This study proposes a multi-objective optimization (MOO) strategy with an improved constraint-handling technique to improve the crashworthiness of an excavator rollover protective structure (ROPS). First, the experimental test under the ISO 12117 criteria is conducted and the developed numerical model is verified. Then, the amounts of energy absorption and the cross-sectional forces of components in the ROPS are analyzed. The main energy absorbing and load carrying components are identified. Finally, the thicknesses of the identified components are considered as the design variables. A multi-objective crashworthiness optimization process aims at improving the safety distance and reducing the total mass is designed by the finite element analysis-based surrogate model technique and a modified MOO algorithm. The proposed algorithm modifies the objective function values of an individual with its constraint violations and the true objective function values, of which adaptive penalty weights fed back from the constraint violations are used to keep the balance. Compared with the existing methods, it is found that the optimal solutions obtained by the proposed algorithm show superiority on convergence rate and diversity of distribution. The optimal results show that the safety distance is 27.42% higher while the total mass is 7.06% lower than those of the baseline design when it meets the requirements of ISO 12117. This study provides an alternative crashworthiness design route for the ROPS of the construction machines.
Citation: Chao Ma, Hong Fu, Pengcheng Lu, Hongpeng Lu. Multi-objective crashworthiness design optimization of a rollover protective structure by an improved constraint-handling technique[J]. Electronic Research Archive, 2023, 31(7): 4278-4302. doi: 10.3934/era.2023218
This study proposes a multi-objective optimization (MOO) strategy with an improved constraint-handling technique to improve the crashworthiness of an excavator rollover protective structure (ROPS). First, the experimental test under the ISO 12117 criteria is conducted and the developed numerical model is verified. Then, the amounts of energy absorption and the cross-sectional forces of components in the ROPS are analyzed. The main energy absorbing and load carrying components are identified. Finally, the thicknesses of the identified components are considered as the design variables. A multi-objective crashworthiness optimization process aims at improving the safety distance and reducing the total mass is designed by the finite element analysis-based surrogate model technique and a modified MOO algorithm. The proposed algorithm modifies the objective function values of an individual with its constraint violations and the true objective function values, of which adaptive penalty weights fed back from the constraint violations are used to keep the balance. Compared with the existing methods, it is found that the optimal solutions obtained by the proposed algorithm show superiority on convergence rate and diversity of distribution. The optimal results show that the safety distance is 27.42% higher while the total mass is 7.06% lower than those of the baseline design when it meets the requirements of ISO 12117. This study provides an alternative crashworthiness design route for the ROPS of the construction machines.
| [1] | ISO 12117-2, Earth-moving machinery-Laboratory tests and performance requirements for protective structures of excavators-Part 2: Roll-over protective structures (ROPS) for excavators of over 6 t, Geneva, Switzerland: International Organization for Standardization, 2008. |
| [2] | ISO 3164, Earth-moving machinery-Laboratory evaluations of protective structures-Specifications for deflection-limiting volume, Geneva, Switzerland: International Organization for Standardization, 2013. |
| [3] |
X. Xu, Y. Zhang, X. Wang, J. Fang, J. Chen, J. Li, Searching superior crashworthiness performance by constructing variable thickness honeycombs with biomimetic cells, Int. J. Mech. Sci., 235 (2022), 107718. https://doi.org/10.1016/j.ijmecsci.2022.107718 doi: 10.1016/j.ijmecsci.2022.107718
