Bayesian methods have been widely used to improve the accuracy of finite element model in civil engineering. However, Bayesian methods generally suffer from the computational complexity involved in accurately identifying the posterior distribution. To address this issue, this paper proposes a novel method by combining the Hamiltonian Monte Carlo (HMC) algorithm with the gradient-enhanced Kriging (GEK) model, termed HMC-GEK, for more efficient model updating. The proposed method uses the potential function and gradient information generated during the burn-in phase of the HMC to train the GEK model. By replacing high-cost potential function with the GEK model, the original HMC sampling process is accelerated. An eight-story frame structure and a Y-shaped arch bridge are used to validate the accuracy and efficiency of the proposed method. Furthermore, the HMC-GEK method has been employed to identify damage of a real eight-story steel frame structure. Compared with the HMC method with the traditional Kriging model, HMC-GEK makes more full use of the gradient information of the potential function and significantly improves the sample acceptance rate and computational efficiency. In addition, the successful application of the method in damage identification of the real structure demonstrates its value for engineering applications.

中文翻译：

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使用梯度增强克里金模型的加速哈密顿蒙特卡洛进行贝叶斯更新


贝叶斯方法已被广泛用于提高土木工程中有限元模型的准确性。然而，贝叶斯方法通常受到准确识别后验分布所涉及的计算复杂性的影响。为了解决这个问题，本文提出了一种将哈密顿蒙特卡洛 （HMC） 算法与梯度增强克里金法 （GEK） 模型（称为 HMC-GEK）相结合的新方法，以实现更高效的模型更新。所提出的方法使用 HMC 老化阶段产生的势函数和梯度信息来训练 GEK 模型。通过用 GEK 模型替换高成本的势函数，加快了原始 HMC 采样过程。采用八层框架结构和 Y 形拱桥验证了所提方法的准确性和效率。此外，HMC-GEK 方法已被用于识别真实的 8 层钢框架结构的损坏。与传统 Kriging 模型的 HMC 方法相比，HMC-GEK 更充分地利用了势函数的梯度信息，显著提高了样本接受率和计算效率。此外，该方法在真实结构损伤识别中的成功应用证明了其在工程应用中的价值。