基于KANN-DBSCAN带宽优化的核密度估计载荷谱外推

doi:10.19562/j.chinasae.qcgc.2024.11.016

Abstract

Abstract:

Considering the limitation of global fixed bandwidth of load extrapolation for kernel density estimation， a load extrapolation method based on K-Average Nearest Neighbor Density-Based Spatial Clustering of Applications with Noise （KANN-DBSCAN） kernel density estimation （KDE） is proposed. The load data is grouped and clustered using the KANN-DBSCAN clustering algorithm， and the Rule-of-thumb （ROT） method is used to obtain the optimal bandwidth between different clusters. Then the kernel density estimation is conducted， and finally extrapolation is carried out using Monte Carlo simulation. The extrapolation rationality is verified using the measured load data of a certain electric vehicle on user road as the application object. The extrapolation effect is assessed by the three indicators of statistical parameter quantity， goodness of fit， and pseudo-damage. The results show that compared with the traditional fixed bandwidth kernel density estimation extrapolation method， the extrapolation load obtained by the DBSCSN kernel density estimation extrapolation method is closer to the actual load in statistical parameters， and the error of the mean， standard deviation， and maximum value is only 1.9%， 4.3%， and 1.9%， respectively. The magnitude cumulative frequency curve fits R² are all greater than 0.99， and the pseudo-damage is close to 1. The results show the effectiveness of the clustering method in kernel density estimation load extrapolation， which is helpful for compiling the load spectrum of electric vehicles on customer service road， and can provide reference for the load extrapolation of mechanical parts with similar load distribution characteristics.

Key words: load extrapolation, clustering, kernel density estimation, rule-of-thumb, Monte-Carlo simulation

Jinbao Zhang,Yongle Yang,Zhifei Zhang,Liangfeng Peng,Weixiong Lin,Youyuan Zhang,Zhongming Xu. Extrapolation of Load Spectrum Based on KANN-DBSCAN Bandwidth Optimization Kernel Density Estimation[J].Automotive Engineering, 2024, 46(11): 2100-2109.

Figures/Tables 17

簇	1	2	3	4
$E p s$	53.965	110.629	226.040	3 543.289
$M i n P t s$	23	17	12	66

References 27

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簇	1	2	3	4
h_x /N	30.331	71.994	212.819	666.650
h_y /N	21.211	55.410	85.893	304.726

样本	均值/kN			标准差/kN			最大值/kN
样本	验证载荷	本文方法	固定带宽	验证载荷	本文方法	固定带宽	验证载荷	本文方法	固定带宽
样本1	1.262	1.282	1.342	0.690	0.694	0.742	8.776	8.642	7.709
样本2	1.546	1.576	1.669	0.844	0.818	0.875	10.349	10.320	9.764
样本3	1.188	1.203	1.264	0.653	0.641	0.668	8.334	8.180	7.041
样本4	1.540	1.546	1.629	0.813	0.778	0.855	10.200	10.391	9.752

样本	均值误差/%		标准差误差/%		最大值误差/%
样本	本文方法	固定带宽	本文方法	固定带宽	本文方法	固定带宽
样本1	1.4	3.7	0.1	3.5	1.5	12.2
样本2	1.9	7.9	3.1	3.7	0.3	5.7
样本3	1.3	6.4	2.7	5.2	1.8	15.5
样本4	0.3	5.8	4.3	5.1	1.9	4.4

样本	固定带宽	本文方法
1	0.987 0	0.999 2
2	0.984 5	0.997 6
3	0.979 1	0.999 0
4	0.992 3	0.999 1

样本序号	固定带宽	本文方法
1	1.117	1.021
2	1.127	1.030
3	1.122	1.013
4	1.123	1.031

Extrapolation of Load Spectrum Based on KANN-DBSCAN Bandwidth Optimization Kernel Density Estimation

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Figures/Tables 17

References 27

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外推倍数	固定带宽	本文方法
10	1.112	1.027
20	1.107	1.034
30	1.099	1.028
50	1.102	1.030
100	1.104	1.029

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