Research Papers

Combining Mathematical Programming and SysML for Automated Component Sizing of Hydraulic Systems

[+] Author and Article Information
Aditya A. Shah

Deere & Company,
Dubuque, IA 52001
e-mail: shahadityaa@johndeere.com

Christiaan J. J. Paredis

The G.W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: chris.paredis@me.gatech.edu

Roger Burkhart

Deere & Company,
Moline, IL 61265
e-mail: burkhartrogerm@johndeere.com

Dirk Schaefer

The G.W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Savannah, GA 31407 e-mail: dirk.schaefer@me.gatech.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received November 16, 2011; final manuscript received April 26, 2012; published online November 15, 2012. Assoc. Editor: Ajay Joneja.

J. Comput. Inf. Sci. Eng 12(4), 041006 (Nov 15, 2012) (14 pages) doi:10.1115/1.4007764 History: Received November 16, 2011; Revised April 26, 2012

In this paper, we present a framework for automated component sizing to extend a designer's ability to evaluate a particular configuration during the architecture exploration phase of a design process. Component sizing is a hard problem to solve, both from a computational and modeling aspect. This is because of competing objectives, requirements from multiple disciplines, and the need to find a good solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: (a) solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal and (b) modeling a component sizing problem in a manner that is convenient to designers. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. The object management group systems modeling language (OMG SysML™) is used to model component sizing problems in order to facilitate problem formulation, model reuse and automatic generation of low-level code that can be solved using GAMS and its solvers. This framework is demonstrated by applying it to an example of a hydraulic log splitter. Based on this initial example, we discuss two advantages of this framework—total time taken in solving multiple scenarios for a given configuration and the graphical representation of a problem in SysML.

Copyright © 2012 by ASME
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Sage, A. P., and Armstrong, J. E. J., 2000, Introduction to Systems Engineering, John Wiley & Sons, Hoboken, NJ.
OMG, 2008, “Systems Modeling Language v 1.1,” http://www.omg.org/docs/formal/08-11-02.pdf
Sauer-Sunstrand, 1997, Selection of Driveline Components, Sauer-Sunstrand Company, Ames, IA.
Eaton, 1998, Pump and Motor Sizing Guide, Eaton Corporation Hydraulics Division, Eden Prairie, MN.
Coyne, R. D., Rosenman, M. A., Radford, A. D., Balachandran, M., and Gero, J. S., 1989, Knowledge-Based Design Systems, Addison-Wesley Longman Publishing Co., Inc., Boston, MA.
Dym, C. L., and Levitt, R. E., 1991, Knowledge-Based Systems in Engineering, McGraw-Hill, Inc., New York, NY.
Malak, R. J., Tucker, L., and Paredis, C. J., 2008, “Composing Tradeoff Models For Multi-Attribute System-Level Decision Making,” Proceedings of the ASME 2008 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE, ASME Paper Number 49970.
Westman, R., Sargent, C., and Burton, R., 1987, “A Knowledge-Based Modular Approach to Hydraulic Circuit Design,” Comput. Eng., 1, pp. 37–41.
Sargent, C. M., Burton, R. T., and Westman, R. W., 1988, “Expert Systems and Fluid Power,” Proceedings of the 8th International Fluid Power Symposium, pp. 68–272.
Dunlop, G., and Rayudu, R., 1993, “An Expert Design Assistant for Hydraulic Systems,” Artificial Neural Networks and Expert Systems, Proceedings, First New Zealand International Two-Stream Conference on, pp. 314–316.
Fujita, K., Akagi, S., and Sasaki, M., 1995, “Adaptive Synthesis of Hydraulic Circuits From Design Cases Based on Functional Structure,” Proceedings of the 1995 ASME International Design Engineering Technical Conferences—21st Annual Design Automation Conference, Vol. 82, pp. 875–882.
da Silva, J. C., and Back, N., 2000, “Shaping the Process of Fluid Power System Design Applying an Expert System,” Res. Eng. Des., 12(1), pp. 8–17. [CrossRef]
Hughes, E. J., Richards, T. G., and Tilley, D. G., 2001, “Development of a Design Support Tool for Fluid Power System Design,” J. Eng. Design, 12, pp. 75–92. [CrossRef]
Modelica, 2009, Modelica Language Specification v 3.1. http://www.modelica.org/documents/ModelicaSpec31.pdf
Fritzson, P., 2004, Principles of Object-Oriented Modeling and Simulation With Modelica 2.1, IEEE Press, Washington, DC.
Gross, M. D., 1986, “Design as Exploring Constraints,” Ph.D. thesis, Massachusetts Institute of Technology, Department of Architecture, Boston, MA.
Russell, S. J., and Norvig, P., 2003, “Constraint Satisfaction Problems,” Artificial Intelligence: A Modern Approach, Chap. V, 4th ed., Prentice Hall, pp. 137–160.
Freuder, E. C., and Mackworth, A. K., 2006, “Constraint Satisfaction: An Emerging Paradigm,” Handbook of Constraint Programming, Chap. II, F.Rossi, P.van Beek, and T.Walsh, eds., Elsevier, Atlanta, GA, pp. 13–28.
GAMS, 2009, General Algebraic Modeling System (GAMS), www.gams.com
Marc, C., Granvilliers, L., and Sorin, V., 2005, Elisa, http://sourceforge.net/projects/elisa/
Granvilliers, L., 2003, RealPaver User's Manual, version 0.3, http://realpaver.sourceforge.net/
Chenouard, R., Granvilliers, L., and Soto, R., 2008, “Model-Driven Constraint Programming,” PPDP’ 08: Proceedings of the 10th international ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, ACM, pp. 236–246.
Kerzhner, A. A., and Paredis, C. J. J., 2009, “Using Domain Specific Languages to Capture Design Synthesis Knowledge for Model-Based Systems Engineering,” Proceedings of the 2009 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, ASME, Paper No. 87286.
OMG, 2006, Meta Object Facility (MOF) Core Specification v 2.0, http://www.omg.org/docs/formal/06-01-01.pdf
Königs, A., and Schürr, A., 2006, “Tool Integration With Triple Graph Grammars—A Survey,” Electron. Notes Theor. Comput. Sci., 148(1), pp. 113–150. [CrossRef]
Brucker, A. D., and Doser, J., 2007, “Metamodel-Based UML Notations for Domain-Specific Languages,” 4th International Workshop on Software Language Engineering (ATEM 2007).
Weisemöller, I., and Schürr, A., 2008, “A Comparison of Standard Compliant Ways to Define Domain Specific Languages,” Models in Software Engineering, Workshops and Symposia at MoDELS 2007, Reports and Revised Selected Papers, H.Giese, ed., Springer, Nashville, TN, Sept. 30–Oct. 5,Vol. 5002, pp. 47–58.
Baresi, L., and Heckel, R., 2002, “Tutorial Introduction to Graph Transformation: A Software Engineering Perspective,” Graph Transformation, First International Conference, ICGT 2002, Barcelona, Spain, Proceedings, A.Corradini, H.Ehrig, H.-J.Kreowski, and G.Rozenberg, eds., Oct. 7–12, Springer, Vol. 2505 of LNCS, pp. 402–429.
Czarnecki, K., and Helsen, S., 2006, “Feature-Based Survey of Model Transformation Approaches,” IBM Syst. J., 45(3), pp. 621–645. [CrossRef]
Fischer, T., Niere, J., Torunski, L., and Zündorf, A., 2000, “Story Diagrams: A New Graph Rewrite Language Based on the Unified Modeling Language and Java,” Theory and Application of Graph Transformations, 6th International Workshop, TAGT’98, Paderborn, Germany, 1998, H.Ehrig, G.Engels, H.-J.Kreowski, and G.Rozenberg, eds., Nov. 16–20, Springer, Vol. 1764, pp. 157–167.
NoMagic, 2009, MagicDraw, http://www.magicdraw.com
Schürr, A., 1995, “Specification of Graph Translators With Triple Graph Grammars,” Graph-Theoretic Concepts in Computer Science, 20th International Workshop, WG’ 94, Herrsching, Germany, 1994, Proceedings, E. W.Mayr, G.Schmidt, and G.Tinhofer, eds., June 16–18, Springer, Vol. 903, pp. 151–163.
Sahinidis, N. V., 2003, “Global Optimization and Constraint Satisfaction: The Branch-and-Reduce Approach,” First International Workshop on Global Optimization and Constraint Satisfaction, COCOS 2002, Valbonne-Sophia Antipolis, France, Oct. 2–4, C.Bliek, C.Jermann, and A.Neumaier, eds., Springer, Vol. 2861, pp. 1–16.


