A multiscale noise tuning stochastic resonance for fault diagnosis in rolling element bearings

Condition monitoring of rotating machinery is important to extend the mechanical system's reliability and operational life. However, in many cases, useful information is often overwhelmed by strong background noise and the defect frequency is difficult to be extracted. Stochastic resonance (SR) is used as a noise-assisted tool to amplify weak signals in nonlinear systems, which can detect weak signals of interest submerged in the noise. The multiscale noise tuning SR (MSTSR), which is originally based on discrete wavelet transform (DWT), has been applied to identify the fault characteristics and has also increased the signal-to-noise ratio (SNR) improvement of SR. Therefore, a novel tri-stable SR method with multiscale noise tuning (MST) is proposed to extract fault signatures for fault diagnosis of rotating machinery. The wavelet packets transform (WPT) based MST can obtain better denoising effect and higher SNR of resonance output compared with the traditional SR method. Thus the proposed method is well-suited for enhancement of rotating machine fault identification, whose effectiveness has been verified by means of practical vibration signals carrying fault information from bearings. Finally, it can be concluded that the proposed method has practical value in engineering.     

Weak signal detection based on underdamped stochastic resonance with an exponential bistable potential

Stochastic resonance (SR) is a vital approach to detect weak signals submerged in strong background noise, which is useful for mechanical fault diagnosis. The underdamped bistable SR (UBSR) is a kind of the most used SR, however, their potential structures are deficient to match with the complicated and diverse mechanical vibration signals and their parameters are selected subjectively which probably resulting in poor performance of UBSR. To overcome these shortcomings, this paper proposes an underdamped SR with exponential potential (UESR) which is generalized by using a harmonic model and a Gaussian potential (GP) model. The dynamics in UESR system is evaluated by the signal-to-noise ratio (SNR) which represents the effectiveness of noise utilization. Then, the effects of system parameters on system performance are investigated by output SNR versus noise intensity D for different parameters. Finally, the proposed method is used to process bearing experimental data and further perform bearing fault diagnosis. The experimental results demonstrate that a larger output SNR and higher spectrum peaks at fault characteristic frequencies can be obtained by the proposed method compared with the UBSR method, which confirm the effectiveness of the proposed method.     

Stochastic resonance in multi-scale bistable array

This Letter explores a new mechanism of stochastic resonance (SR) that is induced by the multi-scale noise decomposed from the input signal, which is promising in signal detection and processing under heavy background noise. The input signal is firstly decomposed to multi-scale signals by orthogonal wavelet transform. Then, the approximate signal, which contains the driving signal, is processed by an uncoupled parallel bistable array with the detailed signal of each scale as the internal noise. At last, a SR mechanism combining the effects of colored noise and array SR is proposed. The simulation results show that a high quality output signal can be obtained by the new mechanism. The proposed model is more adaptive to input signal with high noise intensity than single bistable SR system, which can be seen from the signal-to-noise ratio curves and average noise intensity curves.     

Double Gaussian potential stochastic resonance method and its application in centrifugal fan blade crack detection

Stochastic resonance (SR) has been extensively utilized in the field of weak fault signal detection for its characteristic of enhancing weak signals by transferring the noise energy. Aiming at solving the output saturation problem of the classical bistable stochastic resonance (CBSR) system, a double Gaussian potential stochastic resonance (DGSR) system is proposed. Moreover, the output signal-to-noise ratio (SNR) of the DGSR method is derived based on the adiabatic approximation theory to analyze the effect of system parameters on the DGSR method. At the same time, for the purpose of overcoming the drawback that the traditional SNR index needs to know the fault characteristic frequency (FCF), the weighted local signal-to-noise ratio (WLSNR) index is constructed. The DGSR with WLSNR can obtain optimal parameters adaptively, thereby establishing the DGSR system. Ultimately, a DGSR method is proposed and applied in centrifugal fan blade crack detection. Through simulations and experiments, the effectiveness and superiority of the DGSR method are verified.     

