High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

高温设计方法依赖于非弹性变形和破坏的本构模型，通常根据实验数据的平均值进行校准，而不考虑相关的散射。可变性可能来自实验数据采集过程，来自热对热材料属性的变化，或两者兼而有之，需要准确捕获以预测参数界限，从而实现高效的组件设计。应用贝叶斯马尔可夫链蒙特卡罗 (MCMC) 方法来生成统计模型来捕捉实验数据中的潜在不确定性，这是一个持续的研究兴趣领域。这项工作改变了贝叶斯 MCMC 方法的各个方面，并使用综合生成的参考数据探索了它们对单轴弹粘塑性损伤模型的后验参数分布的影响。根据我们对单轴非弹性模型的分析，我们确定包括不同类型测试条件的知情先验分布会导致更准确的后验参数分布。然而，当增加类似实验数据的数量时，参数后验分布并没有改善。此外，改变数据中的分散量会影响后验分布的质量，尤其是对于不太敏感的模型参数。此外，我们在贝叶斯分析之前针对似然函数对模型参数进行了敏感性研究。敏感性分析的结果有助于确定后验分布的可靠性，并通过固定不敏感参数来降低问题的维数。这项工作中描述的综合研究展示了如何有效地应用贝叶斯 MCMC 方法来捕获高温非弹性材料模型中的参数不确定性。量化非弹性模型中的这些不确定性将改进高温工程设计实践，并导致更安全、更有效的组件设计。