基于稀疏混沌多项式法的电动汽车无线电能传输效率不确定性量化

doi:10.13229/j.cnki.jdxbgxb.20230137

摘要/Abstract

摘要：

提出采用子空间追踪稀疏混沌多项式法（SP-PCE）实现EV-WPT系统传输效率的不确定性量化。首先，通过建立EV-WPT系统三维电磁学仿真模型，并合理设置相关变量的分布类型，利用SP-PCE法计算得到表征EV-WPT系统传输效率不确定性的均值、方差和概率密度曲线等统计特征参数；然后，结合SP-PCE法和Sobol法进行全局灵敏度分析，获得随机输入变量对系统传输效率影响程度的量化指标。最后，通过数值仿真实验验证了本文方法的准确性和高效性，为保证EV-WPT系统高传输效率及系统结构优化提供理论依据。

关键词: 车辆工程, 无线电能传输, 磁耦合, 不确定性量化, 稀疏混沌多项式展开法, 全局灵敏度分析

Abstract:

The subspace pursuit-polynomial chaos expansion method （SP-PCE） was proposed for the uncertainty quantification of EV-WPT system's transfer efficiency. Firstly，by establishing the three-dimensional electromagnetic simulation model of EV-WPT system and reasonably setting the distribution type of relevant variables， the statistical characteristic parameters such as mean， variance and probability density curve that can characterize the uncertainty of EV-WPT system's transfer efficiency were calculated by SP-PCE method. Then， combining the SP-PCE method and Sobol method to carry out the global sensitivity analysis to obtain the influence degree's quantitative index of random input variables on system's transfer efficiency. Finally， the accuracy and efficiency of the proposed method were verified by numerical simulation experiments， which provides a theoretical basis for ensuring the high transfer efficiency of EV-WPT system as well as system's structure optimization.

Key words: vehicle engineering, wireless power transfer, magnetic coupling, uncertainty quantification, sparse polynomial chaos expansion method, global sensitivity analysis

中图分类号:

U469.72

王天皓,李博,于全毅,徐琳琳,贾国强,关珊珊. 基于稀疏混沌多项式法的电动汽车无线电能传输效率不确定性量化[J]. 吉林大学学报(工学版), 2024, 54(12): 3433-3442.

Tian-hao WANG,Bo LI,Quan-yi YU,Lin-lin XU,Guo-qiang JIA,Shan-shan GUAN. Uncertainty quantification of electric vehicle's wireless power transfer efficiency based on sparse polynomial chaos expansion method[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(12): 3433-3442.

图/表 10

图1

图2

表1

常见分布类型对应的正交多项式"

分布类型	变量范围	概率密度函数	正交多项式	权函数
均匀分布	$[- 1, + 1]$	1/2	Legendre $P n (x)$	1
正态分布	$[- ∞, + ∞]$	$1 / 2 π e - x 2 / 2$	Hermite $H n (x)$	$e - x 2 / 2$
指数分布	$[- 0, + ∞]$	$e - x$	Laguerre $L n (x)$	$e - x$
Gamma分布	$[- 0, + ∞]$	$x α e - x / Γ (α + 1)$	广义 Laguerre $L n (α, β) (x)$	$x α e - x$

表1

表2

图3

图4

图5

表3

MC法和不同截断阶数下的SP-PCE法、OLS-PCE法所需的样本点和计算得到的相关参数结果"

不同方法和截断阶数	传输效率均值/%	传输效率方差	计算时间/s	样本点	$ε L O O$
3阶OLS-PCE	84.01	2.69e-3	25 203.88	440	0.012 7
3阶SP-PCE	84.07	2.75e-3	15 133.32	293	0.011 9
4阶OLS-PCE	84.06	2.72e-3	90 662.89	1 430	0.007 9
4阶SP-PCE	84.06	2.70e-3	45 262.83	715	0.007 7
5阶OLS-PCE	84.08	2.75e-3	253 857.11	4 004	0.007 2
5阶SP-PCE	83.98	2.66e-3	100 972.74	1 601	0.007 4
MC	83.94	2.70e-3	651 235.04	10 000	—

表3

图6

图7

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变量	分布类型	分布参数
d₀/m	均匀分布	（-0.05， 0.05）
z₀/m	均匀分布	（-0.15， 0.15）
x₀/m	均匀分布	（-0.15， 0.15）
s₀/m²	正态分布	（3e-6， 1e-7）
s₁/m²	正态分布	（3e-6， 1e-7）
C₁/nF	正态分布	（120， 4）
C₂/nF	正态分布	（130， 4.3）
R₁₁/Ω	正态分布	（0.2， 3.3e-3）
R₂₂/Ω	正态分布	（10， 0.17）