﻿ 基于最小二乘支持向量机与熵特征的地震事件性质辨识研究
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 大地测量与地球动力学  2022, Vol. 42 Issue (6): 655-660  DOI: 10.14075/j.jgg.2022.06.019

引用本文

PANG Cong, LIAO Chengwang, JIANG Yong, et al. Research on Identification of Seismic Event Properties Based on Least Squares Support Vector Machine and Entropy Feature[J]. Journal of Geodesy and Geodynamics, 2022, 42(6): 655-660.

Foundation support

Natural Science Foundation of Hubei Province, No. ZRMS2020000813; Scientific Research Fund of Institute of Seismology, CEA and National Institute of Natural Hazards, MEM, No. IS201856290, IS2018126178, IS201726156; National Natural Science Foundation of China, No. 41174053; Special Fund for China Integrated Geophysical Field Observation Instrument Research and Development, No. Y201707.

第一作者简介

PANG Cong, engineer, majors in seismic observation technology and application of artificial intelligence, E-mail: ponspc@foxmail.com.

文章历史

1. 中国地震局地震研究所, 武汉市洪山侧路40号, 430071;
2. 地震预警湖北省重点实验室, 武汉市洪山侧路48号, 430071;
3. 湖北省地震局, 武汉市洪山侧路48号, 430071;
4. 运城学院数学与信息技术学院, 山西省运城市复旦西街1155号, 044031;
5. 南华大学计算机学院, 湖南省衡阳市常胜西路28号, 421001

1 事件性质分类方法

LVSVM的分类过程为：

1) 对于LSSVM分类问题，约束条件是不等式约束：

 $\begin{gathered} \min \nolimits_{\omega, b, e} J(\boldsymbol{\omega}, e)=\frac{1}{2} \boldsymbol{\omega}^{\mathrm{T}} \boldsymbol{\omega}+\frac{1}{2} \gamma \sum\limits_{k=1}^{N} e_{k}^{2}, \\ y_{k}\left[\boldsymbol{\omega}^{\mathrm{T}} \varphi\left(x_{k}\right)+b\right]=1-e_{k}, k=1,2, \cdots, N \end{gathered}$ (1)

2) 采用Lagrange乘数法转换为求解α的极大值问题：

 $\begin{gathered} \boldsymbol{L}(\boldsymbol{\omega}, b, e ; \boldsymbol{\alpha})=J(\boldsymbol{\omega}, e)- \\ \sum\limits_{k=1}^{N} \alpha_{k}\left\{y_{k}\left[\boldsymbol{\omega}^{\mathrm{T}} \varphi\left(x_{k}\right)+b\right]-1+e_{k}\right\} \end{gathered}$ (2)

 $\left\{\begin{array}{l} \frac{\partial \boldsymbol{L}}{\partial \boldsymbol{\omega}}=0 \rightarrow \boldsymbol{\omega}=\sum\limits_{k=1}^{N} \alpha_{k} y_{k} \varphi\left(x_{k}\right) \\ \frac{\partial \boldsymbol{L}}{\partial b}=0 \rightarrow \sum\limits_{k=1}^{N} \alpha_{k} y_{k}=0 \\ \frac{\partial \boldsymbol{L}}{\partial e_{k}}=0 \rightarrow \alpha_{k}=\gamma e_{k}, k=1,2, \cdots, N \\ \frac{\partial \boldsymbol{L}}{\partial \alpha_{k}}=0 \rightarrow y_{k}\left[\boldsymbol{\omega}^{\mathrm{T}} \varphi\left(x_{k}\right)+b\right]-1+e_{k}=0, \\ \ \ \ \ k=1,2, \cdots, N \end{array}\right.$ (3)

 $\left[\begin{array}{cc} 0 & \boldsymbol{y}^{\mathrm{T}} \\ \boldsymbol{y} & \boldsymbol{\varOmega}+I / \gamma \end{array}\right]\left[\begin{array}{l} b \\ \boldsymbol{\alpha} \end{array}\right]=\left[\begin{array}{c} 0 \\ 1_{v} \end{array}\right]$ (4)

