Fault Diagnosis For Discrete Systems With Multiplicative Noise Using A Moving Window Approach

In order to ensure the safety and reliability of increasingly complicated and large-scale industrial systems,adopting timely and effective fault diagnosis strategy based on analytic redundancy is one of the most successful measures at present.Linear discrete time-varying(LDTV)systems with multiplicative noise is a state space model which is commonly applied to describe a class of uncertain/unexpected phenomena such as attenuation,scattering,distortion of its own parameters or imperfect signal transmission.It is recognized that it will more in line with the complex and changeable physical background of the actual industrial systems.Up to now,in view of its advantages of robustness to model uncertainties and modeling errors,fault diagnosis strategy with finite observations is developed as the hot research topic at home and abroad,while the research results in the application on fault diagnosis for linear discrete time-varying systems with multiplicative noise are relatively few or need further research.It is thus theoretically important and practically significant to devote more efforts to robust fault diagnosis based on a moving window approach for LDTV systems with multiplicative noise.Its main research work and innovations are as follows:1.Based on a new robustness index in stochastic sense,the parity space method is extended to the fault detection field for LDTV systems with multiplicative noise.The analytical expression of the optimal parity space vector is derived,which is used to design the optimal residual generator,and the calculation formulas of all unknown key matrices involved are provided.By means of Randomized Algorithms(RA),two methods of selecting threshold are proposed to achieve residual evaluation.2.A new performance index of minimum estimation error is proposed to design the optimal Finite Impulse Response(FIR)Filter gain to realize the fault estimation of LDTV systems with multiplicative noise.The optimal FIR filter gain design problem is transformed into a random optimization problem.The necessary and sufficient conditions to ensure the existence of the optimal FIR filter are established.The analytical solution of the random optimization problem and two calculation methods of the unknown key matrix involved are given.3.Using all the state information of the previous time window to construct a new analytical redundancy relation,a new FIR filter is designed to realize the optimal fault estimation for LDTV systems with multiplicative noise under the performance index of minimum estimation error.For ensuring the existence of the analytic expression of the optimal FIR filter gain matrix,the necessary and sufficient conditions,which is considered less design conservatism,are derived.Two calculation methods with obvious calculation advantages to obtain the unknown key matrix involved are analytically given.