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1

Integrated preprocessing techniques with linear stochastic approaches in groundwater level forecasting

Azari Arash, Zeynoddin Mohammad, Ebtehaj Isa, Sattar Ahmed M. A., Gharabaghi Bahram, Bonakdari Hossein

Acta Geophysica

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2021

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Vol. 69, no. 4

1395--1411

EN

Accurate modeling of groundwater level (GWL) is a critical and challenging issue in water resources management. The GWL fuctuations rely on many nonlinear hydrological variables and uncertain factors. Therefore, it is important to use an approach that can reduce the parameters involved in the modeling process and minimize the associated errors. This study presents a novel approach for time series structural analysis, multi-step preprocessing, and GWL modeling. In this study, we identifed the time series deterministic and stochastic terms by employing a one-, two-, and three-step preprocessing techniques (a combination of trend analysis, standardization, spectral analysis, diferencing, and normalization techniques). The application of this approach is tested on the GWL dataset of the Kermanshah plains located in the northwest region of Iran, using monthly observations of 60 piezometric stations from September 1991 to August 2017. By removing the dominant nonstationary factors of the GWL data, a linear model with one autoregressive and one seasonal moving average parameter, detrending, and consecutive non-seasonal and seasonal diferencing were created. The quantitative assessment of this model indicates the high performance in GWL forecasting with the coefcient of determination (R2 ) 0.94, scatter index (SI) 0.0004, mean absolute percentage error (MAPE) 0.0003, root mean squared relative error (RMSRE) 0.0004, and corrected Akaike’s information criterion (AICc) 151. Moreover, the uncertainty and accuracy of the proposed linear-based method are compared with two conventional nonlinear methods, including multilayer perceptron artifcial neural network (MLP-ANN) and adaptive neuro-fuzzy inference systems (ANFIS). The uncertainty of the proposed method in this study was±0.105 compared to±0.114 and±0.126 for the best results of the ANN and the ANFIS models, respectively.

2

Studium stochastyki obciążeń w aspekcie zdefiniowania trwałości zmęczeniowej wieloczynnościowego agregatu do sadzenia ziemniaków

Spadło M.

Journal of Research and Applications in Agricultural Engineering

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2013

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Vol. 58, nr 1

162--167

PL

W artykule zawarto opis studium stochastyki obciążeń. Badania przeprowadzono na potrzeby oszacowania trwałości zmęczeniowej agregatu do sadzenia ziemniaków. Określono wpływ obciążeń na naprężenia w wybranych miejscach konstrukcji. Przeprowadzono analizę widmową sygnałów i zidentyfikowano źródła pochodzenia poszczególnych pasm częstotliwości naprężeń. Obliczono funkcję koherencji zwyczajnej pomiędzy badanymi sygnałami oraz wyznaczono transmitancje widmowe układu. Zebrane dane są podstawą do dalszych rozważań na temat wytrzymałości zmęczeniowej konstrukcji.

EN

The article presents a study of stochastics loads. The research was performed for calculation of fatigue life of potato planter. The effect of loads on stress at selected locations on the structure was calculated. Spectral analysis was carried out and sources of frequency bands of stress were localized. Coherence between signals was calculated and spectral transmittance of the system was computed. The obtained information shall be used for estimating the fatigue life of machine.

3

Stochastic impulsive pressure calculations for time dependent human hip joint lubrication

Wierzcholski K.

Acta of Bioengineering and Biomechanics

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2012

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Vol. 14, no. 4

81-100

EN

The present paper is concerned with the calculation of the stochastic unsteady, impulsive pressure distributions and load carrying capacities in human hip joint for unsteady stochastic conditions, various standard deviations and Gaussian probability density function. The total changes of hydrodynamic pressure caused by viscoelastic synovial fluid properties are completely estimated. Calculations are performed in a super thin layer of biological synovial fluid inside the slide hip joint gap limited by a spherical bone head. Using a new unified operator of summation (UOS) method, the numerical topology of pressure calculation for a difference method is applied. From numerical standpoint the proposed method of solving modified hydrodynamic equations reduces this problem to resolving the partial recurrence non-homogeneous equation of second order with variable coefficients.

