基于复数神经网络的粘弹性材料动态模量拟合方法

固体火箭发动机药柱粘弹性材料除具有弹塑性特性，还具有粘滞性，这一特性使得材料变形具有明显的时间效应，本构关系复杂，进行动态力学分析时，动态模量难以有效拟合．本文提出了一种基于(Levenberg-Marquardt, L-M)算法的复数神经网络拟合粘弹性材料动态模量的方法．通过广义Maxwell模型推导得到材料的动态模量表达式，以此构造未定网络参数为复数的神经网络，从而提供了一种输入、输出样本均为复数的神经网络解决方法．将实数L-M训练算法进行改进，衍生到复数领域，提出复数L-M训练算法．通过粘弹性材料实验，将实验数据时温等效转换，获得复数神经网络的训练及测试样本．通过对神经网络进行训练，实现粘弹性材料动态模量的高精度拟合．数值算例表明，与传统神经网络拟合方法相比，所提方法在训练速度和泛化能力方面都有其优越性．

Dynamic Modulus Fitting Method of Viscoelastic Materials Based on Complex Neural Network

The viscoelastic material of solid rocket motor propellant grain not only has elasta-plastic property, but also possesses viscosity property. This property makes the material deformation exhibit obvious time-delay effect and the constitutive relation complex. Therefore it is difficult to fit the dynamic modulus effectively during the dynamic mechanical analysis. In this paper, a complex neural network method based on Levenberg-Marquardt (L-M) algorithm was proposed to fit the dynamic modulus of viscoelastic material. The dynamic modulus of material was obtained by the generalized Maxwell model, and the neural network with undecided complex network parameters was constructed. In this way, a neural network solution with complex input and output samples was provided. The real L-M algorithm was improved and extended to the complex field. Through viscoelastic material experiments, the training and testing samples of the complex neural network were obtained by time-temperature equivalent conversion of experimental data. Through training of the neural network, we achieved high precision fitting for the dynamic modulus of viscoelastic material. Numerical examples showed that compared with the traditional neural network fitting method, the proposed method has superiority in training speed and generalization ability.