(PDF) Multi-Objective Design Exploration and its Application to F1 Airfoils

Review Paper Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) DOI:10.5139/IJASS.2010.11.4.247 Multi-Objective Design Exploration and its Applications Shigeru Obayashi*, Shinkyu Jeong* and Koji Shimoyama* Institute of Fluid Science, Tohoku University, Katahira, Aoba, Sendai, Japan Kazuhisa Chiba** Department of Mechanical Systems Engineering, Hokkaido Institute of Technology, Teine, Sapporo, Japan Hiroyuki Morino*** Mitsubishi Aircraft Corporation, Oye-cho, Minato, Nagoya, Japan Abstract Multi-objective design exploration (MODE) and its applications are reviewed as an attempt to utilize numerical simulation in aerospace engineering design. MODE reveals the structure of the design space based on trade-off information. A self-organizing map (SOM) is incorporated into MODE as a visual data mining tool for the design space. SOM divides the design space into clusters with specific design features. This article reviews existing visual data mining techniques applied to engineering problems. Then, we discuss three applications of MODE: multidisciplinary design optimization for a regional-jet wing, silent supersonic technology demonstrator and centrifugal diffusers. Key words: Multidisciplinary design optimization, Evolutionary computation, Multiobjective optimization, Data mining, Self- organizaing map, Response surface method 1. Introduction require a large number of function evaluations. To alleviate the computational burden, the use of the response surface Multidisciplinary design optimization (MDO) is gaining method (RSM) has been introduced as a surrogate model great importance in aerospace engineering. A typical MDO (Queipo et al., 2005). The surrogate model used in this study problem involves multiple competing objectives. While is the Kriging model (Jeong and Obayashi, 2005; Jones et al., single objective problems may have a unique optimal 1998; Keane, 2003). solution, multi-objective problems (MOPs) have a set This approach for finding many Pareto solutions operates of compromising solutions, largely known as the trade- sufficiently in its present condition; however, smooth off surface, Pareto-optimal solutions or non-dominated operation is achieved only when the number of objectives solutions. These solutions reveal trade-off information remains small. To reveal the trade-off information from the among different objectives. They are optimal in the sense resultant Pareto front for real-world problems containing that no other solutions in the search space are superior to many objectives, visualization of the Pareto front becomes them when all objectives are taken into consideration. A an issue. The next section reviews visual data mining in designer will be able to choose a final design with further engineering design. considerations. A MDO system denoted multi-objective design Evolutionary algorithms (EAs) (Deb, 2001) are suitable for exploration (MODE) was proposed in Obayashi et al. (2005) finding many Pareto-optimal solutions. However, because and is illustrated in Fig. 1. MODE is not intended to provide EAs are population-based approaches, they generally an optimal solution. MODE reveals the structure of the * Professor, Corresponding author ** Associate Professor E-mail:

Tel: +81-22-217-5265 *** Assistant Manager Copyright ⓒ The Korean Society for Aeronautical & Space Sciences 247 http://ijass.or.kr pISSN: 2093-274x eISSN: 2093-2480 10-review(247-265).indd 247 2010-12-23 오후 2:25:35 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) Define design space Parameterization: non-uniform rational B-spline Choose sample points Design of experiment: Latin hypercube Construct surrogate model Response surface method: Kriging model Find non-dominated front Optimization: adaptive range multi of EIs objective genetic algorithms Uncertainty analysis: expected improvement Check the model and front based on Kriging model, statistics of design variables, etc. Extract design knowledge Data mining: analysis of variance, self- organizing map, rough set theory, etc. Fig. 1. Flowchart of multi-objective design exploration with component algorithms. Fig. 1. Flowchart of multi-objective design exploration with component algorithms. design space from trade-off information and visualizes it as a Inselberg, 1997; Inselberg and Dimsdale, 1990; van Wijk panorama2. Review of Visual for a decision Data maker. TheMining present form of MODE and Liere, 1993; Wong and Bergeron, 1997). Among the consists of the Kriging model, adaptive range multi objective methods developed to date, parallel coordinates (Inselberg, 2.1 Multi-dimensional multivariate visualization genetic algorithms, analysis of variance and a self-organizing 1997; Inselberg and Dimsdale, 1990) and the scatter plot map (SOM) Wong (Kohonen, 1995).(1997) and Bergeron SOM reported divides thethat design matrix are of “the main objectives themulti-dimensional most widely used multivariate approaches in the field of (MDMV) space into clusters. Each cluster represents a set of designs engineering design because of their ease of use. Recently, visualization are to visually summarize an MDMV data set, and find key trends and relationships among the containing specific design features. A designer may find an SOMs (Cios et al., 1998; Deb, 2001) have attracted attention variates.” interesting clusterTowith achieve goodthis goal,features. design extensive research Such designhas beenas conducted in manyfor a novel means fields MDMV(Alpern and Carter, The visualization. 1991;SOM featuresChernoff, are composed1973; ofInselberg, 1997; Inselberg a combination and Dimsdale, approach of design variables. 1990; vanentails Wijk and Liere, 1993; neural an unsupervised Wong network and Bergeron, technique If a particular combination of design variables is identified as that classifies, organizes, and 1997). Among the methods developed to date, parallel coordinates (Inselberg, 1997; Inselberg and Dimsdale, visualizes large data sets. It a sufficient condition belonging to a cluster of interest, it can projects multidimensional data on a 2-D map without any 1990) and the scatter plot matrix are the most widely used approaches in the field of engineering design because be considered as a design rule. Rough set theory (Pawlak, information loss. In this study, we applied SOM to find the of their ease of use. Recently, SOMs (Cios 1982) and other data mining techniques have been employed et al., 1998; Deb, 2001)between tradeoffs have attracted objectiveattention as arelationships functions, novel meansbetween for MDMV to extract designvisualization. rules. Through ThetheSOM approach applications entails an unsupervised of MODE, neural and objective functions, network designtechnique variables.that classifies,SOM Additionally, this article illustrates the importance of understanding the was employed to determine the sweet spot of the design organizes, and visualizes large data sets. It projects multidimensional data on a 2-D map without any information design problem better instead of obtaining a single optimal space (Jeong et al., 2005 a and B; Kumano et al., 2006a; loss. solution. In this study, we applied SOM to find the tradeoffs betweenet objective Obayashi al., 2007).functions, Parashar et relationships between al. (2008) used SOM for Thisobjective functions, article reviews andvisual existing design datavariables. Additionally, SOM mining techniques wassolution Pareto employed to determine analysis the sweet spotGenerative and decision-making. of the applieddesign to engineering space (Jeong problems. Then, we Kumano et al., 2005a?b?; discuss three topographic et al., 2006a; Obayashi mapping (GTM) et al., 2007). (Svensen, Parashar et al.1998) (2008)is used another applications of MODE: MDO for a regional-jet wing, the novel MDMV visualization method, which is based on a SOM for Pareto solution analysis and decision-making. Generative topographic mapping (GTM) (Svensen, 1998) silent supersonic technology demonstrator (S3TD) and constrained mixture of Gaussians the parameters which is another centrifugal novel MDMV visualization method, which is diffusers. canbased on a constrained be optimized using the mixture of Gaussians expectation the maximization parameters which can be optimized using the expectation maximization algorithm. algorithm. Holden Holden and Keane and Keane (2004) used GTM(2004) used to visualize GTM to visualize the high-dimensional data of aircraft design. Pryke et al. (2007) adopted “Heatmaps” toet al. the high-dimensional data of aircraft design. Pryke 2. Review of Visual Data Mining (2007) adopted “Heatmaps” to visualize the results of visualize the results of MOP. These novel visualization methods can supply more information than primitive MOP. These novel visualization methods can supply more 2.1 Multi-dimensional multivariate visualization information than primitive visualization methods. However, Wong and Bergeron (1997) reported that “the main users are required to be familiar with reading the results. objectives of multi-dimensional multivariate (MDMV) For visualization of the Pareto frontier of MOP, Mattson and visualization are to visually summarize an MDMV data set, Messac (2003) introduced the s-Pareto Frontier method, and find key trends and relationships among the variates.” and Agrawal et al. (2004) proposed hyper-space diagonal To achieve this goal, extensive research has been conducted counting (HSDC) and hyperspace Pareto frontier (HPF) in many fields (Alpern and Carter, 1991; Chernoff, 1973; (Agrawal et al., 2006). DOI:10.5139/IJASS.2010.11.4.247 248 10-review(247-265).indd 248 2010-12-23 오후 2:25:35 Shigeru Obayashi Multi-Objective Design Exploration and its Applications 2.2 Visual design steering of the design results (Ligetti and Simpson, 2005; Simpson et Recent developments have sought to support visual design al., 2005). steering (VDS), which is a modification of the computational steering paradigm (Parker et al., 1997). VDS was first suggested 2.3 Non-visual data mining by Winer and Bloebaum (2002a; 2002b) to incorporate the Recently, non-visual data mining techniques have designer’s experiences and intuition into the optimization been applied to MDO data to extract specific design rules. process in order to efficiently obtain an optimum solution. The most widely used non-visual data mining method in They used graph morphing to show trends in the performance engineering design is the analysis of variance (ANOVA). space corresponding to changes in the design variables. ANOVA quantitatively illustrates the effects of each design In VDS, the designer can stop and change the direction of variable or interaction of design variables of the objective exploration at any stage during the optimization. Eddy and function (Jeong et al., 2005a; Shimoyama et al., 2010). Lewis (2002) introduced cloud visualization (CV) to support Sugimura et al. (2010) and Graening et al. (2008) introduced visual steering. In CV, all previously obtained design points decision tree analysis (Witten and Frank, 2005) in order to ANOVA quantitatively illustrates the effects of each design variable or interaction of design variable are presented as clouds in both the design and performance obtain the design rules and knowledge for a centrifugal objective function spaces. These spaces are displayed in separate windows and (Jeong et al., 2005a; impeller andShimoyama 3-D turbineetblade, al., 2010). Sugimura respectively. et al. (2010) and Graenin Decision are linked to each other. A similar visualization (2008) system called introduced tree analysis decision tree analysis, developed (Witten and in the field of Frank, statistical 2005) science, in order to obtain the design ru synchronous visualization (SV) was suggested by Jeong et uses a type of ANOVA to extract design rules that support al. (2007) to visualize parameter knowledge subspacesfor a centrifugal and function impeller and 3-D Figure decision-making. turbine2 shows blade,arespectively. Decision tree diagram obtained bytree analysis, develope space at the same time. Recently, field ARLof statistical trade science, uses space visualizer a typetree decision of analysis. ANOVABytotracing extract design a path rulesa that to reach support