Robust fault detection filter using linear matrix inequalities’ approach for shaft crack diagnosis

Detecting cracks in rotating shafts is a challenging problem when using vibration-based diagnostics. This is due to the fact that a localized crack has a minimal influence on the global vibration response of the system. To increase sensitivity and reliability, the vibration response needs to be coupled with additional sources of information such as a mathematical model of the machine. Modern control theory techniques offer system-level mathematical models for both control and diagnostics. Focusing on the latter, a new and promising approach involves the use of unknown input observers. Such observers can be designed to employ robust fault detection filters (RFDFs) for isolating fault signatures while reducing the influence of real-world disturbances and noise. For the present study, a modified design procedure coupled with robust fault detection is utilized for shaft crack detection. The filter is designed using the linear matrix inequalities (LMI) technique. The LMI approach is applied to obtain the solution of the mixed H_/H-infinity optimization problem, which arises during the synthesis of the RFDF. By reformulating the LMI conditions, the proposed RFDF design procedure is simplified and thus requires less iteration steps to find the optimal solution. A new feature of the present approach involves the application of the rigid finite element method for the formulation of the mathematical model of the rotor and the shaft crack. The numerical and experimental results confirm the advantages of the designed robust fault detection filter and its ability to detect shaft cracks. The filter is minimally sensitive to measurement noise while allowing for the identification of shallow cracks (2% or 5% deep). The cracks are manifested through the observance of very subtle vibration response changes. The results also confirm the effectiveness and accuracy of the rigid finite element modeling concerning the cracked rotor.