Response analysis and optimization of the air spring with epistemic uncertainties
Source abstract
Abstract
Abstract Traditional methods for the optimization design of the air spring are based on the deterministic assumption that the parameters are fixed. However, uncertainties widely exist during the manufacturing stage of the air spring. To model the uncertainties in air springs, evidence theory is introduced. For the response analysis of the air spring system under evidence theory, an evidence theory-based polynomial chaos method, called the sparse grid quadrature-based arbitrary orthogonal polynomial (SGQ-AOP) method, is proposed. In the SGQ-AOP method, the response of the air spring is approximated by AOP expansion, and the sparse grid quadrature is introduced to calculate the expansion coefficient. For optimization of the air spring, a reliability-based optimization model is established under evidence theory. To improve the efficiency of optimization, the SGQ-AOP method is used to establish the surrogate model for the response of the air spring. The proposed response analysis and the optimization method were employed to optimize an air spring with epistemic uncertainties, and its effectiveness has been demonstrated by comparing it with the traditional evidence theory-based AOP method.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Structural Response to Dynamic Loads · Vibration Control and Rheological Fluids
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Transportation Equipment and Control Engineering, School of Traffic & Transportation Engineering, Central South University , Changsha , Hunan, 410075 , China
Key Laboratory of Traffic Safety on Track, Ministry of Education , Changsha , China
References (36)
Show source-provided references
1. Chen, Y., A. W. Peterson, and M. Ahmadian. Achieving anti-roll bar effect through air management in commercial vehicle pneumatic suspensions. Vehicle System Dynamics, Vol. 57, No. 12, 2019, pp. 1775–1794.10.1080/00423114.2018.1552005 ↗
2. Maeda, S., J. Yoshida, Y. Ura, H. Haraguchi, and J. Sugawara. Air springs for railways available for very cold environments. SEI Technical Review, Vol. 81, 2015, pp. 63–66.
3. Hongxue, L., L. Shiwu, S. Wencai, W. Linhong, and L. Dongye. The optimum matching control and dynamic analysis for air suspension of multi-axle vehicles with anti-roll hydraulically interconnected system. Mechanical Systems and Signal Processing, Vol. 139, 2020, id. 106605.10.1016/j.ymssp.2019.106605 ↗
4. Yiqian, Z., S. Wenbin, and R. Subhash. Modeling and performance analysis of convoluted air springs as a function of the number of bellows. Mechanical Systems and Signal Processing, Vol. 159, 2021, id. 107858.10.1016/j.ymssp.2021.107858 ↗
5. Zhou, W., T. Han, X. Liang, J. Bao, G. Li, H. Xiao, et al. “Load identification and fatigue evaluation via wind-induced attitude decoupling of railway catenary”. Reviews on Advanced Materials Science, Vol. 60, No. 1, 2021, pp. 377–403.10.1515/rams-2021-0037 ↗
6. Hengjia, Z., J. Yang, and Z. Yunqing. Dual-chamber pneumatically interconnected suspension: Modeling and theoretical analysis. Mechanical Systems and Signal Processing, Vol. 147, 2020, id. 107125.10.1016/j.ymssp.2020.107125 ↗
7. Hongguang, L., G. Konghui, C. Shuqi, W. Wei, and C. Fuzhong. Design of stiffness for air spring based on ABAQUS. Mathematical Problems in Engineering, Vol. 2013, 2013, pp. 206–226.
8. Oman, S. and M. Nagode. On the influence of the cord angle on air-spring fatigue life. Engineering Failure Analysis, Vol. 27, 2012, pp. 61–73.10.1016/j.engfailanal.2012.09.002 ↗
9. Meng, X., J. Liu, L. Cao, Z. Yu, and D. Yang. A general frame for uncertainty propagation under multimodally distributed random variables. Computer Methods in Applied Mechanics and Engineering, Vol. 367, 2020, id. 113109.10.1016/j.cma.2020.113109 ↗
10. Finette, S. A stochastic response surface formulation of acoustic propagation through an uncertain ocean waveguide environment. Journal of the Acoustical Society of America, Vol. 126, No. 5, 2009, pp. 2242–2247.10.1121/1.3212918 ↗
11. Wang, M., D. S. Li, X. Q. Li, and W. J. Yang. Probabilistic design of uncertainty for aluminum alloy sheet in rubber fluid forming process. Reviews on Advanced Materials Science, Vol. 33, No. 8, 2013, pp. 442–451.
12. Yager, R., M. Fedrizzi, and J. Kacprzyk. Advances in the Dempster-Shafer Theory of Evidence, John Wiley & Sons, New York, 1994.
