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航空宇宙技術研究所 16-18 Jun. 1999 東京 日本, National Aerospace Laboratory 16-18 Jun. 1999 Tokyo Japan, 航空機の概念設計では、しばしば非凸面設計空間と複数の局所最適化に帰着する多数の非線形の制約条件を必然的に伴う。高速度民間航空機(HSCT)の設計は、26の設計変数と68の制約条件を持った非常に複雑な概念設計の例として用いられている。本稿では、HSCTの問題および数千の局所最適条件を課せられたテスト問題に関して3つの包括的最適化技術を比較した。1つは逐次2次計画(SQP)またはSnymanの動的探索法を用いた多点開始局所最適化法であり、もう1つはHSCT問題に関するJonesのDIRECT大域的最適化アルゴリズムである。SQPは局所最適化法であり、一方Snymanのアルゴリズムは浅い局所極小値を通って動くことが出来る。DIRECTアルゴリズムは、設計空間で小さな有望な領域を見出し、局所最適化法を用いて最適値に収束させるLipschitzの最適化法をベースにした大域的探索法である。DIRECTアルゴリズムは、ノイズ成分の大きな関数の大域的最適値を見出すのには最も費用効率が良いことが分かった。, The conceptual design of aircraft often entails a large number of nonlinear constraints that result in a nonconvex design space and multiple local optima. The design of the High Speed Civil Transport (HSCT) is used as an example of a highly complex conceptual design with 26 design variables and 68 constraints. This paper compares three global optimization techniques on the HSCT problem and a test problem with thousands of local optima: multistart local optimizations using either Sequential Quadratic Programming (SQP) or Snyman's dynamic search method, and Jones' DIRECT global optimization algorithm on the HSCT problem. SQP is a local optimizer, while Snyman's algorithm is capable of moving through shallow local minima. The DIRECT algorithm is a global search method based on Lipschizian optimization that locates small promising region of design space and uses a local optimizer to converge to the optimum. The DIRECT algorithm is found to be the most cost effective for locating the global optimum of noisy function., 資料番号: AA0001961002, レポート番号: NAL SP-44

The presence of numerical noise in engineering design optimisation problems inhibits the use of many gradient-based optimisation methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimisation, or it may promote convergence to spurious local optima. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expense of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimisation. To address these issues, a procedure has been developed to create noise-free algebraic models of subsonic and supersonic aerodynamic performance quantities, for use in the optimisation of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modelling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

Different sources of uncertainty in CFD simulations are illustrated by a detailed study of two-dimensional, turbulent, transonic flow in a converging-diverging channel. Runs were performed with the commercial CFD code GASP using different turbulence models, grid levels, and flux-limiters to see the effect of each on the CFD simulation uncertainties. Two flow conditions were studied by changing the exit pressure ratio: the first is a complex case with a strong shock and a separated flow region, the second is the weak shock case with no separation. The uncertainty in CFD simulations has been studied in terms of four contributions: (1) discretization error, (2) error in geometry representation, (3) turbulence model, and (4) the downstream boundary condition. In this paper, we have quantified the relative contribution and the importance of each source of uncertainty and shown the level of scatter in results that a well informed CFD user may obtain in a typical design activity. The nozzle efficiency results obtained in this study showed that the range of variation for the strong shock case was much larger than that observed in the weak shock case. The discretization errors were up to 6% and the relative uncertainty originating from the selection of different turbulence models was as large as 9% for the strong shock case. Furthermore, the results demonstrated that grid convergence is not achieved with grid levels that have moderate mesh sizes and showed that highly refined grids are required to obtain solutions with an acceptable level of accuracy in design problems that involve simulations of complex flow fields. The results illustrated the interaction of different sources of uncertainty and showed that the magnitudes of numerical errors are influenced by the physical models used.

The preliminary design space exploration for large,interdisciplinary engineering problems is often a difficult and time-consuming task. General techniques are needed that efficiently and methodically search the design space. This work focuses on the use of parallel load balancing techniques integrated with a global optimizer to reduce the computational time of the design space exploration. The method is applied to the multidisciplinary design of a High Speed Civil Transport (HSCT). A modified Lipschitzian optimization algorithm generates large sets of design points that are evaluated concurrently using a variety of load balancing schemes.The load balancing schemes implemented in this study are: static load balancing, dynamic load balancing with a master-slave organization, fully distributed dynamic load balancing, an fully distributed dynamic load balancing via threads. All of the parallel computing schemes have high parallel efficiencies. When the variation in the design evaluation times is small, the computational overhead needed for fully distributed dynamic load balancing is substantial enough so that it is more efficient to use a master-slave paradigm. However, when the variation in evaluation times is increased, fully distributed load balancing is the most efficient.

