An Efficient Monte Carlo Simulation Technique for Derivation of the Probability Distribution of the Extreme Values of Offshore Structural Response

Abstract

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. To this end, the conventional simulation technique (CTS) is frequently used for predicting the probability distribution of the extreme values of response. However, this technique suffers from excessive sampling variability and hence a large number of simulated response extreme values (hundreds of simulated response records) are required to reduce the sampling variability to acceptable levels. In this paper, a more efficient version of the time simulation technique (ETS) is introduced to derive the probability distribution of response extreme values from a much smaller sample of simulated extreme values.

Short-term probability distribution of the extreme values of offshore structural response by an efficient time simulation technique

“…The probability distribution of response extreme values for each group is then calculated individually based on a relatively small number of simulations, and then the total probability theorem is used to derive the probability distribution of response extreme values. In a recently published paper (Abu Husain and Najafian 2010;Abu Husain et al 2013), the ETS procedure was validated against results from the CTS procedure by comparing the probability distribution of extreme values of base shear and overturning moment from the two methods. The ETS procedure was found to be many times more efficient than the CTS method.…”

Comparison of Various Spectral Models for the Prediction of the 100-Year Design Wave Height

“…According to Mihram [4], a discussion of the elements of queues reveals an exemplary class of complex systems whose simulation often is best accomplished by the application of the Monte Carlo method and then Jensen [5] studied the predictions of extreme value on increasing load spectrum by using Monte Carlo approach. Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making [6]. Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values that come up with a probability distribution which is any factor that has inherent uncertainty.…”

Derivation of the Probability Distribution of Extreme Values of Offshore Structural Response by Efficient Time Simulation Method

“…It is therefore expected that the ETS procedure based on linear response extreme values will perform better than the ETS method based on the surface elevation extreme values. The ETS method based on surface elevation extreme values has already been described in [10]. The version based on linear response extreme values is now explained.…”

“…In terms of the number of simulated records for the ETS procedure, two cases have been considered as defined in Table 6 The probability distributions of the extreme values of nonlinear quasi-static response for Case 1 (based on a total number of 220 simulations, refer to Table 6) and for three different sea states (H s = 15m, 10m, 5m) are shown in Figs. (8)(9)(10), respectively. As observed, in all cases, the linear response version of the ETS procedure is in better agreement with corresponding distributions from the CTS procedure (CTS based on 20000 simulations).…”

“…By considering an exponential model for the mean upcrossing rate of high response values, Naess et al [1] have succeeded in reducing the required number of simulated response records without sacrificing the accuracy of the predicted probability distribution of response extreme values. Another efficient version of the time simulation (ETS) technique has recently been introduced which takes advantage of the correlation between surface elevation and their corresponding response extreme values [10]. The method has proved to be very efficient for high-intensity sea states; however, its efficiency and accuracy reduces for sea states of lower intensity.…”