An Efficient Iterative Methods for Solving Transcendental Equations

Kaur, Samandeep; Sharma, Shiv K.

doi:10.1007/978-981-99-2468-4_15

Cited by 1 publication

(1 citation statement)

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“…However, this approach necessitates determining two parameters: the atenua-�on coefficient α and the constant c . Employing the method of least squares in this context necessitates solving a system of two transcendental equa�ons, which demands the applica�on of numerical methods [31]. Such a requirement significantly complicates the algorithm and reduces its computa�onal speed.…”

Section: Mathematical Model Of Anisotropic Spectral Synthesismentioning

confidence: 99%

Generation of Anisotropic Cloud Cover

Martyniuk,

Zhuikov

2023

Microsyst., Electron. & Acoust.

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This paper introduces an advanced mathematical model for generating and analyzing cloud cover images, specifically designed to enhance photovoltaic (PV) partial shading studies. The model development involved a detailed analysis of real cloud cover images, with a particular emphasis on capturing their anisotropic spectral characteristics. This was achieved through a combination of spectral analysis and advanced image processing techniques. The research methodologically focused on developing a four-parameter model to accurately represent cloud formations' spectral properties. Key parameters were identified and fine-tuned to match the real cloud formations' characteristics. This involved analyzing the magnitude and phase spectra of the cloud covers and fitting them to a model capable of replicating these properties accurately. A significant part of the research was dedicated to formulating a novel phase spectrum generation technique. This technique was specifically designed to control the degree of similarity between the synthesized and original images, thereby ensuring the model's effectiveness in various simulation scenarios. The process involved manipulating the phase information of cloud cover images while maintaining their high-frequency components to enhance the detail and realism of the synthesized images. The model's accuracy in replicating cloud cover features was tested against traditional spectral synthesis methods. This comparative analysis involved generating cloud cover images using the developed model and established methods, then comparing these images to the original cloud covers in terms of visual similarity and approximation error. Additionally, the model was utilized to generate pseudo-random cloud cover images by varying the phase spectrum parameters. This process ensured that the generated images, while being random, adhered to the spectral characteristics of the original cloud covers. The research methodology also involved a detailed examination of the images' key characteristics, such as direction, length, and density, to ensure fidelity to the original samples. In summary, this paper details an approach to cloud cover image synthesis, with a focus on the accuracy of spectral properties and the development of an algorithm of model parameters estimation. The research highlights the use of advanced spectral analysis and image processing techniques in deriving key model parameters, leading to a significant advancement in cloud imaging for solar energy applications.

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Section: Mathematical Model Of Anisotropic Spectral Synthesismentioning

confidence: 99%