Journal of Jilin University(Engineering and Technology Edition) ›› 2022, Vol. 52 ›› Issue (4): 829-836.

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Linear identification method of hysteresis characteristic of composite leaf springs

Wei LI1(),Hai-sheng SONG1,Hao-yu LU1,Wen-ku SHI2,Qiang WANG1,Xiao-jun WANG3()   

  1. 1.School of Automotive Engineering,Shandong Jiaotong University,Jinan 250357,China
    2.State Key Laboratory of Automotive Simulation and Control,Jilin University,Changchun 130022,China
    3.School of Engineering and Machinery,Shandong Jiaotong University,Jinan 250357,China
  • Received:2022-02-04 Online:2022-04-01 Published:2022-04-20
  • Contact: Xiao-jun WANG E-mail:163.lw@163.com;lw-wxj@163.com

Abstract:

Aiming at the identification of hysteresis characteristic parameter of composite leaf springs, a linear algorithm was proposed based on the stochastic gradient decent method and the recursive formular was deduced. From the two dimensions of identification accuracy and calculation time, the linear identification method and the improved firefly algorithm in the existing work are compared and verified. On this basis, a momentum term is introduced to improve the linear identification method. The results show that the improved algorithm accelerates the convergence time and reduces the convergence error. Finally, the improved algorithm was applicated to identify the hysteresis characteristics of a certain composite leaf spring and good results were obtained. The results show that the linear algorithm, which can get results in 2.5 ms, is more suitable for hysteresis characteristic parameter identification of composite leaf springs than nonlinear algorithm and can be used in online parameter identification and digital twin simulation.

Key words: vehicle engineering, composite material, leaf springs, parameter identification, linear algorithm, online parameter identification

CLC Number: 

  • U467.3

Fig.1

Principle of parameter linear identification method"

Table 1

Comparison of results between linear method and MFA method"

方 法对比结果计算时间/s

w1

/(N·mm-1

RMSE17

/%

MFA17125.5540.70922.4014
本文方法128.7440.8510.003
比较标准131.0520-

Fig.2

Curve fitting results of hysteresis characteristics"

Fig.3

Performance error surfaces"

Table 2

Comparison of influence of momentum term on algorithm"

方 法对比结果计算时间/s

w1

/(N·mm-1

RMSE17

/%

无动量128.7440.8510.003
有动量131.1990.7620.0024
比较标准131.0520-

Fig.4

Error performance projection trajectory of wo1"

Fig.5

Error performance projection trajectory of wo2"

Fig.6

Error performance projection trajectory of wo3"

Fig.7

Comparison of fitting mean square error MSE with variation of wo1"

Fig.8

Comparison of fitting mean square error MSE with variation of wo2"

Fig.9

Comparison of fitting mean square error MSE with variation of wo3"

Fig.10

Composite leaf spring sample"

Fig.11

Test of composite leaf spring sample"

Fig.12

Test results of composite leaf spring"

Fig.13

Fitting results of composite leaf spring"

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