Improved Consistency on a Common Virtual Sensing Scheme

A widely used approach for virtual sensing takes a set of eigenvectors not larger (in cardinality) than the number of measurements, selects the partition associated with the measurements, and computes the modal amplitudes that justify the measurements. The full response is subsequently estimated by using the computed modal amplitudes and the truncated basis over the full domain. Since the approach projects the measured response, which has contributions from all the modes, on a truncated basis, the obtained result is not an approximation of the truncated modal series, nor is it an approximation of the response from all the modes. This paper puts forth a modification based on appropriate filtering that improves consistency. It is shown that uniqueness does not restrict the number of modes in the projection basis to the number of sensors but only the number of modes that can be simultaneously considered in an approach that can be applied sequentially to include as many modes as desired.