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Indirect Measurement of Tensile Strength of Materials by Grey Prediction Models GMC(1,n) and GM(1,n)

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Titel: Indirect Measurement of Tensile Strength of Materials by Grey Prediction Models GMC(1,n) and GM(1,n)
Autoren: Tzu-Li Tien
Quelle: Engineering Proceedings ; Volume 92 ; Issue 1 ; Pages: 4
Verlagsinformationen: Multidisciplinary Digital Publishing Institute
Publikationsjahr: 2025
Bestand: MDPI Open Access Publishing
Schlagwörter: GM(1,n) model, GMC(1,n) model, unit impulse response function, convolution integral, indirect measurement
Beschreibung: Grey theory is applied to forecasting, decision-making, and control as this theory is appropriate for predictive analysis. Incomplete information is a primary characteristic of the grey system, necessitating the supplementation of information to transform the relationships between various information elements from grey to white and improve the accuracy of predictive models. However, for the first-order grey prediction model with n variables, specifically the traditional GM(1,n) model, modelling values are derived using a rough approximation method. It is assumed in this method that the elements of the one-order accumulated generating series of each associated series are constant, leading to an unreasonable relationship between the forecast series and the associated series, which is fundamentally an incorrect model. The elements of a non-negative series’s one-order accumulated generating series cannot be constants; even if they are constant series, this is not true. Consequently, the traditional GM(1,n) model yields significant errors. There have been few papers addressing the errors of this model. To improve the GM(1,n) model, correct algorithms must be used by incorporating convolution algorithms or fitting system action quantities with basic functions to derive particular solutions. The modelling procedure of the grey convolution prediction model GMC(1,n) demonstrates that the traditional grey prediction model GM(1,n) is incorrect.
Publikationsart: text
Dateibeschreibung: application/pdf
Sprache: English
Relation: https://dx.doi.org/10.3390/engproc2025092004
DOI: 10.3390/engproc2025092004
Verfügbarkeit: https://doi.org/10.3390/engproc2025092004
Rights: https://creativecommons.org/licenses/by/4.0/
Dokumentencode: edsbas.A300A761
Datenbank: BASE
Beschreibung
Abstract:Grey theory is applied to forecasting, decision-making, and control as this theory is appropriate for predictive analysis. Incomplete information is a primary characteristic of the grey system, necessitating the supplementation of information to transform the relationships between various information elements from grey to white and improve the accuracy of predictive models. However, for the first-order grey prediction model with n variables, specifically the traditional GM(1,n) model, modelling values are derived using a rough approximation method. It is assumed in this method that the elements of the one-order accumulated generating series of each associated series are constant, leading to an unreasonable relationship between the forecast series and the associated series, which is fundamentally an incorrect model. The elements of a non-negative series’s one-order accumulated generating series cannot be constants; even if they are constant series, this is not true. Consequently, the traditional GM(1,n) model yields significant errors. There have been few papers addressing the errors of this model. To improve the GM(1,n) model, correct algorithms must be used by incorporating convolution algorithms or fitting system action quantities with basic functions to derive particular solutions. The modelling procedure of the grey convolution prediction model GMC(1,n) demonstrates that the traditional grey prediction model GM(1,n) is incorrect.
DOI:10.3390/engproc2025092004