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1

Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation

Veni G. Krishna, Satyanarayana Chirala, Krishnareddy M. Chenna

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 1

37--46

EN

In infinitely smooth Radial Basis Function (RBF) based interpolation, the scaling parameter plays an important role to obtain an accurate and stable numerical solution. When this method is applied to interpolate a function with sharp gradients, then adaptive methods will also play a significant role in determining an optimal number of centers according to the user desired accuracy. In this article, we test an optimization algorithm developed using the nonlinear optimization to find a scaling parameter for RBF along with an adaptive residual subsampling method [1] RBF interpolation. In this process, at each stage of adoption, the available optimal shape parameters have been obtained by solving the system of non-linear equations.

2

Comparison of MLP and RBF Neural Networks in the Task of Classifying the Diameters of Water Pipes

Gvishiani Zurab, Dawidowicz Jacek

Rocznik Ochrona Środowiska

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2022

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Tom 24

505--519

EN

Hydraulic calculations of water distribution systems are currently performed using computer programs. In addition to the basic calculation procedure, modules responsible for evaluating the obtained calculation results are introduced more and more often into the programs. This article presents the results of research on artificial neural networks with a radial base function (RBF) and a multilayer perceptron (MLP), aimed at determining whether they can be used to model the relationship between the variables describing the computational section of the water distribution system and the diameter of the water pipe. The classification capabilities of the RBF and MLP networks were analyzed according to the number of neurons in the hidden layer of the network. A comparative analysis of RBF networks with multilayer perceptron (MLP) networks was performed. The results showed that the MLP networks have much better classification properties and are better suited for the task of assessing the selected diameters of the water pipes.

3

Integrated fault-tolerant control of a quadcopter UAV with incipient actuator faults

Kantue Paulin, Pedro Jimoh O.

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 4

601--617

EN

An integrated approach to the fault-tolerant control (FTC) of a quadcopter unmanned aerial vehicle (UAV) with incipient actuator faults is presented. The framework is comprised of a radial basis function neural network (RBFNN) fault detection and diagnosis (FDD) module and a reconfigurable flight controller (RFC) based on the extremum seeking control approach. The dynamics of a quadcopter subject to incipient actuator faults are estimated using a nonlinear identification method comprising a continuous forward algorithm (CFA) and a modified golden section search (GSS) one. A time-difference-of-arrival (TDOA) method and the post-fault system estimates are used within the FDD module to compute the fault location and fault magnitude. The impact of bi-directional uncertainty and FDD detection time on the overall FTC performance and system recovery is assessed by simulating a quadcopter UAV during a trajectory tracking mission and is found to be robust against incipient actuator faults during straight and level flight and tight turns.

4

Stokes flow in lid-driven cavity under inclined magnetic field

Gürbüz-Çaldag M., Çelik E.

Archives of Mechanics

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2022

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Vol. 74, nr 6

549--564

EN

Stokes flow in a lid-driven cavity under the effect of an inclined magnetic field is studied. The radial basis function (RBF) approximation is employed to the magnetohydrodynamic (MHD) equations which include Navier-Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law with the Stokes approximation. Numerical results are obtained for the moderate Hartmann number (0 ≤ M ≤ 80) and different angles of a magnetic field (0 ≤ α ≤ π). It is found that the increase in the Hartmann number causes the development of new vortices under the main flow due to the impact of a magnetic field. However, the type of the inclination angle (acute or obtuse) determines the location of the vortices.

5

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.

6

Neuro-adaptive cooperative control for high-order nonlinear multi-agent systems with uncertainties

Peng Cheng, Zhang Anguo, Li Junyu

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 4

635--645

EN

The consensus problem for a class of high-order nonlinear multi-agent systems (MASs) with external disturbance and system uncertainty is studied. We design an online-update radial basis function (RBF) neural network based distributed adaptive control protocol, where the sliding model control method is also applied to eliminate the influence of the external disturbance and system uncertainty. System consensus is verified by using the Lyapunov stability theorem, and sufficient conditions for cooperative uniform ultimately boundedness (CUUB) are also derived. Two simulation examples demonstrate the effectiveness of the proposed method for both homogeneous and heterogeneous MASs.

