基于局部自适应带宽扩散核密度估计的载荷外推

doi:10.13229/j.cnki.jdxbgxb.20231198

摘要/Abstract

摘要：

为实现由有限载荷数据外推得到全周期载荷谱，针对传统自适应带宽优化算法在参数选择上存在局限性，本文提出一种基于局部自适应带宽扩散核密度估计的载荷外推方法。该方法首先将二维雨流矩阵降维至一维等效幅值，然后基于局部积分均方误差优化局部带宽，利用局部最优带宽，通过扩散核密度估计构建概率密度分布模型，最后结合蒙特卡洛模拟方法外推目标频次载荷。对某特种车辆综合传动装置的预处理载荷数据进行对比验证，结果表明：与传统方法相比，本文所提方法得到的概率密度分布曲线和累计频次曲线更接近实际等效幅值，相关系数与决定系数均更趋近于1，其中相关系数分别为0.983 8与0.999 6，决定系数分别为0.967 9与0.999 1；均方根误差也更小，分别为5.05×10^－5与15.9。

关键词: 机械工程, 特种车辆, 综合传动装置, 载荷谱, 载荷外推, 局部自适应带宽, 扩散核密度估计

Abstract:

To achieve the extrapolation of the full-cycle load spectrum from limited load data， this paper proposes a load extrapolation method based on local adaptive bandwidth diffusion kernel density estimation， in view of the limitations of traditional adaptive bandwidth optimization algorithms in parameter selection. This method first reduces the two-dimensional rainflow matrix to one-dimensional equivalent amplitude， then optimizes the local bandwidth based on the local integral mean square error， and uses the local optimal bandwidth to construct a probability density distribution model through diffusion kernel density estimation. Finally， the target frequency load is extrapolated by combining the Monte Carlo simulation method. The preprocessed load data of a certain special vehicle's comprehensive transmission device are compared and verified. The results show that compared with the traditional method， the probability density distribution curve and cumulative frequency curve obtained by the method proposed in this paper are closer to the actual equivalent amplitude. The correlation coefficients and determination coefficients are both closer to 1， with the correlation coefficients being 0.983 8 and 0.999 6 respectively， and the determination coefficients being 0.967 9 and 0.999 1 respectively. The root mean square errors are also smaller， being 5.05×10^-5 and 15.9 respectively.

Key words: mechanical engineering, special vehicle, integrated transmission device, load spectrum, load extrapolation, local adaptive bandwidth, diffusion kernel density estimation

中图分类号:

U463.22+1

王立勇,郑存金,张金乐,李乐. 基于局部自适应带宽扩散核密度估计的载荷外推[J]. 吉林大学学报(工学版), 2025, 55(8): 2511-2519.

Li-yong WANG,Cun-jin ZHENG,Jin-le ZHANG,Le LI. Load extrapolation based on local adaptive bandwidth diffusion kernel density estimation[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(8): 2511-2519.

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参数	符号
发动机转速/（r·min^－1）	S_e
转向高压/mV	U_h
主轴转速/（r·min^－1）	S_s
油门开度/%	T_p
变速箱档位	G
汇流排输出转速/（r·min^－1）	S_o
汇流排输出转矩/（N·m）	T_o

外推方法	相关系数R	决定系数R²	RMSE
DKDE-FB-EXP	0.908 6	0.825 6	1.09×10^－4
DKDE-FB-ISJ	0.970 0	0.940 9	7.12×10^－5
DKDE-AB-EXP	0.908 6	0.825 6	1.09×10^－4
DKDE-AB-ISJ	0.970 0	0.940 9	7.12×10^－5
KDE-LAB	0.974 2	0.949 0	6.04×10^－5
本文	0.983 8	0.967 9	5.05×10^－5

外推方法	相关系数R	决定系数R²	RMSE
DKDE-FB-EXP	0.993 7	0.987 4	71.3
DKDE-FB-ISJ	0.998 8	0.997 6	27.8
DKDE-AB-EXP	0.992 7	0.985 4	71.9
DKDE-AB-ISJ	0.998 7	0.997 4	26.6
KDE-LAB	0.998 4	0.996 8	41.5
本文	0.999 6	0.999 1	15.9