Abstract
We present a constraint-based methodology which is successfully applied to a variety of engineering problems from a wide range of disciplines. Initially conceived from investigations of the engineering design process, the methodology has helped design engineers to identify and understand the initial limitations placed upon a system. Written as a set of algebraic expressions, the design objectives and design constraints can be formulated and minima found using numerical optimization techniques. These solutions provide initial configurations for the system, corresponding to how “true” all of the constraints are. A bespoke constraint-based modelling environment has been created which embodies the methodology. This is able to resolve large systems, comprising over 100 degrees-of-freedom, using an assortment of optimization routines—direct, gradient and evolutionary algorithms. These algorithms are appropriate for a number of problem types and their inclusion increase the scope of applicability of the methodology which is demonstrated using case studies from a number of engineering domains. Machines and mechanisms; human modelling; force and flow; structural geology and discrete disassembly processes are all studied using constraint-based formulations. The contribution of the paper lies in thus proving that complex (heterogeneous) systems-of-systems can be solved if the connectivity between the systems is expressed using constraint-rules.
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References
Blundell A (1982) Bond graphs for modelling engineering systems. Ellis Horwood, Chichester, UK
Boon JA, Budd CJ, Edmunds R, Hunt GW (2010) Level set modelling for the parallel folding of layered structures: comparisons with experiments. J Mech Phys Solids (in progress)
Budd CJ, Edmunds R, Hunt GW (2003) A nonlinear model for parallel folding with friction. Proc R Soc Lond A 459:2097–2119
Cadence Design Systems, Inc. Datasheet: Cadence P pice A/D Circuit Simulation (Online) (2009) Available from http://www.cadence.com/rl/Resources/datasheets/pcb_pspice_simulation_ds.pdf. Accessed Dec 2009
Department of Mechanical Engineering Centre for PTMC (2005) Introduction to Hydraulic Circuits and Components. Technical report, University of Bath
Clarkson PJ, Coleman R, Hosking I, Waller S (2007) Inclusive design toolkit. EDC, Cambridge, UK. Available from http://www.inclusivedesigntoolkit.com. Accessed Jan 2010
De Fazio TL, Whitney DE (1987) Simplified generation of all mechanical assembly sequences. IEEE J Robot Autom 3(6):640–658
Ding L, Matthews J, Feldman J, Mullineux G (2010) Constraint modelling of food processing systems. Food Manuf Effic 3(1):15–23
Donne MS, Tilley DG, Richards W (1995) The use of multi-objective parallel genetic algorithms to aid fluid power systems design. Proc. Inst Mech Eng 209:53–61
Dulay IK (1988) Fundamentals of hydraulic power transmission. Elsevier, Amsterdam, Netherlands
Edmunds R, Hicks BJ, Mullineux G (2010) Drawing parallels: modelling geological phenomena using constraint satisfaction. J Struct Geol 32(7):997–1008
Edmunds R, Hicks BJ, Mullineux G (2010) Using constraint-based modelling for parallel folding evolution. IMA J Appl Math (Submitted 10/09)
Edmunds R, Hunt GW, and Wadee MA (2006) Parallel folding in multilayered structures. J Mech Phys Solids 2:384–400
Feldman J, Mullineux G, Hicks BJ (2010) A comparison of optimization methods for mechanical synthesis. J Mech Mach Theory (in progress)
Fletcher R (2000) Practical methods of optimization, 2nd edn. Wiley, Chichester, UK
Gawthrop P, Smith L (1996) Metamodelling: Bond graph and dynamic systems. Prentice Hall, London, UK
Ge JX, Chou SC, Gao XS (1999) Geometric constraint satisfaction using optimization methods. Comput Aided Des 31:867–879
Gill P, Murray W, Saunders M (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIOPT 12:979–1006
Goodwin AB (1976) Fluid power systems: theory, worked examples and problems. Macmillan, London, UK
Güngör A, Gupta SM (1997) An evaluation for disassembly processes. Comput Ind Eng 33(1–2):329–332
Hicks BJ, Medland AJ, Mullineux G (2001) A constraint-based approach to the modelling and analysis of packaging machinery. Packag Technol Sci 14:209–225
Hicks BJ, AJ. Medland, Mullineux G (2006) The representation and handling of constraints for the design, analysis, and optimization of high speed machinery. Artif Intell Eng Design Anal Manuf (AIEDAM) 20:313–328
Hicks BJ, Mullineux G, Berry C, McPherson CJ, Medland AJ (2003) Energy method for modelling delamination buckling in geometrically constrained systems. Proc Inst Mech Eng Part C J Mech Eng Sci 217:1015–1026
Hunt GW, Edmunds R, Budd CJ, Cosgrove JW (2006) Serial parallel folding with friction: a primitive model using cubic B-splines. J Strut Geol 28:444–455
Karnopp D, Margolis DL, Rosenberg RC (2006) System dynamics: modeling and simulation of mechatronic systems, 4th edn. Wiley, New Jersey
Kernighan B, Richie D (1988) The C programming language. Prentice Hall, London
