Optimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation Method
Optimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation Method
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发表时间：
2002
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通讯作者：
X. Xing;M. Damodaran
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作者：
X. Xing;M. Damodaran
同时摄动随机逼近方法在统计参数估计、反馈控制、基于仿真的优化、信号与图像处理以及实验设计等领域有着广泛的应用。本文在分析了现有文献资料的基础上，首先，将它应用于一个简单的机翼几何形状设计问题，然后，将它应用于一个跨音速风扇叶片设计问题，在这个跨音速风扇叶片设计问题中，目标函数不是用任何显式函数表示，而是在每次设计迭代中用计算流体动力学方法来估计，从而证明了它作为一种可行的优化工具的性能求解Navier-Stokes方程的算法I.引言他需要解决多变量优化问题是普遍的工程，物理和社会科学。这类问题的典型特征是存在大量的设计变量、复杂的约束、甚至离散的设计参数值。许多优化算法，局部和全局优化算法已被开发用于优化这样的问题。除了确定性方法外，随机性方法如遗传算法、模拟退火算法等近年来在实际工程设计优化问题中得到了应用。与确定性方法相比，这些算法本质上都是随机的，并且易于在鲁棒的计算机代码中实现。然而，SA和GA方法需要大量的功能评估和相对较长的计算时间，特别是在复杂的设计问题的情况下。一
—Simultaneous Perturbation Stochastic Approximation method has attracted considerable application in many different areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal & image processing, and experimental design. In this paper, its performance as a viable optimization tool is demonstrated by applying it first to a simple wing geometry design problem for which the objective function is described by an empirical formula from aircraft design practice and then it is used in a transonic fan blade design problem in which the objective function is not represented by any explicit function but is estimated at each design iteration by a computational fluid dynamics algorithm for solving the Navier-Stokes equations I. INTRODUCTION he need for solving multivariate optimization problems is pervasive in engineering, the physical and social sciences. The characteristic features of such problems are the presence of a large number of design variables, complex constraints, and even discrete design parameter values. A number of optimization algorithms, both local and global optimization algorithms have been developed for optimizing such problems. Besides deterministic methods, stochastic methods such as genetic algorithm (GA) and simulated annealing (SA) algorithm etc have recently found applications in practical engineering design optimization problems. These algorithms are all stochastic in nature and easily implemented in robust computer codes as compared with deterministic methods. However, SA and GA methods require large number of function evaluations and relative long computation time especially in the case of complex design problems. One