Radial Base Functions Research Articles

Partial reconstruction of sparse and incomplete point clouds applied to the generation of corneal topographic maps of healthy and diseased patients

The presence of unmeasured areas or areas with missing data in corneal topographies greatly affect the quality of digital corneal models. These are more frequent in posterior than in anterior corneal surface. This work seeks to complete and improve digital corneal models generated from incomplete point clouds obtained with commercial tomographic equipment, applying three interpolation/extrapolation techniques based on population data (Polynomial, Biharmonic Splines and Cubic Radial Base Functions). 43 personalized corneal models of patients with different grades of keratoconus were used to test each interpolation method. All interpolation results were compared using the Mean Average Percentage Error (MAPE) index, observing that it is possible to interpolate/extrapolate up to the radius 5.2 mm on the anterior face and up to 4.2 mm on the posterior face in general, but none of the methods stand out above the others for all the situations considered. Consequently, extrapolation method must be chosen carefully.

An Investigation into the Friction of Cold-Rolled Low-Carbon DC06 Steel Sheets in Sheet Metal Forming Using Radial Basis Function Neural Networks

This article presents the friction test results for cold-rolled low-carbon DC06 steel sheets, which are commonly processed into finished products using sheet metal forming methods. A strip drawing test with flat dies was used in the experimental tests. The strip-drawing test is used to model the friction phenomena in the flange area of the drawpiece. The tests were carried out using a tester that enabled lubrication with a pressurised lubricant. The friction tests were carried out at different nominal pressures, oil pressures, and friction conditions (dry friction and oil lubrication). Oils destined for deep-drawing operations were used as lubricants. Neural networks with radial base functions (RBFs) were used to explore the influence of individual friction parameters on the value of the coefficient of friction (COF). Under lubrication with both oils considered, the value of the COF increased with decreasing oil pressure. This confirms the correctness of the concept of the device for reducing friction in the flange area of the drawpiece. The developed concept of pressurised lubrication is most effective at relatively small nominal pressures of 2–4 MPa. This range of nominal pressures corresponds to the actual nip pressures when forming deep-drawing steel sheets. Under conditions of dry friction, the values obtained for the COF rise above 0.3, while under lubrication conditions, even without pressure-assisted lubrication, the COF does not exceed 0.2. As the nominal pressure increases, the effectiveness of the lubrication exponentially decreases. It was found that the Sq parameter carries the most information regarding the value of the COF. The RBF neural network with nine neurons in the hidden layer (RBF-8-9-1) and containing the Sq parameter as the input was characterised by an R2 of 0.989 and an error of 0.000292 for the testing set.

Early and High-Accuracy Diagnosis of Parkinson's Disease: Outcomes of a New Model.

Parkinson's disease (PD) is one of the significant common neurological disorders of the current age that causes uncontrollable movements like shaking, stiffness, and difficulty. The early clinical diagnosis of this disease is essential for preventing the progression of PD. Hence, an innovative method is proposed here based on combining the crow search algorithm and decision tree (CSADT) for the early PD diagnosis. This approach is used on four crucial Parkinson's datasets, including meander, spiral, voice, and speech-Sakar. Using the presented method, PD is effectively diagnosed by evaluating each dataset's critical features and extracting the primary practical outcomes. The used algorithm was compared with other machine learning algorithms of k-nearest neighbor (KNN), support vector machine (SVM), naive Baye (NB), multilayer perceptron (MLP), decision tree (DT), random tree, logistic regression, support vector machine of radial base functions (SVM of RBFs), and combined classifier in terms of accuracy, recall, and combination measure F1. The analytical results emphasize the used algorithm's superiority over the other selected ones. The proposed model yields nearly 100% accuracy through various trials on the datasets. Notably, a high detection speed achieved the lowest detection time of 2.6 seconds. The main novelty of this paper is attributed to the accuracy of the presented PD diagnosis method, which is much higher than its counterparts.

Methodology Based on Artificial Neural Networks for Hourly Forecasting of PV Plants Generation

We propose a methodology for the hourly forecast of the photovoltaic (PV) power of two plants (6.03 kWp and 7.37 kWp) installed in the metropolitan region of Fortaleza - CE. The methodology uses two Artificial Neural Networks (ANN) to predict time series: Perceptron type with Multiple Layers (MLP) and radial base functions (RBF), trained with historical data of hourly PV power collected during the year 2020 in the locations under study. System performance meters are applied (correlation coefficient - R, Nash-Sutcliffe efficiency - NSE and relative trend - VR). The data evaluated in each plant are treated using MLP and RBF networks, as well as the Persistence method, seeking to increase the study reliability. ANN results indicate potential to learn the behavior of the plants, with R above 80%, VR close to zero and NSE above 0.50 in two of the applications. In this specific case, despite being similar networks, MLP shows a higher accuracy than RBF.