A novel parameter-induced adaptive stochastic resonance system based on composite multi-stable potential model

Stochastic resonance (SR) is used widely as a weak signal detection method by using noise in many fields. In order to improve the weak signal processing capability of SR, a novel composite multi-stable model is proposed, which is constructed by the joint of the tristable model and the Gaussian Potential (GP) model. The SR system based on this model is constructed and the signal-to-noise ratio (SNR) is regarded as the index to measure the SR effect. The differential brain storm optimization (DBSO) algorithm is used to optimize the system parameters collaboratively to achieve parameter-induced adaptive SR. The influences of the system parameters V and R and the noise intensity D on the output response of SR system are analyzed under Gaussian white noise and α stable noise environments, and the advantages of the composite multi-stable SR system over the traditional tristable system are verified. For different levels of weak signals, the output performances of SR systems based on composite multi-stable model, traditional tristable model, composite tristable model are compared and analyzed. The results prove that the proposed model has better performance. Meanwhile, the adaptive detection of the multiple high-frequency weak signal is realized using the composite multi-stable SR system. The simulation results show that the proposed system has strong weak signal processing capability and good immunity to noise types, which widens the application range of SR in practical engineering.     

滤波器与随机共振结合检测微弱信号

基于双稳随机共振系统及滤波器的不同特性,本文提出了一种将两者结合起来检测微弱周期信号的方法,先用自适应前置滤波器对输入的弱周期信号及噪声进行滤波,再使其通过双稳随机共振系统,进而检测出弱信号。对比只有双稳随机共振的系统,仿真结果表明此时的输出信号中待测信号频谱幅度得到了很大的提高,且周围的干扰信号也得到了明显的削弱,即两者的结合使用可以更好的检测出微弱信号,这对强噪声背景下的信号检测有很强的实用性。     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

基于EMD-AWPP和HOSA-SVM算法的分布式光纤振动入侵信号的特征提取与识别

针对传统的信号处理方法无法有效区分不同振动入侵信号,提出一种基于EMD-AWPP和HOSA-SVM算法的振动信息特征提取与识别方法,用于解决分布式光纤振动入侵检测系统的高精度信号识别问题。处理不同振动类型时,该方法首先利用基于经验模态分解的自适应小波包处理算法,不仅对信号的低频部分进行了分解,而且对高频部分即信号的细节部分也进行了更好的时频局部化处理,改善了信号特征提取精度,减少传感信号异常值的影响; 其次采用高阶谱分析中的双谱和双相干谱,精确提取包含不同振动入侵信号类型的特征矢量; 最后在BPNN参比模型的基础上,用粒子群算法优化SVM的识别参数,使识别模型具有更强的自适应和自学习能力,克服了神经网络易陷入局部最优的不足之处,实现不同振动入侵信号的特征矢量识别。分析结果表明,针对不同类型的入侵源识别,该方法可以有效剔除随机噪声的影响,提取传感信息的特征矢量,降低异常值的影响,算法的预测类别与输出类别几乎一致,振动识别的精确率达到95%以上,识别效果明显强于BPNN网络的检测算法,提高了信息分析的准确性。     

Research and application of coupled two-dimensional asymmetric bistable stochastic resonance system

Considering that the vibration signal of rolling bearing is very weak and difficult to be extracted under the working environment noise, a two-dimensional asymmetric bistable system (TDAB) is proposed. The system is coupled by two systems, and the weak signal is enhanced by adjusting the control system (monostable system) to adjust the controlled system (asymmetric bistable system). First, under the condition of adiabatic approximation system, the signal-to-noise ratio (SNR) is deduced, and analyzes the influence of different system parameters on the shape of potential function. Then the effects of each parameter on the SNR of the system are analyzed theoretically. Finally, combined with the adaptive intelligent algorithm, the parameters of the controlled system are optimized, and then the coupling coefficient and control system parameters are adjusted to obtain better system performance. The TDAB system obtained is applied to different bearing fault diagnosis and compared with different coupling systems. The experimental results show that the method can extract the characteristic frequency effectively and has good spectrum amplification performance and anti-noise capability. It is proved that the TDAB system can also have good detection effect in practical application.     

A weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance

Aiming at detecting the weak signal in a strong noise background, an enhanced weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance is proposed. Firstly, because the system can switch among the monostable, bistable and tri-stable state, the potential function characteristic of tri-stable systems is studied by analyzing the potential function curves with different system parameters. And the dynamic characteristics of system parameters on the depth of the potential well is analyzed. The ranges of R and the system parameters are determined, which is essential for ensuring the system is tri-stable state. Secondly, the range of R is used as the constraint condition and the average output signal-to-noise ratio is used as the fitness function of the adaptive algorithm. The system parameters a, b, c are optimized by the differential evolution particle swarm optimization (DEPSO) method to obtain the best output effect. Finally, the proposed adaptive parameter-induced tri-stable stochastic resonance method is adopted to detect the mixed multiple high-frequency weak signal. The detection results are compared with that of adaptive bistable stochastic resonance. At the meanwhile, the method is also applied to detect the fault signal of single crystal furnace. Both the simulation analysis and experiment results show that the proposed method can effectively improve the output signal-to-noise ratio and detect multi-frequency weak signal in the strong noise background.     

An improved multiscale noise tuning of stochastic resonance for identifying multiple transient faults in rolling element bearings

Stochastic resonance (SR), a noise-assisted tool, has been proved to be very powerful in weak signal detection. The multiscale noise tuning SR (MSTSR), which breaks the restriction of the requirement of small parameters and white noise in classical SR, has been applied to identify the characteristic frequency of a bearing. However, the multiscale noise tuning (MST), which is originally based on discrete wavelet transform (DWT), limits the signal-to-noise ratio (SNR) improvement of SR and the performance in identifying multiple bearing faults. In this paper, the wavelet packet transform (WPT) is developed and incorporated into the MSTSR method to overcome its shortcomings and to further enhance its capability in multiple faults detection of bearings. The WPT-based MST can achieve a finer tuning of multiscale noise and aims at detecting multiple target frequencies separately. By introducing WPT into the MST of SR, this paper proposes an improved SR method particularly suited for the identification of multiple transient faults in rolling element bearings. Simulated and practical bearing signals carrying multiple characteristic frequencies are employed to validate the performance improvement of the proposed method as compared to the original DWT-based MSTSR method. The results confirm the good capability of the proposed method in multi-fault diagnosis of rolling element bearings.     

A Novel Feature Extraction Method for Power Transformer Vibration Signal Based on CEEMDAN and Multi-Scale Dispersion Entropy

Effective diagnosis of vibration fault is of practical significance to ensure the safe and stable operation of power transformers. Aiming at the traditional problems of transformer vibration fault diagnosis, a novel feature extraction method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multi-scale dispersion entropy (MDE) was proposed. In this paper, CEEMDAN method is used to decompose the original transformer vibration signal. Additionally, then MDE is used to capture multi-scale fault features in the decomposed intrinsic mode functions (IMFs). Next, the principal component analysis (PCA) method is employed to reduce the feature dimension and extract the effective information in vibration signals. Finally, the simplified features are sent into density peak clustering (DPC) to get the fault diagnosis results. The experimental data analysis shows that CEEMDAN-MDE can effectively extract the information of the original vibration signals and DPC can accurately diagnose the types of transformer faults. By comparing different algorithms, the practicability and superiority of this proposed method are verified.     

Asymmetric delay feedback stochastic resonance detection method based on prior knowledge particle swarm optimization

For the adjustable parameters stochastic resonance system, the selection of the structural parameters plays a decisive role in the performance of the detection method. The vibration signal of rotating machinery is non-linear and unstable, and its weak fault characteristics are easily concealed by noise. Under strong background noise interference, the detection of fault features is particularly challenging. Therefore, a type of weak fault feature extraction method, named knowledge-based particle swarm optimization algorithm for asymptotic delayed feedback stochastic resonance (abbreviated as KPSO-ADFSR) is proposed. Through deduction under adiabatic approximation, we observe that both the asymmetric parameters, the length of delay and the feedback strength, impact the potential function. After adjusting the asymmetric parameters of the system, the output signal-to-noise ratio (SNR) is used as the fitness function, and the setting of the relationship between the noise intensity and barrier height is used as the prior knowledge of the particle swarm algorithm. Through this algorithm, the delay length and the feedback strength are optimized. This method achieves global optimization of system parameters in a short time; it overcomes the shortcomings of the traditional stochastic resonance method, which has a long convergence time and tends to easily fall into local optimization. It can effectively improve the detection of weak fault features. In the bearing rolling body pitting corrosion failure experiment and steel field engineering experiment, the proposed method could extract the characteristics of a weak fault more effectively than the traditional stochastic resonance method based on the standard particle swarm algorithm.     

Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics

De-noising and extraction of the weak signature are crucial to fault prognostics in which case features are often very weak and masked by noise. The wavelet transform has been widely used in signal de-noising due to its extraordinary time-frequency representation capability. In this paper, the performance of wavelet decomposition-based de-noising and wavelet filter-based de-noising methods are compared based on signals from mechanical defects. The comparison result reveals that wavelet filter is more suitable and reliable to detect a weak signature of mechanical impulse-like defect signals, whereas the wavelet decomposition de-noising method can achieve satisfactory results on smooth signal detection. In order to select optimal parameters for the wavelet filter, a two-step optimization process is proposed. Minimal Shannon entropy is used to optimize the Morlet wavelet shape factor. A periodicity detection method based on singular value decomposition (SVD) is used to choose the appropriate scale for the wavelet transform. The signal de-noising results from both simulated signals and experimental data are presented and both support the proposed method.     

基于HHT变换的起动电动机特征信号时频分析

针对车辆起动电动机电气和机械故障发生时特征信号的时变不平稳特性,进行了时频域分析处理,提出了利用现代信号处理方法对故障信号提取特征向量的方法,主要对起动电动机的电枢和轴承故障进行诊断。在构建电机故障测试实验平台的基础上,利用破坏性实验构造了故障类型,测取了电枢电流和振动信号,分别采用小波分析理论和HHT变换对信号进行分析,通过分解再重构的方式将信号分解成了频率由高到低的不同分量,并获得了故障的特征频率,提取了特征向量。实验结果表明,基于HHT变换的现代信号处理方法在处理时变非平稳信号方面比小波分析理论更具有自适应性,更易识别。     

Matching pursuit of an adaptive impulse dictionary for bearing fault diagnosis

The sparse decomposition based on matching pursuit is an adaptive sparse expression of the signals. An adaptive matching pursuit algorithm that uses an impulse dictionary is introduced in this article for rolling bearing vibration signal processing and fault diagnosis. First, a new dictionary model is established according to the characteristics and mechanism of rolling bearing faults. The new model incorporates the rotational speed of the bearing, the dimensions of the bearing and the bearing fault status, among other parameters. The model can simulate the impulse experienced by the bearing at different bearing fault levels. A simulation experiment suggests that a new impulse dictionary used in a matching pursuit algorithm combined with a genetic algorithm has a more accurate effect on bearing fault diagnosis than using a traditional impulse dictionary. However, those two methods have some weak points, namely, poor stability, rapidity and controllability. Each key parameter in the dictionary model and its influence on the analysis results are systematically studied, and the impulse location is determined as the primary model parameter. The adaptive impulse dictionary is established by changing characteristic parameters progressively. The dictionary built by this method has a lower redundancy and a higher relevance between each dictionary atom and the analyzed vibration signal. The matching pursuit algorithm of an adaptive impulse dictionary is adopted to analyze the simulated signals. The results indicate that the characteristic fault components could be accurately extracted from the noisy simulation fault signals by this algorithm, and the result exhibited a higher efficiency in addition to an improved stability, rapidity and controllability when compared with a matching pursuit approach that was based on a genetic algorithm. We experimentally analyze the early-stage fault signals and composite fault signals of the bearing. The results further demonstrate the effectiveness and superiority of the matching pursuit algorithm that uses the adaptive impulse dictionary. Finally, this algorithm is applied to the analysis of engineering data, and good results are achieved.     

