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Research Papers: Design for Manufacture and the Life Cycle

Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

[+] Author and Article Information
Jie Hu, Aiguo Cheng, Zhihua Zhong

The State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China

Yan Wang

Multiscale Systems Engineering Research Group,
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 9, 2013; final manuscript received December 17, 2014; published online February 6, 2015. Assoc. Editor: Rikard Söderberg.

J. Mech. Des 137(4), 041701 (Apr 01, 2015) (11 pages) Paper No: MD-13-1458; doi: 10.1115/1.4029513 History: Received October 09, 2013; Revised December 17, 2014; Online February 06, 2015

Interval is an alternative to probability distribution in quantifying uncertainty for sensitivity analysis (SA) when there is a lack of data to fit a distribution with good confidence. It only requires the information of lower and upper bounds. Analytical relations among design parameters, design variables, and target performances under uncertainty can be modeled as interval-valued constraints. By incorporating logic quantifiers, quantified constraint satisfaction problems (QCSPs) can integrate semantics and engineering intent in mathematical relations for engineering design. In this paper, a global sensitivity analysis (GSA) method is developed for feasible design space searching problems that are formulated as QCSPs, where the effects of value variations and quantifier changes for design parameters on target performances are analyzed based on several proposed metrics, including the indeterminacy of target performances, information gain of parameter variations, and infeasibility of constraints. Three examples are used to demonstrate the proposed approach.

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Topics: Design
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References

Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M., 2004, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, Wiley, New York.
Millwater, H., and Feng, Y., 2011, “Probabilistic Sensitivity Analysis With Respect to Bounds of Truncated Distributions,” ASME J. Mech. Des., 133(6), p. 061001. [CrossRef]
Caro, S., Wenger, P., Bennis, F., and Chablat, D., 2005, “Sensitivity Analysis of the Orthoglide: A Three-DOF Translational Parallel Kinematic Machine,” ASME J. Mech. Des., 128(2), pp. 392–402. [CrossRef]
Youn, B. D., and Wang, P., 2008, “Bayesian Reliability-Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method,” Struct. Multidiscip. Optim., 36(2), pp. 107–123. [CrossRef]
Zou, T., Mourelatos, Z. P., Mahadevan, S., and Tu, J., 2008, “An Indicator Response Surface Method for Simulation-Based Reliability Analysis,” ASME J. Mech. Des., 130(7), p. 071401. [CrossRef]
Kleijnen, J. P., 1998, “Experimental Design for Sensitivity Analysis, Optimization, and Validation of Simulation Models,” Handbook of Simulation, J.Banks, ed., Wiley, New York, pp. 173–223. [CrossRef]
Box, G. E., Hunter, W. G., and Hunter, J. S., 1978, Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, Wiley, New York.
Morris, M. D., 1991, “Factorial Sampling Plans for Preliminary Computational Experiments,” Technometrics, 33(2), pp. 161–174. [CrossRef]
Chen, W., Jin, R., and Sudjianto, A., 2005, “Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty,” ASME J. Mech. Des., 127(5), pp. 875–886. [CrossRef]
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S., 2008, Global Sensitivity Analysis: The Primer, Wiley-Interscience, New York. [CrossRef]
Iman, R. L., and Helton, J. C., 1988, “An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models,” Risk Anal., 8(1), pp. 71–90. [CrossRef]
Helton, J., Garner, J., Marietta, M., Rechard, R., Rudeen, D., and Swift, P., 1993, “Uncertainty and Sensitivity Analysis Results Obtained in a Preliminary Performance Assessment for the Waste Isolation Pilot Plant,” Nucl. Sci. Eng., 114(4), pp. 286–331.
Drignei, D., and Mourelatos, Z. P., 2012, “Parameter Screening in Statistical Dynamic Computer Model Calibration Using Global Sensitivities,” ASME J. Mech. Des., 134(8), p. 081001. [CrossRef]
Chatterjee, S., and Hadi, A. S., 2009, Sensitivity Analysis in Linear Regression, Wiley, New York. [CrossRef]
Liu, Y., Yin, X., Huang, H.-Z., Arendt, P., and Chen, W., 2010, “A Hierarchical Statistical Sensitivity Analysis Method for Multilevel Systems With Shared Variables,” ASME J. Mech. Des., 132(3), p. 031006. [CrossRef]
Yue, J., Camelio, J. A., Chin, M., and Cai, W., 2006, “Product-Oriented Sensitivity Analysis for Multistation Compliant Assemblies,” ASME J. Mech. Des., 129(8), pp. 844–851. [CrossRef]
Saltelli, A., Tarantola, S., and Chan, K.-S., 1999, “A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output,” Technometrics, 41(1), pp. 39–56. [CrossRef]
Chan, K., Saltelli, A., and Tarantola, S., 1997, “Sensitivity Analysis of Model Output: Variance-Based Methods Make the Difference,” 29th Conference on Winter Simulation, IEEE Computer Society, pp. 261–268. [CrossRef]
Liu, H., Sudjianto, A., and Chen, W., 2006, “Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design,” ASME J. Mech. Des., 128(2), pp. 326–336. [CrossRef]
Hutcheson, R. S., and McAdams, D. A., 2010, “A Hybrid Sensitivity Analysis for Use in Early Design,” ASME J. Mech. Des., 132(11), p. 111007. [CrossRef]
Neumaier, A., 1989, “Rigorous Sensitivity Analysis for Parameter-Dependent Systems of Equations,” J. Math. Anal. Appl., 144(1), pp. 16–25. [CrossRef]
Rump, S. M., 1990, “Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations,” Math. Comput., 54(190), pp. 721–736. [CrossRef]
Wallner, J., Schröcker, H. P., and Hu, S. M., 2005, “Tolerances in Geometric Constraint Problems,” Reliab. Comput., 11(3), pp. 235–251. [CrossRef]
Goldsztejn, A., 2008, “Sensitivity Analysis Using a Fixed Point Interval Iteration,” Techncial Report Hal No. 00339377.