Design Hybrid Intelligent system for Cattle Diseases Diagnosis and Treatment

Cattle is one of the main concerns of people and companies in various countries of the world. This paper built the architecture of the cattle diseases by combining the characteristics of an expert system with a neural network Expert system focuses on diagnosing the possible diseases that affect the life of cattle through constructing knowledge bases. While the Radial base functions, a neural network is proposed for the cattle diseases treatments. A tightly coupled model is used to implement a hybrid intelligence technique for diagnosing and Treatment cattle diseases. The result generated by the system was enough to demonstrate its performance.

Solución de la ecuación de Navier para el cálculo de elasticidad lineal en materiales nanoreforzados utilizando el método de elementos de frontera.

En este paper se plantea el estudio de elasticidad lineal en un material compuesto nano reforzado sometido a una fuerza externa constante con el fin de ser utilizado en la fabricación de prótesis de miembro inferior, para lo cual se desarrolló un algoritmo computacional que resuelve la ecuación de elasticidad lineal (ecuación de Navier), utilizando el método de elementos de frontera y funciones de base radial.
 Se determinó si el uso de un algoritmo puede predecir el cambio en una geometría bidimensional a nivel de deformaciones, desplazamientos y esfuerzos en un material compuesto reforzado con nanotubos de carbono; utilizado en la fabricación de prótesis de miembro inferior y evidenciar el cumplimiento de los requerimientos deseados al ser sometido a una fuerza constante. Por lo anterior el análisis de la información obtenida, se apoya el proceso de selección de un material compuesto nanoreforzado para uso en el desarrollo de prótesis de miembro inferior al ser sometido a una fuerza constante. Según el algoritmo desarrollado y los resultados encontrados, el método de elementos de frontera permite la simulación del comportamiento mecánico de un material compuesto (acero A36, a concentraciones de nanotubos de carbono de 1%, 2%, 3%)

Design and Construction of Zana Robot for Modeling Human Player in Rock-paper-scissors Game using Multilayer Perceptron, Radial basis Functions and Markov Algorithms

In this paper, the implementation of artificial neural networks (multilayer perceptron [MLP] and radial base functions [RBF]) and the upgraded Markov chain model have been studied and performed to identify the human behavior patterns during rock, paper, and scissors game. The main motivation of this research is the design and construction of an intelligent robot with the ability to defeat a human opponent. MATLAB software has been used to implement intelligent algorithms. After implementing the algorithms, their effectiveness in detecting human behavior pattern has been investigated. To ensure the ideal performance of the implemented model, each player played with the desired algorithms in three different stages. The results showed that the percentage of winning computer with MLP and RBF neural networks and upgraded Markov model, on average in men and women is 59%, 76.66%, and 75%, respectively. Obtained results clearly indicate a very good performance of the RBF neural network and the upgraded Markov model in the mental modeling of the human opponent in the game of rock, paper, and scissors. In the end, the designed game has been employed in both hardware and software which include the Zana intelligent robot and a digital version with a graphical user interface design on the stand. To the best knowledge of the authors, the precision of novel presented method for determining human behavior patterns was the highest precision among all of the previous studies.

