Research On Improved Multi-objective Particle Swarm Algorithm For Aerodynamic Shape Optimization

Aerodynamic optimization design problems always involve multiple objectives,which cannot be expressed explicitly by means of some mathematical formulations.This ?black box? feature raises difficulty of solving aerodynamic optimization greatly.Based on Computational Fluid Dynamics(CFD)along with the continuous improvement of aircraft design criteria and rapid development of computer science,great step forward have been made on aerodynamic optimization technology in last decade.These new technologies have promoted aerodynamic design advance quickly,while more and more challenges emerged in practical applications.Numerical simulation,meta-model,parametrization method and optimization algorithm are indispensable parts to build accurate and efficient aerodynamic optimization system.The optimization algorithm has profound influence on design efficiency and accuracy.Therefore,this paper studies the multi-objective particle swarm optimization with respect to efficiency and precision to develop two multi-objective optimization algorithms,and combined them with conventional aerodynamic design technologies to optimize three aerodynamic design applications in different complexity.The major research topics and achievements are listed as below:1)A novel hybrid multi-objective particle swarm optimization(MOPSO)algorithm is proposed to improve the convergence precision of PSO and preserve the diversity of non-dominated set.A local optimal particle search strategy is developed after particular analysis on disadvantage of global optimal particle search method and integrated it into multi-objective particle swarm optimization.The new optimizer combines the strong global search ability of PSO with the local search ability of optimal particle.Our algorithm selects some non-dominated solutions lied in the less-crowded region of external archive based upon crowding distance value to form a leader particles set and utilize their adjacent solutions to construct unique local optimal particles for them.Then,make full use of bound optimization by quadratic approximation(BOBYQA)algorithm or exterior penalty function method to compel leader particles approach the Pareto front quickly and guide the whole swarm move forward.A multi-dimensional uniform mutation operator is performed to prevent the algorithm from trapping into local optimum caused by loss of swarm diversity.Furthermore,adaptive archive maintenance strategy is applied to reduce the possibility of removing non-dominated solutions from the external archive mistakenly.Simulation results from various kinds of benchmark functions show that our approach is highly competitive in convergence speed and generates a well distributed and accurate set of non-dominated solutions easily.2)In order to enhance search efficiency of the multi-objective optimization algorithm,a hypervolume-based expected improvement multi-objective particle swarm optimization method based upon a self-adaptive Kriging meta-model is studied and developed.In this method,the sample points are generated by optimal Latin hyper cube design,then utilize these samples to construct Kriging model to evaluate approximate results of objective functions.The multi-objective particle swarm optimization is adopted to execute proxy optimization.Calculate hypervolume-based expected improvement value for each particle employ spatial and confidence information of approximate results;choose several promising members are evaluated by means of the exact-costly tools;the mata-model database and non-dominated solution set are updated after enriching the sample database and the above procedures are repeated until loop termination.In that case,the spatial distribution and probability information of approximated optimization have been fully utilized to improve accuracy of promising region of meta-model,which lift the optimization efficiency.3)For weaken the computation complexity,two efficient strategies are proposed on basis of deep research on the principle of hypervolume-based expected improvement contribution function.Firstly,the active cells in hypervolume grids are classified as two types and applied different contribution calculate formulas each other,which reduce computation complexity of expected improvement slightly.Secondly,a principle of expected improvement contribution of Kriging model response focuses on the fixed region adjacent to mean value come into view after specific analysis on the response of Kriging surrogate model is a random variable with normal distribution.An algorithm is proposed for partition the hypervolume cells adaptively and calculates the expected improvement contribution value of active cells dynamically.This method reduces computation complexity of expected improvement significantly,and it has a certain theoretical guideline.4)An advanced Diverterless Supersonic Inlet(DSI or Bump)is designed to take advantage of the cone derived wave rider theory.A program for solving the supersonic conical flow field is coded based on the Taylor-Maccoll formula,and the Bump contour of the DSI inlet that suitable for supersonic,transonic and subsonic flight is obtained by the method of streamline tracing;according to the center line and area distribution law to devise S-shaped subsonic diffuser of DSI;the cross-section of inlet entrance is C type and cowling lip sweep forward.With respect to streamline on the Bump surface,distribution of Mach number in the diffuser exit,total pressure recovery coefficient and distortion on the exit plane are evaluated by CFD simulation via solving three-dimensional Reynolds Averaged Navier-Stokes(RANS)functions.The solving of supersonic,transonic and subsonic aerodynamic performances validates the preliminary design of DSI inlet is effective and meets the requirements of engineering application.5)Hybrid multi-objective particle swarm optimization and self-adaptive meta-model multi-objective optimization algorithms are applied to solve multi-objective airfoil,multi-foil and DSI inlet design respectively.Class/shape function transformation(CST)technique and second order CFD simulation are adopted to parameterize the airfoil shape and solve aerodynamic performance of airfoil relatively.Drag,lift and moment coefficients are regarded as objectives and constrained them with drag,lift,moment coefficients and geometry size,etc.The two new optimization algorithms are employed to optimize these problems and obtain a satisfactory Pareto front which proving the proposed algorithms are effective.Multi-foil and DSI inlet optimization are performed to validate our self-adaptive meta-model optimization algorithm further.Multi-foil design utilize slat and flap relative position to the wing,deflection angles as design variables to maximize the lift coefficients,which increases lift coefficients of two design conditions and ameliorate lift curve.In DSI inlet design,the Bump surface is parameterized by the free form deformation(FFD)method;the total pressure distortions under supersonic and transonic flight of inlet exit are treated as two minimize objectives and take advantage of total pressure recovery coefficients and mass flow rate of the exit plane to constraint them.An excellent non-dominated solution set is generated within the context of a small number of call cost evaluations.