Dan Wenjiao, Yue Xinxin, Yu Min, Li Tongjie, Zhang Jian
College of Mechanical Engineering, Anhui Science and Technology University, Chuzhou 233100, China.
College of Architecture, Anhui Science and Technology University, Bengbu 233000, China.
Materials (Basel). 2023 Jun 28;16(13):4671. doi: 10.3390/ma16134671.
Reinforced concrete (RC) is the result of a combination of steel reinforcing rods (which have high tensile) and concrete (which has high compressive strength). Additionally, the prediction of long-term deformations of RC flexural structures and the magnitude of the influence of the relevant material and geometric parameters are important for evaluating their serviceability and safety throughout their life cycles. Empirical methods for predicting the long-term deformation of RC structures are limited due to the difficulty of considering all the influencing factors. In this study, four popular surrogate models, i.e., polynomial chaos expansion (PCE), support vector regression (SVR), Kriging, and radial basis function (RBF), are used to predict the long-term deformation of RC structures. The surrogate models were developed and evaluated using RC simply supported beam examples, and experimental datasets were collected for comparison with common machine learning models (back propagation neural network (BP), multilayer perceptron (MLP), decision tree (DT) and linear regression (LR)). The models were tested using the statistical metrics R2, RAAE, RMAE, RMSE, VAF, PI, A10-index and U95. The results show that all four proposed models can effectively predict the deformation of RC structures, with PCE and SVR having the best accuracy, followed by the Kriging model and RBF. Moreover, the prediction accuracy of the surrogate model is much lower than that of the empirical method and the machine learning model in terms of the RMSE. Furthermore, a global sensitivity analysis of the material and geometric parameters affecting structural deflection using PCE is proposed. It was found that the geometric parameters are more influential than the material parameters. Additionally, there is a coupling effect between material and geometric parameters that works together to influence the long-term deflection of RC structures.
钢筋混凝土（RC）是由具有高抗拉强度的钢筋和具有高抗压强度的混凝土组合而成的。此外，预测RC受弯结构的长期变形以及相关材料和几何参数的影响程度，对于评估其在整个生命周期内的适用性和安全性至关重要。由于难以考虑所有影响因素，预测RC结构长期变形的经验方法有限。在本研究中，使用了四种流行的代理模型，即多项式混沌展开（PCE）、支持向量回归（SVR）、克里金法和径向基函数（RBF）来预测RC结构的长期变形。使用RC简支梁实例开发并评估了代理模型，并收集了实验数据集，以便与常见的机器学习模型（反向传播神经网络（BP）、多层感知器（MLP）、决策树（DT）和线性回归（LR））进行比较。使用统计指标R2、RAAE、RMAE、RMSE、VAF、PI、A10指数和U95对模型进行了测试。结果表明，所有四个提出的模型都能有效预测RC结构的变形，PCE和SVR的精度最高，其次是克里金模型和RBF。此外，就RMSE而言，代理模型的预测精度远低于经验方法和机器学习模型。此外，还提出了使用PCE对影响结构挠度的材料和几何参数进行全局敏感性分析。结果发现，几何参数比材料参数的影响更大。此外，材料和几何参数之间存在耦合效应，共同影响RC结构的长期挠度。
