Likelihood-Based Approach to Multidisciplinary Analysis Under Uncertainty

This paper proposes a new methodology for uncertainty quantification in systems that require multidisciplinary iterative analysis between two or more coupled component models. This methodology is based on computing the probability of satisfying the interdisciplinary compatibility equations, conditioned on specific values of the coupling (or feedback) variables, and this information is used to estimate the probability distributions of the coupling variables. The estimation of the coupling variables is analogous to likelihood-based parameter estimation in statistics and thus leads to the proposed likelihood approach for multidisciplinary analysis (LAMDA). Using the distributions of the feedback variables, the coupling can be removed in any one direction without loss of generality, while still preserving the mathematical relationship between the coupling variables. The calculation of the probability distributions of the coupling variables is theoretically exact and does not require a fully coupled system analysis. The proposed method is illustrated using a mathematical example and an aerospace system application—a fire detection satellite.

[1]  James R. Wertz,et al.  Space Mission Analysis and Design , 1992 .

[2]  Sankaran Mahadevan,et al.  Decoupled approach to multidisciplinary design optimization under uncertainty , 2007 .

[3]  Earl A. Thornton,et al.  Thermal Structures for Aerospace Applications , 1996 .

[4]  Natasha Leigh Smith.  Probabilistic Design of Multidisciplinary Systems , 2007 .

[5]  Natasha Smith,et al.  Efficient first-order reliability analysis of multidisciplinary systems , 2006 .

[6]  Robert D. Braun,et al.  Collaborative optimization: an architecture for large-scale distributed design , 1996 .

[7]  John E. Renaud,et al.  Uncertainty quantification using evidence theory in multidisciplinary design optimization , 2004, Reliab. Eng. Syst. Saf..

[8]  Ilan Kroo,et al.  Collaborative Approach to Launch Vehicle Design , 1997 .

[9]  Shapour Azarm,et al.  Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation , 2008 .

[10]  J. Aldrich.  R.A. Fisher and the making of maximum likelihood 1912-1922 , 1997 .

[11]  William M. McKeeman.  Algorithm 146: Multiple integration , 1962, Commun. ACM.

[12]  N. M. Alexandrov,et al.  Algorithmic Perspectives on Problem Formulations in MDO , 2000 .

[13]  Jaroslaw Sobieszczanski-Sobieski,et al.  Optimization by decomposition: A step from hierarchic to non-hierarchic systems , 1989 .

[14]  Jack J. McNamara,et al.  Studies on Fluid-Thermal-Structural Coupling for Aerothermoelasticity in Hypersonic Flow , 2010 .

[15]  Nozer D. Singpurwalla,et al.  Betting on residual life: The caveats of conditioning , 2007 .

[16]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[17]  van Eh Harald Brummelen,et al.  A monolithic approach to fluid–structure interaction , 2004 .

[18]  Y. Pawitan.  In all likelihood : statistical modelling and inference using likelihood , 2002 .

[19]  Ted Belytschko,et al.  Fluid-structure interaction , 1980 .

[20]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[21]  Christina Bloebaum,et al.  Application of global sensitivity equations in multidisciplinary aircraft synthesis , 1990 .

[22]  W. M. McKeeman,et al.  Algorithm 145: Adaptive numerical integration by Simpson's rule , 1962, Communications of the ACM.

[23]  J. Sobieszczanski-Sobieski,et al.  Bilevel Integrated System Synthesis for Concurrent and Distributed Processing , 2002 .

[24]  John E. Renaud,et al.  Worst case propagated uncertainty of multidisciplinary systems in robust design optimization , 2000 .

[25]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[26]  Jia Guo,et al.  Sequential optimization and reliability assessment for multidisciplinary systems design , 2008 .

[27]  R. Fisher.  001: On an Absolute Criterion for Fitting Frequency Curves. , 1912 .

[28]  Panos Y. Papalambros,et al.  Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty , 2006 .

[29]  Hong-Zhong Huang,et al.  Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties , 2009 .

[30]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[31]  Wei Chen,et al.  Collaborative Reliability Analysis under the Framework of Multidisciplinary Systems Design , 2005 .

[32]  Nozer D. Singpurwalla,et al.  Reliability and risk , 2006 .

[33]  Wei Chen,et al.  Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty , 2006 .