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Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (5): 1047-1058    DOI: 10.3785/j.issn.1008-973X.2026.05.014
    
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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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 wordsmagnetorheological damper      mechanical model      model fidelity      model business value      model software-driven quality      fuzzy comprehensive evaluation     
Received: 06 June 2025      Published: 06 May 2026
CLC:  TP 393  
Fund:  国家自然科学基金资助项目(52205135).
Cite this article:

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.

URL:

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


磁流变减振器力学模型的模糊综合评价方法

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 
Fig.1 Internal structure of magnetorheological damper
Fig.2 Force-displacement diagram for mechanical model of magnetorheological damper
Fig.3 Bench test equipment
Fig.4 Parameter characteristic curves of magnetorheological damper obtained from bench tests
Fig.5 Parameter characteristic curves of magnetorheological damper fitted by Bingham model
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
Tab.1 Results of Bingham model fidelity
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
Tab.2 Results of Bingham model business value
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
Tab.3 Results of Bingham model software-driven quality
Fig.6 Parameter characteristic curves of magnetorheological damper fitted by magic formula model
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
Tab.4 Results of magic formula model fidelity
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
Tab.5 Results of magic formula model business value
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
Tab.6 Results of magic formula model software-driven quality
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]
Tab.7 Rating interval classification of secondary evaluation indexes for model fidelity
Fig.7 Secondary evaluation indexes and rating intervals for Bingham model fidelity
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, +∞)
Tab.8 Rating interval classification of secondary evaluation indexes for model business value
Fig.8 Secondary evaluation indexes and rating intervals for Bingham model business value
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, +∞)
Tab.9 Rating interval classification of secondary evaluation indexes for model software-driven quality
Fig.9 Secondary evaluation indexes and rating intervals for Bingham model software-driven quality
一级评价指标hpq
U1U2U3
U1137
U21/315
U31/71/51
Tab.10 Correspondence table of first-level evaluation index importance
Fig.10 Secondary evaluation indexes and rating intervals for magic formula model fidelity
Fig.11 Secondary evaluation indexes and rating intervals for magic formula model business value
Fig.12 Secondary evaluation indexes and rating intervals for magic formula model software-driven quality
参数模型z1z2z3J
Bingham70.372980.688094.288874.9352
魔术公式95.588492.052774.058693.0913
Tab.11 Comparison of evaluation indexes for different parametric models
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