4

Random walk - fuzzy aspects

Frič R., Papčo M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2011

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Vol. 16

205--212

EN

Some beautiful and powerful mathematical ideas are hard to present to students because of the involved abstract language (notation, definitions, theorems, proofs, formulas) and lack of time. Animation and “mathematical experiments” provide a remedy. In the field of stochastics, the Galton board experiment presents several fundamental stochastic notions: a random event, independent random events, the binomial distribution, limit distribution, normal distribution, interpretation of probability, and leads to their better understanding. Random walk is a natural generalization of the Galton board. We use random walks as a motivation and presentation of basic principles of fuzzy random events and fuzzy probability. Fuzzy mathematics and fuzzy logic generalize classical (Boolean) mathematics and logic, reflect everyday experience and decision making and have broader applications. Experimenting with random walks also sheds light on the transition from classical to fuzzy probability.

5

Stochastyczna analiza dynamiczna wrażliwości układu belkowo-kratowego

Grzywiński M., Hien T. D.

Pomiary Automatyka Kontrola

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2009

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R. 55, nr 6

330-333

PL

W pracy przedstawiono procedury numeryczne dynamicznej analizy wrażliwości układów konstrukcyjnych. Oprócz zagadnienia różniczkowania bezpośredniego, sformułowano sprzężone zagadnienie końcowe, bazujące na pierwotnym zagadnieniu początkowym. Całość zilustrowano przykładem numerycznym, układu belkowo-kratowego, obliczonym metodą stochastycznych elementów skończonych.

EN

A numerical formulation for stochastic sensitivity in dynamic analysis of structural systems is presented in the paper. The stochastic finite element method, basing on the perturbation methodology, is an advanced computer technique for solving engineering problems with randomness taken into account. It allows one to analyze a wide class of static and dynamic systems with geometrical and /or material random parameters. Besides the well-known direct differentiation setting, an adjoint terminal-value system is formulated in accordance with the prescribed fundamental initial-value system. Once the original initial-value equations (15) and (16) are solved for by a step-by-step forward integration scheme over time from 0 to t and the adjoint terminal-value equations (23) and (24) are integrated backward form t to 0, the sensitivity gradients (25) are summed up. Analysis of a symmetrical portal frame with two strut trusses is given. The dynamic sensitivity of the displacements at two representative points B and C with respect to the change of the cross-sectional areas of the truss and beam members is discussed. Two complete sets of stochastic solutions are obtained. One includes the expectations and cross-covariances for the nodal displacements, while the other describes the first two probabilistic moments of their sensitivity gradients.

6

A computer code for eliminating secularity in perturbed systems

Hien T. D.

Pomiary Automatyka Kontrola

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2009

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R. 55, nr 6

385-388

EN

In the paper an efficient algorithm is formulated to eliminate inherent secular effects in solving engineering problems by the perturbation technology. Basing upon the modified data-window concept, a computer procedure written in Fortran is worked out in the standard form and can be applied to deal with a large class of nonlinear and/or stochastic engineering systems of dynamics, control, identification and optimization. An illustrating numerical example related to a structural dynamics system with random parameters is presented.

PL

W pracy sformułowano skuteczny algorytm wyeliminowania efektów sekularnych, swoistych w rozwiązywaniu zagadnień inżynierskich drogą perturbacyjną. Bazując na zmodyfikowanym pojęciu okien-danych, opracowano w języku Fortran podprogram komputerowy. Będący w standardowej formie, kod ten może być stosowany w szerokiej klasie nieliniowych lub/i stochastycznych układów dynamiki, kontroli, identyfikacji czy optymalizacji. Przedstawiono ilustrujący przykład dotyczący dynamiki konstrukcyjnego układu z parametrami losowymi.

7

Stochastic graphs and their applications

Tlustý P., Rost P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

435-440

EN

The article deals with one example of so called stochastic graph. The paper demonstrates some of possible applications of stochastic graphs in practice using the well known example about seven bridges of the town of Königsberg.

8

Geometric constructions as probabilistic spaces constructions

Płocki A., Muzyczka Z.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

335-346

EN

The study proposes a visualization of the discrete probabilistic space idea as well as its construction.

9

The Justice of Chance as a Stochastic Dilemma

Major M., Nawolska B.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2003

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Vol. 9

155--161

EN

The paper deals with the problem of a fair draw of one or two elements out of n elements. It presents an attempt to construct a generalisation of the term "a fair draw" (i.e. a draw in which it is equally likely to select each element) from the case of selection of one element of a certain population to the case where two elements are drawn.