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@misc{49526,
author = {Charvátová Campbell, Anna and Geršlová, Zdeňka and Šindlář, Vojtěch and Šlesinger, Radek and Šperka, Jiří and Wimmer, Gejza and Zámečník, Stanislav},
address = {Neuveden},
keywords = {Instrumented indentation; uncertainties; Oliver-Pharr method; orthogonal data regression; experimental design; Niget software; R (programming language)},
language = {eng},
location = {Neuveden},
publisher = {Technology Agency of the Czech Republic},
title = {Advanced mathematical and statistical methods in evaluating instrumented indentation measurements},
url = {https://is.muni.cz/auth/publication/1842419/TJ02000203-V2.pdf},
year = {2021}
}
TY - GEN
ID - 49526
AU - Charvátová Campbell, Anna - Geršlová, Zdeňka - Šindlář, Vojtěch - Šlesinger, Radek - Šperka, Jiří - Wimmer, Gejza - Zámečník, Stanislav
PY - 2021
TI - Advanced mathematical and statistical methods in evaluating instrumented indentation measurements
VL - Neuveden
PB - Technology Agency of the Czech Republic
CY - Neuveden
KW - Instrumented indentation
KW - uncertainties
KW - Oliver-Pharr method
KW - orthogonal data regression
KW - experimental design
KW - Niget software
KW - R (programming language)
UR - https://is.muni.cz/auth/publication/1842419/TJ02000203-V2.pdf
N2 - This publicly available research report provides a detailed overview of the results achieved within the TACR project TJ02000203 "Advanced mathematical and statistical methods in evaluating instrumented indentation measurements". The introductory section contains necessary background on instrumented indentation data evaluation procedures using the method due to Oliver and Pharr, as described in ISO 14577 standard. The next section provides detailed derivation of a novel algorithm "OEFPIL" for nonlinear data regression with errors in both variables, as well as guidelines for efficient implementation of the algorithm. The algorithm calculates both the optimum estimate of function parameters and an estimate of the parameter covariance matrix. The algorithm performance is demonstrated on reference data for nonlinear regression, and validated by comparison to another method. In the next section some existing advanced methods for uncertainty propagation (higher-order uncertainty propagation, Latin hypercube sampling for Monte Carlo) are also discussed. The last section presents application of the aforementioned methods for data regression and uncertainty propagation in processing data from instrumented indentation measurements. These methods have been newly added to the the free software tool Niget to improve data fitting of the unloading curve and to provide capability for indenter contact area function calibration. Combination of the regression and uncertainty propagation methods enables a better insight into evaluation of indentation data and provides basis for e.g. identifying main sources of measurement uncertainty or designing measurement strategy. Although the methods were designed and assessed with Oliver and Pharr's evaluation method in mind, they can be easily adapted to other evaluation models, too. All software developed and used in this project is freely available.
ER -
CHARVÁTOVÁ CAMPBELL, Anna, Zdeňka GERŠLOVÁ, Vojtěch ŠINDLÁŘ, Radek ŠLESINGER, Jiří ŠPERKA, Gejza WIMMER a Stanislav ZÁMEČNÍK. \textit{Advanced mathematical and statistical methods in evaluating instrumented indentation measurements}. Neuveden: Technology Agency of the Czech Republic, 2021, 67 s.
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