A Data-Driven and Probabilistic Approach to Residual Evaluation for Fault Diagnosis

An important step in fault detection and isolation is residual evaluation where residuals, signals ideally zero in the no-fault case, are evaluated with the aim to detect changes in their behavior caused by faults. Generally, residuals deviate from zero even in the no-fault case and their probability distributions exhibit non-stationary features due to, e. g., modeling errors, measurement noise, and different operating conditions. To handle these issues, this paper proposes a data-driven approach to residual evaluation based on an explicit comparison of the residual distribution estimated on-line and a no-fault distribution, estimated off-line using training data. The comparison is done within the framework of statistical hypothesis testing. With the Generalized Likelihood Ratio test statistic as starting point, a more powerful and computational efficient test statistic is derived by a properly chosen approximation to one of the emerging likelihood maximization problems. The proposed approach is evaluated with measurement data on a residual for diagnosis of the gas-flow system of a Scania truck diesel engine. The proposed test statistic performs well, small faults can for example be reliable detected in cases where regular methods based on constant thresholding fail.