Application of a probabilistic approach to restoring force model parameter identification

Taking into account the uncertainty of model and model parameters, a Bayesian probabilistic approach was applied for parameter identification of restoring force model using tested data. Negative log-likelihood function of model parameters was derived. Bayesian computational frame for parameter identification of restoring force model was proposed. According to the tested hysteresis curves of multi-grid composite walls under low cyclic loadings, a restoring force model for multi-grid composite walls was proposed for identification. The most probable values and covariance matrixes of restoring force model parameters of two multi-grid composite wall specimens of 1/2 scale whose cyclic loading histories were different were identified based on the tested data. The rules for model selection and effect of model error on response prediction were analyzed. The results show that the hysteresis curves obtained through the most probable values without considering the model prediction errors agree well with those tested ones, which validates the identification results. Through Bayesian probabilistic approach, quantitative uncertainty of model parameters is obtained, which can be used for further analysis.