In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.

翻译：近几十年来，马尔可夫链蒙特卡罗（MCMC）方法已广泛应用于结构健康监测领域中结构动力学模型的贝叶斯更新。近年来，研究人员开发了多种结合神经网络的MCMC算法，以提升其在特定贝叶斯模型更新问题中的性能。然而，这些方法普遍面临一个挑战：当面对新任务时，嵌入的神经网络通常需要重新训练，这一过程耗时显著，严重削弱了这些方法的竞争力。本文提出了一种新开发的自适应元学习随机梯度哈密顿蒙特卡罗（AM-SGHMC）算法。AM-SGHMC的核心思想是通过训练自适应神经网络来优化采样策略，由于网络输入和输出的自适应设计，训练后的采样器可直接应用于同一类结构的不同贝叶斯更新问题而无需进一步训练，从而实现元学习。此外，本文还解决了AM-SGHMC算法在结构动力学模型更新中可行性的实际问题，并通过两个涉及不同模型保真度的多层建筑模型贝叶斯更新算例，展示了所提方法的有效性和泛化能力。