A method for quantitative fault diagnosability analysis of stochastic linear descriptor models

Abstract

Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like "How difficult is it to detect a fault fi?" or "How difficult is it to isolate a fault fi from a fault fj?". The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback-Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

Robust residual selection for fault detection

“…In this case the key factor is the fault magnitude to noise ratio [10]. Also when designing robust residual generators using the H ∞ norm, the ratio between faults and disturbances is optimized [15].…”

“…For time-discrete descriptor models with additive faults and noise, Eriksson, et al [10] propose a diagnosability measure which can be used for quantifying diagnosability performance. This measure is used for online selection of the best set of residuals for different conditions [11].…”

Development of misfire detection algorithm using quantitative FDI performance analysis

“…Here a stochastic representation of T during misfires and in the fault-free case is presented similar to [9].…”

“…The contribution from the moving mass is a given function of the crankshaft angle and proportional to ω 2 and can easily be compensated for, see equation (9) in [8]. In this work, this component is included in T cyl,i since the effects are known and will be taken into consideration in the misfire detection algorithm.…”

Sensor selection for fault diagnosis in uncertain systems

“…or 'Is a fault f i isolable from another fault f j ?' (Eriksson, Frisk, & Krysander, 2013). One problem of using qualitative fault detectability and isolability to formulate performance requirements is that there is no way of specifying how easy it should be to detect or isolate different faults of different magnitudes.…”