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非线性结构地震响应的神经网络算法

许泽坤 陈隽

许泽坤, 陈隽. 非线性结构地震响应的神经网络算法[J]. 工程力学, 2021, 38(9): 133-145. doi: 10.6052/j.issn.1000-4750.2020.09.0645
引用本文: 许泽坤, 陈隽. 非线性结构地震响应的神经网络算法[J]. 工程力学, 2021, 38(9): 133-145. doi: 10.6052/j.issn.1000-4750.2020.09.0645
XU Ze-kun, CHEN Jun. NEURAL NETWORK ALGORITHM FOR NONLINEAR STRUCTURAL SEISMIC RESPONSE[J]. Engineering Mechanics, 2021, 38(9): 133-145. doi: 10.6052/j.issn.1000-4750.2020.09.0645
Citation: XU Ze-kun, CHEN Jun. NEURAL NETWORK ALGORITHM FOR NONLINEAR STRUCTURAL SEISMIC RESPONSE[J]. Engineering Mechanics, 2021, 38(9): 133-145. doi: 10.6052/j.issn.1000-4750.2020.09.0645

非线性结构地震响应的神经网络算法

doi: 10.6052/j.issn.1000-4750.2020.09.0645
基金项目: 国家自然科学基金重点项目(U1711264);土木工程防灾国家重点实验室项目(SLDRCE19-B-22)
详细信息
    作者简介:

    许泽坤(1996−),男,山东人,博士生,主要从事工程结构抗震研究(E-mail: xzk8559@163.com)

    通讯作者:

    陈 隽(1972−),男,河南人,教授,博士,博导,主要从事工程结构抗震、土木工程大数据研究(E-mail: cejchen@tongji.edu.cn)

  • 中图分类号: TU311.41

NEURAL NETWORK ALGORITHM FOR NONLINEAR STRUCTURAL SEISMIC RESPONSE

  • 摘要: 提出一种基于长短期记忆(long short-term memory, LSTM)神经网络模型计算非线性结构地震响应的新方法,采用单向多层堆叠式LSTM架构,并借助滑动时间窗实现递推计算。改进了模型预测效果的评价指标,可考虑响应在不同幅值区间的敏感性差异,避免了传统评价指标的相位敏感问题。利用实测地震动和多层框架结构进行了新方法的验证,给出了网络超参数的取值原则,并讨论了不同工况下模型的泛化能力。结果表明,LSTM模型的计算精度较好、对地震动类型具有鲁棒性。由于神经网络模型便于分布式、云部署的特点,该方法可在城市区域地震响应快速模拟等传统数值方法受限的应用场景发挥作用。
  • 图  1  学习率衰减曲线

    Figure  1.  Learning rate decay curve

    图  2  滑动时间窗的预测流程

    Figure  2.  Forecasting process with sliding time window

    图  3  LSTM模型的响应预测流程图

    Figure  3.  Flowchart of response prediction of LSTM model

    图  4  10层框架结构示意图

    Figure  4.  Schematic diagram of a 10-story frame structure

    图  5  损失函数变化趋势

    Figure  5.  Tendency of loss function

    图  6  例1中4条地震动响应时程的预测结果

    Figure  6.  Four prediction results of the seismic response time history in Example 1

    图  7  例2中4条地震动响应时程的预测结果

    Figure  7.  Four prediction results of the seismic response time history in Example 2

    图  8  某地震动时程出现的发散现象

    Figure  8.  The divergence of a certain earthquake time history

    图  9  M1-50模型的测试集预测结果分布

    Figure  9.  Distribution of prediction results of the test set of the M1-50 model

    图  10  代表性地震动的傅里叶幅值谱与加速度时程

    Figure  10.  Fourier amplitude spectrum and acceleration time history of representative ground motions

    图  11  滤波前后16号地震动预测结果对比

    Figure  11.  Comparison of prediction results of No. 16 ground motion before and after filtering

    表  1  LSTM网络结构

    Table  1.   LSTM network structure

    类型激活函数输出形状
    InputInputLayer(None, n, f+1)
    LSTM1LSTMtanh(None, n, 200)
    LSTM2LSTMtanh(None, n, 200)
    LSTM3LSTMtanh(None, 200)
    FCDenseLinear(None, s×f)
    注:n为输入时间序列长度;s为输出时间序列长度;f为预测自由度数量。
    下载: 导出CSV

    表  2  10层框架结构参数与恢复力模型

    Table  2.   Parameters and restoring force model of a 10-story frame structure

    楼层123~67~910
    层高h/m4.604.003.203.203.20
    质量/(×105 kg)1.521.451.361.321.15
    弹性模量/(×104 MPa)3.253.253.153.003.00
    屈服强化系数α10.40
    屈服后强化系数α20.10
    开裂位移xch/550
    屈服位移xyh/70
    极限位移xph/45
    下载: 导出CSV

