Multidisciplinary aerospace design optimization survey of recent developments.pdf

structural optimization 14 1 23 9 springer verlag 1997 review article multidisciplinary aerospace design survey of recent developments optimization j sobieszczanski sobieski nasa langley research center hampton va 23681 0001 usa j sobieski lar c nasa gov r t haftka university of florida gainesville fl 32611 6250 usa haftka ufl edu abstract the increasing complexity of engineering sys tems has sparked rising interest in multidisciplinary optimization mdo this paper surveys recent publications in the field of aerospace in which the interest in mdo has been particularly intense the primary challenges in mdo are computational ex pense and organizational complexity accordingly this survey fo cuses on various methods used by different researchers to address these challenges the survey is organized by a breakdown of mdo into its conceptual components reflected in sections on mathemat ical modelling approximation concepts optimization procedures system sensitivity and human interface because the authors pri mary area of expertise is in the structures discipline the majority of the references focus on the interaction of this discipline with others in particular two sections at the end of this review focus on two interactions that have recently been pursued with vigour the simultaneous optimization of structures and aerodynamics and the simultaneous optimization of structures with active control 1 introduction webster s collegiate dictionary 10 th edition defines methodology as a body of methods rules and postu lates etc in this vein we define multidisciplinary opti mization mdo as methodology for the design of systems in which strong interaction between disciplines motivates de signers to simultaneously manipulate variables in several dis ciplines by this definition structural optimization of aircraft wings to prevent flutter is not mdo in this case the inter action of structures and aerodynamics is analysed however the aerodynamic shape of the wing is not oflimized the interdisciplinary coupling that is inherent in mdo presents tougher computational and organizational chal lenges than single discipline optimization the computa tional challenge may simply reflect increased dimensionality with analysis and design variables that accumulate from all disciplines one discipline for example structural optimiza tion can contribute tens of thousands of analysis variables and several thousands of design variables berkes 1990 for airframe design because analysis and optimization solution times usually increase at superlinear rates mdo typically costs much more than the sum of the costs of the constituent single discipline optimizations additionally system analysis can require costly nonlinear methods even if each discipline uses linear analysis for example wing pressure distributions may be predicted by linear aerodynamics and displacements may then be predicted by linear structural analysis tiow ever the dependence of pressures on displacements may be nonlinear finally each disciplinary optimization may call for a single objective function however mdo may require more expensive multiobjective optimization in the mdo of complex systems analysis and optimiza tion codes for disciplines and subsystems interact by exchang ing data these codes usually belong to disparate groups of people who are often dispersed geographically interaction between these groups a prerequisite to the successful inte gration of the codes presents formidable organizational chal lenges part of the solution to the organizational challenge lies in teaching engineering students to work in teams and be familiar with multidisciplinary interactions see 1 in addition because people are an intrinsic and key com ponent of mdo systems providing users with an effective means for using mdothese systems becomes a challenge com parable infor which the importance and difficulty are compa rable with those of the other challenges mentioned above finally engineering system s must meet the rigours of the marketplace throughout their life cycle from inception to disposal consequently the list of challenges would be in complete without the inclusion of economic factors with the governing physics in mdo three categories of approaches to mdo problems can be discerned two of these categories include approaches that circumvent the organizational challenge the third attempts to address this challenge directly 1 in the first category in which two or three disciplines typically interact a single analyst can acquire the re quired expertise at the analysis level such acquisition may spawn a new discipline that focuses on the inter action of the involved disciplines such as aeroelasticity or thermoelasticity one result is mdo for which design variables in several disciplines must be manipulated si numerals in refer to the bibliographical notes section preceding the references a bibiliographical note contains pointers to a set of references contained in the references that have something in common the intent is not to clutter the text with long strings of the refel ence calls multaneously to ensure an efficient design in the past two decades anmysts who are well versed in both struc tures and control system analysis and design have created the discipline of structural control much work has also been done on the simultaneous optimization of structures and control systems e g haftka 1990 typical for this category is a group of researchers or practitioners working with a single computer code this reduces organizational difficulties and helps to deal with complications such as multiobjective optimization see for example 2 2 the second category includes works where mdo is car ried out at the conceptual level by using simple analysis tools for aircraft design the acsynt vanderplaats 1976 jayaram et ai 1992 and flops mccullers 1984 programs represent this level of mdo application sim plicity of the analysis tools enables