Research On Dimension Reduction Of Feature Variables And Meta-model During Modeling And Optimization

Modeling in the engineering is a complicated problem,such as the bending spring back of a large scale U shape sheet,preform model of gear blank,graphene oxide organic coating model,and so on.In general,these models have some common properties,namely,there are many variables and the models have highly complex non-linear properties,which cannot be described with simple models.The trial and errors empirical or FEM will be applied to simulate these engineering models in the applications.However,the complex FEM simulations are still time-consuming although the performance of computers has been changing with each passing day.Thus,it is necessary to propose a common approach,namely,an approximate(compressed)model to substitute these time-consuming models.The meta-model has a widespread application in industrial by constructing approximate and simple models to replace those complex and expensive models.However,the traditional meta-models are gradient-based mathematical approaches with relatively high time cost.The newest development of the meta-model is the merging with the machine learning meta-model.However,there are rarely researches on the combination of dimensions reduction of characteristic variables with the meta-model technology.Therefore,in this work,we optimize and construct the machine learning meta-model,such as ELM,BPNN and SVM/SVR,and so on by the technology of dimensions reduction of characteristic variables.This method can greatly reduce the time of iterations while it still can guarantee the accuracy.GPLVM is a very potential model of dimensions reduction of characteristic variables.However,the previous GPLVM only consider the observation samples without considering the regression constrains.This will cause the method lacking of generalization in the applications.For this reason,we propos an improved mode named as R-GPLVM,This model overcome the disadvantage of previous GPLVM by constructing the constrains topology with regressions of observation space,and it is very proper for the small samples with high dimensions.The experiments of regression analyses show that the performance of R-GPLVM is superior to the previous GPLVM in different kinds of dimensional space.In addition,the accuracy of meta-model depends on the accuracy of training samples of models,and the time cost is high when precise sample data sets are generated.As a result,we improve the previous machine learning meta-model with two aspects.Fist,the sample and time dimensions of generating precise training sample data sets have been effectively reduced to decrease the time cost.Second,machine learning meta-model of the ELM,SVM/SVR,BPNN,and so on,have been effectively constructed.The input variables with high fidelity and meta-models with high generalization and prediction have been obtained.In Chapter 1,we introduce the objective and meaning,selection and screening of characteristic variables for dimensions reduction and optimization of multi-objective;In Chapter 2,the construction of R-GPLVM is introduced in detail.And,the method of SCG is applied to induce the maximization of posterior probability and to output the optimal latent variable and hyper parameters.And,we use the SVR with MIV improved to decrease the searching time of previous BB algorithm.Further,we propose an improved recursive kernel matrix of SVR based on the quadratic ?-SVR and deploy it to BB enumeration to screen out those optimal characteristic subset.This method can greatly reduce the iteration times of computation,while it still can guarantee the accuracy of models.In Chapter 3,we introduce the idea of variables fidelity and we induce the LSSVM based on the SVM.In the end,we construct the scale function between the high and low fidelity by using the multi-output LSSVM,and the variables fidelity-LSSVM meta-model is constructed.In Chapter 4,we propose the strategy of using GA to adjust the function of fitness and optimization of connection parameters of ELM network,so as to improve the generalization,reliability and stability of previous ELM model.The optimization results show that the stability and accuracy of GA-ELM outperform the BP,DE-ELM and ELM models.In the end of the chapter,optimization of multi-objective is used to obtain the optimal the gear blank preform.In Chapter 5,we screen out and reduce the variables dimensions of LSSVM meta-model for bending spring back by using the proposed R-GPLVM model,This approach can guarantee the variable fidelity during the spring back process.In the end of the chapter,strategy of minimal layers according the demand is proposed to avoid the unnecessary non-dominant fronts.And,strategy of neighbors comparisons is applied to recognize the non-dominant individuals.The DE operator is exploited to improve the NSGA algorithm so as to rapidly obtain the optimal solution set of bending parameters.This can provide designing parameters for compensation of bending spring back for the mold's mechanism with spring back reparation;In Chapter6,for the controlling of organic coatings of GO,the R-GPLVM-ELM model is applied the screen out those two important variables of deposition duration and voltage.And,the MIV improved SVR proposed in Chapter 2 is used to presort variables so as to decrease the searching time of BB method.The improved recursive kernel matrix of SVR proposed in Chapter 2 is also used to screen the optimal characteristic subset.This approach greatly save the iterations time of computation while still can guarantee the accuracy of meta-models.