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Occupant’s lower extremities’ impact-based model calibration for vehicle under-belly blast

  • Industrial Application Paper
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Abstract

Computer-aided engineering (CAE) technology is an important tool in the research of vehicle under-belly blast. A high-quality CAE model is required to guarantee accurate prediction. This requires an efficient model calibration process with physical testing, but the traditional model calibration method based on trial and error and operators’ experience is usually very inefficient and arbitrary. In this paper, an automatic model calibration process based on the Error Assessment of Response Time Histories (EARTH) metric is applied. The EARTH metric evaluates the discrepancies between test and CAE by quantifying the phase error, magnitude error, and slope error between their time histories. Then, an automatic calibration process can be achieved by solving a multi-objective optimization problem for which the optimization object is minimizing discrepancies between testing and CAE and results in automatic calibration of key parameters of the blast simulation CAE model. A case of occupant’s lower extremities’ responses under vehicle under-belly blast load is studied as an example to demonstrate the feasibility of the applied method.

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Data availability

Keyword files and test data files are not available. DOE used for multi-objective optimization is available.

Abbreviations

A :

Constant parameter in JWL equation

A i :

Face area of ALE element

B :

Constant parameter in JWL equation

d DTW :

DTW distance

d i :

Penetration distance

d[i, j]:

Cost matrix

D[i, j]:

Cumulative cost matrix

E 0 :

Specific internal energy in JWL equation

\( \overline{\varepsilon} \) :

Average error

ε m :

Magnitude error

ε p :

Phase error

ε s :

Slope error

\( {\overline{\varepsilon}}_{\mathrm{p}} \) :

Average phase error

\( {\overline{\varepsilon}}_{\mathrm{m}} \) :

Average magnitude error

\( {\overline{\varepsilon}}_{\mathrm{s}} \) :

Average slope error

\( {\overline{\varepsilon}}_{\mathrm{p},\mathrm{b}} \) :

Average phase error of baseline model

\( {\overline{\varepsilon}}_{\mathrm{m},\mathrm{b}} \) :

Average magnitude error of baseline model

\( {\overline{\varepsilon}}_{\mathrm{s},\mathrm{b}} \) :

Average slope error of baseline model

\( {\overline{\varepsilon}}_{\mathrm{p},\mathrm{nor}} \) :

Normalized average phase error

\( {\overline{\varepsilon}}_{\mathrm{m},\mathrm{nor}} \) :

Normalized average magnitude error

\( {\overline{\varepsilon}}_{\mathrm{s},\mathrm{nor}} \) :

Normalized average slope error

\( {\overline{\varepsilon}}_{\mathrm{overall}} \) :

Overall error

f si :

Scale factor for interface spring stiffness

F i :

Interface force

h :

Minimum sampling time step of data

k i :

Stiffness of interface spring

K i :

Bulk modulus of ALE element

n c :

Value for maximum cross-correlation

p :

Pressure of blast gas in JWL equation

\( \overline{R} \) :

Average residual

R 1 :

Constant parameter in JWL equation

R 2 :

Constant parameter in JWL equation

r(n):

Cross-correlation

ρ :

Correlation coefficient

SS :

Sum of squares

σ R :

Standard deviation of residual

t′:

Minimum time interval (ms)

V :

Volume fraction of blast gas in JWL equation

V i :

Volume of ALE element

w k :

kth element of warping sequence

w K :

End point of warping sequence

W :

Warping sequence

ω :

Constant parameter in JWL equation

References

  • Aquelet N, Souli M, Olovsson L (2006) Euler-Lagrange coupling with damping effects: application to slamming problems. Comput Methods Appl Mech Eng 195(1–3):110–132

    Article  MathSciNet  Google Scholar 

  • Assent I, Wichterich M, Krieger R, Kremer H, Seidl T (2009) Anticipatory DTW for efficient similarity search in time series databases. Proc VLDB Endowment 2(1):826–837

    Article  Google Scholar 

  • Blum H, Lin Q, Rannacher R (1986) Asymptotic error expansion and Richardson extrapolation for linear finite elements. Numer Math 49(1):11–37

    Article  MathSciNet  Google Scholar 

  • Chang YW, Seong PH (2002) A signal pattern matching and verification method using interval means cross correlation and eigenvalues in the nuclear power plant monitoring systems. Ann Nucl Energy 29(15):1795–1807

    Article  Google Scholar 

  • Chung KY, Langdon GS, Nurick GN et al (2012) Response of V-shape plates to localised blast load: experiments and numerical simulation. Int J Impact Eng 46(4):97–109

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Kumar M (2002) A three-point finite difference method for a class of singular two-point boundary value problems. J Comput Appl Math 145(1):89–97

    Article  MathSciNet  Google Scholar 

  • Liu X, Chen W, Paas M (2005) Automated occupant model evaluation and correlation. In: ASME 2005 international mechanical engineering congress and exposition. American Society of Mechanical Engineers digital collection, pp 353-358

  • LSTC (2006) LS-DYNA theory manual. Livermore. https://www.dynasupport.com/manuals/additional/ls-dyna-theory-manual-2005-beta/view. Accessed March 2006

  • LSTC (2018) LS-DYNA keyword user’s manual version R11. Livermore. https://www.dynasupport.com/manuals. Accessed 18 October 2018

