ベイズ統計を用いた回帰係数分布の更新による損傷同定モデルの高精度化

概要

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This study is about improvement of the accuracy of damage identification with simple multiple regression model using bayesian update. In this study, regression coefficients for multiple regression model are estimated as not fixed value but the distribution parameter using MCMC. Goodness of fit of the regression model is evaluated by a likelihood estimate of the regression coefficients. By estimating the regression coefficients as distribution, probabilistic assessment of the diagnostic result is become possible. Moreover, from the hierarchical bayesian model, estimation of highly presumed model from small sampling by using the estimated regression coefficients as the primal distribution of other individual is become possible. From the beyesian theorem, distribution of the individual of a small sample(= posterior distribution) is presumed from an update of distribution of the information on other individuals( = prior distribution). For example, for the damage diagnosis of the machine structure, diagnostic model for an FEM model or a structure before modification corresponds to prior distribution. By using prior information effectively, construction of the better diagnostic model for arbitral structure from small sampling become possible. In this paper, verification of the method by adoption of the method to the delamination identification of CFRP structure via the electric potential method was conducted.