Derivation of extreme non-Gaussian stochastic offshore structural responses using finite memory nonlinear system

Abstract

For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. A nonlinear wave analysis is recommended to represent a realistic ocean wave for an accurate prediction of extreme offshore structural response. Nevertheless, the contribution of nonlinearity especially due to the wave-wave interaction leads to a complex solution. In fact, the random wave load itself experienced a nonlinearity due to the drag component of Morison’s load, the effect of load intermittency around the member in the splash zone, and the presence of current; which result in a non-Gaussian offshore structural response. The most accurate and versatile method for predicting the statistical properties of extreme responses on a subjected load is the Monte Carlo time simulation method, which can account for all sorts of nonlinearities without introducing any approximations. However, it is computationally very demanding due to its complex procedure in simulating the structural response as reliable results require a very large number of simulations. Therefore, a simple method using finite-memory nonlinear system (FMNS) has been introduced by previous researchers and is proven to improve the efficiency of evaluating offshore structural responses without sacrificing its accuracy. The method is, however, only applicable based on the linear wave analysis. Hence, by taking advantage of the efficiency of FMNS method, a new model needs to be developed by integrating the FMNS method with a nonlinear wave analysis for a more reliable result. It is the derivation of non-Gaussian stochastic offshore structural response using finite-memory nonlinear system, known as FMNSNL (subscript NL indicates nonlinear). In the model development process, the surface elevation is generated first according to a nonlinear wave analysis with at least second-order wave. Then, two components of system are introduced, in which the first component enabled the transformation from a reference surface elevation to a second-order linearized quasi-static responses, while the second component involved the development of nonlinear function based on the relationship of second-order nonlinear and linearized quasi-static responses. Four models have been developed, in which the best model can produce an output of approximate values of second-order nonlinear quasi-static response that is very close to its corresponding values obtained using Monte Carlo time simulation method and will then be used for further examination. Based on the correlation coefficient between those two methods, the best relationship with value of 0.9783 was obtained by model 4 on the drag-induced quasi-static base shear for high significant wave height. The procedure of model development based on those two components is examined for all sea state conditions with Hs = 5, 10 and 15 m, and with the presence of current, U̅= 0 m/sec and ±0.90 m/sec. As a result, the relationship of model 4 fits the data better for all cases. It should be noted that this investigation of in-service analysis is carried out only for quasi-static structure by neglecting the dynamic effect. Based on the result of the short-term analysis, FMNSNL method provided a good accuracy of prediction of 100-year responses compared with the corresponding prediction using Monte Carlo time simulation method for all cases. A comparison has been made according to the ratio of prediction between FMNSNL and Monte Carlo time simulation methods. Overall, the accuracy level achieved by FMNSNL method is in the range of 82% to 99.8%, in which the accuracy level improved with the presence of positive current and vice versa with negative current. The same conclusion is valid for long-term analysis since the accuracy performance of FMNSNL followed exactly as previous analysis for short-term distribution. Without the presence of current along the wave propagation, the accuracy level of FMNSNL method is in the range of 80% to 96%. If there exist a current with the same direction of the wave (positive current), the accuracy improved with an increment of 1% to 7%. However, the opposite direction of current (negative current) provided a severe impact on its prediction with a reduction of 1% to 18% of accuracy. Hence, the method of FMNSNL can then be used with an excellent efficiency and accuracy to determine the extreme offshore structural response. With that, the offshore structure is towards optimization that leads to cost reduction and preservation of safety.