Surrogate Model–Assisted Learning of Conditional Probability Tables of Bayesian Networks Describing Structural Systems

Bayesian network (BN) is an effective tool to describe and interpret the probability distribution of a complex phenomenon. Essential building blocks in discrete BNs are conditional probability tables (CPTs) quantifying statistical dependence between random variables. In various structural engineering problems, CPTs are generally constructed by generating computational simulation samples for each discretized domain of random variables and then estimating the conditional probabilities based on the samples. However, it is challenging to choose an appropriate discretization scheme and estimate conditional probabilities from sparse sample points within each discretized domain. Therefore, this paper proposes a comprehensive CPT learning framework that is applicable to a computational model with multidimensional input and one-dimensional output. First, a surrogate model is employed to generate a large-size training sample of input and output. Then, we introduce a score function for discretizing the input variable of the computational model to minimize the inherent loss of accuracy of the developed CPT. The proposed framework is demonstrated using a benchmark problem and further investigated with two computational models comprising ground motion simulation and structural dynamic analysis.