Sensor location for nonlinear state estimation

Abstract

The structure of the sensor network installed in the plant strongly influences the performance of state estimation techniques. One of them, the Unscented Kalman Filter (UKF), provides significant improvement over other filtering methods. It approximates the true mean and covariance of random variables that undergo nonlinear transformations correctly up to the third order with low computational effort. In this work, a Sensor Network Design strategy for monitoring nonlinear dynamic chemical processes using UKF is presented. In contrast to previous works, the tradeoff between cost and estimates precision is addressed in a systematic and efficient way. A novel procedure is proposed to calculate a sensible upper bound for the estimation error. This avoids fixing bounds based on engineer judgment about the new process. Regarding efficiency, the obtained sensor network is generally cheaper and provides a global precision which is between the maximum possible for a given budget and the precision obtained by the sensor network that satisfices the maximum system observability for the same budget. This formulation is important when the budget is limited and it is desired to minimize the cost, without losing the quality of the estimates. The proposed methodology can be easily extended to other nonlinear state estimation techniques. The optimal solution is obtained using a level transversal search algorithm with cutting and stopping criteria. A copolymerization process taken from the literature is used to demonstrate the performance of the proposed instrumentation design technique.