Time-domain dimension-reduction representation for stochastic ground motion utilizing filtered white noise基于过滤白噪声的随机地震动时域降维表达
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Liu ZJ, Liu M, Xu BH, Fan YF, Ruan XX, 2024. Time-domain dimension-reduction representation for stochastic ground motion utilizing filtered white noise. Probabilistic Engineering Mechanics, 77: 103678.DOI: 10.1016/j.probengmech.2024.103678
提出了一种表征和模拟平稳和完全非平稳随机地震动的方法。该方法基于离散过滤白噪声模型，包括单层滤波和双层滤波，后者用于抑制低频分量。具体地，该方法将地震动表示为正交随机变量和确定性函数乘积的线性组合。此外，通过将高维正交随机变量定义为极低维基本随机变量的正交函数，可以实现原地震动过程的有效降维 (dimension-reduction, DR)。为说明此概念，研究了三类仅涉及一个或两个基本随机变量的随机正交函数，采用过滤白噪声模型模拟地震动加速度过程，从而证明了所提方法的精度和效率。同时，基于各参数对随机地震动过程的影响分析，建议采用所提方法进行模拟。算例研究验证了所提方法与蒙特卡罗 (Monte Carlo, MC) 方法相比的精度和鲁棒性。此外，完全非平稳地震动的算例研究凸显了该方法在实际工程中的适用性。关键词: 随机地震动, 时域, 双层过滤白噪声, 降维表示, 随机正交函数A method is proposed for characterizing and simulating both stationary and fully non-stationary stochastic ground motions. This method is based on discrete filtered white noise models, including single and double filtered, with the latter is introduced to suppress low-frequency components. Specifically, the proposed method expresses seismic ground motion as a linear combination of products involving orthogonal random variables and deterministic functions. Further, by defining high-dimensional orthogonal random variables as orthogonal functions of extremely low dimensional elementary random variables, efficient dimension-reduction (DR) of primitive ground motion process can be achieved. To illustrate this concept, three distinct categories of random orthogonal functions involving only one or two elementary random variables are examined, employing filtered white noise models to simulate ground motion acceleration processes, thereby demonstrating the accuracy and efficiency of the proposed method. Simultaneously, recommendations for employing the proposed method in simulations are provided based on an analysis of the impacts of various parameters on random ground motion processes. Case studies demonstrate the accuracy and robustness of the proposed method compared to Monte Carlo (MC) methods. Furthermore, case studies on fully non-stationary ground motion highlight the practical applicability of the proposed method in engineering.Keywords: Stochastic ground motion; Time-domain; Double-filtered white noise; Dimension-reduction representation; Random orthogonal functions.提出了一种基于双层过滤白噪声的随机地震动模拟方法
- 该方法是一种时域降维方法，只需一或两个基本随机变量即可模拟
A method for simulating random ground motion is proposed based on a double-filtered white noise.
The seismic ground motion simulated by this method exhibits non stationarity in both the time and frequency domains.
- The method is a dimension-reduction method in time domain, only requiring one or two basic random variables for simulation.
Recommendations for using the method in simulations of random ground motionare provided based on a parametric analysis.
Fig. 1. Schematic representation of the double-filtered white noise model for ground motion simulation
图 2: 单层过滤平稳地震动均值与标准差的平均相对误差Fig. 2. Average relative error of Mean and StD of single-filtered stationary ground motion
图 3: 双层过滤平稳地震动均值与标准差的平均相对误差Fig. 3. Average relative error of Mean and StD of double-filtered stationary ground motion
图 4: 不同时间步长下单层滤波的均值与标准差误差Fig. 4. Mean and standard deviation errors of single-filtered under various time step sizes
图 5: 不同时间步长下双层滤波的均值与标准差误差Fig. 5. Mean and standard deviation errors of double-filtered under various time step sizes
Fig. 6. Representative time histories simulated by the proposed scheme with random functions
图 7: 平稳地震加速度过程的目标统计量与其单层滤波模拟的对比: (a) 均值与标准差; (b) 功率谱密度Fig. 7. Comparison between target statistics and those of simulated stationary seismic acceleration processes in single-filtered with respect to: (a) Mean and standard deviation; (b) Power spectral density
图 8: 平稳地震加速度过程的目标统计量与其双层滤波模拟的对比: (a) 均值与标准差; (b) 功率谱密度Fig. 8. Comparison between target statistics and those of simulated stationary seismic acceleration processes in double-filtered with respect to: (a) Mean and standard deviation; (b) Power spectral density.
Fig. 9. Representative samples from different site categories
图 10: 模拟样本与其相应目标的均值与标准差对比Fig. 10. Comparison of mean value and standard deviation of simulated samples with its corresponding target (with the number of samples: 610)
Fig. 11. Comparison of simulated EPSD against the corresponding target (with the number of samples: 610)
图 12: 目标与所提方法模拟的非平稳加速度过程 10 s 时刻演变功率谱密度Fig. 12. Target and simulated EPSD of non-stationary acceleration processes by proposed method at instants of time 10s (with the number of samples: 610)
作者信息 | Authors
武汉工程大学 (Wuhan Institute of Technology) 土木工程与建筑学院
武汉工程大学 (Wuhan Institute of Technology) 土木工程与建筑学院
武汉工程大学 (Wuhan Institute of Technology) 土木工程与建筑学院
美国得克萨斯农工大学 (Texas A & M University) 土木与环境工程系
阮鑫鑫 Xin-Xin Ruan, 通讯作者 (Corresp.)信阳师范大学 (Xinyang Normal University) 建筑与土木工程学院Email: ruanxinxin@xynu.edu.cn
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)
