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The phenomenon of artificial cavitation is a significant and practical aspect of reducing drag forces on devices interacting with water. Among various regimes, the supercavity regime, where the entire body or a substantial portion of it is enveloped by a cavity, plays a crucial role. This study investigates the cavitation phenomenon using a combination of numerical experimental methods and machine learning techniques. Specifically, the Support Vector Machine (SVM) classification model is employed to identify the type of artificial cavitation regime and to determine the occurrence of the supercavity regime based on input variables. The findings indicate that the Radial Basis Function (RBF) model outperforms other machine learning models in accurately detecting the cavity regime type, achieving an accuracy of over 95% in identifying the supercavity regime. Additionally, results from the RBF model demonstrate that the supercavity regime is observed at low cavitation numbers, exhibiting the longest cavity length.

Developing a novel and practical method based on the radial-base grid network (RBF) as well as the third-order polynomial of the exponential function $(f(t)=e^t)$ in order to solve the first-order differential equations based on $Z$-numbers is the aim of this paper. It is worth mentioning that the advantage of the proposed RBF is that sufficient information is not required. The RBF contains three distinct layers as follows: the input layer including the elementary nodes; the second layer including the hidden layers via high dimensions; and the output layer for responding and activating the patterns of the input layer. The obtained results revealed that this method could solve and approximate such problems under acceptable confidence.

This paper presents spatio-temporal modeling and analysis methods to fMRI data. Based on the nonlinear autoregressive with exogenous inputs (NARX) model realized by the Bayesian radial basis function (RBF) neural networks, two methods (NARX-1 and NARX-2) are proposed to capture the unknown complex dynamics of the brain activities. Simulation results on both synthetic and real fMRI data clearly show that the proposed schemes outperform the conventional t-test method in detecting the activated regions of the brain.

Along with the development of the motion capture (mocap) technique, large-scale 3D motion databases have become increasingly available. In this paper, a novel approach is presented for motion retrieval based on double-reference index (DRI). Due to the high dimensionality of motion's features, Isomap nonlinear dimension reduction is used. In addition, an algorithmic framework is employed to approximate the optimal mapping function by a Radial Basis Function (RBF) in handling new data. Subsequently, a DRI is built based on selecting a small set of representative motion clips in the database. Thus, the candidate set is obtained by discarding the most unrelated motion clips to significantly reduce the number of costly similarity measures. Finally, experimental results show that these approaches are effective for motion data retrieval in large-scale databases.

In practical applications, recognition accuracy is sometimes not the only criterion; capability to reject erroneous patterns might also be needed. We show that there is a trade-off between these two properties. An efficient solution to this trade-off is brought about by the use of different algorithms implemented in various modules, i.e. multi-modular architectures.

We present a general mechanism for designing and training multi-modular architectures, integrating various neural networks into a unique pattern recognition system, which is globally trained. It is possible to realize, within the system, feature extraction and recognition in successive modules which are cooperatively trained. We discuss various rejection criteria for neural networks and multi-modular architectures.

We then give two examples of such systems, study their rejection capabilities and show how to use them for segmentation. In handwritten optical character recognition, our system achieves performances at state-of-the-art level, but is eight times faster. In human face recognition, our system is intended to work in the real world.

A preprocessing stage in every speech/music applications including audio/speech separation, speech/speaker recognition and audio/genre transcription task is inevitable. The importance of such pre-processing stage is originated from the requisite of determining each frame of the given signal is belonged to which classes, namely: speech only, music only or speech/music mixture. Such classification can significantly decrease the computational burden due to exhaustive search commonly introduced as a problem in model-based speech recognition or separation as well as music transcription scenarios. In this paper, we present a new method to separate mixed type audio frames based on support vector machine (SVM) and neural network. We present a feature type selection algorithm which seeks for the most appropriate features to discriminate possible classes (hypotheses) on the mixed signal. We also propose features based on eigen-decomposition on the mixed frame. Experimental results demonstrate that the proposed features together with the selected audio classifiers achieve acceptable classification results. From the experimental results, it is observed that the proposed system outperforms other classification systems including k-nearest neighbor (k-NN) and multi-layer perceptron (MLP).

Inertial navigation system (INS) is often integrated with satellite navigation systems to achieve the required precision at high-speed applications. In global navigation system (GPS)/INS integration systems, GPS outages are unavoidable and a severe challenge. Moreover, because of the usage of low-cost microelectromechanical sensors (MEMS) with noisy outputs, the INS will get diverged during GPS outages, and that is why navigation precision severely decreases in commercial applications. In this paper, we improve GPS/INS integration system during GPS outages using extended Kalman filter (EKF) and artificial intelligence (AI) together. In this integration algorithm, the AI receives the angular rates and specific forces from the inertial measurement unit (IMU) and velocity from the INS at $t$ and $t-1$. Therefore, the AI has positioning and timing data of the INS. While the GPS signals are available, the output of the AI is compared with the GPS increment; so that the AI is trained. During GPS outages, the AI will practically play the GPS role. Thus, it can prevent the divergence of the GPS/INS integration system in GPS-denied environments. Furthermore, we utilize neural networks (NNs) as an AI module in five different types: multi-layer perceptron (MLP) NN, radial basis function (RBF) NN, wavelet NN, support vector regression (SVR) and adaptive neuro-fuzzy inference system (ANFIS). To evaluate the proposed approach, we utilize a real dataset that has been gathered by a mini-airplane. The results demonstrate that the proposed approach outperforms the INS and GPS/INS integration systems with the EKF during GPS outages. Meanwhile, the ANFIS also reached more than 47.77% precision compared to the traditional method.

