Transient Load Modeling: Clipped Normal Processes

Abstract

Clipped normal processes are considered from the point of view of modeling transient loads on structures. Sample curves of these types of processes are pulse like, each pulse corresponding to an exceedance Of the zero level by a Gaussian process. The pulses are the more narrow the larger negative is the mean of the Gaussian process. In contrast to current transient load models the pulses are of random shape. How to calculate bounds on the mean up‐crossing rate of any level by a sum of several clipped normal processes is demonstrated. For high levels these bounds are close. Thus, they may be used to obtain an accurate evaluation of a well‐known upper bound on the probability of the sum exceeding the level within a given time period. The particular example of the sum of several mutually independent, stationary clipped normal processes permits an exact calculation of the upcrossing rate of any constant level. The upcrossing problem is, in fact, solved by observing the equivalence of the problem with a Gaussian vector process outcrossing problem from a certain convex polyhedral region in the n‐dimensional space. Reliability theoretical methods for this case have been reported earlier. These methods also make it possible to calculate a lower bound on the exceedance probability giving an evaluation of the upper bound as an approximation to the exact probability.