基于SGMD及LWOA-ELM的有限元模型修正

为得到待修正参数与结构响应之间的关系,提高模型修正的效率和精度,提出了一种基于辛几何模态分解(SGMD)和Lévy飞行鲸鱼优化算法(LWOA)优化极限学习机(ELM)的有限元模型修正(FEMU)方法。首先,对加速度频响函数(AFRF)进行SGMD分解,采用能量熵增量法确定重组辛几何分量(SGC)构成SGC矩阵。然后,利用LWOA对ELM的权值和阈值进行优化,提高ELM模型的预测效率,以LWOA-ELM为代理模型映射出待修正参数与SGC矩阵之间的关系。最后,以试验频响函数SGC矩阵与LWOA-ELM模型输出所得矩阵差值的F-范数最小为目标函数,结合LWOA求解待修正参数。算例分析表明,提出的方法用于有限元模型修正有较好的可行性和有效性。以SGC矩阵表征AFRF的修正方法,有较好的噪声鲁棒性;LWOA-ELM作为代理模型预测精度高,泛化能力强。

Finite element model updating based on SGMD and LWOA-ELM

In order to obtain the relationship between updating parameters and structural responses,and improve the efficiency and accuracy of model updating,finite element model updating (FEMU) method based on symplectic geometry mode decomposition (SGMD) and extreme learning machine (ELM) optimized by Lévy flight based whale optimization algorithm (LWOA) is proposed.Firstly,SGMD is applied to decompose acceleration frequency response function (AFRF) data.The reconstructed symplectic geometry components (SGCs) are selected by energy entropy increment method to make the SGC matrix.Then,to improve the prediction accuracy,LWOA is used to optimize the weightings and thresholds of ELM.LWOA-ELM model is established as the surrogate model for the mapping between updating parameters and the SGC matrix of experimental AFRF.Finally,with the minimum Frobenius norm of error between the SGC matrix from tests and those from LWOA-ELM model as the objective function,the updating parameters are obtained by LWOA.Case studies demonstrate that the proposed method is feasible and effective for FEMU.The updating method with SGC to indicate AFRF has good noise robustness.As the surrogate model,LWOA-ELM has high prediction accuracy and strong generalization ability.