﻿ 基于遗传编程技术的强地震动参数预测方法
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 大地测量与地球动力学  2024, Vol. 44 Issue (8): 776-782  DOI: 10.14075/j.jgg.2023.11.198

### 引用本文

WANG Chengcheng, HU Qizhi, ZHANG Jie, et al. Research on the Prediction Method of Strong Ground Motion Parameters Based on Genetic Programming Techniques[J]. Journal of Geodesy and Geodynamics, 2024, 44(8): 776-782.

### Foundation support

Guiding Project of Scientific Research Project of Hubei Provincial Education Department, No.B2022369; Project of Big Data Management and Digital Commerce Discipline Group of Wuchang Institute of Technology, No.2022JGXK08; Scientific Research Project of Wuchang Institute of Technology, No.2023KY13.

### Corresponding author

HU Qizhi, professor, majors in geotechnical engineering, E-mail: hqz0716@163.com.

### 第一作者简介

WANG Chengcheng, lecturer, majors in geotechnical earthquake engineering, E-mail: wangcc@wuit.edu.cn.

### 文章历史

1. 武昌工学院城市建设学院，武汉市白沙洲大道110号，430065;
2. 湖北工业大学土木建筑与环境学院，武汉市南李路28号，430068

1 遗传编程技术

 图 1 遗传编程的树形示意图 Fig. 1 Tree schematic of the genetic programming

 图 2 遗传编程流程 Fig. 2 Genetic programming flowchart
2 强地面运动模型

 $\ln \mathrm{PGA}, \ln \mathrm{PGV}, \ln \mathrm{PGD}=f\left(M_W, \ln R, V_{\mathrm{S} 30}, \lambda\right)$ (1)

2.1 强地震动数据

 图 3 NGA地震事件集的断层距与震级 Fig. 3 Fault distance and magnitude for the NGA seismic events set
2.2 地震动峰值参数的显式模型

 图 4 最佳个体平均绝对误差的进化收敛情况 Fig. 4 Evolutionary convergence of the mean absolute error of the best individual

 $\begin{gathered} \operatorname{lnPGA}= \\ C_1-\ln R+C_2(\ln R)^2+C_3 M_W \ln R+\frac{C_4}{V_{\mathrm{S} 30}}+\frac{(\ln R)^3}{V_{\mathrm{S} 30}}+\frac{C_5}{C_6-V_{\mathrm{S} 30}+C_7 V_{\mathrm{S} 30} \lambda+\frac{V_{\mathrm{S} 30}}{M_{\mathrm{W}}+C_8}} \end{gathered}$ (2)
 \begin{aligned} & \ln \mathrm{PGV}=M_W-\ln R- \\ & \frac{C_1}{\left(C_2+\frac{\ln R\left[C_5 \ln R+C_6 M_W+M_W\left(\ln R+C_7\right)\left(C_5 \ln R-M_W+C_8\right)+M_W \ln R \lambda\right]}{C_3 M_W \lambda-V_{\mathrm{S} 30}+C_4}\right)} \\ & \end{aligned} (3)
 $\begin{gathered} \ln \mathrm{PGD}=C_2+M_W+ \\ \frac{C_1\left(M_W-\ln R\right)}{C_3+\frac{\ln R}{C_2+\ln R+M_W^2 / \ln R}+\frac{M_W \ln R\left(M_W+C_7\right)\left(C_6 M_{\mathrm{W}}+C_8 \ln R\right)}{C_4-(\ln R)^2-\lambda+V_{\mathrm{S} 30}+C_4 M_W\left(M_W+C_5\right)}} \end{gathered}$ (4)

3 信度检验与模型对比 3.1 信度检验

 $\mathrm{RMSE}=\sqrt{\frac{1}{n} \sum\limits_{j=1}^n\left(y_j-Y_j\right)^2}$ (5)
 $\text { MAE }=\frac{1}{n} \sum\limits_{j=1}^n\left|y_j-Y_j\right|$ (6)
 $r=\frac{\sum\limits_{j=1}^n\left(y_j-\bar{y}\right)\left(Y_j-\bar{Y}\right)}{\sqrt{\frac{1}{n} \sum\limits_{j=1}^n\left(y_j-\bar{y}\right)^2\left(Y_j-\bar{Y}\right)^2}}$ (7)

