Distributed Framework for Micro Aerial Vehicle Design Automation D. Lundström * , K. Amadori † and P. Krus ‡ Linköping University, Linköping, 581 83, Sweden Micro or mini aerial vehicles are characterized by being simple and inexpensive to build, and due to their small size very important to optimize. They are also likely to be built in relatively small series and be tailored for the sensors and equipment available at the time of deployment. Therefore "design and build on demand" is very attractive, where a modular concept with a more or less automated design process is desirable. In this paper design automation of a Micro or Mini Aerial Vehicle (MAV) is demonstrated using a distributed design optimization framework that involves selections of components from a database of propulsion system equipment and geometrical shape optimization. The framework links together a CAD system, responsible for the aircraft shape generation, with a panel code for aerodynamic evaluations. Nomenclature CAD cL cdi cm c MDF MDS SOA SOAP WSDL T = = = = = = = = = = Angle of attack Computer Aided Design Lift coefficient at given angle of attack Induced drag coefficient at given angle of attack Pitching moment coefficient at given angle of attack Chord length CAD datums model CAD surfaces model Service Oriented Architecture Simple Object Access Protocol Web Service Description Language I. Introduction HE term Micro Aerial Vehicle (MAV) was originally defined by American Defense Advanced Research Projects Agency, DARPA, to describe an aircraft with a physical size of lesser than 150mm. In layman’s terms the description MAV is however used more loosely and a more general description is an aerial vehicle of dimensions lesser then 500mm. Within this paper this is the definition MAV is referring to. Micro Aerial Vehicles are getting increased interest from both military and civilian authorities. Research conducted during the last years has proven that fully autonomous MAVs flying in a “real world” environment (wind, rain etc) today are feasible. A commercial break through is likely not far away. At Linköping University work is being done to automate the design process of Micro Aerial Vehicles (MAVs). Scenario driven design is considered important where the MAV quickly can be designed and built for a specific scenario. A major part of the process is to create a design tool and optimization methodology for MAVs. Work on this is ongoing and in a previous paper by Lundström1, MAV design optimization was demonstrated using a Genetic Algorithm to configure an optimal propulsion system from a database of components, while simultaneously establishing the optimum geometrical plan form described by continuous parameters. In this work traditional models for aerodynamic calculations were used, such as skin friction corrected with form factor for parasite drag and lifting line equations for induced drag. No consideration was taken for airfoil shape, wing twist etc. Therefore as a next * PhD Student, Department of Mechanical Engineering, David.Lundstrom@liu.se, AIAA Student Member. PhD Student, Department of Mechanical Engineering, Kristian.Amadori@liu.se, AIAA Student Member. ‡ Professor, Department of Mechanical Engineering, Petter.Krus@ liu.se. † 1 American Institute of Aeronautics and Astronautics step the aerodynamic calculations has been improved. Amadori et al.2,3 have shown that panel code can be effectively used within distributed frameworks for design optimization, where they can be linked to parametric CAD models. In the present paper the discrete propulsion system modeling used in Ref.1 is combined with a parametric CAD model and a panel code for aerodynamic performance prediction, as shown in Figure 1. Spreadsheet model Obj. function Optimizer Control variables Weight wetted area etc. Geometry parameters Parametric CAD model cD, Geometry mesh cm, cL Aerodynamic model Figure 1. The design framework A. Design automation. Design automation is of general interest in aeronautics, and automated methods for coupling aerodynamic calculations, CAD modeling, FEM analysis etc are getting an increased usage in the design of manned aircraft, but primarily during the conceptual and preliminary design phases. Completely automating the design, from concept to production is, however, far from possible. MAVs on the other hand are small, simple to build, and requires relatively few components. This is an application where fully automated design has great potential. The ideal design automation procedure is described in Figure 2. a. Component List Design Requirements b. c. Figure 2. MAV design automation 2 American Institute of Aeronautics and Astronautics From a mission scenario a design specification is created. This is information such as performance, payload requirements etc. A design tool, such as the presented “design framework”, then uses several coupled computer software’s, to generate the following. a. b. c. List of optimal propulsion system components. From a database of off the shelf components. A full CAD model that is used for production. Production may be accomplished in composite material, foam plastic, rapid prototyping etc. Control scheme for Flight control system. Basically the configuration software to upload in