Compressive sensing‐based data loss recovery in the feedback channel of the structural vibration control systems

The resiliency of the communication channels to data loss is of prime importance in the networked control of civil structures. In this study, compressive sensing (CS) as an emerging data acquisition technique is used to recover the lost packets in real‐time in the communication channel from sensors to the controller. The basic idea is to apply CS to the state vector, for example, displacement and velocity profile of the building, in the feedback channel of the closed‐loop control system. The encoded measurement vector is first packetized and then transmitted over the unreliable communication channel. On the controller side, rather than waiting for the unreceived packets to be received, the state vector is recovered using the partially observed data. Dictionary learning is used to train the sparsifying dictionary via the application‐specific data set. In addition, the smoothed zero norm (SL‐0) algorithm is employed for solving the underdetermined system of linear equations at the decoding stage. This approach is fully data‐driven and does not require knowledge of the system. Once the state vector is reconstructed, any state feedback control strategy can be used to calculate the required control force. In this study, a 76‐story benchmark building equipped with an active tuned mass damper (ATMD) is used to investigate the performance of the proposed data transmission scheme. The reconstruction accuracy of the signals is compared to the K‐nearest neighbor (KNN) method and the perfect communication case. Simulation results revealed that the CS‐based approach yields high accuracy with reasonable computational time.