Ke-Shi Zhang

Surrogate-Based Optimization

Surrogate-based optimization (Queipo et al. 2005, Simpson et al. 2008) represents a class of optimization methodologies that make use of surrogate modeling techniques to quickly find the local or global optima. It provides us a novel optimization framework in which the conventional optimization algorithms, e.g. gradient-based or evolutionary algorithms are used for sub-optimization(s). Surrogate modeling techniques are of particular interest for engineering design when high-fidelity, thus expensive analysis codes (e.g. Computation Fluid Dynamics (CFD) or Computational Structural Dynamics (CSD)) are used. They can be used to greatly improve the design efficiency and be very helpful in finding global optima, filtering numerical noise, realizing parallel design optimization and integrating simulation codes of different disciplines into a process chain. Here the term “surrogate model” has the same meaning as “response surface model”, “metamodel”, “approximation model”, “emulator” etc. This chapter aims to give an overview of existing surrogate modeling techniques and issues about how to use them for optimization.

Bilevel Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.

Coupled Aerodynamic/Structural Optimization of a Subsonic Transport Wing Using a Surrogate Model

[Abstract] Coupled aerodynamic and structural optimization is performed for the preliminary design of a high-subsonic transport-aircraft wing using surrogate models. The aerodynamic performance of wing/body combination in transonic flow is calculated with full-potential equation in conjunction with viscous correction method. Structural analysis is performed using finite-element method (FEM) to obtain stress and deform distribution. The span, taper ratio, sweep angle and linear twist angle are chosen as design variables that define the aerodynamic configuration of the wing. And another four representing thicknesses of spars and skin are selected as the design variables for structural discipline. After the aeroelastic analysis of the various candidate wings, the aerodynamic and structural performances are obtained such as the lift coefficient, the drag coefficient, and the deformation and equivalent stress of the wing. Based on these sample data, the approximation models for analyzing the aerodynamic and structural performances are established using surrogate models including quadratic response surface method (RSM), kriging model (KM) and radial-basis function (RBF) Network. The modeling accuracy is evaluated by numerical-error analysis. We aim to select the approximation models with best accuracy to replace the complicated and time-consuming analysis in optimization. It is found that KM and RSM has comparative high accuracy and both are more accurate than RBF. Multi-objective optimization for the supercritical wing is performed based on RSM, for maximizing lift-to-drag ratio and minimizing weight. And the optimization is constrained by lift, reference area, deform, equivalent stress. The performance of the optimal design is proven to be improved based on the initial design. And compared with the optimal design without considering aeroelastic effect, lift-to-drag ratio is increased by 5.77% and lift is increased by 19.55%. It is proven by practice that considering aeroelastic effect is necessary in priliminary design of aircraft when optimizing high-aspect-ratio wing.

Optimization of Active Flow Control over an Airfoil Using a Surrogate-Management Framework

An efficient method based on the surrogate-management framework has been excised to optimize the actuation parameters of active flow control over an airfoil via a synthetic jet. In this approach, sample points are chosen by the design of experiments method, and approximation models are built based on the sampled data obtained from unsteady Reynolds-averaged Navier―Stokes simulations. The accuracy of these approximation models is evaluated at some test points by comparing the approximated values with the accurate values obtained from unsteady Reynolds-averaged Navier―Stokes simulations. Three types of approximation models (quadratic response-surface model, kriging model, and radial-basis-function neutral network) are built from the same data set. The model with highest accuracy is chosen as the surrogate model to be used to replace the unsteady Reynolds-averaged Navier― Stokes analysis during optimization. The optimization objective is to maximize the lift coefficient of a NACA 0015 airfoil at given angles of attack (14 to 22°), with the jet momentum coefficient, nondimensional frequency, and jet angle being the design variables. The surrogate model is coupled with a simulated annealing genetic algorithm optimizer to efficiently obtain the global optimum. As a result of the optimization process, the lift coefficient at an angle of attack of 16° is increased by 16.9% and the corresponding drag is decreased by 13.4% with respect to the initial controlled flow. It is preliminarily shown that the presented method is efficient and applicable for optimization of active flow control via a synthetic jet.

Flight Performance Analysis of Hybrid Airship: Revised Analytical Formulation

A hybrid airship denotes one kind of aircraft that combines the use of aerodynamic and buoyant lift. It is supposed to achieve the best combination of the high-speed characteristics of the airplane and the heavy-lifting capacity of the airship. In this work, an improved flight performance analysis method for a hybrid airship is proposed, aiming to provide a set of new formulas that are more suitable for a hybrid airship. The new formulas for analyzing the steady and accelerated performances of a hybrid airship are derived in a systematic way. The main advantage of the new formulas is that the relationship between the flight performances of a hybrid airship and airplane is indicated in a clearer and simpler expression. Base on the derivation, the theoretical comparisons are performed to show the advantage and disadvantage of the hybrid airship. An example of estimating flight performance of a model hybrid airship is presented to preliminarily demonstrate and evaluate the developed method, which shows a reasonable result.