the intended autopilot. The current work focuses on task a. and b. while the control system optimization requires flight mechanical modeling and will be subject to future work. Imagine for instance a scenario requiring a high quality live video, thermal imaging, and high resolution photos for object identification or geo localization. All these sensors exist in sizes small enough to be carried on a MAV, but one MAV do not have the payload capability to carry all at once. Using multiple MAVs carrying different sensors is an attractive solution. Due to different weights and sizes of these sensors it may be difficult to design a MAV that can be adopted for each sensor while achieving proper stability and performance. This is an example where design automation could have a great impact. Design automation allows a much more flexible way of using MAVs for missions previously solved by larger more expensive UAVs. For different scenarios one can focus on what sensors to use rather then compromising on what sensors can be adapted to one existing platform. II. Distributed Design Framework The design framework presented in this work has been created from the experience gathered from the Modelith framework which was developed within the research group4. The Modelith framework is based on Web Service Technology and implements as so-called Service Oriented Architecture (SOA)5. This architecture is based a set of standards for distributed computing developed by World Wide Web Consortium which enables distribution and integration of tools at the same time. The interconnected modules communicate using standardized messages formatted according to the SOAP standard (Simple Object Access Protocol). These messages include the transmitted data and instructions for which method to invoke on the connected service. Each module is also described using WSDL (Web Service Description Language). This description provides enough information to automatically create the computational interface between the modules. Please refer to Ref.4 and Ref.5 for a more detailed and technical description. B. Excel Spreadsheet The base of the design framework is a user-friendly Excel spreadsheet. It serves as an input interface for the different design variables, and also links together the calculations between CAD software and the Panel Code. In Excel the calculations of the different propulsion system components are made. Excel then calls the CAD software for weight calculations and the Panel Code for aerodynamic calculations. Lastly it calculates the MAV performance. The different parts of the excel program are shortly explained below. 1. Geometry In Excel there is a simple to use geometry input module which is used by the CAD program to update the parametric CAD model. In this module the MAV is defined as a tailless aircraft. The wing is defined by total area, aspect ratio, dihedral and twist angle. Two parameters are also controlling the curvature of the leading and trailing edges, allowing the wing to be shaped with a “non trapezoidal” contour. The wing profiles at the wing root and tip can be chosen from a catalog and are controlled through two dedicated parameters. The fuselage is completely blended with the wing and its size depends on the Figure 3. MAV Geometry wing root length and thickness. It is however possible to specify the cross section 3 American Institute of Aeronautics and Astronautics size and length of the portion of the fuselage ahead of the wing. The fins are placed at the wing tips and their dimension is defined by a tail volume coefficient. Other parameters that can be set are sweep and taper ratio, plus a coefficient that controls how the fins surface is distributed above and below the chord line. Figure 3 shows a principal sketch of a typical geometry created in the geometry module. The geometry includes also three different payload boxes and all control system equipment. Each component is represented as a rectangular box of given length, height, width and weight, all taken from a database included in the spreadsheet. It is then possible to review their placement in order to balance the aircraft and to verify that everything fits inside the outer surface. 2. Propulsion The propulsion system consists of propeller, electric motor, PWM motor controller, and battery (Fig. 4). Each component is modeled individually. The models used are briefly described below. Pd Pb ηd ηb Pm Pout ηm ηp ηtot=ηb*ηd*ηm*ηp Figure 4. MAV propulsion system. The propeller is modeled using blade element theory software by Hepperle7. The model gives an estimation of power coefficient Cp and thrust coefficient Ct as function of advance ratio v/nD. It requires geometric shape of the propeller together with information of its airfoil along the blade radius. Accordingly to Hepperle the accuracy of the model is very god, when the power and thrust loading is relatively low, as in the case of MAV propellers. The motor is described by the motor constants Kv, I0 and Rm. This is data that is usually given by motor manufacturers. A model of an electric motor using these constants is shown in Figure 5. The electric motor has its rpm (n) proportional to motor EMF. Kv is the RPM proportionality constant. Losses in the motor are characterized by