A model-based method will be presented for the simultaneous selection of test conditions and sensors for fault detection and isolation (FDI). The proposed framework is based on prior work on the design of dynamic and steady state tests for FDI with a finite pre-selected set of sensors [1–4]. The method is reformulated so that it is deployable in passive or active FDI, depending on the capability of the system to control the values of admissible inputs for the purpose of FDI. The methodology is intended for FDI in systems that are limited to a finite number of input design scenarios and can record from multiple sensors. The challenge for such systems is the selection of the “best possible†combination of sensors and tests out of a superset of options that lead to steady state or dynamic measurements used for FDI. Sensors and test conditions are selected (or designed) based on their contribution to information gain in the system, using an accurate fundamental or semi-empirical system model. Trajectories or disparate sets of discrete admissible inputs are selected from an existing set or designed so that they maximize the sensitivity of sensed outputs with respect to faults and minimize the joint confidence between faults and system uncertainty. The optimization of discrete sensors and input designs (including all their possible combinations) is formulated as a constrained mixed integer non-linear problem that maximizes a measure of the Fisher Information Matrix (FIM) of the system outputs with respect to faults and uncertainty represented as parameters in the system model. A normalized FIM is presented and used for FDI, to account for tests of variable sample set sizes and datasets of sensed information of variable size. Further, the isolation capability of the FDI tests in systems with uncertainty in inputs and parameters is performed using information metrics, such as the Kullback-Leibler divergence and the Hellinger distance. FDI tests are then deployed using
k-nearest neighbor classification, which is used as a verification method for test designs and sensor networks that result in high correct classification rates. The proposed design framework is tested on a virtual benchmark three-tank system, subject to multiple faults and sources of uncertainty.
Acknowlegments
This work was sponsored by the United Technologies Corporation Institute for Advanced Systems Engineering (UTC-IASE) of the University of Connecticut. Any opinions expressed herein are those of the authors and do not represent those of the sponsor.
References
[1] K.A. Palmer, G.M. Bollas, Active fault diagnosis for uncertain systems using optimal test designs and detection through classification, ISA Trans. (2019). doi:10.1016/j.isatra.2019.02.034.
[2] K.A. Palmer, G.M. Bollas, Analysis of transient data in test designs for active fault detection and identification, Comput. Chem. Eng. (2018). doi:10.1016/j.compchemeng.2018.06.020.
[3] K.A. Palmer, W.T. Hale, K.D. Such, B.R. Shea, G.M. Bollas, Optimal design of tests for heat exchanger fouling identification, Appl. Therm. Eng. 95 (2016) 382–393. doi:10.1016/j.applthermaleng.2015.11.043.
[4] K.A. Palmer, W.T. Hale, G.M. Bollas, Active Fault Identification by Optimization of Test Designs, IEEE Trans. Control Syst. Technol. (2018) 1–15. doi:10.1109/TCST.2018.2867996.
