TY - JOUR

T1 - Bayesian maximum entropy method for stochastic model updating using measurement data and statistical information

AU - Wang, Chenxing

AU - Yang, Lechang

AU - Xie, Min

AU - Valdebenito, Marcos

AU - Beer, Michael

N1 - Funding Information: The authors gratefully acknowledge the support of the National Natural Science Foundation of China under Grant 52005032 , 72271025 , the Aeronautical Science Foundation of China under Grant 2018ZC74001 , the Hong Kong Scholars Program under Grant No. XJ2021003 , the Fundamental Research Funds for the Central Universities of China under Grant QNXM20220032, the Research Grant Council of Hong Kong under Grant 11203519 , 11200621 and the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA).

PY - 2023/4/1

Y1 - 2023/4/1

N2 - The presence of summarized statistical information, such as some statistics of the system response, is not rare in practical engineering as the acquisition of precisely measured point data is expensive and may not be always accessible. In this paper, we integrate the Bayesian framework with the maximum entropy theory and develop a Bayesian Maximum Entropy (BME) approach for model updating in a scenario where measurement data and statistical information are simultaneously available. Within the scope of this contribution, it is assumed that measurement data denote direct observations, e.g. point data, representing system response measurements while statistical information involves summarized information, e.g. moment and/or reliability information, of the system response. The basic principle of our approach is to convert point data and various statistical information into constraints under the BME framework and use the method of Lagrange multipliers to find the optimal posterior distributions. We then extend this approach to imprecise probabilistic models which have not been addressed so far. The approximate Bayesian computation is employed to facilitate the estimation of cumbersome likelihood functions which results from the involvement of entropy terms accounting for statistical information. Furthermore, a Wasserstein distance-based metric is proposed and embedded into the framework to capture the divergence information in an effective and efficient way. The effectiveness of the proposed approach is verified by a numerical case of simply supported beam and an engineering problem of fatigue crack growth. It shows some promising aspects of this research as better calibration results are produced with less uncertainty, and hence potential of our approach for engineering applications.

AB - The presence of summarized statistical information, such as some statistics of the system response, is not rare in practical engineering as the acquisition of precisely measured point data is expensive and may not be always accessible. In this paper, we integrate the Bayesian framework with the maximum entropy theory and develop a Bayesian Maximum Entropy (BME) approach for model updating in a scenario where measurement data and statistical information are simultaneously available. Within the scope of this contribution, it is assumed that measurement data denote direct observations, e.g. point data, representing system response measurements while statistical information involves summarized information, e.g. moment and/or reliability information, of the system response. The basic principle of our approach is to convert point data and various statistical information into constraints under the BME framework and use the method of Lagrange multipliers to find the optimal posterior distributions. We then extend this approach to imprecise probabilistic models which have not been addressed so far. The approximate Bayesian computation is employed to facilitate the estimation of cumbersome likelihood functions which results from the involvement of entropy terms accounting for statistical information. Furthermore, a Wasserstein distance-based metric is proposed and embedded into the framework to capture the divergence information in an effective and efficient way. The effectiveness of the proposed approach is verified by a numerical case of simply supported beam and an engineering problem of fatigue crack growth. It shows some promising aspects of this research as better calibration results are produced with less uncertainty, and hence potential of our approach for engineering applications.

KW - Approximate Bayesian computation

KW - Bayesian Maximum Entropy

KW - Measurement data

KW - Statistical information

KW - Stochastic model updating

KW - Wasserstein distance

UR - http://www.scopus.com/inward/record.url?scp=85144062950&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2022.110012

DO - 10.1016/j.ymssp.2022.110012

M3 - Article

AN - SCOPUS:85144062950

VL - 188

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 110012

ER -