Lexicographic Optimization Based Sensor Network Design for Robust Fault Diagnosis

An appropriately designed sensor network is crucial for the success of any fault diagnostic strategy. In previous works (Bhushan and Rengaswamy, 2002a,b) strategies for optimally locating sensors based on criteria of reliability maximization and cost minimization have been devised. These opposing objectives were treated in a lexicographic (a special type of multiobjective optimization) manner. Signed digraph (SDG) based process models were used to generate the cause-effect information and fault occurrence and sensor failure probabilities were used to calculate a measure of reliability of a sensor network. While reliability and cost were considered in selecting the optimal sensor network, the robustness of the selected network with respect to uncertainties/errors in the underlying signed directed graph models and the available probability data was not considered explicitly. In this article, lexicographic formulations which incorporate some robustness enhancing criteria while designing cost-optimal sensor network for reliable fault diagnosis are presented. Some robustness to modeling errors in the SDG can be incorporated by choosing a distributed sensor network. Robustness to available probability data can be incorporated by maximizing reliability of the faults involving uncertain probability data. Integer linear programming (ILP) formulations incorporating these criteria in a lexicographic manner along with overall reliability-maximization and cost-minimization objectives are presented. The utility of the proposed approach is demonstrated through application to the Tennessee Eastman case study.