On the Distribution of the First-Passage Time for Normal Stationary Random Processes
On the Distribution of the First-Passage Time for Normal Stationary Random Processes
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DOI：
10.1115/1.3423521
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发表时间：
1975-03
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通讯作者：
E. Vanmarcke
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作者：
E. Vanmarcke
随机过程理论在工程系统的分析和设计中的许多应用中，一个重要的问题是随机运动X（t）在系统运行时间内保持在规定范围内的概率，或首次通过指定障碍的时间的概率分布。注意力在这里被限制到平稳高斯过程与零均值和三个障碍配置被认为是，在克兰德尔等人。〔我〕。1第一种配置涉及单个势垒，X（t）= a，其中a是不能被超过的临界水平。在第二种情况下，边界由一对直线X（t）= a和X（t）=-a组成，安全区域定义为：|Xft）|< a.第三个障碍R（t）= a是根据随机过程X（t）的包络R（t）定义的，主要考虑它，因为它导致了对单障碍和双障碍的首次通过概率的有用近似。所使用的包络定义是Cramer和Leadbetter [2]的包络定义，其基本上等同于Rice [3]的包络定义。这三种屏障配置随后分别被称为B型、D型和E型屏障，并且进入不安全域的偏移分别被称为B交叉、D交叉和E交叉[1]。
A quantity of central interest in many applications of the theory of stochastic processes to the analysis and design of engineering systems is the probability that a random motion X (t) will be kept within prescribed bounds during the system operating time, or the probability distribution of the time to first passage across specified barriers. Attention is restricted herein to stationary Gaussian processes with zero mean value and three barrier configurations are considered, as in Crandall, et al.[I]. 1 The first configuration involves a single barrier, X (t)= a, where a is a critical level not to be surpassed. In the second, the bounds consist of a pair of lines, X (t)= a and X (t)=—a, and the safe region is defined by| Xft)|< a. The third barrier, R (t)= a, which is defined in terms of the envelope R (t) of the random process X (t), is considered principally because it leads to useful approximations to the first-passage probability for single and double barriers. The envelope definition used is that of Cramer and Leadbetter [2] which is essentially equivalent to that of Rice [3]. The three barrier configurations are subsequently referred to as type-B, type-D, and type-£ barriers, respectively, and the excursions into the unsafe domain are called B-crossings, D-crossings and E-crossings, respectively [1].