Distance Fibonacci Polynomials—Part II

Wind energy is one of the speedy processing technologies in the energy generation industry and the most economical methods of electrical power generation. For the reliability of system, it is wanted to improve highly appropriate wind speed forecasting methods. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. This technique has proven useful in a nonstationary time series forecasting. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Lucas polynomials, as well as a comparison between an artificial neural network (ANN) and wavelet-artificial neural network (WNN). We used the proposed wavelet, Mexican hat, Morlet, Gaussian, Haar, Daubechies, and Coiflet to transform the wind speed data using the continuous wavelet transform (CWT). MATLAB software was used to implement the CWT and ANN. The proposed models were applied in the meteorological field to forecast the daily wind speed data that were collected from the meteorological directorate of Sulaymaniyah which is a city located in the Kurdistan region of Iraq for the period (Jan. 2011–Dec. 2020). Five different performance criteria during calibration and validation, the root mean square error ( R M S E ), mean square error ( M S E ), mean absolute percentage error M A P E , mean absolute error M A E , and coefficient of determination ( R 2 ), were evaluated. When studying, analyzing, and comparing these models, the results of the study concluded that the proposed wavelet-ANN is the best result ( M S E = 0.00072 , R M S E = 0.02683 , M A P E = 2.32400 , and R 2 = 0.99983 .

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“…Bicknell studied the Lucas polynomials in 1970 [37]. It is defned as the sum of the two terms immediately preceding it.…”

Section: Methodsmentioning

confidence: 99%

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

Mohammed

Ahmed

2023

Discrete Dynamics in Nature and Society

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“…In [4], the authors gave a new generalization of Lucas polynomials in the distance sense. Moreover, L(k, n)-Lucas hybrid numbers LH k n were investigated in [22].…”

Section: Corollarymentioning

confidence: 99%

A new hybrid generalization of Fibonacci and Fibonacci-Narayana polynomials

Bród,

Szynal-Liana

2023

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Special Issue Editorial “Special Functions and Polynomials”

Ricci

2022

Symmetry

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This Special Issue contains 14 articles from the MDPI journal Symmetry on the general subject area of “Special Functions and Polynomials”, written by scholars belonging to different countries of the world. A similar number of submitted articles was not accepted for publication. Several successful Special Issues on the same or closely related topics have already appeared in MDPI’s Symmetry, Mathematics and Axioms journals, in particular those edited by illustrious colleagues such as Hari Mohan Srivastava, Charles F. Dunkl, Junesang Choi, Taekyun Kim, Gradimir Milovanović, and many others, who testify to the importance of this matter for its applications in every field of mathematical, physical, chemical, engineering and statistical sciences. The subjects treated in this Special Issue include, in particular, the following Keywords.

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Distance Fibonacci Polynomials—Part II

Cited by 4 publications

References 17 publications

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

A new hybrid generalization of Fibonacci and Fibonacci-Narayana polynomials

Special Issue Editorial “Special Functions and Polynomials”

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