基于POD-代理模型的连接结构非线性振动响应轻量化表征方法研究

Lightweight characterization method of nonlinear vibration responses of jointed structures based on POD- surrogate model

  • 摘要: 本文采用本征正交分解(proper orthogonal decomposition, POD)对非线性振动响应进行降维,利用自适应神经网络(adaptive neural network, ANN)代理模型预测POD正交基的投影系数,建立了一种连接结构非线性动力学响应的轻量化表征与高效预测方法。本文以含螺栓连接的非线性动力学系统为研究对象,使用拉丁超立方采样技术构造设计参数样本,运用时-频域转换的谐波平衡法(alternating frequency-time harmonic balance method, AFT-HBM)构建非线性频率响应快照数据集,利用POD-ANN建立了连接部位特征参数、激励幅值与投影系数的映射关系。利用改进的赤池信息准则(Akaike’s information criterion, AIC)量化评估模型的预测效果,并与三种文献方法进行对比。结果表明:本文方法能够实现非线性振动响应的高效预测,在大规模采样问题中的计算效率优于文献方法;在规模为104的采样任务中耗时仅为AFT-HBM单次计算的1/4,降维比可达50倍,而误差不超过1.5%。

     

    Abstract: In this study, a methodology is proposed for the lightweight characterization and efficient prediction of the nonlinear dynamic responses in jointed structures. Proper orthogonal decomposition (POD) is employed to reduce the dimensionality of nonlinear vibration responses, whereas an adaptive neural network (ANN) surrogate model is utilized to predict the projection coefficients associated with the POD orthogonal basis. A nonlinear dynamic system with a bolted joint is considered as the research object. Latin hypercube sampling is employed to generate a sample set of design parameters. The alternating frequency-time harmonic balance method (AFT-HBM) is used to generate a snapshot dataset of nonlinear frequency responses. The mapping relationship between the characteristic parameters of the joint, the excitation amplitude, and the projection coefficients is established using the POD-ANN approach. The predictive performance of the model is quantitatively evaluated using the improved Akaike’s information criterion (AIC) and compared with three methods reported in the literature. The results demonstrate that the proposed method achieves efficient prediction of nonlinear vibration responses and is computationally more efficient than existing methods for large-scale sampling problems. In a sampling task with a scale of 104, the computational time is reduced to one-quarter of that required for a single AFT-HBM calculation, and the dimensionality reduction ratio reaches 50, with the error remaining below 1.5%.

     

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