Quantification of Uncertainty in the Mathematical Modelling of a Multivariable Suspension Strut Using Bayesian Interval Hypothesis-Based Approach


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Mathematical models of a suspension strut such as an aircraft landing gear are utilized by engineers in order to predict its dynamic response under different boundary conditions. The prediction of the dynamic response, for example the external loads, the stress and the strength as well as the maximum compression in the spring-damper component aids engineers in early decision making to ensure its structural reliability under various operational conditions. However, the prediction of the dynamic response is influenced by model uncertainty. As far as the model uncertainty is concerned, the prediction of the dynamic behavior via different mathematical models depends upon various factors such as the model's complexity in terms of the degrees of freedom, material and geometrical assumptions, their boundary conditions and the governing functional relations between the model input and output parameters. The latter can be linear or nonlinear, axiomatic or empiric, time variant or time-invariant. Hence, the uncertainty that arises in the prediction of the dynamic response of the resulting different mathematical models needs to be quantified with suitable validation metrics, especially when the system is under structural risk and failure assessment. In this contribution, the authors utilize the Bayesian interval hypothesis-based method to quantify the uncertainty in the mathematical models of the suspension strut.



Edited by:

Peter F. Pelz and Peter Groche




S. Mallapur and R. Platz, "Quantification of Uncertainty in the Mathematical Modelling of a Multivariable Suspension Strut Using Bayesian Interval Hypothesis-Based Approach", Applied Mechanics and Materials, Vol. 885, pp. 3-17, 2018

Online since:

November 2018


* - Corresponding Author

[1] Oberkampf, W., Timothy, T., Verification and Validation in Computational Fluid Dynamics,, Progress in Aerospace Sciences, 2002, pp.209-272.

DOI: https://doi.org/10.1016/s0376-0421(02)00005-2

[2] Oberkampf, W., DeLand, S., Rutherford, B., Diegert, K., Alvin, K., Error and uncertainty in modelling and simulation,, Reliability Engineering and System Safety, 2002, pp.333-357.

DOI: https://doi.org/10.1016/s0951-8320(01)00120-x

[3] Kennedy, M., O'Hagan, A., Bayesian Calibration of Computer Models,, Journal of the Royal Statistical Society, Vol. 63, No. 3, 2001, pp.425-464.

[4] Rebba, R., Huang, S., Liu, Y., Mahadevan, S.,Statistical validation of simulation models,, Int. J. Materials and Product Technology, Vol. 25, (2006).

[5] Liu, Y., Chen, W., Arendt, P., Huang, H., Toward a better understanding of model validation metrics,, Journal of Mechanical Design, Vol.133, (2011).

[6] Zhao, L., Lu, Z., Yun, W., Wang, W., Validation metric based on Mahalanobis distance for models with multiple correlated responses,, Reliability Engineering and System Safety, 2017, pp.80-89.

DOI: https://doi.org/10.1016/j.ress.2016.10.016

[7] Roy, C., Oberkampf, W., A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing,, Comput. Methods Appl. Mech. Engrg., Orlando, 2011, pp.2131-2144.

[8] ASME, Guide for Verification and Validation in Computational Solid Mechanics,, ASME Standard 10-2006, New York, (2006).

[9] Zhan Z., Fu, Y., Jang, R.,Bayesian based multivariate model validation method under uncertainty for dynamic systems,, Journal of Mechanical Design,Vol. 134, (2012).

DOI: https://doi.org/10.1115/1.4005863

[10] Mahadevan, S.,Uncertainty quantification for Decision-Making in Engineered Systems,, In: Proceedings of the International Symposium on Engineering under Uncertainty: Safety Assessment and Management, (2013).

DOI: https://doi.org/10.1007/978-81-322-0757-3_5

[11] Ling, Y., Sankaraman, S.,Quantitative model validation techniques: New insights,, Reliability Engineering and System Safety, 2013, pp.217-231.

DOI: https://doi.org/10.1016/j.ress.2012.11.011

[12] Sankararaman, S., Mahadevan, S., Model validation under epistemic uncertainty,, Reliability Engineering and System Safety, 2011, pp.1232-1241.

