Volterra Series Identification Method Based On Quantum Particle Swarm Optimization And Its Application In Fault Diagnosis

This thesis is supported by the National Natural Science Foundation of China (No.50775208), introduces Quantum Particle Swarm Optimization (QPSO) algorithm for Volterra series identification of nonlinear system, deeply studies the identification method of Volterra time domain kernel based on QPSO and its application in fault diagnosis of rotating machinery. Some preferable innovative products are obtained in this paper. The primary contents of this study involve the following:Chapter one illuminates the meaning of proposing and studying on this thesis, summarizes the research status at home and abroad of Volterra series model, as well as its application in fault diagnosis. At last the primary contents and innovation points of this paper are presented.Chapter two introduces the basic ideas of Volterra series model, the identification of Volterra time domain kernel (GIRF) and Volterra frequency domain kernel (GFRF). The idea of fault diagnosis based on Volterra series model is given. The content of this chapter is the basic theory of the overall paper.Chapter three aims at the deficiency of the Volterra time domain kernel (GIRF) identification method based on traditional Least Mean Square algorithm, introduces QPSO for GIRF identification of nonlinear system. The GIRF identification method based on QPSO is proposed and compared with traditional Least Mean Square (LMS) algorithm. The simulation study shows that this method is superior to LMS in identification precision, convergence and anti-interference. Furthermore this superiority is more obvious along with the memory length of Volterra kernels increases. Then the proposed method is applied into the rotor fault diagnosis of rotating machinery. The GIRF of rotor crack and normal state are identified and compared. The experiment result shows that the proposed method is effective, and the GIRF of rotor crack state can well reflect the nonlinearity of rotor system in this state.Chapter four proposes a fault diagnosis method based on Volterra time domain kernels (GIRF) and Kernel Principal Component Analysis (KPCA). In this method, firstly Volterra kernels are identified by QPSO algorithm, then the Volterra kernels are used as original spatial data for KPCA, the distribution and projection of principle component are utilized for classification. The proposed method is applied to recognize four states of rotor system, i.e. normal, rotor crack, rotor rub and pedestal looseness in experiment. The result verifies that this method is very effective. The second-order and third-order Volterra kernels can be used for recognition when the states are hard distinguished with first-order Volterra kernels only. Here embodies the advantage of fault diagnosis method based on Volterra series, namely, fault feature information is rich.Chapter five discusses the fundamental of Support Vector Machine (SVM) and the classification algorithm of multi-category SVM. On this basis, a fault recognition method based on Volterra time domain kernels (GIRF) and SVM is proposed. This method uses the Volterra kernels which are identified by QPSO algorithm as feature vectors to input into SVM classifier for recognizing states of nonlinear system. The experiment result shows that when fault dada is abundant, perfect classification effect is gained by either only first-order kernels or first three order kernels, but when fault data is not abundant, classification effect gained by first three order kernels is better than that gained by only first-order kernels. This result indicates that nonlinear Volterra kernels contain faults feature which can not be reflected by first-order Volterra kernel, and this method is superior in fault diagnosis with small sample size.Chapter six combines Volterra time domain kernels (GIRF) with Hidden Markov model (HMM), proposes a new fault diagnosis method based on Volterra time domain kernels and HMM. In the proposed method, first three order Volterra kernels are extracted by QPSO algorithm from vibration signals of known states. Then they are used as observation sequence to input into HMM for training. Next first three order Volterra kernels of test data are identified using QPSO algorithm and are input into HMM of every state. The corresponding state of the HMM with the maximum output probability is the current running state of the equipment. In experiment, with vibration signals in run-up process of rotating machinery, four states of rotor system are recognized by the proposed method. The result shows the validity of this method. In the training step of HMM, the logarithm probabilities of four states which are obtained with first three order Volterra kernels have obviously bigger difference than those obtained with only first-order Volterra kernels, the classification effect is improved distinctly. The proposed method provides an effective solution for fault diagnosis of non-stationary process of rotating machinery, has important theoretical significance and actual application value.Chapter seven sums up the research results of this paper, and proposes the problems which are worth further studying.