Development And Application Of Kriging Surrogate Modeling Based On SiPESC Platform

The implementation of engineering structural optimization is often limited by the highly nonlinear optimization model,the costly numerical simulation,the time-consuming optimization process.It is difficult to obtain effective optimization results in limited resources and time."Design of Experiment(DOE)+ Surrogate Model(SM)" technology can effectively reduce the cost of computing,which is helpful to optimization designs.Among this techniques,the optimal Latin hypercube design can effectively adapt to different design variables and samples,while Kriging is one of the most effective surrogate models.The software containing optimal Latin hypercube design and Kriging surrogate model is an essential tool in optimal designs.This thesis,which is based on general DOE-SM framework of the SiPESC platform,implements the software development of optimal Latin hypercube design and Kriging surrogate model using C++ object oriented language and abstract factory pattern,and then the above software modules are applied to engineering structure optimization.As for DOE,the widely used criterions for the optimal Latin hypercube design are employed in the thesis,including the max-min distance criterion,the column orthogonal criterion and the multi-objective criterion.Furthermore,the evolutionary algorithm based on element exchange is implemented in the optimization of experimental design matrix.Numerical examples using JavaScripts and Python scripts verify the optimization searching ability and the accuracy of the algorithm,and the characteristics of each criterion are provided.As for SM,this thesis uses constant regression model to construct Kriging surrogate model,in which the SiPESC platform genetic algorithm is invoked to optimize the Kriging correlation coefficients,in conjunction to MathML language to construct the Kriging response function expression,therefor the expression can be applied to JavaScript,Python and Matlab Environment.Comparing with the results of DACE toolbox,numerical examples verify the accuracy of the algorithm implemented.Two dimensional classical examples are used to compare the characteristics of two add-point algorithms.The influence of sample points on the accuracy of surrogate model is also discussed through three-dimensional examples.This thesis applies the above software modules to engineering optimization problems.The first example uses the surrogate model to optimize the beam sectional parameters of a 3D printer and compares it with the result of using the genetic algorithm directly,which verifies the speediness and accuracy.The second example uses the surrogate model technic to optimize the shape of airfoil based on CST reverse design method.The third example uses stress constraints and frequency constraints to achieve the purpose of weight loss.These example also validates that the software implemented can effectively promote the work for design optimization of practical engineering problems.