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浙江大学学报(工学版)  2026, Vol. 60 Issue (5): 1047-1058    DOI: 10.3785/j.issn.1008-973X.2026.05.014
机械工程     
磁流变减振器力学模型的模糊综合评价方法
王骏骋(),章世伟
浙江理工大学 机械工程学院,浙江 杭州 310018
Fuzzy comprehensive evaluation method for mechanical model of magnetorheological damper
Juncheng WANG(),Shiwei ZHANG
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China
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摘要:

提出用于磁流变减振器力学模型的新评价方法,构建包含统计学参数、模型滞回曲线形状和模型运行效率的三维评价指标体系,配套选取7项二级评价指标,以突破单维度评价局限. 为了解决传统主观赋权法局限,采用融合熵权法与变异系数法的组合赋权策略,通过线性加权融合实现二级评价指标综合权重分配;基于模糊综合评价理论构建多级评判矩阵,结合层次分析法确定一级评价指标权重系数,通过加权计算得到模型综合评价值. 基于磁流变减振器动态特性试验,对Bingham与魔术公式模型开展参数拟合与性能评价分析. 结果表明:所提评价方法在统计学参数、模型滞回曲线形状和模型运行效率上实现了量化解耦评估.

关键词: 磁流变减振器力学模型模型保真度模型业务价值模型软件驱动质量模糊综合评价    
Abstract:

A new evaluation method for the mechanical models of magnetorheological damper was proposed. A three-dimensional evaluation index system was established, incorporating statistical parameters, hysteresis curve shape, and model computational efficiency. Seven secondary evaluation indexes were selected to overcome the limitations of single-dimensional assessment. To address the constraints of traditional subjective weighting methods, a combined weighting strategy integrating the entropy weight method and the coefficient of variation method was adopted. The comprehensive weights of secondary evaluation indexes were determined through linear weighting integration. A multi-level evaluation matrix was constructed based on fuzzy comprehensive evaluation theory, while the analytic hierarchy process was applied to determine the weight coefficients of first-level evaluation indexes. The overall evaluation value of the model was subsequently calculated via weighted synthesis. Based on dynamic characteristic tests of magnetorheological dampers, parameter fitting and performance evaluation were conducted for both the Bingham and magic formula models. Results demonstrate that the proposed method enables quantitative decoupled assessment across statistical parameters, hysteresis curve shape, and computational efficiency.

Key words: magnetorheological damper    mechanical model    model fidelity    model business value    model software-driven quality    fuzzy comprehensive evaluation
收稿日期: 2025-06-06 出版日期: 2026-05-06
CLC:  TP 393  
基金资助: 国家自然科学基金资助项目(52205135).
作者简介: 王骏骋(1990—),男,副教授,硕导,从事新能源汽车底盘系统动力学、自动驾驶决策控制研究. orcid.org/0000-0003-0539-0063. E-mail:wangjc90@163.com
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引用本文:

王骏骋,章世伟. 磁流变减振器力学模型的模糊综合评价方法[J]. 浙江大学学报(工学版), 2026, 60(5): 1047-1058.

Juncheng WANG,Shiwei ZHANG. Fuzzy comprehensive evaluation method for mechanical model of magnetorheological damper. Journal of ZheJiang University (Engineering Science), 2026, 60(5): 1047-1058.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.05.014        https://www.zjujournals.com/eng/CN/Y2026/V60/I5/1047

