Exploiting the inter-correlation of structural vibration signals for data loss recovery: A distributed compressive sensing based approach

Abstract Compressive Sensing (CS) is a novel signal sampling technique that can enhance the resiliency of the data transmission process in Structural Health Monitoring (SHM) systems by projecting the raw signal into another domain and transmitting the projected signal instead of the original one. The original signal can later be recovered in the fusion center using the received projected vector and the corresponding projection matrix. In this study, data loss recovery of multiple signals with variable loss ratio is investigated. Unlike previously proposed CS-based single-signal approaches, the inter-correlation across vibration signals is exploited in this study. The inter-correlation type for vibration signals is characterized as having common sparse supports (the same location of non-zero elements in the sparse domain) and is dealt with in the context of Distributed Compressive Sensing (DCS). In this approach, vibration signals are encoded separately without extra inter-sensor communication overhead and are decoded jointly. Adopting the DCS-based approach enabled handling non-uniform data loss pattern across channels by allowing the use of a different projection matrix for each channel. Furthermore, a new projection matrix, named Permuted Random Demodulator (PRD), is proposed that not only reduces the coherence of the sensing matrix and enhances the reconstruction accuracy, but also makes the proposed approach robust to continuous data loss. The performance of the proposed method is evaluated using acceleration responses of a real-life bridge structure under traffic excitation. Modal parameters of the bridge are also identified using the recovered signals with reasonable accuracy.