Coupled systems mechanics

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Simple factor analysis of measured data

  • Received : 2021.08.08
  • Accepted : 2021.10.11
  • Published : 2022.02.25
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Abstract

Quite often we have a lot of measurement data and would like to find some relation between them. One common task is to see whether some measured data or a curve of known shape fit into the cumulative measured data. The problem can be visualized since data could generally be presented as curves or planes in Cartesian coordinates where each curve could be represented as a vector. In most cases we have measured the cumulative 'curve', we know shapes of other 'curves' and would like to determine unknown coefficients that multiply the known shapes in order to match the measured cumulative 'curve'. This problem could be presented in more complex variants, e.g., a constant could be added, some missing (unknown) data vector could be added to the measured summary vector, and instead of constant factors we could have polynomials, etc. All of them could be solved with slightly extended version of the procedure presented in the sequel. Solution procedure could be devised by reformulating the problem as a measurement problem and applying the generalized inverse of the measurement matrix. Measurement problem often has some errors involved in the measurement data but the least squares method that is comprised in the formulation quite successfully addresses the problem. Numerical examples illustrate the solution procedure.

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Acknowledgement

The research described in this paper was financially supported through project HRZZ 7926 "Separation of parameter influence in engineering modeling and parameter identification" and project KK.01.1.1.04.0056 "Structure integrity in energy and transportation", which is gratefully acknowledged.

References

  1. Gibbs, B.P. (2011), Advanced Kalman Filtering, Least-Squares and Modeling, Wiley, Hoboken, New Jersey.
  2. Ibrahimbegovic, A., Herve, G. and Villon, P. (2009), "Nonlinear impact dynamics and field transfer suitable for parametric design studies", Eng. Comput., 26(1/2), 185-204. https://doi.org/10.1108/02644400910924861.
  3. Ibrahimbegovic, A., Mathies, H.G. and Karavelic, E. (2020), "Reduced model of macro-scale stochastic plasticity identification by Bayesian inference in application to quasi-brittle failure of concrete", Comput. Meth. Appl. Mech. Eng., 372, 113428. https://doi.org/10.1016/j.cma.2020.113428.
  4. JCGM 100 (2008), Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement, Joint Committee for Guides in Metrology.
  5. Kozar, I. (2016), "Relating structure and model", Computational Methods for Solids and Fluids, Multiscale Analysis, Probability Aspects and Model Reduction, Ed. A. Ibrahimbegovic, Springer, New York, USA,
  6. Kozar, I. and Lozzi-Kozar, D. (2017), "Flux determination using finite elements: global vs. local calculation", Technical Gazette, 24, 247-252. https://doi.org/10.17559/TV-20160208123711.
  7. Kozar, I., Lozzi Kozar, D. and Jericevic, Z. (2011), "Limit kriging in finite element environmental modeling", International Convention on Information, Communication and Electronic Technology MIPRO, Opatija, Croatia.
  8. Kozar, I., Toric Malic, N. and Rukavina, T. (2018), "Inverse model for pullout determination of steel fibers", Couple. Syst. Mech., 7, 197-209. https://doi.org/10.12989/csm.2018.7.2.197.
  9. Kozar, I., Toric Malic, N., Simonetti, D. and Bozic, Z. (2020), "Stochastic properties of bond-slip parameters at fibre pull-out", Eng. Fail. Anal., 111, 104478. https://doi.org/10.1016/j.engfailanal.2020.104478.
  10. Lozzi-Kozar, D. and Kozar, I. (2017), "Estimation of the eddy thermal conductivity for Lake Botonega", Eng. Rev., 37, 322-334.
  11. Menke, W. (2012), Geophysical Data Analysis: Discrete Inverse Theory, Academic Press Elsevier, Cambridge, Massachusetts, USA.
  12. Nielsen, M.A. (2015), Neural Networks and Deep Learning, Determination Press.
  13. Sarfaraz, S.M., Rosic, B.V, Matthies, H.G. and Ibrahimbegovic, A. (2018), "Stochastic upscaling via linear bayesian updating", Couple. Syst. Mech., 7, 211-231. http://doi.org/10.12989/csm.2018.7.2.211.