ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

# Differential Equations and Control Processes (Differencialnie Uravnenia i Protsesy Upravlenia)

## Fault Detection Algorithm for a 1-dof Nonlinear Dynamic System with Random Excitation

### Author(s):

Russia, 620002, Ekaterinburg, ul. Mira, 28
Ural States Engeneering University
Department of computation methods and mathematical physics equation

P. Kruchinin

Russia, 119899, Moscow, Vorobievi gori
Moscow Lomonosov States University
Faculty of mechanics and mathematics
Department of applied mechanics and control

kruch@mech.math.msu.su

### Abstract:

The fault detection algorithm for a dynamic system with polynomial nonlinearities is offered. The system is perturbed by stochastic process such as white noise. The exact expressions of a method of the moments are used. The relations of this method allow to note expressions for a derivative with time from the probability distribution moments as functions of parameters of system and thems. We use in the capacity of check variables right members of these relations. They are calculated with a priori known ("nominal") values of system parameters and estimations of moments. If the values of parameters, realized in a system, is equal its a priori values, these expressions accept zero values on stationary regimes of a system motion, when the distribution moments do not vary in time. At a varification of parameters (or structures) of the dynamic system the entered magnitudes change the values. The procedure of fault detection consists in the following: on stationary regimes of motion the estimations of the moments are calculated; theirs values and "nominal" values of parameters are used for calculation of the absolute value of check variables. At overflow even one of these values of the given threshold value arrests violation of normal operation of a system. The effectiveness of application of such procedure is considered on an example of a 1-DOF system with cubic nonlinear expressions for elastic and damping forces. For this system the series of check variables is constructed, the numerical modeling and analysis of responsivity them to a varification of separate parameters of a system is carried out. Is shown, that the procedure allows steadily to discover a varification of separate parameters on 1-5%, and its responsivity the above, than more nonlinearity of a system.