decision-making desired (ATSV) (Stump et al., 2002, 2004), originally introduced as node, a single design rule can be obtained. For example, the shows a tree diagram obtained by decision tree analysis. By tracing a path to reach a desired node, a singl a graphical user interface tool supporting the “design by following if-then type rule can be found by tracing the path shopping” paradigm, has beenrule can bewith equipped obtained. For example, the visual the following represented if-then by the thick type line in Fig. rule 3 can be found by tracing the path represe steering command (Simpson et the al., 2008; thickStump line inetFig. al., 2009) 3 if (dv1>a1) and if (dv3≤a3) and ,......, then(P>bn) (1) in order to reinforce the trade (or design) space exploration process. VDS linked with high-performance computing and where dvi is the i-th design variable and ai is the criterion (1) A quantitatively illustrates the effects meta-modeling of each provides techniques design the variable or interaction possibility of finding offordesign variables dividing dvi. P is of the performance and bi is the criterion for dv i the i-th a better solution in complicated system designs usingdesign where is less variable and a is the criterion dividing the performance P. for dividing dvi. P is performance and bi is the e function (Jeong et al., 2005a; Shimoyama et al., 2010). Sugimura et al. (2010) and Graening et al. i design time. for dividing the performance P. Rough set and association rules are additional non-visual ntroduced decision treeKodiyalam analysis et (Witten andintroduced al. (2004) Frank, 2005)a rapidinmethod order forto obtain datathe design mining rulesused methods andto extract design rules. Rough set the visualization of physical model behavior during an theory, a developed mathematical ge for a centrifugal impeller and 3-D turbine blade, respectively. Decision tree analysis, inmethod the developed by Pawlak (1982), optimization run by adopting high-performance computing was originally applied to analyze human senses because how statistical science, uses anda type of ANOVA surrogate modeling.toThis extract method design rules how identifies that the support itdecision-making. treats ambiguous data Fig.and 2 extracts underlying rules from tree diagram obtained responses by decisionof the physical tree model analysis. Bywill change tracing with changes a path to reachina desired node,The the data. a single conceptdesign and procedure for extracting design the design variables as optimization is running. Messac and rules from engineering design data using rough set theory are be obtained. For example, Chenthe(2000) suggestedif-then following type a method forrule can be real-time found byoftracing the path represented by visualization briefly explained in Fig. 3. In contrast to decision tree theory, line in Fig. 3 the optimization process. The technique for the visualization multiple design rules are obtained from the rough set theory. of the path through the design space of the solutions during Fig. 2.meaningful Diagram of arule decision tree. (1) To only obtain rules, sets are screened by evolutionary optimization run was developed by Pohlheim (1999). Ligetti et al. (2003) investigated the impact of vi is the i-th design variable and a is the criterion for dividing dvi. P is performance and bi is the criterion graphical interface delay on the efficiency and effectiveness i ing the performance P. Fig. 2. Diagram Fig.of2.a decision Diagramtree. of a decision tree. Fig. 3. Procedure for extracting rule sets with the rough set theory. Fig. 3. Procedure for extracting rule sets with the rough set theory. Rough set and association rules are additional non-visual data mining methods used to extract desig http://ijass.or.kr 249 Rough set theory, a mathematical method developed by Pawlak (1982), was originally applied to analyze senses because how it treats ambiguous data and extracts underlying rules from the data. The conc procedure for extracting design rules from engineering design data using rough set theory are briefly expl 10-review(247-265).indd 249 Fig. 3. In contrast to decision tree theory, multiple design rules are obtained from the rough set theory. 2010-12-23 오후 8:31:02 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) reduction and filtering. Similar to the rough set theory, the 3.1 Definition of optimization problem association rule generates many different rules. To select only The application shown here is the MDO tool for a the important rules, criteria such as support, confidence, and regional-jet wing design with engine-airframe integration lift are used in the association rule. Sugimura et al. (2009a, b) (Kumano et al., 2006b). It should be noted that the optimized applied rough set and association rules to obtain the tradeoff wing is not the exact MRJ wing; rather, the acquired design rules of a robust centrifugal fan design. Proper orthogonal knowledge from the present application has been utilized decomposition (POD), which is known as the principal for the MRJ wing design. Integration is an imperative issue component analysis in statistical science, has been used in aircraft design. The shock wave generated inboard of the to extract dominant features of designed transonic airfoil pylon may lead to flow separation and buffeting. To prevent geometry. In this method, the design data are decomposed these phenomena, the wing shape near the pylon has been into a set of optimum orthogonal base vectors. Subsequently, optimized. The following design objectives are considered features of these vectors are investigated in order to extract here. information. This method has been extended to extraction of the flow field characteristic of a transonic airfoil (Oyama et <Objective functions> al., 2010). Minimize - Drag under cruising conditions (CD). - Shock strength near wing-pylon junction (–Cp,max). 3. MDO for the Regional-Jet Wing with - Structural weight of the main wing (Wing weight). Engine-Airframe Integration <Design variables> - Airfoil shapes of lower surface at 2 spanwise sections In Japan, the New Energy and Industrial Technology = 26 variables Development Organization (NEDO) subsidized the - Twist angles at 4 sections = 4 variables development of an environmentally friendly high 30 variables in total performance small jet aircraft. Mitsubishi Heavy Industries, <Constraints> Ltd. (MHI) was the prime contractor for the project. The - Wing thickness > specified value purpose of this project was to build a prototype aircraft using - Rear spar height > specified value advanced technologies, such as low-drag wing design, and - Strength margin > specified value lightweight composite structures, which were necessary - Flutter margin > specified value for the reduction of environmental burdens. In March 2008, MHI decided to bring this conceptual aircraft into 3.2 Optimization results commercial use. This commercial jet aircraft, named the During the optimization, the update of the Kriging models Mitsubishi regional jet (MRJ), has a capacity of about 70-90 was performed six times. A total of 149 sample points were passengers. This project focused on environmental issues, used. Figure 4 shows the performance of the baseline such as reduction of exhaust emissions and noise. Moreover, configuration and those of additional sample points at every in order to bring the jet to market, lower-cost development iteration. As the iteration progressed, sample points moved methods using computer-aided design were also employed toward the optimum direction indicating that the additional in this project. sample points for update were selected successfully. Several Under this project, Tohoku University participated as a solutions with improvements in all objective function values collaborator and published a number of research results. compared with the baseline shape were obtained. One Obayashi et al. (2005) and Takenaka et al. (2005) provided an of the solutions was improved in 7.0 counts in CD, 0.503 in overview of the collaborative works. Chiba et al. (2007) and –Cp,max, and 21.6 kg in the wing weight compared with the Kumano et al. (2006a) gave an account of the MDO system performance of the baseline shape. development for the main wing. Hatanaka et al. (2006) and Kumano et al. (2006b) described the MDO system for engine- 3.3 Airfoil parameters used in data mining airframe integration. The winglet design was performed by Data mining was performed using airfoil parameters Takenaka et al. (2008). Aeroelastic simulations were also that differed from non-uniform rational B-spline (NURBS) performed in the works provided by Kumano et al. (2008) design variables. The difference is due to the fact that and Morino et al. (2009). NURBS control points have no aerodynamic or structural significance. Figure 5 shows the airfoil parameters of interest. XmaxL represents the distance from the leading DOI:10.5139/IJASS.2010.11.4.247 250 10-review(247-265).indd 250 2010-12-23 오후 2:25:35 Shigeru Obayashi Multi-Objective Design Exploration and its Applications Table 1. Airfoil parameters used for data mining Number Airfoil parameters dv1 XmaxL @ η = 0.12 dv2 XmaxL @ η = 0.29 dv3 maxL @ η = 0.12 dv4 maxL @ v= 0.29 dv5 XmaxTC @ η = 0.12 dv6 XmaxTC @ η = 0.29 dv7 maxTC @ η = 0.12 dv8 maxTC @ η = 0.29 dv9 sparTC @ η = 0.12 dv10 sparTC @ η = 0.29 (a) CD - –Cp,max (a) CD - –Cp,max (b) –Cp,max - Wing weight edge to the maximum thickness point of the lower half of the airfoil. maxL is the corresponding maximum thickness of the lower half. XmaxTC is the distance from the leading edge to the maximum thickness point. maxTC is the corresponding maximum thickness. In addition, sparTC is the thickness at the front spar. These parameters are taken at two wing sections as shown in Table 1. (a) CD - –Cp,max (b) –Cp,max - Wing weight3.4 Analysis of variance ANOVA is a statistical data mining technique that reveals (a) CD - –Cp,max (b)(b) –Cp,max –Cp,max- -Wing Wingweight weight the effects of each design variable on the objective and the constraint functions (Jones et al., 1998). ANOVA uses the (c) CD - Wing weight variance of the model due to individual variables and pairs of Fig. 4. Comparison of design performance among the baseline shapevariables and sample (interactions) points throughof the approximation Kriging updates. function based on the Kriging model. By decomposing the total variance of the model into components due to main effects and 3.3 Airfoil parameters used in data mining interactions, the influences of individual variables and their Data mining was performed using airfoil parameters that differed pairs on the non-uniform from objective function canB-spline rational be calculated. Because the present Kriging model allows nonlinear approximation, (NURBS) design variables. The difference is due to the fact that NURBS control points have no aerodynamic or ANOVA is sufficient for the present data mining. structural significance. Fig. 5 shows the airfoil parameters of interest. XmaxL represents the distance from the Figure 6 shows the results of ANOVA for each objective leading edge to the maximum thickness point of the lower half of thefunction. airfoil. maxL is the corresponding According to the results,maximum dv2, dv7, and dv9 largely thickness of the lower (c)(c)Chalf. XmaxTC D -- Wing CD Wing is the distance from the leading edge to the maximum thickness point. weight weight influence CD. dv6, dv10, and dv2 largely influence −Cp,max. maxTC is the corresponding maximum thickness. In addition, sparTC Furthermore, dv6, at is the thickness dv8, the and frontdv2 spar.largely These influence wing Fig. 4. Comparison of design Fig. (c) C performance 4. Comparisonamong of design theperformance baseline shape andthe among sample points baseline throughweight. shape Kriging updates. D - Wing weight parameters are taken and sample pointsatthrough two wing sections Kriging as shown in Table 1. updates. esign performance among the baseline shape and sample points through Kriging updates. .3 Airfoil parameters used in data mining 3.5 Visualization of design space In order to visualize the design space, SOMs proposed by usedData mining in data was performed using airfoil parameters that differed from non-uniform rational B-spline mining (Kohonen, 1995) were employed. The following SOMs were NURBS) design variables. The difference is due to the fact that NURBS control points have no aerodynamic generated by orViscovery SOMine (http://www.eudaptics. erformed using airfoil parameters that differed from non-uniform rational B-spline tructural significance. Fig. 5 shows the airfoil parameters of interest. XmaxL represents the com/somine. distance from theaccessed March 5, 2010). Once the user es. The difference is due to the fact that NURBS control points have no aerodynamic or specifiesmaximum eading edge to the maximum thickness point of the lower half of the airfoil. maxL is the corresponding the size of the map, this software automatically Fig. 5 shows the airfoil parameters of interest. XmaxL represents the distance from the hickness of the lower half. XmaxTC is the distance from the leading edge to the maximuminitializes thicknessthe map based on the first two principal axes. The point. mum thickness point of the lower half of the airfoil. maxL is the corresponding maximum aspect ratio of the map is also determined according to the maxTC is the corresponding maximum thickness. In addition, sparTC is the thickness at the front spar. These half. XmaxTC is the distance from the leading edge to the maximum thickness point. ratio of the corresponding principal components. The size of arameters are taken at two wing sections as shown in Table 1. the map is usually 2000 neurons, which provides a reasonable ding maximum thickness.Fig. In 5.addition, Airfoil parameters sparTC isused theforthickness data mining. at the front spar. These Fig. 5. Airfoil parameters used for data mining. wo wing sections as shown in Table 1. 