Influence of Poisson White Noise on the Response Statistics of Nonlinear System and Its Applications to Bearing Fault Diagnosis

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Dengji Zhou ◽  
Grzegorz Litak ◽  
Houguang Liu
Keyword(s):  
Nonlinear System ◽  
White Noise ◽  
Noise Intensity ◽  
Arrival Rate ◽  
Scale Transformation ◽  
Poisson White Noise ◽  
Noise Background ◽  
Bearing Fault ◽  
Fault Features ◽  
Bearing Structure

In view of complex noise background in engineering practices, this paper presents a rescaled method to detect failure features of bearing structure in the Poisson white noise background. To realize the scale transformation of the fault signal with Poisson white noise, a general scale transformation (GST) method is introduced based on the second-order underdamped nonlinear system. The signal features are successfully extracted through the proposed rescaled method in the simulated and experimental cases. We focus on the influence of Poisson white noise parameters and damping coefficient on the response of nonlinear system. The impulse arrival rate and noise intensity have opposite effects on the realization of stochastic resonance (SR) and the extraction of bearing fault features. Poisson white noise with smaller impulse arrival rate or larger noise intensity is easier to induce SR to extract bearing fault features. The optimal matching between the nonlinear system and the input signal is formed by the optimization algorithm, which greatly improves the extraction efficiency of fault features. Compared with the normalized scale transformation (NST) method, the GST has significant advantages in recognizing the bearing structure failure. The differences and connections between Poisson white noise and Gaussian white noise are discussed in the rescaled system excited by the experiment signal. This paper might provide several practical values for recognizing bearing fault mode in the Poisson white noise.

Stochastic Resonance and Self-Induced Stochastic Resonance in Bearing Fault Diagnosis

2021 ◽  
pp. 2150047
Author(s):  
Shuai Zhang ◽  
Jianhua Yang ◽  
Canjun Wang ◽  
Houguang Liu ◽  
Chen Yang
Keyword(s):  
Nonlinear System ◽  
Stochastic Resonance ◽  
Evolutionary Process ◽  
Vibration Signal ◽  
Bearing Failure ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
Fault Features ◽  
Characteristic Signal ◽  
Sr Method

Stochastic resonance (SR) and self-induced stochastic resonance (SISR) are two kinds of important dynamical phenomena in the nonlinear system. SR occurs at the frequency of the characteristic signal. However, SISR can occur at a frequency that is included in the excitation. In present, there are volumes of literatures focusing on extracting the bearing fault characteristics from the vibration signal by SR method. However, the occurrence of SISR may result in the fault features misjudgment in SR processing. Through experimental verifications, we find that the interference of SISR is illustrated strongly in the fault characteristics identification. More importantly, the transition from SISR to SR corresponds to the evolution process of bearing state from normal to damage. Therefore, this evolutionary process can not only judge the state of bearing, but also describe the severity of bearing failure. The result is verified by processing the signals of bearing fault with different severity in noise background. They are the most important findings in this work.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

scholarly journals Wavelet Co-movement Significance Testing with Respect to Gaussian White Noise Background

2018 ◽  
Vol 16 ◽  
pp. 01002
Author(s):  
Jitka Poměnková ◽  
Eva Klejmová ◽  
Tobiáš Malach
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Real Data ◽  
Significance Testing ◽  
Noise Background ◽  
Advantages And Disadvantages ◽  
The United Kingdom ◽  
Long Run ◽  
Short Run ◽  
White Noise Background

The paper deals with significance testing of time series co-movement measured via wavelet analysis, namely via the wavelet cross-spectra. This technique is very popular for its better time resolution compare to other techniques. Such approach put in evidence the existence of both long-run and short-run co-movement. In order to have better predictive power it is suitable to support and validate obtained results via some testing approach. We investigate the test of wavelet power cross-spectrum with respect to the Gaussian white noise background with the use of the Bessel function. Our experiment is performed on real data, i.e. seasonally adjusted quarterly data of gross domestic product of the United Kingdom, Korea and G7 countries. To validate the test results we perform Monte Carlo simulation. We describe the advantages and disadvantages of both approaches and formulate recommendations for its using.

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