Ma Hongguang

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction. It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement (AD) in AD algorithm. Thereafter, by means of the iterative algorithm of multiple autocorrelation and Γ test, the near-optimum parameters of embedding dimension and delay time are estimated. This algorithm is provided with a sound theoretic basis, and its computing complexity is relatively lower and not strongly dependent on the data length. The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4% when using conventional algorithm to 1.06% when using this algorithm. The accuracy of invariants in phase space reconstruction is greatly improved.

A chaos-GFRF based fault diagnosis method

This paper presents a fault-diagnosis method based on the approaches of phase space reconstruction and generalized frequency response functions (GFRF) for the complex electronic system. The system parameter-evolving induced nonstationary is treated as the studying object. The phase space reconstruction and Gamma-test algorithm are employed to convert the system observing data into the pseudo-input/output pairs, and then three order of GFRF kernels are computed by means of the general formula of GFRF. The system fault data are generated by using the surrogate algorithm. The system fault detection and identification are realized by tracking and estimating the distortion of intermodulation. The experimental results depict that this fault diagnosis method can correctly detect the fault phenomena of electronic system

DATA-MINING BASED FAULT DETECTION

This paper presents a fault-detection method based on the phase space reconstruction and data mining approaches for the complex electronic system. The approach for the phase space reconstruction of chaotic time series is a combination algorithm of multiple autocorrelation and Γ-test, by which the quasi-optimal embedding dimension and time delay can be obtained. The data mining algorithm, which calculates the radius of gyration of unit-mass point around the centre of mass in the phase space, can distinguish the fault parameter from the chaotic time series output by the tested system. The experimental results depict that this fault detection method can correctly detect the fault phenomena of electronic system.

State Estimation and Fault Diagnosis for Nonlinear Analog Circuits

This paper demonstrates a new approach of fault diagnosis for the nonlinear analog circuits, which is based on the computation of maximum Lyapunov exponent of chaotic time series. We use this method to estimate the operating states of strong nonlinear analog circuits, and make a discussion on selecting a proper pair of embedding dimension and time delay for phase space reconstruction. This new fault diagnosis method is validated by an instance: the output signal of a harmonic oscillator with variable periods in radar is taken as the testing object, the surrogate method is used to generate the fault data, and the maximum Lyapunov exponent is calculated by means of the small data-set approach. The simulation testing results indicate that this method can efficiently find out the abnormal changes in nonlinear analog circuits