251 http://ijass.or.kr 10-review(247-265).indd 251 2010-12-23 오후 2:25:36 SOM colored by- the The lower three right These objectives. corner corresponds color figures show to thatthose with the SOM low CinD,Fig. indicated can,be −C7p,max and light grouped wing we of individual variables and their pairs on the objective function ascan be calculated. Because the present Kriging follows: - The upper left corner corresponds to those with high CD. model allows nonlinear approximation, ANOVA is sufficient for the present dataright - The upper mining. corner corresponds to the designs containg heavy wing weight and low CD. components. The size of the map is usually - 2000 -neurons, The The upper areawhich edgelower provides left corner corresponds a reasonable corresponds to those with heavy to resolution those wing within with high weight. a −Cp,max. CD, and Fig. 6 shows the results of ANOVA for each objective function. According to the results, dv2, dv7, and dv9 reasonable computational time. As- The a result, the corner lower right lowercorresponds right corner is the to those withsweet low CD,spot −Cp,maxin thislight , and design space, improving all three o wing weight. largely influence CD. dv6, dv10, and dv2 largely influence −Cp,max. - Furthermore, dv6, The upper left corner dv8, toand corresponds thosedv2 largely with high CD. Solutions uniformly sampled from the design space were projected onto the two-dimensional SOM. Fig. 7 influence wing Int’l weight. & Space Sci. 11(4), 247–265 (2010) J. of Aeronautical - The lower left corner corresponds to those with high CD, and −Cp,max. shows the resulting SOM with 12 clusters considering the three objectives. Furthermore, Fig. 8 shows the same As a result, the lower right corner is the sweet spot in this design space, improving all three objective functions. SOM colored by the three objectives. These color figures show that the SOM indicated in Fig. 7 can be grouped as follows: - The upper right corner corresponds to the designs containg heavy wing weight and low CD. - The upper edge area corresponds to those with heavy wing weight. - The lower right corner corresponds to those with low CD, −Cp,max, and light wing weight. sindividual and their variables pairs on the andobjective their pairsfunction on the can be calculated. objective function Because the presentBecause can be calculated. Krigingthe present Kriging - The upper left corner corresponds to those with high C . D ar approximation, odel ANOVA allows nonlinear is sufficient approximation, for the is ANOVA present data for sufficient mining. the - The lower left present data mining. corner corresponds to those with high CD, and −Cp,max. esults Fig. 6ofshows ANOVA for each the results of objective ANOVA function. for each According objective to the function.results, dv2, According dv7, to theand dv9indv2, results, As a result, the lower right corner is the sweet spot this dv7, designand dv9improving all three objective functions. space, dv6, influence rgely dv10, andCDdv2 largely . dv6, dv10,influence and dv2 −C p,max. Furthermore, largely dv6,. Furthermore, influence −Cp,max dv8, and dv2dv6, largely dv8,7. Sand Fig. dv2 largely elf-organizing map based on the design performance uni- Fig. 7. Self-organizing map based on the design performance uniformly sampled from the design space. formly sampled from the design space. t. fluence wing weight. Fig. 7. Self-organizing map based on the design performance uniformly sampled from t (a)CCD (a) (b) −Cp,max D (a) CD (b) –Cp,max Fig. 7. Self-organizing map based on the design performance uniformly sampled from the design space. (a) C (a) CDD (b) –Cp,max (a) CD (a) CD (b)(b) −Cp,max −Cp,max (b) −Cp,max (c) Wing weight Fig. 6. ANOVA results for each objective function based on airfoil parameters. 3.5 Visualization of design space In order to visualize the design space, SOMs proposed by (Kohonen, 1995) were employed. The following SOMs were generated by Viscovery SOMine (http://www.eudaptics.com/somine. accessed March 5, 2010). Once the user specifies the size of the map, this software automatically initializes the map based on the first two principal axes. The aspect ratio of the map is also determined according to the ratio of the corresponding principal (a) CD (b) –Cp,max (b) –Cp,max (c) Wing weight Fig.(c) 6. AWing NOVA weight (c) Wing results for each weight objective function based on airfoil pa- 6. ANOVA results Fig. for 6. ANOVA rameters. each objective resultsfunction for eachbased on airfoil objective parameters. function based on airfoil parameters. of3.5 design space of design space Visualization resolution within a reasonable computational time. ze In the design order space, SOMs to visualize proposed the design space,bySOMs (Kohonen, 1995) proposed bywere employed. (Kohonen, The 1995) following were employed. The following Solutions uniformly sampled from the design space were d by Viscovery OMs SOMine were generated (http://www.eudaptics.com/somine. by Viscovery projected ontoSOMine two-dimensionalaccessed March7 5, the (http://www.eudaptics.com/somine. SOM. Figure 2010). Once accessed shows March 5, 2010). Once ee size user of the map, specifies thethis software sizethe automatically of resulting the map, with initializes this software SOM theconsidering map initializes automatically 12 clusters basedthe on three the map the first based two on the first two pect ratio incipal of the axes. Themap objectives. is also aspect ratiodeterminedFurthermore, of the mapaccording Fig. 8 shows to the ratio is also determined the same SOM colored of the corresponding according to the ratio ofprincipal the corresponding principal(c) Wing weight by the three objectives. These color figures show that the (c) Wing weight SOM indicated in Fig. 7 can be grouped as follows: Fig. 8. S elf-organizing map based on the design performance colored - The upper right corner corresponds to theFig. 8. Self-organizingby designs map eachbased on the objective design performance colored by each objective function. function. Fig. 9 shows the same SOM colored by four airfoil parameters (dv2, dv6, dv7, and dv10, respectively). In Fig. DOI:10.5139/IJASS.2010.11.4.247 9(a) colored by dv2,252 large dv2 values can be found at the right edge. This area corresponds to small CD and −Cp,max values as shown in Fig. 8(a) and (b), respectively. This signifies that large dv2 values lead to acceptable CD and −Cp,max performance. Furthermore, in Fig. 9(c) colored by dv7, low dv7 values can be found at the right edge. This color pattern is very similar to that for CD. This also indicates that low dv7 values lead to acceptable CD 10-review(247-265).indd 252 performance. 2010-12-23 오후 2:25:36 performance. In Fig. 9(b) colored by dv6, large dv6 values can be found at the right edge. This means that large dv6 values lead(c) toWing good weight performance of −Cp,max. In addition, the color pattern of Fig. 9(d) is very similar to that for −Cp,max. This means that low dv10 values lead to good performance of −Cp,max. As shown in Fig. 10, large dv6 and low f-organizing map based ondv10 the design (a) dv2 (b) dv6 valuesperformance mitigate the colored blockagebybetween each objective the wingfunction. and nacelle. Therefore, the shockwave between the wing and (c) dv7 Shigeru Obayashi Multi-Objective Design Exploration and its Applications (d) dv10 nacelle is weakened. e same SOM colored by four airfoil parameters (dv2, dv6, dv7, and dv10, respectively). In Fig. Fig. 9. Self-organizing map based on the design performance colored by the airfo 2, large dv2 values can be found at the right edge. This area corresponds to small CD and −Cp,max Fig. 8(a) and (b), respectively. This signifies that large dv2 values lead to acceptable CD and e. Furthermore, in Fig. 9(c) colored by dv7, low dv7 values can be found at the right edge. This ery similar to that for CD. This also indicates that low dv7 values lead to acceptable CD ored by dv6, large dv6 values can be found at the right edge. This means that large dv6 values rmance of −Cp,max. In addition, the color pattern of Fig. 9(d) is very similar to that for −Cp,max. w dv10 values lead to good performance of −Cp,max. As shown in Fig. 10, large dv6 and low (c) dv7 (d) dv10 te the blockage between the wing and nacelle. Therefore, the shockwave between the wing and (a) High –Cp,max design (c) Low –Cp,max d Fig. 9. Self-organizing map based on the design performance colored (a) Highby the airfoil –Cp,max parameters. design d. Fig. 10. Comparisons of airfoil lower surfaces and corresponding pressure distributions (a) dv2 junction. 3.6 Extraction of design rules Rough set theory was originally developed by Pawlak (1982). This mathematical me to human sense analysis because of its capability of handling ambiguous data and rules from that data. Because simulation data is deterministic, only the latter function theory extracts design rules (decision rules) through the classification of set elemen Since details of the mathematical aspects of rough set theory can be found in the refer (a) High –Cp,max design flowchart of applying (c) Low rough–Cset designto an engineering design database are briefly ex theory p,max (c) Low –Cp,max design Fig. 10. Comparisons of airfoil lower surfaces and corresponding pressurewith First, design samples distributions nearvariables continuous the wing-pylon are discretized to make logical set ope junction. Fig. 10. C omparisons of airfoil lower surfaces and corresponding (a) dv2 design (b) dv6 variables are categorized into three levels. Each level is assigned to a differen (b) dv6 pressure distributions near the wing-pylon junction. 