Sensor Location for Stable Nonlinear Systems: Placing Multiple Sensors

This paper presents a new technique for placing sensors on processes described by stable nonlinear systems. The methodology can compute locations for individual sensors as well as networks of sensors where a trade-off between process information, sensor cost, and information redundancy is taken into account. The novel features of the approach are (1) that the nonlinear behavior that a process can exhibit over its operating region can be taken into account, (2) that the technique reduces to already established methods, if the system is linear and only some of the objectives are looked at, (3) that the results obtained from the procedure can be easily interpreted, and (4) that the resulting optimization problem can be decomposed resulting in a significant reduction of the computational effort required for its solution
The trade-off between the different objectives is achieved by formulating a mixed-integer nonlinear programming problem. While computation of process information and information redundancy are computationally the most expensive parts of the procedure, it is shown that most of this analysis can be performed outside of the optimization, resulting in a significant reduction of the computational effort for evaluating the objective function. The resulting optimization problem is ideally suited for solution by a genetic algorithm, due to its structure, the presence of multiple local optima, and the low effort required for evaluating the objective function. The presented technique has been applied to a nonlinear binary distillation column where up to six sensors are placed along the height of the column.