Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty
This paper presents a novel method for determining parameters and uncertainty bands of nonlinear functions fitted to data obtained from measurements. In this procedure, one or two new variables are implemented to linearize this function for using the linear regression method. The best parameters of...
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MDPI AG
2024-12-01
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| Series: | Metrology |
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| Online Access: | https://www.mdpi.com/2673-8244/4/4/42 |
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| author | Zygmunt L. Warsza Jacek Puchalski Tomasz Więcek |
| author_facet | Zygmunt L. Warsza Jacek Puchalski Tomasz Więcek |
| author_sort | Zygmunt L. Warsza |
| collection | DOAJ |
| description | This paper presents a novel method for determining parameters and uncertainty bands of nonlinear functions fitted to data obtained from measurements. In this procedure, one or two new variables are implemented to linearize this function for using the linear regression method. The best parameters of the straight-line in new variables are adjusted to the transformed coordinates of tested points according to the weighted total mean square criterion WTLS, or WTLS-C of data points are also correlated. Uncertainties of measured points are found according to the rules of the GUM Guide. The parameters and the uncertainty band of the nonlinear function result from the parameters of this straight line and of its uncertainty band. A few examples determining the parameters and uncertainty bands of different types of nonlinear functions are presented. There are also examples of measurements using the presented method and conclusions. |
| format | Article |
| id | doaj-art-5621b10fd3974e069cfcc31cf39b4813 |
| institution | OA Journals |
| issn | 2673-8244 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metrology |
| spelling | doaj-art-5621b10fd3974e069cfcc31cf39b48132025-08-20T02:00:29ZengMDPI AGMetrology2673-82442024-12-014471873510.3390/metrology4040042Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and UncertaintyZygmunt L. Warsza0Jacek Puchalski1Tomasz Więcek2Industrial Research Institute for Automation and Measurements, Polish Metrological Society PTM, Warsza Szmaragdowych Żuków 32, 05-540 Zalesie Górne, PolandCentral Office of Measures GUM, Elektoralna 2, 00-139 Warsaw, PolandDepartment of Applied Optics, University of Technology Rzeszow, 35-959 Rzeszów, PolandThis paper presents a novel method for determining parameters and uncertainty bands of nonlinear functions fitted to data obtained from measurements. In this procedure, one or two new variables are implemented to linearize this function for using the linear regression method. The best parameters of the straight-line in new variables are adjusted to the transformed coordinates of tested points according to the weighted total mean square criterion WTLS, or WTLS-C of data points are also correlated. Uncertainties of measured points are found according to the rules of the GUM Guide. The parameters and the uncertainty band of the nonlinear function result from the parameters of this straight line and of its uncertainty band. A few examples determining the parameters and uncertainty bands of different types of nonlinear functions are presented. There are also examples of measurements using the presented method and conclusions.https://www.mdpi.com/2673-8244/4/4/42linear regression of nonlinear functionsfit to data of measured pointsWTLS weighted total least squares criteriumcorrelationcovariance matrixband of uncertainty |
| spellingShingle | Zygmunt L. Warsza Jacek Puchalski Tomasz Więcek Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty Metrology linear regression of nonlinear functions fit to data of measured points WTLS weighted total least squares criterium correlation covariance matrix band of uncertainty |
| title | Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty |
| title_full | Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty |
| title_fullStr | Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty |
| title_full_unstemmed | Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty |
| title_short | Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty |
| title_sort | novel method of fitting a nonlinear function to data of measurement based on linearization by change variables examples and uncertainty |
| topic | linear regression of nonlinear functions fit to data of measured points WTLS weighted total least squares criterium correlation covariance matrix band of uncertainty |
| url | https://www.mdpi.com/2673-8244/4/4/42 |
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