Research On Topology Optimization Based On Data Driven And Physical Constraint Assistance

Topology optimization is an effective method for lightweight design of aircraft structure,and has been widely used in the design of vehicle cabin and inter-stage,satellite main structure and secondary structure in recent years.However,topology optimization is faced with the problem of high computational cost,and the change of boundary conditions need to be optimized and solved again,so that existing solution data cannot be fully used to guide the solution of the new structure design.Therefore,deep learning technology is used in this work to improve the computational efficiency of topology optimization and build a low-cost surrogate model.Its core idea is to use neural network model to learn a large number of existing sample data.And the trained model can solve the new problem quickly.At the same time,this work studies the comprehensive influence of data drive and physical performance(compliance,heat conduction,etc.)on the neural network model,aiming to build a more comprehensive surrogate model with better physical performance prediction.The results show that the surrogate model can speed up the design process,improve the design efficiency,and has the characteristics of wide ability,fast calculation and high precision.The main works and conclusions are as follows:(1)Aiming at the problem of large computation consumption and slow solving speed in topology optimization solution process,the method framework of data-driven topology optimization surrogate model is studied,including modeling method,training data generation,loss function and evaluation metric,etc.The key point is to construct the mapping relationship between the design subject and the optimized structure under given boundary conditions,load and constraints by learning the information in the existing data,and then train the surrogate model that can output the optimized structure quickly by selecting the appropriate model.The validity of the proposed framework is verified by experiments.(2)In order to solve the problem that the solution of the structural compliance takes a long time in topology optimization or model training,an efficient prediction method of structure compliance based on data-driven is proposed.In this work,the combination model of convolutional neural network and fully connected neural network are established to build the mapping relationship between the high-dimensional data composed of structural condition parameters and material distribution and the low-dimensional data of compliance value,which can effectively solve the nonlinear and complex problem of compliance.The experimental results show that the prediction errors of the model are less than 0.01,which indicates that the surrogate model is high precision.(3)As for the purely data-driven surrogate model,its construction process ignores the mechanics knowledge of topology optimization,which can not guarantee the continuity of structure and better physical properties(compliance).In this section,the surrogate model is constructed by introducing physical constraints into the neural network model.The key method is to construct the compliance value as the regular term of the loss function,and the back propagation of gradient is used to update the parameters of the neural network during model training.The experimental results show that the surrogate model with physical constraints can effectively reduce the disconnection of the structure and ensure good physical performance.In addition,experiments with different dataset scale show that the introduction of physical constraints can reduce the sample scale of model training when obtaining the same precision model.(4)In view of the difficulties in constructing surrogate model for multi-material topology optimization,such as the inability to clearly represent the types of multi-materials and the lack of the better modeling method,the construction method of surrogate model for multi-material topology optimization based on data drive is studied in this work.In this study,each material in the multi-material topology optimization is characterized as a single channel and coded by combining neural network.Experiments show that the proposed coding method is effective and solves the difficult combination of multi-material topology optimization and deep learning.In addition,the effects of multi-material topology optimization modeling as regression task and classification task are compared in this section.Several examples are used to verify that the regression task is slightly better than the classification task,and a better modeling method is obtained.In addition,the experimental results show that the main factors affecting the prediction accuracy of the surrogate model are topology optimization problem,the number of material classes,and the scale of data,while the irrelevant factors mainly include the size of design domain and the elastic modulus of material.In summary,aiming at accelerating the solving speed of topology optimization and improving the computational efficiency,a topology optimization method based on data drive and physical constraint assistance is studied in this paper.The paper focuses on accelerating the solving speed of topology optimization and improving the computational efficiency,and studies the topology optimization method based on data drive and physical constraint assistance.The surrogate model is built by data-driven principle which learn the information in the existing data samples.The trained model can guide the rapid solution of new problems.By further introducing physical constraints and considering the mechanics knowledge of topology optimization,the prediction effect of the model is improved.On the whole,The method studied in this paper realizes the quick solution of topology optimization,enriches the method system of topology optimization,and further improves the design ability of topology optimization.