Abstract
We present a sensitivity analysis based uncertainty reduction approach, called Multi-dIsciplinary Multi-Output Sensitivity Analysis (MIMOSA), for the analysis model of a multi-disciplinary engineering system decomposed into multiple subsystems with each subsystem analysis having multiple inputs with reducible uncertainty and multiple outputs. MIMOSA can determine: (1) the sensitivity of system and subsystem outputs to input uncertainties at both system and subsystem levels, (2) the sensitivity of the system outputs to the variation from subsystem outputs, and (3) the optimal “investment” required to reduce uncertainty in inputs in order to obtain a maximum reduction in output variations at both the system and subsystem levels. A numerical and an engineering example with two and three subsystems, respectively, have been used to demonstrate the applicability of the MIMOSA approach.
Similar content being viewed by others
References
Acar E, Haftka RT, Johnson TF (2007) Tradeoff of uncertainty reduction mechanisms for reducing weight of composite laminates. J Mech Des 129(3):266–274. doi:10.1115/1.2406097
Agarwal H, Renaud JE, Preston EL, Padmanabhan D (2004) Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliab Eng Syst Saf 85(1–3):281–294. doi:10.1016/j.ress.2004.03.017
Anonymous (2005) Bosch builds better bluecore battery. http://www.danshapiro.com/blog/archives/000171bosch_builds_better_bluecore_batteries.html. Accessed 14 Dec 2007
Aute V, Azarm S (2006) A genetic algorithms based approach for multidisciplinary multiobjective collaborative optimization. AIAA-2006-6953. In: Proceedings of the 11th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, Sep. 6–8
Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127(5):875–886. doi:10.1115/1.1904642
Chiralaksanakul A, Mahadevan S (2007) Decoupled approach to multidisciplinary design optimization under uncertainty. Optim Eng 8(1):21–42. doi:10.1007/s11081-007-9014-2
Deb K (2001) Multiobjective optimization using evolutionary algorithms. Wiley, New York
Du X, Chen W (2002) Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J 40(3):545–552
Du X, Chen W (2005) Collaborative reliability analysis under the framework of multidisciplinary systems design. Optim Eng 6(1):63–84. doi:10.1023/B:OPTE.0000048537.35387.fa
Frey HC, Patil SR (2002) Identification and review of sensitivity analysis methods. Risk Anal 22(3):553–578. doi:10.1111/0272-4332.00039
Gu X, Renaud JE, Batill SM (1998) Investigation of multidisciplinary design subject to uncertainties. AIAA Paper 1998–4747. In: Proceedings of the 7th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference, St. Louis, MO, Sep. 2–4
Gu X, Renaud JE, Penninger CL (2006) Implicit uncertainty propagation for robust collaborative optimization. J Mech Des 128(4):1001–1013. doi:10.1115/1.2205869
Hamby DM (1994) Review of techniques for parameter sensitivity analysis of environmental models. Environ Monit Assess 32(2):135–154. doi:10.1007/BF00547132
Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81(1):23–69. doi:10.1016/S0951-8320(03)00058-9
Iman RL, Helton JC (1988) An investigation of uncertainty and sensitivity analysis techniques for computer models. Risk Anal 8(1):71–90. doi:10.1111/j.1539-6924.1988.tb01155.x
Kale AA, Haftka RT (2008) Tradeoff of weight and inspection cost in reliability-based structural optimization. J Aircr 45(1):77–85. doi:10.2514/1.21229
Kern D, Du X, Sudjianto A (2003) Forecasting manufacturing quality during design using process capability data. In: Proceedings of the IMECE’ 03, ASME 2003 International Mechanical Engineering Congress and RD&D Expo, Washington, DC, Nov. 15–21
Kokkolaras M, Mourelatos ZP, Papalambros PY (2006) Design optimization of hierarchically decomposed multilevel systems under uncertainty. J Mech Des 128(2):503–508. doi:10.1115/1.2168470
Li M (2007) Robust optimization and sensitivity analysis with multi-objective genetic algorithms: single- and multi-disciplinary applications. Ph.D. Dissertation, University of Maryland, College Park, Maryland
Li M, Azarm S (2008) Multiobjective collaborative robust optimization (McRO) with interval uncertainty and interdisciplinary uncertainty propagation. J Mech Des 130(8):081402/1–081402/11. doi:10.1115/1.2936898
Li M, Williams N, Azarm S (2009) Interval uncertainty reduction and sensitivity analysis with multi-objective design optimization. J Mech Des 131(3):031007/1–031007/11. doi:10.1115/1.3066736
Noor AK, Starnes JH, Peters JM (2000) Uncertainty analysis of composite structures. Comput Methods Appl Mech Eng 185(2–4):413–432. doi:10.1016/S0045-7825(99)00269-8
Padula SL, Gumbert CR, Li W (2006) Aerospace applications of optimization under uncertainty. Optim Eng 7(3):317–328. doi:10.1007/s11081-006-9974-7
Qiu ZP, Ma Y, Wang XJ (2004) Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters. Commun Numer Methods Eng 20:279–290. doi:10.1002/cnm.668
Rao SS, Cao LT (2002) Optimum design of mechanical systems involving interval parameters. J Mech Des 124(3):465–472. doi:10.1115/1.1479691
Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis. Wiley, New York
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New York
Smith N, Mahadevan S (2005) Integrating system-level and component-level designs under uncertainty. J Spacecr Rockets 42:752–760
Sobieszczanski-Sobieski J (1990) Sensitivity of complex, internally coupled systems. AIAA J 28(1):153–160
Sobieszczanski-Sobieski J, Bloebaum C, Hajela P (1991) Sensitivity of control-augmented structure obtained by a system decomposition method. AIAA J 29(2):264–270
Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280. doi:10.1016/S0378-4754(00)00270-6
Williams N, Azarm S, Kannan PK (2008) Engineering product design optimization for retail channel acceptance. J Mech Des 130(6):061402/1–061402/10. doi:10.1115/1.2898874
Wu WD, Rao SS (2007) Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis. Reliab Eng Syst Saf 92(1):54–64. doi:10.1016/j.ress.2005.11.009
Yin X, Chen W (2008) A hierarchical statistical sensitivity analysis method for complex engineering systems design. J Mech Des 130(7):071402/1–071402/10. doi:10.1115/1.2918913
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, M., Hamel, J. & Azarm, S. Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis. Struct Multidisc Optim 40, 77–96 (2010). https://doi.org/10.1007/s00158-009-0372-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-009-0372-6