基于BKA协同的BP神经网络有限元模型修正

Finite Element Model Updating Based on BKA-BP Collaborative Optimization

摘要: 针对传统有限元模型修正方法收敛缓慢、易陷入局部最优，以及BP神经网络初始参数敏感、易早熟收敛等问题，本文提出一种黑翅鸢优化算法(BKA)协同BP神经网络的有限元模型修正方法。该方法利用BKA算法全局优化能力确定BP网络最优初始权值与阈值，以神经网络构建参数–响应代理模型替代耗时有限元计算，实现待修正参数的全局最优搜索。以6.4米单层平面桁架为研究对象，考虑5根杆件刚度退化，采用拉丁超立方采样生成样本数据，建立5-15-6结构的BP神经网络代理模型。结果表明：杆件弹性模量识别平均误差仅0.47%，前六阶自振频率最大预测误差仅0.0199%，目标函数均方误差收敛至0.0002，验证了方法的高精度与强鲁棒性。本研究为结构的有限元模型修正提供了一种可行的代理模型优化思路，后续有望进一步将该方法拓展至三维复杂结构、含噪声实测数据及多损伤工况等场景。

Abstract: To address the issues of slow convergence and susceptibility to local optima in traditional finite element model updating methods, as well as the sensitivity to initial parameters and premature convergence in BP neural networks, this paper proposes a finite element model updating method based on the Black-winged Kite Algorithm (BKA) collaborating with BP neural networks. This method leverages the global optimization capability of BKA to determine the optimal initial weights and thresholds of the BP network, constructs a parameter-response surrogate model using neural networks to replace time-consuming finite element calculations, and achieves global optimal search for parameters to be updated. Taking a 6.4-meter single-layer planar truss as the research object, considering stiffness degradation of five members, sample data are generated using Latin Hypercube Sampling, and a BP neural network surrogate model with a 5-15-6 structure is established. The results show that the average error of elastic modulus identification for the members is only 0.47%, the maximum prediction error of the first six natural frequencies is only 0.0199%, and the mean square error of the objective function converges to 0.0002, verifying the high accuracy and strong robustness of the proposed method. This study provides a feasible surrogate model optimization approach for finite element model updating of structures, and it is expected that the method can be further extended to scenarios such as three-dimensional complex structures, noisy measured data, and multi-damage cases in future work.