Multi-channel lost data recovery for structural health monitoring by structured low-rank matrix completion

Data loss is a common case in structural health monitoring, which undermines the accuracy and reliability of the monitoring data. Although most of the existing methods have achieved tremendous success in lost data recovery, they mainly focus on single-channel data recovery and limited to some simple data loss patterns, such as random data loss (Pattern 1) as well as continuous but not synchronized data loss (Pattern 2). In practice, all sensors may suffer from faults simultaneously under some extreme conditions, leading to continuous and synchronized data loss (Pattern 3). Since all channel data are lost synchronously, this makes the data recovery more challenging compared with the first two data loss patterns. This study proposes a novel data recovery algorithm based on structured low-rank matrix completion to handle multi-channel data with multiple data loss patterns from Patterns 1-3. By arranging the multi-channel data into a Hankel structure, the newly constructed Hankel matrix is demonstrated to be low rank. Then, the data recovery problem is transferred into a low-rank matrix completion problem, which is solved via nuclear norm minimization. To investigate the recovery performance of the proposed method, the instrumented Canton Tower is employed as a testbed. Two sets of acceleration data of the tower under ambient excitations (stationary data) and earthquake excitations (non-stationary data) are used for validation. Moreover, a comparative study with existing data recovery methods, as well as the effects of data loss rates and loss segment lengths on the recovery performance, is investigated.