Robust Fault Diagnosis for Adaptive Structures With Unknown Stochastic Disturbances

Adaptive structures can react to environmental impacts and can significantly improve the load-bearing behavior of, e.g., building structures. For building structures, reliability and safety are major concerns, and thus, a fault diagnosis system, detecting and isolating actuator and sensor faults, is necessary. Adaptive building structures are exposed and adapt to unknown, stochastic wind and surface loads that are difficult to model and can therefore not be considered in model-based fault diagnosis methods, which decreases their performance. For this reason, this article combines the model-based method of parity equation with the data-based method of principal component analysis (PCA) for the fault diagnosis in adaptive structures. The proposed approach characterizes the unknown disturbance in the residual data derived by parity equations using PCA. PCA determines orthogonal directions of decreasing variance in the residual which are decoupled to decrease the sensitivity of the residual to disturbances. Since decoupling of residual directions influences the diagnosability of faults, the number of decoupled principal components is determined such that the diagnosability is not significantly affected. The diagnosability is analyzed by the Kullback–Leibler divergence based on the system model and disturbance characterization. The resulting decoupled residual significantly improves the fault detection performance using a cumulative sum algorithm for change detection. Moreover, the fault input matrix of the system model and the knowledge of the fault time profile yield reliable fault isolation using a Bayes classifier as illustrated in a simulation study.