Investigation of Identification and Uncertainty Quantification Methods for Constitutive Model
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摘要: 典型基于输入的最佳估算加不确定性(BEPU)分析方法需要全面考虑各种来源的不确定性,但作为重要不确定性来源之一的最佳估算程序内部本构模型不确定性却很难得到准确量化。针对传统BEPU方法的不足,采用函数型数据分析加次序敏感性分析方法识别重要模型,贝叶斯校准方法加高斯过程代理模型量化模型参数不确定性,得到了一种准确的关键本构模型识别与不确定性量化方法。使用该方法量化了FLECHT-SEASET实验中重要模型的不确定性,并将量化的不确定性抽样传播至包壳温度。另外对该方法与传统的关键本构模型识别方法进行对比。结果表明,该方法可以准确识别瞬态过程中的关键本构模型,传播计算结果能够很好地包络实验值。Abstract: Typical input-based best estimate plus uncertainty (BEPU) analysis methods require comprehensive consideration of uncertainty from all sources. Uncertainty of the input parameters is then propagated to the output by many sampling calculations through the best estimate (BE) code. In the past, the uncertainty of the code constitutive model, which was one of the most important sources of uncertainty, was often not properly analyzed. For the purpose of quantifying the uncertainty of code constitutive models and including it into the BEPU analysis, a methodology for the identification and uncertainty quantification of key constitutive models was developed in this paper. First of all, the figure of merit (FOM) of the sensitivity analysis needed to be defined. Time series data were chosen as the target in order to better characterize the effect of the parameters on the whole transient process, and a dimension reduction was performed for the time series data using functional data analysis (FDA) method to obtain the FOMs. Then, sensitivity analysis was performed on several FOMs to get the importance ranking of the constitutive models. The sensitivity analysis approach was a two-step process, where the input model parameters were firstly screened by the Morris method, and then the screened model parameters were subjected to a quantitative sensitivity analysis by the Sobol method to obtain a parameter importance ranking. Finally, uncertainty quantification was performed for the high ranking models selected based on the sensitivity analyses. The posterior probability distributions of the parameters were calculated using the Markov chain Monte Carlo (MCMC) method based on Bayesian calibration approach. In order to validate the applicability of the above method, it was used to quantify the uncertainties of the important models based on the FLECHT-SEASET experiment, and to propagate the quantified uncertainties to the cladding temperature. In addition, the result of the sensitivity analysis of the FOM obtained by FDA analysis was compared with two traditional FOMs, which were the integral of the difference between the sampling calculation results and the experimental values, and the peak cladding temperature (PCT), respectively. The results show that it is difficult to obtain an accurate ranking of model importance when using PCT as FOM. This approach can accurately identify the key constitutive models in transient processes, and the propagation calculation results can well envelope the experimental values.
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