Failure detection in dynamic systems with modeling errors

Abstract

This paper determines the theoretical limits of failure detectability in systems with modeling errors. Such errors are the main obstacle to accurate failure detection in aircraft, jet engines, power generation systems, and most other systems that include mechanical components and/or thermofluid processes. The paper then introduces the reachable measurement intervals (RMI) failure detection method that performs at the limit of detectability. RMI is capable of detecting the smallest theoretically detectable failures in systems with modeling errors, and is implementable in real time on microprocessors. The method is illustrated on a jet engine example. Nomenclature a — entry of the matrix A A = system matrix b = entry of the matrix B B = input matrix Bj = input matrix equal to the identity matrix C = output matrix C{ = output matrix for additional measurements D = direct transmission matrix H = Pontryagin's function K — matrix of gains for additional measurements L = vector of Lagrange multipliers m = entry of the matrix M M = matrix of Lagrange multipliers associated with uncertain entries of A n = entry of the matrix N N = matrix of Lagrange multipliers associated with uncertain entries of B p = discrete-time index corresponding to current time P = performance index for optimization q - vector of system parameters / = time t0 — current time ts = length of the processing window T - sampling time u = input vector x = state vector y = output vector z - vector of additional measurements Subscripts d = discrete e = uncertain and uncorrelated n = nominal v = uncertain