Exploitation of Sensitivity Derivatives for Improving Sampling Methods

Many application codes, such as finite element structural analyses and computational fluid dynamics codes, are capable of producing many sensitivity derivatives at a small fraction of the cost of the underlying analysis. A simple variance reduction method is described that exploits such inexpensive sensitivity derivatives to increase the accuracy of sampling methods. Five examples, including a finite element structural analysis of an aircraft wing, are provided that illustrate an order of magnitude improvement in accuracy for both Monte Carlo and stratified sampling schemes.

[1]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[2]  Gene Hou,et al.  First- and Second-Order Aerodynamic Sensitivity Derivatives via Automatic Differentiation with Incremental Iterative Methods , 1996 .

[3]  Duc T. Nguyen,et al.  Computational Mechanics Analysis Tools for Parallel-Vector Supercomputers , 1993 .

[4]  Gene Hou,et al.  High-Fidelity Computational Optimization for 3-D Flexible Wings: Part II—Effect of Random Geometric Uncertainty on Design , 2005 .

[5]  Gene Hou,et al.  Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing , 2001 .

[6]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[7]  Robert W. Walters,et al.  Uncertainty analysis for fluid mechanics with applications , 2002 .

[8]  Perry A. Newman,et al.  Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis , 2001 .

[9]  T. A. Zang,et al.  Uncertainty Propagation for a Turbulent, Compressible Nozzle Flow Using Stochastic Methods , 2004 .

[10]  Peter Mathé,et al.  Hilbert space analysis of Latin Hypercube Sampling , 2000 .

[11]  E. Novak.  Deterministic and Stochastic Error Bounds in Numerical Analysis , 1988 .

[12]  P. Glasserman,et al.  Variance Reduction Techniques for Estimating Value-at-Risk , 2000 .

[13]  Alan Carle,et al.  Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D , 1998 .

[14]  Thomas A. Zang,et al.  An Efficient Monte Carlo Method for Optimal Control Problems with Uncertainty , 2003, Comput. Optim. Appl..

[15]  Cecilia Reyes,et al.  MONTE CARLO WITHIN A DAY , 2001 .

[16]  Gene Hou,et al.  EFFECT OF RANDOM GEOMETRIC UNCERTAINTY ON THE COMPUTATIONAL DESIGN OF A 3-D FLEXIBLE WING , 2002 .

[17]  Gene Hou,et al.  FIRST-AMD SECOND-ORDER SENSITIVITY ANALYSIS OF FINITE ELEMENT EQUATIONS VIA AUTOMATIC DIFFERENTIATION , 1998 .

[18]  Pichuraman Sundaram,et al.  Aerospace vehicle MDO shape optimization using ADIFOR 3.0 gradients , 2000 .