Reliability-Based Sensor Placement Design in Nonlinear Processes Using Cumulative Residual Kullback–Leibler Divergence

In the current work, we propose optimal sensor placement for reliable estimation of both steady-state as well as dynamical nonlinear systems. While there is significant work on reliability-based sensor placement for linear processes, there is hardly any work for nonlinear systems. For nonlinear systems, we use appropriate structural matrices to check system observability for a given set of measurements and hence, our work is applicable at the design stage where exact operating conditions or values of various parameters may not be known. Characterization of system observability, along with knowledge of sensor failure probabilities as functions of time, allows us to define system reliability of estimation as a function of time. Subsequently, we propose to use an information theoretic, cumulative residual Kullback–Leibler (CRKL) divergence-based sensor placement design approach for reliable estimation of variables for both steady-state and dynamical nonlinear processes where the objective is to minimize the difference between a user-specified target system reliability of estimation function and the one obtained by a given set of sensors. Thus, this approach enables an end user to obtain a tailored optimal design by specifying their preference as the target system reliability in the objective function. Explicit incorporation of the time-varying nature of system reliability in computing the CRKL objective ensures a sensor placement design that leads to desired reliability throughout the life of the plant. The proposed sensor placement design problem is a nonlinear integer programming problem, and a greedy heuristic is used to solve the problem. The utility of the proposed approach is demonstrated on benchmark continuous stirred tank reactor and Tennessee Eastman case studies taken from the literature.