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Coupled Systems Mechanics Volume 11, Number 1, February 2022 , pages 33-41 DOI: https://doi.org/10.12989/csm.2022.11.1.033 |
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Simple factor analysis of measured data |
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Ivica Kozar, Danila Lozzi Kozar and Neira Toric Malic
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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. | ||
| Key Words | ||
| factor analysis; least squares method; measurement data; measurement error; measurement problem | ||
| Address | ||
| Ivica Kozar: Faculty of Civil Engineering, University of Rijeka, Radmile Matejcic 3, 51000 Rijeka, Croatia Danila Lozzi Kozar: Croatian Waters-Unit Rijeka, dure Sporera Street 3, 51000 Rijeka, Croatia Neira Toric Malic: Faculty of Civil Engineering, University of Rijeka, Radmile Matejcic 3, 51000 Rijeka, Croatia | ||