|
| [4] |
J. Latorre-Biel, T. Ballesteros, I. Arana, J. R. Alfaro, Development of an inexpensive rollover energy dissipation device to improve safety provided by ROPS, Biosyst. Eng., 185 (2019), 88–102. https://doi.org/10.1016/j.biosystemseng.2019.02.004 doi: 10.1016/j.biosystemseng.2019.02.004
|
| [5] |
B. Clark, N. Perera, D. Thambiratnam, Enhancing the impact energy absorption in roll over protective structures, Int. J. Crashworthiness, 13 (2008), 167–183. https://doi.org/10.1080/13588260701788427 doi: 10.1080/13588260701788427
|
| [6] |
T. N. Tran, A. Baroutaji, Q. Estrada, A. Arjunan, H. Le, N. P. Thien, Crashworthiness analysis and optimization of standard and windowed multi-cell hexagonal tubes, Struct. Multidiscip. Optim., 63 (2021), 2191–2209. https://doi.org/10.1007/s00158-020-02794-y doi: 10.1007/s00158-020-02794-y
|
| [7] |
X. Xu, Y. Zhang, J. Wang, J. Feng, C. H. Wang, Crashworthiness design of novel hierarchical hexagonal columns, Compos. Struct., 194 (2018), 36–48. https://doi.org/10.1016/j.compstruct.2018.03.099 doi: 10.1016/j.compstruct.2018.03.099
|
| [8] |
Y. Zhang, Z. Pan, S. Zhang, N. Qiu, Probabilistic invertible neural network for inverse design space exploration and reasoning, Electron. Res. Arch., 31 (2023), 860–881. https://doi.org/10.3934/era.2023043 doi: 10.3934/era.2023043
|
| [9] |
S. Dong, T. Jing, J. Zhang, A few-shot learning-based crashworthiness analysis and optimization for multi-cell structure of high-speed Train, Machines, 10 (2022), 696. https://doi.org/10.3390/machines10080696 doi: 10.3390/machines10080696
|
| [10] |
F. Lei, X. Lv, J. Fang, G. Sun, Q. Li, Multiobjective discrete optimization using the TOPSIS and entropy method for protection of pedestrian lower extremity, Thin-Walled Struct., 152 (2020), 106349. https://doi.org/10.1016/j.tws.2019.106349 doi: 10.1016/j.tws.2019.106349
|
| [11] |
N. Qiu, Y. Gao, J. Fang, G. Sun, Q. Li, N. H. Kim, Crashworthiness optimization with uncertainty from surrogate model and numerical error, Thin-Walled Struct., 129 (2018), 457–472. https://doi.org/10.1016/j.tws.2018.05.002 doi: 10.1016/j.tws.2018.05.002
|
| [12] |
G. Sun, R. Qu, H. Zhang, G. Li, Robust optimization of automobile door structure based on Taguchi and TOPSIS-entropy, Mod. Manuf. Eng., 450 (2018), 11–18. https://10.16731/j.cnki.1671-3133.2018.03.003 doi: 10.16731/j.cnki.1671-3133.2018.03.003
|
| [13] |
G. Sun, J. Tian, T. Liu, X. Yan, X. Huang, Crashworthiness optimization of automotive parts with tailor rolled blank, Eng. Struct., 169 (2018), 201–215. https://doi.org/10.1016/j.engstruct.2018.05.050 doi: 10.1016/j.engstruct.2018.05.050
|
| [14] |
Y. Zhou, X. Xu, J. Fang, W. Huang, J. Wang, Load characteristics of triangular honeycomb structures with self-similar hierarchical features, Eng. Struct., 257 (2022), 114114. https://doi.org/10.1016/j.engstruct.2022.114114 doi: 10.1016/j.engstruct.2022.114114
|
| [15] |
N. Qiu, D. Wang, Y. Li, M. Xiao, Q. Gao, N. H. Kim, Influence of spherical triggers on axial collapse of tapered tubes, Int. J. Crashworthiness, 2023 (2023). https://doi.org/10.1080/13588265.2023.2183791 doi: 10.1080/13588265.2023.2183791
|
| [16] |
N. Qiu, J. Zhang, C. Li, Y. Shen, J. Fang, Mechanical properties of three-dimensional functionally graded triply periodic minimum surface structures, Int. J. Mech. Sci., 246 (2023), 108118. https://doi.org/10.1016/j.ijmecsci.2023.108118 doi: 10.1016/j.ijmecsci.2023.108118
|
| [17] |
X. Xu, X. Chen, Z. Liu, Y. Zhang, Y. Xu, J. Fang, et al., A feasible identification method of uncertainty responses for vehicle structures, Struct. Multidiscip. Optim., 64 (2021), 3861–3876. https://doi.org/10.1007/s00158-021-03065-0 doi: 10.1007/s00158-021-03065-0
|
| [18] |
K. C. More, G. M. Patil, A. A. Belkhede, Design and analysis of side door intrusion beam for automotive safety, Thin-Walled Struct., 153 (2020), 106788. https://doi.org/10.1016/j.tws.2020.106788 doi: 10.1016/j.tws.2020.106788
|
