灰色神经元拟合算法在有限元模型修正中的应用

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To conquer the difficulty in using less data to establish precise mathematical prediction model of the parameters and modal in the process of updating finite element model, a new mathematical model based on the gray theory of adjusting vector neurons weights is introduced. Several different mathematical prediction models are fitted by using the least squares method of model calculation. Two models with the highest prediction accuracy are picked out to constitute the input of the neuron prediction model. The neuron vector summation method is defined with the purpose of a quick and accurate weight calculation. The network is trained by the samples and the final value of the weights is predicted by Gray prediction theory based on the sequence of the weights, which are established by the vector neuron prediction model. The model based on less data can obtain higher accuracy prediction, which is versatile to meet the requirement of engineering calculation. The effectiveness of this model is verified by update instance of the gearbox＇s finite element model, therefore, an effective way to update the finite element model is provided.针对参数化修正有限元模型过程中难以利用较少数据建立参数与模态的精准数学预测模型问题,提出一种基于灰色理论调整矢量神经元权重的新型数学模型。使用最小二乘法将结构进行模态计算得到的数据拟合出几种不同的数学预测模型,挑取两个预测精度最高的模型作为输入端,建立神经元模型。为快速准确地计算权重,自定义神经元矢量求和运算方法。输入样本训练网络,根据权重的变化序列运用灰色理论预测权重的最终值,完成矢量神经元预测模型的建立。这种建模方法依据较少数据即可得到较高的预测精度,通用性好,符合工程计算需要。通过齿轮箱有限元模型修正实例对这种预测模型的有效性进行验证,该方法可以为结构的有限元模型修正提供有效路径。