Shock and Vibration

Volume 2016 (2016), Article ID 1485412, 13 pages

http://dx.doi.org/10.1155/2016/1485412

## Adaptive Multiscale Noise Control Enhanced Stochastic Resonance Method Based on Modified EEMD with Its Application in Bearing Fault Diagnosis

^{1}College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China^{2}College of Liren, Yanshan University, Qinhuangdao 066004, China

Received 30 June 2016; Accepted 28 September 2016

Academic Editor: Ganging Song

Copyright © 2016 Jimeng Li and Jinfeng Zhang. 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 structure of mechanical equipment becomes increasingly complex, and tough environments under which it works often make bearings and gears subject to failure. However, effective extraction of useful feature information submerged in strong noise that is indicative of structural defects has remained a major challenge. Therefore, an adaptive multiscale noise control enhanced stochastic resonance (SR) method based on modified ensemble empirical mode decomposition (EEMD) for mechanical fault diagnosis is proposed in the paper. According to the oscillation characteristics of signal itself, the algorithm of modified EEMD can adaptively decompose the fault signals into different scales and it reduces the decomposition levels to improve calculation efficiency of the proposed method. Through filter processing with the constructed filters, the orthogonality of adjacent intrinsic mode functions (IMFs) can be improved, which is conducive to enhancing the extraction of weak features from strong noise. The constructed signal obtained by using IMFs is inputted into the SR system, and the noise control parameter of different scales is optimized and selected with the help of the genetic algorithm, thus achieving the enhancement extraction of weak features. Finally, simulation experiments and engineering application of bearing fault diagnosis demonstrate the effectiveness and feasibility of the proposed method.

#### 1. Introduction

With the fast development of modern technology, the structure of mechanical equipment becomes increasingly complex, and the automation degree becomes more and more high, but tough environments under which it works often make bearings and gears subject to failure. The failure may deteriorate mechanical performance and even lead to fatal breakdowns. Therefore, how to ensure the safe and reliable operation of mechanical equipment and reduce economic losses is increasingly becoming a hot topic concerned by enterprises. The health monitoring and fault diagnosis technology provides an effective solution for the predictive maintenance of mechanical equipment operating state. In view of the inherent link between machine operation and vibration, vibration signals collected from mechanical equipment carry rich information on machine health conditions. Therefore, vibration signal analysis [1–3] has been extensively investigated during the past decades. The emergence of periodic components is often associated with component failures in vibration analysis. However, fault signals collected from mechanical equipment are often corrupted by strong noise coming from other coupled machine components and the working environment, which increases the difficulty in fault identification. Thus, effective extraction of weak features submerged in strong noise that are indicative of structural defects has remained a major challenge. In order to obtain vital feature information from vibration signals, various signal processing techniques, like variational mode decomposition (VMD) [4, 5], synchrosqueezing transform (SST) [6, 7], wavelet transform (WT) [8–10], and so forth, have been extensively studied and used in machinery fault diagnosis. Traditionally, noise is always considered an undesirable disturbance, thus these signal processing techniques mainly focus on filtering and denoising the signals to extract fault features. In fact, noise is not just a source of signal contamination, but it also represents a kind of signal energy. If the energy generated by noise can be used properly, it is conducive to extracting the feature information from the signals submerged under strong noise. Stochastic resonance (SR) [11] is a kind of typical noise-assisted data processing method. Unlike traditional denoising techniques, SR realizes the detection of weak signal by utilizing noise instead of eliminating noise, and the weak signal features are not weakened but enhanced.

The concept of SR was first introduced in the 1980s, which was applied to describe the periodicity associated with Earth’s ice ages in climatology [12, 13]. SR, as a nonlinear physical phenomenon, emphasizes the synergistic effect between a nonlinear dynamic system, a small parameter signal, and noise. As a special “low-pass filter,” SR can transfer noise energy to useful signal with the assistance of nonlinear system, thereby realizing the elimination of noise and enhancement of useful signal features. Consequently, by virtue of the unique advantage of using noise to enhance weak signals, SR has been widely studied in machinery fault diagnosis field [14, 15]. Qin et al. [16] proposed an adaptive and fast SR method based on dyadic wavelet transform and least square parameters solving algorithm to extract the fault feature of a rotor system, which can increase the noise utilization and does not need to set up the searching range and searching step size of system parameters. Aiming at the problem of detecting the multifrequency signals buried under strong noise, Han et al. [17] proposed a multistable SR method by using wavelet transform and parameter compensation band-pass algorithm, which enhanced the signal amplitude and achieved the effective extraction of bearing fault features. Wang et al. [18] proposed an adaptive multiscale noise tuning SR based on wavelet transform and weighted power kurtosis to diagnose the rolling bearing fault and realized the adaptive selection of control parameters through the artificial fish swarm algorithm. In order to realize the fault diagnosis of planetary gear transmission, a weak fault feature information extraction method based on ensemble empirical mode decomposition (EEMD) and adaptive SR was proposed [19]. Through EEMD, the effective IMFs containing main fault feature information are selected and reconstructed. Then the reconstructed signal is inputted into adaptive SR system, and the weak fault feature information can be extracted from the output signal of SR system. By analyzing the SR phenomenon of a two-dimensional duffing oscillator, Lai and Leng [20] proposed a generalized parameter-adjusted SR model, which can be used for the fault diagnosis of rolling bearing. In addition, many researches have also been conducted on the SR model and SR enhancement methods [21, 22].

