Optimized fault detection using bond graph in linear fractional transformation form

This article deals with the optimal robust fault detection problem using the bond graph in its linear fractional transformation form. Generally, this form of the bond graph allows the generation of two perfectly separate analytical redundancy relations, that are used as residual and threshold. However, the uncertainty calculation method gives overestimated thresholds. This may, for instance, lead to undetectable faults. Therefore, enhancing the robustness of fault detection and isolation algorithms is of utmost importance in designing a bond graph-based fault detection system. The main idea of this article is to develop optimized thresholds to ensure an optimal detection, otherwise this article proposes a method to detect tiny magnitude faults concerning parameter's uncertainties. This work considers the issue of optimal fault detection as an optimization problem of the gap between the residuals and its threshold. New uncertainty values will be calculated in a way that these estimated parameters ensure the desired optimized gap between residuals and thresholds. These estimated uncertainty values will be used to generate optimized adaptive thresholds. Through these thresholds, we increase the sensitivity of the residuals to tiny magnitude faults, and we ensure an optimal and early detection.