    表  3  地震动数据集

    Table  3.   Earthquake ground motion dataset

    数据集地点持时/s数量
    训练集East Japan30027
    测试集Imperial Valley37.06~50.0824
    Coalinga58.162
    Whittier Narrows40.002
    Superstition Hills29.852
    下载: 导出CSV

    表  4  6层框架结构参数与恢复力模型

    Table  4.   Parameters and restoring force model of a 6-story frame structure

    楼层123~6
    层高h/m4.604.003.20
    质量/(×105 kg)1.521.451.36
    弹性模量/(×104 MPa)3.253.253.15
    屈服强化系数α10.60
    屈服后强化系数α20.20
    开裂位移xch/800
    屈服位移xyh/80
    极限位移xph/40
    下载: 导出CSV

    表  5  窗口大小取值分析的模型评价结果

    Table  5.   Model evaluation results of window size analysis

    LSTM模型 M1-25M1-50M1-75M1-100M1-125M2-50M2-75M2-100
    模型参数窗口大小 2550751001255075100
    训练集 train1train1train1train1train1train2train2train2
    测试集 test1test1test1test1test1test2test2test2
    评价指标(1层) 峰值百分误差/(%) 10.8700 9.3000 10.0300 12.9100 10.2500 13.9700 15.5400 15.7900
    P相关系数 0.7021 0.8697 0.8155 0.8399 0.7487 0.7628 0.7252 0.7663
    WRMSE/m 0.0020 0.0015 0.0017 0.0017 0.0019 0.0040 0.0035 0.0034
    加权决定系数 0.7425 0.8639 0.8137 0.8226 0.7625 0.2995 0.6970 0.7292
    评价指标(5层) 峰值百分误差/(%) 16.3400 10.4400 10.9600 10.7600 19.5100 16.7800 15.2000 12.4600
    P相关系数 0.6208 0.8560 0.8298 0.8363 0.7136 0.7618 0.7336 0.7739
    WRMSE/m 0.0121 0.0081 0.0084 0.0084 0.0109 0.0205 0.0169 0.0169
    加权决定系数 0.4798 0.8219 0.7927 0.7963 0.5212 0.1327 0.6969 0.7266
    评价指标(9层) 峰值百分误差/(%) 12.4000 8.3600 10.1100 10.2100 16.2500 15.1600 15.4700 12.7500
    P相关系数 0.6412 0.8649 0.8170 0.8405 0.7301 0.7678 0.7351 0.7750
    WRMSE/m 0.0153 0.0103 0.0122 0.0110 0.0137 0.0257 0.0221 0.0223
    加权决定系数 0.5695 0.8471 0.7712 0.8147 0.6360 0.3349 0.7015 0.7324
    评价指标(均值) 峰值百分误差/(%) 13.2000 9.3700 10.3700 11.2900 15.3400 15.3000 15.4000 13.6700
    P相关系数 0.6547 0.8635 0.8208 0.8389 0.7308 0.7642 0.7313 0.7717
    WRMSE/m 0.0098 0.0067 0.0074 0.0070 0.0089 0.0167 0.0142 0.0142
    加权决定系数 0.5973 0.8443 0.7925 0.8112 0.6399 0.2557 0.6985 0.7294
    下载: 导出CSV

    表  6  不同地震动与结构的响应主周期

    Table  6.   Response main period under different ground motions and structures

    PGA/(m/s2) 0.5 2.5 4
    数据集 traintest traintest traintest
    结构1 0.762 0.764 0.878 0.839 0.950 0.923
    结构2 0.494 0.483 0.517 0.512 0.564 0.552
    注:响应主周期为响应时程主频率的倒数,表示响应的波长特征,单位为s。增加PGA=0.5 ${\rm{m/}}{{\rm{s}}^2}$的对照组以说明结构在线性状态下的响应波长。
    下载: 导出CSV

    表  7  地震动泛化能力分析的模型评价结果

    Table  7.   Model evaluation results of earthquake generalization ability analysis

