Surrogate modeling for large-scale black-box systems

This research introduces a systematic method to reduce the complexity of large-scale blackbox systems for which the governing equations are unavailable. For such systems, surrogate models are critical for many applications, such as Monte Carlo simulations; however, existing surrogate modeling methods often are not applicable, particularly when the dimension of the input space is very high. In this research, we develop a systematic approach to represent the high-dimensional input space of a large-scale system by a smaller set of inputs. This collection of representatives is called a multi-agent collective, forming a surrogate model with which an inexpensive computation replaces the original complex task. The mathematical criteria used to derive the collective aim to avoid overlapping of characteristics between representatives, in order to achieve an effective surrogate model and avoid redundancies. The surrogate modeling method is demonstrated on a light inventory that contains light data corresponding to 82 aircraft types. Ten aircraft types are selected by the method to represent the full light inventory for the computation of fuel burn estimates, yielding an error between outputs from the surrogate and full models of just 2.08%. The ten representative aircraft types are selected by first aggregating similar aircraft types together into agents, and then selecting a representative aircraft type for each agent. In assessing the similarity between aircraft types, the characteristic of each aircraft type is determined from available light data instead of solving the fuel burn computation model, which makes the assessment procedure inexpensive. Aggregation criteria are specified to quantify the similarity between aircraft types and a stringency, which controls the tradeoff between the two competing objectives in the modeling  – the number of representatives and the estimation error. The surrogate modeling results are compared to a model obtained via manual aggregation; that is, the aggregation of aircraft types is done based on engineering judgment. The surrogate model derived using the systematic approach yields fewer representatives in the collective, yielding a surrogate model with lower computational cost, while achieving better accuracy. Further, the systematic approach eliminates the subjectivity that is inherent in the manual aggregation method. The surrogate model is also applied to other light inventories, yielding errors of similar magnitude to the case when the reference light inventory is considered.

[1]  D. Sorensen,et al.  A Survey of Model Reduction Methods for Large-Scale Systems , 2000 .

[2]  A. Giunta,et al.  Use of data sampling, surrogate models, and numerical optimization in engineering design , 2002 .

[3]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[4]  Jacques Ferber,et al.  Multi-agent systems - an introduction to distributed artificial intelligence , 1999 .

[5]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[6]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[7]  Wayne L. Tabor,et al.  RESPONSE SURFACE MODEL DEVELOPMENT FOR GLOBAL/LOCAL OPTIMIZATION USING RADIAL BASIS FUNCTIONS* , 2000 .

[8]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[9]  R. Lewis,et al.  A MULTIGRID APPROACH TO THE OPTIMIZATION OF SYSTEMS GOVERNED BY DIFFERENTIAL EQUATIONS , 2000 .

[10]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[11]  P. A. Newman,et al.  Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models , 2001 .

[12]  Eric James Grimme,et al.  Krylov Projection Methods for Model Reduction , 1997 .

[13]  W. K. Anderson,et al.  First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization , 2000 .

[14]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments: Design and Analysis , 2001 .

[15]  S. McCormick,et al.  A multigrid tutorial (2nd ed.) , 2000 .

[16]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[17]  Joosung Joseph Lee,et al.  Modeling aviation's global emissions, uncertainty analysis, and applications to policy , 2005 .

[18]  Ilan Kroo,et al.  Distributed optimization and flight control using collectives , 2005 .

[19]  Ilan Kroo,et al.  Two-Level Multifidelity Design Optimization Studies for Supersonic Jets , 2005 .

[20]  Andy J. Keane,et al.  Optimization using surrogate models and partially converged computational fluid dynamics simulations , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  E. Grimme,et al.  Pade approximation of large-scale dynamic systems with Lanczos methods , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[22]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[23]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[24]  Christopher J. Steffen.  Fuel Injector Design Optimization for an Annular Scramjet Geometry , 2003 .

[25]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[26]  Seongim Choi,et al.  Two-Level Multi-Fidelity Design Optimization Studies for Supersonic Jets , 2005 .

[27]  Theresa Dawn Robinson,et al.  Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping , 2008 .

[28]  I. Kevrekidis,et al.  Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders , 1991 .

[29]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[30]  Robert Haimes,et al.  Strategies for Multifidelity Optimization with Variable-Dimensional Hierarchical Models , 2006 .

[31]  P. C. Gehlen,et al.  Computer Experiments , 1996 .

[32]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[33]  Ian S. Lustick.  Agent-based modelling of collective identity: testing constructivist theory , 2000, J. Artif. Soc. Soc. Simul..

[34]  J. Neter,et al.  Applied linear statistical models : regression, analysis of variance, and experimental designs , 1974 .

[35]  Thilo Penzl.  Algorithms for model reduction of large dynamical systems , 2006 .

[36]  Dimitri N. Mavris,et al.  Architecture Study for the Aviation Environmental Portfolio Management Tool , 2006 .

[37]  R. Haftka,et al.  Multiple Surrogates for the Shape Optimization of Bluff Body-Facilitated Mixing , 2005 .

[38]  Michael S. Eldred,et al.  Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies , 2004 .

[39]  C Otto John,et al.  A Surrogate Approach to the Experimental Optimization of Multielement Airfoils , 1996 .

[40]  J. H. Starnes,et al.  Construction of Response Surface Approximations for Design Optimization , 1998 .

[41]  Jacob K. White,et al.  Low-Rank Solution of Lyapunov Equations , 2004, SIAM Rev..

[42]  Danny C. Sorensen,et al.  The Sylvester equation and approximate balanced reduction , 2002 .

[43]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[44]  Ian A. Waitz.  Assessment of the effects of operational procedures and derated thrust on American Airlines B777 emissions from London's Heathrow and Gatwick airports , 2006 .