its internal resistance Rm and no load current I0. Im Rm I Uemf + Um I0 M n U emf K v (rpm) P in I m U m (W) P out I U emf (W) Pout (W) Figure 5. Model of electric motor. This is a well known motor model and as long as the motor constants are defined properly by the motor manufacturer, the accuracy of the model is very good for normal operating conditions. Modeling the losses in the motor controller is complex. The losses in the controller are depending of several factors. According to Lawrence8, the main controller losses for low inductance motors, such as the ones suitable for MAV:s, are due to the insufficient filtering of the PWM harmonics. Lawrence presents a mathematical model that uses the PWM frequency, power setting, and motor inductance to estimate these losses. This model has been implemented in the design tool. Battery is modeled using its capacity C, rated nominal voltage U, and internal resistance Rb. The total energy source (battery pack) consists of several battery cells coupled in series and/or in parallel. The weight of the battery pack is the number of cells multiplied by cell weight and with a correction for the weight of the material surrounding the cells. This is material such as cable, connector and plastic wrapping. For each component a large database has been created storing data from many off the shelf components used in hobby applications. To insure a broad spectrum of possible designs the database contains as much as 130motors, 15 motor controllers, 30 propellers and 30 batteries. 4 American Institute of Aeronautics and Astronautics 3. Weight and Aerodynamics The weight prediction is carried out with the parametric CAD model of the aircraft, while the aerodynamic performance calculation is done by a panel code. See more in the following paragraph. The panel code used is considering only inviscid flows hence not taking into account the viscosity effects. Skin friction drag is there fore calculated based on the wetted area from the CAD software. Prandtl and von Karman equations for turbulent boundary layer have been used (ref. 6). Hoerner6 equations have been used to correct skin friction for threedimensional bodies. 4. Performance From the results of the CAD program weight predictions, the panel code aerodynamics calculations, and propulsion system modeling, the performance is calculated. As results the endurance, range, and climb is presented as a function of speed. Interesting parameters such as efficiency of individual components, propeller rpm, motor current etc can also be plotted. Some examples of results obtained from the performance module are shown in Figure 6. flight envelope Efficiency 3,0 drag (N) T (N) 2,5 v stall 90,0 45,0 80,0 40,0 70,0 2,0 Endurance 35,0 30,0 1,5 25,0 % 50,0 20,0 40,0 15,0 30,0 10,0 20,0 5,0 10,0 1,0 0,5 0,0 0,00 60,0 min F (N) 100,0 50,0 0,0 5,00 10,00 15,00 20,00 v (m/s) 0,0 0,00 25,00 (a) η prop η motor η ESC η batt η tot 5,00 10,00 15,00 v(m/s) 20,00 25,00 (b) Figure 6. Results from modeling. C. Parametric CAD Model The design of a MAV is clearly less difficult than a conventional aircraft. Nevertheless some important features are required by the CAD model. First of all, the model should be highly flexible, so that the largest range of possible design variants can be represented. Secondly, it should comprise the internal systems that the aircraft will carry. Among these are payload equipment as well as control and powering devices. Given the very limited dimensions that characterize MAVs, it can be difficult to be able to fit all the needed systems, still meeting requirements for balance and control of the aircraft. Obviously it is a time consuming task to build a highly flexible, fully parametric CAD model. And of course each CAD model will have limits so that not all configurations can be represented through it. On the other hand each model can be stored in a library of sort, where each type of basic configuration can be selected through a given parameter. Each time a new CAD model is created it can be added to the library for future use. A CAD model of a generic MAV has been developed at Linköping University (Figure 7). The CAD tool used for the task is CATIA V5 R17. The parameters described in paragraph II.B.1, are used to determine the outer surfaces in this model. Then the internal systems and structural elements are placed within them. As previously explained the spreadsheet includes catalogues within which it is possible to choose the following components: 5 American Institute of Aeronautics and Astronautics - Engine Speed regulator Receiver Servos Autopilot Camera Video link Since the aircraft is of very simple nature and of a very small size, the structural requirements are quite simple. The aircraft is designed to be manufactured as an outer shell of glass or carbon fiber which is more than enough to withstand all aerodynamic loads. Nevertheless a simple structure composed by two spars made of polystyrene extending along the whole wing span is included. Their task is mainly to prevent the shell from buckling or collapsing inward when handling the Figure 7. The parametric MAV CAD model aircraft, and at landing. From the CAD model it is possible to retrieve a precise measure of the aircraft weight9 and mass