基于人工神经网络的非均匀固相应力模型

RESEARCH ON HETEROGENEOUS SOLID STRESS MODEL BASED ON ARTIFICIAL NEURAL NETWORK

最小多尺度理论EMMS已经被引入多相质点网格法MP-PIC中,建立了非均匀EMMS固相应力模型.但现有的非均匀固相应力模型计算中,中间步骤繁琐且花费时间长.采用人工拟合的方式能获得非均匀固相应力表达式,但需要人为确定拟合变量和拟合函数,且针对于非均匀固相应力这种高度非线性函数所得到的拟合精度不高、用于MP-PIC模拟的结果相比原EMMS固相应力模型结果存在偏差.针对上述问题,本文提出通过机器学习的方法,规避对固相体积分数的局部分布情况的表征,并提出和建立能考虑颗粒浓度详细分布的人工神经网络ANN固相应力模型.首先,基于局部颗粒浓度和颗粒非均匀分布指数建立了双变量的ANN固相应力模型;进一步将当前网格及其周边网格颗粒浓度组成的序列来详细表征颗粒浓度分布,并建立相应的ANN固相应力模型.然后,将两种模型与EMMS固相应力模型进行了对比并测试了网格分辨率和粗化率对模型的影响.研究表明:基于ANN固相应力模型的模拟结果对EMMS固相应力模型结果有较高的还原度,同时具有一定的网格分辨率无关性和粗化率无关性.

The Energy-Minimization Multi-Scale(EMMS)theory has been introduced into the multiphase particle-incell(MP-PIC)method to establish the heterogeneous EMMS solid stress model to account for the effect of non-uniform solid distribution.However,the calculation process is very complex and also very time consuming for this heterogeneous solid stress model.The expression of the heterogeneous EMMS solid stress can be obtained by manual fitting method.However,the fitting variable describes heterogeneous solid distribution as well as the fitting function describe the shape of solid stress are required for manually fitting.Since the heterogeneous solid stress function is highly nonlinear in nature,the fitting precision is not high enough for the manually fitting model.And there is an obvious deviation between the fitting correlation and the original EMMS solid stress,because it is hard to find out an appropriate parameter to characterize the heterogeneous solid concentration distribution as well as to find out an appropriate fitting function.In order to solve the above problems,an artificial neutral network(ANN)based machine learning method was proposed to avoid the characterization of the local distribution of solid volume fraction.Subsequently an ANN solid stress model which accounts for the detailed distribution of particle concentration was proposed to improve the fitting accuracy.Firstly,a two-marker based ANN solid stress model was established based on local particle concentration and particle non-uniform distribution index.Further,particle concentrations in the current cell and its neighboring cells were arrayed to represent the particle concentration distribution,thus to establish the ANN solid stress model based on particle concentration distribution.Then,the two models are compared with the EMMS solid stress model,and the effects of grid resolution and coarse-graining ratio on the model are also tested.The simulation results predicted with ANN model agreed well with that of the EMMS solid stress model,and the dependence of simulation results on grid resolution and coarse-graining ratio was also reduced.