Metamodel Based Robust Optimization Design And Its Improvements

Traditional optimization design of project structure is based on deterministic structure parameters and optimization model which is solved by classical optimal algorithms.It does not take the uncertainty of design variables and other inputs into consideration,which is likely to lead to the failure of structure design.However,robust optimization design not only ensures the optimal solution can satisfy probability constraints but also makes the objective value insensitive to fluctuation,thus showing very important engineering meaning.Based on the existing researches,robust optimization design,metalmodel and global sensitivity analysis are detailedly investigated in this paper.The main work and innovative points are summarized as follows:1.The modified GMDH neural network algorithm is presented,which is based on the classical GMDH neural network algorithm.The new method improves the selection criteria of neurons as well as the coupling mode of these neurons in each layer.It maintains the advantages of traditional method in constructing the optimal network structure.Meanwhile,it reduces the required samples and increases the precision of model.Besides,inspired by cut-point theory,Cut-GMDH algorithm is proposed.2.HDMR expansion is combined with GMDH-NN algorithm,and proposed GMDHHDMR method can solve the variance-based global sensitivity indices more precisely and efficienctly.In addition,the new method extends the application to variables’ distribution and its precision and efficiency were proved by numerical examples and engineering examples.3.A new global sensitivity measure which is based on probability weighted moments is proposed.Then two numerical methods are introduced to estimate the proposed measure,i.e.,the double-loop-repeated-set numerical estimation and the double-loopsingle-set numerical estimation.The new measure needs quite less sample points and is insensitive to outliers when comparing with traditional variance-based global sensitivity indices.What’s more,it can reflect the influence of function coefficients in some situation.4.The main issues of robust optimization design are studied,containing robustness assessment,objective function handling,mathematical models and solution strategies.Firstly,a criterion which judges the deterministic solution whether satisfies robustness or not is offered.The multi-objective optimization problem is transformed into the single-objective optimization problem by weighted sum method,whose weights are decided by hyperplane method.Maximum entropy,a new robustness assessment,and its application ways are introduced.Finally,the single loop solution strategy of robust optimization is provided.5.Robust optimization design is combined with global sensitivity analysis and metamodel.To begin with,in order to reduce the model dimension,input variables can be selected by global sensitivity indices.Then,metamodelling can give the explicit expression of objective function or constraints.In the end,genetic algorithm can help search the global optimal solution in the robust optimization design.