distribution that can be used for both performance prediction as well as flight simulations. Especially when compared to the previous method of calculating the expected total weight (see Ref.1), the use of a CAD model represents a further improvement. Finally, the outer surfaces of the MAV are discretized with a mesh, and the node coordinates are gathered to be sent to the panel code for aerodynamic analysis. D. Panel Code At the moment, the aerodynamic analysis tool adopted is a panel code, PANAIR. Panel codes are numerical schemes for solving (the Prandtl-Glauert equation) for linear, inviscid, irrotational flow about aircraft flying at subsonic or supersonic speeds10. As pointed out by Amadori et. al.2, panel codes are not as precise as modern CFDs can be, but they have other advantages. Considering that during a conceptual design phase, the aircraft geometry and its outer shape is not precisely defined and that the detail level is quite rough, it is clear that it can be unpractical and not justified to use tools that have a much higher accuracy. Moreover CFDs requires the space around the studied body to be accurately meshed, while for a panel code it is sufficient to approximate the aircraft’s outer surfaces with proper rectangular panels. Therefore the meshing time required by a panel code is lower by several orders of magnitude, compared to a CFD code. When much powerful and faster computers will be available or if higher accuracy was required, PANAIR could be substituted with other solvers, thanks to the modular nature of the framework. The CAD model described here above is also responsible for generating a mesh of the surfaces of the aircraft. This is performed by an in-house tool developed at Linköping University. This grid is then used by the panel code algorithm to calculate basic aerodynamic coefficients for a given mission section. The parameters that are required for an analysis to be carried out are angle of attack, yaw angle, air speed and altitude. Outputs of this module are lift coefficients cL and cL, induced drag coefficient cdi and pitching moment coefficients cm and cm. PANAIR returns also the pressure values and speed vectors in each node of the mesh that is input. The analysis of one given configuration is carried out in two steps (Figure 8). First PANAIR is run at two different and arbitrary angles of attack, i.e. 1 and 6 degrees. The only requirement here is that the angles must be within the linear range of the lift coefficient. The results from this analysis permit to retrieve the slope of the cL curve as function of the angle of attack (cL). Given now the weight of the aircraft, its cruising speed and altitude, the cruising angle of attack cruise is calculated. Then PANAIR is run a second time at this specific angle of attack, in order to predict the induced drag coefficient (cdi-cruise) in cruise condition. Moreover, the knowledge of three cdi – values enables to easily estimate the relationship between induced drag and angle of attack which is used for performance calculations other then at the cruise condition. 6 American Institute of Aeronautics and Astronautics PANAIR run at 1 and 6 degrees cL cL, m·g = cL·S·q cL = cL,·a + cL,=0 PANAIR run at cL,cruise cL,cruise cDi() cDi,cruise Figure 8. Each configuration is analyzed in two steps. E. Optimization Algorithms Two different optimization algorithms can be used. First is a genetic algorithm that is programmed as a macro add-in for Microsoft Excel. This algorithm has already proven to be successful for MAV-design optimization1. A second possibility is to adopt the Complex-RD algorithm. It is a modified variant of the Complex algorithm11,12,13 that is capable of handling discrete variables together with continuous ones. So far only the genetic algorithm has been tested, while the Complex algorithm has only been plugged in into the framework but any optimization has not been carried out yet. III. Design Automation and Optimization The design optimization task comprises two different aspects: the optimization of the aircraft shape and the optimization of the components of control and propulsion system. These can be run separately, in sequence or simultaneously. Every function evaluation becomes more time expensive when using CATIA and PANAIR to analyze the aircraft geometry and aerodynamics. Thus it is possible to select whether the framework should use them or not for computing weight, center of gravity location, lift and drag coefficients. Figure 5 shows the information flow within the framework. The scheme shows clearly where the new module has been inserted and how it now possible to choose between calculating weight and induced drag by means of CATIA and PANAIR or not. Geometry Definition CATIA PANAIR Propulsion System Definition Weight Lifting-Line Theory Thrust Induced Drag Parasite Drag Performance Prediction Figure 9. Information flow within the framework. Since each function evaluation involving the new module containing CATIA and PANAIR takes between 10 and 40 seconds, depending mostly on how many parameters are changed from the previous configuration, the design optimization has been divided into two successive parts. First the framework is run without invoking the new module. This ensures