AN AUTOMATIC STRUCTURAL MODAL PARAMETERS IDENTIFICATION METHOD BASED ON HHT AND ITS EXPERIMENTAL VERIFICATION
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摘要: 建筑结构的模态参数识别是健康监测系统中的核心算法。模态参数识别经过多年的发展已经非常成熟，种类繁多。但是基于Hilbert-Huang变换(Hilbert-Huang transform, HHT)的结构模态参数识别中多个步骤均需要研究人员对参数进行主观判断与筛选，不能直接用于长期的结构健康自动监测。该文提出了一种基于HHT的结构模态自动识别方法，利用深度神经网络(Deep neural network, DNN)结合K-L散度实现了EMD(Empirical mode decomposition)虚假分量的识别与剔除，利用奇异谱分析(Singular spectrum analysis, SSA)结合Butterworth滤波器对EMD产生的模态混叠现象进行分离，对只包含单一模态信息的固有模态函数(Intrinsic mode function, IMF)进行Hilbert变换后通过最小二乘法拟合实现模态参数识别。将上述方法应用于一3层混凝土结构振动台试验的监测数据分析，结果表明：该方法可以在不依赖研究人员的主观参数选择前提下，有效实现结构模态参数的自动化识别。Abstract: Structural modal parameter identification is a core algorithm in structural health monitoring system. Modal parameter identification methods have been very mature after years of development, and there are many types. The modal parameter identification method based on Hilbert-Huang Transform require researchers to subjectively select parameters in multiple steps, and cannot be directly used for long-term automatic structural monitoring. An automatic structural modal parameter identification method based on HHT is proposed. K-L divergence and DNN are used to identify and eliminate the false components generated by EMD in the first step of HHT. SSA and Butterworth filter are used to separate the aliasing modes of IMF. Hilbert transform is applied to IMF that only contains single mode information and least squares fitting is used to realize the modal parameter identification. The method is applied to a shaking table test of a three-story concrete structure, and the results show that the method can effectively and automatically identify the structural modal parameters without subjective parameter selection process.
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图 1 基于HHT的自动化模态参数识别步骤
Figure 1. Steps of automatic modal parameter identification method based on HHT
图 3 EMD分量与原信号K-L散度
Figure 3. K-L divergences between structural response signal and its EMD components
图 6 原信号及前3阶IMF的自相关函数
Figure 6. Autocorrelation functions of original signal and IMF1- IMF3
图 7 原信号及前3阶IMF的自功率谱
Figure 7. Auto-power spectrum functions of original signal and IMF1- IMF3
图 8 IMF1.1自相关函数及自功率谱
Figure 8. Autocorrelation function and auto-power spectrum function of IMF1.1
图 9 IMF1.2自相关函数及自功率谱
Figure 9. Autocorrelation function and auto-power spectrum function of IMF1.2
图 10 IMF1.3自相关函数及自功率谱
Figure 10. Autocorrelation function and auto-power spectrum function of IMF1.3
图 12 EMD虚假分量识别DNN学习曲线
Figure 12. EMD false component identification DNN learning curve
图 13 原信号及IMF1~IMF3自功率谱
Figure 13. Auto-power spectrum functions of original signal and IMF1- IMF3
图 14 模态分离后IMF1.1~IMF1.3自功率谱
