Least-Squares- and Information-Theory-Based Inferential Sensor Design for Fault Diagnostics

This work illustrates the design and use of inferential sensors for reducing the impact of uncertainty on information gained from fault diagnostics and prognostics. A novel algorithm is presented for the sequential design of inferential sensors and admissible input settings to be used during maintenance testing. The inferential sensors are symbolically regressed to create mathematical representations of the noisy, uncertain system input and output measurements that infer richer information about the system health status. The performance of the inferential sensor and test design is assessed using k-NN classification and exemplified in an aircraft air management system component. A benefit of the inferential sensors developed in this work is their symbolic representations. The developed inferential sensors are explainable in the form of mathematical equations, which enables application of information theory to further improve inferential sensor development by leveraging methods of symbolic mathematics and automatic differentiation to calculate inferential sensors whose sensitivities with respect to the parameters of interest relating to fault and uncertainty are optimal. The extension of the algorithm to developing inferential sensors and admissible inputs of the system using the D
_s
-optimality criterion for the Fisher Information Matrix, is presented at the end of this paper.