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投稿时间：2022-02-22 修订日期：2022-06-09
投稿时间：2022-02-22 修订日期：2022-06-09
中文摘要: 大坝变形监控模型的优劣主要体现在模型泛化能力的高低。模型泛化能力指模型对训练集以外样本的预测能力，而欠拟合和过度拟合是导致模型泛化能力不高的主要原因。AIC和BIC准则是目前常用的模型识别方法，但是不能定量比较和评价模型的过度拟合程度。本文通过定义过度拟合系数OC量化模型过度拟合程度，同时采用复相关系数R定量评判模型是否欠拟合，建立了R–OC模型识别准则。首先，将大坝变形监测序列划分为拟合时段数据和验证时段数据，采用全回归方法对拟合时段数据进行拟合，构建多种位移监控模型。再根据监控模型的估计值和估计误差的概率分布确定异常监测数据的预警界限，计算各监控模型的误警率FAR。最后，根据不同监控模型对拟合时段和验证时段的拟合和预测误差评价指标（均方根误差RMSE、平均绝对误差MAE、平均绝对百分比误差MAPE），确定过度拟合系数OC；结合复相关系数R，绘制2维散点图，并对各监控模型的泛化能力进行评价。结果表明：过度拟合系数OC同模型的误警率呈良好的相关关系，当过度拟合系数OC小于1时，监控模型没有过度拟合，模型误警率FAR为0，不会发出错误预警；当OC大于1时，模型误警率FAR与OC呈正相关关系。一方面，R–OC模型识别准则通过复相关系数R刻画模型的拟合精度；另一方面，通过过度拟合系数OC定量评判模型的过度拟合程度。对于不同数量的待选模型，R–OC准则均能识别出拟合和预测精度都较高的模型。
Abstract:The advantages and disadvantages of dam deformation monitoring model are mainly reflected in the generalization ability of the model. Model generalization ability refers to the prediction ability of the model for samples outside the training set, and under-fitting and over-fitting are the main reasons for the low generalization ability of the model. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are two commonly used model identification methods at present, but they cannot quantitatively compare and evaluate the over-fitting degree of the model. In this paper, the over-fitting degree of the model is quantified by defining the over-fitting coefficient (OC). At the same time, the complex correlation coefficient (R) is used to quantitatively judge whether the model is under-fitting, and the R–OC model recognition criterion is established. Firstly, the dam deformation monitoring sequence is divided into fitting data and verification data, and the fitting data are fitted by the total regression method to construct a variety of deformation monitoring models. Then, according to the estimation value of the monitoring model and the probability distribution of the estimation error, the early-warning limits of the abnormal monitoring data is determined. The False Alarm Rate (FAR) of each monitoring model is then calculated. Finally, according to the evaluation indexes (root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE)) of fitting and prediction errors of fitting period and verification period of different monitoring models, the OC was determined. The two-dimensional scatter plot was drawn with the use of R, and the generalization ability of each monitoring model was evaluated. The results show that the OC has a good correlation with the FAR of the model. When the OC is less than 1, the monitoring model does not over-fit and will not issue error warning, and the FAR of the model is 0. When OC is greater than 1, the model FAR is positively correlated with OC. On the one hand, the R–OC model identification criterion describes the fitting accuracy of the model by the R. On the other hand, the over-fitting degree of the model is quantitatively evaluated by the OC. For different number of models to be selected, R–OC criteria can identify models with high fitting and prediction accuracy.
文章编号：202200135 中图分类号：TV698.1+1 文献标志码：
基金项目:国家重点研发计划项目（2018YFC0407103）
作者简介:第一作者：张博张 博（1998—），男，硕士生. 研究方向：水工结构工程及基础工程. E-mail：2425345305@qq.com;通信作者：吴震宇, 副教授，E-mail：wuzhenyu@scu.edu.cn
引用文本：
张博,刘健,吴震宇,陈建康,尹川.大坝变形监控模型识别的R–OC准则[J].工程科学与技术,2023,55(3):175-185.
ZHANG Bo,LIU Jian,WU Zhenyu,CHEN Jiankang,YIN Chuan.R–OC Criterion for Dam Deformation Monitoring Model Identification[J].Advanced Engineering Sciences,2023,55(3):175-185.
引用文本：
张博,刘健,吴震宇,陈建康,尹川.大坝变形监控模型识别的R–OC准则[J].工程科学与技术,2023,55(3):175-185.
ZHANG Bo,LIU Jian,WU Zhenyu,CHEN Jiankang,YIN Chuan.R–OC Criterion for Dam Deformation Monitoring Model Identification[J].Advanced Engineering Sciences,2023,55(3):175-185.