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The influence of rainfall time series fractality on forecasting models’ efficiency

Rahmani Farhang, Fattahi Mohammad Hadi

Acta Geophysica

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2022

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Vol. 70, no 3

1349--1361

EN

Forecasting rainfall time series is of great significance for hydrologists and geoscientists. Thus, this study represents a contribution to understanding the impact of the fractal time series variety on forecasting model performance. Multiple fractal series were generated via p-model and used for modeling. Subsequently, the forecasting was delivered based on existing observed monthly rainfall data (three stations in the UK, from 1865 to 2002) through five forecasting models. Finally, the association between series fractality and models’ performance was examined. The results indicated that the forecasting based on the mono-fractal series resulted in the most reliable results (R2=1 and RMSE less than 0.02). In the case of multifractal series, modeling based on series with the right side of the asymmetric curve of the multifractal spectrum presented series with the lowest RMSE (0.96) and highest R2 (0.99) (desirable performance). In contrast, the forecasting based on series with the left side of the asymmetric curve of the multifractal spectrum suggested the most unreliable outcomes (R2 range [−0.0007 ~ 0.988] and RMSE range [0.8526 ~ 39.3]). The forecasting based on the symmetric curve of the multifractal spectrum series delivered regular performance. Accordingly, high and low errors are expected from forecasting based on the time series with a left-skewed multifractal spectrum and right-skewed multifractal spectrum (and mono-fractal time series), respectively. Hybrid models were the best options for forecasting mono-fractal and multifractal time series with right side asymmetric and symmetric multifractal spectrum curves. The ARIMA model was suitable to predict multifractal time series with left side asymmetric multifractal spectrum curves.

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Structure, physical properties and fractal characteristics of the arc PVD coatings deposited onto the ceramics materials

Kwaśny W.

Archives of Computational Materials Science and Surface Engineering

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2010

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Vol. 2, nr 4

189-200

EN

Purpose: The goal of the presented study was to develop a methodology giving a possibility to predict functional properties of coatings obtained in the arc PVD process onto the ceramics materials, based on fractal and multi-fractal quantities describing their surface. Design/methodology/approach: Effect of process type and deposition conditions on structure and shape of surface, as well as mechanical and service properties of the obtained coatings were determined. Methodology and detailed description of coatings topography obtained in the PVD process on ceramics materials, including use of the fractal- and multi-fractal geometry based on images obtained on the atomic forces microscope were worked out. Relationships between fractal- and multi-fractal quantities and their mechanical and service properties were determined. Findings: The investigation results confirmed the feasibility to predict the service properties defined in the cutting ability test for coatings obtained in the arc PVD process, based on the surface fractal dimension Ds value for their surface topography. Research limitations/implications: The geometrical features description of surfaces of the coatings obtained in the PVD processes. Practical implications: Determining significant quantitative correlations between fractal quantities defining coatings' surfaces, as well as their service and/or mechanical properties provides the opportunity to predict their end-user properties. Originality/value: Fractal and multifractal analysis gives possibility to characterise the extent of irregularities of the analysed surface in the quantitative way.

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A modification of the method for determination of surface fractal dimension and multifractal analysis

Kwaśny W.

Journal of Achievements in Materials and Manufacturing Engineering

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2009

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Vol. 33, nr 2

115-125

EN

Purpose: In this work modification of the PCM method for determination of the surface fractal dimension is proposed. Complete reasoning, leading to correct formula for determination Ai(ä) is presented. In order to test modified method, data sets characterised by fractional fractal dimension were generated. Design/methodology/approach: Three different algorithms to receive data sets describing surfaces with fractional fractal dimension were exploited (two algorithms of midpoint displacement and Falconer algorithm). Findings: In this work detailed methodology for surface multifractal description, which may be directly applied for data obtained from the AFM microscope, was presented. Research limitations/implications: The geometrical features description of surfaces of the coatings obtained in the PVD and CVD processes. Practical implications: In presented work modified PCM method for determination of the surface fractal dimension was proposed. Performed calculations proved that new method make possible to determine this parameter more correctly. Differences are especially significant for rough surfaces, as what tested using series of data sets generated by algorithms for modelling surfaces with fractional fractal dimension. Proposed modified method for determination of the fractal dimension can be used for description of the geometrical features of coatings obtained in the PVD and CVD processes. Originality/value: Fractal and multifractal analysis gives possibility to characterise the extent of irregularities of the analysed surface in the quantitative way.