基于压缩感知理论重构压电阻抗信号的钢结构损伤识别

基于压电阻抗(electromechanical impedance, EMI)技术，针对结构损伤识别提出了阻抗/导纳数据压缩与重构的方法，利用随机矩阵将监测系统中的原始阻抗数据向量进行线性映射，并将映射后的向量输入到接收系统中；基于压缩感知理论将重构原始数据的问题转化成非确定性多项式问题，并基于凸优化(convex optimization, CO)理论求解；在损伤识别阶段，利用均方根偏差(root mean square deviation, RMSD)统计指标对重构阻抗数据的识别效果进行评估，并与使用原始阻抗数据的效果进行对比。利用简支钢梁的局部损伤识别试验采集的阻抗数据证明所提出方法的有效性。结果表明：基于重构阻抗数据能够有效识别结构损伤，基系数矩阵的稀疏度随着测量数的减少而降低，一致球集合对应的稀疏度区间低于其他测量矩阵，阻抗数据重构效果随着压缩率的增加而减弱，当压缩率高于2.0时，部分使用重构阻抗数据识别结构损伤的误差将大于20%，损伤识别精度降低。

Damage identification of steel structures based on reconstructed electromechanical impedance signals using compressed sensing theory

An impedance/admittance data compression and reconstruction approach for the electromechanical impedance (EMI) technique-based structural damage identification was proposed. A linear projection of the original impedance data vector in the monitoring system was performed onto a new vector by a random matrix and subsequently the mapped vector was input to the receiving system. Based on compressed sensing theory, the solution of recovering original data was transformed into a non-deterministic polynomial problem, and the convex optimization (CO) theory was utilized to solve this problem. As for the damage identification stage, a statistical index called root mean square deviation (RMSD) was introduced to evaluate the effectiveness of the reconstructed impedance data in comparison with that of utilizing the original impedance data. The proposed approach was validated with the impedance data collected in an experiment of local damage identification on a simply-supported steel beam.The results indicate that structural damage can be effectively identified via the reconstructed data. As the measurement number reduces, the sparsity of basis coefficient matrix decreases. The interval of the sparsity level corresponding to uniform spherical ensemble (USE) is lower than the other kinds of measurement matrices.The reconstruction effectiveness of EMI data decreases with the compression ratio (CR). When the CR is higher than 2.0, errors for identifying structural damage via reconstructed EMI data exceeds 20% and the identification accuracy declines.