13. Liu, J., L. Cao, C. Jiang, B. Ni, and D. Zhang. Parallelotope-formed evidence theory model for quantifying uncertainties with correlation. Applied Mathematical Modelling, Vol. 77, 2020, pp. 32–48.10.1016/j.apm.2019.07.017 ↗
14. De Gersem, H., D. Moens, W. Desmet, and D. Vandepitte. A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 2—Numerical case studies. Journal of Sound and Vibration, Vol. 288, 2005, pp. 463–486.10.1016/j.jsv.2005.07.002 ↗
15. Wang, C. and Z. Qiu. Uncertain temperature field prediction of heat conduction problem with fuzzy parameters. International Journal of Heat and Mass Transfer, Vol. 91, 2015, pp. 725–733.10.1016/j.ijheatmasstransfer.2015.08.023 ↗
16. Chen, N., D. Yu, B. Xia, and M. Beer. Uncertainty analysis of a structural–acoustic problem using imprecise probabilities based on p-box representations. Mechanical Systems and Signal Processing, Vol. 80, 2016, pp. 45–57.10.1016/j.ymssp.2016.04.009 ↗
17. Zhiping, Q. and C. Suhuan. Elishakoff. Bounds of eigenvalues for structures with an interval description of uncertain-but-non-random parameters. Chaos Solitons and Fractals, Vol. 7, No. 3, 1996, pp. 425–434.10.1016/0960-0779(95)00065-8 ↗
18. Baizhan, X. and Y. Dejie. Modified interval perturbation finite element method for a structural–acoustic system with interval parameters. Journal of Applied Mechanics, Transactions ASME, Vol. 80, No. 4, 2013, id. 041027.10.1115/1.4023021 ↗
19. Bae, H. R., R. V. Grandhi, and R. A. Canfield. Epistemic uncertainty quantification techniques including evidence theory for large-scale structures. Computers and Structures, Vol. 82, No. 13, 2004, pp. 1101–1112.10.1016/j.compstruc.2004.03.014 ↗
20. Qingzhu, W., Z. Meng, and H. Biao. Object detection based on fusing monocular camera and lidar data in decision level using D-S evidence theory. 2020 IEEE 16th International Conference on Automation Science and Engineering (CASE), 2020, pp. 476–481.
21. Hu, Y., L. Gou, X. Deng, and W. Jiang. Failure mode and effect analysis using multi-linguistic terms and Dempster–Shafer evidence theory. Quality and Reliability Engineering International, Vol. 37, No. 3, 2021, pp. 920–934.10.1002/qre.2773 ↗
22. Zhang, Z. and C. Jiang. Evidence-theory-based structural reliability analysis with epistemic uncertainty: a review. Structural and Multidisciplinary Optimization, Vol. 63, No. 6, 2021, pp. 2935–3953.10.1007/s00158-021-02863-w ↗
23. Bai, Y. C., C. Jiang, X. Han, and D. A. Hu. Evidence-theory-based structural static and dynamic response analysis under epistemic uncertainties. Finite Elements in Analysis and Design, Vol. 68, No. 3, 2013, pp. 52–62.10.1016/j.finel.2013.01.007 ↗
24. Shengwen, Y., Y. Dejie, Y. Hui, L. Hui, and X. Baizhan. Hybrid evidence theory-based finite element/statistical energy analysis method for mid-frequency analysis of built-up systems with epistemic uncertainties. Mechanical Systems and Signal Processing, Vol. 93, 2017, pp. 204–224.10.1016/j.ymssp.2017.02.001 ↗
25. Chen, N., Y. Dejie, and X. Baizhan. Evidence-theory-based analysis for the prediction of exterior acoustic field with epistemic uncertainties. Engineering Analysis with Boundary Elements, Vol. 50, 2015, pp. 402–411.10.1016/j.enganabound.2014.09.014 ↗
26. Helton, J. C., J. D. Johnson, W. L. Oberkampf, and C. B. Storlie. A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Computer Methods in Applied Mechanics and Engineering, Vol. 196, 2007, pp. 3980–3998.10.1016/j.cma.2006.10.049 ↗
27. Jiang, C., Z. Zhang, X. Han, and J. Liu. A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty. Computers & Structures, Vol. 129, No. 4, 2013, pp. 1–12.10.1016/j.compstruc.2013.08.007 ↗
28. Shengwen, Y., Y. Dejie, Y. Hui, and X. Baizhan. A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion. Computer Methods in Applied Mechanics and Engineering, Vol. 322, 2017, pp. 419–440.10.1016/j.cma.2017.04.020 ↗
29. Chen, N., Y. Hu, D. Yu, J. Liu, and M. Beer. A polynomial expansion approach for response analysis of periodical composite structural–acoustic problems with multi-scale mixed aleatory and epistemic uncertainties. Computer Methods in Applied Mechanics and Engineering, Vol. 342, 2018, pp. 509–31.10.1016/j.cma.2018.08.021 ↗
30. Chong, W. Evidence-theory-based uncertain parameter identification method for mechanical systems with imprecise information. Computer Methods in Applied Mechanics and Engineering, Vol. 351, 2019, pp. 281–296.10.1016/j.cma.2019.03.048 ↗
31. Shengwen, Y., Y. Dejie, L. Zhen, and X. Baizhan. An arbitrary orthogonal polynomial expansion approach for response analysis of acoustic systems with epistemic uncertainty. Computer Methods in Applied Mechanics and Engineering, Vol. 332, 2018, pp. 280–302.10.1016/j.cma.2017.12.025 ↗
32. Szegö, G. Orthogonal Polynomials. Colloquium Publications, Vol. 23, 4th edn, American Mathematical Society, USA, 1975.
33. Plaskota, L. and G. W. Wasilkowski. Smolyak’s algorithm for integration and L 1 approximation of multivariate functions with bounded mixed derivatives of second order. Numerical Algorithms, Vol. 36, No. 3, 2004, pp. 229–246.10.1023/B:NUMA.0000040060.56819.a7 ↗
34. Vu-Bac, N., T. X. Duong, T. Lahmer, X. Zhuang, R. A. Sauer, H. S. Park, et al. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics & Engineering, Vol. 331, 2018, pp. 427–455.10.1016/j.cma.2017.09.034 ↗
35. Vu-Bac, N., T. Lahmer, X. Zhuang, T. Nguyen-Thoi, and T. Rabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, Vol. 100, 2016, pp. 19–31.10.1016/j.advengsoft.2016.06.005 ↗
36. Waisman, H., E. Chatzi, and A. W. Smyth. Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms. International Journal for Numerical Methods in Engineering, Vol. 82, 2010, pp. 303–328.10.1002/nme.2766 ↗