Novel Adaptive Time Frequency Distribution Method And Its Application In Fault Diagnosis

This dissertation was supported by the National Natural Science Foundation of China(No. 51265039, 51261024, 51075372, 50775208), Science and Technology Projects of Education Department of Jiangxi Province, China(No. GJJ12405), the Open Fund of Key Laboratory of Mechanical Equipment Health of Hunan Province(No. 201204), the Guangdong Province Figures Key Laboratory of Signal Processing Research Topics(No. 2014GDDSIPL-01) and the Innovation Fund Designated for Graduate Students of Jiangxi Province, China(No. YC2013-S214). Based on the deficiencies of lacking self-adaptively in the traditional time-frequency analysis method, the project put forward some new adaptive time-frequency analysis methods, and these methods was applied in mechanical fault diagnosis. The simulation and experiment results showed that these methods were effective, and some innovative achievements have achieved. The main contents of this paper include the following aspects:1. Based on the unique features of the adaptive generalized S transform(AGST), i.e. AGST has good self-adaptively, inherits all the advantages of short time Fourier transform, wavelet transform and standard S transform, and makes up for their shortcomings. Here, the AGST is introduced in the mechanical fault diagnosis, and a new mechanical fault diagnosis method based on AGST is proposed. The proposed method is compared with the traditional time-frequency distribution method such as short time Fourier transform, Wigner-Ville distribution, wavelet transform and standard S transform. The simulation results show that the generalized S transform has obvious advantage, can be flexibly adjust the parameters adaptively to adjust the width of window function in order to achieve the optimum frequency resolution. Finally, the proposed method was successfully applied to the rub-impact fault diagnosis of a rotor system and the rolling bearing fault diagnosis. The rub-impact fault experiment results showed that the proposed method can effectively reveal the frequency structure in rubbing fault and discern the severity of rub-impact fault. The rolling bearing fault experiment results showed that the proposed method can accurately reveal the rolling bearing fault features frequency.2. Two new adaptive kernel time-frequency distribution methods were proposed according to the design criteria of adaptive optimal kernel. They are adaptive radial Mexican-hat kernel(RMK) time-frequency distribution methods and adaptive radial Sinc kernel(RSK) time-frequency distribution methods. The characteristic of the proposed methods is that RMK and RSK can self-adaptively adjust the expansion direction and width of the kernel function according to the distribution of the analyzed signal. The RMK and the RSK are as far as possible extended in auto-term direction, and as far as possible suppressed in cross-term direction, overcomes the deficiency of the fixed kernel in the traditional time-frequency distribution, which is lack of selfadaptability. Here, the definition and the algorithm of RMK and RSK are given, and the proposed methods were compared with the traditional time-frequency distribution. The simulation results showed that the proposed methods are superior to the traditional time-frequency distribution, can be effectively process the non-stationary signal, and obtain the higher time-frequency resolution and the anti-interference performance. Finally, the RMK time-frequency distribution method was applied to the fault diagnosis of rotor crack and the experiment results show that the proposed method is very effective and can be discern the severity of rotor crack fault. The RSK time-frequency distribution method was applied to the rolling bearing fault experiment, and the experiment results show that the proposed method can accurately reveal the rolling bearing fault features frequency.3. Empirical wavelet transform(EWT) is a new self adaptive signal decomposition method. This method inherited the advantages of EMD and wavelet transform, adaptively segment the Fourier spectrum by extracting the maxima point in the frequency domain in order to separate the different modes, and then construct adaptive band-pass filters in the frequency domain so as to construct orthogonal wavelet function and extract AM-FM components, which have a compact support Fourier spectrum. Here, the EWT is introduced into the mechanical fault diagnosis, a new mechanical fault diagnosis method based on the EWT. The EWT method is compared with the traditional EMD method. The simulation results show that the EWT method is obviously superior to the EMD method. The proposed method can effectively decompose the intrinsic mode of signals. Compared with the EMD method, this method has some distinct advantages, such as lesser modes, which can adapt the classic wavelet formalism to be understood in theory, no virtual modes, and limited amount calculation, etc. Finally, the proposed method was successfully applied to the rub-impact fault diagnosis of a rotor system and the rolling bearing fault diagnosis. The rub-impact fault experiment results showed that the proposed method can effectively reveal the frequency structure in rubbing fault and discern the severity of rub-impact fault. The rolling bearing fault experiment results showed that the proposed method can accurately reveal the rolling bearing fault features frequency.4. Variational mode decomposition(VMD) is a new self adaptive signal decomposition method. The idea of this method is that assuming that each mode is mostly tightly around a center frequency, then the problem solving mode bandwidth is converted into a constrained optimization problem, finally solve each mode. Here, the VMD is introduced into the mechanical fault diagnosis, a new mechanical fault diagnosis method based on the VMD. The VMD method is compared with the EEMD method. The simulation results show that the VMD method is obviously superior to the EEMD method. The proposed method can effectively decompose the intrinsic mode of signals. Compared with the EEMD method, this method has some distinct advantages, such as weak mode mixing phenomenon, high calculation efficiency and sufficient theory, etc. Finally, the proposed method was successfully applied to the rub-impact fault diagnosis of a rotor system and the rolling bearing fault diagnosis. The rub-impact fault experiment results showed that the proposed method can effectively reveal the frequency structure in rubbing fault and discern the severity of rub-impact fault. The rolling bearing fault experiment results showed that the proposed method can accurately reveal the rolling bearing fault features frequency.