Partitioning ideal sensor distributions of cable PDEs using modified CVT

This paper uses computational geometry techniques to partition position and velocity sensor distributions for second order in time PDEs representing structural systems. These distributions are assumed to be idealization of sensor distributions obtained by optimization enhancing system theoretic properties of the system such as approximate observability and improved filter performance. To ensure that realistic sensor devices can be used, a network of sensor distributions representing available sensing devices is used to approximate the ideal distributions. This approximation is based on a modification of the Centroidal Voronoi Tessellations (CVT) which ensures that the ideal distributions are partitioned into cells of equal areas of the distributions thus ensuring equal sensor authority. A single pointwise sensor is placed in each cell and an associated weight for that pointwise sensor is obtained via optimization. A filter is subsequently designed for the system with the approximate realistic sensors and compared to the filter utilizing ideal but unrealizable sensor distributions.