A new method for weak fault feature extraction based on piecewise mixed stochastic resonance

In a continuous bistable system, when the input signal is continuously increased, the output signal tends to be stable and no longer increases. At this time, the weak signal under strong background noise is difficult to be extracted, which means saturation occurs. Aiming at the saturation characteristics of stochastic resonance (SR), the proposed piecewise nonlinear bistable system (PNBSR) model has achieved certain results. However, the potential barrier in the middle of the PNBSR method still completely uses the potential function of classical bistable stochastic resonance (CBSR). There is no fundamental solution to the fourth-order limitation. This paper explores an improved piecewise mixed stochastic resonance (PMSR) potential model. The fourth-order potential function that restricts particle motion in CBSR is improved to a piecewise second-order potential function. This potential function subverts the shape of the traditional potential function and presents a symmetrical double-hook shape. Based on PMSR model, this paper uses particle swarm optimization (PSO) to select system parameters and elaborates the characteristics of the potential function curve in detail. Under the same conditions, the output signal-to-noise ratio (SNR) curve of the improved system is generally higher than that of the CBSR and PNBSR systems. Experiments on bearings and gears show that the proposed method can accurately extract weak fault features, and the effect is better than the PNBSR method.     

An intelligent approach for engine fault diagnosis based on Hilbert–Huang transform and support vector machine

Based on the techniques of Hilbert–Huang transform (HHT) and support vector machine (SVM), a noise-based intelligent method for engine fault diagnosis (EFD), so-called HHT–SVM model, is developed in this paper. The noises of a sample engine under normal and several fault states are first measured and denoised by using the wavelet packet threshold method to initially lower the noise level with negligible signal distortion. To extract fault features of the engine, then, the HHT is selected and applied to the measured noise signals. A nine-dimensional vector, which consists of seven intrinsic mode functions (IMFs) from the empirical mode decomposition (EMD), maximum value of HHT marginal spectrum and its corresponding frequency component, is specified to represent each engine fault feature. Finally, an optimal SVM model is established and trained for engine failure classification by using the fault feature vectors of the noise signals. Cross-validation results show that the proposed noise-based HHT–SVM method is accurate and effective for engine fault diagnosis. Due to outstanding time–frequency characteristics and pattern recognition capacity of the HHT and SVM, the newly proposed HHT–SVM can be used to deal with both the stationary and nonstationary signals, and even the transient ones. In the view of applications, the HHT–SVM technique may be suggested not only to detect the abnormal states of vehicle engines, but also to be extended to other fields for failure diagnosis in engineering.     

The analysis of stochastic resonance and bearing fault detection based on linear coupled bistable system under lévy noise

In this paper, the stochastic resonance (SR) phenomenon of the linear coupled bistable system induced by Lévy noise is analyzed. Meanwhile, the characteristics of Lévy noise is also analyzed according to its probability density functions (PDFs) of different stability index α, symmetry parameter β, scale parameter σ and location index μ. The mean of signal-noise ratio increase (MSNRI) is regarded as an index to measure the SR phenomenon. Then, the rules for MSNRI affected by noise intensity D are explored under different charastic indexes of Lévy noise, system parameters a, b, c and coupling coefficient r. The results are beneficial to the numerical simulation of single-frequency and multi-frequency weak signals detection based on single bistable system and linear coupled system respectively. It is found that the performance of the proposed system is better than single bistable system and results of bearing fault detection could also verify the conclusion.     

Identification of vehicle suspension shock absorber squeak and rattle noise based on wavelet packet transforms and a genetic algorithm-support vector machine

The squeak and rattle (S&R) noise of a vehicle’s suspension shock absorber substantially influences the psychological and physiological perception of passengers. In this paper, a state-of-the-art method, specifically, a genetic algorithm-optimized support vector machine (GA-SVM), which can select the most effective feature subsets and optimize the model’s free parameters, is proposed to identify this specific noise. A vehicular road test and a shock absorber rig test are conducted to investigate the relationship between these features, and then an approach for quantifying the shock absorber S&R noise is given. Pre-processed signals are decomposed through a wavelet packet transform (WPT), and two criteria, namely, the wavelet packet energy (WPE) and wavelet packet sample entropy (WPSE), are introduced as the feature extraction methods. Then, the two extracted feature sets are compared based on this genetic algorithm. Another advanced method, known as the genetic algorithm-optimized back propagation neural network (GA-BPNN), is introduced for comparison to illustrate the superiority of the newly developed GA-SVM model. The result shows that the WPSE can extract more useful features than the WPE and that the GA-SVM is more effective and efficient than the GA-BPNN. The proposed approach could be retrained and extended to address other fault identification problems.