B-splines chaos and Kalman Filters for solving a stochastic differential equation

IF 3.5 3区 工程技术 Q2 ENGINEERING, MECHANICAL
Luis Sánchez , Andrew J. Simpkin , Norma Bargary
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引用次数: 0

Abstract

A methodology is proposed to solve stochastic differential equations (SDEs) using B-spline chaos and Kalman Filters. The Fokker–Planck equation is employed to model physical processes involving nonlinear structures, non-Gaussian distributions, and multimodal distributions. B-spline chaos is used to approximate the solution of the SDE, while state estimation is achieved using Ensemble and Unscented Kalman Filter algorithms. To validate the approach, a time series of temperature and humidity data collected from manufacturing sensors is used, demonstrating the accuracy of the methodology in reconstructing the true system states. The proposed method is specifically designed for solving SDEs related to known physical processes. Additionally, numerical comparisons with existing approaches are presented to highlight the advantages in terms of performance and accuracy.
解随机微分方程的b样条混沌和卡尔曼滤波
提出了一种利用b样条混沌和卡尔曼滤波器求解随机微分方程的方法。采用Fokker-Planck方程来模拟涉及非线性结构、非高斯分布和多模态分布的物理过程。利用b样条混沌来逼近SDE的解,同时使用Ensemble和Unscented卡尔曼滤波算法实现状态估计。为了验证该方法,使用了从制造传感器收集的温度和湿度数据的时间序列,证明了该方法在重建真实系统状态方面的准确性。所提出的方法是专门为求解与已知物理过程相关的SDEs而设计的。此外,还与现有方法进行了数值比较,以突出在性能和精度方面的优势。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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