Kumar R, Izui K, Yoshimura M, Nishiwaki S (2009) Optimal multilevel redundancy allocation in series and series-parallel systems. Comput Ind Eng 57(1):169–180
Lambert AJD, Gupta SM (2005) Disassembly modeling for assembly, maintenance, reuse, and recycling. CRC, Boca Raton
Leigh RD, Medland AJ, Mullineux G, Potts IRB (1989) Model spaces and their use in mechanism simulation. Proc IME B J Eng Manuf 203:167–174
LMS International. The LMS Imagine.Lab AMESim-Introduction (Online) (2009) Available from http://www.lmsintl.com/imagine-amesim-intro. Accessed Dec 2009
Ma W, Zhong Y, Tso SK, Zhou T (2004) A hierarchically structured and constraint-based data model for intuitive and precise solid modeling in a virtual reality environment. Comput Aided Des 36:903–928
Martínez ML, Félez J (2005) A constraint solver to define correctly dimensioned and over-dimensioned parts. Comput Aided Des 37:1353–1369
Massachusetts Institute of Technology (2007) GAlib: A C++ library of genetic algorithm components. Massachusetts, USA
Matthews J, Singh B, Mullineux G, Medland AJ (2006) Constraint-based approach to investigate the process flexibility of food processing equipment. Comput Ind Eng 54(4):809–820
Mitchell RH, Medland AJ, Salo AIT (2007) A design methodology to create constraint-based human movement patterns for ergonomic analysis. J Eng Des 18(4):293–310
Molenbroek JFM, Medland AJ (2000) The application of constraint processes for the manipulation of human models to address ergonomic design problems. In: Proceedings of 3rd international symposium on tools and methods of competitive engineering, pp 827–835
Mullineux G (1987) Optimization scheme for assembling components. Comput Aided Des 19:35–40
Mullineux G (1988) The introduction of constraints into a graphics system. Eng Comput 3:201–205
Mullineux G (2001) Constraint resolution using optimisation techniques. Comput Graph 25:483–492
Mullineux G (2002) Improvement of free-form surfaces for product styling applications. Comput Aided Des 34:871–880
Mullineux G, Feldman J, Hicks BJ (2010) Catalogues as a starting point for mechanism synthesis. J Mech Mach Theory (Submitted 09/08)
Mullineux G, Feldman J, Matthews J (2010) Using constraints at the conceptual stage of the design of carton erection. J Mech Mach Theory 45(12):1897–1908
Mullineux G, Hicks BJ, Medland AJ (2005) Constraint-aided product design. Acta Polytech 45:31–36
Pahl G, Beitz W (1996) Engineering design: a systematic approach, 2nd edn. Springer, London
Price NJ, Cosgrove JW (1990) Analysis of geological structures. Cambridge University Press, Cambridge
Pugh S (1990) Total design: integrated methods for successful product design. Addison-Wesley, Harlow
Sitharam M, Oung J-J, Zhou Y, Arbree A (2006) Geometric constraints within feature hierarchies. Comput Aided Des 38:22–38
Smith IM (1987) Hughes electrical technology. Longman, Singapore
Subramani AK, Dewhurst P (1991) Automatic generation of product disassembly sequences. Ann CIRP 40(1):115–118
The Math Works, Inc. (2009) MATLAB: high-performance numeric computation and visualization software. Natick, Massachussets, USA
The Numerical Algorithms Group, Ltd. (2009) The NAG Fortran Library (FL21). Oxford, UK
Thoma JU (1975) Introduction to Bond graphs and their applications. Pergamon, Oxford
Tu Y, Chen L, Sun F, Wu C (2006) Optimization of cooling load and coefficient of performance for real regenerated air refrigerator. Proc Inst Mech Eng Part E J Process Mech Eng 220:207–215
Ullman D (1992) The mechanical design process. McGraw-Hill, New York
University of Ballarat (2006) GANSO Library: Global and Non-Smooth Optimization library. Ballarat, Australia
Walsh G (1975) Methods of optimization. Wiley, London
Yoshimura M, Izui K (2002) Smart optimization of machine systems using hierarchical genotype representations. J Mech Des 124(3):375–384
Zhang YM, He XD, Liu QL, Wen BC (2005) An approach of robust reliability design for mechanical components. Proc Inst Mech Eng Part E J Process Mech Eng 219:275–283
Acknowledgments
The authors would like to thank Dr. David Branson and Dr. Baljinder Singh from the University of Bath and Dr. Kazuhiro Izui from Kyoto University for their contributions to this paper. Dr. Branson and Dr. Izui for their insight and discussions on the topics of fluid power systems and disassembly processes respectively, and Dr. Singh for his invaluable input to the human modelling section of this paper; in particular the figures contained therein. The work reported in this paper has been undertaken as part of the EPSRC Innovative Design and Manufacturing Research Centre at the University of Bath (grant reference GR/R67507/0) and the authors gratefully acknowledge this support and express their thanks for the advice and support of all concerned.
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Edmunds, R., Feldman, J.A., Hicks, B.J. et al. Constraint-based modelling and optimization to support the design of complex multi-domain engineering problems. Engineering with Computers 27, 319–336 (2011). https://doi.org/10.1007/s00366-010-0201-y
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DOI: https://doi.org/10.1007/s00366-010-0201-y