This is the author accepted manuscript. The final version is available from UKACM via the link in this recordAircraft design is fundamentally a multidisciplinary design activity which involves different models and tools for
various aspects of the design. This paper uses a Multidisciplinary Design Optimisation (MDO) for design of a
simplified commercial aircraft, aiming to optimise the objectives of cost, weight and drag. NSGA-II is used to
optimise the weight and cost by changing the geometry to introduce lightweight airframe materials and composites
with lower density. Reducing weight of the structure is one of the major ways to improve the performance of
aircraft. Lighter, stronger material will allow a higher speed and greater range which may contribute to reducing
operational costs. Drag reduction is also a major factor in aircraft design. Reduction of drag in an aircraft means
that it can have a lower fuel consumption or travel at higher speed, both of which are beneficial to plane
performance. A smart structural optimisation algorithm helps to optimise the cost, weight and drag, while drag is
analysed based on CFD modelling results. The results are validated against some wind tunnel tests

Akrami, M

Chan, LC

Dibaj, M

Javadi, A

Khanjanpour, MH

Tabor, GR

English

Open Research Exeter

1  2019 UKACM Conference City, University of London    OPTIMISATION OF A CONCEPTUAL AIRCRAFT MODEL USING A GENETIC ALGORITHM AND 3D COMPUTATIONAL FLUID DYNAMICS Lok Chun Chan, *Mohammad Akrami, Akbar A. Javadi, Gavin Tabor, Mahdieh Dibaj,  Mohammad Hassan Khanjanpour  Department of Engineering, University of Exeter, Exeter, EX4 4QF, UK *m.akrami@exeter.ac.uk  Summary  Aircraft design is fundamentally a multidisciplinary design activity which involves different models and tools for various aspects of the design. This paper uses a Multidisciplinary Design Optimisation (MDO) for design of a simplified commercial aircraft, aiming to optimise the objectives of cost, weight and drag. NSGA-II is used to optimise the weight and cost by changing the geometry to introduce lightweight airframe materials and composites with lower density. Reducing weight of the structure is one of the major ways to improve the performance of aircraft. Lighter, stronger material will allow a higher speed and greater range which may contribute to reducing operational costs. Drag reduction is also a major factor in aircraft design. Reduction of drag in an aircraft means that it can have a lower fuel consumption or travel at higher speed, both of which are beneficial to plane performance. A smart structural optimisation algorithm helps to optimise the cost, weight and drag, while drag is analysed based on CFD modelling results. The results are validated against some wind tunnel tests.   Key Words: Optimisation, aircraft, NSGA-II, CFD  Introduction The first commercial aircraft started back on 1st January 1914. It operated between St. Petersburg and Tampa, yet only lasted for four months. Since then, engineers and scientists start to design and investigate different methods to improve the performance of aircraft. The original aims are to increase the distance of travel and the capacity of the aircraft. Nowadays, commercial aircrafts are fairly developed and improved compared to the first commercial aircraft. Even though the aircrafts have massively improved compared to the earlier designs, but there are still areas to improve. Designers always try to come up with better designs and the aims have changed from achieving basic performance to improving the performance of flight such as reducing the fuel consumption. To achieve these aims, designers have applied various techniques and technologies to assist with their design works. For example, the use of computational simulation, wind tunnel experiment and mathematical models has helped to refine, improve and optimise the aircrafts in terms of their structure, material choice and geometry in order to achieve a “better” design. Aircraft design always contains more than one objective; e.g., reduction of fuel consumption, reduction of weight and increase in the payload; and involves various disciplines such as structure dynamics, fluid dynamics and materials engineering. In this paper, MDO is used to optimise a simplified model of a commercial aircraft in order to reduce weight, drag and cost, simultaneously.   