Surrogate-based Aerodynamic Shape Optimization with Application to Wind Turbine Airfoils

Design of airfoils specially tailored for wind turbine blades has dramatic influence on the performance of a wind turbine. The traditional way for wind turbine airfoil design is a kind of trial and error process. In order to improve the design efficiency was well as the performance of the design, numerical optimization methods coupling optimization algorithm with CFD codes in an automatic process chain are of great interest. This study is focused on the development of efficient numerical optimization design methods for wind turbine airfoils. The main feature is to use surrogate-based optimization. Surrogate-based optimization is very efficient and has the capability of finding global optima; it can be classified as the third-type optimization method other than the traditional gradient-based methods and gradient-free searching methods, such as evolutional algorithms. Optimization designs of FFA-W3-211, inverse design of NPU-WA-300 and realistic numerical optimization of NPU-WA-250 are exercised. Examples show that the developed methods are efficient and robust, with sufficient flexibility of handling both geometric and aerodynamic constraints, multi-points design and multi-objective design.

Support Vector Regression-based Multidisciplinary Design Optimization in Aircraft Conceptual Design

Surrogate modeling plays an increasingly important role in multidisciplinary design optimization (MDO) associated with different areas of aerospace science and engineering. As a recent developed surrogate modeling method, support vector regression (SVR) has good capability of filtering numerical noise and is well suited for surrogate modeling problems with high nonlinearity. This work is focused on evaluation of SVR-based surrogate modeling method for the potential applications in aircraft conceptual design. Three numerical examples and an aerodynamic data prediction example are presented to show the accuracy of SVR for functions of varying complexity with and without numerical noises, and the key parameters of SVR model are studied. The SVR model is applied to the MDO problem of designing a general aviation airplane and good design result is obtained. The examples show that, SVR provides sufficient flexibility of switching between regression and interpolation, can filter noise and predict the functions well with a small number of samples, and is promising in aerodynamic data prediction and aircraft conceptual design.

Bi-Level Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.

Concurrent Subspace Optimization for Aircraft System Design

Concurrent Subspace Optimization (CSSO) is one of the main decomposition approaches in Multidisciplinary Design Optimization (MDO). It supports a collaborative and distributed multidisciplinary design optimization environment among different disciplinary groups. Sobieski first proposed the subspace optimization method (Sobieszczanski-Sobieski, 1988), and Sobieski’s blueprint was further developed by Bloebaum and subsequently named the concurrent subspace optimization method (Bolebaum, 1991). Renaud developed a secondorder variant of the Global Sensitivity Equation (GSE) method and an alternative potential coordination procedure for the CSSO method (Renaud & Gabriele, 1993a, 1993b, 1994). Sellar proposed to replace GSE with the neutral-network based response surface method (Sellar et al., 1996). The CSSO method allows a complex couple system to be decomposed into smaller, temporarily decoupled subsystems, each corresponding to different disciplines (subspaces). Each subspace optimization minimizes the system objective function subject to its own constraints as well as constraints contributed from the other subspaces. Each subspace optimization use its own high-fidelity analysis tools as well as given surrogate models or low-fidelity analysis tool provided by the other subspaces for analysis. Subsequently, the subspace optimizations can be performed concurrently. The system-level coordination optimization will be implemented completely based on approximation analysis tools. The subspace optimizations and the coordination optimization will be alternatively performed until results are finally decided by the coordination optimization. Therefore, the CSSO method is particularly suited to applications in a design organization where tasks are distributed among different design groups. The CSSO method was developed initially for a single objective MDO problem. However, most MDO problems are essentially multi-objective. In recent years more work (Aute & Azarm, 2006; Huang & Bloebaum, 2004; McAllister et al., 2000; McAllister et al., 2004; Orr & Hajela, 2005; Parashar & Bloebaum, 2006; Tappeta & Renaud, 1997; Zhang et al., 2008) has focused on extending existing MDO method to handle such multi-objective MDO problems, by means of integrating a multi-objective optimization method within the MDO framework. This kind of method can be called a multi-objective MDO method. It is an effective way to integrate multi-objective optimization method within the CSSO framework to develop the multi-objective MDO method. CSSO was extended to solve multiobjective MDO problems, including the Multi-objective Pareto CSSO (MOPCSSO) method,