The conditional random fields, by integrating on-site measured data information, provide a more practical and realistic tool for the engineering analysis of phenomena that exhibit random characteristics in both space and time across multiple dimensions. However, traditional simulation methods of conditional random fields still face significant computational bottlenecks when dealing with large-scale problems. To this end, this paper proposes a novel and efficient simulation technique for conditional random fields. The core of the proposed method lies in a refined approach to the Karhunen-Loève (K-L) expansion. Instead of approximating the full conditional covariance function, we directly compute or more accurately approximate the dominant eigenvalues and eigenfunctions of the theoretically exact conditional covariance function. This computation is achieved by using the Nyström approximation, conditional multivariate Gaussian distribution, and selected quadrature points. This streamlined process allows us to directly generate conditional random field realizations within the K-L expansion framework. The effectiveness and robustness of the proposed method are demonstrated through three numerical examples, including one-dimensional, two-dimensional, and large-scale three-dimensional conditional random field simulations. Results confirm that the proposed approach achieves an optimal balance between computational efficiency and simulation accuracy, providing a powerful tool for data-inform probabilistic engineering analysis.
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