多向不规则波浪模拟的降维方法

基于多向不规则波的3种传统Monte Carlo模拟方法，提出了相应的时空随机场源谱表达，通过引入随机函数的降维思想，推导了3种多向不规则波模拟的降维方法，实现了仅用2个～4个基本随机变量即可精确表达多向不规则波随机场。数值算例表明，采用三种降维方法模拟所得代表性样本集的有效波高均符合规范要求。同时，代表性样本集的二阶统计量(模拟值)与目标值拟合一致，且总体上比传统Monte Carlo方法精度更高，验证了降维方法的有效性。此外，通过对比分析三种降维方法的模拟精度和效率，建议了最适用于工程应用的多向不规则波模拟方法，这为结合概率密度演化理论进行海洋工程结构在随机海浪作用下的动力可靠度精细化分析提供了有效途径。

DIMENSION-REDUCTION METHOD FOR MUTIDIRECTIONAL IRREGULAR WAVE SIMULATION

Based on three kinds of conventional Monte Carlo simulation methods for multidirectional irregular waves, the corresponding original spectral representations of a spatio-temporal random field are proposed. Then three dimension-reduction methods for simulating multidirectional irregular waves are derived by introducing the dimension-reduction idea of a random function. As a result, the random field of multidirectional irregular waves is accurately represented by employing merely 2-4 elementary random variables. Numerical examples show that the effective wave heights of the representative samples simulated by the three dimension-reduction methods can satisfy the normative requirements. Meanwhile, the second-order statistics (simulated values) of the representative sample set fit well with the target values. In general, the accuracy of the proposed method is higher than that of the conventional Monte Carlo scheme, which verifies the validity of the former. In addition, by analyzing the simulation accuracy and efficiency of the three dimension-reduction methods, the most suitable scheme of multidirectional irregular waves for engineering application is proposed. This provides an effective way, combining the probability density evolution theory, for the refined dynamic analysis of offshore engineering structures subjected to random waves.