Several convex hull manipulation methods have been proposed for tensor product (TP) model transformation, such as CNO, INO, IRNO, minimum volume simplex, and optimized CNO. Among the five convex hull manipulation methods, CNO, INO, and IRNO are the most often used convex hull manipulation methods; minimum volume simplex is an analysis method to shrink the tightness value of the TP model transformation, and optimized CNO convex hull manipulation method is used for convex hull rectification; it also uses core tensor unfolding and folding to obtain tight convex hull. However, all these convex hull manipulation methods are designed based on classical sampling method, while the local extrema are often omitted by the classical sampling method. To obtain a more precise sampling model, in this paper, most of the existing convex hull manipulation methods are extended with local extrema refinement strategy; a uniform local extrema refinement-based convex hull manipulation framework is proposed for the existing convex hull manipulation methods. A single gantry system is used for simulation demonstration; results show that local extrema refinement strategy is needed in convex hull manipulation of TP model transformation; it might be a preferable way to enhance classical sampling method. Minimum volume simplex is more suitable than the optimized CNO in convex hull manipulation of TP model transformation with respect to computational efficiency.

中文翻译：

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具有问题无关采样方法的基于局部极值细化的张量积模型变换控制器

已经提出了几种用于张量积 (TP) 模型转换的凸包操作方法，例如 CNO、INO、IRNO、最小体积单纯形和优化的 CNO。在五种凸包操作方法中，CNO、INO和IRNO是最常用的凸包操作方法；最小体积单纯形是收缩TP模型变换紧密度值的一种分析方法，优化的CNO凸包操作方法用于凸包校正；它还使用核心张量展开和折叠来获得紧凸包。然而，所有这些凸包操作方法都是基于经典采样方法设计的，而经典采样方法往往会忽略局部极值。为了获得更精确的采样模型，在本文中，大多数现有的凸包操作方法都扩展了局部极值细化策略；针对现有的凸包操作方法，提出了一种基于统一局部极值细化的凸包操作框架。采用单台架系统进行仿真演示；结果表明，TP模型变换的凸包操作需要局部极值细化策略；这可能是增强经典采样方法的更好方法。就计算效率而言，最小体积单纯形比优化的 CNO 更适合于 TP 模型变换的凸包操作。采用单台架系统进行仿真演示；结果表明，TP模型变换的凸包操作需要局部极值细化策略；这可能是增强经典采样方法的更好方法。就计算效率而言，最小体积单纯形比优化的 CNO 更适合于 TP 模型变换的凸包操作。采用单台架系统进行仿真演示；结果表明，TP模型变换的凸包操作需要局部极值细化策略；这可能是增强经典采样方法的更好方法。就计算效率而言，最小体积单纯形比优化的 CNO 更适合于 TP 模型变换的凸包操作。