| [19] |
X. Du, F. Zhu, A novel principal components analysis (PCA) method for energy absorbing structural design enhanced by data mining, Adv. Eng. Software, 127 (2019), 17–27. https://doi.org/10.1016/j.advengsoft.2018.10.005 doi: 10.1016/j.advengsoft.2018.10.005
|
| [20] |
A. Ghadianlou, S. B. Abdullah, Crashworthiness design of vehicle side door beams under low-speed pole side impacts, Thin-Walled Struct., 67 (2013), 25–33. https://doi.org/10.1016/j.tws.2013.02.004 doi: 10.1016/j.tws.2013.02.004
|
| [21] |
P. Zhu, F. Pan, W. Chen, F. A. C. Viana, Lightweight design of vehicle parameters under crashworthiness using conservative surrogates, Comput. Ind., 64 (2013), 280–289. https://doi.org/10.1016/j.compind.2012.11.004 doi: 10.1016/j.compind.2012.11.004
|
| [22] |
L. Yu, X. Gu, L. Qian, P. Jiang, W. Wang, M. Yu, Application of tailor rolled blanks in optimum design of pure electric vehicle crashworthiness and lightweight, Thin-Walled Struct., 161 (2021), 107410. https://doi.org/10.1016/j.tws.2020.107410 doi: 10.1016/j.tws.2020.107410
|
| [23] |
Y. Shang, H. Wu, S. Cen, C. Li, An efficient 4-node facet shell element for the modified couple stress elasticity, Int. J. Numer. Methods Eng., 123 (2022), 992–1012. https://doi.org/10.1002/nme.6885 doi: 10.1002/nme.6885
|
| [24] |
M. Shirazi, H. Z. Aashtiani, L. Quadrifoglio, Estimating the minimal revenue tolls in large-scale roadway networks using the dynamic penalty function method, Comput. Ind. Eng., 107 (2017), 120–127. https://doi.org/10.1016/j.cie.2017.03.008 doi: 10.1016/j.cie.2017.03.008
|
| [25] |
B. Wang, H. Li, Y. Feng, W. Shen, An adaptive fuzzy penalty method for constrained evolutionary optimization, Inf. Sci., 571 (2021), 358–374. https://doi.org/10.1016/j.ins.2021.03.055 doi: 10.1016/j.ins.2021.03.055
|
| [26] |
C. Ma, Y. Gao, J. Yang, Y. Duan, Z. Liu, Finite element-based safety prediction for hydraulic excavator rollover protective structure and experimental validation, Int. J. Crashworthiness, 27 (2022), 955–967. https://doi.org/10.1080/13588265.2021.1888563 doi: 10.1080/13588265.2021.1888563
|
| [27] |
J. R. Harris, G. L. Winn, P. D. Ayers, E. A. Mckenzie, Predicting the performance of cost-effective rollover protective structure designs, Saf. Sci., 49 (2011), 1252–1261. https://doi.org/10.1016/j.ssci.2011.04.011 doi: 10.1016/j.ssci.2011.04.011
|
| [28] |
F. Khorsandi, P. D. Ayers, T. J. Truster, Developing and evaluating a finite element model for predicting the two-posts rollover protective structure nonlinear behaviour using SAE J2194 static test, Biosyst. Eng., 156 (2017), 96–107. https://doi.org/10.1016/j.biosystemseng.2017.01.010 doi: 10.1016/j.biosystemseng.2017.01.010
|
| [29] |
T. Chen, Y. Zhang, J. Lin, Y. Lu, Theoretical analysis and crashworthiness optimization of hybrid multi-cell structures, Thin-Walled Struct., 142 (2019), 116–131. https://doi.org/10.1016/j.tws.2019.05.002 doi: 10.1016/j.tws.2019.05.002
|
| [30] |
Z. Du, L. Duan, A. Cheng, Z. Xu, G. Zhang, Theoretical prediction and crashworthiness optimization of thin-walled structures with single-box multi-cell section under three-point bending loading, Int. J. Mech. Sci., 157–158 (2019), 703–714. https://doi.org/10.1016/j.ijmecsci.2019.05.013 doi: 10.1016/j.ijmecsci.2019.05.013
|
| [31] |
W. Rust, K. Schweizerhof, Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination, Thin-Walled Struct., 41 (2003), 227–244. https://doi.org/10.1016/S0263-8231(02)00089-7 doi: 10.1016/S0263-8231(02)00089-7
|
| [32] | ASTM E8/E8M-11, Standard test methods for tension testing of metallic materials, in Annual book of ASTM standards, 2001. |
| [33] |
L. Duan, Z. Du, H. Jiang, W. Xu, Z. Li, Theoretical prediction and crashworthiness optimization of top-hat thin-walled structures under transverse loading, Thin-Walled Struct., 144 (2019), 106261. https://doi.org/10.1016/j.tws.2019.106261 doi: 10.1016/j.tws.2019.106261
|
| [34] |