Materials and Methods During the conceptual design, ideas were formulated, rephrased, rejected or modified. Traditionally, aircraft design is separated into different areas of focus, such as structure, materials, dynamics and cost and there are aims and constraints in each area.  2  2019 UKACM Conference City, University of London   For example, the design of airframe focuses on structure and shape while the design of the wing will focus on lift and drag. All parts of an aircraft are closely related and interlinked with each other. Therefore, achieving one objective might have an adverse effect on the other design objective. For instance, replacing aluminium alloy by light-weight materials such as carbon fibre and other composites to achieve a weight reduction will have a trade-off of increased production cost. A complex design, such as aircraft, need to achieve different design objectives while there are different trade-offs. An MDO is a methodology to achieve the “best” solution by changing the design variables and maintaining different design constraints [1].                Figure 1: Application of the NSGA-II algorithm and the assigned parameters in the model  Traditionally, design is a process focusing on one area at a time and the areas down the stream are heavily dependent on the previous results. As modern design has developed and become more complex, it has become very difficult to optimise multiple design objectives. MDO is a design process which evaluates all design variables simultaneously and considers the trade-off and interaction between different objectives and disciplines. MDO is a methodology for the design of complex engineering systems that are governed by mutually interacting physical phenomena and made up of distinct interacting subsystems in their design.  Parameter Description X1 Length of fuselage X2 Fuselage diameter X3 Length of nose X4 Length of tail X5 Wingspan X6 Wing sweep angle X7 Horizontal stabilizer span X8 Horizontal stabilizer sweep angle X9 Vertical stabilizer span X10 Vertical stabilizer sweep angle 3D conceptual CAD model of aircraft Determine the drag by conducting a CFD analysis on the conceptual aircraft model  Surrogate model NSGA II Update 3  00.511.520 5 10 15 20 25DRAG (N) VELOCITY (M/S)Wind tunnel and CFD results Series1 Series2 Poly. (Series1) Poly. (Series2)2019 UKACM Conference City, University of London   The rapid development in the computational analysis in recent years has been largely influencing MDO. Many simulation results can now be linked and considered in the calculation process, which could be a significant aid, especially in aircraft design. Areas like wing lift and drag can be more easily considered during the design process. Apart from CFD or FEA, MDO can also involve diverse tools such as cost modelling and even experimental results. Non-dominated Sorting Genetic Algorithm (NSGA-II) is a modified version of NSGA which is a multi-objective optimisation model and was one of the first evolutionary algorithms [2, 3]. It generates a set of solutions, also known as Pareto-optimised solutions, which are superior to the rest of the solutions. There is no absolute better solution within this Pareto-optimised solutions and hence the choice of an optimal solution over the others requires problem knowledge and other problem factors. In this study, the ten initial parameters (Figure 1) were defined in order to optimise the three main objectives. These ten parameters will update in each iteration based on the geometrical parameters’ ranges of the aircraft models to generate the optimal solution. Also, a surrogate model was constructed based on the initial results from the CFD model and the remaining simulations were analysed based on this model predictions to observe and choose the most promising ones until a “good design” can be achieved. By generating a surrogate model using CFD simulation which has been validated by the wind tunnel results (Figure 2) and adapted in the NSGA-II model, the range of optimal solutions are generated.         