Active Fault Detection Based On Set-membership Approach

In modern industries,operational safety and product quality of systems are important issues.If a fault occurs,it will not only affect the quality of the product,but it can also consequently bring security risks to the systems and operators.Therefore,fault diagnosis plays a crucial role in industrial processes.However,in some specific environment,the occurrence of small fault can't be detected at the first time,and with the passage of time,small fault can becomes a significant fault,which has a serious impact on the system.Therefore,timely detection of small faults will avoid the occurrence of significant faults.The main contributions of this paper is to design the auxiliary input signal by using the set member method to realize the active fault detection.For linear time invariant systems,an active fault detection method based on state set-membership is proposed.The existing active fault detection methods based on set-membership mainly focus on the analysis of the output set of the system,while the state set of the system is less noisy than the output set of the system at the next moment.Therefore,using the set of states to design the auxiliary input signal will reduce some conservatism.Firstly,active fault detection based on state ellipsoid is presented.The H? observer is designed to estimate the state of the system,and the ellipsoid of sate is obtained.The auxiliary input signal is designed by the state ellipsoid of the healthy model and the state ellipsoid of the fault model,and the auxiliary input signal is injected into the system to realize the small fault detection.Compared with ellipsoids,zonotopes produces less conservative results when designing auxiliary input signals.Therefore,in this paper,based on the framework of state ellipsoid,the active fault detection based on the state zonotope is proposed.Different from the method based on state ellipsoid,this method estimates the system state by designing a zonotopic Kalman observer,and describes the state with process disturbance and measurement noise by using the zonotopic Kalman observer.For discrete-time system with bounded uncertainties in this paper,an active fault detection method is proposed based on zonotopic Kalman filter observer.The existing active fault detection methods based on the set-membership approach mainly use the idea of the set theory to bound system outputs using sets.It should be mentioned that the uncertain system contains not only process disturbance and measurement noise,but also the uncertainties of system parameters,increasing the size of output sets.The observer design method can not only used to reduce the size of the system output sets but to guarantee the convergence.Therefore,in this paper,the zonotopic Kalman filter method is used,which reduces the size of the system output sets.Following the earlier work regarding active fault detection based on set-membership approach.In this paper,the active fault detection method based on the zonotopic Kalman observer is applied to the discrete system with parameter uncertainty,and the auxiliary input signal is designed to realize the active fault detection.Finally,the effectiveness of the proposed method is verified by simulation.