图 1  磁流变减振器内部结构
图 2  磁流变减振器力学模型的力-位移图
图 3  台架试验设备
图 4  台架试验得到的磁流变减振器参数特性曲线
图 5  Bingham模型拟合的磁流变减振器参数特性曲线
fl/HzIC/Au11u12fl/HzIC/Au11u12
10140.82730.965330177.26040.9842
0.5176.60490.95950.5190.78800.9831
1.0212.79560.97001.0289.99710.9741
1.5262.27930.97161.5346.59830.9733
2.0313.02420.97152.0431.43270.9695
2.5364.62290.97032.5436.41880.9754
3.0378.53980.97313.0527.62790.9679
20170.33270.9755100112.90170.9942
0.5182.28070.97640.5134.70940.9932
1.0282.40860.96691.0210.90370.9888
1.5337.39370.96841.5291.77600.9845
2.0387.54260.96922.0374.06230.9811
2.5478.70020.96342.5509.83530.9726
3.0534.88620.96043.0677.55010.9595
表 1  Bingham模型保真度结果
fl/HzIC/Au21/%u22/%u23/%
100.01491.08033.7329
0.50.01211.15184.2791
1.00.01360.56213.4933
1.50.01350.19184.9035
2.00.01760.08955.4025
2.50.02160.99655.8992
3.00.02420.15456.5548
200.14270.51543.6284
0.50.10600.09553.5557
1.00.26190.14094.6963
1.50.21790.11884.3538
2.00.23530.48254.6931
2.50.23560.48935.2297
3.00.17560.29565.3954
300.04200.96171.0887
0.50.04870.49341.1622
1.00.09480.09852.6257
1.50.09880.71402.6121
2.00.11170.94743.3687
2.50.10670.86872.7479
3.00.11310.90613.7842
1000.00740.61394.3078
0.50.00510.52734.4172
1.00.00080.70752.6381
1.50.00150.27160.7305
2.00.00260.56680.2494
2.50.00851.04282.3044
3.00.02451.23954.3657
表 2  Bingham模型业务价值结果
fl/HzIC/Au31/su32/MBfl/HzIC/Au31/su32/MB
102.0406197.44302.2096222.60
0.51.7626205.620.51.6176223.11
1.01.8016198.591.01.6706206.61
1.51.6956197.631.51.8146214.86
2.01.6826205.732.01.7366222.96
2.51.7076197.632.51.6556223.04
3.01.7216197.633.01.7186214.86
201.9566204.4810010.0306425.03
0.51.7716187.910.59.5936425.10
1.01.8576196.021.09.3296426.15
1.51.7666204.271.59.6836425.10
2.01.6286204.192.09.7366427.01
2.51.7406204.272.59.6856425.13
3.01.6676187.843.09.5256408.90
表 3  Bingham模型软件驱动质量结果
图 6  魔术公式模型拟合的磁流变减振器参数特性曲线
fl/HzIC/Au11u12fl/HzIC/Au11u12
1059.39030.994030103.94630.9946
0.569.12220.99400.5107.44480.9947
1.091.28760.99461.0131.44040.9948
1.5113.23690.99481.5153.82150.9948
2.0138.57010.99452.0178.44850.9949
2.5167.21430.99392.5201.75300.9948
3.0175.38740.99433.0210.97800.9950
2079.43370.9948100131.89470.9921
0.582.81290.99520.5128.81220.9938
1.0108.89470.99521.0149.09380.9944
1.5137.03880.99491.5167.96760.9949
2.0156.47420.99512.0186.91030.9954
2.5179.01500.99502.5228.85370.9946
3.0187.32740.99533.0291.32980.9927
表 4  魔术公式模型保真度结果
fl/HzIC/Au21/%u22/%u23/%
100.04811.00250.4587
0.50.05331.01440.7076
1.00.04470.54581.3298
1.50.05000.24860.5929
2.00.05560.15410.7675
2.50.04350.20330.7906
3.00.05160.01100.5664
200.05320.54910.3476
0.50.05100.05970.2994
1.00.05030.08160.5289
1.50.05980.06510.1090
2.00.05970.42800.2799
2.50.04000.42330.4092
3.00.04060.23060.1987
300.02621.41370.9577
0.50.01140.89910.9491
1.00.01280.68660.6106
1.50.00810.12220.7443
2.00.01370.04420.4846
2.50.01160.00770.7614
3.00.01970.13870.4908
1000.01010.60180.0753
0.50.00700.46605.3871
1.00.00890.73074.5847
1.50.00990.83093.4373
2.00.01050.70662.8868
2.50.01101.30151.7233
3.00.00572.32920.7684
表 5  魔术公式模型业务价值结果
fl/HzIC/Au31/su32/MBfl/HzIC/Au31/su32/MB
1024.4196268.073019.4526260.52
0.528.2216251.940.520.2816260.84
1.022.0146260.451.019.6126260.81
1.521.8956259.431.520.2696260.84
2.020.8676259.432.018.5556269.09
2.522.6596259.432.518.2716260.84
3.031.8776241.383.018.2396260.84
2019.0686253.7210017.1986461.91
0.517.6836254.300.515.1256468.10
1.018.8116254.331.015.5126460.00
1.517.8146262.511.515.2256459.97
2.022.1096262.512.014.9706460.00
2.518.5376262.512.515.0386468.16
3.023.1536254.333.016.6716460.03
表 6  魔术公式模型软件驱动质量结果
评级得分评级区间
u11u12
优秀100[0, 146.66](0.99, 1.00]
良好85(146.66, 254.92](0.98, 0.99]
中等70(254.92, 420.20](0.97, 0.98]
较差55(420.20, +∞)[0, 0.97]
表 7  模型保真度二级评价指标评级区间划分
图 7  Bingham模型保真度二级评价指标与评级区间
评级得分评级区间
u21/%u22/%u23/%
优秀100[0, 0.03][0, 0.35][0, 1.56]
良好85(0.03, 0.08](0.35, 0.81](1.56, 3.28]
中等70(0.08, 0.17](0.81, 1.69](3.28, 4.79]
较差55(0.17, +∞)(1.69, +∞)(4.79, +∞)
表 8  模型业务价值二级评价指标评级区间划分
图 8  Bingham模型业务价值二级评价指标与评级区间
评级得分评级区间
u31/su32/MB
优秀100[0, 5.71][0, 6232.27]
良好85(5.71, 13.76](6232.27, 6341.08]
中等70(13.76, 21.20](6341.08, 6442.90]
较差55(21.20, +∞)(6442.90, +∞)
表 9  模型软件驱动质量二级评价指标评级区间划分
图 9  Bingham模型软件驱动质量二级评价指标与评级区间
一级评价指标hpq
U1U2U3
U1137
U21/315
U31/71/51
表 10  一级评价指标重要性对应表
图 10  魔术公式模型保真度二级评价指标与评级区间
图 11  魔术公式模型业务价值二级评价指标与评级区间
图 12  魔术公式模型软件驱动质量二级评价指标与评级区间
参数模型z1z2z3J
Bingham70.372980.688094.288874.9352
魔术公式95.588492.052774.058693.0913
表 11  不同参数模型的评价指标对比
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