M. K. Abu Husain

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

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. Wave loading on slender members of bottom-supported jacket structures is frequently calculated by Morisons equation. Due to nonlinearity of the drag component of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of their extreme response probability distributions are not available. To this end, the conventional time 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. The ETS procedure is found to be many times more efficient than the CTS method.

Extreme structural response values from various methods of simulating wave kinematics

In offshore engineering, the main forces that are loaded onto ocean structures come from wind-generated random waves. The prediction of wave forces that are applied onto slender cylindrical members is usually based on the Morisons equation, in which the wave force at any section of a member is expressed directly in terms of wave kinematics. It is essential to be able to estimate sensible kinematics at all levels of a structure to determine accurate prediction of wave forces and corresponding responses of these structures in a random wave field. Linear random wave theory (LRWT) is the simplest and most often used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, water particle kinematics calculated from LRWT grossly overpredicts the kinematics above the mean water level (MWL). Methods have been introduced to overcome this problem of high kinematics above the MWL, which consists of using linear wave theory (such as Wheeler, vertical stretching, effective node elevation and effective water depth methods) to provide a more realistic representation of near-surface wave kinematics. This is promising as there is some evidence that the water particle kinematics from the Wheeler method are underestimated and that those from the vertical stretching method are somewhat exaggerated. In this paper, the comparisons of the probability distributions of extreme values from different methods of simulation wave kinematics are investigated by using conventional time simulation procedure.

Extreme response prediction for fixed offshore structures by Monte Carlo time simulation technique

For an offshore structure, wind, wave, current, tide, ice and gravitational forces are all important sources of loading which exhibit a high degree of statistical uncertainty. The capability to predict the probability distribution of the response extreme values during the service life of the structure is essential for safe and economical design of these structures. Many different techniques have been introduced for evaluation of statistical properties of response. In each case, sea-states are characterised by an appropriate water surface elevation spectrum, covering a wide range of frequencies. In reality, the most versatile and reliable technique for predicting the statistical properties of the response of an offshore structure to random wave loading is the time domain simulation technique. To this end, conventional time simulation (CTS) procedure or commonly called Monte Carlo time simulation method is the best known technique for predicting the short-term and long-term statistical properties of the response of an offshore structure to random wave loading due to its capability of accounting for various nonlinearities. However, this technique requires very long simulations in order to reduce the sampling variability to acceptable levels. In this paper, the effect of sampling variability of a Monte Carlo technique is investigated.

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

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. A more efficient method (ETS) was recently introduced which takes advantage of the correlation between the extreme values of surface elevation and their corresponding response extreme values. The method has proved to be very efficient for high-intensity sea states; however, the correlation and hence the efficiency and accuracy of the technique reduces for sea states of lower intensity. In this paper, a more efficient version of the ETS technique is introduced which takes advantage of the correlation between the extreme values of the nonlinear response and their corresponding linear response values.

Short-Term Distribution of the Extreme Values of Offshore Structural Response by Modified Finite-Memory Nonlinear System Modeling

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 of great value in the design of these structures. Due to nonlinearity of the drag component of Morison’s wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of the probability distribution of extreme responses are not available. However, it has recently been shown that the short-term response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system (FMNS). Previous investigation shows that the developed FMNS models perform better for high Hs values and their performance for low Hs value is not particularly good. In this paper, the modified version of FMNS models is referred to as MFMNS models is discussed. The improvement of MFMNS model is simply by dividing the structure into two zones (Zones 1 and 2) so that the horizontal distance between the nodes in each zone is relatively small compared to the wavelength. The modified version of MFMNS is used to determine the short-term probability distribution of the response extreme values with great efficiency.Copyright

Derivation of Morison's force coefficients by three alternative forms of the method of moments

