Robust Design Optimization and Improvement by Metamodel

The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.

Variable Importance Measure System Based on Advanced Random Forest

The variable importance measure(VIM)can be implemented to rank or select important variables,which can effectively reduce the variable dimension and shorten the computational time.Random forest(RF)is an ensemble learning method by constructing multiple decision trees.In order to improve the prediction accuracy of random forest,advanced random forest is presented by using Kriging models as the models of leaf nodes in all the decision trees.Referring to the Mean Decrease Accuracy(MDA)index based on Out-of-Bag(OOB)data,the single variable,group variables and correlated variables importance measures are proposed to establish a complete VIM system on the basis of advanced random forest.The link of MDA and variance-based sensitivity total index is explored,and then the corresponding relationship of proposed VIM indices and variance-based global sensitivity indices are constructed,which gives a novel way to solve variance-based global sensitivity.Finally,several numerical and engineering examples are given to verify the effectiveness of proposed VIM system and the validity of the established relationship.

Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties

The uncertainties can generate fluctuations with aerodynamic characteristics. Uncertainty Quantification（UQ） is applied to compute its impact on the aerodynamic characteristics.In addition, the contribution of each uncertainty to aerodynamic characteristics should be computed by uncertainty sensitivity analysis. Non-Intrusive Polynomial Chaos（NIPC） has been successfully applied to uncertainty quantification and uncertainty sensitivity analysis. However, the non-intrusive polynomial chaos method becomes inefficient as the number of random variables adopted to describe uncertainties increases. This deficiency becomes significant in stochastic aerodynamic analysis considering the geometric uncertainty because the description of geometric uncertainty generally needs many parameters. To solve the deficiency, a Sparse Grid-based Polynomial Chaos（SGPC） expansion is used to do uncertainty quantification and sensitivity analysis for stochastic aerodynamic analysis considering geometric and operational uncertainties. It is proved that the method is more efficient than non-intrusive polynomial chaos and Monte Carlo Simulation（MSC） method for the stochastic aerodynamic analysis. By uncertainty quantification, it can be learnt that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region. The uncertainty sensitivity analysis reveals the individual and coupled effects among the uncertainty parameters.

Machine learning for adjoint vector in aerodynamic shape optimization

Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for it to obtain the gradients of all design variables. However, the computational cost of adjoint vector is approximately equal to that of flow computation. In order to accelerate the solution of adjoint vector and improve the efficiency of adjoint-based optimization, machine learning for adjoint vector modeling is presented. Deep neural network (DNN) is employed to construct the mapping between the adjoint vector and the local flow variables. DNN can efficiently predict adjoint vector and its generalization is examined by a transonic drag reduction of NACA0012 airfoil. The results indicate that with negligible computational cost of the adjoint vector, the proposed DNN-based adjoint method can achieve the same optimization results as the traditional adjoint method.