7

ANN-based failure modeling of classes of aircraft engine components using radial basis functions

Al-Garni Ahmed, Abdelrahman Wael, Abdallah Ayman

Eksploatacja i Niezawodność

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2019

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Vol. 21, no. 2

311--317

EN

The objective of this research is to present a model to predict failure of two categories of critical aircraft engine components; nonrotating components such as valves and gearboxes, and rotating components such as engine turbines. The work utilizes Weibull regression and artificial neural networks employing Back Propagation (BP) as well as Radial Basis Functions (RBF). The model utilizes training failure data collected from operators of turboprop aircraft working in harsh desert conditions, where sand erosion is a detrimental factor in reducing turbine life. Accordingly, the model is more suited for accurate prediction of life of critical components of such engines. The algorithm, which uses Radial Basis Function (RBF) NN, uses a closest point specifier. The activation is based on the deviation of the earlier prototype from the input vector. Two earlier models are used for comparison purposes; namely Weibull regression modeling and Feed-Forward BP network. Comparison results show that the failure times represented by RBF are in better compromise with actual failure data than both earlier modeling methods. Moreover, the technique has comparatively higher efficiency as the neuron’s number in each layer of ANN is reduced, to decrease computation time, with minimum effect on the accuracy of results.

PL

Celem pracy jest przedstawienie modelu służącego do predykcji uszkodzeń dwóch kategorii krytycznych elementów silnika samolotowego: elementów nieobrotowych, takich jak zawory i skrzynie biegów oraz elementów obrotowych, takich jak turbiny silnika. W pracy wykorzystano regresję Weibulla i sztuczne sieci neuronowe oparte na propagacji wstecznej oraz radialnych funkcjach bazowych (RBF). Model wykorzystuje dane o błędach zebrane od operatorów samolotów turbośmigłowych pracujących w trudnych warunkach pustynnych, gdzie erozja powodowana przez piasek stanowi szkodliwy czynnik ograniczający żywotność turbin. Prezentowany model jest więc szczególnie przydatny do trafnego prognozowania żywotności krytycznych elementów takich silników. Algorytm, który wykorzystuje sieci neuronowe o radialnych funkcjach bazowych, używa specyfikatora najbliższego punktu. Aktywacja bazuje na odchyleniu wcześniejszego prototypu od wektora wejściowego. Dwa wcześniejsze modele oparte na regresji Weibulla (Weibull regression modeling) oraz sieciach typu Feed-Forward Backpropagation wykorzystano do badań porównawczych. Wyniki porównania pokazują, że czasy uszkodzeń odwzorowane przez RBF pozostają w większej zgodzie z rzeczywistymi danymi o uszkodzeniach niż w przypadku obu wcześniejszych metod modelowania. Co więcej, technika ta ma porównywalnie większą efektywność, ponieważ liczba neuronów w każdej warstwie sieci neuronowej została zredukowana tak aby zmniejszyć czas obliczeń, przy minimalnym wpływie na dokładność wyników.

8

Meshless local radial point interpolation (MLRPI) for generalized telegraph and heat diffusion equation with non-local boundary conditions

Shivanian E., Khodayari A.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 2

571—582

EN

In this paper, the meshless local radial point interpolation (MLRPI) method is formulated to the generalized one-dimensional linear telegraph and heat diffusion equation with non-local boundary conditions. The MLRPI method is categorized under meshless methods in which any background integration cells are not required, so that all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. A technique based on the radial point interpolation is adopted to construct shape functions, also called basis functions, using the radial basis functions. These shape functions have delta function property in the frame work of interpolation, therefore they convince us to impose boundary conditions directly. The time derivatives are approximated by the finite difference time- -stepping method. We also apply Simpson’s integration rule to treat the non-local boundary conditions. Convergency and stability of the MLRPI method are clarified by surveying some numerical experiments.

