinsic mode functions (IMFs) and a residual. And the energy of the first four IMFs is extracted as vibration signal fault feature. A probabilistic neural network (PNN) model is established to achieve the fault classification. However, these methods all use the signal processing method to extract the time-frequency characteristic information of the vibration signal, and the feature information extracted is often not comprehensive enough.

In order to comprehensively extract the fault feature information, many scholars have studied the method of multidomain feature fault diagnosis. Tang et al. [19] proposed a novel method for fault diagnosis based on manifold learning and Shannon wavelet support vector machine. And the Shannon wavelet support vector machine (SWSVM) is established to recognize faults by using the mixed-domain features extracted. Gan et al. [20] obtain the time domain and frequency domain characteristics of vibration signals by singular value decomposition (SVD) and utilize the multidomain manifold learning to achieve this method to realize the fault diagnosis of mechanical equipment. Shen et al. [21] decompose the vibration signal into IMFs by empirical mode decomposition (EMD). 13 time domain characteristic parameters and 16 frequency domain characteristic parameters were extracted, and the parameters into the support vector machine model for fault diagnosis were input. However, there are still some shortcomings in the current research of multidomain feature fault diagnosis. It includes that the effect of traditional time-frequency signal processing methods is often not ideal, and with the increase of feature vectors, it is more difficult for the wind turbine to diagnose and there will be redundant feature information in multidomain feature vectors.

Complex empirical mode decomposition (CEMD) is based on the principle of bivariate empirical mode decomposition, which uses the correlation information between two-dimensional signals to decompose synchronously and utilizes the principle of ensemble empirical mode decomposition (EEMD) through adding white noise to suppress mode mixing. This method can effectively improve the problem of mode mixing in EMD. As a classical algorithm in ensemble learning, random forest (RF) can not only effectively solve the problems of artificial neural network such as slow convergence and over-fitting but can also solve the shortcomings of the SVM algorithm’s inability to process large sample data [22–24].

Considering the advantages of the two algorithms, this paper proposes a multidomain feature fault diagnosis method based on complex empirical mode decomposition and random forest theory and applies it to the fault diagnosis of wind turbines. The specific arrangement of this paper is organized as follows. The view on the principle of complex empirical mode decomposition (BEMD) is illustrated in Section 2. Section 3 describes the method of multidomain feature vector extraction. Section 4 gives brief introductions of random forest theory. Section 5 describes the multidomain feature fault diagnosis method based on CEMD and random forest theory. Section 6 is the simulation verification of CEMD this paper proposed. Section 7 applies the proposed method to fault signals of rolling bearing. Conclusions come in Section 8.

#### 2. The Principle of Complex Empirical Mode Decomposition

##### 2.1. The Basic Theory of CEMD

At present, many scholars have done some research on the algorithm of CEMD. Tanaka and Mandic [25, 26] proposed a complex empirical mode decomposition to process two-dimensional signals, but the essence of this method is to perform empirical mode decomposition on the real and imaginary parts of the complex data composed of two-dimensional signals. But this method does not consider the correlation between real and imaginary parts in the decomposition process. Rilling et al. [27] proposed a new algorithm of bivariate empirical mode decomposition (BEMD) which fully considers the correlation between the real and imaginary parts, and unified decomposed complex data signals contained real and imaginary parts so that the decomposition results also have physical meanings. Therefore, this paper uses this method to perform complex data empirical mode decomposition. The main process is as follows [27]:

*Step 1. *Determine the projection direction , where .

*Step 2. *The two-dimensional signal () is projected onto the .

*Step 3. *Extract the corresponding moment for the local maximum of ; then, the set is interpolated. Get the maximum envelope in the direction .

*Step 4. *Calculate the mean of the maximum envelope in each direction.

*Step 5. *Similar to the EMD decomposition process, calculate the residual component:
whether the meets the requirements of IMF. If satisfied, proceed to Step 6. If not, repeat carried out Steps 2–6, until satisfies the conditions of the intrinsic mode function IMF.

*Step 6. *Record the resulting IMF, and remove it from the original signal. And obtain the IMF1 as ; residual component can be expressed as

*Step 7. *Repeat the above steps until you get all the IMFs. The original signal can be expressed as
where represents the total number of IMFs.

##### 2.2. The Decomposition Principle of CEMD

The decomposition principle of CEMD this paper proposed is based on the bivariate empirical mode decomposition proposed by Rilling et al. [27]. The specific construction ideas are as follows:

Let be the original vibration signal collected by the vibration sensor. Let be the white noise signal with a certain amplitude. Thus, a complex signal constitutes as follows:

Project the complex signal into all directions [19]:

Substituting (7) into Euler’s formula can simplify

Formula (6) indicates, when , in other words, . The projection is equivalent to adding white noise with limited amplitude to observation signals that scale at different scales. It can be seen that, in the given direction, the added noise has an effect on the selection extreme points for the signal. Then, the complex data can be obtained by again projecting the resulting project. That is to say, the data should be interpolated in Step 3 which can be expressed as :

Then, the real and imaginary parts of the complex signal obtained are interpolated separately. Assume that the interpolated value of the real part of the complex signal is . Assume that the interpolated value of the imaginary part of the complex signal is . So the interpolation of the complex signal can be expressed as

After finding the envelope of the maximal values in each direction, we need to average the projections of the complex signal to obtain the centroids in all directions. When the number of projection directions selected approaches infinity, the idea of integration can be used. Considering that the processing object of this method is the real part of the complex data that collected original vibration signal, therefore, only the real part of the complex signal needs to be integrated. The result is as follows:

It can be seen that white noise is added as the imaginary part of the complex data, and the projection that the decomposition of imaginary noise projects on the real part can assist in the selection of extreme points of the real part. So the phenomenon of mode mixing can be reduced. In addition, the added white noise is completely canceled when the average is calculated, and it does not affect the original signal.

#### 3. Multidomain Feature Vector Extraction

In order to obtain comprehensive fault feature information, this paper uses parameter statistical analysis, Fourier transform, and complex empirical mode decomposition to extract multidomain feature vectors from fault diagnosis signals. There are 11 time domain feature vectors, 13 frequency domain feature vectors, and specific time-frequency characteristics [28]. The specific parameters are shown in Tables 1 and 2.