Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis
AbstractA fractional-calculus-based model is used to analyze the data obtained from the image analysis of mixtures of olive and soybean oil, which were quantified with the RGB color system. The model consists in a linear fractional differential equation, containing one fractional derivative of order α and an additional term multiplied by a parameter k. Using a hybrid parameter estimation scheme (genetic algorithm and a simplex-based algorithm), the model parameters were estimated as k = 3.42 ± 0.12 and α = 1.196 ± 0.027, while a correlation coefficient value of 0.997 was obtained. For the sake of comparison, parameter α was set equal to 1 and an integer order model was also studied, resulting in a one-parameter model with k = 3.11 ± 0.28. Joint confidence regions are calculated for the fractional order model, showing that the derivative order is statistically different from 1. Finally, an independent validation sample of color component B equal to 96 obtained from a sample with olive oil mass fraction equal to 0.25 is used for prediction purposes. The fractional model predicted the color B value equal to 93.1 ± 6.6. View Full-Text
Share & Cite This Article
Lenzi, E.K.; Ryba, A.; Lenzi, M.K. Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis. Fractal Fract 2018, 2, 11.
Lenzi EK, Ryba A, Lenzi MK. Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis. Fractal and Fractional. 2018; 2(1):11.Chicago/Turabian Style
Lenzi, Ervin K.; Ryba, Andrea; Lenzi, Marcelo K. 2018. "Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis." Fractal Fract 2, no. 1: 11.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.