The algorithm of multiscale noise tuning provides an effective control strategy for realizing the SR. However, there are some shortcomings in the method of multiscale noise tuning based on wavelet decomposition, such as the selection of optimal wavelet bases, which makes it have some limitations in processing diverse signals in engineering practice. Adaptive signal decomposition methods provide an effective solution for complicated signal analysis and feature extraction, which can adaptively decompose the signal into different scales according to the oscillation characteristics of signal itself, thus avoiding artificial intervention and optimizing the data analysis flow. As a noise-assisted adaptive signal decomposition method, EEMD can eliminate the mode mixing phenomenon in empirical mode decomposition (EMD) through adding white noise to signal, and it decomposes the complicated signal into a set of simple components named intrinsic mode function (IMF) [23–25]. The IMFs represent the natural oscillatory mode embedded in the signal, which are determined by the signal itself, instead of predetermined kernels. Therefore, a new adaptive multiscale noise control enhanced SR method based on modified EEMD for bearing fault diagnosis is studied by using the adaptive decomposition capability of EEMD and the unique advantage of SR using noise to enhance weak signal features. EEMD is used for signal multiscale decomposition, and through improving the EEMD algorithm, the decomposition levels are reduced to increase the computation efficiency of the proposed method. The band-pass filters are constructed in terms of the spectrum distribution characteristics of IMFs, so as to eliminate some aliasing components and improve the orthogonality of adjacent IMFs through filter processing, which is conducive to enhancing and extracting of weak information features to some extent. And then, the signal, used as the input of SR system, is reconstructed with the IMFs obtained by the modified EEMD algorithm, and the noise control parameter of different scales is optimized and selected with the help of the genetic algorithm to achieve the extraction of weak features. Therefore, the proposed method can not only adaptively decompose the signal into different scales but also realize the adaptive selection of noise control parameter of different scales, which is well-suited for enhancement of rotating machine weak fault identification. Experiments and application demonstrate that the proposed method is validated to be effective in detecting the weak fault features in bearing fault diagnosis.

The rest of the paper is arranged as follows. A brief introduction to the theoretical background of SR is provided in Section 2. The method of adaptive multiscale noise control enhanced SR based on modified EEMD is described in detail in Section 3. Some experimental and practical data are applied to verify the effectiveness of the proposed method in Section 4. Finally, conclusions are drawn in Section 5.

#### 2. SR Basic Theory

SR describes a phenomenon that the weak signal is enhanced and the noise is weakened through the interaction of the nonlinear system, small parameter signal, and noise, whose dynamic behavior can be represented by the Brownian motion equation of particles. And the overdamped SR equation with a nonlinear bistable model in the presence of periodic force and noise can be written as follows:where denotes the system output, parameters and are positive real numbers, and are the amplitude and frequency of the periodic force, respectively, and is a Gaussian white noise with zero mean and variance. The potential function is with two stable points and one critical stable point . The height of potential barrier is . From (1), the system output is actually the Brownian particle trajectory in the potential function under the combined action of periodic force and noise. And, the crucial process of using SR to detect weak signal is to adjust system parameters or noise intensity to make the transition rate of the particle caused by noise match the oscillation period of the input signal, thus amplifying the particle movements in single potential well to the transition motions between double potential wells to realize the feature enhancement of input signal.

It is generally known that the theory basis of SR is the adiabatic approximation theory, which requires the amplitude and frequency of periodic signal as well as noise intensity to be smaller than 1. However, the defective signals caused by components fault of rotating machine have difficulty in satisfying the above requirements in engineering application. Therefore, in order to solve the problem of using SR to detect large parameter signals, several parameter tuning SR methods have been researched based on a normalized scale transformation.

Mathematically, let , , and (1) be written as

Equation (2) indicates that the frequency of the periodic signal is normalized to be times that of original signal through the normalized scale transform, and the normalized frequency of larger parameter signal can satisfy the small parameters requirements of SR for input signal by selecting a corresponding larger parameter . And importantly, according to (1) and the derivation process of (2), the process of realizing SR by adjusting the system parameters is consistent with that of realizing SR by adjusting the input signal strength and noise intensity on the premise of the constant system parameters in nature. Consequently, we can adjust the input signal strength and noise intensity to realize the SR detection of weak signal.

