Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (8): 2511-2519.doi: 10.13229/j.cnki.jdxbgxb.20231198

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Load extrapolation based on local adaptive bandwidth diffusion kernel density estimation

Li-yong WANG1(),Cun-jin ZHENG1,Jin-le ZHANG2,Le LI1   

  1. 1.Key Laboratory of Modern Measurement & Control Technology，Ministry of Education，Beijing Information Science & Technology University，Beijing 100192，China
    2.China North Vehicle Research Institute，Beijing 100072，China
  • Received:2023-11-05 Online:2025-08-01 Published:2025-11-14

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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

CLC Number: 

  • U463.22+1

Fig.1

Load extrapolation process based on local adaptive bandwidth diffusion kernel density estimation"

Fig.2

Schematic diagram of torque sensor placement position"

Table 1

Main parameters"

参 数符号
发动机转速/（r·min－1）Se
转向高压/mVUh
主轴转速/（r·min－1）Ss
油门开度/%Tp
变速箱档位G
汇流排输出转速/（r·min－1）So
汇流排输出转矩/（N·m）To

Fig.3

Preprocessed output torque data of the busbar"

Fig.4

Rain flow matrix for the composite operating condition"

Fig.5

Density distribution of equivalent amplitude and different load extrapolation methods"

Table 2

The fitting result of the equivalent amplitude distribution"

外推方法相关系数R决定系数R2RMSE
DKDE-FB-EXP0.908 60.825 61.09×10－4
DKDE-FB-ISJ0.970 00.940 97.12×10－5
DKDE-AB-EXP0.908 60.825 61.09×10－4
DKDE-AB-ISJ0.970 00.940 97.12×10－5
KDE-LAB0.974 20.949 06.04×10－5
本文0.983 80.967 95.05×10－5

Fig.6

Cumulative frequency curve of equivalent amplitude and different load extrapolation methods"

Table 3

Fitting effect of cumulative frequency curve for equivalent amplitude"

外推方法相关系数R决定系数R2RMSE
DKDE-FB-EXP0.993 70.987 471.3
DKDE-FB-ISJ0.998 80.997 627.8
DKDE-AB-EXP0.992 70.985 471.9
DKDE-AB-ISJ0.998 70.997 426.6
KDE-LAB0.998 40.996 841.5
本文0.999 60.999 115.9
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