We describe a problem solving environment (PSE) named VizCraft that aids aircraft designers during the conceptual design stage. At this stage,an aircraft design is defined by a vector of 10-30 parameters. The goal is to find a vector that minimizes a performance-based objective function while meeting a series of constraints. VizCraft integrates the simulation code that evaluates a design with visualization for analyzing a design individually or in contrast to other designs. VizCraft allows the designer to easily switch between the view of a design in the form of a parameter set, and a visualization of the corresponding aircraft geometry. The user can easily see which, if any, constraints are violated. VizCraft also allows the user to view a database of designs using parallel coordinates. Keywords: Problem solving environment,scientific data visualization, mutlidiimensional visualization, aircraft design, multidisciplinary design optimization.

A method has been developed to generate and use polynomial approximations to the range and cruise drag components in a highly constrained, multidisciplinary design optimization of a High Speed Civil Transport configuration. The method improves optimization performance by eliminating the numerical noise present in the analyses through the use of response surface methodology. In our implementation, we fit quadratic polynomials within variable bounds to data gathered from a series of numerical analyses of different aircraft designs. Because the HSCT optimization process contains noise and suffers from a nonconvex design space even when noise is filtered out, multiple optimization runs are performed from different starting points with and without the response surface models in order to evaluate their effectiveness. It is shown that response surface methodology facilitates design space exploration, allowing improvements in terms of both convergence performance and computational effort when multiple starting points are required.

Multidisciplinary design optimization (MDO) for large-scale engineering problems poses many challenges (e.g., the design of an efficient concurrent paradigm for global optimization based on disciplinary analyses, expensive computations over vast data sets, etc.) This work focuses on the application of distributed schemes for massively parallel architectures to MDO problems, as a tool for reducing computation time and solving larger problems. The specific problem considered here is configuraton optimization of a high speed civil transport (HSCT), and the efficient parallelization of the embedded paradigm for reasonable design space identification. Two distributed dynamic load balancing techniques (random polling and global round robin with message combining) and two necessary termination detection schemes (global task count and token passing) were implemented and evaluated in terms of effectiveness and scalability to large problem sizes and a thousand processors. The effect of certain parameters on execution time was also inspected. Empirical results demonstrated stable performance and effectiveness for all schemes, and the parametric study showed that the selected algorithmic parameters have a negligible effect on performance.

A method has been developed to generate and use polynomial approximations to the range and cruise drag components in a highly constrained, multidisciplinary design optimization of a High Speed Civil Transport configuration. The method improves optimization performance by eliminating the numerical noise present in the analyses through the use of response surface methodology. In our implementation, we fit quadratic polynomials within variable bounds to data gathered from a series of numerical analyses of different aircraft designs. Because the HSCT optimization process contains noise and suffers from a nonconvex design space even when noise is filtered out, multiple optimization runs are performed from different starting points with and without the response surface models in order to evaluate their effectiveness. It is shown that response surface methodology facilitates design space exploration, allowing improvements in terms of both convergence performance and computational effort when multiple starting points are required.

A method has been developed to efficiently implement supersonic aerodynamic predictions from Euler solutions into a highly constrained, multidisciplinary design optimization of a High-Speed Civil Transport. The method alleviates the large computational burden associated with performing computational fluid dynamics analyses through the use of variable-complexity modeling techniques, response surface methodologies, and coarse grained parallel computing. Using information gained from lower fidelity aerodynamic models, reduced term response surface models representing a correction to the linear theory response surface model predictions are constructed using Euler solutions. Studies into five, ten, fifteen, and twenty variable design problems show that accurate results can be obtained with the reduced term models at a fraction of the cost of creating the full term quadratic response surface models. Specifically, a savings of 255 CPU hours out of 392 CPU hours required to create the full term response surface model is obtained for the twenty variable problem on a single 75 MHz IP21 processor of a SGI Power Challenge.

A procedure for generating and using polynomial approximations to the range or to the cruise drag components in terms of 29 design variables for a High Speed Civil Transport configuration design is presented. Response surface methodology is used to fit quadratic polynomials to data gathered from a series of numerical analyses of different aircraft designs. Several techniques are employed to minimize the number of required analyses and to maintain accuracy. Approximate analysis techniques are used to find regions of the design space where reasonable aircraft designs could occur and response surface models are built using higher fidelity analysis results of designs in this "reasonable" region. This is a means of using results from advanced CFD methods at the early design stage. Regression analysis and analysis of variance are used to reduce the number of polynomial terms in the response surface model functions. Optimization runs of the aircraft configuration are then carried out with the response surface models and compared to the previous optimization runs without the response surface models. It is shown that considerable reduction of the amount of numerical noise in optimization is achieved with response surface models and the convergence rate is improved. Careful attention was required to keep the accuracy of the models at an acceptable level.

