AMFGP: An active learning reliability analysis method based on multi-fidelity Gaussian process surrogate model

Multi-fidelity modeling is widely available in theoretical research and engineering practice. Although high-fidelity models often necessitate substantial computational resources, they yield more accurate and reliable results. Low-fidelity models are less computationally demanding, while their results may be inaccurate or unreliable. For the reliability analysis based on complex limit state functions, a method based on active learning multi-fidelity Gaussian process model, called AMFGP, is proposed by combining surrogate model with adaptive strategy, ensuring a balance between prediction accuracy and computational cost in terms of both surrogate modeling and active learning: A dependent Gaussian process surrogate model using complete statistical characteristics is developed under the multi-fidelity framework, and the surrogate performances of different single-fidelity and multi-fidelity models with different learning functions are investigated; based on the proposed model, an adaptive strategy considering the dependence between predictions, the model correlation, and the sample density is designed, and the adaptive performance of different learning functions in different models is explored. The proposed method is validated for effectiveness and adaptability in three mathematical examples with different dimensions and demonstrated for efficiency and practicality in an engineering application to aero engine gear.