Figure 2: Validating the CFD model against the wind tunnel results based on the Drag force (N) and the Velocity (m/s) Results and conclusion By combining the surrogate optimisation model generated by multiple CFD simulations and NSGA II,  multiobjective genetic algorithm, a Pareto front is generated which clearly shows a trade-off between different objectives. There is a significant trade-off between weight and cost, as weight decreases, the costs increases (Figure 3) [4, 5]. This trend clearly exists between the weight and Fuselage volume and also cost and the volume. The results help to find a range of solutions in order to optimise the the topology of the structure [6].        4  2019 UKACM Conference City, University of London                   Figure 3: Optimisation results from the NSGA-II algorithm for the three main objectives of Cost, Weight and Fuselage volume  Based on the developed algorithm, the optimised ranges for the main 10 parameters are illustarted (Table 1) in order to minimise the aforementioned objectives.   Parameters Initial range  Optimised range X1 15 – 50  36.86 – 50  X2 3.76 – 8.5  6.648 – 8.5  X3 3.96 – 5  4.173 – 5  X4 7 – 15    8.115 – 13.473  X5 26 – 80 26 – 31.62 X6 90 – 125 105.03 – 123.23  X7 10 – 30 10 – 15.834  X8  115 – 140 119.694 – 127.67 X9 6 – 15 6 – 10.559 X10 115 – 140 115 – 139.07   References  1. Sobieszczanski-Sobieski, J., Multidisciplinary Design Optimization: An Emerging New Engineering Discipline, Advances in Structural Optimization (483-496), Kluwer Academic Publishers, the Netherlands, 1995  2. N. Srinivas, Kalyanmoy Deb, Multiobjective Optimization using Non-dominated sorting in Genetic Algorithms, 1994 3. Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. Evolutionary Computation, IEEE Transactions on, 6, 2 2002) 4. Wang X, Hirsch C, Kang S, Lacor C. Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model. Computer Methods in Applied Mechanics and Engineering. 2011;200(9-12):883-95.  5. Bellary SAI, Adhav R, Siddique MH, Chon B-H, Kenyery F, Samad A. Application of computational fluid dynamics and surrogate-coupled evolutionary computing to enhance centrifugal-pump performance. Engineering Applications of Computational Fluid Mechanics. 2016;10(1):171-81.   6. Niemann, S., Kolesnikov, B., Lohse-Busch, H., Hühne, C., Querin, O.M., Toropov, V.V. and Liu, D., 2013. The use of topology optimisation in the conceptual design of next generation lattice composite aircraft fuselage structures. The Aeronautical Journal, 117(1197), pp.1139-1154. 5  2019 UKACM Conference City, University of London  function [y, cons] = TP_CONSTR_objfun(x) [Ane, Ate]= elliptical (x);  Abo=pi*x(1)*x(2); An=integral(Ane,-x(3),0);Ata=integral(Ate,-x(4),0); Awis= ((x(5)/4)+1.5)*(x(5)/2); Awint= (2*(((x(5)/2))/sind(x(6)))+1.5)*0.75; Awi=Awis+2*Awint; Astas= ((x(7)/2.5)+1.5)*(x(7)/2); Astat=(2*(((x(7)/2))/sind(x(8)))+1.5)*0.4; Asta=Astas+2*Astat; Arus=(((x(9)/1.2)+1.5)*x(9))/2; Arut=(2*(((x(9)/2))/sind(x(10)))+1.5)*0.3; Aru=Arus+Arut; En= (1.5/2)^2*pi*3; tbl = readtable('test2.xlsx','range','A1:K101','ReadVariableNames',false); tbl.Properties.VariableNames = {'X1','X2','X3','X4','X5','X6','X7','X8','X9','X10','drag'};  gprMd = fitrgp(tbl,'drag','KernelFunction','squaredexponential','FitMethod','fic','PredictMethod','exact','Standardize',1);  C={x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),[]}; T = cell2table(C); T.Properties.VariableNames = {'X1','X2','X3','X4','X5','X6','X7','X8','X9','X10','drag'}; y = [0,0,0]; cons = [0,0];  y(1) = predict(gprMd,T); y(2) = ((x(11)/(x(11)+x(12)+x(13)))*1750+(x(12)/(x(11)+x(12)+x(13)))*2800+(x(13)/(x(11)+x(12)+x(13)))*7850)*0.5*(((Abo)+(abs(An))+(abs(Ata))+(2*Awi)+(2*Asta)+(2*Aru)+(2*En))); y(3) = ((x(11)/(x(11)+x(12)+x(13)))*1750*6.38+(x(12)/(x(11)+x(12)+x(13)))*2800*1.38+(x(13)/(x(11)+x(12)+x(13)))*7850*0.3)*(0.5*((Abo)+(abs(An))+(abs(Ata))+(2*Awi)+(2*Asta)+(2*Aru)+(2*En))); c(1)= x(1)*(x(2)/2)^2*pi; c(2)= x(1)*(x(2)/2)^2*pi; %c(3)= y(3);  if(c(1)<150)% new