The presence of numerical noise in engineering design optimization problems inhibits the use of many gradient-based optimization methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimization, or it may promote convergence to spurious local optima. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expenses of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimization. To address these issues, a procedure has been developed to create noise-free algebraic models of subsonic and supersonic aerodynamic performance qualities for use in the optimization of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modeling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

The presence of numerical noise inhibits gradient-based optimization and therefore limits the practicality of performing aircraft multidisciplinary design optimization (MDO). To address this issue, a procedure has been developed to create noise free algebraic models of subsonic and supersonic aerodynamic performance for use in the MDO of high-speed civil transport (HSCT) configurations. This procedure employs methods from statistical design of experiments theory to select a set of HSCT wing designs (fuselage/tail/engine geometry fixed) for which numerous detailed aerodynamic analyses are performed. Polynomial approximations (i.e., response surface models) are created from the aerodynamic data to provide analytical models relating aerodynamic quantities (e.g., wave drag and drag-due-to-lift) to the variables which define the HSCT wing configuration. A multidisciplinary design optimization of the HSCT is then performed using the response surface models in lieu of the traditional, local gradient based design methods. The use of response surface models makes possible the efficient and robust application of MDO to the design of an aircraft system. Results obtained from five variable and ten variable wing design problems presented here demonstrate the effectiveness of this response surface modeling method.

A procedure for generating and using a polynomial approximation to wing bending material weight of a High Speed Civil Transport (HSCT) is presented. Response surface methodology is used to fit a quadratic polynomial to data gathered from a series of structural optimizations. Several techniques are employed in order to minimize the number of required structural optimizations and to maintain accuracy. First, another weight function based on statistical data is used to identify a suitable model function for the response surface. In a similar manner, geometric and loading parameters that are likely to appear in the response surface model are also identified. Next, simple analysis techniques are used to find regions of the design space where reasonable HCST designs could occur. The use of intervening variables along with analysis of variance reduce the number of polynomial terms in the response surface model function. Structural optimization is then performed by the program GENESIS on a 28-node Intel Paragon. Finally, optimizations of the HSCT are completed both with and without the response surface.

Modern aerospace vehicle design requires the interaction of multiple discipines, traditionally processed in a sequential order. Multidisciplinary optimization (MDO), a formal methodology for the integration of these disciplines, is evolving towards methods capable of replacing the traditional sequential methodology of aerospace vehicle design by concurrent algorithms, with both an overall gain in product performance and a decrease in design time. A parallel MDO paradigm using variable-complexity modeling and multipoint response surface approximations is presented here for the particular instance of the design of a high speed civil transport (HSCT). This paradigm interleaves the disciplines at one level of complexity, and processes them hierarchically at another level of complexity, achieving parallelism within disciplines, rather than across disciplines. A master-slave paradigm manages a coarse grained parallelism of the analysis and optimization codes required by the disciplines showing reasonable speedups and efficiencies on an Intel Paragon.

A parallel variable-complexity modeling approach, permitting the efficient use of emerging parallel computing in multidisciplinary optimization (MDO) technology, is presented for the particular instance of High Speed Civil Transport (HSCT) design. In this method simple analyses are used to limit the approximation domain based on the D-optimality criterion through the use of a genetic alogorithm. At the D-optimal points, a refined analysis is performed. The optimization code is composed of a sequence of analysis cycles between aerodynamic and structural calculations. Results for coarse grained parallelization of the aerodynamic and structural codes on an Intel Paragon are presented for an example HSCT design problem involving only two variables. The full HSCT design problem employs twenty-eight design variables.

Convergence difficulties were encountered in our recent efforts towards a combined aerodynamic-structural optimization of the High Speed Civil Transport (HSCT). The underlying causes of the convergence problems were traced to numerical noise in the calculation of aerodynamic drag components for obstacles to convergence. The first technique employed a sequential approximation optimization method which used large initial move limits on the design variables. This helped dislodge the optimizer out of the local minima in the design space created by the noisy drag data. The second method utilized the aircraft. Two techniques were developed to circumvent the response surface methods to construct smooth approximations to the noisy data. The response surfaces were formed by analyzing several individual HSCT configuration and then fitting polynomial functions to selected objective function data. A simplified example design problem was used to demonstrate the response surface technique and to investigate various other issues relating to the construction of the response surfaces.