Abstract: To address the problems of long training time and low prediction accuracy due to the need to build a neural network model for each frequency point independently and to select the initial value of the neural network model independently and randomly for multipoint frequency-domain vibration response prediction by a Multiple Input Multiple Output Artificial Neural Network (MIMO-ANN),a multi-point frequency-domain vibration response prediction method based on MIMO-ANN and model transfer learning was proposed.The data-driven multipoint frequency-domain vibration response prediction problem under unknown uncorrelated multi-source loads was described formally,and its differences was compared with the data-driven multi-point frequency-domain vibration response prediction problem under known uncorrelated multi-source loads.The self-power spectra known vibration response at a certain frequency point were constructed as the input and the self-power spectra of with unknown vibration response as the output,and the unknown point vibration response prediction model at that frequency was built using MIMO-ANN;based on the continuity of the transfer function in the frequency domain,the weights of the trained MIMO-ANN at this frequency were used as the initial values of the MIMO-ANN at neighboring frequency;the historical data at this neighboring frequency were used for training to obtain the prediction model at this frequency;the process was repeated until all the models at all frequencies were trained.This method solved the matrix pathological inverse problem,obtained better initial values of the neural network model,was not easy to fall into local optimum and speeded up the convergence of the neural network.The results of multi-point response prediction on the experimental data set of cylindrical shell acoustic vibration showed that the proposed method had higher prediction accuracy and better training efficiency than the methods based on no transfer learning ANN,multiple linear regression and transfer function under the condition of unknown load from multiple sources.

Key words: multi-point frequency domain response prediction, unknown multi-source load, multiple inputs and multiple outputs neural network, model transfer learning, network weights

摘要： 针对多输入多输出神经网络(MIMO-ANN)进行多点频域振动响应预测时需要为每个频率点独立建立神经网络模型、独立随机选择神经网络模型初值导致的训练时间长、预测精度低等问题,提出了一种基于多输入多输出人工神经网络(MIMO-ANN)和模型迁移学习的多点频域振动响应预测方法。本研究对于多源不相关载荷未知条件下的基于数据驱动的振动响应预测问题进行了形式化描述,并比较了其与不相关多源载荷已知情况下基于数据驱动的多点频域振动响应预测问题的不同之处。首先,将某频率点下的多个振动响应已知的测点的自功率谱作为输入,多个振动响应未知的测点的自功率谱作为输出,将两部分历史数据集构造成为训练集,利用MIMO-ANN建立该频率下的未知点振动响应预测模型;其次,根据传递函数在频域的连续性,利用该频率下训练好的MIMO-ANN的权值迁移到相邻频率作为其MIMO-ANN的初值;再次,利用此相邻频率下的历史数据进行训练,从而得到此频率下的预测模型;最后,不断循环此过程,直到所有频率点的模型全部训练完成。该方法解决了矩阵病态求逆问题,可以获得更好的神经网络模型的初值,不容易陷入局部最优,加快了神经网络的收敛速度。在圆柱壳声振实验数据集的多点响应预测结果表明,在多源载荷未知条件下,该方法比基于无迁移学习神经网络、多元线性回归、传递函数的方法,预测精度、训练效率更高。

关键词: 多点频域振动响应预测, 多源未知载荷, 多输入多输出神经网络, 模型迁移学习, 网络权值