deisgn has a lower payload than the original Boeing 737 100      cons(1) = abs(c(1)-150)*100000;  if (c(2)>=150)         cons(2)=150/((abs(c2)-150)*100000); end  %if (c(3)<=0) %        cons(3)=0.001/((abs(c2)-150)*100000); %end end clear All  boundary   options = nsgaopt();                    % create default options structure options.popsize = 100;                  % populaion size options.maxGen  = 100;                  % max generation  options.numObj = 2;                     % number of objectives options.numVar = 13;                    % number of design variables options.numCons = 2;                    % number of constraints options.lb = lb;                        % lower bound of x options.ub = ub;                        % upper bound of x options.objfun = @TP_CONSTR_objfun;     % objective function handle options.plotInterval = 5;               % interval between two calls of "plotnsga".   result = nsga2(options);                % begin the optimization!  %plotting %optimisation_history function varargout = plotnsga(varargin) gui_Singleton = 1; gui_State = struct('gui_Name',       mfilename, ...                    'gui_Singleton',  gui_Singleton, ...                    'gui_OpeningFcn', @plotnsga_OpeningFcn, ...                    'gui_OutputFcn',  @plotnsga_OutputFcn, ...                    'gui_LayoutFcn',  [], ... 6                                                           2019 UKACM Conference City, University of London                  'gui_Callback',   []); if nargin && ischar(varargin{1})    gui_State.gui_Callback = str2func(varargin{1}); end  if nargout     [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else     gui_mainfcn(gui_State, varargin{:}); end function plotnsga_OpeningFcn(hObject, eventdata, handles, varargin) handles.output = hObject; guidata(hObject, handles);  handles.bLoadFromFile = 0;           if( isempty(varargin) )     error('PLOTNSGA:ParamError', 'Error: plotnsga should be called : plotnsga(result, curGen) or plotnsga(''pops.txt'')');  elseif(length(varargin) == 1)     if( isstruct(varargin{1}) )         handles.result  = varargin{1};         handles.currentGen = 1;             elseif( ischar(varargin{1}) )         global oldresult;         oldresult = loadpopfile(varargin{1});         evalin('base', 'global oldresult');              handles.bLoadFromFile   = 1;         handles.strPopFile      = varargin{1};         handles.result          = oldresult;         handles.currentGen      = 1;     end     elseif(length(varargin) == 2)     if( isstruct(varargin{1}) && isscalar(varargin{2}) )         handles.result  = varargin{1};         handles.currentGen = varargin{2};     else         error('PLOTNSGA:ParamError', ...             'Error: plotnsga should be called : plotnsga(result, curGen) or plotnsga(''pops.txt'')');     end end popsize = size(handles.result.pops, 1); strList = repmat({''}, [1,popsize]); for i = 1:popsize     strList{i} = sprintf('%d', i); end  curSel = handles.currentGen;   set(handles.listPop, 'string', strList); set(handles.listPop, 'value', curSel);  dispState(handles, curSel); plotPopulation( handles, curSel ); guidata(hObject,handles);  function varargout = plotnsga_OutputFcn(hObject, eventdata, handles) varargout{1} = handles.output;  function btnStop_Callback(hObject, eventdata, handles) global STOP_NSGA; STOP_NSGA = 1;  function btnPause_Callback(hObject, eventdata, handles) if isempty(getappdata(0,'gadsSolverState'))     setappdata(0,'gadsSolverState','pause');     set(hObject,'String','Continue');         waitfor(hObject,'String'); else     setappdata(0,'gadsSolverState','');     set(hObject,'String','Pause'); end  

Optimisation of a conceptual aircraft model using a genetic algorithm and 3D Computational Fluid Dynamics (CFD)

https://ore.exeter.ac.uk/repository/bitstream/10871/36789/1/P14_Lok%20Chun%20Chan_Optimisation%20Of%20A%20Conceptual%20Aircraft%20Model%20Using%20A%20Genetic%20Algorithm%20And%203D%20Computational%20Fluid%20Dynamics.pdf

Optimisation of a conceptual aircraft model using a genetic algorithm and 3D Computational Fluid Dynamics (CFD)

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