A decomposition‐based approach to uncertainty analysis of feed‐forward multicomponent systems

SUMMARY To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today's modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms. This paper proposes an approach for decomposing the uncertainty analysis task among the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to be provably convergent in distribution under certain conditions. The proposed method is illustrated on quantification of uncertainty for a multidisciplinary gas turbine system and is compared to a traditional system-level Monte Carlo uncertainty analysis approach. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Sankaran Mahadevan,et al.  Uncertainty Quantification and Propagation in Multidisciplinary Analysis and Optimization , 2008 .

[2]  Jeremy S. Agte,et al.  Bi-Level Integrated System Synthesis , 1998 .

[3]  Michel van Tooren,et al.  Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles , 2011 .

[4]  Jun S. Liu,et al.  Metropolized independent sampling with comparisons to rejection sampling and importance sampling , 1996, Stat. Comput..

[5]  Dongbin Xiu,et al.  Numerical approach for quantification of epistemic uncertainty , 2010, J. Comput. Phys..

[6]  R. Reed.  The Superalloys: Fundamentals and Applications , 2006 .

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

[8]  Jay D. Martin,et al.  A Methodology to Manage System-level Uncertainty During Conceptual Design , 2006 .

[9]  Xiao Chen,et al.  A flexible uncertainty quantification method for linearly coupled multi-physics systems , 2013, J. Comput. Phys..

[10]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

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

[12]  Ilan Kroo,et al.  Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment , 1995 .

[13]  Dongbin Xiu,et al.  A flexible numerical approach for quantification of epistemic uncertainty , 2013, J. Comput. Phys..

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

[15]  Roger Ghanem,et al.  Measure transformation and efficient quadrature in reduced‐dimensional stochastic modeling of coupled problems , 2011, 1112.4772.

[16]  Sankaran Mahadevan,et al.  Likelihood-Based Approach to Multidisciplinary Analysis Under Uncertainty , 2012 .

[17]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[18]  Natalia Alexandrov,et al.  Multidisciplinary design optimization : state of the art , 1997 .

[19]  Tao Jiang,et al.  Target Cascading in Optimal System Design , 2003, DAC 2000.

[20]  Roger Ghanem,et al.  Reduced chaos expansions with random coefficientsin reduced‐dimensional stochastic modeling of coupled problems , 2012, 1207.0910.

[21]  Panos Y. Papalambros,et al.  Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty , 2006, DAC 2004.

[22]  Paul G. Constantine,et al.  Efficient uncertainty propagation for network multiphysics systems , 2013, 1308.6520.

[23]  Roger Ghanem,et al.  Dimension reduction in stochastic modeling of coupled problems , 2011, 1112.4761.

[24]  Clark S. Penrod,et al.  The strong uniform convergence of multivariate variable kernel estimates , 1986 .

[25]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[26]  Christian Soize,et al.  Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems , 2013, SIAM/ASA J. Uncertain. Quantification.

[27]  M. C. Jones,et al.  On optimal data-based bandwidth selection in kernel density estimation , 1991 .

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

[29]  Christian B Allen,et al.  12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference , 2008 .

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

[31]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[32]  John E. Renaud,et al.  Implicit Uncertainty Propagation for Robust Collaborative Optimization , 2006 .

[33]  Russell V. Lenth,et al.  Some Practical Guidelines for Effective Sample Size Determination , 2001 .