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes\u2019s formula

Current International Association of Geodesy efforts within regional geoid determination include the comparison of different computation methods in the quest for the “1-cm geoid.” Internal (formal) and external (empirical) approaches to evaluate geoid errors exist, and ideally they should agree. Spherical radial base functions using the spline kernel (SK), least-squares collocation (LSC), and Stokes’s formula are three commonly used methods for regional geoid computation. The three methods have been shown to be theoretically equivalent, as well as to numerically agree on the millimeter level in a closed-loop environment using synthetic noise-free data (Ophaug and Gerlach in J Geod 91:1367–1382, 2017. https://doi.org/10.1007/s00190-017-1030-1). This companion paper extends the closed-loop method comparison using synthetic data, in that we investigate and compare the formal error propagation using the three methods. We use synthetic uncorrelated and correlated noise regimes, both on the 1-mGal (=10^{-5}~{mathrm {m s}}^{-2}) level, applied to the input data. The estimated formal errors are validated by comparison with empirical errors, as determined from differences of the noisy geoid solutions to the noise-free solutions. We find that the error propagations of the methods are realistic in both uncorrelated and correlated noise regimes, albeit only when subjected to careful tuning, such as spectral band limitation and signal covariance adaptation. For the SKs, different implementations of the L-curve and generalized cross-validation methods did not provide an optimal regularization parameter. Although the obtained values led to a stabilized numerical system, this was not necessarily equivalent to obtaining the best solution. Using a regularization parameter governed by the agreement between formal and empirical error fields provided a solution of similar quality to the other methods. The errors in the uncorrelated regime are on the level of sim 5 mm and the method agreement within 1 mm, while the errors in the correlated regime are on the level of sim 10 mm, and the method agreement within 5 mm. Stokes’s formula generally gives the smallest error, closely followed by LSC and the SKs. To this effect, we note that error estimates from integration and estimation techniques must be interpreted differently, because the latter also take the signal characteristics into account. The high level of agreement gives us confidence in the applicability and comparability of formal errors resulting from the three methods. Finally, we present the error characteristics of geoid height differences derived from the three methods and discuss them qualitatively in relation to GNSS leveling. If applied to real data, this would permit identification of spatial scales for which height information is preferably derived by spirit leveling or GNSS leveling.

A Very High-Speed Validation Scheme Based on Template Matching for Segmented Character Expiration Codes on Beverage Cans.

This paper expands upon a previous publication and is the natural continuation of an earlier study which presented an industrial validator of expiration codes printed on aluminium or tin cans, called MONICOD. MONICOD is distinguished by its high operating speed, running at 200 frames per second and validating up to 35 cans per second. This paper adds further detail to this description by describing the final stage of the MONICOD industrial validator: the process of effectively validating the characters. In this process we compare the acquired shapes, segmented during the prior stages, with expected character shapes. To do this, we use a template matching scheme (here called “morphologies”) based on bitwise operations. Two learning algorithms for building the valid morphology databases are also presented. The results of the study presented here show that in the acquisition of 9885 frames containing 465 cans to be validated, there was only one false positive (0.21% of the total). Another notable feature is that it is at least 20% faster in validation time with error rates similar to those of classifiers such as support vector machines (SVM), radial base functions (RBF), multi-layer perceptron with backpropagation (MLP) and k-nearest neighbours (KNN).

Regional modeling of the ionosphere using adaptive neuro-fuzzy inference system in Iran

In recent years, new techniques and algorithms such as Artificial Neural Networks (ANNs), Fuzzy Inference Systems (FIS) and Genetic Algorithm (GA) have been used as alternative statistical tools in modeling and forecasting issues. These methods have been extensively used in the field of geosciences and atmospheric physics. The main purpose of this paper is to combine FIS and ANNs for local modeling of the ionosphere Total Electron Content (TEC) in Iran. An Adaptive Neuro-Fuzzy Inference System (ANFIS) is developed for TEC modeling. Also, Multi-Layer Perceptron ANN (MLP-ANN) and ANN based on Radial Base Functions (RBF) have been designed for analyzing ANFIS results. Observations of 29 Global Positioning System (GPS) stations from the Iranian Permanent GPS Network (IPGN) have been used in 3 different seasons in 2015 and 2016. These stations are located at geomagnetic low latitudes region. Out of these 29 stations, 24 stations for training and 5 stations for testing and validating were selected. The relative and absolute errors have been used to evaluate the accuracy of the proposed model. Also, the results of this paper are compared with the International Reference Ionosphere model (IRI2016). The maximum values of the average relative error for RBF, MLP-ANN, ANFIS and IRI2016 methods are 13.88%, 11.79%, 10.06%, and 18.34%, respectively. Also, the maximum values of the average absolute error for these methods are 2.38, 2.21, 1.5 and 3.36 TECU, respectively. Comparison of diurnal predicted TEC from the ANFIS, RBF, MLP-ANN and IRI2016 models with GPS-TEC revealed that the ANFIS provides more accurate predictions than the other methods in the test area.

