Research On Statistical Modelling For Mechanical Fault Signal And Related Fault Diagnosis Methods

The machine fault diagnosis methods based on the statistical analysis of the mechanical fault signals have been widely studied and applied in industry. These methods are based on the analysis of statistical characteristics or model of the mechanical signals to obtain the information on machine faults or conditions, and perform fault diagnosis or performance assessment of the machine conditions. In these methods, some researchers paid close attention to the fault diagnosis methods based on probability distribution features of the mechanical fault signals. However these methods have achieved limited success since there is no in-depth research for probability distribution of the fault signals. Therefore this thesis will be focused on the new parametric probability distribution model for fault signals and propose new fault diagnosis methods. The contents in the thesis include the followings:(1) The mechanical fault signals are modeled using Gaussian mixture model (GMM), and corresponding fault diagnosis methods are studied. In the modeling process, the thesis implements the Iterative Pairwise Replacement Algorithm (IPRA) to determine the number of mixture components with the considerations of the performance of fault classification, in turn, a GMM modeling scheme for mechanical fault signals is established.(2) A new feature extraction method based on wavelet coefficients clustering is studied. The thesis improves the feature extraction method using Shannon entropy concept to measure the difference among different fault signals, then the non-stationary characteristics of the fault signals are extracted and modeled using GMM. Finally a new fault diagnosis method based on GMM and non-stationary characteristics of the fault signals is proposed. In the meantime, performance assessment methods based on GMM are proposed, and verified by actual whole life cycle bearing data.(3) Based on alpha-stable distribution modeling theory and the study of statistical characteristics of alpha-stable distribution, a complete modeling method based on alpha-stable distribution for mechanical fault signals is proposed, which expands common probability density function goodness-of-fitting test method depended on subjective judgment into an objective judgment method based on characteristic function of the fault signals. At the same time, a new method for testing the stability property of the signal is provided. In the two testing process, bootstrap method is applied to estimate the null hypothesis distribution of the test statistic. Finally, bearing fault signals are proved to follow alpha-stable distribution. (4) Based on statistical characteristic of alpha-stable distribution, some new fault diagnosis methods are studied. Firstly, bearing incipient fault detection method is studied, and some comparative studies are performed based on alpha-stable distribution parameter and kurtosis. Secondly, two mechanical fault classification and identification methods are provided respectively based on alpha-stable distribution characteristic function and its coefficients. Thirdly, bearing performance assessment method based on alpha-stable distribution is given. Finally, we apply the blind source separation (BSS) methods for alpha-stable distribution signals to the mechanical fault signal separation. After the state-of-the-art of machine fault diagnosis technique based BSS is summarized, some BSS methods for alpha-stable signals are studied, and then a new BSS method based on characteristic function of the alpha-stable distribution is proposed. Separation performance is evaluated based on comparative studies with traditional BSS methods.