利用复分数矩处理最大熵原理

IF 2.1 3区工程技术 Q3 MECHANICS

Meccanica Pub Date : 2025-03-01 DOI:10.1007/s11012-025-01949-9

Lizhi Niu, Mario Di Paola, Antonina Pirrotta, Wei Xu

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引用次数: 0

摘要

提出了一种受复分数阶矩约束的最大熵原理方法，该方法可用于具有少量复分数阶矩的近似概率分布方程的重构。通过在熵泛函中引入具有不同虚参的复分数阶矩，构造了具有未知拉格朗日乘子的扩展熵泛函，并利用该扩展熵泛函导出了近似的概率密度函数。将该方法推广到基于由Fokker-Planck-Kolmogorov方程导出的复分数阶矩方程的随机动力系统的概率密度函数。数值仿真验证了该方法的有效性。

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Maximum entropy principle handled by using complex fractional moments

A novel Maximum Entropy Principle method constrained by Complex Fractional Moments is proposed in this paper, which can be applied for reconstructing of approximate probability distribution equations with few complex fractional moments. By introducing complex fractional moments with different imaginary parameters into the entropy functional, an extended entropy functional with unknown Lagrange multipliers is constructed, which is utilized for deriving the approximate probability density function. The new method is extended to obtaining probability density function in stochastic dynamic systems based on the complex fractional moment equations which is derived from Fokker–Planck-Kolmogorov equation. Numerical simulations verified the effectiveness of the approach.

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来源期刊

Meccanica 物理-力学

CiteScore

4.70

自引率

3.70%

发文量

151

审稿时长

7 months

期刊介绍： Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.