Guo, J., and Du, X., 2009, “Reliability Sensitivity Analysis With Random and Interval Variables,” Int. J. Numer. Eng., 78(13), pp. 1585–1617. [CrossRef]
Li, M., and Williams, N., 2009, “Interval Uncertainty Reduction and Single-Disciplinary Sensitivity Analysis With Multi-Objective Optimization,” ASME J. Mech. Des., 131(3), pp. 1–11. [CrossRef]
Li, M., Hamel, J., and Azarm, S., 2010, “Optimal Uncertainty Reduction for Multi-Disciplinary Multi-Output Systems Using Sensitivity Analysis,” Struct. Multidiscip. Optim., 40(1), pp. 77–96. [CrossRef]
Börner, F., Bulatov, A., Jeavons, P., and Krokhin, A., 2003, “Quantified Constraints: Algorithms and Complexity,” Computer Science Logic, M. Baaz and J. A. Makowsky eds., Springer Publishing, New York, pp. 58–70.
Shary, S. P., 2002, “A New Technique in Systems Analysis Under Interval Uncertainty and Ambiguity,” Reliab. Comput., 8(5), pp. 321–418. [CrossRef]
Hu, J., Aminzadeh, M., and Wang, Y., 2014, “Searching Feasbile Design Space by Solving Quantified Constraint Satisfaction Problems,” ASME J. Mech. Des., 136(3), p. 031002. [CrossRef]
Zeleny, M., 1973, “Compromise Programming,” Multiple Criteria Decision Making, J. L. C. A. M.Zeleny, ed., University of South Carolina Press, Columbia, SC, pp. 262–301.
Sobek, D. K., Ward, A. C., and Liker, J. K., 1999, “Toyota’s Principles of Set-Based Concurrent Engineering,” Sloan Manage. Rev., 40(2), pp. 67–84.
Singer, D. J., Doerry, N., and Buckley, M., 2009, “What Is Set-Based Design?,” Nav. Eng. J., 121(4), pp. 31–43. [CrossRef]
Chen, W., Wiecek, M. M., and Zhang, J., 1999, “Quality Utility—A Compromise Programming Approach to Robust Design,” ASME J. Mech. Des., 121(2), pp. 179–187. [CrossRef]
Apt, K. R., 1999, “The Essence of Constraint Propagation,” Theor. Comput. Sci., 221(1–2), pp. 179–210. [CrossRef]
Klir, G. J., 2006, Uncertainty and Information: Foundations of Generalized Information Theory, Wiley-Interscience, Hoboken, NJ. [CrossRef]
Eastman, C. M., 1973, “Automated Space Planning,” Artif. Intell., 4(1), pp. 41–64. [CrossRef]
Medjdoub, B., and Yannou, B., 2000, “Separating Topology and Geometry in Space Planning,” Comput. Aided Des., 32(1), pp. 39–61. [CrossRef]
Dohmen, M., 1995, “A Survey of Constraint Satisfaction Techniques for Geometric Modeling,” Comput. Graphics, 19(6), pp. 831–845. [CrossRef]
Yannou, B., Moreno, F., Thevenot, H. J., and Simpson, T. W., “Faster Generation of Feasible Design Points,” ASME Paper No. DETC2005-85449. [CrossRef]
Titus, N., and Ramani, K., 2005, “Design Space Exploration Using Constraint Satisfaction,” Configuration Workshop at the 19th International Joint Conference on Artificial Intelligence (IJCAI'05), pp. 31–36.
Sébastian, P., Chenouard, R., Nadeau, J. P., and Fischer, X., 2007, “The Embodiment Design Constraint Satisfaction Problem of the BOOTSTRAP Facing Interval Analysis and Genetic Algorithm Based Decision Support Tools,” Int. J. Interact. Des. Manuf., 1(2), pp. 99–106. [CrossRef]
Panchal, J. H., Gero Fernández, M., Paredis, C. J. J., Allen, J. K., and Mistree, F., 2007, “An Interval-Based Constraint Satisfaction (IBCS) Method for Decentralized, Collaborative Multifunctional Design,” Concurrent Eng., 15(3), pp. 309–323. [CrossRef]
Yvars, P. A., 2009, “A CSP Approach for the Network of Product Lifecycle Constraints Consistency in a Collaborative Design Context,” Eng. Appl. Artif. Intell., 22(6), pp. 961–970. [CrossRef]
Lottaz, C., Sam-Haroud, D., Faltings, B., and Smith, I., “Constraint Techniques for Collaborative Design,” IEEE International Conference on Tools With Artificial Intelligence, Taipei, Nov. 10–12, pp. 34–41. [CrossRef]
Dantan, Y. J., 2005, “Tolerance Synthesis: Quantifier Notion and Virtual Boundary,” Comput.-Aided Des., 37(2), pp. 231–240. [CrossRef]
Qureshi, A. J., Dantan, J. Y., Bruyere, J., and Bigot, R., 2010, “Set Based Robust Design of Mechanical Systems Using the Quantifier Constraint Satisfaction Algorithm,” Eng. Appl. Artif. Intell., 23(7), pp. 1173–1186. [CrossRef]
Wang, Y., 2008, “Interpretable Interval Constraint Solvers in Semantic Tolerance Analysis,” Comput. Aided Des. Appl., 5(5), pp. 654–666. [CrossRef]
