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Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (3): 622-634    DOI: 10.3785/j.issn.1008-973X.2024.03.019
    
Variable weight PSO-Elman neural network based roadadhesion coefficient estimation
Juncheng WANG(),Fahui WANG
1. School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China
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Abstract  

The variable weight particle swarm optimization (PSO)-Elman neural network was proposed for road adhesion coefficient estimation, in order to address the issue that the unstable weight update of traditional neural network leads to the poor accuracy in the estimation of road adhesion coefficient. The neural network model was constructed on the basis of a seven degrees-of-freedom vehicle dynamic model. The particle swarm algorithm was applied in the Elman neural network model to reduce the training absolute error. The linear decreasing weight strategy was used to change the weight of the particle swarm algorithm, which was useful for balancing the particle’s global and local search ability. Thus, the optimization of network weight arrays were realized. Then, the correlation curve of optimal slip ratio and rood adhesion coefficient was fitted by the Fourier approximation method. Theoretical analysis and simulation verification proved that this method can improve the estimation accuracy of road adhesion coefficient. Simulation results showed that, under both fixed and unfixed adhesion coefficient roads, the root-mean-square error of the road adhesion coefficient obtained by the proposed variable weight PSO-Elman neural network estimation method was reduced by 35.62% and 19.20% on average compared with that of the traditional Elman neural network. Furthermore, the anti-lock control effect was also effectively improved.



Key wordsvehicle state      road adhesion coefficient      neural network      particle swarm      anti-lock control     
Received: 21 June 2023      Published: 05 March 2024
CLC:  U 461.3  
Fund:  国家自然科学基金资助项目(52205135).
Cite this article:

Juncheng WANG,Fahui WANG. Variable weight PSO-Elman neural network based roadadhesion coefficient estimation. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 622-634.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.03.019     OR     https://www.zjujournals.com/eng/Y2024/V58/I3/622


基于变权重PSO-Elman神经网络的路面附着系数估计

针对传统神经网络权值更新不稳定导致路面附着系数预估精度不高的问题,提出基于变权重粒子群优化(PSO)-Elman神经网络的路面附着系数估计方法. 搭建基于7自由度汽车动力学模型的神经网络模型,在Elman神经网络模型中引入粒子群算法降低训练绝对误差,并使用线性权重递减策略对粒子群算法中的权重进行改变,平衡粒子全局和局部搜索能力,实现网络权值矩阵优化;采用傅里叶函数方法拟合出理想滑移率-路面附着系数相关曲线;通过理论分析和仿真验证,证明采用该方法能够提升路面附着系数预估精度. 仿真结果表明:在定附和变附路面行驶工况下,相比于传统Elman神经网络,采用变权重PSO-Elman神经网络的路面附着系数估计方法获得的路面附着系数均方根误差分别平均降低了35.62%和19.20%,有效提升了防抱死控制效果.


关键词: 车辆状态,  路面附着系数,  神经网络,  粒子群,  防抱死控制 
Fig.1 Modeling of vehicle longitudinal dynamics and single wheel
参数数值参数数值
m/kg1 825tf/m1.535
hg/m0.48tr/m1.531
Iz/(kg·m2)1 600$ {R_{{\text{ω }}}} $/m0.29
la/m1.26lb/m1.38
CD0.3A/m22
Cσ/N68 900Cα/(N·rad?162 900
Tab.1 Vehicle motion state parameters
Fig.2 Topology architecture of Elman neural network
Fig.3 Optimization flow chart of variable weight PSO weight arrays
Fig.4 Estimation unit of ideal slip rate
路面c1c2c3λpμa
覆冰0.05306.390.010.020.05
覆雪0.2094.100.050.060.19
潮湿鹅卵石0.4033.720.100.140.39
重潮湿沥青0.6333.770.200.110.60
典型潮湿沥青0.8533.800.350.130.80
轻潮湿沥青1.0329.490.440.140.95
干水泥1.2025.170.540.161.09
干沥青1.2823.990.520.171.17
Tab.2 Parameter values of typical road
Fig.5 Friction coefficient curve of typical tire-road
Fig.6 Fitted curve of road adhesion coefficient and slip rate
n$ {E_{{\text{rmse\_}}\mu }} $n$ {E_{{\text{rmse\_}}\mu }} $
40.010990.0112
50.0087100.0100
60.0118110.5401
70.0090120.0249
80.0086130.0090
Tab.3 Trial calculation results of number of neurons in hidden layer or undertaking layer
工况λpμa
10.04970.0239
20.19630.0630
30.38250.1454
40.79400.1304
Tab.4 Representative road parameters
Fig.7 Curve of value of road adhesion coefficient over time under four types of road conditions
工况Ermse-μp/%工况Ermse-μp/%
传统变权重传统变权重
10.038 3020.023 791?37.8930.131 3800.091 050?30.70
20.071 7640.037 732?47.4240.356 0600.261 800?26.47
Tab.5 Estimated root mean square error statistics of road adhesion coefficient
Fig.8 Curve of wheel slip rate changing over time under four types of road conditions
工况前轮后轮
Emse_λq/%Emse_λq/%
传统变权重传统变权重
10.227 80.212 6?6.660.227 70.212 6?6.64
20.103 10.095 5?7.410.103 20.095 7?7.32
30.067 30.064 2?4.830.069 00.064 7?6.63
40.002 80.002 7?3.500.004 00.003 2?20.74
Tab.6 Mean square error statistics of wheel slip rate
Fig.9 Curve of value of road adhesion coefficient over time under condition 5
Fig.10 Curve of wheel slip rate changing over time under condition 5
Fig.11 Curve of predicted value of road adhesion coefficient over time under fixed-adhesion and changing-adhesion coefficient conditions
估计方法Ermse_μp1/%p2/%p3/%
传统ElmanPSO-Elman变权重PSO-Elman
定附着路面0.016 0800.010 9140.007 576?32.13?52.89?30.59
变附着路面0.030 2810.019 1560.017 237?36.70?43.08?10.02
Tab.7 Root-mean-square error statistics of road adhesion coefficient in fixed and changing adhesion conditions
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