DOI: https://doi.org/10.1016/j.ress.2010.07.014

[13] Sankararaman, S., Ling, Y., Mahadevan, S.,Uncertainty quantification and model validation of fatigue crack growth prediction,, Reliability Engineering and System Safety, 2011, pp.1487-1504.

DOI: https://doi.org/10.1016/j.engfracmech.2011.02.017

[14] Mahadevan, S., Rebba, R.,Validation of reliability computational models using Bayes networks,, Reliability Engineering and System Safety, 2011, pp.223-232.

DOI: https://doi.org/10.1016/j.ress.2004.05.001

[15] Jiang, X., Mahadevan, S.,Bayesian validation assessment of multivariate computational models,, Journal of Applied Statistics, Vol. 35, 2008, pp.45-65.

[16] Zhan, Z., Fu, Y., Yang, R., An Enhanced Bayesian based model validation method for dynamic systems,, Journal of Mechanical Design, Vol. 133, (2011).

[17] Platz, R., Ondoua, S., Habermehl, K., Bedarff, T., Hauer, T., Schmitt, S., Hanselka, H.: Approach to validate the influences of uncertainties in manufacturing on using load-carrying structures, USD 2010 International Conference on Uncertainty in Structural Dynamics, 20-22 Sep., Leuven, pp.5319-5333, (2010).

[18] Melzer, C., Platz, R., Melz, T., Comparison of Methodical Approaches to Describe and Evaluate Uncertainty in the Load-Bearing Capacity of a Truss Structure,, Fourth International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering, Civil-Comp Press, Stirlingshire, United Kingdom, paper 26, (2015).

DOI: https://doi.org/10.4203/ccp.109.26

[19] Li, S. and Platz, R. (2017).

[20] Jiang, X., Mahadevan, S., Bayesian wavelet method for multivariate model assessment of dynamic systems,, Journal of Sound and Vibration, (2007).

[21] Enss, G., Gehb, C., Götz, B.; Melz, T., Ondoua, S., Platz, R., Schäffner, M., Load transferring device, Patent DE102014106858.A1, (2015).

[22] Schaeffner, M., Goetz, B., Platz, R., Active buckling control of a beam-column with circular cross-section using piezoelastic supports and integral LQR control,, Journal of Smart Materials and Structures, (2016).

DOI: https://doi.org/10.1088/0964-1726/25/6/065008

[23] Gehb, C. ,Platz, R., Melz, T., Active load path adaption in a simple kinematic load-bearing structure due to stiffness change in the structure supports,, Journal of Physics, Conference Series 744, (2016).

DOI: https://doi.org/10.1088/1742-6596/744/1/012168

[24] Goetz, B., Schaeffner, M., Platz, R., Melz, T.: Lateral vibration attenuation of a beam with circular cross-section by a support with integrated piezoelectric transducers shunted to negative capacitances,, Journal of Smart Materials and Structures, (2016).

DOI: https://doi.org/10.1088/0964-1726/25/9/095045

[25] Enss, G., Platz, R., Evaluation of uncertainty in experimental active buckling control of a slender beam-column using Weibull analysis,, Journal of Mechanical Systems and Signal Processing, (2016).

DOI: https://doi.org/10.1016/j.ymssp.2016.02.066

[26] Schaeffner, M., Platz, R., Gain-Scheduled H∞ Buckling control of a Circular Beam-Column Subject to Time-Varying Axial Loads,, Smart Materials and Structures (IOP Publishing Ltd), 27(6), 065009, (2018).

DOI: https://doi.org/10.1088/1361-665x/aab63a

[27] Goetz, B. , Platz, R. and Melz, T. (2018), Effect of static axial loads on the lateral vibration attenuation of a beam with piezo-elastic supports,, Smart Materials and Structures (IOP Publishing Ltd), 27(3), 035011, (2018).

DOI: https://doi.org/10.1088/1361-665x/aaa937

[28] Goetz, B., Platz, R. and Melz, T. (2017).

[29] Dean, A., Voss, D. Design and Analysis of Experiments,, Springer Verlag New York, (1999).

[30] Pan, H., Castanier, M., Model Validation for simulations of vehicle systems,, In: Proccedings of MSTV Mini Symposium, Michigan, (2012).

[31] Winkler, R.: Introduction to Bayesian Inference and Decision,, Holt, Rinehart and Winston Inc., (1972).