 $\begin{gathered} \boldsymbol{\varOmega}_{k l}=y_{k} y_{l} \varphi\left(x_{k}\right)^{\mathrm{T}} \varphi\left(x_{l}\right)=y_{k} y_{l} K\left(x_{k}, x_{l}\right), \\ k, l=1,2, \cdots, N \end{gathered}$ (5)

3) 解以上方程组可以得到αb，最终得到LSSVM的分类表达式为：

 $f(x)=\operatorname{sign}\left[\sum\limits_{k=1}^{N} \alpha_{k} y_{k} K\left(x, x_{k}\right)+b\right]$ (6)
2 数据特征提取

2.1 排列熵

 $\left[\begin{array}{cccc} x(1) & x(1+\tau) & \cdots & x(1+(m-1) \tau) \\ x(2) & x(2+\tau) & \cdots & x(2+(m-1) \tau) \\ \vdots & \vdots & \ddots & \vdots \\ x(k) & x(k+\tau) & \cdots & x(k+(m-1) \tau) \end{array}\right]$ (7)

 $\begin{gathered} x\left(i+\left(j_{1}-1\right) \tau\right) \leqslant x\left(i+\left(j_{2}-1\right) \tau\right) \leqslant \cdots \\ \leqslant x\left(i+\left(j_{m}-1\right) \tau\right) \end{gathered}$ (8)

 $S(l)=\left(j_{1}, j_{2}, \cdots, j_{m}\right)$ (9)

 $H_{p}(m)=-\left(\sum\limits_{j=1}^{k} P_{j} \ln P_{j}\right)$ (10)

Pj=1/m!时，排列熵达到最大值ln(m!)。

2.2 近似熵

1) 按照式(11)构建m维向量，用y(i)表示，即{y(i), i=1, 2, …, M, M=Nm+1}，其中y(i)={x(i), x(i+1), …, x(i+m－1)}，m为嵌入维数，是重构序列的长度。计算y(i)与y(j)任意分量之间的欧氏距离d{y(i), y(j)}，并将各分量之间最大的距离定义为最大贡献成分距离D{y(i), y(j)}，得到：

 $D\{\boldsymbol{y}(i), \boldsymbol{y}(j)\}=\max \{|\boldsymbol{y}(i+k)-\boldsymbol{y}(j+k)|\}$ (11)

2) 给定阈值r(r>0)，给定嵌入维数m，计算代表序列{y(i)}规律性的概率大小量度Cim(r)，即统计D{y(i), y(j)} < r的个数Nm(i)与总数N-m+1的比例，也叫概率大小，即

 $C_{i}^{m}(r)=N^{m}(i) /(N-M+1), i \leqslant N-m+1$ (12)

 $\varphi^{m}(i)=\left(\sum\limits_{i=1}^{N-m+1} \ln C_{i}^{m}(r)\right) /(N-m+1)$ (13)

3) 将嵌入维数变为m+1，重复上述步骤，得到Cim(r)和φm(i)。该序列的近似熵(ApEn)表示为：

 $\operatorname{ApEn}(m, r)=\varphi^{m}(i)-\varphi^{m+1}(i)$ (14)

2.3 香农熵

 $H=-\sum\limits_{i=0}^{l-1} p(i) \log _{2} p(i)$ (15)
3 实验与分析

1) 根据中国地震台网中心测定，2021-05-21 21:21云南省大理州漾濞县发生MS5.6地震，震源深度10 km，共有28个台站(表 1)记录到此次强震动事件，其中漾濞台震中距最小，为5.4 km，东西、南北及垂直向加速度峰值分别为－339.2 cm/s2、267.2 cm/s2、－220.1 cm/s2，计算仪器地震烈度为7.7度。

2) 2021-05-21 21:48云南省大理州漾濞县(25.67°N，99.87°E)发生MS6.4地震，震源深度8 km，其中漾濞台震中距最小，为7.9 km，东西、南北、垂直向加速度峰值分别为－379.9 cm/s2、720.3 cm/s2、－448.4 cm/s2，速度峰值分别为30.4 cm/s、－29.8 cm/s、－7.2 cm/s，计算仪器地震烈度为8.3度。