    LSTM模型 M1-50 M1-100 M2-100 M3-100
    模型参数窗口大小 50 100 100 100
    训练集 train1 train1 train2 train3
    测试集 test1test2 test1test2 test1test2 test1test2
    评价指标(1层) 峰值百分误差/(%) 9.3000 16.5900 12.9100 13.4800 16.6500 15.7900 13.7300 12.1300
    P相关系数 0.8697 0.7090 0.8399 0.8035 0.7892 0.7663 0.8384 0.8029
    WRMSE/m 0.0015 0.0037 0.0017 0.0031 0.0020 0.0034 0.0018 0.0029
    加权决定系数 0.8639 0.6617 0.8226 0.7742 0.7526 0.7292 0.8152 0.7537
    评价指标(5层) 峰值百分误差/(%) 10.4400 12.2300 10.7600 13.8200 15.3500 12.4600 14.7800 10.9800
    P相关系数 0.8560 0.6672 0.8363 0.8061 0.7851 0.7739 0.8338 0.7918
    WRMSE/m 0.0081 0.0198 0.0084 0.0154 0.0101 0.0169 0.0088 0.0153
    加权决定系数 0.8219 0.5844 0.7963 0.7663 0.7216 0.7266 0.7976 0.7158
    评价指标(9层) 峰值百分误差/(%) 8.3600 11.7900 10.2100 14.7600 15.1100 12.7500 13.7500 10.8300
    P相关系数 0.8649 0.6827 0.8405 0.8063 0.7912 0.7750 0.8390 0.8022
    WRMSE/m 0.0103 0.0252 0.0110 0.0203 0.0132 0.0223 0.0117 0.0197
    加权决定系数 0.8471 0.6362 0.8147 0.7716 0.7395 0.7324 0.8059 0.7302
    评价指标(均值) 峰值百分误差/(%) 9.3700 13.5400 11.2900 14.0200 15.7000 13.6700 14.0900 11.3100
    P相关系数 0.8635 0.6863 0.8389 0.8053 0.7885 0.7717 0.8371 0.7990
    WRMSE/m 0.0067 0.0162 0.0070 0.0129 0.0084 0.0142 0.0074 0.0126
    加权决定系数 0.8443 0.6274 0.8112 0.7707 0.7379 0.7294 0.8062 0.7332
    下载: 导出CSV

    表  8  结构模型泛化能力分析的模型评价结果

    Table  8.   Model evaluation results of structural model generalization ability analysis

    LSTM模型 M1-25M1-25M1-50M1-50M2-25M2-50M2-75M2-100M3-100
    模型参数窗口大小 25255050255075100100
    训练集 train1train1train1train1train2train2train2train2train3
    测试集 test1test2test1test2test2test2test2test2test2
    评价指标(1层) 峰值百分误差/(%) 7.7200 11.9500 7.4900 8.4400 12.1700 12.6200 9.2700 8.3800 9.2800
    P相关系数 0.9042 0.8534 0.9309 0.8884 0.8010 0.8043 0.9044 0.8783 0.8714
    WRMSE/m 0.0010 0.0021 0.0008 0.0017 0.0022 0.0025 0.0017 0.0017 0.0020
    加权决定系数 0.8992 0.8599 0.9269 0.9013 0.8247 0.7769 0.8974 0.8706 0.8560
    评价指标(3层) 峰值百分误差/(%) 6.5700 9.0200 7.1600 6.6600 11.2300 12.2900 9.9900 7.5600 8.3900
    P相关系数 0.9016 0.8550 0.9297 0.8878 0.7853 0.8130 0.8980 0.8901 0.8785
    WRMSE/m 0.0029 0.0059 0.0023 0.0049 0.0064 0.0071 0.0048 0.0048 0.0055
    加权决定系数 0.8994 0.8657 0.9223 0.9041 0.7976 0.7881 0.9012 0.8962 0.8690
    评价指标(6层) 峰值百分误差/(%) 6.2200 7.7200 6.5600 5.6400 9.8100 11.5400 9.6200 7.0600 8.2500
    P相关系数 0.9024 0.8544 0.9302 0.8875 0.8135 0.8067 0.8953 0.8554 0.8732
    WRMSE/m 0.0041 0.0084 0.0033 0.0070 0.0085 0.0104 0.0069 0.0072 0.0080
    加权决定系数 0.8976 0.8643 0.9244 0.9038 0.8324 0.7812 0.8994 0.8873 0.8663
    评价指标(均值) 峰值百分误差/(%) 6.8400 9.5600 7.0700 6.9100 11.0700 12.1500 9.6300 7.6700 8.6400
    P相关系数 0.9027 0.8543 0.9303 0.8879 0.7999 0.8080 0.8992 0.8746 0.8744
    WRMSE/m 0.0027 0.0055 0.0021 0.0045 0.0057 0.0067 0.0045 0.0046 0.0052
    加权决定系数 0.8988 0.8633 0.9245 0.9031 0.8183 0.7820 0.8993 0.8847 0.8637
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-09-07
  • 修回日期:  2021-01-07
  • 网络出版日期:  2021-04-21
  • 刊出日期:  2021-09-13

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