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1

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.

2

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.

3

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.

4

Soft computing-based technique as a predictive tool to estimate blast-induced ground vibration

Arthur Clement Kweku, Temeng Victor Amoako, Ziggah Yao Yevenyo

Journal of Sustainable Mining

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2019

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Vol. 18, iss. 4

287--296

EN

The safety of workers, the environment and the communities surrounding a mine are primary concerns for the mining industry. Therefore, implementing a blast-induced ground vibration monitoring system to monitor the vibrations emitted due to blasting operations is a logical approach that addresses these concerns. Empirical and soft computing models have been proposed to estimate blast-induced ground vibrations. This paper tests the efficiency of the Wavelet Neural Network (WNN). The motive is to ascertain whether the WNN can be used as an alternative to other widely used techniques. For the purpose of comparison, four empirical techniques (the Indian Standard, the United State Bureau of Mines, Ambrasey-Hendron, and Langefors and Kilhstrom) and four standard artificial neural networks of backpropagation (BPNN), radial basis (RBFNN), generalised regression (GRNN) and the group method of data handling (GMDH) were employed. According to the results obtained from the testing dataset, the WNN with a single hidden layer and three wavelons produced highly satisfactory and comparable results to the benchmark methods of BPNN and RBFNN. This was revealed in the statistical results where the tested WNN had minor deviations of approximately 0.0024 mm/s, 0.0035 mm/s, 0.0043 mm/s, 0.0099 and 0.0168 from the best performing model of BPNN when statistical indicators of Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Relative Root Mean Square Error (RRMSE), Correlation Coefficient (R) and Coefficient of determination (R2) were considered.

5

A fast neural network learning algorithm with approximate singular value decomposition

Jankowski Norbert, Linowiecki Rafał

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

581--594

EN

The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is O(mn2). We consider algorithms with a complexity of O(mnl), where l < n and l is often significantly smaller than n. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.

6

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.

7

Training subset selection for support vector regression

Liu Cenru, Cen Jiahao

Annals of Computer Science and Information Systems

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2019

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Vol. 18

11--14

EN

As more and more data are available, training a machine learning model can be extremely intractable, especially for complex models like Support Vector Regression (SVR) train- ing of which requires solving a large quadratic programming optimization problem. Selecting a small data subset that can effectively represent the characteristic features of training data and preserve their distribution is an efficient way to solve this problem. This paper proposes a systematic approach to select the best representative data for SVR training. The distribution of both predictor and response variables are preserved in the selected subset via a 2-layer data clustering strategy. A 2-layer step-wise greedy algorithm is introduced to select best data points for constructing a reduced training set. The proposed method has been applied for predicting deck's win rates in the Clash Royale Challenge, in which 10 subsets containing hundreds of data examples were selected from 100k for training 10 SVR models to maximize their prediction performance evaluated using R-squared metric. Our final submission having a R2 score of 0.225682 won the 3rd place among over 1200 solutions submitted by 115 teams.

8

Comparison of prototype selection algorithms used in construction of neural networks learned by SVD

Jankowski N.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 4

719--733

EN

Radial basis function networks (RBFNs) or extreme learning machines (ELMs) can be seen as linear combinations of kernel functions (hidden neurons). Kernels can be constructed in random processes like in ELMs, or the positions of kernels can be initialized by a random subset of training vectors, or kernels can be constructed in a (sub-)learning process (sometimes by k-means, for example). We found that kernels constructed using prototype selection algorithms provide very accurate and stable solutions. What is more, prototype selection algorithms automatically choose not only the placement of prototypes, but also their number. Thanks to this advantage, it is no longer necessary to estimate the number of kernels with time-consuming multiple train-test procedures. The best results of learning can be obtained by pseudo-inverse learning with a singular value decomposition (SVD) algorithm. The article presents a comparison of several prototype selection algorithms co-working with singular value decomposition-based learning. The presented comparison clearly shows that the combination of prototype selection and SVD learning of a neural network is significantly better than a random selection of kernels for the RBFN or the ELM, the support vector machine or the kNN. Moreover, the presented learning scheme requires no parameters except for the width of the Gaussian kernel.

9

Application of an RBF blending interpolation method to problems with shocks

Harris M., Kassab A., Divo E.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 3

229--241

EN

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high conditioning number for the interpolation matrix, rendering the RBF smooth [1–10]. However, this strategy fails for a problem with a shock or sharp discontinuity. Instead, in such cases the conditioning number must be kept small. The focus of this work is then to demonstrate the use of RBF interpolation in the approximation of sharp gradients or shocks by use of a RBF blending interpolation approach. This RBF blending interpolation approach is used to maintain the optimum shape parameter depending on the field. The approach is able to sense gradients or shocks in the field and adjust the shape parameter accordingly to keep excellent accuracy. Presented in this work, is an explanation of the RBF blending interpolation methodology and testing of the RBF blending interpolation approach by solving the Burger’s equation using the virtual finite difference method.

10

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.

11

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.

12

Stabilising solutions to a class of nonlinear optimal state tracking problems using radial basis function networks

Ahmida Z., Charef A., Becerra V. M.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 3

369-381

EN

A controller architecture for nonlinear systems described by Gaussian RBF neural networks is proposed. The controller is a stabilising solution to a class of nonlinear optimal state tracking problems and consists of a combination of a state feedback stabilising regulator and a feedforward neuro-controller. The state feedback stabilising regulator is computed online by transforming the tracking problem into a more manageable regulation one, which is solved within the framework of a nonlinear predictive control strategy with guaranteed stability. The feedforward neuro-controller has been designed using the concept of inverse mapping. The proposed control scheme is demonstrated on a simulated single-link robotic manipulator.