Sensor Location for Nonlinear Dynamic Systems via Observability Analysis and Max-Det Optimization

This paper presents an approach for determining the optimal placement of multiple sensors for processes described by a class of nonlinear dynamic systems. This approach is based upon maximizing a criterion, i.e., the determinant, applied to the empirical observability gramian in order to optimize certain properties of the process state estimates. The determinant directly accounts for redundancy of information for placing multiple sensors via the covariance terms in the observability matrix. However, the resulting optimization problem is nontrivial to solve as it is a mixed integer nonlinear programming problem. In order to address this point, this paper also presents a decomposition of the optimization problem such that the formulated sensor placement problem can be solved quickly and accurately on a desktop PC. Properties of the presented technique are demonstrated and discussed in two case studies, one involving a binary distillation column and the other a packed bed reactor.