计算机系统应用  2001, Vol. 29 Issue (9): 212-218 PDF

Structure Deformation Prediction Model Based on LSTM and Orthogonal Parameter Optimization
GAN Wen-Juan, CHEN Yong-Hong, HAN Jing, WANG Ya-Fei
School of Information Engineering, Chang’an University, Xi’an 710064, China
Foundation item: National Key Research and Development Program of China (2018YFC0808706)
Abstract: With the vigorous development of social economy, the demand for large buildings such as subways, tunnels, and bridges is growing. Through analyzing the structural deformation data, it can judge the future development trend of the structure so that emergency measures can be taken in advance to prevent the occurrence of disasters. Due to the instability and nonlinearity of deformation monitoring data, the prediction of monitoring data has become a problem in structural monitoring researches. Aiming at the problems of structural deformation prediction models, a long and short-term memory network (LSTM) structural deformation prediction model is proposed based on orthogonal parameter optimization. The long-term memory of the time series can be obtained through the LSTM network structure, and the internal time characteristics of the structural deformation data can be fully mined, the parameters of the LSTM model can be optimized through the orthogonal experiment. Finally, the model was verified by measured data. Experimental results show that the predicted value of the model is closed to the actual monitoring value. Compared with the WNN, DBN-SVR, and GRU models, the average RMSE, MAE, and MAPE are reduced by 56.01%, 52.94%, and 52.78%, respectively. The LSTM structural deformation prediction model based on orthogonal parameter optimization proposed in this study is an effective structural settlement method, which provides reliable information for the safe construction and operation of the structure, and is of great significance to ensure the safety of the structure.
Key words: structural deformation prediction     deep learning     LSTM     orthogonal experiment

1 引言

2 基本理论 2.1 循环神经网络

RNN作为一种典型的神经网络(图1), 依然由输入层, 隐藏层, 输出层组成, 其本质特点是在网络层中既有前馈连接又有反馈连接, 因此网络的输出取决于当前时刻的输入和前一时刻隐藏层的输出, 能够有效利用时间序列的依赖关系来获得时间特征, 使它在处理时间序列上有更大的优势. 同时RNN模型也存在问题, 当时间跨度过大时, 会出现由于梯度爆炸和梯度消失而导致RNN模型难以训练, 预测结果不准确等问题.

 图 1 RNN网络模型展开图

2.2 长短时记忆模型

 图 2 LSTM模型结构图

 图 3 LSTM记忆块结构图

 ${c_t} = {f_t} \odot {c_{t - 1}} + {i_t} \odot {\tilde c_t}$ (1)
 ${h_t} = {o_t} \odot \tanh \left( {{c_t}} \right)$ (2)
 $\left[ {\begin{array}{*{20}{l}} {{{\tilde c}_t}} \\ {{o_t}} \\ {{i_t}} \\ {{f_t}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\tanh } \\ \sigma \\ \sigma \\ \sigma \end{array}} \right]\left( {W\left[ {\begin{array}{*{20}{l}} {{x_t}} \\ {{h_{t - 1}}} \end{array}} \right] + b} \right)$ (3)

2.3 正交试验

3 基于正交参数优化对的LSTM结构变形预测模型

 ${X_{tr}} = {\left[ {\begin{array}{*{20}{c}} {{x_1}}\!\!&{{x_2}}\!\!&{{x_3}}\!\!& \cdots \!\!&{{x_L}} \\ {{x_2}}\!\!&{{x_3}}\!\!&{{x_4}}\!\!& \cdots \!\!&{{x_{L + 1}}} \\ \cdots\!\! & \cdots \!\!& \cdots \!\!& \cdots \!\!& \cdots \\ {{x_{M - L}}}\!\!&{{x_{M - L + 1}}}\!\!&{{x_{M - L + 2}}}\!\!& \cdots \!\!&{{x_{M - 1}}} \end{array}} \right]_{\left( {M - L} \right) \times L}}$ (4)
 ${Y_{tr}}{\rm{ = }}{\left[ {\begin{array}{*{20}{c}} {{{{x}}_{L + 1}}}&{{x_{L + 2}}}&{{x_{L + 3}}}& \ldots &{{x_M}} \end{array}} \right]^{\rm T}}_{1 \times \left( {M - L} \right)}$ (5)
 ${\hat Y_{tr}} = \Phi \left( {{X_{tr}}} \right)$ (6)
 ${X_T} = {\left[ {\begin{array}{*{20}{c}} {{x_{M - L + 1}}}\!\!&{{x_{M - L + 2}}}\!\!&{{x_{M - L + 3}}}\!\!& \ldots \!\!&{{x_M}} \\ {{x_{M - L + 2}}}\!\!&{{x_{M - L + 3}}}\!\!&{{x_{M - L + 4}}}\!\!& \ldots \!\!&{{x_{M + 1}}} \\ \ldots \!\!& \ldots \!\!& \ldots \!\!& \ldots \!\!& \ldots \\ {{x_{N - L}}}\!\!&{{x_{N - L + 1}}}\!\!&{{x_{N - L + 2}}}\!\!& \ldots \!\!&{{x_{N - 1}}} \end{array}} \right]_{\left( {N - M} \right) \times L}}$ (7)