integration of vari ous disciplinary analyses into a single usually modular computer program and radically reduces computational burdens 3 as the design process progresses from the conceptual stage the level of analysis can increase ei ther uniformly throughout or selectively adelman et al 1992 present an example of the latter which leads to the organizational challenges that are common to mdo at advanced stages of the design process 3 the third category comprises developments that directly address the organizational and computational chmlenges these include decomposition methods and global sensitiv ity techniques that permit the overall system optimization to proceed with minimal changes to disciplinary codes as well as tools that facilitate efficient organization of modules and intermodular data transfer finally also in cluded here are approximation techniques that help elim inate some computational and organizational challenges this review emphasizes papers that fall into the third category the survey organization reflects a modified version of the mdo breakdown into its conceptual components sug gested by sobieszczanski sobieski 1995 accordingly this review includes sections on mathematical modelling approx imation concepts optimization procedures system sensitiv ity optimization procedures with decomposition and human interface and an appendix on the design space search algo rithms the authors primary expertise is in the structures discipline as a result the majority of the references focus on the interaction of the structures discipline with another dis cipline for example structures and electromagnetic perfor mance padula et al 1989 in particular two sections of this review focus on two such interactions that have been pursued recently with particular vigour simultaneous optimization of structures and aerodynamics and structures combined with active control this emphasis on structures also reflects the roots of aerospace mdo in structural optimization and the central role of structures technology in the design of aerospace vehicles 2 mdo components this section comprises references grouped by the mdo con ceptual components defined as proposed by sobieszczanski sobieski 1995 2 1 mathematical modelling of a system mathematical models of engineering systems are usually im plemented as assemblages of software modules each mod ule represents an aspect of the system such as a physical phenomenon or part to increase their usefulness in de sign these modules evolved at tributes of design oriented analysis a term introduced by storaasli and sobieszczanski 1973 these attributes include the ability to select the level of analysis which ranges from inexpensive and approximate to accurate and costly smart analys is for rapid evaluation of design change effects computation of sensitivity deriva tives of output with respect to input and the inclusion of the data management and visualization infrastructure nec essary to handle volumes of data which in a design process can be quite large an example of a design oriented analy sis code is the program ls class developed by livne et al 1990 and livne et al 1992a 1993 for the structures control and aerodynamic optimization of flexible wings with active controls the program uses analysis based on vibra tion modes and permits the calculation of aeroservoelastic response at different levels of accuracy that range from a full to a reduced model additionally various approximations are available depending on the response quantity that is to be calculated coupled modules tend to exchange voluminous data that may require extensive processing for example if the sys tem is a flexible wing then the aerodynamic pressure from an aerodynamics module must be reduced to concentrated forces that act on the structure finite element model nodal points conversely the nodal structural displacements must be entered into the aerodynamic model as shape corrections the overhead computational cost generated by the volu minous data exchange can become particularly large when a system sensitivity analysis requires derivatives of module output with respect to module input e g global sensitiv ity equation gse see sobieszczanski sobieski 1990a b these costs can be decreased by condensing the exchanged data with reduced basis techniques for instance in the above wing example one may represent pressure and displace ment fields with a small number of base functions defined over the wing planform and transfer only the coefficients of these functions rather than the large volumes of discrete load and displacement data for examples of such condensation see barthelemy et al 1992 and unger et al 1992a and karpel 1996 when two modules exchange large volumes of data that cannot be condensed the excessive computational cost can be reduced by unifying the two modules see for example au gust et al 1992 or merging the two modules at the equation level a heat transfer and structural analysis code described by thornton 1992 is an example of such a merger this line of development is extended to include fluid mechanics by sutjahjo and chamis 1994 tradeoff of accuracy and cost through the judicious use of alternate models with different levels of complexity is an other means for controlling computational cost in single discipline optimization it is common to have an analysis model which is more accurate and more costly than an op timization model in mdo this tradeoff between accuracy and cost is exercised in various ways firstly without changing the underlying theories disci plinary models may be made coarser for mdo e g compare the coarse combined aerodynamic and structural optimiza tion by dudley et al 1994 and the more refined aeroelastie analysis by seotti 1995 secondly simpler models may be based on less sophisticated underlying theories as illustrated by low fidelity aerodynamic analysis and weight equations in aircraft design codes 4 and equivalent plate instead of finite element modeis for structures and control