Robust fault detection based on adaptive threshold generation using interval LPV observers

Abstract

SUMMARYIn this paper, robust fault detection based on adaptive threshold generation of a non-linear system described by means of a linear parameter-varying (LPV) model is addressed. Adaptive threshold is generated using an interval LPV observer that generates a band of predicted outputs taking into account the parameter uncertainties bounded using intervals. An algorithm that propagates the uncertainty based on zonotopes is proposed. The design procedure of this interval LPV observer is implemented via pole placement using linear matrix inequalities. Finally, the minimum detectable fault is characterized using fault sensitivity analysis and residual uncertainty bounds. Two examples, one based on a quadruple-tank system and another based on a two-degree of freedom helicopter, are used to assess the validity of the proposed fault detection approach.᭧

Filtering and fault detection for nonlinear systems with polynomial approximation

“…1) We are interested in designing the filter gain K k in (30) for the system (28) such that the resulting estimation error covariance is bounded and such a bound is subsequently minimized. 2) Based on the proposed filter design scheme, the associated fault detection problem is to generate a residual signal whose threshold is adaptively computed by reflecting the approximation errors and external disturbances.…”

“…So far, many existing results have focused on adaptive threshold generation for linear systems [29][30][31]43]. However, the corresponding results for nonlinear systems have been scattered in spite of their engineering significance [24,34].…”

Entwurf robuster modellbasierter Fehlerisolationsfilter

“…Die Idee der systematischen Auslegung von Grenzwerten geht auf [66] zurück. Erweiterungen hat das Konzept in [40,41,57,75,103,116,153,178] erfahren, wobei vielfach dynamische Grenzwerte zum Einsatz kommen, die einen besseren Kompromiss zwischen Fehlalarmen und nicht gemeldeten kritischen Situationen ermöglichen. Eine ausführlicheÜbersichẗ uber normbasierte und statistische Verfahren zur Residuenauswertung findet sich in [58, Kapitel 9 und 10].…”

Fault tolerance evaluation of nonlinear systems using viability theory

“…Such systems have a dynamics matrix of the form A = exp(A c ) which is always invertible [3]. Following computation algorithm in [7], we can find this reachable set using zonotopes by…”

“…where 'mid' denotes the center and 'diam' the diameter of the interval and ♦ is zonotope inclusion [7]. For computation of viability kernel, this backward reachable set is calculated step by step.…”