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Modelling and Sensitivity Analysis of Nonlinear Firefighting Systems Using Maple

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Maple in Mathematics Education and Research (MC 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1414))

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Abstract

Mathematical modelling and numerical simulations have greatly contributed to the development of technical sciences in the recent decades. With powerful tools, like Maple, the examination of ever newer engineering applications in simulation environment was made possible. This paper gives an overview of mathematical modelling and numerical examination of nonlinear fire truck suspension systems using Maple. The examined models are the suspension system of a heavy-duty fire truck with different degrees of freedom and a special double-cabin fire truck suspension system with a crew compartment. The construction of mathematical models, their implementation to Maple and the numerical simulation results are explained. Detailed One-at-a-Time sensitivity analysis results using a novel fuzzy logic based evaluation method developed in Maple are also presented. With the proposed method an extended parameter range can be examined and the parameters can be easily compared. From the sensitivity analysis it was concluded that the spring characteristics and the road models greatly affect simulation results.

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References

  1. Pidl, R.: Analytical approach to determine vertical dynamics of a semi-trailer truck from the point of view of goods protection. In: Podgorski, J., et al. (eds.) AIP Conference Proceedings 2018, vol. 1922, Paper No. 120003 (2008). https://doi.org/10.1063/1.5019118

  2. Wu, W., Zhang S., Zhang Z.: athematical simulations and on-road experimentations of the vibration energy harvesting from mining dump truck hydro-pneumatic suspension. Shock and Vibration (2019). Article ID: 4814072

    Google Scholar 

  3. Danko, J., Milesich, T., Bucha, J.: Nonlinear model of the passenger car seat suspension system. Strojnícky časopis - J. Mech. Eng. 67(1), 23–28 (2017)

    Article  Google Scholar 

  4. Avesh, Mohd, Srivastava, Rajeev: Passenger car active suspension system model for better dynamic characteristics. Natl. Acad. Sci. Lett. 43(1), 37–41 (2019). https://doi.org/10.1007/s40009-019-00807-z

    Article  Google Scholar 

  5. Kovtun, V., Korotkevich, S., Mirchev, Y., Lodnya, V.: Optimization of fire truck’s tanks on the chassis MAZ-6317 by the method of computer simulation. Int. J. “NDT Days” 2(4), 495–500 (2019)

    Google Scholar 

  6. Kovtun, V.A., Korotkevich, S.G., Zharanov, V.A.: Computer simulation and research of the stress-strain state of fire tank truck construction. Vestnik Universiteta grazhdanskoy zashchity MCHS Belarusi (Bulletin of the University of Civil Protection of the MES of Belarus) 2017(1), 81–90 (2017). (in Russian)

    Google Scholar 

  7. Sund, S. M., Plouvier, M., Lie, B.: Comparison of simulation tools for dynamic models. In: Proceedings of The 59th Conference on Simulation and Modelling (SIMS 59), 26–28 September 2018, Oslo Metropolitan University, Norway, pp. 177–184 (2018)

    Google Scholar 

  8. Molnárka, Gy., Gergó, L., Wettl, F., Horváth, A., Kallós, G.: Maple V and its applications. Springer Hungarica, Budapest (1996)

    Google Scholar 

  9. Zhao, X.X., Ing, A.H., Azad, N.L., McPhee, J.: An optimal gear-shifting strategy for heavy trucks with trade-off study between trip time and fuel economy. Int. J. Heavy Veh. Syst. 22(4), 356–374 (2015)

    Article  Google Scholar 

  10. Zhao, X., Yang, J.: An optimal gear-shifting strategy for heavy trucks with trade-off study between trip time and fuel economy. Int. J. Heavy Veh. Syst. 22(4), 356–374 (2015)

    Article  Google Scholar 

  11. Maplesoft: Engineering Solutions for Heavy Vehicles. https://www.maplesoft.com/solutions/engineering/IndustrySolutions/HeavyVehicles.aspx. Accessed 10 Dec 2020

  12. Chonacky, N., Winch, D.: Maple, mathematica, and matlab: the 3M’S without the tape. Comput. Sci. Eng. 7, 8–16 (2005)

    Article  Google Scholar 

  13. GarVan, F.: The Maple Book. CRC Press, Boca Raton (2001)

    Book  Google Scholar 

  14. Saltelli, A., Chan, K., Scott, E.M.: Sensitivity Analysis. Wiley, Hoboken (2009)

    MATH  Google Scholar 

  15. Iwaniec, J.: Sensitivity analysis of an identification method dedicated to nonlinear systems working under operational loads. J. Theorethical Appl. Mech. 49, 419–438 (2011)

    Google Scholar 

  16. Murray-Smith, D.J.: The application of parameter sensitivity analysis methods to inverse simulation models. Math. Comput. Model. Dyn. Syst. 19(1), 1–24 (2012)

    Google Scholar 

  17. Zádor, J., Zsély, I. Gy., Turányi, T., Ratto, M., Tarantola, S., Saltelli, A.: Local and global uncertainty analyses of a methane flame model. J. Phys. Chem. A. 109(43), 9795–9807 (2005)

