Geometric Approach to Fault Detection and Isolation in Multivariate Structural Systems: An Experimental Investigation

In this paper, fault isolation of a laboratory scale structural frame, as a multivariate system, has been investigated, using a geometric approach in conjunction with parametric system identification. The proposed geometric approach is based on the assumption that each fault mode may be regarded as a hyper-surface in an appropriate topological space, where the hyper-surfaces are constructed based on the estimated parameters. Finally, by defining proper metric and assuming the unknown mode (of a system) being as a point in space, where the estimated parameters are the coordinates, the fault mode can be identified by minimizing the obtained distances between the point and each of the hyper-surfaces. Based on the number of inputs and measured outputs, the frame was modeled by standard ARX and VARX models in four different forms as Single-Input Single-Output (SISO), Single-Input Multiple-Output (MISO), Single-Input Multiple-Output (SIMO) and Multiple-Input Multiple-Output (MIMO). Also, the performance of the scheme was evaluated in deterministic and probabilistic spaces. The obtained results revealed that the MIMO representation of the frame in the probabilistic space had an acceptable performance which was the highest in comparison with the others and the SISO representation system in the deterministic space had the lowest performance.