A new hierarchical Bayesian framework (HBM) is proposed for identification of Gaussian processes or fields, which are usually used for simulating uncertainty in temporal variability of loads or spatial variability of material properties. An improved orthogonal series expansion (iOSE) is embedded into the proposed framework by simulating the Gaussian process or field through correlated Gaussian variables, and then HBM is applied to quantify their uncertainty. Hyper parameters to be identified are set to be the mean value and standard deviation vectors of these Gaussian variables, as well as the parameters in autocorrelation function (ACF) of the Gaussian process or field which are used to replace correlation coefficients of correlated Gaussian variables for reducing the number of hyper parameters. With the identified hyper parameters, a simulation model of the Gaussian process or field can be obtained based on the iOSE expression. In addition, model class selection is introduced to select the optimal number of orthogonal functions and integral points involved in iOSE as well as select the category of ACF among several alternative models, known to influence the simulated expression and accuracy. Studies conducted on two dynamic examples verify the effectiveness of proposed framework.

提出了一种新的分层贝叶斯框架 (HBM) 来识别高斯过程或场，这些过程或场通常用于模拟载荷时间变化或材料特性空间变化的不确定性。通过相关高斯变量模拟高斯过程或场，将改进的正交级数展开 (iOSE) 嵌入到所提出的框架中，然后应用 HBM 来量化它们的不确定性。待识别的超参数设置为这些高斯变量的均值和标准差向量，以及高斯过程或场的自相关函数（ACF）中的参数，用于替换相关高斯变量的相关系数减少超参数的数量。有了确定的超参数，基于iOSE表达式可以得到高斯过程或场的仿真模型。此外，还引入了模型类选择，以选择iOSE中涉及的正交函数和积分点的最佳数量，以及在已知影响模拟表达和准确性的几个备选模型中选择ACF的类别。对两个动态示例进行的研究验证了所提出框架的有效性。