Application of a PCA-DBN-based surrogate model to robust aerodynamic design optimization

An efficient method employing a Principal Component Analysis(PCA)-Deep Belief Network(DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study.In order to reduce the number of design variables for aerodynamic optimizations,the PCA technique is implemented to the geometric parameters obtained by parameterization method.For the purpose of predicting aerodynamic parameters,the DBN model is established with the reduced design variables as input and the aerodynamic parameters as output,and it is trained using the k-step contrastive divergence algorithm.The established PCA-DBN-based surrogate model is validated through predicting lift-to-drag ratios of a set of airfoils,and the results indicate that the PCA-DBN-based surrogate model is reliable and obtains more accurate predictions than three other surrogate models.Then the efficient optimization method is established by embedding the PCA-DBN-based surrogate model into an improved Particle Swarm Optimization(PSO)framework,and applied to the robust aerodynamic design optimizations of Natural Laminar Flow(NLF)airfoil and transonic wing.The optimization results indicate that the PCA-DBN-based surrogate model works very well as a prediction model in the robust optimization processes of both NLF airfoil and transonic wing.By employing the PCA-DBN-based surrogate model,the developed efficient method improves the optimization efficiency obviously.

Numerical simulation of effects of operating conditions on the molecular weight of polypropylene using a response surface method

A L463^5 Box-Behnken design was used for developing a model to predict and optimize the molecular weight （Mw ） of polypropylene （PP） ; a second-order polynomial regression equation was derived to predict responses. The significance of variables and their interactions were tested by means of the ANOVA with 95% confidence limits; the standardized effects were investigated by Pareto chart, the optimum values of the selected variables were obtained by analyzing the response surface contour plots. The optimized Mw value of 1. 217 × 10^5 g/mol was very close to the industrial value （ （ 1.22 ±0. 004） ×10^6 g/tool） at the optimum values.