TY - JOUR

T1 - Efficient inner-outer decoupling scheme for non-probabilistic model updating with high dimensional model representation and Chebyshev approximation

AU - Mo, Jiang

AU - Yan, Wang Ji

AU - Yuen, Ka Veng

AU - Beer, Michael

N1 - Funding Information: Financial support to complete this study was provided by the Science and Technology Development Fund, Macau SAR (File no.: FDCT/017/2020/A1, FDCT/0101/2021/A2, FDCT/0010/2021/AGJ and SKL-IOTSC(UM)-2021-2023), the Research Committee of University of Macau (File no.: MYRG2020-00073-IOTSC, MYRG2022-00096-IOTSC and SRG2019-00194-IOTSC) and Guangdong-Hong Kong-Macau Joint Laboratory Program (Project No.: 2020B1212030009). Furthermore, the authors are grateful to professors at the Hong Kong Polytechnic University for sharing the ambient vibration data of Canton Tower on their website. The views and opinions expressed in this article are those of the authors and do not necessarily reflect those of the sponsors.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - Interval arithmetic offers a powerful tool for structural model updating when uncertain-but-bounded parameters are considered. However, the application of interval model updating for practical engineering structure is hindered due to model complexity and huge computational burden involved in the repeated evaluations of non-probabilistic constraints. In this light, an efficient inner-outer decoupling scheme is proposed for non-probabilistic model updating in this study. The mathematical operation of interval model updating is decomposed into two layers labelled as inner layer with the operation of uncertainty propagation and outer layer with the operation of interval optimization. In the inner uncertainty propagation, the High Dimensional Model Representation (HDMR) is utilized to enable the decomposition of the model outputs in terms of multivariate inputs into the sum of multiple single-variate functions, which is further approximated by Chebyshev polynomials so that the stationary points of each function can be derived. In the outer layer, a fast-running optimization strategy based on the stationary points of Chebyshev polynomial approximation is proposed to accelerate tracking the bounds of model parameters by avoiding time-consuming brute-force interval optimization. As a result, the original non-probabilistic updating process with two interacted layers can be completely decoupled into two independent operations of the inner uncertainty propagation and outer interval optimization so as to enhance the search efficiency and convergence rate significantly. Two numerical case studies illustrate capability of the proposed method in updating the structural parameters intervals efficiently with the model outputs intervals agreeing well with the testing outputs intervals. Two experimental cases of steel plates and the Canton Tower also demonstrate the efficiency and advantages of the method in interval model updating.

AB - Interval arithmetic offers a powerful tool for structural model updating when uncertain-but-bounded parameters are considered. However, the application of interval model updating for practical engineering structure is hindered due to model complexity and huge computational burden involved in the repeated evaluations of non-probabilistic constraints. In this light, an efficient inner-outer decoupling scheme is proposed for non-probabilistic model updating in this study. The mathematical operation of interval model updating is decomposed into two layers labelled as inner layer with the operation of uncertainty propagation and outer layer with the operation of interval optimization. In the inner uncertainty propagation, the High Dimensional Model Representation (HDMR) is utilized to enable the decomposition of the model outputs in terms of multivariate inputs into the sum of multiple single-variate functions, which is further approximated by Chebyshev polynomials so that the stationary points of each function can be derived. In the outer layer, a fast-running optimization strategy based on the stationary points of Chebyshev polynomial approximation is proposed to accelerate tracking the bounds of model parameters by avoiding time-consuming brute-force interval optimization. As a result, the original non-probabilistic updating process with two interacted layers can be completely decoupled into two independent operations of the inner uncertainty propagation and outer interval optimization so as to enhance the search efficiency and convergence rate significantly. Two numerical case studies illustrate capability of the proposed method in updating the structural parameters intervals efficiently with the model outputs intervals agreeing well with the testing outputs intervals. Two experimental cases of steel plates and the Canton Tower also demonstrate the efficiency and advantages of the method in interval model updating.

KW - Finite element model updating

KW - HDMR

KW - Interval arithmetic

KW - Non-probabilistic uncertainty

KW - Polynomial approximation

UR - http://www.scopus.com/inward/record.url?scp=85144619365&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2022.110040

DO - 10.1016/j.ymssp.2022.110040

M3 - Article

AN - SCOPUS:85144619365

VL - 188

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 110040

ER -