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)...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。展开更多
In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly c...In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly convex vector function, and the uniqueness of α major efficient solution when the objective function is weak strictly H α convex vector function.展开更多
The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function b...The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.展开更多
Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup&g...Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup> stand for the column space, the transpose andany g-inverse of A, respectively; P<sub>A</sub>=A（A’A）<sup>-</sup>A’;for s×t matrix B=（b<sub>1</sub>…b<sub>t</sub>）,vec（B） de-notes the st-dimensional vector （b<sub>1</sub>′b<sub>2</sub>′…b<sub>t</sub>′）′, trA stands for the trace of the square ma-trix A.展开更多
In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rat...In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.展开更多
文摘In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly convex vector function, and the uniqueness of α major efficient solution when the objective function is weak strictly H α convex vector function.
基金supported by the Ningbo Youth Foundation(0 2 J0 1 0 2 - 2 1 )
文摘The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.
文摘Throughout this note, the following notations are used. For matrices A and B,A】B means that A-B is positive definite symmetric, A×B denotes the Kroneckerproduct of A and B R（A）, A’ and A<sup>-</sup> stand for the column space, the transpose andany g-inverse of A, respectively; P<sub>A</sub>=A（A’A）<sup>-</sup>A’;for s×t matrix B=（b<sub>1</sub>…b<sub>t</sub>）,vec（B） de-notes the st-dimensional vector （b<sub>1</sub>′b<sub>2</sub>′…b<sub>t</sub>′）′, trA stands for the trace of the square ma-trix A.
基金Supported by National Natural Science Foundation of China(Grant Nos.10871226,11001247 and 61179041)Natural Science Foundation of Zhejiang Province(Grant No.Y6100096)
文摘In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.
