地震研究

易损性曲线将结构破坏等级与地震动强度相关联,能够直观地反映结构破坏的概率,但在建立易损性曲线的过程中需要大量的结构非线性时程分析结果,因而计算效率不高。机器学习方法已被证明能较好地解决这一问题,但当训练数据的规模较大时,由于训练过程涉及求解大规模逆矩阵致使计算效率依然低下。为此,本文提出了一种特征向量信息支持向量机(EILS-SVM)的新方法克服此类方法的不足。在大规模数据集下,EILS-SVM能够筛选小规模子样本建立低秩核矩阵。这使得其训练过程只需求解小规模低秩矩阵的逆矩阵,进而极大提高计算效率。为了验证EILS-SVM的准确性和高效性,基于16500个钢筋混凝土(RC)框架在地震作用下的破坏数据,分别与支持向量机(LS-SVM)、随机森林、神经网络、线性判别分析(LDA)、贝叶斯作对比。结果表明,EILS-SVM 能准确预测 RC框架的易损性曲线,其计算效率最高能提升近27倍。

Fragility curves establish a correlation between structural damage levels and seismic intensity,offering an intuitive depiction of the probability of structural failure. However,the generation of these curves necessitates a substantial amount of structural nonlinear time-history analysis results,thereby rendering the computational process inefficient. Machine learning techniques have been proven to effectively address this issue,yet their efficacy diminishes with the increase in the scale of training data due to the computational demands of solving large-scale inverse matrices during the training phase. In response,this paper proposes a novel methodology,the Eigenvector Information-supported Support Vector Machine(EILS-SVM),which surmounts the limitations associated with these techniques. By employing a selective subsample to construct a low-rank kernel matrix in the context of large-scale datasets,the EILS-SVM method requires only the inversion of small-scale,low-rank matrices,significantly enhancing computational efficiency. To validate the accuracy and efficiency of the EILS-SVM,it is benchmarked against conventional models such as the Least Squares Support Vector Machine(LS-SVM),Random Forest,Neural Networks,Linear Discriminant Analysis(LDA),and Bayesian methods,using a dataset comprised of 16500 instances of damage in Reinforced Concrete(RC)frames subjected to seismic activities. The results indicate that the EILS-SVM is capable of accurately predicting the fragility curves of RC frames,with a computational efficiency improvement of up to 27 times compared to existing methodologies.

引言
1 EILS-SVM的原理及易损性预测应用
2 大规模RC框架分类数据集的创建
3 EILS-SVM模型性能分析
4 结论

图1 基于EILS-SVM的易损性曲线预测模型建立步骤<br/>Fig.1 Establishment of fragility curve prediction model based on EILS-SVM

图1 基于EILS-SVM的易损性曲线预测模型建立步骤
Fig.1 Establishment of fragility curve prediction model based on EILS-SVM

表1 输入变量信息<br/>Tab.1 Details of the input variables

表1 输入变量信息
Tab.1 Details of the input variables

图2 RC框架MSA结构响应分布图<br/>Fig.2 MSA response distribution of the RC frame structure

图2 RC框架MSA结构响应分布图
Fig.2 MSA response distribution of the RC frame structure

图3 子样本规模与预测准确率(a)和训练时间(b)的关系<br/>Fig.3 Subsample size vs accuracy(a)and training time(b)

图3 子样本规模与预测准确率(a)和训练时间(b)的关系
Fig.3 Subsample size vs accuracy(a)and training time(b)

表2 EILS-SVM模型与其它5种传统机器学习模型性能指标对比<br/>Tab.2 Comparison between the performance of EILS-SVM model and the performance of other 5 traditional machine learning models

表2 EILS-SVM模型与其它5种传统机器学习模型性能指标对比
Tab.2 Comparison between the performance of EILS-SVM model and the performance of other 5 traditional machine learning models

图4 EILS-SVM模型与其它5种模型预测得到的建筑物破坏状态的混淆矩阵<br/>Fig.4 Confusion matrixes of the predicted damage states by EILS-SVM model and other 5 models

图4 EILS-SVM模型与其它5种模型预测得到的建筑物破坏状态的混淆矩阵
Fig.4 Confusion matrixes of the predicted damage states by EILS-SVM model and other 5 models

图5 基于EILS-SVM的6层RC框架在不同退化参数下结构破坏状态预测结果的混淆矩阵<br/>Fig.5 Confusion matrix of the predicted results of the structural failure state of a six-storey RC frame based on EILS-SVM model according to different degradation parameters

图5 基于EILS-SVM的6层RC框架在不同退化参数下结构破坏状态预测结果的混淆矩阵
Fig.5 Confusion matrix of the predicted results of the structural failure state of a six-storey RC frame based on EILS-SVM model according to different degradation parameters

图6 基于EILS-SVM的6层RC框架在不同退化参数下的易损性曲线预测结果<br/>Fig.6 Predicted fragility curves of a 6-storey RC frame according to different degradation parameters based on EILS-SVM model

图6 基于EILS-SVM的6层RC框架在不同退化参数下的易损性曲线预测结果
Fig.6 Predicted fragility curves of a 6-storey RC frame according to different degradation parameters based on EILS-SVM model

表3 使用EILS-SVM模型和有限元方法计算得到的易损性参数Θ和σ<br/>Tab.3 Calculated fragility parameters Θ and σ by EILS-SVM model and Finite Element Method

表3 使用EILS-SVM模型和有限元方法计算得到的易损性参数Θ和σ
Tab.3 Calculated fragility parameters Θ and σ by EILS-SVM model and Finite Element Method

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备注

引言

1 EILS-SVM的原理及易损性预测应用

2 大规模RC框架分类数据集的创建

3 EILS-SVM模型性能分析

4 结论

期刊信息