Grahic Jump Location
Fig. 1

GAMS metamodel definition. Semantics of GAMS are represented as objects in the metamodel. For instance, a model object can have multiple gamsvariables but a gamsvariable can belong to only one model.

Grahic Jump Location
Fig. 2

Profile to represent mathematical programming semantics in SysML. Used to enable object-oriented modeling of component sizing problems in SysML. For instance, a gamsvariable extends the class property and specifies additional tags related to GAMS.

Grahic Jump Location
Fig. 3

Process of model transformation from source to target model (Czarnecki et al. [29])

Grahic Jump Location
Fig. 4

Example of a graphical model transformation. This transformation converts a SysML model to a MOF model based on the GAMS metamodel discussed previously. The SysML block input is processed iteratively until the complete output model is created.

Grahic Jump Location
Fig. 5

Sequence of model transformations to solve a component sizing problem modeled in SysML. Converts a SysML model to executable GAMS code and updates SysML model with the solution.

Grahic Jump Location
Fig. 6

A horizontal acting hydraulic log splitter

Grahic Jump Location
Fig. 7

A block diagram for a horizontal acting hydraulic log splitter

Grahic Jump Location
Fig. 8

SysML requirements modeling for log splitter problem. Requirements modeling aids in decomposing the problem into different analyses, such as cost analysis, force analysis. These analyses verify the requirements, which is indicated by the verify association in the diagram.

Grahic Jump Location
Fig. 9

System level view for the log splitter component sizing model using a SysML BDD. Based on object-oriented concepts, each block in the model hierarchy contains the equations specific to that block. This object-oriented modeling approach simplifies the process of compilation and executable code generation.

Grahic Jump Location
Fig. 10

Schematic view for the hydraulic open center circuit using a SysML IBD. A designer can construct circuits by reusing components and connecting them together. Equations are automatically generated for the connections between components.

Grahic Jump Location
Fig. 11

SysML IBD view showing the explicit connections that maintain consistency between sizing variables throughout all of the analyses and use-phases



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