基于近似非凸RPCA的Lamb波损伤监测

Damage Detection Based on an Approximate Non-Convex RPCA For Lamb Wave

中文关键词:  秩近似函数  非凸惩罚函数  Lamb波  有限元

英文关键词:rank approximation function  non-convex penalty function  Lamb wave  finite elements

中文摘要:

      在结构健康监测（Structural Health Monitoring,SHM）技术中，基于Lamb波的损伤监测方法在板状结构中显示出了巨大的潜力。提出了一种基于近似非凸鲁棒主成分分析（Approximate Non-Convex Robust Principal Component Analysis,ANC-RPCA）的异常值分析方法。该算法对于高维测量信号，能够在降维条件下实现有效的损伤诊断。通过使用秩近似函数逼近矩阵的秩，采用非凸惩罚函数逼近0范数，非凸惩罚函数在一定条件下可以保证稀疏解的唯一性。随着数据矩阵规模的扩大，传统的RPCA采用核范数近似时，奇异值分解的计算复杂度也会上升。新的近似方法能在使计算效率更高的情况下，针对波场图像能够在更低秩的水平下保留有效信息，识别出异常值。将该算法运用到基于Lamb波的波场图像中，通过仿真和实验数据验证其有效性，使用非精确增广拉格朗日乘子（Inexact Augmented Lagrange Multiplier,IALM）法求解，并与目前使用较多的主流RPCA算法进行了效果对比。实验结果表明ANC-RPCA算法在异常值识别中具有良好的性能，相较于其他算法,在计算效率和低秩性等方面具有巨大的优势，证明了所提算法的可靠性和完整性。

英文摘要:

      In structural health monitoring(SHM) technology,Lamb wave-based damage detecting method shows great potential in plate structures.An outlier analysis method based on an approximate non-convex robust principal component analysis(ANC-RPCA) algorithm is proposed.The algorithm is capable of achieving effective defect diagnosis for high-dimensional measurement signals under the condition of dimensionality reduction.By approximating the rank of the matrix using a rank approximation function,and approximating the 0-norm with a non-convex penalty function,the non-convex penalty function can guarantee the uniqueness of the sparse solution under certain conditions.As the scale of the data matrix expands,the computational complexity of singular value decomposition also increases when the traditional RPCA uses the kernel norm approximation.The new approximate method can retain effective information and identify outliers at a lower rank level for wave field images with higher computational efficiency.This algorithm is applied to wavefield images based on Lamb waves and validated through simulations and experimental data.The solution is obtained using the inexact augmented Lagrange multiplier (IALM) method and compared with mainstream robust principal component analysis (RPCA) algorithms commonly used in the field.The experimental results demonstrate the excellent performance of the ANC-RPCA algorithm in outlier identification.It exhibits significant advantages in terms of computational efficiency and low-rank characteristics compared to other algorithms,substantiating the reliability and completeness of the proposed algorithm.