(601g) Optimal Input and Sensor Selection for System Health Assessment

Fault diagnosis is an area of significant research activity with a plethora of methods, as a result of the complexity of modern industrial engineered systems. Modern cyber-physical systems are in need for advanced fault detection and isolation (FDI) test design methods that are accurate, robust against uncertainty, capable of reducing maintenance costs, and can, thus, improve system performance and reliability. Modelling techniques such as unknown input observers can mitigate the implications of uncertainty in fault detection capability and false alarm rates. The latter can be more effective if reconfiguration of system inputs is feasible for the purpose of fault diagnosis in lieu of environmental and system uncertainty. In the same context, sensor design and selection can also improve the precision of fault diagnosis, and methods for singling out informative sensors in diagnosis have been extensively studied.¹ However, efforts that consider active test design and sensor selection simultaneously for the purpose of fault diagnosis are scarse.² In this presentation, we discuss an integrated approach to active FDI with sensor selection. In the proposed framework, test design optimization using system inputs and sensors is first performed. Then, an evaluation of the FDI test accuracy across a range of decision thresholds via classification techniques and receiver operating characteristics provides optimal FDI tests in terms of both design and execution.

The selection of active FDI test designs and sensors is formulated as a constrained optimization problem. Constraints of this problem include the allowable operating space, sensor availability and accuracy. This optimization is achieved using models that represent the anticipated steady-state or transient system performance within sufficient accuracy. It is assumed that each fault targeted for diagnosis can be characterized as a model parameter. System uncertainty caused by environmental variability or modelling error is also considered as parametric variance in the model. As shown in Palmer et al.,³ the rate of successful fault diagnosis can be improved by maximizing the sensitivity of the outputs with respect to faults, and minimizing the correlation between faults and uncertain parameters. In this communication, we present a method for calculating optimal test designs using output sensitivities of the outputs for a fixed (limited) number of discrete sampling points and locations, subject to system faults and uncertainty. The sensitivities of all the feasible measurements with respect to all the anticipated faults and uncertain inputs or conditions are compiled into a variation of the Fisher Information Matrix (FIM). Sensor selection is incorporated into the FIM using a vector of binary elements.

Two optimal test design formulations are considered for active FDI: optimal designs for tests containing only steady-state information, and information obtained from steady-state and transient responses. We present the optimal test designs generated in a simulated case study that satisfy Ds-optimality. Ds-optimal criterion, also known as subset D-optimal criterion, was selected for its ability to selectively reduce the volume of the joint confidence region between parameters of interest (e.g. system faults). The resulting data generated from implementing FDI with the optimal test design are then used to train and classify the faults in the system. Principal Component Analysis (PCA) followed by k-Nearest Neighbor (k-NN) classification are performed to determine the condition of the system. The k-NN algorithm is preferred in fault diagnosis for its capability of multi-class classification and its simplicity.⁴ However, in systems with large datasets, k-NN has been known to over-fit the data resulting in precision issues. Thus, PCA is implemented to reduce the dimensionality of the test data and identify the most informative system features. After PCA, Monte Carlo simulations are implemented at anticipated fault and fault-free scenarios to train the k-NN algorithm for each fault scenario. The effectiveness of the selected FDI test and sensor set is then evaluated by testing the system at various conditions to determine the frequency of correct classification in each scenario. The correct classification rate (CCR) and overall classification accuracy obtained using the selected FDI test designs are then compared to determine the success of the method. Probabilistic k-NN is also performed for a comprehensive evaluation of the trade-off between selectivity and sensitivity of the FDI test. A decision threshold is used to determine the maximum allowed probability for a system to be considered fault-free based on any given set of test data. Finally, receiver operating characteristic (ROC) curves are generated for comparing correct classification and false positives, using k-NN with a decision threshold based on the allowable proportion of neighbors.

The proposed method is demonstrated on the air-handling system of a diesel engine. This diesel engine subsystem was simulated using a model reported by Wahlström and Eriksson⁵, and it is subject to multiple actuator faults and leaks in various components of the system. Four faults are considered: actuator fault in the exhaust gas recirculator (EGR); actuator fault in the variable geometry turbine (VGT); leak in the inlet manifold; and leak in the exhaust manifold. Including the fault-free system state, the FDI has to discriminate between each system state and determine the system health status. Application of the proposed method shows significant improvement in correct fault classification as a result of the test design optimization performed simultaneously with sensor selection. The classification accuracy for the Ds-optimal test design with sensor selection is shown to be superior than that with the nominal sensor selection set.

Acknowledgment

This work was sponsored by the UTC Institute for Advanced Systems Engineering (UTC-IASE) of the University of Connecticut and the United Technologies Corporation. Any opinions expressed herein are those of the authors and do not represent those of the sponsor.

References

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