3) 2021-05-22 02:04青海省果洛州玛多县(34.59°N，98.34°E)发生MS7.4地震，震源深度17 km，共有16个台站(表 2)记录到此次强震动事件，其中大武台震中距175.6 km，东西、南北、垂直向加速度峰值分别为46.0 cm/s2、40.6 cm/s2、－19.1 cm/s2，计算仪器地震烈度为6.0度。

4) 人工爆破事件数据来自中国水利水电科学研究院岩土工程研究所，使用PCB 350B01型加速度计和PCB 350D02型加速度计进行采集，频率响应为1 Hz~10 kHz，得到共计342条加速度波形记录，记录长度皆为40 000 m/s2

 图 1 熵值计算结果 Fig. 1 Calculation results of entropy

 图 2 LSSVM模型二分类结果 Fig. 2 Two-class results of LSSVM model

4 结语

1) 将排列熵、近似熵、香农熵引入地震识别中，具有一定新颖性，其特征提取结果也具有明显的事件区分效果。

2) LSSVM模型收敛速度较快，在训练量较少的情况下依然可以保持较理想的识别效果，且整体识别效果要优于QDA、LDA、朴素贝叶斯、决策树、LogitBoost及RobustBoost等经典机器学习方法，基于准确率、召回率、特效度、精确度、F-measure等指标的多重评价结果也证明LSSVM模型在地震识别领域具有一定的优越性。

3) 基于RBF核函数的LSSVM模型性能会受惩罚因子、RBF等参数的影响，在样本学习和目标泛化方面仍有一定的改进空间，下一步将结合智能优化算法对其正则化超参数进行寻优，增强LSSVM模型的稳健性，并提高其对含噪地震样本的非线性求解能力。另外，本文研究仅限于识别地震波形，若用于地震预警等，需要考虑辨识模型的运算速度与预警时效，将在后续研究中对此进行补充。

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Research on Identification of Seismic Event Properties Based on Least Squares Support Vector Machine and Entropy Feature
PANG Cong1,2,3     LIAO Chengwang1,2,3     JIANG Yong1,2,3     CHENG Cheng4     WU Tao1,2,3     SHU Peng5     DING Wei1,2,3
1. Institute of Seismology, CEA, 40 Hongshance Road, Wuhan 430071, China;
2. Hubei Key Laboratory of Early Warning, 48 Hongshance Road, Wuhan 430071, China;
3. Hubei Earthquake Agency, 48 Hongshance Road, Wuhan 430071, China;
4. School of Mathematics and Information Technology, Yuncheng University, 1155 West-Fudan Street, Yuncheng 044031, China;
5. School of Computer Science, Nanhua University, 28 West-Changsheng Road, Hengyang 421001, China
Abstract: Natural seismic event property recognition used to rely on manual detection of seismic waveforms, leading to insufficient automation and large errors. To solve this problem, using least squares support vector machine(LSSVM) in machine learning and feature parameters such as permutation entropy, approximate entropy and Shannon entropy in information theory, we develop the Entropy-LSSVM seismic waveform feature extraction and event property recognition model. Based on a total of 500 waveform data from the 2021 Qinghai Maduo MS7.4 earthquake, Yunnan Yangbi seismic event and an artificial blast disturbance event, we design several random extraction sub-experiments with different training and testing ratios to verify the effectiveness of the model using accuracy, recall, effectiveness, precision and F-measure. The experimental results show that the entropy feature is effective in distinguishing natural and non-natural seismic event waveforms, and the overall performance of the model is better than that of QDA, LDA, plain Bayes, decision tree, LogitBoost, and RobustBoost, etc. The recognition accuracy and recall of the training set/test set ratio of 3∶2 can reach 99.00% and 96.97%. The recognition accuracy can reach more than 98%, even with only 50 entries in the training set, which provides some reference value for the effective screening of natural seismic events.
Key words: seismic event identification; least squares support vector machine(LSSVM); entropy feature; Maduo earthquake; Yangbi earthquake