Application of Simultaneous Perturbation Stochastic Approximation Method for Aerodynamic Shape Design Optimization

Abstract

Aerodynamic shape design optimization problems, such as inverse and constrained airfoil design and axisymmetric nozzle design, are investigated by applying the simultaneous perturbation stochastic approximation (SPSA) method to objective functions that are estimated during each design iteration using a finite volume computational fluid dynamics technique for solving the compressible Navier-Stokes equations. The SPSA method has been demonstrated in the literature as having significant advantages over stochastic global optimization methods such as the simulated annealing (SA) method. In this work the SPSA is compared with SA method for a class of twodimensional and axisymmetric aerodynamic design optimization problems. The numerical studies show that the SPSA method is robust in reaching optimal aerodynamic shapes, is easy to implement, and is highly efficient. The SPSA method can also decrease the computational costs significantly compared with the SA method.

Improved centrifugal compressor impeller optimization with a radial basis function network and principle component analysis

“…The performance parameters are parameterized from evaluation results of flow solvers, and should be easily evaluated by designers. The chosen performance parameters can be efficiency [1,2], total pressure ratio [5], losses [5,6], velocity distribution [7,8], pressure distribution [9], and loading [2,10]. The 3D CFD flow solvers could be applicable for calculating the compressor performances.…”

Simultaneous Perturbation Stochastic Approximation Algorithm for Solving Stochastic Problems of Transportation Network Analysis

“…Hutchison and Spall (38) give a criterion for stopping stochastic approximation. Some of the SPSA applications in different fields are given elsewhere (39)(40)(41). The SPSA has also been used in neural network applications.…”

A discrete adjoint harmonic balance method for turbomachinery shape optimization

“…Traditionally, investigators have used two families of optimization techniques, namely stochastic and deterministic methods in aerodynamic design optimization. Examples of stochastic methods include genetic algorithms (GAs) and simulated annealing (SA) algorithms, which are capable of determining global minimum points and are easy to implement in well-established CFD codes [50]. However, these approaches tend to be computationally expensive as they generally require a very large number of CFD computations.…”