Research On Rolling Bearing Fault Diagnosis Based On Mathematical Morphology And Chaos Theory

As a key part of rotating machinery,rolling bearing plays a vital role in the operation of equipment,which determines whether the whole mechanical equipment can run safely and reliably.Timely diagnosis of the condition of rolling bearings,identification of fault types and evaluation of fault severity can effectively avoid the equipment falling into the failure state and minimize the risk of mechanical equipment operation.In this paper,on the basis of mathematical morphology theory and chaos theory,the research work of rolling bearing fault diagnosis is carried out by analyzing the dynamic characteristics of the measured object reflected from vibration signals.The main work of this paper is as follows:(1)Based on the basic theory of mathematical morphology,the application of morphological operation based on partial differential equations(PDE's)in rolling bearing vibration signal denoising is studied.Aiming at the problem of parameter selection and waveform distortion of traditional morphological filtering,a kind of adaptive smoothed multiscale morphological filtering based on PDEs(PSMMF)method for noise suppression of vibration signal is proposed.Firstly,the multiscale permutation entropy based on the residual difference of different scale morphological filtering results is used to select the optimal scale combination.Then the continuous-scale morphological filter is constructed to filter the contaminated signal.And the problem of waveform distortion is improved by using B-spline interpolation smoothing morphological filtering.The proposed method is applied to the noise reduction and preprocessing of rolling bearing vibration signals,and the nonlinear dynamic characteristics of the signals are enhanced by improving the signal to noise ratio of the vibration signals.Simulation and experimental results demonstrate the effectiveness of the proposed method in rolling bearing vibration signal denoising.(2)On the basis of morphological operations of PDEs and the fractal theory,a fractal dimension estimation method based on composite multiscale morphology(CMMFD)is studied.The algorithm is used to extract the fractal features of rolling bearing fault signals.Firstly,the PSMMF method is used to preprocess the vibration signals to suppress the interference noise and enhance the nonlinear dynamic characteristics without damaging the dynamic structural characteristics of the vibration signals.Then,the denoised vibration signal is processed by using compound-scale coarse grain-analysis.Morphological operations based on flux corrected transport(FCT)scheme are used to estimate the fractal dimensions of coarse grain-sequences at different scales and construct CMMFD feature vectors.Finally,the feature vector is input to the classifier to identify the fault type.The experimental results show that the CMMFD method can effectively solve the state space overlap problem of fractal dimension of a single scale,and provide a reliable diagnostic basis for operating condition analysis and fault type identification.(3)Aiming at the problem that the weak characteristic signals of rolling bearings are often submerged in the strong background noise and difficult to identify in the early stage of rolling bearing faults,a method for weak fault identification of rolling bearing based on chaotic oscillator and morphological analysis is proposed.Through the study of nonlinear dynamic behavior of typical chaotic oscillator,according to the variation characteristics of attractor shape in different states,the morphological operation based on PDEs is applied to the analysis of attractor characteristics of the output signal of chaotic oscillator.CMMFD is used to extract the morphological characteristics of vibration signals of chaotic system under different parameters,and the change of morphological characteristics of chaotic oscillator is analyzed,which is used as the quantitative basis to estimate the change of chaotic oscillator state.Finally,the method of combining variable scale and oscillator array is used to identify the characteristic frequency of fault signal.Simulation and experimental analysis show that the method based on the combination of CMMFD and chaotic oscillator can effectively realize the early weak fault identification of rolling bearing?(4)The performance degradation of rolling bearings is difficult to evaluate effectively,a continuous-scale mathematical pattern difference spectrum(CMPDS)analysis method is proposed to evaluate the performance degradation of bearing based on mathematical morphology spectrum and PDEs morphology operation.Firstly,CMPDS is used to extract the morphological spectral features of bearing signals,and the locality preserving projection(LPP)method is used to reduce the dimension of high-dimensional features.Then,the initial embedded hidden Markov model(EHMM)is trained with low-dimensional features,and all the initial EHMMs are combined to construct the global EHMM model.Finally,the CMPDS feature vector is input into the global EHMM to realize the evaluation of bearing degradation performance.The vibration signal analysis results of the whole life cycle bearing show that the proposed method can effectively evaluate the bearing degradation performance.