改进自适应指数平滑法及其在基坑变形预测中的应用

燕俊松; 石泉彬; 刘如兵

doi:10.20265/j.cnki.issn.1007-2993.2024-0168

改进自适应指数平滑法及其在基坑变形预测中的应用

doi: 10.20265/j.cnki.issn.1007-2993.2024-0168

泰州职业技术学院建筑工程学院，江苏泰州　225300

基金项目: 江苏省发改委省级工程研究中心建设项目（JPERC2021-168）；江苏省高等职业教育高水平专业群建设项目（2020-80）

详细信息

作者简介:
燕俊松，男，1992年生，博士，讲师，主要从事地下工程风险管理研究。E-mail：yanjunsong@tzpc.edu.cn

中图分类号: TU473; TU196
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- 文章访问数: 4
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出版历程
- 收稿日期: 2024-04-16
- 修回日期: 2024-07-29
- 录用日期: 2024-10-29
- 刊出日期: 2025-10-10

Improved adaptive exponential smoothing method and its application evaluation in excavation deformation prediction

Institute of Architectural Engineering, Taizhou Polytechnic College, Taizhou 225300, Jiangsu, China

摘要

摘要: 对基坑开挖变形作出可靠预测有助于提高施工安全性。对现有自适应指数平滑法进行了改进，摒弃采用遍历法求解最优平滑系数α的传统思路，以均方误差（MSE）作为损失函数，推导了一次、二次和三次指数平滑模型的MSE对α的梯度表达式，进而采用梯度下降法求解最优α值。与原方法相比，改进方法在最优平滑模型选择及平滑系数优化方面展现出与原方法相当的性能，且在适当的超参数（尤其是学习率）设置情况下，寻优效率显著提升。在此基础上，基于1900组基坑变形序列的应用，较为系统地评估了改进自适应指数平滑法在基坑变形预测中的适用性和可靠性，并探讨了预测步长和训练序列长度对预测性能的影响，据此提出了基坑变形预测优化方案。
- 深基坑 /
- 变形预测 /
- 改进自适应指数平滑法 /
- 梯度下降法 /
- 应用评价
Abstract: Reliable prediction of excavation deformation contributes to improved construction safety. The existing adaptive exponential smoothing method has been improved by abandoning the traditional approach of solving for the optimal smoothing coefficient α through exhaustive search. Instead, mean squared error (MSE) was used as the loss function, and the gradient expressions of MSE with respect to α for single, double, and triple exponential smoothing models were derived. Subsequently, the gradient descent method is applied to solve for the optimal α value. Compared to the original method, the improved method demonstrates comparable performance in optimal model selection and coefficient optimization, and significantly enhances optimization efficiency with appropriate hyper-parameter (especially learning rate) settings. Based on the application to 1900 sets of excavation deformation sequences, the applicability and reliability of the improved adaptive exponential smoothing method in deformation prediction have been systematically evaluated, and the effects of prediction step size and training sequence length on prediction performance have been explored. Consequently, an optimized scheme for excavation deformation prediction is proposed.
- deep foundation pit /
- deformation prediction /
- improved adaptive exponential smoothing method /
- gradient descent algorithm /
- application evaluation

HTML全文

图 1 改进自适应指数平滑法流程图

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图 2 改进方法与原方法的平滑系数优化结果对比

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图 3 指数平滑模型的MSE-$ \alpha $曲线以及改进方法与原方法的平滑系数优化过程对比

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图 4 改进方法与原方法拟合训练数据的结果对比

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图 5 改进方法与原方法训练时间对比

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图 6 不同预测步长下的预测表现

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图 7 不同训练序列长度下的预测表现

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表 1 改进自适应指数平滑法预测评价指标

训练序列长度	预测步长/期	$ \mathrm{RMSE} $/mm	$ {P}_{2} $
10	1	0.8	0.98
	2	1.13	0.94
	3	1.59	0.82
	4	2.1	0.75
	5	2.7	0.66
15	1	0.72	0.99
	2	1.04	0.96
	3	1.46	0.86
	4	1.91	0.78
	5	2.43	0.69
20	1	0.72	0.99
	2	1.03	0.95
	3	1.41	0.86
	4	1.83	0.78
	5	2.31	0.7
25	1	0.69	0.99
	2	0.98	0.96
	3	1.33	0.87
	4	1.73	0.8
	5	2.18	0.71
30	1	0.7	0.99
	2	0.99	0.96
	3	1.31	0.87
	4	1.7	0.79
	5	2.08	0.71

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