The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S&P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout the study with the cubic spline interpolation. An analysis of the densities and the local volatility shows that RBF are an effective and practical tool for interpolating the implied volatility surface.

In this paper, a hybrid feature extraction technique using 2D principal component analysis (2DPCA) and discrete orthogonal Krawtchouk moment (KM) are used to extract the global and local features from the face. Ensemble of RBF classifiers are used to classify the image. Decision-level fusion is done using fuzzy integral to generate more accurate classification than each of the constituent classifiers. The proposed system is evaluated using ORL and YALE databases. Experimental results show that the combination of global and local features promotes the system performance. The fusion of multiple RBFs using fuzzy integral performed better as compared to conventional aggregation rules.

The content of massive image changing the brightest brightness is an impasse between most tests of sorted image realizations with low-resolution representation. I have done this research through image security, which will help curb crime in the coming days, and we propose a novel receipt for their strong and effective counterpart. Image classification using low levels of the image is a difficult method, so for this, I have adopted the method of automating the semantic image classification of this research and used it with different SVM classifiers, based on the normalized weighted feature support vector machine for semantic image classification. This is a novel approach given that weighted feature or normalized biased feature is applied and it is found that the normalized method is the best. It also uses normalized weighted features to compute kernel functions and train SVM. The trained SVM is then used to classify new images. During training and generalization, we displayed a decrease of identification error rate and there have been many benefits of using SVM with better performance in normalized image-cataloging systems. The importance of this technique and its role will be highlighted in the years to come.

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modeling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is finite difference method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of FPDEs.

The linear and nonlinear flexure analysis of laminated plates with twenty theories with the five variable higher order shear deformation theory (HSDT) is investigated using multiquadratic radial basis function based meshfree method. The mathematical formulation of the actual physical problem of the plate subjected to transverse loading is presented utilizing von Karman nonlinear kinematics. These non-linear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. The different results for deflection and stresses are obtained for thin to a thick plate and compared with some published results. It is observed that some of the theories taken here are well suited for analysis of thin as well as a thick plate while some theories are suited only for thin plates.

This paper presents the torsional analysis of isotropic, orthotropic, and functionally graded material (FGM) triangular and rectangular sections. The formulation of the governing equation of the torsion problem is done using the Saint–Venant torsion theory. Classical power law has been considered for the modeling of FGM material. A meshfree technique based on various radial basis functions is used for the solution of the governing differential equation. MATLAB code is developed to solve the discretized partial differential equations. To demonstrate the effectiveness and accuracy of this technique, convergence study and numerical examples are presented by varying the various parameters. The torsional rigidity factors and shear stress factors are obtained for different new conditions. The solution presented here is validated from the analytical and numerical results along with some new results, which shows the satisfactory performance of the present method.

This paper proposes an intelligent classification technique to identify two categories of MRI volume data as normal and abnormal. The manual interpretation of MRI slices based on visual examination by radiologist/physician may lead to incorrect diagnosis when a large number of MRIs are analyzed. In this work, the textural features are extracted from the MR data of patients and these features are used to classify a patient as belonging to normal (healthy brain) or abnormal (tumor brain). The categorization is obtained using various classifiers such as support vector machine (SVM), radial basis function, multilayer perceptron and k-nearest neighbor. The performance of these classifiers are analyzed and a quantitative indication of how better the SVM performance is when compared with other classifiers is presented. In intelligent computer aided health care system, the proposed classification system using SVM classifier can be used to assist the physician for accurate diagnosis.

This study proposes a diagnosis system for liver masses based on the improved radial basis function (RBF) neural networks. In this article, RBF networks are improved by sigmoid function and the growing and pruning algorithm. The proposed improved RBF networks adopt the sigmoid function as their kernel due to its increased flexibility over the Gaussian kernel. Furthermore, the growing and pruning algorithm is used to adjust the network size dynamically according to the neuron's significance. This investigation formulates discriminating among cysts, hepatoma, cavernous hemangioma, and normal tissue as a supervised learning problem. The current work calculates several texture and gray-level features derived from regions of interest as input in the proposed classifier. Receiver operating characteristic (ROC) curves evaluate the diagnosis performance, and demonstrate the proposed method's good performance.

In practical applications, recognition accuracy is sometimes not the only criterion; capability to reject erroneous patterns might also be needed. We show that there is a trade-off between these two properties. An efficient solution to this trade-off is brought about by the use of different algorithms implemented in various modules, i.e. multi-modular architectures.

We present a general mechanism for designing and training multi-modular architectures, integrating various neural networks into a unique pattern recognition system, which is globally trained. It is possible to realize, within the system, feature extraction and recognition in successive modules which are cooperatively trained. We discuss various rejection criteria for neural networks and multi-modular architectures.

We then give two examples of such systems, study their rejection capabilities and show how to use them for segmentation. In handwritten optical character recognition, our system achieves performances at state-of-the-art level, but is eight times faster. In human face recognition, our system is intended to work in the real world.

First the paper explains why fuzzy inference system can be regarded as just another interesting grey-box way of approximating non-linear mapping. Then it contributes at clarifying the current confusion raised by a lot of works comparing or merging neural nets with fuzzy inference systems. Practical comparisons with RBF are performed which show that the small structural addition leading to fuzzy systems can be of interest for function identification. To face the curse of dimensionality problem, the paper presents an algorithm developed in a biological spirit and dedicated to the on-line incremental building of fuzzy systems for function approximation. It is called EFUSS (Evolving Fuzzy Systems Structure) and aims at automatically and incrementally finding the minimal number of membership functions along with their appropriate shaping. Its main characteristics are that the structural additions occur at a lower time scale than the parametric changes. They are guided by the endogenous dynamics of the parametric learning and aim at compensating for the weakest parts of the systems.