Multimode Diagnosis for Switched Affine Systems with Noisy Measurement

TL;DR

This paper introduces a noise-robust diagnosis scheme for switched affine systems that accurately detects active modes in real-time, using an optimized filter bank and probabilistic thresholds, with improved false-alarm guarantees.

Contribution

It presents a novel finite optimization framework for designing filters that minimize noise impact and a probabilistic thresholding policy with logarithmic false-alarm guarantees.

Findings

The proposed method effectively detects system modes under noisy conditions.

The approach provides probabilistic false-alarm guarantees with logarithmic dependency.

Numerical and building system examples validate the method's effectiveness.

Abstract

We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a bank of filters, and (ii) the introduction of a residual/threshold-based diagnosis rule. We develop an exact finite optimization-based framework to numerically solve an optimal bank of filters in which the contribution of measurement noise to the residual is minimized. The design problem is safely approximated through linear matrix inequalities and thus becomes tractable. We further propose a thresholding policy along with probabilistic false-alarm guarantees to estimate the active system mode in real-time. In comparison with the existing results, the guarantees improve from a polynomial dependency in the probability of false alarm to a logarithmic form. This improvement is achieved under the additional assumption of sub-Gaussianity, which is expected in many applications. The performance of the proposed approach is validated through a numerical example and an application of the building radiant system.