模糊逻辑控制在双曲型微分方程中的应用

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2025-08-27 DOI:10.1016/j.padiff.2025.101278

Ruchika Lochab , Luckshay Batra

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引用次数: 0

摘要

在计算流体动力学（CFD）中，选择合适的模糊逻辑控制系统来稳定双曲守恒律（hcl）仍然是一个悬而未决的问题，特别是对于冲击捕获方案。这项工作通过采用双重方法策略来解决这一差距：(i)系统回顾了50多项关于通量限制FLC方法的研究（2000-2025），以及（ii） Mamdani型和sugeno型FLC应用于hcl不连续溶液的比较基准。我们的研究结果表明，与基于Mamdani质心的方法相比，使用加权平均去模糊化，sugeno型系统在冲击主导下的均方误差降低了约20%。这种性能增益与自适应CFD实践相一致，这些实践优先考虑基于规则的、计算成本低廉的平滑。通过理论分析和实验验证相结合，加强了pde驱动建模中模糊控制的数学基础。

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Application of fuzzy logic controls on hyperbolic differential equations

The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modelling.

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