一种基于伪Wigner-Ville分析的动态优化问题网格重构策略

为了解决控制向量参数化方法逼近精度和计算时间之间的矛盾,提出了一种基于伪Wigner-Ville时频分析的控制向量参数化方法。该方法首先给定较少的网格进行第一次优化迭代,快速获得控制变量的大致轨迹。然后通过伪Wigner-Ville分析得出不同时间网格节点瞬时频率变化对性能指标的影响,籍此对原有网格节点进行重构,包括对时间节点的消除、细化。并且结合变时间节点控制向量参数化方法的思想,将瞬时频率为极大值时对应的时间节点作为待优化参数,与控制变量一同进行求解优化,从而找到准确的最优时间切换点。三个经典的化工反应实例用于验证所提方法,计算结果表明：与传统的控制向量参数化方法和文献结果相比,所提方法可以更有效地重构时间网格,找到准确的时间切换点,不仅计算成本低,而且计算精度更出色。

A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem

In order to solve the contradiction between approximation accuracy and computation time of control vector parameterization (CVP) method, a control vector parameterization method based on pseudo Wigner-Ville time-frequency analysis is proposed. The method first gives a small number of meshes for the first optimization iteration, and quickly obtains the approximate trajectory of the control variables. Then, through the pseudo Wigner-Ville analysis, the influence of the instantaneous frequency change of the mesh nodes on the performance index is obtained, and the original mesh nodes are reconstructed based on above analysis, including the elimination and refinement of the time nodes. And then combined with the variable time node CVP method, the corresponding time nodes with the maximum instantaneous frequency are used as parameters, which are optimized together with the control variables to find accurate time switching points. Three classical chemical reaction examples are used to verify the proposed method. The calculation results show that compared with the traditional CVP method and literature results, the proposed method can reconstruct the time grid more effectively and find more accurate time switching points, leading to lower calculation cost and more accurate solution.