Numerical approaches for collaborative data processing

被引：0
作者：
Pete Seiler
Michael Frenklach
Andrew Packard
Ryan Feeley
机构：
[1] Honeywell Labs in Minneapolis,Department of Mechanical Engineering
[2] University of California,undefined
来源：
Optimization and Engineering | 2006年 / 7卷
关键词：
Model validation; Prediction; Sums-of-squares polynomials; Semidefinite programming;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. The approach relies on a solution mapping technique to approximate mathematical models by polynomial surrogate models. We use these surrogate models to formulate prediction bounds in terms of polynomial optimizations. Recent results on polynomial optimizations are then applied to solve the prediction problem. Two examples which illustrate the key aspects of the proposed algorithm are given. The proposed algorithm offers a framework for collaborative data processing among researchers.
引用
收藏
页码：459 / 478
页数：19
相关论文
共 29 条
[1]  
Choi M(1995)Sums of squares of real polynomials Proc Symp Pure Math 58 103-126
[2]  
Lam T(2001)Resolution of conflicts involving many aircraft via semidefinite programming AIAA J Guidance, Control, Dynamics 24 79-86
[3]  
Reznick B(1985)Statistically rigorous parameter estimation in dynamic modeling using approximate empirical models AIChE J 31 498-500
[4]  
Frazzoli E(2004)Collaborative data processing in developing predictive models of complex reaction systems J Chemical Kinetics 36 57-66
[5]  
Mao Z-H(2004)Symmetry groups, semidefinite programs, and sums of squares Journal of Pure and Appl. Algebra 192 95-128
[6]  
Oh J-H(2001)Global optimization with polynomials and the problem of moments SIAM J Optim 11 796-817
[7]  
Feron E(1983)Sensitivity analysis and parameter estimation in dynamic modeling of chemical kinetics Int J Chem Kinetics 15 677-696
[8]  
Frenklach M(1993)Modeling the cell division cycle: M-phase trigger, oscillations, and size control J Theor Biol 165 101-134
[9]  
Miller D(2003)Semidefinite programming relaxations for semialgebraic problems Mathematical Programming Ser. B 96 293-320
[10]  
Frenklach M(1998)An algorithm for sums of squares of real polynomials J Pure Appl Alg 127 99-104
123