Wang, Y., 2008, “Closed-Loop Analysis in Semantic Tolerance Modeling,” ASME J. Mech. Des., 130(6), p. 061701. [CrossRef]
Dantan, J. Y., and Qureshi, A. J., 2009, “Worst-Case and Statistical Tolerance Analysis Based on Quantified Constraint Satisfaction Problems and Monte Carlo Simulation,” Comput.-Aided Des., 41(1), pp. 1–12. [CrossRef]
Benhamou, F., Goualard, F., Languenou, E., and Cheristie, M., 2004, “Interval Constraint Solving for Camera Control and Motion Planning,” ACM Trans. Comput. Logic, 5(4), pp. 732–767. [CrossRef]
Jirstrand, M., 1997, “Nonlinear Control System Design by Quantifier Elimination,” J. Symbolic Comput., 24(2), pp. 137–152. [CrossRef]
Herrero, P., Sainz, M. A., Vehi, J., and Jaulin, L., 2005, “Quantified Set Inversion Algorithm With Applications to Control,” Reliab. Comput., 11(5), pp. 369–382. [CrossRef]
Herrero, P., Sainz, M. Á., Vehí, J., and Jaulin, L., 2004, “Quantified Set Inversion With Applications to Control,” IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Sept. 4, pp. 179–183. [CrossRef]
Ratschan, S., and Vehı, J., “Robust Pole Clustering of Parametric Uncertain Systems Using Interval Methods,” 4th IFAC Symposium on Robust Control Design, S.Bittanti, and P.Colaneri, eds., pp. 323–328.
Benedetti, M., Lallouet, A., and Vautard, J., 2007, “Modeling Adversary Scheduling With QCSP+,” Proceedings of the 23rd Annual ACM Symposium on Applied Computing, ACM Press, New York, pp. 151–155. [CrossRef]
Benedetti, M., Lallouet, A., and Vautard, J., “QCSP Made Practical by Virtue of Restricted Quantification,” 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 38–43.
Sachenbacher, M., and Maier, P., 2008, “Test Strategy Generation Using Quantified CSPs,” Proceedings of the 14th International Conference on Principles and Practice of Active of Constraint Programming (CP-08), P. J.Stuckey, ed., Springer, New York, pp. 566–570. [CrossRef]
Sachenbacher, M., and Schwoon, S., 2008, “Model-Based Testing Using Quantified CSPs: A Map,” Workshop at the ECAI 2008 on Model-Based Systems, pp. 37–41.
Gardeñes, E., Sainz, M. Á., Jorba, L., Calm, R., Estela, R., Mielgo, H., and Trepat, A., 2001, “Modal Intervals,” Reliab. Comput., 7(2), pp. 77–111. [CrossRef]
Dimitrova, N., Markov, S., and Popova, E., 1992, “Extended Interval Arithmetics: New Results and Applications,” Computer Arithmetics Enclosure Methods, L.Atanasova, and J.Herzberger, eds., Elsevier, Amsterdam, The Netherlands, pp. 225–232.
Kaucher, E., 1980, “Interval Analysis in the Extended Interval Space IR,” Comput. Suppl., 2, pp. 33–49. [CrossRef]
Moore, R. E., Kearfott, R. B., and Cloud, M. J., 2009, Introduction to Interval Analysis, Society for Industrial Mathematics, Philadelphia, PA.
Rényi, A., 1970, Introduction to Information Theory, Probability Theory, North-Holland, Amsterdam, The Netherlands, pp. 540–616.
Hu, J., and Wang, Y., 2014, “Sensitivity Analysis for Quantified Interval Constraints,” Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures, G.Deodatis, B. R.Ellingwood, and D. M.Frangopol, eds., CRC Press, Boca Raton, FL, pp. 2931–2938. [CrossRef]
Homma, T., and Saltelli, A., 1996, “Importance Measures in Global Sensitivity Analysis of Nonlinear Models,” Reliab. Eng. Syst. Safety, 52(1), pp. 1–17. [CrossRef]
Chen, M., and Guo, L., 2011, “The Parameters Sensitivity Analysis of Battery Electric Vehicle Dynamic,” Appl. Mech. Mater., 80–81, pp. 837–840. [CrossRef]
Chad, H., and Rosen, D. W., “Identification of Platform Variables in Product Family Design Using Sensitivity Analysis,” ASME Paper No. DETC2012-71198. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The relations among the concepts developed in the proposed method

Grahic Jump Location
Fig. 2

Sensitivity zones of X1X3 with respect to Y

Grahic Jump Location
Fig. 3

Result comparison between the (a) proposed method and (b) traditional local SA method

Grahic Jump Location
Fig. 4

Sensitivity zones of design parameters in scenario 1 (all universal) and scenario 2 (Nf existential)

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