基于稀疏多项式混沌展开模型的钢筋混凝土结构长期挠度预测

Long-term Deflection Prediction of Reinforced Concrete Structures Based on Sparse Polynomial Chaos Expansion

钢筋混凝土受弯结构的长期挠度预测对于评价其全寿命周期的可服役性和安全性具有重要意义。文章传统的经验法难以考虑所有的影响因素,为了能够准确预测钢筋混凝土结构的长期挠度,本文使用稀疏多项式混沌展开(polynomial chaos expansion,PCE)模型预测钢筋混凝土结构的长期挠度,并对影响结构挠度的参数进行全局灵敏度分析。使用实验数据集建立和评估稀疏PCE模型,与常见的代理模型(RBF、SVR和Kriging)和常见的机器学习模型(BP神经网络)进行比较,采用十折交叉验证算法对模型进行训练和检验。结果表明,稀疏PCE模型在预测钢筋混凝土结构长期挠度方面均优于常见的代理模型和机器学习模型,其相关系数R^(2)、相对平均绝对误差(RAAE)、相对最大绝对误差(RMAE)和均方根误差(RMSE)分别为0.970、0.108、0.537和0.062。稀疏PCE模型的RMSE值远远优于经验方法。最后,基于稀疏PCE的全局灵敏度分析结果对影响结构挠度的参数进行了重要性排序,其中,瞬时或即时测量的挠度a(i)、跨深比l/h、龄期t’混凝土强度fc’重要性程度较高,且依次递减。稀疏PCE模型可用于钢筋混凝土结构长期挠度预测,并且可量化评估影响钢筋混凝土结构长期适用性的关键因素。

Long-term deflection prediction of reinforced concrete flexural structures is important for evaluating their serviceability and safety throughout their life cycle.Since it is difficult to consider all the influencing factors by empirical methods,in order to be able to accurately predict the long-term deflection of reinforced concrete structures.In this paper,we propose to predict the long-term deflection of reinforced concrete structures by using a sparse polynomial chaos expansion(PCE)model and perform global sensitivity analysis of the parameters affecting the deflection of the structure.Sparse PCE models are built and evaluated by using experimental datasets,compared with common surrogate models(RBF,SVR and Kriging)and common machine learning model(BP neural network).The models are trained and tested by using a ten-fold cross-validation algorithm.The results show that the sparse PCE model outperforms both common surrogate models and machine learning models in predicting the long-term deflection of reinforced concrete structures,with correlation coefficients R^(2),relative average absolute error(RAAE),relative maximum absolute error(RMAE),and root-mean-square error(RMSE)of 0.970,0.108,0.537,and 0.062,respectively.Moreover,the sparse PCE model's RMSE value is much better than the empirical method.Finally,the parameters affecting structural deflection were ranked in order of importance based on the results of global sensitivity analysis of the sparse PCE,where the instantaneous or immediate measured deflection a(i),span-to-depth ratio l/h,and age t'concrete strength fc'are more important,and successively decreasing.The sparse PCE model can be used for long-term deflection prediction of reinforced concrete structures and can be evaluated to quantify the key factors affecting the long-term suitability of reinforced concrete structures.