Morisons equation is the most widely used method of predicting wave forces on slim cylindrical members of offshore structures. The equation assumes that the wave force is composed of two components: a drag force and an inertial force, where the drag component is due to water particle velocity and the inertial component is due to water particle acceleration. Morisons equation has two empirical coefficients, which are usually referred to as the drag and inertia coefficients. The values of these empirical coefficients are determined from laboratory and/or field experiments. In a typical wave load investigation, the wave force together with corresponding water particle velocity and acceleration are measured. The measured data is then analysed to calculate constant values for drag and inertia coefficients. One of the methods used in derivation of these coefficients is the (conventional) method of moments. However, the coefficients obtained from this method show considerable scatter due to large sampling variability. The purpose of this paper is to compare the sampling variability of drag and inertia coefficients from the conventional method of moments with those derived from two alternative forms of the method, i.e. methods of linear and low-order moments. Simulated data has been used to compare the efficiency of the three methods of moments. The results indicate that in most cases, the method of linear moments is superior to the other two methods. This is particularly true for drag-dominated forces.

Accurate estimation of the 100-year responses from the probability distribution of extreme surface elevations

Accurate estimation of the 100-year responses (derived from the long-term distribution of extreme responses) is required for the safe and economical design of offshore structures. However, due to nonlinearity of the drag component of Morison’s wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of the probability distribution of extreme responses are not available. To this end, conventional Monte Carlo time simulation technique could be used for predicting the long-term probability distribution of the extreme responses. However, this technique suffers from excessive sampling variability and hence a large number of simulated response records are required to reduce the sampling variability to acceptable levels. This paper takes advantage of the correlation between extreme responses and their corresponding extreme surface elevations to derive the values of the 100-year responses without the need for extensive simulations. It is demonstrated that the technique could be used for both quasi-static and dynamic responses.Copyright

Comparison of Extreme Offshore Structural Response from Two Alterna- tive Stretching Techniques

Linear random wave theory (LRWT) has successfully explained most properties of real sea waves with the ex- ception of some nonlinear effects for surface elevation and water particle kinematics. Due to its simplicity, it is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record; however, predicted water particle kinematics from LRWT suffer from unrealistically large high-frequency compo- nents in the vicinity of mean water level (MWL). To overcome this deficiency, a common industry practice for evaluation of wave kinematics in the free surface zone consists of using linear random wave theory in conjunction with empirical techniques (such as Wheeler and vertical stretching methods) to provide a more realistic representation of near-surface wave kinematics. It is well known that the predicted kinematics from these methods are different; however, no systematic study has been conducted to investigate the effect of this on the magnitude of extreme responses of an offshore structure. In this paper, probability distributions of extreme responses of an offshore structure from Wheeler and vertical stretching methods are compared. It is shown that the difference is significant; consequently, further research is required to deter- mine which method is more reliable.

Efficient Estimation of Offshore Structural Response Based on Threshold Upcrossing Rates

Reliable estimation of offshore structural response due to random wave loading is essential for ensuring safe and economical designs. However, the conventional Monte Carlo time simulation method requires the simulation of an extremely large number of response records in order to derive extreme response probability distributions with acceptably low sampling variability. The Efficient Threshold Upcrossing (ETU) method, presented in this paper, enables rapid calculation of these probability distributions by using information about threshold upcrossing rates in conjunction with an Efficient Time Simulation (ETS) technique. Extreme response probability distributions from this novel technique are compared with those from the conventional and the ETS methods using a simple structural model exposed to Morison wave loading. It is shown that the method allows a very efficient calculation of response statistics.

Comparison of Extreme Responses From Wheeler and Vertical Stretching Methods

Linear random wave theory (LRWT) is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, it is well known that LRWT leads to water particle kinematics with exaggerated high-frequency components in the vicinity of mean water level (MWL). To avoid this problem, empirical techniques such as Wheeler and vertical stretching methods are frequently used to provide a more realistic representation of the wave kinematics in the near surface zone. In this paper, the Monte Carlo time simulation technique is used to investigate the effect of these two different methods of simulating water particle kinematics on the probability distribution of extreme responses. It is shown that the difference could be significant leading to uncertainty as to which method should be used.