Spatial prediction of landslide susceptibility in Taleghan basin, Iran

Identifying landslide-susceptible zones is warranted to prevent and mitigate associated hazards in mountainous regions, where a landslide is a destructive type of erosion. A landslide susceptibility map was developed for the Taleghan basin based on frequency ratio (FR), logistic regression (LR), maximum entropy (MaxEnt), and support vector machine (SVM) with radial base (RBF), sigmoid (SIG), linear (LN), and polynomial (PL) kernel functions. To this end, an inventory map with 166 landslide locations was prepared and partitioned into 70% and 30% to train and validate the models, respectively. Subsequently, the models were designed based on 13 factors including elevation, slope degree, slope aspect, distance to stream, Stream Power Index, Topographic Wetness Index, Stream Transport Index, distance to fault, lithology, soil texture, land use, distance to road and precipitation. The performance of the methods was assessed using the area under the receiver operating characteristic curve, the Seed Cell Area Index (SCAI), the precision index (P). Moreover, statistical measures including sensitivity, specificity, and accuracy were calculated. Friedman test was also applied to confirm significant statistical differences among the seven models employed in this research. The validation results showed that MaxEnt had the maximum area under the curve (0.812). The results obtained using the models LR, FR, PL-SVM, SIG-SVM, LN-SVM, and RBF-SVM were 0.807, 0.732, 0.679, 0.663, 0.643 and 0.660, respectively. The obtained P index showed the better performance of MaxEnt and LR models. Moreover, the trend of changes in the SCAI values, from low- to high-susceptibility, indicated that the MaxEnt and LR models had the best performance. Decision makers can effectively use the findings of the present study to mitigate the financial and human costs resulting from the landslides.

A Novel Approach for Objective Assessment of White Blood Cells Using Computational Vision Algorithms.

In the field of medicine, the analysis of blood is one of the most important exams to determine the physiological state of a patient. In the analysis of the blood sample, an important process is the counting and classification of white blood cells, which is done manually, being an exhaustive, subjective, and error-prone activity due to the physical fatigue that generates the professional because it is a method that consumes long laxes of time. The purpose of the research was to develop a system to identify and classify blood cells, by the implementation of the networks of Gaussian radial base functions (RBFN) for the extraction of its nucleus and subsequently their classification through the morphological characteristics, its color, and the distance between objects. Finally, the results obtained with the validation through the coefficient of determination showed an overall accuracy of 97.9% in the classification of the white blood cells per individual, while the precision in the classification by type of cell evidenced results in 93.4% for lymphocytes, 97.37% for monocytes, 79.5% for neutrophils, 73.07% for eosinophils, and a 100% in basophils with respect to the professional. In this way, the proposed system becomes a reliable technological support that contributes to the improvement of the analysis for identification of blood cells and therefore would benefit the low-level hematology establishments as well as to the processes of research in the area of medicine.

Optimal Rotor Fault Detection in Induction Motor Using Particle-Swarm Optimization Optimized Neural Network

This study examined and presents an effective method for detection of failure of conductor bars in the winding of rotor of induction motor in low load conditions using neural networks of radial-base functions. The proposed method used Hilbert method to obtain the stator current signal push. The frequency and signal amplitude of the push stator were used as the input of the neural network and the network outputs were rotor fault state, and the number of conductive bars with broken fault. Moreover, particle-swarm optimization algorithm was used to determine the optimal network weights and neuron penetration radius in the neural network. The results obtained from the proposed method showed the optimal and efficient performance of the method in detecting conductive bars broken fault in induction motor in low load conditions.

Métodos de Interpolación Basados en Funciones de Base Radial con Aplicaciones a la Reconstrucción de Imágenes

This article presents the Radial Base Functions (RBFs) as a functional interpolation method for implicit surface reconstruction from points cloud. These methods allow not only to improve inaccuracies resulting from scanners, but also possible discontinuities that occur in the point clouds. The complexity of three-dimensional objects makes reconstruction difficult since devices such as scanners do not always faithfully reproduce the objects, which can lead to information gaps or an incomplete reconstruction. Interpolation methods based on RBFs allow to correct these errors. Three-dimensional surface reconstruction has wide applications in biomedical engineering, in the design of industrial parts, among others. With the algorithm, we developed we have been able to make reconstructions of both explicit and implicit functions, in two and three dimensions.Keywords: Radial Basis Functions, Three-dimensional reconstruction, Interpolation Methods.

On the equivalence of spherical splines with least-squares collocation and Stokes\u2019s formula for regional geoid computation

This work is an investigation of three methods for regional geoid computation: Stokes’s formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223–232, 1995. doi:10.1007/BF00806734) that the equivalence of Stokes’s formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes’s formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

Modelling and Simulation of Transport Mechanisms of Electro-Migration and Diffusion of Ionic Species in the Concrete through Meshless Methods

The transport of ions such as chloride ion through the concrete has been the subject of study, because the entrance of these, affects the useful life of the structure. The mechanism of ionic transport is described by the Nernst-Planck equation and to solve the problem numerical techniques such as the Finite Difference Method (MDF) or Finite Element (MEF) are used which require a meshing process and a higher cost Computational. In this work, relatively new methods such as the Radial Base Functions (FBR) method and the Fundamental Solution Method (MSF) were applied, which do not require a mesh to solve the ion transport problem.

