Fractional order modeling and recognition of nitrogen content level of rubber tree foliage

Hu, Wenfeng; Tang, Rongnian; Li, Chuang; Zhou, Teng; Jing, Chen; Chen, Kai

doi:10.1177/0967033520966693

Cited by 15 publications

(3 citation statements)

References 50 publications

(48 reference statements)

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“…Many mathematical definitions of the FOD have been developed, such as the Riemann-Liouville, Caputo, and Grunwald-Letnikov methods [34]. Among these methods, the Grunwald-Letnikov method performs well in inversion and evaluation [35].…”

Section: Fodmentioning

confidence: 99%

Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods

Dou,

Zhang,

Deng

et al. 2024

Horticulturae

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Citrus tangerines are famous fruits worldwide, and monitoring the water content of citrus leaves is highly important for citrus production. However, there are still challenges in quantitatively estimating the water content of citrus leaves using hyperspectral technology, and the random noise generated during spectral acquisition and the overlapping peaks in the sensitive band of the citrus leaf water content will affect estimation accuracy. To solve these problems and further explore the roles of the continuous wavelet transform (CWT) and fractional-order derivative (FOD) in the estimation of citrus leaf water content, this study intends to use of CWT and FOD to decompose the original spectrum, and then compare the correlation between the original spectrum and leaf water content to explore whether the decomposition treatment has improved the correlation between spectrum and leaf moisture content. Then, the successive projections algorithm (SPA) was used to select feature bands and combine spectral vegetation indices. Partial least squares regression (PLSR) was used to construct water-content inversion models for citrus leaves, and the inversion accuracies of two commonly used spectral preprocessing methods were compared. The results indicate that (1) the CWT can improve the sensitivity of the spectrum to the citrus leaf water content to a certain extent, and the inversion accuracy of the CWT is approximately 5% greater than that of the FOD. (2) On the basis of the CWT and FOD methods, the inversion accuracy of the citrus leaf water content based on SPA screening increased by 9.61% and 9.29%, respectively, compared with the original spectrum. (3) Under CWT decomposition, Scale4 of the Gaus1 wavelet was screened by the SPA, and the inversion model of citrus leaf water content was constructed by combining the spectral vegetation index NDVI with the best results. The R-squared (R2) and root mean square error (RMSE) values were 0.7491 and 0.0284, respectively, which were both 0.0138 greater than those of the best inversion model for the FOD R2. In conclusion, the CWT-SPA combined with the spectral vegetation index can improve the sensitivity of the spectrum to the citrus leaf water content, eliminate a large amount of redundant data, and enhance the prediction ability and stability of the citrus leaf water content.

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Section: Fodmentioning

confidence: 99%

Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods

Dou,

Zhang,

Deng

et al. 2024

Horticulturae

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“…The same idea, i.e., to augment Vis-NIR data using the G-L derivative to improve machine learning estimates, is used in both [24,25] to estimate the nitrogen content of rubber tree cultivations and in [26] for cotton farming. The employed machine learning algorithms range from partial least squares regression, extreme learning machines, convolutional neural networks, and support vector machines.…”

Section: Spectroscopymentioning

confidence: 99%

Combining Fractional Derivatives and Machine Learning: A Review

Raubitzek

Mallinger²,

Neubauer³

2022

Entropy

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Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of which is that fractional derivatives inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It has provided many further insights and discoveries in various scientific disciplines. As these two modern-day topics hold a lot of potential for combined approaches in terms of describing complex dynamics, this article review combines approaches from fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there is already extensive literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning and fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools, and enhance their existing approaches.

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“…The same idea, i.e., to augment Vis-NIR data using the G-L derivative to improve machine learning estimates, is used in both [22] and [23] to estimate the nitrogen content of rubber tree cultivations and in [24] for cotton farming. The employed machine learning algorithms range from partial least squares regression, extreme learning machines, convolutional neural networks, and support vector machines.…”

Section: Spectroscopymentioning

confidence: 99%

Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

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Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

show abstract

Fractional order modeling and recognition of nitrogen content level of rubber tree foliage

Cited by 15 publications

References 50 publications

Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods

Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods

Combining Fractional Derivatives and Machine Learning: A Review

Combining Fractional Derivatives and Supervised Machine Learning: A Review

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