A bayesian model calibration under insufficient data environment

doi:10.1007/s00158-022-03196-y

2022-02-28

PRE

Jeonghwan Choo

Yongsu Jung

Ikjin Lee *

DOI：10.1007/s00158-022-03196-y

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摘要

En 中文

In recent years, remarkable advances in computing performance and computer-aided engineering have enabled reliability-based design optimization (RBDO) to guarantee the target reliability of a product. For successful product development through RBDO, it is indispensable to clarify uncertainties of unknown model variables. In most cases, however, due to cost and time constraints, there are not enough test data, which can lead to a less reliable optimum. For this reason, the primary purpose of this study is to propose a pragmatic approach to perform an inverse uncertainty quantification or a statistical model calibration more accurately and efficiently under an insufficient data environment. Based on the Bayesian model calibration framework, the proposed method consists of two main steps: (1) prior distribution prediction using output (i.e., component) test data and (2) posterior distribution prediction using input (i.e., coupon) test data. In the prior distribution prediction step, the maximum likelihood estimate (MLE) is used to obtain the estimated statistical parameters, the distribution type of unknown model variables, and the Fisher information matrix (FIM) to calculate variances of the estimated statistical parameters. The posterior distribution prediction step utilizes the Bayes' theorem, which combines the prior distribution with the likelihood obtained by reflecting the input test data into the probability density of the estimated unknown model variable. During this process, each test data that is insufficient to directly model or indirectly predict the probability density of the unknown model variable can be integrated to address the crucial issue of the insufficient data effectively. Mathematical and engineering examples are utilized to validate the proposed method for quantification of unknown model variables.

Keyword:

Statistical model calibration

Maximum likelihood estimate

Fisher information matrix

Area metric

Bayesian inference

Epistemic uncertainty