TY - JOUR

T1 - Transmissibility-based damage detection with hierarchical clustering enhanced by multivariate probabilistic distance accommodating uncertainty and correlation

AU - Mei, Lin Feng

AU - Yan, Wang Ji

AU - Yuen, Ka Veng

AU - Ren, Wei Xin

AU - Beer, Michael

N1 - Funding Information: This research has been supported by the Science and Technology Development Fund, Macau SAR (File no.: 017/2020/A1, 101/2021/A2, 0010/2021/AGJ, SKL-IOTSC(UM)-2021-2023), the Research Committee of University of Macau (File no.: MYRG2020-00073-IOTSC and MYRG2022-00096-IOTSC), Guangdong-Hong Kong-Macau Joint Laboratory Program (Project No.: 2020B1212030009) and Shenzhen Science and Technology Program (Grant Nos. JSGG20210802093207022, KQTD20180412181337494 and ZDSYS20201020162400001). Also, the authors are deeply appreciative to professors at the University of Leuven in Belgium for providing the experimental datasets of the benchmark structure.

PY - 2023/11/15

Y1 - 2023/11/15

N2 - This paper proposes a new damage detection method by integrating the advantage of transmissibility function (TF) as a health index sensitive to damage but robust to excitation and agglomerative hierarchical clustering (AHC) with intuitive explanation and visualization but avoiding specifying the number of clusters. Different from conventional AHC-based damage detection methods utilizing deterministic distance as a similarity metric and ignoring the distribution of structural features, a multivariate probabilistic distance-based similarity metric is proposed in this study to account for the uncertainty and correlation of multiple TFs following multivariate complex-valued Gaussian ratio distribution. To realize this, an analytically tractable approximation of the multivariate probabilistic distance is derived by Laplace's asymptotic expansion to avoid high-dimensional numerical integration. To accelerate the computation of probabilistic distances over a wide frequency band that are fused to formulate the similarity metric in AHC, a function vectorization scheme is proposed to avoid the time-consuming loop operation among different frequency points. A threshold is established via bootstrapped Monte Carlo simulation to cut the dendrogram produced by AHC. Two case studies are used to validate the performance of the proposed method, indicating that, compared to the damage detection methods based on the deterministic distance of the TF, the proposed method exhibits better performance due to improving the similarity metric based on multivariate probabilistic distance properly accommodating the correlation of different TFs.

AB - This paper proposes a new damage detection method by integrating the advantage of transmissibility function (TF) as a health index sensitive to damage but robust to excitation and agglomerative hierarchical clustering (AHC) with intuitive explanation and visualization but avoiding specifying the number of clusters. Different from conventional AHC-based damage detection methods utilizing deterministic distance as a similarity metric and ignoring the distribution of structural features, a multivariate probabilistic distance-based similarity metric is proposed in this study to account for the uncertainty and correlation of multiple TFs following multivariate complex-valued Gaussian ratio distribution. To realize this, an analytically tractable approximation of the multivariate probabilistic distance is derived by Laplace's asymptotic expansion to avoid high-dimensional numerical integration. To accelerate the computation of probabilistic distances over a wide frequency band that are fused to formulate the similarity metric in AHC, a function vectorization scheme is proposed to avoid the time-consuming loop operation among different frequency points. A threshold is established via bootstrapped Monte Carlo simulation to cut the dendrogram produced by AHC. Two case studies are used to validate the performance of the proposed method, indicating that, compared to the damage detection methods based on the deterministic distance of the TF, the proposed method exhibits better performance due to improving the similarity metric based on multivariate probabilistic distance properly accommodating the correlation of different TFs.

KW - Damage detection

KW - Hierarchical clustering

KW - Multivariate distribution

KW - Probabilistic distance

KW - Transmissibility

UR - http://www.scopus.com/inward/record.url?scp=85169977391&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2023.110702

DO - 10.1016/j.ymssp.2023.110702

M3 - Article

AN - SCOPUS:85169977391

VL - 203

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 110702

ER -