9

Tea Category Identification using Computer Vision and Generalized Eigenvalue Proximal SVM

Wang S., Phillips P., Liu A., Du S.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

325--339

EN

(Objective) In order to increase classification accuracy of tea-category identification (TCI) system, this paper proposed a novel approach. (Method) The proposed methods first extracted 64 color histogram to obtain color information, and 16 wavelet packet entropy to obtain the texture information. With the aim of reducing the 80 features, principal component analysis was harnessed. The reduced features were used as input to generalized eigenvalue proximal support vector machine (GEPSVM). Winner-takes-all (WTA) was used to handle the multiclass problem. Two kernels were tested, linear kernel and Radial basis function (RBF) kernel. Ten repetitions of 10-fold stratified cross validation technique were used to estimate the out-of-sample errors. We named our method as GEPSVM + RBF + WTA and GEPSVM + WTA. (Result) The results showed that PCA reduced the 80 features to merely five with explaining 99.90% of total variance. The recall rate of GEPSVM + RBF + WTA achieved the highest overall recall rate of 97.9%. (Conclusion) This was higher than the result of GEPSVM + WTA and other five state-of-the-art algorithms: back propagation neural network, RBF support vector machine, genetic neural-network, linear discriminant analysis, and fitness-scaling chaotic artificial bee colony artificial neural network.

10

Pattern Classification of Fabric Defects Using a Probabilistic Neural Network and Its Hardware Implementation using the Field Programmable Gate Array System

Hasnat A., Ghosh A., Khatun A., Halder S.

Fibres & Textiles in Eastern Europe

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2017

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Vol. 25, no. 1 (121)

42--48

EN

This study proposes a fabric defect classification system using a Probabilistic Neural Network (PNN) and its hardware implementation using a Field Programmable Gate Arrays (FPGA) based system. The PNN classifier achieves an accuracy of 98 ± 2% for the test data set, whereas the FPGA based hardware system of the PNN classifier realises about 94±2% testing accuracy. The FPGA system operates as fast as 50.777 MHz, corresponding to a clock period of 19.694 ns.

PL

W pracy zaprezentowano system klasyfikacji wad tkanin przy użyciu probabilistycznej sieci neuronowej (PNN) i przy zastosowaniu systemu Field Programmable Gate Array (FPGA). PNN pozwala na osiągnięcie dokładności 98 ± 2% dla zbioru danych testowych, podczas gdy system FPGA pozwala na osiągnięcie dokładności około 94 ± 2%. System FPGA pracuje przy częstotliwości 50,777 MHz, co odpowiada 19,694 ns.

11

Zastosowanie radialnych funkcji bazowych do analizy akustycznych drgań własnych kabiny pojazdu

Majkut L., Olszewski R.

Autobusy : technika, eksploatacja, systemy transportowe

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2017

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R. 18, nr 12

1110--1113, CD

PL

W artykule opisano możliwości zastosowania Metody Funkcji Radialnych do wyznaczania akustycznych częstotliwości drgań własnych w przestrzeniach ograniczonych. Porównano metodyki popularnych narzędzi obliczeniowych takich jak Metoda Elementów Skończonych i Metoda Elementów Brzegowych wraz ze wskazaniem wad i zalet do Metody Funkcji Radialnych.

EN

In the paper the possibility of Radial Basis Function Method for the calculation of acoustic eigenvalues is described. The proposed method is compared with other numerical methods of wave acoustic. The advantages and disadvantages of Finite Element Method and Boundary Element Method are described and compared to proposed Radial Basis Function Method.

12

Hydrous Methanol Fuelled HCCI Engine Using Ignition Improver CAI Method - ANN Approach

Venkatesan M., Moorthi N. S. V., Franco P. A., Manivannan A., Karthikeyan R.