3.6 Extraction of design rules design parameter and an objective function in such a way that the levels 1, 2 and Rough set theory was originally developed by Pawlak (1982). This mathematical method has been applied to human sense analysis because of its capability of handling containg ambiguous heavy data and wing weight and extracting low CD. underlying - The upperonly rules from that data. Because simulation data is deterministic, edgethe area corresponds latter to used. function was thoseRough with heavy set wing theory extracts design rules (decision rules) through the weight. classification of set elements and set operations. - The lower right corner corresponds to those with low CD, Since details of the mathematical aspects of rough set theory can be found in the reference, the concept and −Cp,max, and light wing weight. flowchart of applying rough set theory to an engineering design database are briefly explained using Fig. 11. - The upper left corner corresponds to those with high CD. First, design samples with continuous variables are discretized to make logical set operation possible. Here, - Th e lower left corner corresponds to those with high CD, design variables are categorized into three levels. Each and level −Cp,maxis. assigned to a different range of values of a (a) dv2 design parameter (c)(b) dv7dv6 and an objective function in such a result, the the a As dv10 (d) way that levels lower right1,corner 2 andis3the correspond to in sweet spot thethis (c) dv7 design Fig. 9. Self-organizing map based on the design performance colored by space, improving the airfoil all three objective functions. parameters. Figure 9 shows the same SOM colored by four airfoil parameters (dv2, dv6, dv7, and dv10, respectively). In Fig. 9(a) colored by dv2, large dv2 values can be found at the right edge. This area corresponds to small CD and −Cp,max values as shown in Figs. 8(a) and (b), respectively. This signifies that large dv2 values lead to acceptable CD and −Cp,max performance. Furthermore, in Fig. 9(c) colored by dv7, low dv7 values can be found at the right edge. This color pattern is very similar to that for CD. This also indicates that low dv7 values lead to acceptable CD performance. (a) High –Cp,max design (c) Low –Cp,max design (c) dv7 (d) dv10 In Fig. 9(b) colored by dv6, large dv6 values can be found Fig. 10. Comparisons of airfoil lower surfaces and corresponding pressure distributions near the wing-pylon (d) dv10 elf-organizing map based on the design performance colored by the airfoil parameters. junction. at the right edge. This means that large dv6 values lead to Fig. 9. Self-organizing map based on the design performance colored good performance of −Cp,max. In addition, the color pattern of by the airfoil 3.6 Extraction parameters. of design rules Fig. 9(d) is very similar to that for −Cp,max. This means that low Rough set theory was originally developed by Pawlak (1982). This mathematical method has been applied to human sense analysis because of its capability of handling ambiguous data and extracting underlying 253 http://ijass.or.kr rules from that data. Because simulation data is deterministic, only the latter function was used. Rough set theory extracts design rules (decision rules) through the classification of set elements and set operations. Since details of the mathematical aspects of rough set theory can be found in the reference, the concept and flowchart of applying rough set theory to an engineering design database are briefly explained using Fig. 11. (a) High –Cp,max design First, design 10-review(247-265).indd (c) Low –Cp,max 253 samples with continuous designare discretized to make logical set operation possible. Here, variables 2010-12-23 오후 2:25:37 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) dv10 values lead to good performance of −Cp,max. As shown in values of a design parameter and an objective function in such Fig. 10, large dv6 and low dv10 values mitigate the blockage a way that the levels 1, 2 and 3 correspond to the minimum, between the wing and nacelle. Therefore, the shockwave middle and maximum ranges, respectively. For objective between the wing and nacelle is weakened. functions, clusters can be considered as a discrete category instead of these levels. Each design is then regarded as a 3.6 Extraction of design rules deterministic rule describing conditions (design variables) Rough set theory was originally developed by Pawlak (1982). and results (objective functions and clusters). Hence, all This mathematical method has been applied to human sense the data becomes a collection of rule sets. However, the rule analysis because of its capability of handling ambiguous sets still have as many conditions as the number of design data and extracting underlying rules from that data. Because variables, making it difficult for designers to understand simulation data is deterministic, only the latter function was them. Since some design variables do not affect the results or used. Rough set theory extracts design rules (decision rules) decisions, reducing the number of design variables required through the classification of set elements and set operations. to obtain the same results is possible. This operation used Since details of the mathematical aspects of rough set theory for the purpose of obtaining minimum sets of conditions to can be found in the reference, the concept and flowchart of determine the desired decision attributes is called ‘reduct,’ applying rough set theory to an engineering design database which makes obtaining simple rules with fewer conditions are briefly explained using Fig. 11. First, design samples possible. Reduct is obtained from set operations. After with continuous variables are discretized to make logical set obtaining reduced rule sets, the rule sets are filtered on the operation possible. Here, design variables are categorized basis of the frequency to determine dominant rule sets. into three levels. Each level is assigned to a different range of Finally, the meaning of the filtered rule sets is interpreted. Open software ROSSETA (Ohrn, 2000) was used for the necessary calculations. The resulting rule appears, for example, ‘dv1(medium) AND dv2(large) AND dv5(medium) AND dv7(medium) AND dv9(small) AND dv10(small) => Cluster(C6), occurrence(10).’ It still appears complicated because the condition consists of a combination of five design parameters. In order to interpret the design rules more comprehensively, the frequency of appearance of small, medium and large for each design parameter was counted according to the sweet-spot cluster, small objective function values (CD, −Cp,max and wing weight), respectively, as summarized in Table 2. For example, dv2- sweet reads +9. This signifies that the condition dv2(large) appears 9 times among the rules to belong to the sweet spot cluster. In other words, to belong to the sweet spot cluster, Fig. 11. Flowchart Fig. 11. Flowchart ofof datadata mining mining using using rough setrough theory. set theory. dv2, dv4 and dv6 should be large and dv9 and dv10 should be small. able 2. Frequency of appearance in design rules (+ indicates large, - indicates Table 2. Frequency of appearance in design rules (+ indicates large, - small and no The design sign discussed by using SOM in Section knowledge indicates small and no sign indicates medium) 3.3 can be summarized as indicates medium) Sweet Cd -Cp WW 1) Large dv2 improves CD and –Cp. dv1 Sweet11 Cd 1 -Cp +1 WW 5 2) Small dv7 improves CD. dv1 dv2 11 +9 +2 1 +6+1 +3 5 3) Large dv6 improves -Cp. dv2 dv3 +9 8 +2 -5 +6 6 +3 4 4) Small dv10 improves -Cp. dv3 dv4 +10 8 -5 -3 +5 6 +11 4 Table 2 exhibits information consistent with these dv4 dv5 +10 13 +8 -3 +1 +5 +11 7 visualization results. Table 2, however, provides much more dv5 dv6 13 +8 +1 7 +7 +6 +3 +3 than the visualization. For example, dv4 should be large in dv6 +7 +6 +3 +3 dv7 9 -5 -6 5 order to belong to the sweet spot cluster, but it should be dv7 9 -5 -6 5 dv8 2 -4 3 2 small in order to improve only the drag. Similarly, dv7 should dv8 2 -4 3 2 dv9 -9 -2 -2 -3 be medium although it should be small in order to improve dv9 -9 -2 -2 -3 dv10 -14 -9 -8 -8 CD and –Cp. This illustrates the power of rough set theory. dv10 -14 -9 -8 -8 DOI:10.5139/IJASS.2010.11.4.247 254 3 tep MDO for S TD Airplane the flight experiment of the non-powered supersonic experimental scaled airplane NEXST-1 d in October 2005 (Ohnuki 254 10-review(247-265).indd et al., 2006), research and development of the S3TD has garnered the 2010-12-23 오후 2:25:37 Shigeru Obayashi Multi-Objective Design Exploration and its Applications Visualization results depend on who looks at the figures and study, functional ANOVA (Sobol, 1993) and a SOM (Deb, how deeply one reads. The result of rough set theory reduces 2001) were used for data mining. The distinguishing feature oversights and reveals more detailed conditions. of a SOM is the generation of a qualitative description. When two methods are combined together, the results obtained compensate for the disadvantages of the individual methods 4. Two-Step MDO for S3TD Airplane (Chiba and Obayashi, 2008). Since the flight experiment of the non-powered supersonic 4.1.3 Evaluation methods experimental scaled airplane NEXST-1 succeeded in October 2005 (Ohnuki et al., 2006), research and development of The present exploration system prepared three evaluation the S3TD has garnered the focus of the Japan Aerospace modules for aerodynamics (including stability), structures, Exploration Agency (JAXA) (Murakami, 2006). and boom noise. It took roughly seven days to evaluate one This paper presents the practical two-step multidisciplinary generation using the central numerical simulation system design exploration (MDE) for S3TD airplane. The wing (CeNSS) of Numerical Simulator III in JAXA. planform was re-designed in order to improve lift 1) Aerodynamic evaluation: TAS-Code, parallelized performance at low speeds and also to restrain low boom unstructured Euler/Navier-Stokes solver was employed. performance for wing-fuselage simple configuration. Then, a Three-dimensional Euler equations were solved with a three-dimensional main wing and a stabilizer were designed finite-volume cell-vertex scheme on the unstructured mesh for intimate configuration constructed as the main wing, (Ito and Nakahashi, 2002). fuselage, vertical tail wing, stabilizer, and engine system. 2) Structural evaluation: In the present MDE systems, structural optimization was performed in order to realize 4.1 design-exploration system minimum wing weight with constraints of strength, vibration, and flutter requirements. The strength, vibration, and flutter 4.1.1 Optimizer characteristics were evaluated by using the commercial A hybrid method between particle swarm optimization software MSC. NASTRANTM. and genetic algorithm was employed. Recent optimization 3) Sonic boom evaluation: The computer-aided design- work often used a response surface model (RSM) based on a based automatic panel analysis system (CAPAS) (Makino Kriging surrogate model in order to restrain evaluation time and Naka, 2007) was used. (Jeong et al., 2005b). However, when the optimization problem with many design variables is taken into consideration, many 4.2 First-step multidisciplinary design exploration initial sample points are needed to maintain the accuracy of the response surface. In the present study, RSM was not MDE was defined in the consideration of the sequence selected in order to avoid extensive evaluation time for the of the projecting flight experiment. The initial 0th shape initial samples. In addition, since the designers were required of S3TD was designed to focus on low boom and low drag. to present many optimum solutions for the decision of a However, its shape exhibited insufficient performance in compromised one, an evolutionary-based Pareto approach regards to lift at low speed. Therefore, the second shape with a as an efficient multi-thread algorithm was employed instead primary purpose of lift-performance improvement would be of a gradient-based method. re-designed to maintain low boom intensity (the first shape was for minor change to re-design low-boom geometry). 4.1.2 Data mining Detailed information of this MDE work is provided in Chiba et al. (2008). Although design optimization is important for engineering, the most significant design consideration is the extraction of knowledge in a design space. The results obtained by 4.2.1 Objective functions multiobjective (MO) optimization are not a sole solution, The following five objective functions were defined. The but an optimum set. That is, MO optimization results first three objective functions are for aerodynamics, the are insufficient information for practical design because fourth is for noise, and last is for structures. designers need a conclusive shape. However, the results 1) The minimization of the pressure drag at supersonic acquired from MO optimization can be accounted for as a cruising condition: S•CDp (Mach number of 1.6, altitude of hypothetical design database. Data mining as a post-process 16 km, and target CL of 0.132 for the reference configuration for optimization is essential for efficiently obtaining fruitful of S3TD. S • CL supersonic = const. S denotes the one-sided wing design knowledge (Obayashi and Sasaki, 2003). In the present reference area). 