The Ensemble Surrogate Model Optimization Of The Loading Path For T-shape Tube Hydroforming

Tube Hydroforming(THF)is to press the tube into the mold cavity by inter pressure and axial feed of the tube to form the desired shapes.Hydroforming technology has become more and more widely used in aviation and automotive area because of its advantages such as high forming strength,light weight,and lower processing time.The optimal design of the loading path has always been a key link in the THF technology.The direct use of finite element analysis to optimize is inefficient.Use the surrogate model to fit and predict the response of the structure is the hotspot.However,in practical engineering problem.The application of the surrogate model still faces problems such as low accuracy and insufficient forecasting ability.In order to improve the ability and accuracy of prediction of surrogate model,this paper takes the optimization design of loading path of T-shape tube hydroforming as an example,summarizes the current research status of tube hydroforming technology,and uses cross-validation to solve the problems of insufficient predictability and low prediction accuracy.The cross-validation method constructs a combined surrogate model,and uses this model to optimize single-objective,multi-objective and adaptive single-objective questions.The main research work is as follows:(1)First,select four kinds of models and analyze their predictive abilities.Using the test function to analyze their prediction ability,and then introduce the evaluation function,the prediction accuracy of each model was analyzed,and the model with higher accuracy was selected and used to build an ensemble surrogate model.(2)Using the cross-validation error to approximate the mean square error to calculate the weight coefficient to continue to construct the surrogate model.And use this model to perform the single-objective problem of loading path of the T-shape tube hydroforming.First step,introduce the mechanism of construction of the ensemble surrogate model.Then the three selected models are combined using the method of cross-validation error,and numerical examples are used to verify the prediction effect of the ensemble surrogate model.Compared with using only a single model,the accuracy and robustness of the prediction are improved.Then,the finite element model of T-shape tube hydroforming was established,and carry out the single objective optimization design of the loading path of the T-shape hydroforming based on the combined approximate model was carried out.(3)Taking into account that most of the actual engineering problems are multi-objective,the multi-objective objective optimization design of the loading path of the T-shape tube hydroforming based on the ensemble model is constructed.First,a multi-objective numerical example is used to illustrate the effectiveness of the combined approximation model.Then,ensemble surrogate model is applied to the multi-objective optimization design of the loading path of the T-shape hydroforming,and the multi-objective optimized pareto solution set is obtained.Finally,a Pareto solution is selected by using the ideal point method,which is to compromise the optimal solution for reference by the engineering designer.(4)The adaptive ensemble surrogate model is introduced to improve the optimization efficiency and prediction accuracy of the ensemble surrogate model.Under the condition of ensuring that the height and the thinning rate are not bad,with a small number of sample points,and through iterative operations,add sample points in the key area,so that the optimal solution gradually converges to the real value.Improves the computational efficiency and prediction accuracy of the model.Two numerical examples are used to verify the effectiveness of the method.After that,this method was successfully applied to the optimization design of the loading path of the T-shape tube hydroforming...