Mechanics and Mechanical Engineering

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2015

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Vol. 19, nr 1

31--49

EN

The present study is to examine the performance and emission characteristics of a Homogeneous Charge Compression Ignition (HCCI) engine where hydrous methanol (85% methanol and 15% water) is used as primary fuel and Diethyl ether (DEE) as an ignition improver. A modified diesel engine has been used as a HCCI engine. By measuring the excess air ratio (λDEE), the quantity of DEE flow rate is measured and excess air ratio (fiDEE) is varied from fiDEE5.6 to fiDEE 9.5. Experimental results reveal that HCCI engine gives better brake thermal efficiency (BTE) at high loads (λDEE 9.5). It shows decrease in oxides of nitrogen (NOx) emission, slightly high emission of carbon monoxide (CO) and unburned hydrocarbon (HC) compared to conventional compression ignition (CI) engine. Radial basis function neural network (RBFN) model has been developed with brake power, excess air ratio and energy share as input and BTE, CO, HC, NOx, rate of pressure rise as output. About 80% of total experimental data is used for training purposes, and 20% is used for testing. The performance of the developed RBFN model were compared with experimental data, and were statistically evaluated which was found to be in good agreement.

13

Free vibration of structures by radial basis function – pseudospectral method

Krowiak A.

Vibrations in Physical Systems

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2014

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Vol. 26

113--120

EN

The paper deals with the use of the radial basis function-pseudospectral method in vibration analysis of twodimensional mechanical structures. The method combines meshless features of radial basis function (RBF) with efficiency and simplicity of the pseudospectral method. In present work the main emphasis is laid on appropriate assumption of the interpolant for the sought function due to the number of the boundary conditions in analysed problem. This interpolation function enables to obtain the weighting coefficients for derivative approximation in a governing equation. The method is applied to free vibration analysis of arbitrarily shaped membrane and plate.

14

A new hybrid finite element approach for three-dimensional elastic problems

Cao C., Qin Q. H., Yu A.

Archives of Mechanics

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2012

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Vol. 64, nr 3

261-261

EN

A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.

15

Recent developments in stabilized Galerkin and collocation meshfree methods

Chen J-S., Chi S-W., Hu H-Y.

Computer Assisted Mechanics and Engineering Sciences

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2011

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Vol. 18, no. 1-2

3-21

EN

Meshfree methods have been developed based on Galerkin type weak formulation and strong formulationwith collocation. Galerkin type formulation in conjunction with the compactly supported approximation functions and polynomial reproducibility yields algebraic convergence, while strong form collocationmethod with nonlocal approximation such as radial basis functions offers exponential convergence. In thiswork, we discuss rank instability resulting from the nodal integration of Galerkin type meshfree methodas well as the ill-conditioning type instability in the radial basis collocation method. We present the recentadvances in resolving these diffculties in meshfree methods, and demonstrate how meshfree methods can be applied to problems di?cult to be modeled by the conventional ?nite element methods due to their intrinsic regularity constraints.

16

Artificial neural network with radial basis function in model predictive control of chemical reactor

Samek D., Dostal P.

Mechanics / AGH University of Science and Technology

|

2009

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Vol. 28, no. 3

91-95

EN

This paper describes the application of artificial neural network with radial basis function as a predictor in model predictive control. Radial basis function neural networks are known for their fast training. Thus, this type of artificial neural networks offers promising way how to reduce computational cost during offline predictor training and eventual online adaptation. The features of this type of artificial neural network are presented in simulations in MATLAB/Simulink on the nonlinear system control. The aim of this paper is to suggest one approach how to solve nonlinear prediction problem using artificial neural network respecting computational demands of the predictor.

PL

Artykuł jest poświęcony zastosowaniu sztucznych sieci neuronowych z radialnymi funkcjami bazowymi jako predykatora w modelach sterowania predyktywnego. Sieci radialne są znane z możliwości ich szybkiego uczenia. Dlatego ten typ sztucznych sieci neuronowych umożliwia redukcję czasu obliczeń podczas uczenia sieci w trybie off-line i ewentualnych zastosowań on-line. Cechy omawianych aplikacji sieci neuronowych przedstawiono w symulacyjnych obliczeniach sterowania nieliniowego układu z wykorzystaniem środowiska MATLAB/Simulink.

