面向冷弯型钢构件弹性屈曲临界荷载预测的BP神经网络训练算法比选  

Evaluation of BP Neural Network Algorithms for Predicting Elastic Buckling Loads on Cold-Formed Steel Components

作　　者：戴宜凌 王少快 尹凌峰[1] DAI Yiling;WANG Shaokuai;YIN Lingfeng(School of Civil Engineering,Southeast University,Nanjing 211189,P.R.China)

机构地区：[1]东南大学土木工程学院,南京211189

出　　处：《应用数学和力学》2025年第2期129-141,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(52278150)。

摘　　要：弹性屈曲临界荷载是准确评价冷弯型钢构件承载力的重要指标.利用人工神经网络(artificial neural networks,ANNs)模型对冷弯C型截面轴压构件的屈曲临界载荷进行了预测,将影响屈曲的几何参数和有限条法所得的计算结果作为数据集,对神经网络模型进行了训练、验证和测试.基于最优化理论,采用6种不同的优化算法进行了模型的训练,并比较了不同算法的网络模型性能.通过随机网格搜索确定最优超参数,使用3种统计参数来评估训练后的人工神经网络的性能,以得到最适合预测屈曲临界荷载的神经网络模型.结果表明:Levenberg-Marquardt(L-M)算法在非线性最小二乘问题上相较于其他算法具有更高的准确性,多次训练后,L-M算法使模型预测误差非常小,而其他算法在准确度上不及L-M算法.The elastic buckling critical load is a crucial indicator for accurately assessing the load-bearing capacity of cold-formed steel components.The artificial neural networks were used to predict the buckling loads on cold-formed flanged steel columns,with geometric parameters and finite strip method results as the dataset.Six optimization algorithms based on the optimization theory were applied to train the networks,with their performances compared.Optimal hyperparameters were determined through random grid search.Three statistical parameters were used to evaluate the networks’post-training performances.The Levenberg-Marquardt(L-M)algorithm demonstrates higher accuracy in nonlinear least squares problems,significantly reducing prediction errors after multiple trainings,and outperforming other algorithms.

关 键 词：BP神经网络 最优化理论 弹性屈曲临界荷载 冷弯型钢 非线性最小二乘 

分 类 号：O31[理学—一般力学与力学基础]