 ${\hat Y_t} = g\left( {W \cdot {S_t} + b} \right)$ (8)

 图 4 LSTM预测模型

4 实验 4.1 数据及数据预处理

 ${\tilde X_i}\; = \;\frac{{\left( {{X_i}\; - \;{X_{\rm min}}} \right)\;}}{{\left( {{X_{\rm max}}\; - \;{X_{\rm min}}} \right)}}\;1 \le i \le N$ (9)

 图 5 数据预处理

4.2 模型评价指标

 $RMSE = \sqrt {\dfrac{1}{N}\displaystyle \sum\limits_{i = 1}^N {{{({y_i} - {{\hat y}_i})}^2}} }$ (10)
 $MAE = \frac{1}{N}\mathop \sum \limits_{i = 1}^N |{\hat y_i} - {y_i}|$ (11)
 $MAPE = \frac{1}{N}\mathop \sum \limits_{i = 1}^N \Bigg|\frac{{{{\hat y}_i} - {y_i}}}{{{y_i}}}\Bigg| \times 100{\rm{\% }}$ (12)

4.3 实验结果及分析 4.3.1 模型参数优化

LSTM模型的超参数对预测结果的影响很大, 因此通过分析对模型预测性能影响较大的参数, 将正交试验的因素种类设置为LSTM预测模型的迭代次数、隐含层节点个数、学习率、输入层节点数、批处理大小, 分别用A、B、C、D、E表示, 并依据现有经验将每种因素的水平设置为4个等级, 分别用数字1、2、3、4表示, 具体的参数设置情况如表1所示.

 图 6 模型预测结果图

4.3.2 模型对比分析

 图 7 不同模型对比实验

5 结论

 [1] Armstrong JS, Green KC, Graefe A. Golden rule of forecasting: Be conservative. Journal of Business Research, 2015, 68(8): 1717-1731. DOI:10.1016/j.jbusres.2015.03.031 [2] Stojanovic B, Milivojevic M, Ivanovic M, et al. Adaptive system for dam behavior modeling based on linear regression and genetic algorithms. Advances in Engineering Software, 2013, 65: 182-190. DOI:10.1016/j.advengsoft.2013.06.019 [3] Wang QJ, Wang CC, Xie RA, et al. An improved SCGM(1, m) model for multi-point deformation analysis . Geosciences Journal, 2014, 18(4): 477-484. DOI:10.1007/s12303-014-0012-z [4] Dai B, Gu CS, Zhao EF, et al. Statistical model optimized random forest regression model for concrete dam deformation monitoring. Structural Control and Health Monitoring, 2018, 25(6): e2170. DOI:10.1002/stc.2170 [5] Deng JL. Introduction to grey system theory. The Journal of Grey System, 1989, 1(1): 1-24. [6] 朱惠群, 陈洪凯. 基于灰色-模糊马尔可夫链模型的滑坡变形预测. 三峡大学学报(自然科学版), 2013, 35(2): 53-55, 60. [7] 郝忠, 付操, 丁欣, 等. 优化的多变量变步长灰色模型及其在路基沉降预测中的应用. 路基工程, 2018(3): 55-61, 68. [8] 陈国良, 林训根, 岳青, 等. 基于时间序列分析的桥梁长期挠度分离与预测. 同济大学学报(自然科学版), 2016, 44(6): 962-968. [9] 徐北海, 徐旭, 刘淑官, 等. 时间序列分析方法在变形数据处理中的应用研究. 测绘地理信息, 2016, 41(1): 61-64, 69. [10] Luo JH, Wu C, Liu XL, et al. Prediction of soft soil foundation settlement in Guangxi granite area based on fuzzy neural network model. IOP Conference Series: Earth and Environmental Science, 2018, 108(3): 032034. [11] Guo J, Ding LY, Luo HB, et al. Wavelet prediction method for ground deformation induced by tunneling. Tunnelling and Underground Space Technology, 2014, 41: 137-151. DOI:10.1016/j.tust.2013.12.009 [12] Pu FL, Xu ZZ, Chen HY, et al. A DLM-LSTM framework for north-south land deformation trend analysis from Low-Cost GPS sensor time series. Journal of Sensors, 2018, 2018: 3054295. [13] Jiang YZ, Liu HZ, Liu JY. LS-SVM-Markov model for dam deformation prediction. Applied Mechanics and Materials, 2013, 423–426: 1144-1149. [14] Chen SY, Gu CS, Lin CN, et al. Safety monitoring model of a super-high concrete dam by using RBF neural network coupled with kernel principal component analysis. Mathematical Problems in Engineering, 2018, 2018: 1712653. [15] Xin JZ, Zhou JT, Yang SY, et al. Bridge structure deformation prediction based on GNSS data using Kalman-ARIMA-GARCH model. Sensors, 2018, 18(1): 298. DOI:10.3390/s18010298 [16] Yang BB, Yin KL, Lacasse S, et al. Time series analysis and long short-term memory neural network to predict landslide displacement. Landslides, 2019, 16(4): 677-694. DOI:10.1007/s10346-018-01127-x