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Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

机译：基于粒子群算法的条件非线性最优摄动及其在可预测性问题中的应用

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In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1)?when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2)?when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.
机译：在可预测性问题研究中，条件非线性最优摄动（CNOP）描述了满足特定约束条件并在预测时引起最大预测误差的初始摄动。 CNOP已成功应用于估计最大可预测时间（LBMPT）的下限。通常，CNOP是根据基于伴随模型的梯度下降算法（称为ADJ-CNOP）来计算的。这项研究通过二维Ikeda模型，研究了非线性对ADJ-CNOP的影响以及使用ADJ-CNOP估计LBMPT时相应的精度问题。我们的结论是：（1）？当初始扰动大或预测时间长时，动力学模型在预测变量中的强非线性将导致ADJ-CNOP方法的失败;（2）何时？如果目标函数具有多个极值，则ADJ-CNOP产生局部CNOP的可能性很大，因此对LBMPT进行了错误的估计。此外，引入了一种粒子群优化（PSO）算法，以解决该问题。使用PSO计算CNOP的方法称为PSO-CNOP。数值实验结果表明，即使初始扰动较大且预测时间较长，或者目标函数具有多个极值时，PSO-CNOP始终可以获得全局CNOP。由于PSO算法是一种基于总体的启发式搜索算法，因此可以克服非线性的影响以及目标函数多个极端的干扰。另外，为了检查由PSO-CNOP和ADJ-CNOP提出的LBMPT的估计精度，我们将初始摄动的约束域划分为足够精细的网格，并以通过滤波方法获得的LBMPT作为基准。结果表明，随着预报时间的增加，PSO-CNOP提出的估计比ADJ-CNOP提出的估计更接近真实值。

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