255 http://ijass.or.kr 10-review(247-265).indd 255 2010-12-23 오후 2:25:37 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) 2) The minimization of the friction drag at supersonic condition: S•CDf . In this study, since the Prandtle-Hoerner’s simple equation was used for CDf evaluation, the each fidelity of CDp and CDf was different. Therefore, the objective functions were separated to avoid disappearing one influence for the inconsistency. 3) The maximization of the lift at subsonic condition: S•CL (Mach number of 0.2 and angle of attack of 10.0 deg). 4) The minimization of sonic boom intensity Iboom at supersonic condition. This objective function value was defined as |∆Pmax| + |∆Pmin| at the location with largest peak of (a) Reference configuration (b) Compromise solution sonic-boom signature across boom carpet. Fig. (a) 12. Reference Comparisonconfiguration of wing shape colored by C(b) Compromise solution p and displacement distributions. 5) The minimization of a composite structural weight Wc Fig. 12. Comparison of wing shape colored by Cp and displacement 4.3.1 Objective functions for wing using fiber angle of ply and a number of ply with the distributions. 1) The minimization of the pressure drag CDp at supersonic cruising, which is defined by a Mach number fulfillment of the strength and vibration requirements. When of 1.6, altitude of 14 km, and target the experiences CL of 0.055. cultivated The target by the CL is constant development of due to the fixed planform. real-world an individual could not be satisfied with the requirements, the penalty was given to the rank in the optimizer. aircrafts. 2) The minimization of Four shapes the intensity of were selected sonic boom Iboom taking into consideration at supersonic cruising. This objective function value is defined the as |∆Pmax| +competence. low-boom |∆Pmin| at the location The with compromise final the largest (smallest) peak of sonic-boom solution The present objective functions were selected in order to signature across which boom is carpet. improvable due to the refinements on the fuselage define no constraint conditions due to tradeoffs. Tradeoffs were expected between S•CDp and Wc as well as that between and cross-section 3) The minimization of structural geometries weight W for was a main ultimately wing. Thedetermined. inboard and outboard wings are S•CDp and S•CL. Since asthe respectively defined compromise aluminum solution and composite secured materials. the wing The minimum area, is solved with wing weight the fulfillment of the strength low-speed and flutter requirements. aerodynamic performance For the inboard could bewing made of aluminum, the improved 4.2.2 Decision of a compromise solution from design- thicknesses andof it skin was and multi-frames to re-designed arehave optimized. In addition, practical capabilityfor the foroutboard takeoff wing made of exploration results composite material, the stacking sequence is optimized. These are the combination optimizations, and and landing. However, as the objective functions regarding these are the nesting constitution for the present MDO. The total evolutionary computation of 12 generations aerodynamics depended on wing area, the design knowledge 4) The minimization about wing of thecross difference between section centers of pressure and of gravity |xcp − xcg| to trim. wastheinsufficient. was performed, and 75 non-dominated solutions were “MAC” denotes A mean aerodynamic comparison ofchord. the The center of pressure planform between is calculated as follows. the reference obtained. Here, the derived non-dominated solutions are focused because a compromise solution was selected. The configuration and the selected C Mp compromise solution xcp = xref − targetC × MAC evolution might not converge yet. However, the result was (called ‘compromise’) is shown Lin Fig. 12. Also, airfoils of satisfactory because several non-dominated solutions the reference and xref =compromise 25%MAC configurations near the (1) achieved improvements over the reference configuration. junction relative to the fuselage, kink, and tip are shown. It On the other hand, the center of gravity xcg is computed from the aerodynamic center N0 as follows. Furthermore, a sufficient number of solutions were searched is notable that the reference configuration does not possess so that data mining of the design space can be performed. twists, and its airfoil is described by NACA64A series. The This provides useful knowledge for designers. thickness ratios are respectively defined as 6% at root, 5% The 75 non-dominated solutions were extracted using at kink, and 3% at tip. The installed angle of the wing is −0.5 an SOM in order to determine a compromise solution. deg relative to the fuselage. As S•CL is the maximization The applicable solutions to the following conditions were objective, compromise has a larger wing area than that of the excluded from the 75 non-dominated solutions: 1) The reference configuration. Furthermore, the inner wing area structural requirements were not fulfilled, 2) S•CL is low, or of compromise becomes large as a means of securing the wing area was low (this means the constraint for the landing structural strength. The sweepback angle was more subtle speed), 3) S•CDp and S•CDf were impractically large. As a result so as to not affect Iboom. Thus, the wing area and structural of this operation, 24 non-dominated solutions as the practical strength are also secured. But, the chord length near the kink designs were sorted. The SOM was re-generated using derived was designed short in order to achieve low Wc and S • CDf . 24 non-dominated solutions taking into consideration the Therefore, the number of ply increased to augment the eigen five objective functions. The compromise solution was frequency. The supersonic leading edge of compromise was determined from these individuals taking into consideration located near the root in order to reduce the effect on Iboom of the balance of the five objective functions and the low- the front boom. Also, the blunt leading edge of compromise boom competence as the primary objective of the S TD on 3 was located near the kink in order to improve the strength, SOM. The designers clustered similar planform shapes, and eigen frequency, and subsonic aerodynamic performance. selected the exploitable shape group as a demonstrator using Data-mining results indicate that the sharp leading edge DOI:10.5139/IJASS.2010.11.4.247 256 10-review(247-265).indd 256 2010-12-23 오후 2:25:37 1) The minimization of the pressure drag CDp at supersonic cruising, which is defined by a Mach number of 1.6, altitude of 14 km, and target CL of 0.055. The target CL is constant due to the fixed planform. 2) The minimization of the intensity of sonic boom Iboom at supersonic cruising. This objective function value is defined as |∆Pmax| + |∆Pmin| at the location with the largest (smallest) peak of sonic-boom signature across boom carpet. Shigeru Obayashi Multi-Objective Design Exploration and its Applications 3) The minimization of structural weight W for a main wing. The inboard and outboard wings are respectively near the tip affects Iboom. But, the wing defined area provides as aluminum and a strong and composite multi-framesmaterials. The minimum are optimized. wingfor In addition, weight the is solved with effect on the objectives. Therefore, the thefulfillment knowledgeof the strength and outboard regarding flutter requirements. For the inboard wing made of composite wing material, made of aluminum, the the stacking the airfoil shape is unreliable. sequence is optimized. These are the combination thicknesses of skin and multi-frames are optimized. In addition, for the outboard wing made of Finally, the boom intensity as the primary objective optimizations, and these are the nesting constitution composite material, the stacking sequence is optimized. These are the combination optimizations, and function was compared between the reference and for the present MDO. these are the compromise configurations. Although Iboom performance nesting constitution 4) Ththe for present MDO. e minimization of the difference between the centers of the reference configuration was better, compromise also of pressure and of gravity |xcp − xcg| to trim. “MAC” 4) The minimization of the difference between the centers of pressure and of gravity |xcp − xcg| to trim. maintained a non-N-shaped signature to restrain the initial denotes mean aerodynamic chord. The center of peak. Compromise exhibited better “MAC” S • CLdenotes mean for performance aerodynamic pressure chord. The center ofas is calculated pressure follows.is calculated as follows. the landing speed constraint as well as the Iboom restraint. In C this study, the rearward boom intensity cannot be discussed Mp xcp = xref − targetC × MAC because the assumed fuselage-wing configuration ignores L (1) an engine nacelle and vertical/horizontal tail wings. But, computational fluid dynamics (CFD) visualization of Cp xref = 25%MAC (1) distribution on symmetrical plane Onreveals thathand, shockthe wave the other On the xother center of gravity cg is computed hand, the from centerthe of aerodynamic center N0 as follows. gravity xcg is computed occurs in the vicinity of wing trailing edge. It is necessary that from the aerodynamic center N0 as follows. the full configuration is optimized to design the geometry xcg = N0 − const. restrained rearward boom intensity and to obtain the design knowledge regarding cross section shape. xcg = N0 − const. (2) 4.3 Second-step multidisciplinary design explora- ∆CMp = xref − ∆C × MAC − const. (2) tion L Second-step MDE was implemented among aerodynamics, where, the stability, structures, aeroelasticity, andconstant boom noise. valueAnconst. inwhere, Eq. (2) the is defined constant by const. value the results of is in Eq. (2) Navier-Stokes defined by computations in the results of Navier-Stokes computations in advance. It is set intimate configuration of the advance. It isshape 2.5th latest set oncomposed 0.817 m in this study. on 0.817 m in this study. by main wing, fuselage, vertical tail wing, stabilizer, and 4.3.2 Selection engine system was considered in orderand evaluation to strictly of compromise solution from design-exploration results evaluate 4.3.2 S election and evaluation of compromise solution each objective. As the 2.5th shape did not trim, the geometry The objective total evolutionary computation of 18 from design-exploration generations results was performed using 139 individuals, and 37 non- design to trim is the primary of this optimization. The optimization target was the airfoil shapes of the main The total evolutionary computation of 18 generations was dominated solutions were obtained. The concrete presented materials roughly classify into two groups. wing cross section at root, kink, and tip positions, and the performed using 139 individuals, and 37 non-dominated deflection angle of the stabilizer. This MDE work is explained solutions were obtained. The concrete presented materials in detail in Chiba et al. (2009). roughly classify into two groups. One group comprises information regarding tradeoffs 4.3.1 Objective functions among the objective functions. The other group is composed of information concerning the candidates of a compromise 1) The minimization of the pressure drag CDp at supersonic solution. This includes the contour figure of the Cp distribution cruising, which is defined by a Mach number of 1.6, at a supersonic cruising condition (shown in Fig. 13), the wing altitude of 14 km, and target CL of 0.055. The target CL is section and Cp distribution at root (21.62% spanwise location), constant due to the fixed planform. (a) Upper kink (63.33%), andsurface view tip (99.00%).Moreover, the candidates are 2) The minimization of the intensity of sonic boom Iboom selected from the non-dominated solutions and individuals at supersonic cruising. This objective function value adjacent to them, which indicate the relationship between is defined as |∆Pmax| + |∆Pmin| at the location with the the boom intensity and the trim performance. The boom largest (smallest) peak of sonic-boom signature across intensity has priority in this study. The trim performance boom carpet. provides tradeoffs for all of the other objective functions. The 3) The minimization of structural weight W for a main individual with complicated manufacturing is excluded as a wing. The inboard and outboard wings are respectively candidate of the compromise solution. The important points defined as aluminum and composite materials. The are: 1) the performance of all objective functions, and 2) the minimum wing weight is solved with the fulfillment of possibility for the improvement of the other three objectives the strength and flutter requirements. For the inboard to maintain boom performance. On the final decision for wing made of aluminum, the thicknesses of skin 257 http://ijass.or.kr (b) Symmetrical-plane view Fig. 13. Cp distribution of the decided compromise solution. The angle of attack of 2.915deg is set to achieve the target CL. 10-review(247-265).indd 257 2010-12-23 오후 2:25:37 xxcg = N0 − const. cg = N0 − const. ∆CMp = xxref = − ∆CMp × MAC − const. (2) ref − ∆C L × MAC − const. (2) ∆C L where, where, the the constant constant value value const. const. in in Eq. Eq. (2) (2) is is defined defined by by the the results results of of Navier-Stokes Navier-Stokes computations computations in in advance. advance. It is set on 0.817 m It is set on 0.817 m in in this this study. study. 