Authorship Authentication for Twitter Messages Using Support Vector Machine

With the rapid growth of internet usage, authorship authentication of online messages became challenging research topic in the last decades. In this paper, we used a team of support vector machines to authenticate 5 Twitter authors’ messages. SVM is one of the commonly used and strong classification algorithms in authorship attribution problems. SVM maps the linearly non separable input data to a higher dimensional space by a hyperplane via radial base functions. Firstly using the training data, 10 hyperplanes that separate pair wise five authors training data are built. Then the expertise of these SVMs combined to classify the testing data into five classes. 20 tweets with 16 features from each author were used for evaluation. In spite of the randomly choice of the features, one of the author accuracy around 75% is achieved.

Impact of accounting for coloured noise in radar altimetry data on a regional quasi-geoid model

We study the impact of an accurate computation and incorporation of coloured noise in radar altimeter data when computing a regional quasi-geoid model using least-squares techniques. Our test area comprises the Southern North Sea including the Netherlands, Belgium, and parts of France, Germany, and the UK. We perform the study by modelling the disturbing potential with spherical radial base functions. To that end, we use the traditional remove-compute-restore procedure with a recent GRACE/GOCE static gravity field model. Apart from radar altimeter data, we use terrestrial, airborne, and shipboard gravity data. Radar altimeter sea surface heights are corrected for the instantaneous dynamic topography and used in the form of along-track quasi-geoid height differences. Noise in these data are estimated using repeat-track and post-fit residual analysis techniques and then modelled as an auto regressive moving average process. Quasi-geoid models are computed with and without taking the modelled coloured noise into account. The difference between them is used as a measure of the impact of coloured noise in radar altimeter along-track quasi-geoid height differences on the estimated quasi-geoid model. The impact strongly depends on the availability of shipboard gravity data. If no such data are available, the impact may attain values exceeding 10 centimetres in particular areas. In case shipboard gravity data are used, the impact is reduced, though it still attains values of several centimetres. We use geometric quasi-geoid heights from GPS/levelling data at height markers as control data to analyse the quality of the quasi-geoid models. The quasi-geoid model computed using a model of the coloured noise in radar altimeter along-track quasi-geoid height differences shows in some areas a significant improvement over a model that assumes white noise in these data. However, the interpretation in other areas remains a challenge due to the limited quality of the control data.

Сравнение методов интерполяции при построении карты протаивания территории Якутии для расчета глубин закладки геодезических центров

Abstract: The most part of Yakutia Republic territory is located in permafrost zone. A method of permafrost thawing depth map creating have been developed as applied to Yakutia Republic territory. This is necessary to determine necessary depth of geodetic points centers newly established, as well as to evaluate the extent of existing centers of geodetic point’s safety. Creating a thawing depth map requires a choice of rational interpolation method for results obtained at the monitoring stations. Earlier depths thawing maps were created using linear interpolation method. Eight interpolation methods of thawing depth data obtained at the monitoring stations have been compared. ArcGIS software was used. Kriging method and radial base functions method allow obtaining solutions with the best statistical characteristics. Kriging method is proposed to use as a main interpolation method.

Some new operational matrices and its application to fractional order Poisson equations with integral type boundary constrains

Enormous application of fractional order partial differential equations (FPDEs) subjected to some constrains in the form of nonlocal boundary conditions motivated the interest of many scientists around the world. The prime objective of this article is to find approximate solution of a general FPDEs subject to nonlocal integral type boundary conditions on both ends of the domain. The proposed method is based on spectral method. We construct some new operational matrices which have the ability to handle integral type non-local boundary constrains. These operational matrices can be effectively applied to convert the FPDEs together with its integral types boundary conditions to easily solvable matrix equation. The accuracy and efficiency of proposed method are demonstrated by solving some bench mark problems. The proposed method has the ability to solve non-local FPDEs with high accuracy and low computational cost. Different aspects of presented approach are compared with two other recently developed methods, Haar wavelets collocation method and a family of collocation methods which are based on Radial base functions. It is observed that the proposed method is highly accurate, robust, efficient and stable as compared to these methods.