#### 3. Adaptive Multiscale Noise Control Enhanced SR Method Based on Modified EEMD

Recent studies demonstrate that the SR effect can be driven by different scales of noise but with different degree [26]. Therefore, according to the influence of noise at different scales on the SR, multiscale noise tuning SR methods based on wavelet transform have been studied in recent years [27, 28]. However, based on the inner product transform principle, the selection of wavelet bases has important effects on the decomposition results in wavelet transform. When the selected wavelet base is inappropriate, namely, it does not match up with the target signal, the useful signal features may be impaired. Additionally, the width of frequency bands obtained by wavelet decomposition is fixed, which cannot be adjusted adaptively according to the oscillation characteristics of signal itself. Therefore, the existing multiscale noise tuning methods based on wavelet transform still have some shortcomings, which have difficulty in satisfying the demand of the diversity of signals in engineering practice. EMD, as an adaptive signal processing method, has been developed and widely applied in machinery fault diagnosis. Based on the local characteristic time scales of a signal, EMD can adaptively decompose the complicated signal into a set of IMF components. However, it has a major drawback, which is the mode mixing problem. Therefore, EEMD, as an improved method of EMD, is presented to alleviate the mode mixing problem in EMD. The principle of EEMD algorithm is the following: by using the statistical property that Gaussian white noise is uniformly distributed over the whole frequency range, Gaussian white noise is added to a signal, which makes the signal continuous in different scales to alleviate the mode mixing problem in EMD. Finally, the added white noise can be decreased or even completely canceled out through the ensemble mean of enough trials, and the ensemble mean is treated as the true answer. Therefore, according to the oscillation characteristics of signal itself, EEMD algorithm can realize the adaptive multiscale decomposition for input signal, which provides a new control strategy for realizing SR by adjusting multiscale noise. EEMD overcomes the mode mixing problem through enough iterations and trails which is at the cost of increasing the calculation amount. However, in consideration of the requirements of the multiscale noise control SR algorithm in this study, the algorithm of EEMD is modified to simplify the calculation, and a new adaptive multiscale noise control enhanced SR method based on modified EEMD is proposed. By using the oscillation characteristics of signal itself, the modified EEMD algorithm can adaptively decompose the signal into different scales, and by adjusting the noise intensity of different scales the proposed method can achieve the enhanced extraction of weak signal features. The important steps of the proposed method are described in detail below.

##### 3.1. Modified EEMD Algorithm

As mentioned above, EEMD achieves the adaptive partition of frequency band for input signal, and the decomposition level is not set by manual but depends on the local characteristic time scales of signal itself. Therefore, how to select the appropriate IMF components from the IMFs obtained by EEMD, namely, that determines the reconstruction scale to reconstruct the signal used as the input of SR system, is the key of realizing the multiscale noise control SR method based on EEMD.

According to the process of EMD algorithm extracting IMF components, the high-frequency components contained in the signal are extracted first, and the low-frequency components are extracted last. So, the obtained IMFs are arranged in descending order by the center frequency of each IMF component. And the process of determining the reconstruction scale is to seek out the th IMF component containing the target signal from IMFs, thereby obtaining the first IMFs which are served as the reconstruction components of multiscale noise control algorithm, and the remainder IMFs below the target signal frequency are abandoned. Aiming at the requirements of the proposed method, EEMD is applied to decompose the signal into different scales, but the algorithm of multiscale noise control does not need all of the IMFs obtained by EEMD but just the first IMFs. For this reason, the stopping criterion for iteration of EMD algorithm extracting IMF components is modified, and thus a modified EEMD algorithm is presented, which can effectively reduce the decomposition levels of EMD algorithm to improve the overall calculation efficiency of the proposed method in the paper.

The modified EEMD algorithm is described in detail below:(1)Initialize the number of ensemble Num, the standard deviation of added white noise .(2)Add a Gaussian white noise with the given standard deviation to the investigated signal with the length of and the sample frequency , where denotes the th added white noise and indicates the noise-added signal of the th trial.(3)Decompose the noise-added signal with the modified EMD algorithm and determine the decomposition scale by using the target signal frequency and the center frequency of each IMF obtained in the decomposition process, thus obtaining IMFs. The concrete decomposition process is described as shown in Algorithm 1.(4)Repeat steps and again and again, but with different white noise each time, and calculate the ensemble mean of the Num trials for each IMF:(5)Conduct the mean of each of the IMFs as the final IMFs.