    Google Scholar 

  18. Rauh, A., Minisini, J., Hofer, E.P.: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties. Int. J. Appl. Math. Comput. Sci. 19(3), 425–439 (2009). https://doi.org/10.2478/v10006-009-0035-1. https://sciendo.com/downloadpdf/journals/amcs/19/3/article-p425.pdf

  19. Hamby, D.M.: A review of techniques for parameter sensitivity analysis of environmental models. Environ. Monit. Assess. 32(2), 135–154 (1994)

    Article  Google Scholar 

  20. Kóczy, L.T., Tikk, D.: Fuzzy Systems (in Hungarian), Typotex (2012)

    Google Scholar 

  21. Fogel, D.B., Liu, D., Keller, J.M.: Fundamentals of Computational Intelligence: Neural Networks, Fuzzy Systems, and Evolutionary Computation, IEEE Press Series on Computationa Intelligence. Wiley (2016)

    Google Scholar 

  22. Maple FuzzySets. https://16.www.maplesoft.com/applications/view.aspx?SID=96899. Accessed 15 Oct 2020

  23. Ahmad, I., Khan, A.: A comparative analysis of linear and nonlinear semi-active suspension system. Mehran Univ. Res. J. Engi. Technol. 37, 233–240 (2018)

    Article  Google Scholar 

  24. Jiao, L.: Vehicle model for tyre-ground contact force evaluation, M.Sc thesis, KTH Royal Institute of Technology (2013)

    Google Scholar 

  25. Evers, W.J., Besselin, I., Teerhuism, A., Oomen, T., Nijmeijer, H.: Experimental validation of a quarter truck model using asynchronous measurements with low signal-to-noise ratios. In: 10th AVEC conference, Loughborough, UK. 22–26. August, 2010, pp. 177–182, Loughborough University Department of Aeronautical & Automotive Engineering & Transport Studies (2010)

    Google Scholar 

  26. Zhu, Q., Ishitobi, M.: Chaotic vibration of a nonlinear full-vehicle model. Int. J. Solids Struct. 43(3–4), 747–759 (2015)

    MATH  Google Scholar 

  27. Cui, Y., Kurfess, T. R., Messman, M.: Testing and modeling of nonlinear properties of shock absorbers for vehicle dynamics studies. In: Proceedings of the World Congress on Engineering and Computer Science 2010 Vol II WCECS 2010, San Francisco, USA, pp. 949–954. Newswood Limited (2010)

    Google Scholar 

  28. Dixon, J.C.: Suspension Geometry and Computation. Wiley, Chichester (2009)

    Book  Google Scholar 

  29. Hajdu, F., Kuti, R.: Examination of chaotic vibrations during operation of a fire truck. In: Proceedings of MAC 2018 in Prague Prag, Czech Republic, 25–27 May 2018, pp. 163–170. MAC Prague consulting Ltd., Prague, Czech Republic (2018)

    Google Scholar 

  30. Corless, R.M.: What good are numerical simulations of chaotic dynamical systems? Comput. Math. Appl. 28(10–12), 107–121 (1994)

    Article  MathSciNet  Google Scholar 

  31. Corless R.M., Fillion N.: Backward error analysis for perturbation methods. In: Fillion, N., Corless, R., Kotsireas, I. (eds.) Algorithms and Complexity in Mathematics, Epistemology, and Science. Fields Institute Communications, vol. 82. Springer, New York (2019). https://doi.org/10.1063/1.5019118

  32. Hajdu, F.: Modelling of nonlinear active and passive suspension systems (in Hungarian). In: Volume of New National Excellence Program 2018/2019, Széchenyi István University, pp. 197–208 (2019)

    Google Scholar 

  33. Hajdu, F., Molnárka, Gy., Kuti, R.: One-at-a-time sensitivity study of a nonlinear fire truck suspension model. FME Trans. 48(1), 90–95 (2020)

    Google Scholar 

  34. Zhu, Q., Ishitobi, M.: Chaotic vibration of a nonlinear full-vehicle model. Int. J. Solids Struct. 43(3–4), 747–759 (2006)

    Article  Google Scholar 

  35. Hajdu, F., Kuti, R.: Development of a simulation model for analyzing vibrations of a double cabin fire truck and their effects on firefighters. Int. Adv. Res. J. Sci. Eng. Technol. 6(5), 74–79 (2019)

    Article  Google Scholar 

  36. Maple Signal Processing. https://www.maplesoft.com/products/maple/features/Signal_Processing.aspx. Accessed 15 Oct 2020

  37. International Standard 2631 (ISO 1974, 1985): Mechanical vibration and shock - Evaluation of human exposure to whole-body vibration

    Google Scholar 

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Authors and Affiliations

  1. Széchenyi István University, Győr, 9026, Hungary

    Flóra Hajdu, Győző Molnárka & Rajmund Kuti

Authors
  1. Flóra Hajdu
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  2. Győző Molnárka
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  3. Rajmund Kuti
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Corresponding author

Correspondence to Flóra Hajdu .

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Editors and Affiliations

  1. Western University, London, ON, Canada

    Robert M. Corless

  2. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

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Hajdu, F., Molnárka, G., Kuti, R. (2021). Modelling and Sensitivity Analysis of Nonlinear Firefighting Systems Using Maple. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-81698-8_16

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  • Online ISBN: 978-3-030-81698-8

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