The Method Of Phase Space Reconstruction And Its Application In Fault Diagnosis From Multivariate Time Series

In recent years, chaotic and fractal implication in fault diagnosis which provides a quantitative index and makes diagnosis more clearer catches much attention. In nonlinear time series analysis, phase space reconstruction is the first step. Time-delay thory presented by Takens could construct phase space structure of original system from one-dimension time series reversely. But as for many complicated dynamical systems one-dimension time series couldn't obtain perfect reconstruction effect. With further research of phase space reconstruction and its implication, many researchers have realized the malpractice that phase space is reconstructed from univariate time series, so they start exploring reconstruction from multivariate time series. Multivariate fault diagnosis method based on chaotic and fratcal thory is presented in this paper. With a view to the characteristic of data fusion that could combine, transform, correlate and synthesize data from every data origin then extract dominating information, a new multivariate phase space reconstruction method based on data fusion is presented. As for distinction between the attractor reconstructed from every univariate time series and the true one of system, according to Bayes estimation theory the phase points in the same phase space reconstructed from multivariate data are fused, then the new attractor could contain all the charateristics of every univariate time series. Then simulation analysis of Lorenz sysem and coupling Rossler system obtain well results. Because the dimension of real multivariate time series is different, multivariate time series must be normalized, and PCA method is used to simplifying compution.The largest Lyapunov exponent and correlation dimension of multivariate time series are extracted based on the multivariate reconstruction presented in this paper. In addition, a new method of embedding dimension for phase space reconstruction is presented based on EMD method. And a new judgement method of linear region for correlation integral is presented. At last, the multivariate fault diagnosis method presented in this paper is applied in rub-impact, whirling of oil-film and rub-whirling coupling faults of rotor system, as well as familiar faults of motor bearing drive end and fan end. Every fault is diagnosed by multivariate phase space reconstruction information fused and correlation dimension. The attrator which contains more comprehensive information of machine equipment is obtained, which makes the fault characteristic more integrate and steady, and the veracity of fault diagnosis is heightened.