4.3.2 4.3.2 Selection Selection and and evaluation evaluation of of compromise compromise solution solution from from design-exploration design-exploration results results Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) The The total total evolutionary evolutionary computation computation of of 18 18 generations generations was was performed performed using using 139 139 individuals, individuals, and and 37 37 non- non- dominated solutions were obtained. The concrete presented materials roughly classify into two groups. dominated solutions were obtained. The concrete presented materials roughly classify into two groups. the exception of the trim performance. Since the designed reflection angle of the stabilizer can afford to be harder, its modification can improve the trim performance. Figure 13 shows the Cp distributions on the upper surface and on the symmetrical plane. This figure reveals that the (a) Upper surface view (a) (a) Upper Upper surface surface view view shock waves occur around the front location of the engine and bumps into the upper surface of the main wing. Although the shock wave is shielded, the performance of the wing is degraded. It is important to design the geometry of the wing for the alleviation of this shock wave. At the root location, since two shock waves bump into the wing upper surface, the increase of the wing thickness provides insufficient lift performance and augments the induced drag. On the other hand, it reveals the connection between the structural weight and the structural requirements. The constraint of the (b) (b) Symmetrical-plane Symmetrical-plane viewview thickness at the root is 5% ± 1% chord length. The thickness Fig. 13. C Fig. 13. (b) Symmetrical-plane Cpp distribution distribution ofof the the decided view decided compromise compromise solution. solution. of the compromise solution at the root is 4.4% chord length. The The angle angle of of attack attack of of 2.915deg 2.915deg is is set set to to achieve achieve the target C the target CLL.. Its thickness becomes thin with the fulfillment of the Fig. 13. Cp distribution of the decided compromise solution. The angle of attack of 2.915deg is set to achieve the target CL. structural requirements. The upper surface near the leading One One group group comprises comprises information information regarding regarding tradeoffs tradeoffs among among the the objective objective functions. functions. The The other other group edgeis group is at the kink location is dented. Therefore, the shock composed of information Table 3. The composed of information concerning the specification concerning candidates of of the selected the candidates a compromise compromise of a compromise solution. This solution solution. includes the contour This includes the contour wave occurred from the front of the engine is mitigated. The figure figure of the C of the Cpp distribution distribution atatCaaDpsupersonic supersonic cruising cruising condition condition (shown (shown 0.02092 in in Fig. Fig. 13), 13), the the wing wing section and C and Cpp section pressure distribution also indicates the similar effect. This distribution at root (21.62% spanwise location), kink (63.33%), and tip (99.00%).Moreover, the candidates I boom location), kink (63.33%), and distribution at root (21.62% spanwise tip (99.00%).Moreover, 0.9301 psf the candidates hollow component is the key necessary for improving the W 341.3 kg aerodynamic performance. The maximum thickness at the |x cp-x cg | 1.065 m Outboard wing 8 plies * 4 sets kink is 5.4% chord length. The thickness at the kink location Inboard wing skin: 9.0 mm, multi frames: 8.9 mm should be thick in order to provide sufficient aerodynamic Design angle of attack 2.915 deg performance and to fulfill the structural requirements. At Reflection angle of stabilizer -1.608 deg the tip location, the wing exhibits insufficient aerodynamic performance. Since the wing geometry in the vicinity of the tip strictly affects the boom intensity indicated by the data- a compromise solution, the individual with a wing section mining results, the wing tip geometry is evolved to reduce similar to NEXST-1 was selected. That is, the shape of the the boom intensity. In addition, a strong shock wave occurs selected compromise solution is more feasible regarding around the rear part of the fuselage. As this corrupts the rear aerodynamics and manufacture. The conclusion followed boom intensity, re-consideration is needed. that trim performance was improved by the regulation of the The ground pressure signature of the compromise reflection angle of the stabilizer (the outside range set in the solution indicates that both peaks of the front and rear boom present optimization is namely reconsidered). Therefore, a intensity are weakened because it is not N shape. The data weak non-dominated solution was selected as a compromise mining reveals that three design variables for the main wing solution. such as the cant angle for the attachment to the fuselage, Table 3 shows the specification of the compromise solution. twisting angle, and the bluntness of the leading edge affects It is notable that the criteria of the design angle of attack the front boom. It similarly reveals that the design variable and the reflection angle of the stabilizer is the horizontal as the reflection angle of the stabilizer affects the rear line (longitudinal axis of body) for three views. Thus, the boom. In particular, the inboard wing with a camber on the reflection angle is defined for the longitudinal axis of the trailing edge improves the rear boom intensity. The strong body and is independent of the angle of attack. This result expansion wave from the trailing edge extinguishes the shows that the trim performance is insufficient. The results positive pressure from the lifting surface of the rear fuselage. from ANOVA indicate that the cant angle and the geometry Moreover, the large negative reflection angle of the stabilizer of the main wing, which influence trim performance, affect causes strong rear boom intensity due to a similar reason. several objective functions. However, the reflection angle However, the negative reflection angle must be trimmed. The of the stabilizer does not affect any objective function with reflection angle of the stabilizer is essential in the present DOI:10.5139/IJASS.2010.11.4.247 258 10-review(247-265).indd 258 2010-12-23 오후 2:25:37 Shigeru Obayashi Multi-Objective Design Exploration and its Applications design problem. mimics the original map in Ikui (1988). This map represents The two multidisciplinary design explorations for the silent the contour lines of the pressure recovery coefficient Cpr supersonic technology demonstrator were demonstrated. in the nozzle throat to exit section, which are plotted on The process of this approach provided tradeoffs among the plane taking two nozzle geometry parameters into the defined design requirements, i.e., objective functions. consideration (aspect ratio λ and expansion ratio ε). It reveals Furthermore, the important design variables were evident, the Cpr vs. λ and Cpr vs. ε relationships, which are suitable for and the correlations between the design requirements diffusers with flat blades. However, actual diffusers mostly and the variables were also shown. The obtained design consist of cambered blades, and actual diffuser performance information was produced for the designers, and it was seems to be affected by the blade geometries ignored in the employed as the resource of decision making in order to quasi-one-dimensional nozzle theory (blade camber, blade determine a compromise solution. The knowledge was attack angle to flow, etc.). In addition, diffuser hub and produced for future design. case geometries may also affect diffuser performance (e.g., Kitadume et al. (2007) discuss the case geometry effects based on experiments). A further consideration is that actual 5. Performance Studies for Centrifugal Dif- diffusers should ensure good overall performance, i.e., air fusers pressure must be recovered not only in the nozzle section but also upstream and downstream of the nozzle. Thus, This study discusses further applicability of data mining the performance map should be constructed in a higher- techniques (ANOVA and SOM) to a fundamental topic in dimensional form, which allows comprehension of the engineering research, i.e., the construction of performance various relationships among many performance parameters maps that represent relations between performance and and many geometry parameters. Therefore, the centrifugal geometry parameters. Performance maps are often used to diffuser is an appropriate target product to validate the data make a first decision on preliminary specification of a product mining techniques for high-dimensional performance map to be designed. Therefore, performance map construction is construction, as well as to provide useful knowledge about an essential area in the field of engineering. the relations between diffuser performance and geometries. This study was performed using a centrifugal diffuser as The performance studies for centrifugal diffusers have the target product for performance map construction. The also been reported by other researchers. Krain (1981) centrifugal diffuser is one a component commonly used in experimentally measured the internal flow field development various household appliances (air cleaners, vacuum cleaners, within an impeller-diffuser-interacted stage by means of etc.) as well as heavy industrial machineries (aircraft engines, laser velocimeters. Simon et al. (1987) experimentally marine engines, etc.). Conventionally, diffuser performance investigated simultaneous adjustments of inlet guide blades has been evaluated based on the quasi-one-dimensional and diffuser blades in centrifugal compressors for the nozzle theory. Figure 14 illustrates the performance map improvements in both performance and operating range. for a linear nozzle with a rectangular cross-section, which Paxson and Skoch (1998) proposed and demonstrated a wave augmented diffuser that reduces the loss caused by the discharge flow turning from a radial or tangential direction to an axial direction by numerical simulations. However, diffuser geometries considered in those studies were limited to flat blades (Krain, 1981; Paxson and Skoch, 1998) or cambered blades parameterized simply by the angle of attack (Simon et al.,1987). Although Kim et al. (2009) compared and discussed the performance among three different diffusers (wedge, symmetric airfoil, and cambered airfoil) by numerical simulations, it still was lacking in the varieties of diffuser geometries that could be considered for performance map construction. In a recent study conducted by Abdelwahab and Gerber (2008), a three-dimensional aerofoil diffuser geometry, which allows spanwise