Publication details
Advanced mathematical and statistical methods in evaluating instrumented indentation measurements
| Authors | |
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| Year of publication | 2021 |
| MU Faculty or unit | |
| web | https://is.muni.cz/auth/publication/1842419/TJ02000203-V2.pdf |
| Attached files | |
| Description | 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. |
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