Conditional simulation of stationary non-Gaussian processes based on unified Hermite polynomial model基于统一 Hermite 多项式模型的平稳非 Gauss 过程条件模拟
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Zhao Z, Lu ZH, Zhao YG, 2024. Conditional simulation of stationary non-Gaussian processes based on unified Hermite polynomial model. Probabilistic Engineering Mechanics, 76: 103609.DOI: 10.1016/j.probengmech.2024.103609
摘要 | Abstract
利用监测系统记录对非 Gauss 激励进行条件模拟对于减灾具有重要意义。为此，本文提出了一种非 Gauss 条件模拟的新方法。该方法采用统一 Hermite 多项式模型 (unified Hermite polynomial model, UHPM) 描述记录和未记录的非 Gauss 过程及其相应 Gauss 过程之间的变换关系。同时，还提供了它们相关函数之间的显式变换模型。然后，构建相应 Gauss 过程 Fourier 系数的协方差矩阵。基于该协方差矩阵，生成 Fourier 系数的条件样本，并将其代入谱表达方法 (spectral representation method, SRM) 中，进行相应 Gauss 过程的条件模拟。最后，通过统一 Hermite 多项式模型将条件模拟的相应 Gauss 过程样本变换为非 Gauss 样本。为了展示所提方法的精度和有效性，给出了两个数值算例，分别涉及非 Gauss 地震动和非 Gauss 风压系数的条件模拟。关键词: 条件模拟, 非 Gauss, 谱表达方法, Fourier 系数, 统一 Hermite 多项式模型The conditional simulation of non-Gaussian excitations utilizing records from the monitoring system is of great significance for hazard mitigation. To this end, this paper proposes a novel conditional non-Gaussian simulation method. In this method, the Unified Hermite Polynomial Model (UHPM) is used to describe the transformation relationship between recorded and unrecorded non-Gaussian processes and their underlying Gaussian counterparts. Meanwhile, an explicit transformation model between their correlation functions is also provided. Then, the covariance matrix of Fourier coefficients of the underlying Gaussian processes is constructed. Based on this covariance matrix, the conditional samples of Fourier coefficients are generated and substituted into the Spectral Representation Method (SRM) to perform the conditional simulation of the underlying Gaussian processes. Finally, the conditionally simulated samples of the underlying Gaussian processes are transformed into the non-Gaussian samples by the UHPM. To showcase the precision and efficacy of the proposed method, two numerical examples involving the conditional simulations of non-Gaussian ground motions and non-Gaussian wind pressure coefficients are provided.Keywords: Conditional simulation; Non-Gaussian; Spectral representation method; Fourier coefficients; Unified hermite polynomial model![]()
Fig. 1. Flowchart of the proposed conditional non-Gaussian simulation
Fig. 2. Site layout of sensors
图 3: Gauss 与非 Gauss 地震动加速度的记录样本与条件模拟样本Fig. 3. Recorded samples (in blue) and conditionally simuated samples (in red) of Gaussian and non-Gaussian ground motion acceleration
图 4: 例 1 中 2, 4, 6, 8, 10 号场地条件模拟的 Gauss 和非 Gauss 地震动加速度样本Fig. 4. Conditionally simulated samples of Gaussian and non-Gaussian ground motion acceleration at sites 2, 4, 6, 8, and 10 in Example 1
图 5: 例 1 中场地 1 与 2 处非 Gauss 地震动记录与条件模拟样本Fig. 5. Recorded and conditionally simulated samples of non-Gaussian ground motion acceleration at sites 1 and 2 in Example 1
图 6: 例 1 中站点 2, 4, 6 的估计谱与目标谱对比Fig. 6. Comparison between the estimated spectrums and target ones at sites 2, 4, and 6 in Example 1
图 7: 例 1 中站点 2, 4, 6 的估计分布与目标分布对比Fig. 7. Comparison between the estimated distribution and target one at sites 2, 4, and 6 in Example 1
Fig. 8. Tap locations and panel layout
图 9: 例 2 中非 Gauss 风压系数的记录与条件模拟样本Fig. 9. Recorded and conditionally simulated non-Gaussian C_p samples in Example 2
图 10: 例 2 中风压系数记录与条件模拟样本的自谱与互谱Fig. 10. Auto-spectrum and cross-spectrums of the recorded and conditionally simulated C_p samples in Example 2
图 11: 例 2 中测点 4 处的估计分布与目标分布对比Fig. 11. Comparison between the estimated distribution and target distribution at Tap 4 in Example 2
作者信息 | Authors
新加坡国立大学 (National University of Singapore) 土木与环境工程系
卢朝辉 Zhao-Hui Lu, 通讯作者 (Corresp.) 北京工业大学 (Beijing University of Technology) 城市与工程安全减灾教育部重点实验室Email: luzhaohui@bjut.edu.cn
北京工业大学 (Beijing University of Technology) 城市与工程安全减灾教育部重点实验室
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