much more rapid iterations at the cost of less accurate results. In this initial mode, a large number of parameters are involved in the optimization which comprises both the geometry layout of the aircraft as 7 American Institute of Aeronautics and Astronautics well as the selection of the propulsion system. When convergence is reached the system is restarted, this time involving CATIA and PANAIR, using the optimum solution obtained as starting point. The propulsion system is frozen and the geometric design parameters are allowed to vary within a narrower range. In this second phase design parameters that could not be evaluated using the lifting-line theory can be included, such as the tip chord twist or the wing profile. If the result from the second optimization would not agree with the first one, the whole process is repeated until convergence between the results is reached. The process is illustrated in Figure 10. Optimization Fast Simple geometric and aerodynamic model Fast System and performance models Optimization Geometry (continuous) System parameters (discrete and continuous) Expensive Complex geometric and aerodynamic model Geometry (continuous) System parameters (discrete and continuous) Optimization (If geometry changes significantly) Fast System and performance models Figure 10. Optimization procedure. IV. Results In order to test the design framework, design studies of three different MAVs were performed. The scenario is similar to what is described in the introduction, with three MAVs tailored for three different sensors. Each MAV is given different performance and payload requirements. The requirements are summarized in Table 1. Design 1 Design 2 Design 3 Endurance (min) 30 100 40 v cruise (m/s) 25 17 19 v max (m/s) 36 - - Payload (g) gimbaled video camera (45g) Thermal Eye, IR video (72g) 7 M-pix still picture camera (60g) vstall (m/s) 9,7 8,3 8,3 T/W Geometry limitation 0,8 0,6 0,6 Span < 0,4 m Span < 0,6 m Span < 0,4 m Table 1. MAV requirements. Design 1 is specified as a high speed MAV with capability for surveillance of moving objects. It is designed around a small gimbaled video camera developed at Linkoping University, and is required to have a cruise capability of 90km/h (25m/s) for at least 30 min with the sub criterion to have a top speed of as much as 130km/h. This is in order to track for instance a moving car. Design 2 is specified for surveilling a large area over a longer period of time searching for warm objects using a thermal camera. The intended camera is an IR camera, Thermal-Eye 3600AS14, with a weight of 72g. On this MAV the cruise speed is set to 60 km/h (17m/s), and no specific condition is set for the top speed. The over all cruise endurance is set to 100min. In order to limit the physical size of the MAV a condition is set to keep the span smaller then 60cm Design 3 is required to carry a still picture digital camera of 7 mega pixels. It’s intended to be used in collaboration with other MAVs. If an object is located using a conventional video camera or IR camera, the high resolution camera can be used to take a snapshot for accurate geo-localization with satellite images. It can also be used to build accurate maps for a region of interest. Endurance is set to 40 min and cruise speed is required to 70 km/h (19m/s). 8 American Institute of Aeronautics and Astronautics In all three cases a Micropilot MP202815 is intended as autopilot. This is equipment used in existing MAV:s at Linköping University and where compete system weight, size and power consumption is well known. For all three design studies the optimization was done in two steps as described in paragraph III. In the first step the genetic optimizer generally converged in about 30 min, and on that time several thousands of trials were completed. In the second step the CATIA model and PANAIR calculations were plugged in, and the genetic algorithm were used to fine-tune the geometry. For this optimization the parameter values were limited to stay relatively close to the previous step. It was found that at range of ± 15% from the values obtained during step nr 1 was suitable. The GA was then set to do 900 function evaluations and report the optimal configuration. With a population size of 20 individuals this represents 45 generations. Although this may not be a fully converged system it is well within the accuracy of the models, and spending more time to improve the optimum does not make sense. Another reason not to use more function evaluations is that a memory leak in CATIA slowly decreases the available memory to a point where the system finally crashes. During the optimization the objective was set to keep the weight as low as possible while having criteria’s, in the form of penalty functions, for endurance, stall speed, etc (as defined in Table 1). This insures to design the smallest possible MAV that fulfills the requirements. This is different from the optimization in ref 1, where the MAV endurance was optimized while keeping the geometrical size within restricted values. The result of the three design studies has been very successful. Suitable propulsion systems were chosen and the over all plan forms generated give a god impression. The objectives defined in Table 1 were all