Data-driven robust receding horizon fault estimation

Abstract

This paper presents a data-driven receding horizon fault estimation method for additive actuator and sensor faults in unknown linear time-invariant systems, with enhanced robustness to stochastic identification errors. State-of-the-art methods construct fault estimators with identified state-space models or Markov parameters, but they do not compensate for identification errors. Motivated by this limitation, we first propose a receding horizon fault estimator parameterized by predictor Markov parameters. This estimator provides (asymptotically) unbiased fault estimates as long as the subsystem from faults to outputs has no unstable transmission zeros. When the identified Markov parameters are used to construct the above fault estimator, zero-mean stochastic identification errors appear as model uncertainty multiplied with unknown fault signals and online system inputs/outputs (I/O). Based on this fault estimation error analysis, we formulate a mixed-norm problem for the offline robust design that regards online I/O data as unknown. An alternative online mixed-norm problem is also proposed that can further reduce estimation errors when the online I/O data have large amplitudes, at the cost of increased computational burden. Based on a geometrical interpretation of the two proposed mixed-norm problems, systematic methods to tune the user-defined parameters therein are given to achieve desired performance trade-offs. Simulation examples illustrate the benefits of our proposed methods compared to recent literature.

Fault Estimation Filter Design With Guaranteed Stability Using Markov Parameters

“…A, B, C, D, E, G are time-invariant matrices unavailable to the data-driven design. Assume that the system description (4) admits a Kalman filter for its fault-free subsystem, then this system (4) can be equivalently represented by the following Kalman predictor representation [5], [15]:…”

“…The aim of this paper is to construct a state-space SI-FEF with tunable stable poles by using the predictor MPs Note that the identification errors of the predictor MPs affect the fault estimation performance. This issue has been investigated recently in [15] for the robust data-driven design of a receding horizon fault estimator. How to address the same issue for a data-driven state-space FEF can be investigated only after the stability is ensured.…”

“…(16a) is a copy of the residual dynamics (12a) with a feedback term K rr (k + τ ) from the residual reconstruction errorr(k + τ ). Similarly, (16b) constructs the fault estimatef (k) by following (15). By substituting (16b) into (16a) and (16d), respectively, the left inverse (16) can be equivalently rewritten aŝ…”

“…How to design Π in (15) and K r in (22) for our data-driven design problem will be discussed in Section V-A.…”

“…A non-recursive fault estimator was proposed in [13] and [14] by minimizing the squared reconstructed prediction error in the residual subspace of a latent variable model. Recently, a receding horizon leastsquares fault estimator has been proposed in [15] by using identified predictor MPs, which enables robust design that compensates for identification errors of the MPs. Even fewer studies have been reported on data-driven design of recursive fault estimation observers or filters.…”