  • MathWorks (2016) Signal Processing Toolbox Documentation. MathWorks Inc. https://www.mathworks.com/help/signal/. Accessed 13 March 2016

  • Mertz HJ, Hodgson VR, Thomas LM et al (1978) An assessment of compressive neck loads under injury-producing conditions. Phys Sportsmed 6(11):95–106

    Article  Google Scholar 

  • NATO (2014) Procedures for evaluating the protection level of armoured vehicles-mine threat. North Atlantic Treaty Organization no. AEP-55(C) Vol 2, Australia

  • NATO-RTO (2007) Test methodology for protection of vehicle occupants against anti-vehicular landmine effects. North Atlantic Treaty Organization Research and Technology Organisation No. TR-HMF-090, France

  • Oberkampf WL, Barone MF (2005) Measures of agreement between computation and experiment: validation metrics. J Comput Phys 217(1):5–36

    Article  Google Scholar 

  • Ostraich B, Sadot O, Levintant O et al (2011) A method for transforming a full computation of the effects of a complex-explosion scenario to a simple computation by ConWep. Shock Waves 21(2):101–109

    Article  Google Scholar 

  • Sarin H, Kokkolaras M, Hulbert G, Papalambros P, Barbat S, Yang RJ (2008) A comprehensive metric for comparing time histories in validation of simulation models with emphasis on vehicle safety applications. In: ASME 2008 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers digital collection, pp 1275-1286

  • Sarin H, Kokkolaras M, Hulbert G, Papalambros P, Barbat S, Yang R-J (2010) Comparing time histories for validation of simulation models: error measures and metrics. J Dyn Syst Meas Control 132(6):061401

    Article  Google Scholar 

  • Schwer LE (2007) An overview of the PTC 60/V&V 10: guide for verification and validation in computational solid mechanics. Eng Comput 23(4):245–252

    Article  Google Scholar 

  • Trajkovski J, Perenda J, Kunc R (2018) Blast response of Light Armoured Vehicles (LAVs) with flat and V-hull floor. Thin-Walled Struct 131:238–244

    Article  Google Scholar 

  • Untaroiu CD, Shin J, Lu YC (2013) Assessment of a dummy model in crash simulations using rating methods. Int J Automot Technol 14(3):395–405

    Article  Google Scholar 

  • Wang J (2001) Simulation of landmine explosion using LS-Dyna3d software: benchmark work of simulation of explosion in soil and air. Defence Science & Technology Organisation no. DSTO-TR-1168, Australia

  • Wei R (2017) Multidisciplinary optimization of vehicle body structure based on blast shock resistance. Dissertation, Nanjing University of Science & Technology

  • Wei R, Wang X, Zhang M, Zhou Y, Wang L (2017) Application of dimension reduction based multi-parameter optimization for the design of blast-resistant vehicle. Struct Multidiscip Optim 56(4):903–917

    Article  Google Scholar 

  • Yang Y, Liou WW, Sheng J, Gorsich D, Arepally S (2013) Shock wave impact simulation of a vehicle occupant using fluid/structure/dynamics interactions. Int J Impact Eng 52(2):11–22

    Article  Google Scholar 

  • Zhan Z (2012) Bayesian based model validation method for uncertain multivariate dynamic systems under virtual prototype environment. J Mech Eng 48(5):138–138

    Article  Google Scholar 

  • Zhan Z, Fu Y, Yang RJ, Peng Y (2011a) An automatic model calibration method for occupant restraint systems. Struct Multidiscip Optim 44(6):815–822

    Article  Google Scholar 

  • Zhan Z, Fu Y, Yang RJ (2011b) Enhanced error assessment of response time histories (EEARTH) metric and calibration process. SAE 2011-01-0245

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Acknowledgments

The authors would like to acknowledge the Nanjing University of Science and Technology (NJUST) Vehicle Engineering Institute for the test and equipment support and the LetPub for its linguistic assistance during the preparation of this manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (grant number 51405232).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Nanjing University of Science & Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Qichen Zheng, Ran Wei, Mingxing Li, Xianhui Wang, Di Zhou & Tiaoqi Fu

Authors
  1. Qichen Zheng
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  2. Ran Wei
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  3. Mingxing Li
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  4. Xianhui Wang
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  5. Di Zhou
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Corresponding author

Correspondence to Xianhui Wang.

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The authors declare that they have no conflict of interest.

Code availability

MATLAB codes for calculations are available.

Replication of results

The authors cannot provide the keyword files for FEA and detail physical test data because of their confidentiality. So, the results presented in this paper cannot be reproduced perfectly. However, the readers can still replicate the calibration process with your own research object in similar area with codes for calculation available.

For software using, FEM was conducted by Hypermesh 2017; FEA was conducted by LS-Dyna with solver version R11; multi-objective optimization solving was conducted by ISight 2017; other calculations were conducted by MATLAB 2018b (MathWorks 2016). The DOE used for multi-objective optimization and the codes for calculation are available.

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Responsible editor: Raphael Haftka

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Zheng, Q., Wei, R., Li, M. et al. Occupant’s lower extremities’ impact-based model calibration for vehicle under-belly blast. Struct Multidisc Optim 63, 391–405 (2021). https://doi.org/10.1007/s00158-020-02668-3

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  • DOI: https://doi.org/10.1007/s00158-020-02668-3

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