met. Agreement between lifting line theory and panel code is generally quite good. The design does not change much between step 1 and 2. In beginning the panel code had a tendency to reduce the wing sweep found in the first optimization. Since the winglets are mounted on the wing tips, and defined by tail volume coefficient, this lead to winglets of large area and height, but small cord. Apparently the optimizer found that the reduction in induced drag was grater then the increase of parasite drag, but the winglets generated would be fragile and not viable for practical use. To avoid this problem a penalty function was added that penalized the objective function if the winglet grew to much in height. Table 2 below summarizes the results of the 3 different designs. Design 1 “high speed” Design 2 “long endurance” 387 Span Stall speed T/W ratio Endurance at cruise 0,80 32,3 min 101,1 min 46,1 min Max speed 35,9 m/s 27,2 m/s 24,6 m/s Motor Controller Battery Propeller g 616 365 mm 9,6 m/s Design 3 “general MAV” Weight g 426 595 mm 353 mm 8,2 m/s 8,3 m/s 0,78 g 0,80 Apache 20-34T Mfly 180-08-11 Mfly 180-08-15 YGE 8 YGE8 YGE 8 Thunderpower 2000mAh 3s1p Tanic 2200mAh 3s2p Thunderpower 2000mAh 3s1p APC 6x6.9 (repitched 6x5.5) APC electric 6x4 APC electric 6x4 Table 2. Result from design optimization It can be noted that a few propulsion system components was chosen for several of the designs. For instance all got the same controller. None of the designs got the same motor, but design 2 and 3 got the same propeller. That is a bit surprising, but is probably a fact of that the design space is discrete, and not enough propellers are available in 9 American Institute of Aeronautics and Astronautics the database. Design 1 and 3 also got the same batteries. This is a result of that particular battery having the highest energy density in the database and the optimizer tend to find the optimal components and fine tune the geometry to fit this system. V. Future Development The design framework is a helpful tool in MAV design, but there are two important issues, that for time constraints were not dealt with in this paper. That is to insure that during the optimization, the proper balance and size restrictions are met. The MAV must have large enough volume to accommodate its intended components, as well as balance with a proper stability margin. Controlling that a component fits can easily be done by measuring directly in the CAD model. If each component is defined with dimensions in the database, a script can be made that automatically controls if the component fits, by measuring the distance between the upper and lower wing surface in CATIA at each corner of the component. Ensuring that balance is achieved can then be done in two ways. The easiest method to implement is to manually place the components in a fixed pattern, and let the GA evolve the airframe around that pattern, with a penalty function if the balance criterion is not met. The other option is to have an inner loop that for each function evaluation seeks to adjust the component positions to where the balance criteria is met. The use of CATIA and PANAIR is of great help here as one tool gives the pitching moment and neutral point, and the other gives the center of gravity. As always when working with theoretical models, validation is needed before the result can be trusted. The PANAIR code was developed for larger manned aircraft and is not necessarily the ideal tool for MAV design. A correlation with wind tunnel data is needed. It should be clearly pointed out that this paper is demonstrating the possibilities when combining CAD with panel code in design automation. PANAIR could easily be replaced with a different code more suitable for the task. Preferably CFD should be used for aerodynamics calculations, but still that is far too computationally heavy to use in optimization. It would however be interesting to use CFD as a last step of the design automation to get a better view of the final aerodynamics. 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Hoerner, “Fluid Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance”, Midland Park, N.J. 1965 7 M. Hepperle, ”Java Prop - propeller analysis”, URL: www.mh-aerotools.de 8 D. Lawrence, K. Mohseni, “Efficiency Analysis for Long-Duration Electric MAVs”, AIAA Infotech Aerospace, Arlington, Virginia, September, 26-28, 2005, AIAA 2005-7090 9 Jouannet, C., Silva, S.E.R., Krus, P., “Use Of CAD For Weight Estimation In Aircraft Conceptual Design”, 24th International Congress Of The Aeronautical Sciences, Linköping University, Linköping, Sweden, 2004. 10 Erikson, L.L., “Panel Methods – An Introduction”, NASA Technical Paper 2995, 1990 11 Andersson, J., “Design Optimization”, Linköping University, Linköping, Sweden, 2005. 12 Krus, P., Andersson, J., “An Information Theoretical Perspective On Design Optimization”, Design Engineering Technical Conference, Salt Lake City, UT, USA, 2004. 13 Krus, P., Andersson, J., “Optimizing Optimization for Design Optimization”, DETC’03 2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, IL, USA, 2003. 14 www.thermal-eye.com 15 www.micropilot.com 10 American Institute of Aeronautics and Astronautics
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