Disorder indicator for nonstationary stochastic processes

The properties of a statistic called a self-consistent stationarity level of nonstationary time series are examined in this work. It is shown that a change in this statistic can be treated as a disorder in the nonstationarity properties of the series. The significance level of decision making is estimated, characteristic periods in a non-stationary stochastic process are detected, and an optimal sample size for constructing indicators in stochastic control problems is determined. A disorder indicator for electroencephalogram data from epilepsy patients is studied as a practical application.

Systematic Vibration Reliability Analysis of Random Parametered Gear Sets With Analytic and Multi-Crossing Monte Carlo Simulation Methods

Vibration reliability analysis of gear sets considering various kinds of nonlinear random factors is essential for the safety of gear driven systems. In this paper, a rational definition of gear sets vibration reliability was presented at first by taking all kinds of vibration responses including displacement, velocity and acceleration into account uniformly by treating them as a series system with statistically independent components. According to the given definition, a systematic analyzing scheme for the vibration reliability of gear sets was proposed. Vibration reliability estimated via the analyzing scheme would make it conservative but more safely in design of gear driven systems. Subsequently, both analytic and numerical methods for gear sets vibration response reliability estimation were carried out based on the proposed analyzing scheme. The analytic method is suitable for the situations that the vibration responses of gears sets under random circumstances are stationary stochastic responses. While, the numerical method named Multi-crossing Monte Carlo Simulation (MULCMCS) can well solve the reliability estimating problems even when the vibration responses of gear sets are nonstationary stochastic processes. Finally, for illustration, a numerical case of analyzing the vibration response reliability of a single degree-of-freedom (DOF) gear set was given to demonstrate the effectiveness of the MULCMCS method.