variations Fig. 14. Performance map for a linear nozzle with rectangular cross-section (Ikui, 1988).stagger, and lean angles, was developed for in solidity, Fig. 14. Performance map for a linear nozzle with rectangular cross- section (Ikui, 1988). industrial centrifugal compressor stages based on both performance studies for centrifugal diffusers have also been reported by other researchers. Krain (1981) entally measured the internal flow field development within an impeller-diffuser-interacted stage by f laser velocimeters. Simon et al. (1987) experimentally investigated simultaneous 259 adjustments of inlet http://ijass.or.kr lades and diffuser blades in centrifugal compressors for the improvements in both performance and g range. Paxson and Skoch (1998) proposed and demonstrated a wave augmented diffuser that reduces the sed by the discharge flow turning from a radial or tangential direction to an axial direction by numerical 10-review(247-265).indd 259 2010-12-23 오후 2:25:38 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) numerical and experimental analyses. But its performance leading and trailing edges). For simplicity, this study fixed D3 tendencies have not been explained in a high-dimensional and generated 100 diffusers with different shapes through form of geometry parameters. the Latin hypercube sampling (LHS) (McKay et al., 1979), in which the values of D4/D3, D5/D4, Dex/D5, β3, and β4 were 5.1 Geometry and performance definition of cen- treated as five independent random variables for geometry trifugal diffusers definition of the diffuser. As described in the next section, Figure 15 shows the centrifugal diffuser geometries this study implemented the data mining for performance considered in this study. This diffuser has 13 similar cambered map construction based on 12 geometry parameters in the blades of constant thickness. The leadi ng and trailing edges nozzle part (ht, he, lp, ls, lavg, θ, α, κp, κs, κavg, ε, and λ shown in of these blades are linear and parallel to the diffuser center Fig. 15(c)) instead of the five random variables considered axis. The diffuser geometries are defined by the blade size (D3 in LHS. and D4 shown in Fig. 15(a)), the case size (D5 and Dex shown The centrifugal diffuser should work so efficiently that it indefinition Fig. 15(a)),ofand thethediffuser. angle (β3in As described blade camber β4 shown andthe can next section, thisto decelerate internal airthe study implemented flowdata without miningpressure for loss. In in Fig. 15(b), where a linear profile is assumed between the general, such performance can be quantified by a pressure performance map construction based on 12 geometry parameters in the nozzle part (ht, he, lp, ls, lavg, θ, α, κp, κs, recovery coefficient such that a larger value of the coefficient κavg, ε, and λ shown in Fig. 15(c)) instead of the five random variables leads considered in LHS. air deceleration. For general to more efficient discussions on diffuser performance, this study focused on two pressure recovery coefficients in different sections as performance functions: Cpr in-3 for inlet to blade entrance section and Cpr in-4 for inlet to blade exit section. This study was performed to evaluate the values of Cpr in-3 and Cpr in-4, which were obtained at a constant mass flow rate, from the CFD simulations for 100 different diffusers generated by LHS. The present CFD simulations solved the Reynolds-averaged Navier-Stokes (RANS) equations for compressible air, which described in the next section, this study implemented the data mining for were coupled with the high-Reynolds-number k-ε turbulence ased on 12 geometry parameters in the nozzle(a) partSide he, lp, ls, lavg, θ, α, κp, κs, (h , view (b) Upper view definition of the diffuser. As described in the next t section, this study implemented the data using model, miningtheforcommercial software STAR-CDTM (http:// (a) Side view )performance instead of the five map random variables construction based onconsidered 12 geometry in LHS. parameters in the nozzle part (ht, he, lp,www.cd-adapco.com. ls, lavg, θ, α, κp, κs, accessed April 1, 2009). Consequently, in the present implementation, the performance values κavg, ε, and λ shown in Fig. 15(c)) instead of the five random variables considered in LHS. were successfully obtained for 85 diffusers, while the CFD simulations fell into divergence for the rest. 5.2 Data mining results and discussion Figure 16 shows the data mining results obtained by ANOVA. (c) Close-up view of nozzle part Figures 16(a) and (b) show the breakdowns of the main effects and the interaction effects for each performance Fig. 15. Centrifugal diffuser geometries. function. For Cpr in-3, only the variable ht (throat width) has a major contribution. For Cpr in-4, although various contributions The centrifugal diffuser should work so efficiently that it can to decelerate internal air flow without pressure w (b) Upper view of ht, κp (pressure side curvature), ε (expansion ratio), and λ loss. (a) Side In general, such performance view (b) Upper view can be quantified (b) by a pressure Upper recovery view(aspect coefficient such that a larger value of ratio) were revealed, a combination of two variables, the coefficient leads to more efficient air deceleration. For general discussions ht and κp, has on thediffuser largest performance, contribution. this study16(c) and Figures focused on two pressure recovery coefficients in different sections (d) shows the functional-formed as performance functions: Cpr in-3 main and to for inlet interaction effects of the variables that showed large contributions in blade entrance section and Cpr in-4 for inlet to blade exit section. This study was performed to evaluate the values of Figs. 16(a) and (b), respectively. Figure 16(c) indicates that Cpr in-3 and Cpr in-4, which were obtained at a constant mass flowsmaller rate, from the CFD ht leads simulations to larger for 100 Cpr in-3. Figure 16(d) different indicates that a diffusers generated by LHS. The present CFD simulations solved of smaller ht and the Reynolds-averaged combination larger κp, and(RANS) Navier-Stokes a combination of (c) Close-up viewequations of nozzle part larger h and smaller κ for compressible air, which were coupled with the high-Reynolds-number k-ε turbulence model, using t p lead to larger C pr in-4 . (c) Close-up view of nozzle part Figures 17 shows the SOM color images, each of which Fig. 15. Centrifugal diffuser geometries. the commercial (c) Close-up view of nozzleTMpart Fig. 15.software STAR-CD Centrifugal (http://www.cd-adapco.com. diffuser geometries. accessed is colored April 1, to according 2009). Consequently, performance or nozzle in thegeometry present Fig. implementation, 15. Centrifugal the performance values were successfully diffuser geometries. obtained parameters (onlyfor four 85 diffusers, nozzle while geometries the CFD with large ld work so efficiently The centrifugal that should diffuser it can to decelerate work internal so efficiently thatairit flow can towithout pressure decelerate internal air flow without pressure simulations fell into divergence for the rest. celoss. canInbegeneral, quantified suchby a pressure can performance recovery coefficient be quantified by a such thatrecovery pressure a larger coefficient value of such that a larger value of cient air deceleration. the coefficient leads toFor general 5.2 more Datadiscussions mining efficient on diffuser results and air deceleration. DOI:10.5139/IJASS.2010.11.4.247 performance, For discussion general this on discussions study diffuser260 performance, this study ryfocused coefficients on twoinpressure different sectionscoefficients recovery as performance functions: in different Cprasin-3performance sections for inlet tofunctions: Cpr in-3 for inlet to Fig. 16 shows the data mining results obtained by ANOVA. Fig. 16(a) and (b) show the breakdowns of the for inlet blade to blade entrance exit and section section. This Cpr in-4 for study inlet towas performed blade to evaluate exit section. This study thewas values of performed to evaluate the values of btained at aCconstant Cpr in-3 and mass pr in-4, which flow were rate, from obtained at a the CFDmass constant simulations forfrom flow rate, 100 the different CFD simulations for 100 different diffusers generated present CFD by LHS.solved simulations The present CFD simulations solved the Reynolds-averaged 10-review(247-265).indd 260 the Reynolds-averaged Navier-Stokes (RANS) Navier-Stokes (RANS) 2010-12-23 오후 2:25:38 main effects and the interaction maineffects effectsforand each theperformance function. interaction effects eachCprperformance forFor in-3, only thefunction. ht (throat variable For Cpr in-3, only the variable ht (throat width) has a major contribution. width) Cpr ain-4major Forhas , although various contributions contribution. of ht, κpvarious For Cpr in-4, although (pressure of ht, εκp (pressure side curvature), ε side curvature), contributions (expansion ratio), and λ (aspect ratio) were (expansion revealed, ratio), and λ a(aspect combination of two ratio) were variables, revealed, ht and κp, has a combination the largest of two variables, ht and κp, has the largest contribution. Fig. 16(c) and (d) shows the Fig. contribution. functional-formed main and 16(c) and (d) shows the interaction effects of functional-formed theand main variables that effects of the variables that interaction interaction effect results from the ANOVA in Fig. 16(d). Furthermore, other hig showed large contributions inshowed Fig. 16(a) and large (b), respectively. contributions in Fig.Fig. 16(c) 16(a) andindicates Fig.ht16(c) that smaller (b), respectively. leadsindicates to larger that smaller ht leads to larger alsoMulti-Objective Shigeru Obayashi be determinedDesign by comparing the color Exploration and itspatterns of all Applications the SOM images. Thus, Cpr in-3. Fig. 16(d) indicates that a combination Cpr in-3 . Fig. 16(d) indicates ht and of smallerthat larger κp, and a combination a combination of smaller κp, hand of larger ht and larger t and a combination of larger ht and smaller κp lead to larger Cpr in-4smaller . as the high-dimensional performance maps themselves. κp lead to larger Cpr in-4. raction effects for each performance function. For Cpr in-3, only the variable ht (throat bution. For Cpr in-4, although various maincontributions effects and of t, κp (pressure thehinteraction side for effects curvature), ε each performance function. For Cpr in-3, only the variable ht (throat (aspect ratio) were revealed, a combination of two variables, ht and κ p , has the largest width) has a major contribution. For Cpr in-4, although various contributions of ht, κp (pressure side curvature), ε nd (d) shows the functional-formed interaction main and effect results interaction effectsfrom thevariables of the ANOVAthat in Fig. 16(d). Furthermore, other higher-order interaction effects can (expansion ratio), and λ (aspect ratio) were revealed, a combination interaction of two variables, and κp, from effectht results has thethe largest ANOVA in Fig. 16(d). Furthermore, other hig ns in Fig. 16(a) and (b), respectively.also Fig. be determined 16(c) indicates by comparing that smaller h the color leads to patterns of all the SOM images. Thus, the SOM color images can serve larger contribution. Fig. 16(c) and (d) shows the functional-formed main and interaction effects of (a) t the variables C that also be determined by comparing pr in-3 the color patterns of all the SOM images. Thus, (a) C pr in- ht as andthe high-dimensional in performance κp, and a combination and maps themselves. 