Polynomial filtering fault detecting method for nonlinear system

Abstract

The invention discloses a polynomial filtering fault detecting method for a nonlinear system. The polynomial filtering fault detecting method comprises the steps of approximating by a polynomial, i.e., expressing m-order kronecker powers of a system state variable and a measurement output variable of the nonlinear system respectively by a polynomial to obtain a polynomial approximation model composed of a mu-order polynomial and a (mu+1)-order polynomial remainder term; expressing the (mu+1)-order polynomial remainder term in the polynomial approximation model as a low-order polynomial under the condition that no faults exist, wherein the coefficient of the low-order polynomial is equal to the product of a proportion matrix and an indefinite matrix; obtaining an augmented state evolution equation based on the proportion matrix and the indefinite matrix; designing a filter, i.e., establishing a filter function according to the augmented state evolution equation to obtain an estimated value of the system state variable at the (k+1)th moment; determining a filter gain coefficient to ensure that the upper bound of a square deviation of an augmented state evaluation error is minimum at the (k+1)th moment; detecting a fault, i.e., determining a detection threshold at the kth moment, and determining a fault detection policy according to the detection threshold.

Description

technical field [0001] The invention relates to the field of fault detection, in particular to a polynomial filter fault detection method for nonlinear systems. Background technique [0002] Due to the widespread existence of nonlinearity in real systems, the problem of filtering and control of nonlinear systems has received a lot of research attention. If the nonlinearity in the system is not handled well, it can lead to oscillations or even divergence. The Extended Kalman Filter (EKF) is a classic method for dealing with nonlinear estimation problems under the minimum variance criterion. At present, some researches hope to improve the Extended Kalman Filter (EKF) method to improve its handling of nonlinear and The ability to be random. [0003] The Polynomial Kalman Filter (PEKF) extends the Extended Kalman Filter (EKF) based on a polynomial approximation of a nonlinear function. The EKF method only considers the linearized part of the nonlinearity, while the KalmanPEKF...

AI Technical Summary

Problems solved by technology

In the existing polynomial Kalman filter (PEKF) method, the designed filter is not reasonable due to the neglect of high-order polynomial remainders, so faults cannot be detected accurately

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