An inexpensive estimate of failure probability for high-dimensional systems with uncertainty

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• 作者：Matthew Lehar^a ; ^{matt.lehar@stanfordalumni.org} ; Markus Zimmermann^b ; ¹ ; ^{markusz@alum.mit.edu}
• 关键词：Robustness ; Reliability ; High-dimensional systems ; Non-linear systems ; Crash analysis ; Bayesian inference
• 刊名：Structural Safety
• 出版年：2012
• 期刊代码：168_01674730
• 类别：et
• 出版时间：May-July, 2012
• 卷：36-37
• 期：Complete
• 页码：32-38
• 文件大小：659 K

摘要

The failure probability of a system at an uncertain state can be estimated within a precise confidence interval using the Monte-Carlo sampling technique. Using this approach, the number of system parameters may be arbitrarily large, and the system may be non-linear and subject to random noise. For a given confidence level and interval, the number of required simulations can be exactly computed using the Beta Distribution. When failure probabilities are on the order of 1-10%, this technique becomes very inexpensive. In particular, 100 simulations are always sufficient for a failure estimate with a confidence interval of +/鈭?0%at a 95%confidence level.

In an engineering development process, this estimate limits the number of trials required to assess the robustness or reliability of high-dimensional and non-linear systems. When simulations are expensive, for example in vehicle crash development, using such a rule to minimize the number of trials can greatly reduce the expense and time invested in development.