This paper extends a recently developed technique for sensor network design such that interactions between individual sensors are taken into account via principal component analysis. In past work [1] the trace of the empirical observability gramian was determined to be the most promising measure for determining the location of a single sensor. The extension to placing multiple sensors [2, 3] was performed by interpreting the trace of the gramian as the sum of the diagonal elements and defining interactions between sensors as the magnitude that two individual sensors have in the same diagonal entry for their respective empirical observability gramian. However, the diagonal entries of the gramian only represent the variance of the output measurements for perturbations in a state. The co-variances, which are give by the entries of the gramian not on the diagonal, are neglected using such an approach. The presented work will remedy this situation, as all the information contained in the empirical observability gramian will be considered. Principal component analysis is used to extract the contribution of a sensor placed at a specific location on the overall sensor network. Two approaches will be presented for designing sensor networks: the first technique will sequentially place sensors, such that each new sensor maximizes the amount of new information that can be gained from the system. This technique is straightforward to implement with the newly developed principal component analysis-based technique for evaluating the system's empirical observability gramian. The second methodology designs the sensor network by solving an optimization problem that maximizes observability of the system. The first technique has the advantage that it is easier to implement, while the second method will generally result in a larger amount of information that can be gained about the system. Both techniques are illustrated with case studies representing a distillation column and a fixed-bed reactor.

References: [1] Singh, A.K.; Hahn, J. Determining Optimal Sensor Locations for State and Parameter Estimation for Stable Nonlinear Systems. Industrial Engineering Chemistry Research 2005, 44(15), 5645. [2] Singh, A.K.; Hahn. J. Sensor Location for Stable Nonlinear Systems: Placing Multiple Sensors. Proceedings Chemical Process Control 7 2006, Lake Louise, Canada. [3] Singh, A.K.; Hahn, J. Optimal Sensor Locations for State Nonlinear Dynamic Systems: Multiple sensor case. In Press Industrial Engineering Chemistry Research.