17

Stacjonarne przewodzenie ciepła przez wielowarstwową ściankę o zależnym od temperatury współczynniku przewodzenia ciepła

Mierzwiczak M.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2008

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Nr 9

67-79

PL

W artykule przedstawiono numeryczne rozwiązanie stacjonarnego zagadnienia przewodzenia ciepła przez wielowarstwową płaską i cylindryczną ściankę, której współczynnik przewodzenia zależy od temperatury. Do rozwiązania problemu zastosowano bezsiatkową metodę Kansy. Nieznane pole temperatury przyjmuje się w warstwach w postaci liniowej kombinacji radialnych funkcji bazowych (RBF). Kolokacyjne spełnienie równania rządzącego i warunków brzegowych prowadzi do nieliniowego układu równań rozwiązywanego metodą Newtona.

EN

This paper deals with numerical solution of heat transfer problem in multilayered plate and cylinder with temperature-dependent thermal conductivity. The Kansa meshless method was used for the solution of this problem. In this approach, the unknown's temperatures in layers are approximated by the radial basis functions, while the governing equation and the boundary conditions are imposed directly at the collocation points. The multiquadrics are used as the radial basis functions. Non-linear system of algebraic equations for coefficients at radial basis functions is solved by Newton method.

18

Center selection of RBF neural network based on modified k-means algorithm with point symmetry distance measure

Sing J. K., Basu D. K., Nasipuri M., Kundu M.

Foundations of Computing and Decision Sciences

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2004

|

Vol. 29, No. 3

247-266

EN

The hidden layer neurons of a radial basis function (RBF) neural network map input patterns from a nonlinearly separable space to a linearly separable space. To locate the centers of those hidden layer neurons, normally k-means clustering algorithm is used. Normal k-means clustering algorithm cannot detect hyper spherical-shaped clusters along the principal axes. In present study, we propose a modified version of the k-means clustering algorithm to select RBF centers, which can eliminate this drawback. In the proposed algorithm, we modify the k-means algorithm in two stages. In trie first stage, the procedure to select the initial cluster centers has been modified to capture more knowledge about the distribution of input patterns. In the second stage, the initial centers, selected in the first stage are updated using point symmetry distance measure instead of using conventional Euclidean distance. The RBF neural network with the proposed algorithm has been tested with three different machine-learning data sets. It has also been applied for the segmentation of medical images. The experimental results show that the RBF neural network using the proposed modified k-means algorithm performs better than that using normal k-means algorithm.

19

Zastosowanie metod sztucznej inteligencji w sterowaniu procesem konwertorowym

Macioł P.

Hutnik, Wiadomości Hutnicze

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2003

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Vol. 70, nr 12

472--477

PL

Celem badań było sprawdzenie możliwości sterowania objętością dmuchu dodatkowego w tlenowym procesie konwertorowym w oparciu o sztuczne sieci neuronowe. Podjęto próbę budowy modeli opartych na regresji liniowej oraz sieciach neuronowych kilku rodzajów. Przetestowane zostały sieci "przesyłające żetony" (Counterpropagation), wielowarstwowe sieci perceptronowe (Multilayer Perceptron) oraz sieci o radialnej funkcji aktywacji (Radial Basis Function). W pracy przedstawione są wyniki badań oraz propozycje ich wykorzystania w przyszłości.

EN

The paper presents possibility of application artificial neural network models for Basic Oxygen Process (BOP) controlling. Models based on linear regression and few types of neural networks were worked out. Neural models were based on Counterpropagation neural network, Multilayer Perceptron neural network and Radial Basis Function network. Research results and suggestions of their future practical application are presented.

20

Prediction of Drying Kinetics by Means of MLP and RBF

Kamiński W., Tomczak E.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2000

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Vol. 48, nr 3

429-443

EN

Two network types are proposed for modelling a drying process in the vibrofluidized bed, namely multilayer perceptron network and radial basis function network. Network training procedures are based on experimental data obtained for silica gel, green peas, potatoes and cabbage. Capability of prediction of MLP and RBF networks are evaluated in a feed forward and recurrent structures.