Advanced mathematical and statistical methods in evaluating instrumented indentation measurements

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00177016%3A_____%2F21%3AN0000017" target="_blank" >RIV/00177016:_____/21:N0000017 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14310/21:00120017

Výsledek na webu

<a href="http://nanometrologie.cz/niget/TJ02000203-V2.pdf" target="_blank" >http://nanometrologie.cz/niget/TJ02000203-V2.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Advanced mathematical and statistical methods in evaluating instrumented indentation measurements

Popis výsledku v původním jazyce

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" (result TJ02000203-V2). 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 this 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.

Název v anglickém jazyce

Advanced mathematical and statistical methods in evaluating instrumented indentation measurements

Popis výsledku anglicky

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" (result TJ02000203-V2). 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 this 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.

Druh

V_souhrn - Souhrnná výzkumná zpráva

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/TJ02000203" target="_blank" >TJ02000203: Pokročilé matematické a statistické metody ve vyhodnocování měření instrumentovanou indentací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Počet stran výsledku

67

Místo vydání

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Název nakladatele resp. objednatele

Technologická agentura České Republiky

Verze

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