Figure 14. Auto-power spectrum functions of IMF1.1- IMF1.3
图 15 IMF3幅频函数及相频函数
Figure 15. Amplitude frequency function and phase frequency function of IMF3
图 16 IMF1.2幅频函数及相频函数
Figure 16. Amplitude frequency function and phase frequency function of IMF1.2
图 17 IMF1.1幅频函数及相频函数
Figure 17. Amplitude frequency function and phase frequency function of IMF1.1
图 18 IMF1.3幅频函数及相频函数
Figure 18. Amplitude frequency function and phase frequency function of IMF1.3
表 1 EMD虚假分量识别准确率
Table 1. EMD false component identification accuracy
噪声
强度/(%)IMF
数量虚假IMF
数量真实IMF
数量虚假IMF识别
准确率/(%)真实IMF识别
准确率/(%)整体
准确率/(%)5 35 15 20 80.0 90.0 85.7 10 42 21 21 71.4 90.5 81.0 20 41 19 22 68.2 68.4 68.3 30 43 26 17 69.2 47.1 60.5 合计 161 81 80 71.5 75.1 73.3 
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表 2 模态参数识别结果
Table 2. Modal parameter identification results
阶数 频率 阻尼比 识别结果 真实值 识别误差/(%) 识别结果/(%) 1阶 6.25 6.27 0.3 1.6 2阶 18.33 18.38 0.3 6.9 3阶 29.04 29.27 0.8 1.7 4阶 37.58 38.25 1.8 1.8
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表 3 试验工况加载次序
Table 3. Test loading sequence
工况 加载次序 输入激励 加速度峰值/(cm/s2) 框剪方向 框架方向 工况1 工况1-1 第1次白噪声 50 50 工况2 工况2-2 8度多遇 70 − 工况2-3 第2次白噪声 50 50 工况2-4 8度多遇 − 70 工况2-5 第3次白噪声 50 50 工况3 工况3-6 8度基本 200 − 工况3-7 第4次白噪声 50 50 工况3-8 8度基本 − 200 工况3-9 第5次白噪声 50 50 工况4 工况4-10 8度罕遇 400 − 工况4-11 第6次白噪声 50 50 工况4-12 8度罕遇 − 400 工况4-13 第7次白噪声 50 50 工况5 工况5-14 9度罕遇 620 − 工况5-15 第8次白噪声 50 50 工况5-16 9度罕遇 − 620 工况5-17 第9次白噪声 50 50 工况6 工况6-18 8度罕遇 400 − 工况6-19 第10次白噪声 50 50 工况6-20 8度罕遇 − 400 工况6-21 第11次白噪声 50 50 工况7 工况7-22 9度罕遇 620 − 工况7-23 第12次白噪声 50 50 工况7-24 9度罕遇 − 620 工况7-25 第13次白噪声 50 50
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表 4 DNN模型超参数选取
Table 4. DNN model parameter selection
DNN参数 参数选择 DNN层数 输入层：1，隐藏层：4，输出层：1 单层神经元数量 输入层：21，隐藏层：10，输出层：1 激活函数 隐藏层：ReLU，输出层：Sigmoid 损失函数 二元交叉熵函数 学习率 0.1 丢失率 5% 梯度下降算法 小批量梯度下降法 训练批次 20
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表 5 EMD虚假分量识别结果
Table 5. EMD false components identification results
加载
序号IMF主频/Hz及DNN识别结果 IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 工况1
1-113.49
真实7.10
真实1.64
真实1.10
虚假0.05
虚假0.10
虚假0.00
虚假工况2
2-511.72
真实6.46
真实1.61
真实0.81
虚假0.29
虚假0.02
虚假− 工况3
3-912.05
真实5.69
真实1.24
真实0.42
虚假0.02
虚假0.01
虚假− 工况4
4-1311.65
真实4.84
真实0.26
虚假0.95
真实0.04
虚假0.01
虚假0.01
虚假工况5
5-1710.12
真实4.17
真实1.01
真实0.00
虚假0.13
虚假0.12
虚假0.00
虚假工况6
6-2110.63
真实4.23
真实0.00
真实0.73
真实0.26
虚假0.11
虚假− 工况7
7-259.44
真实3.41
真实0.47
虚假0.63
真实0.12
虚假0.11
虚假−
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表 6 模态参数识别结果对比
Table 6. Comparison of modal parameters identification results
阶数 有限元分析 频响函数法 自动化模态参数识别 频率/Hz 频率/Hz 阻尼比/(%) 频率/Hz 阻尼比/(%) 1阶 2.10 1.80 16.7 1.64 10.6 2阶 7.77 7.10 4.3 7.10 5.2 3阶 12.99 13.80 2.2 13.49 3.3 4阶 18.59 15.10 1.7 16.21 5.8
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