3 es that a combination of smallershowed larger large contributions Fig. 16(a)of larger ht respectively. (b), and Fig. 16(c) indicates that smaller ht leads to larger as the high-dimensional performance maps themselves. Cpr in-4. Cpr in-3. Fig. 16(d) indicates that a combination of smaller ht and larger κp, and a combination of larger ht and smaller κp lead to larger Cpr in-4. (a) Breakdowns of main and interaction effects onofCmain (a) Breakdowns (b) Breakdowns pr in-3 and interaction effects onofCmain pr in-3 and interaction effects onofCmain (b) Breakdowns pr in-4 and interaction effects on Cpr in-4 (a) Breakdowns of main and interaction effects on C pr in- 3 effects for each performance function. For Cpr in-3, only the variable ht (throat For Cpr in-4, although various contributions of ht, κp (pressure side curvature), ε ratio) were revealed, a combination of two variables, ht and κp, has the largest interaction effect results from the ANOVA in Fig. 16(d). Furthermore, other higher-order (c) ht interaction effects can shows the functional-formed main and interaction effects of the variables that also be determined by (a) Cpr in-3 the color patterns of all theinteraction comparing SOM images. effect results Thus, the (b) from SOM C in-4 (b) C pr pr the ANOVA color imagesincan Fig. 16(d). Furthermore, other hig serve g. 16(a) and (b), respectively. Fig. 16(c) indicates that smaller ht leads to larger in- 4 (a) Cpr in-3 as the high-dimensional performance maps themselves. also be determined by comparing the color patterns of all the SOM images. Thus, a combination of smaller ht and larger κp, and a combination of larger ht and (c) Functional main effect of h on C vs. as theCinteraction κp on of htFunctional (d) Functional interaction effect(d) high-dimensional pr in-4 performance maps themselves. effect of h vs. κ on C t (c) Functional pr in-3 main effect of ht on Cpr in-3 t p pr in-4 Fig. 16. ANOVA data mining results. Fig. 16. ANOVA data mining results. nd interaction effects on Cpr in-3 (b) Breakdowns of main and interaction effects on Cpr in-4 Fig. 17 shows the SOM colorFig.images, each of 17 shows which iscolor colored according eachonofto performance or nozzle geometry (b) Breakdowns of the mainSOM images, and interaction effects C prwhich in- 4 is colored according to performance or nozzle geometry (a) Breakdowns parameters (only four nozzle geometries with of main large and interaction contributions are effects on Cprhere). considered C (b) Breakdowns becomes of large main in the andCinteraction effects on Cpr in-4 parameters (only four nozzle geometries with large contributions in-3 pr in-3 are considered here). pr in-3 becomes large in the left area on the SOM (denotedleft as “A” area in onFig. the 17(a)), while ht as SOM (denoted becomes “A” in small in thiswhile Fig. 17(a)), area. This relationsmall ht becomes is consistent in this area. This relation is consistent with the main effect results given Cpr in-4 (e) ε withbythethe ANOVA, main as shown effect results in Fig. given 16(c). by the Conversely, ANOVA, as shown becomes in Fig. 16(c).large in the Cpr in-4 becomes Conversely, large in the (c) ht (d) κp Fig. 17. Self-organizing map data mining results upper area on the SOM, whichupperis denoted area onasthe a combination SOM, whichofis“B” and “C” denoted as ain Fig. 17(b). of combination Area“B”Band has “C” small inhFig. t and17(b). Area B has small ht and (c) h (c) h t t large κp, while area C has large h and small κ . Therefore, (a) C each large t κp, while areap C has large htprand of areas B and C is also consistent Among in-3 small κp. Therefore, each of areas B and with thethe C isresults obtained (b) also consistent in the Cpr in-4with thepresent data mining, the interaction effect (a) Cpr in-3because κp is not considered in the quasi-one-dim to discuss diffuser performance (d) Functional interaction effect of ht vs. κp on Cpr in-4 The present results specify a large effect of the blade curvature on the pressu in effect of ht on Cpr in-3 Fig. 16. ANOVA data mining results. diffuser with a curved nozzle. Therefore, this study confirmed that data mining te (c) Functional main effect of ht on Cpr in-3 (d) Functional interaction effect of ht vs. κp on Cpr in-4 M color images, each of which is colored according to performance or nozzle Fig. 16.geometry ANOVA data mining results.new engineering knowledge, and is suitable and applicable to performanc (c) Functional main effect of h t on C pr in- 3 dimensions. zle geometries with large contributions Fig.are 17considered SOM Ccolor shows the here). becomeseach pr in-3 images, largeofinwhich the is colored according to performance or nozzle geometry action effects on Cpr in-3 (b) Breakdowns of main and interaction effects on Cpr in-4 oted as “A” in Fig. 17(a)), while hparameters t becomes small in this area. This ε (e) relation is consistent (f) λ (only four nozzle geometries with large contributions are considered here). Cpr in-3 becomes large in the Fig. 17. Self-organizing map data mining results. (e) ε ts given by the ANOVA, as shownleft in area Fig. 16(c). on the Conversely, Cpr as becomes large in the SOM (denoted in-4“A” (c) ht in Fig. 17(a)), while ht becomes small in this area. This relation(d) isκpconsistent Fig. 17. Self-organizing map data mining results which is denoted as a combinationwithof “B” and “C” in Fig. 17(b). Area B has small ht as andshown (d) κ p theAmong the results main effect obtained results given by the inANOVA, the present data mining, the interaction in Fig. 16(c). Conversely, C effect pr in-4 of h(c) ht is becomes t and κ large p in athe remarkable issue as large ht and small κp. Therefore, each of areas B and C is also consistent with the Among the results obtained in the present data mining, the interaction effect upper area on the to discuss SOM, performance diffuser which is denoted because κp is not considered as a combination of “B” and “C” in Fig. in the 17(b). Area B has small quasi-one-dimensional ht andtheory (Fig. 14). nozzle large κp, present The while area results large ht aand C hasspecify small large κp. Therefore, effect of the blade of to discuss each curvature areas B ondiffuser and performance C ispressure the also consistent recoverywith the κp is notinconsidered because performance the in the quasi-one-dim The present results specify a large effect of the blade curvature on the pressu diffuser with a curved nozzle. Therefore, this study confirmed that data mining techniques can be used to discover diffuser with a curved nozzle. Therefore, this study confirmed that data mining te new engineering knowledge, and is suitable and applicable to performance map construction with high new engineering knowledge, and is suitable and applicable to performanc dimensions. of ht on Cpr in-3 (d) Functional interaction effect of ht vs. κp on Cpr in-4 dimensions. Fig. 16. ANOVA data mining (d) results. (e)of hεt vs. κ p on C pr in- 4 Functional interaction effect (f) λ Fig. 17. Self-organizing map data mining results. (e) ε ε (e) images, each of which isFig.colored 16. ANOVA data mining results. according to performance or nozzle geometry Fig. 17. Self-organizing map data mining results Among the results obtained in the present data mining, the interaction effect of ht and κp is a remarkable issue metries with large contributions are considered here). Cpr in-3 becomes large in the to discuss diffuser performance because κp is not considered in Among the results obtainednozzle the quasi-one-dimensional in the theory present(Fig. data 14 mining, ). the interaction effect “A” in Fig. 17(a)), while ht becomes small in this area. This relation is consistent http://ijass.or.kr 261 to discuss diffuser performance because κ is not considered in the quasi-one-dim by the ANOVA, as shown in Fig.The present 16(c). results C Conversely, specifybecomes pr in-4 a large largeeffectinofthethe blade curvature on the pressure recovery performance p in the Thethat present results techniques specify a can largebeeffect of discover the blade curvature on the pressu denoted as a combination of “B”diffuser and “C”with a curved in Fig. 17(b).nozzle. Area BTherefore, has small this study confirmed ht and data mining used to new engineering knowledge, and is suitable and applicable diffusertowith a curved nozzle. performance Therefore, thiswith map construction studyhigh confirmed that data mining te ht and small κp. Therefore, each of areas B and C is also consistent with the dimensions. new engineering knowledge, and is suitable and applicable to performanc 10-review(247-265).indd 261 2010-12-23 오후 2:25:39 Int’l J. of Aeronautical & Space Sci. 11(4), 247–265 (2010) (d) κp into clusters with specific design features. SOM obtained from the solutions uniformly sampled from the design space revealed that the sweet spot could exist. By comparing the SOM colored by influential design parameters found by ANOVA and the objective functions, several design rules were extracted. Finally, sufficient conditions belonging to the sweet spot cluster were extracted by rough set theory. Similarly sufficient conditions to improve each design (f ) λ λ (f) objectives were extracted. The use of data mining will provide Fig. 17. Self-organizing map data mining results. more knowledge about the design space and extract more Fig. 17. Self-organizing map data mining results. information from the optimization process. n the present data mining, the interaction effect of ht and κp is a remarkable issue because κp is not considered in the quasi-one-dimensional nozzle theory (Fig. 14). arge effect of the blade curvature on the pressure recovery performance in the References contributions are considered here). Cpr in-3 becomes large in herefore, this study confirmed that data mining techniques can be used to discover Abdelwahab, A. and Gerber, G. (2008). A new three- the left area on the SOM (denoted as “A” in Fig. 17(a)), while and is suitable and applicable tosmall ht becomes performance map in this area. Thisconstruction with high relation is consistent with dimensional aerofoil diffuser for centrifugal compressors. the main effect results given by the ANOVA, as shown in Fig. Proceedings of the Institution of Mechanical Engineers, Part 16(c). Conversely, Cpr in-4 becomes large in the upper area A: Journal of Power and Energy, 222, 819-830. on the SOM, which is denoted as a combination of “B” and Agrawal, G., Lewis, K., Chugh, K., Huang, C. H., Parashar, S., “C” in Fig. 17(b). Area B has small ht and large κp, while area and Bloebaum, C. L. (2004). Intuitive visualization of Pareto C has large ht and small κp. Therefore, each of areas B and Frontier for multi-objective optimization in n-dimensional C is also consistent with the interaction effect results from performance space. 10th AIAA/ISSMO Multidisciplinary the ANOVA in Fig. 16(d). Furthermore, other higher-order Analysis and Optimization Conference, Albany, NY. pp. 1523- interaction effects can also be determined by comparing the 1533. color patterns of all the SOM images. Thus, the SOM color Agrawal, G., Parashar, S., and Bloebaum, C. L. (2006). images can serve as the high-dimensional performance Intuitive visualization of hyperspace pareto frontier for maps themselves. robustness in multi-attribute decision-making. 11th AIAA/ Among the results obtained in the present data mining, ISSMO Multidisciplinary Analysis and Optimization the interaction effect of ht and κp is a remarkable issue to Conference, Portsmouth, VA. pp. 729-742. discuss diffuser performance because κp is not considered Alpern, B. and Carter, L. (1991). The Hypebox. IEEE in the quasi-one-dimensional nozzle theory (Fig. 14). The Visualization Conference, San Jose, CA. pp. 133-139. present results specify a large effect of the blade curvature Chernoff, H. (1973). The use of faces to represent points on the pressure recovery performance in the diffuser with in K-dimensional space graphically. Journal of the American a curved nozzle. Therefore, this study confirmed that data Statistical Association, 68, 361-368. mining techniques can be used to discover new engineering Chiba, K., Makino, Y., and Takatoya, T. (2008). knowledge, and is suitable and applicable to performance Evolutionary-based multidisciplinary design exploration for map construction with high dimensions. the silent supersonic technology demonstrator wing. Journal of Aircraft, 45, 1481-1494. Chiba, K., Makino, Y., and Takatoya, T. (2009). Design- 6. Conclusions informatics approach for intimate configuration of silent supersonic technology demonstrator. 47th AIAA Aerospace This article reviewed existing visual data mining Sciences Meeting including the New Horizons Forum and techniques that had been formally applied to engineering Aerospace Exposition, Orlando, FL. pp. AIAA 2009-0968. problems. We discussed three applications of MODE: MDO Chiba, K. and Obayashi, S. (2008). 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