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.

本文以线性分数变换形式的键合图处理最优鲁棒故障检测问题。通常，债券图的这种形式允许生成两个完全独立的分析冗余关系，用作残差和阈值。但是，不确定性计算方法给出了高估的阈值。例如，这可能导致无法检测的故障。因此，在设计基于键合图的故障检测系统时，提高故障检测和隔离算法的鲁棒性至关重要。本文的主要思想是开发优化的阈值以确保最佳检测，否则本文提出了一种检测与参数不确定性有关的微小故障的方法。这项工作将最佳故障检测问题视为残差与其阈值之间的间隙的优化问题。将以这些估计的参数确保残差和阈值之间的理想优化间隙的方式来计算新的不确定性值。这些估计的不确定性值将用于生成优化的自适应阈值。通过这些阈值，我们提高了残差对微小故障的敏感性，并确保了最佳的早期检测。