 图 5 PGA、PGV和PGD的观测值与预测值分布 Fig. 5 Distribution of observed and predicted values of PGA, PGV and PGD

PGA、PGV和PGD在训练集和测试集下的RMSE分别为0.589、0.735、0.852和0.614、0.782、0.882；MAE分别为0.377、0.472、0.751和0.542、0.624、0.821。RMSE和MAE均呈现出训练集表现优于测试集的特征。PGA、PGV、PGD预测方程的RMSE和MAE逐步增大，说明基于遗传编程技术获得的地震动预测方程对地震动高频分量(PGA)的预测效果优于地震动低频长周期分量(PGD)。但总体而言，预测值与观测值之间的相关性大于0.8，且误差值较小，说明地震动预测模型具有较好的预测能力和泛化性能[13]

3.2 模型对比

 图 6 两种地震动预测模型的残差分布 Fig. 6 Residuals distribution of two ground motion prediction models

3.3 敏感性分析

4 地震动衰减特征分析

 图 7 基岩场地条件下地震动PGA、PGV和PGD的衰减情况 Fig. 7 PGA, PGV and PGD attenuation of ground motion under the condition of bedrock

 图 8 C-B模型与本文模型衰减关系的对比 Fig. 8 Comparison of attenuation relationship between C-B model and model in this paper

 图 9 R=25 km时PGA、PGV和PGD的场地放大效应 Fig. 9 Site amplification effect of PGA, PGV and PGD at R=25 km

5 结语

1) 与Campbell-Bozorgnia衰减关系相比，基于遗传编程技术的PGA与PGV预测效果略优，PGD预测模型的RMSE和MAE分别为5.47和1.64，显著小于Campbell-Bozorgnia模型的45.98和4.61，说明本文模型对长周期地震动分量的预测效果更佳，可以应用于实际地震工程。

2) 基于遗传编程技术的地震动参数预测方程获得的地震动衰减特征具备震级效应、场地放大效应和PGA的近场大震饱和效应特征，但尚未反映出足够的软土减震效应特征，可能与所用训练数据集中淤泥质粘土场地的地震观测波形数据较少有关。这种对训练数据依赖所带来的不确定性值得进一步研究。

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Research on the Prediction Method of Strong Ground Motion Parameters Based on Genetic Programming Techniques
WANG Chengcheng1     HU Qizhi1,2     ZHANG Jie1     ZHANG Yanfang1     XU Liqiang1
1. Urban Construction College, Wuchang Institute of Technology, 110 Baishazhou Road, Wuhan 430065, China;
2. School of Civil Engineering Architecture and Environment, Hubei University of Technology, 28 Nanli Road, Wuhan 430068, China
Abstract: Based on NGA database and using genetic programming techniques, we give a set of prediction equations for PGA, PGV and PGD. On the basis of the explicit prediction formula, the reliability test and model comparison are carried out by establishing the correlation between ground motion parameters and key seismological parameters such as magnitude, fault distance, fault mechanism, and site shear wave velocity within 30 meters. The results show that: 1) Compared with the traditional decay relation-like prediction equations based on nonlinear regression techniques, genetic programming techniques do not need to specify the equation form of the decay relation, can model the complex behaviors of PGA, PGV and PGD, and give explicit formulas to meet engineering needs. 2) Compared with the Campbell-Bozorgnia attenuation relationship, the prediction effect of PGA and PGV based on the genetic programming techniques is slightly better; the RMSE and MAE of the PGD prediction model are 5.47 and 1.64, respectively, which are significantly smaller than those of the Campbell-Bozorgnia model, which are 45.98 and 4.61. 3) The obtained ground motion prediction equations are characterized by magnitude effect, site amplification effect, and saturation effect of near-field large earthquakes, but fail to reflect the soft-soil damping effect, and the maximum site amplification coefficients of PGA, PGV and PGD are about 1.42, 2.53 and 2.64.
Key words: strong ground motion; genetic programming; seismic acceleration; attenuation relationship