P. Palanikumar, N. Gnanasekaran, K. Subrahmanya, V. Kaliveeran, Effect of sliding speed and rise in temperature at the contact interface on coefficient of friction during full sliding of SS304, Mater. Today Proc., 27 (2020), 1996–1999. https://doi.org/10.1016/j.matpr.2019.09.046 doi: 10.1016/j.matpr.2019.09.046
|
| [35] |
D. E. Malen, Fundamentals of automobile body structure design, SAE Int., 2011. https://doi.org/10.4271/R-394 doi: 10.4271/R-394
|
| [36] |
Z. Xiao, J. Fang, G. Sun, Q. Li, Crashworthiness design for functionally graded foam-filled bumper beam, Adv. Eng. Software, 85 (2015), 81–95. https://doi.org/10.1016/j.advengsoft.2015.03.005 doi: 10.1016/j.advengsoft.2015.03.005
|
| [37] |
H. Afshari, W. Hare, S. Tesfamariam, Constrained multi-objective optimization algorithms: Review and comparison with application in reinforced concrete structures, Appl. Soft Comput., 83 (2019), 105631. https://doi.org/10.1016/j.asoc.2019.105631 doi: 10.1016/j.asoc.2019.105631
|
| [38] |
X. Xu, X. Chen, Z. Liu, Y. Xu, Y. Zhang, Reliability-based design for lightweight vehicle structures with uncertain manufacturing accuracy, Appl. Math. Modell., 95 (2021), 22–37. https://doi.org/10.1016/j.apm.2021.01.047 doi: 10.1016/j.apm.2021.01.047
|
| [39] |
N. Qiu, Z. Jin, J. Liu, L. Fu, N. H. Kim, Hybrid multi-objective robust design optimization of a truck cab considering fatigue life, Thin-Walled Struct., 162 (2021), 107545. https://doi.org/10.1016/j.tws.2021.107545 doi: 10.1016/j.tws.2021.107545
|
| [40] |
F. Ming, W. Gong, H. Zhen, S. Li, L. Wang, Z. Liao, A simple two-stage evolutionary algorithm for constrained multi-objective optimization, Knowledge-Based Syst., 228 (2021), 107263. https://doi.org/10.1016/j.knosys.2021.107263 doi: 10.1016/j.knosys.2021.107263
|
| [41] |
L. Jiao, J. Luo, R. Shang, F. Liu, A modified objective function method with feasible-guiding strategy to solve constrained multi-objective optimization problems, Appl. Soft Comput., 14 (2014), 363–380. https://doi.org/10.1016/j.asoc.2013.10.008 doi: 10.1016/j.asoc.2013.10.008
|
| [42] |
F. Hossein, M. Fotuhi-Firuzabad, M. Moeini-Aghtaie, A stochastic multi-objective framework for optimal scheduling of energy storage systems in microgrids, IEEE Trans. Smart Grid, 8 (2016), 117–127. https://10.1109/TSG.2016.2598678 doi: 10.1109/TSG.2016.2598678
|
| [43] |
Z. Su, G. Zhang, F. Yue, D. Zhan, M. Li, B. Li, et al., Enhanced constraint handling for reliability-constrained multi-objective testing resource allocation, IEEE Trans. Evol. Comput., 25 (2021), 537–551. https://10.1109/TEVC.2021.3055538 doi: 10.1109/TEVC.2021.3055538
|
| [44] |
N. Srinivas, K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evol. Comput., 2 (1994), 221–248. https://10.1162/evco.1994.2.3.221 doi: 10.1162/evco.1994.2.3.221
|
| [45] | M. Tanaka, H. Watanabe, Y. Furukawa, T. Tanino, GA-based decision support system for multicriteria optimization, in 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, 2 (1995), 1556–1561. https://10.1109/ICSMC.1995.537993 |
| [46] |
E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, V. G. da Fonseca, Performance assessment of multiobjective optimizers: an analysis and review, IEEE Trans. Evol. Comput., 7 (2003), 117–132. https://10.1109/TEVC.2003.810758 doi: 10.1109/TEVC.2003.810758
|
| [47] |
G. Sun, G. Li, S. Zhou, H. Li, S. Hou, Q. Li, Crashworthiness design of vehicle by using multiobjective robust optimization, Struct. Multidiscip. Optim., 44 (2011), 99–110. https://doi.org/10.1007/s00158-010-0601-z doi: 10.1007/s00158-010-0601-z
|
| [48] |
Z. Zhao, H. Zhang, L. Xian, H. Liu, Tensile strength of Q345 steel with random pitting corrosion based on numerical analysis, Thin-Walled Struct., 148 (2020), 106579. https://doi.org/10.1016/j.tws.2019.106579 doi: 10.1016/j.tws.2019.106579
|
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Chao Ma, Hong Fu, Pengcheng Lu, Hongpeng Lu. Multi-objective crashworthiness design optimization of a rollover protective structure by an improved constraint-handling technique[J]. Electronic Research Archive, 2023, 31(7): 4278-4302. doi: 10.3934/era.2023218
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