Sparsity-Promoting Estimator Design for Acceleration Sensor Placement in Civil Structures

Abstract

The scale of civil systems makes it impossible to measure all degrees of freedom. Therefore, a limited number of measurements are leveraged to obtain a full set of state estimates (e.g. displacement and velocity responses). Spatially sparse feedback, which limits the information and the number of sensors, requires the selection of essential measurements. The exact placement problem considers all possible combinations of sensors, which presents computational challenges for large systems. When applied to benchmark structures, the Kalman filter alternating direction method of multipliers (kfadmm) algorithm systematically balances measurement sparsity and estimator error covariance in acceleration sensor selection. Compared to the exact and sequential sensor placement methods, the kfadmm approach selects similar sensors with slightly higher estimation error and fewer combinations considered. In kfadmm, the best number of sensors for a given application can be determined after looking at the increase in the error as sensors are removed from the system.