optimiza tion of flexible wings occasionally models of different com plexity can be employed within one discipline in a system for instance baker and giesing 1995 evaluate drag with a higher fidelity aerodynamic analysis and calculate loads with a lower fidelity model simplified models are also useful in approximation procedures and in fast reanalyses which are discussed later with the increased importance of economics in aerospace vehicle design the development of mathematical models for simulating man made phenomena of manufacturing vehicle operation support and maintenance is inevitable these models will share at least some of their input variables with those based on vehicle physics which will lead to system mathematical models that encompass the principal phases of the product life cycle formulation of goals product design manufacturing and operation such models will permit op timization for a variety of economic objectives that involve the entire life cycle e g minimum cost or maximum return on investment as forecast by tulinius 1992 several ref erences 5 bring life cycle issues into the mdo domain for example mars et al 1996 discuss structural optimization including manufacturing cost sehrage 1993 examines the role of mdo in integrated product and process development also known as concurrent engineering and surveys references on this subject mathematical modelling of an aerospace vehicle critically depends on an efficient and flexible description of the geome try this subject is addressed by smith and kerr 1992 and hajela 1994 2 2 approximation concepts direct coupling of the design space search dss code to a multidiseiplinary analysis may be impractical for several rea sons the dss code may call for analysis execution too fre quently the disciplinary analyses may be dispersed at var ious machines often at different sites their output may be noisy e g giunta et al 1994 toropov et al 1996 because of limited accuracy or for physical reasons e g buckling load is not a smooth function of plate aspect ratio consequently most optimizations of complex engineering systems couple a dss code to easy to calculate approximations of the ob jective function and constraints see for example the ro torcraft optimization in the work of adelman and mantay 1991 the optimum of the approximate problem is found then the approximation is updated by the full analysis ex ecuted at that optimum and the process is repeated this process of sequential approximate optimization is also pop ular in single discipline optimization 6 but its use is more critical in mdo as a principal cost control measure global reduced basis approximations are occasionally used in engineering system optimization e g kirsch 1991 however most often the approximations are either local lin ear or quadratic based on the derivatives occasionally in termediate variables or intermediate response quantities e g kodiyalam and vanderplaats 1989 are used to improve the accuracy of the approximation for example structural re sponse has been approximated by a taylor series in the re ciprocals of all or some of the variables 7 similarly rather than approximating eigenvalues directly we approximate the numerator and denominator of the corresponding rayleigh quotient e g 8 li and livne 1996 explore extensively various approximations for structural control and aerody namic response quantities a procedure for updating the sen sitivity derivatives in a sequence of approximations by using past data is formulated for a general case by scotti 1993 another method for controlling the mdo cost is a variable complexity modelling vcm technique an exam ple can be found in the work of unger et al 1992a in which both simpler and more sophisticated models alternate during the optimization procedure the sophisticated model pro vides a scale factor which is periodically updated to cor rect the simpler model unger et al 1992 apply the vcm technique to the aerodynamic drag calculation for a subsonic transport hutchison et al 1994 apply it to predict the drag of a high speed civil transport hsct similarly huang et al 1996 employ structural optimization with a simple weight equation for predicting structural weight in the com bined aerodynamic and structural optimization of an hsct wing traditional derivative based approximations can be combined with such global vcm approximations by using a derivative based linear approximation for the scale factor chang et al 1993 toropov and markine 1996 generalize this approach constructing an approximation based on both the design variables and the prediction of the simpler model response surface rs techniques e g unal et al 1996 replace the objective and constraints functions with simple functions often polynomials which are fitted to data com puted at a set of carefully selected design points these re placements may be regarded as global approximations be cause they span large subdomains in design space neural networks nn s trained with the values of the objective function and constraints at the selected set of points some times perform the same function after the initial investment in computing data at selected points and the rs fitting or nn training these global approximations are quite inexpen sive as data estimators according to hajela and co workers 10 sensitivity data can also be extracted using the nn tech nique by interpreting the nn weight coefficients as averaged derivatives of output with respect to input neural networks can be viewed as rs based on nonlinear regression in contrast to linear regression based polynomial rs recently there is also interest in rs which do not try to use regression least square fit at all under the terminology of design and analysis of computer experiments dace sacks et al 1989 an example of mdo use of dace is given by otto et al 1996 neither the rs nor the nn technique scales well to large numbers of variables therefore the use of these techniques has been limited in single discipline optimizations however in mdo both t