Optimal sensor placement for reconstructing wind pressure field around buildings using compressed sensing

Tall buildings exposed to wind experience wind-induced loads that create pressure on the building envelope, and their integral effects cause the structure to move in the dominant directions, namely along-wind, across-wind, and torsional [1, 2, 3]. The description of the pressure field around a building does not lend itself to a simple functional relationship with approach flow turbulence. As a result, calls for reliance on wind tunnel experiments have been made. These tests rely heavily on pressure taps connected to pressure sensors to monitor pressure fields over the building surface. A basic question is where to deploy available sensors to accurately predict and reconstruct the structure of a wind pressure field from limited and noisy sensor outputs. In fact, the optimal sensor placement problem has garnered considerable attention for a long time, as fast data acquisition, analysis, and decision in high-performance control for complex systems can be archived with a small number of measurements at limited locations. In practice, the best locations for sensors in regular structures with simple geometry and a small number of degrees of freedom can be determined empirically using engineering judgment and past experience. However, for a complicated large-scale structure, a systematic and efficient approach is required because the solution space is far beyond the capabilities of hand calculation [4, 5, 6, 7, 8]. Mathematically, the goal is to find m positions from a set of n positions that maximize the information about the behaviors of a structural system: n! c =