Detection and diagnosis of incipient faults in sensors of an LTI system using a modified GLR-based approach

• Developing fault signature matrices for pure ramp type and truncated ramp type faults.
• Computation of GLR test statistic for both ramp and truncated ramp type faults and estimated fault magnitudes.
• Development of closed form solutions for fault isolation, estimation of TOF and fault magnitude.
• A new FDI framework which is capable of dealing with ramp, truncated ramp and step type faults at the same time.

This study aims to provide a solution for detection and diagnosis of drift type faults in linear time invariant systems using the generalized likelihood ratio (GLR) test. The main goal of this study is to deal with more realistic ramp type faults instead of abrupt jumps. In this regard, several ramp type fault scenarios are considered: pure ramps, truncated ramps and steptype faults which behave as ramp faults during inter-sample intervals. In addition, a modified GLR-based approach that is capable of accurately detecting the time of occurrence of the fault is used in this study. The proposed method uses statistical fault detection and confirmation tests to obtain a crude estimate of time of occurrence of the fault (TOF) and then refines the estimated TOF using an extended data window and the GLR test. The closed form solutions for all possible scenarios are provided. The proposed method is evaluated by application to an LTI system using Monte Carlo simulations and the results reveal the efficacy of this method in dealing with drift type faults.