Radial Basis Function Parameters Research Articles

Radial basis function neural network optimization algorithm based on dynamic inertial weight particle swarm optimization for separating overlapping peaks in ion mobility spectrometry.

Ion mobility spectrometry (IMS), as a promising analytical tool, has been widely employed in the structural characterization of biomolecules. Nevertheless, the inherent limitation in the structural resolution of IMS frequently results in peak overlap during the analysis of isomers exhibiting comparable structures. The radial basis function (RBF) neural network optimization algorithm based on dynamic inertial weight particle swarm optimization (DIWPSO) was proposed for separating overlapping peaks in IMS. The RBF network structure and parameters were optimized using the DIWPSO algorithm. By extensively training using a large dataset, an adaptive model was developed to effectively separate overlapping peaks in IMS data. This approach successfully overcomes issues related to local optima, ensuring efficient and precise separation of overlapping peaks. The method's performance was evaluated using experimental validation and analysis of overlapping peaks in the IMS spectra of two sets of isomers: 3'/6'-sialyllactose; fructose-6-phosphate, glucose-1-phosphate, and glucose-6-phosphate. A comparative analysis was conducted using other algorithms, including the sparrow search algorithm, DIWPSO algorithm, and multi-objective dynamic teaching-learning-based optimization algorithm. The comparison results show that the DIWPSO-RBF algorithm achieved remarkably low maximum relative errors of only 0.42%, 0.092%, and 0.41% for ion height, mobility, and half peak width, respectively. These error rates are significantly lower than those obtained using the other three algorithms. The experimental results convincingly demonstrate that this method can adaptively, rapidly, and accurately separate overlapping peaks of multiple components, improving the structural resolution of IMS.

A multi-instance multi-label learning algorithm based on radial basis functions and multi-objective particle swarm optimization

Radial basis function (RBF) neural networks for Multi-Instance Multi-Label (MIML) directly can exploit the connections between instances and labels so that they can preserve useful prior information, but they only adopt Gaussian radial basis function as their RBF whose parameters are difficult to determine. In this paper, parameters can be obtained by multi-objective optimization methods with multi performance measures treated as objectives, specifically, parameter estimation of different RBFs by an improved multi-objective particle swarm optimization (MOPSO) is proposed where Recall rate and Precision rate are chosen to obtain the most desirable Pareto optimal solution set. Furthermore, share-learning factor is proposed to modify the particle velocity in standard MOPSO to improve the global search ability and group cooperative ability. It is experimentally demonstrated that the proposed method can estimate the reliable parameters of different RBFs, and it is also very competitive with the state of art MIML methods.

Global iterative optimization framework for predicting cognitive function statuses of patients with end‐stage renal disease

AbstractThe existing methods to determine the cognitive function level of end‐stage renal disease (ESRD) are not only inaccurate but also susceptible to the influence of the patient's education level, emotional state, and examination environment. We proposed a global iterative optimization framework (GIO) to accurately predict cognitive function statuses of ESRD patients without being affected by the above factors. First, the functional magnetic resonance imaging (fMRI) data preprocessed and the time series were extracted to construct brain functional networks. Secondly, the areas under curve (AUC) of topological attribute parameters in the brain functional networks were extracted as features. After statistical analysis, the global efficiency, the characteristic path length, and the shortest path length in the small‐world network were selected as features for linear fusion. Finally, the support vector regression (SVR) was used as the basis of GIO framework, and the global iterative search strategy was introduced to find out the most appropriate penalty factor and radial basis function parameters. Achieving the objective of accurately predicting the cognitive function status of patients with end‐stage renal disease. Since this framework uses SVR which has special advantages in processing small sample data, and introduces appropriate parameter selection method, the prediction ability of GIO framework has been significantly improved. Experimental results demonstrate that the final prediction accuracy of the proposed framework is significantly better than those of SVR, LSSVR, GMO‐SVR, GMO‐LSSVR, and PSO‐SVR. The mean absolute error (MAE) and the mean absolute percentage error (MAPE) of the proposed framework are 0.55% and 2.58%, respectively. It is suggested that this framework is more convenient to determine the current level of cognitive function in ESRD patients and is conducive to the early prevention of cognitive dysfunction in ESRD patients.

GDR-Net: A Geometric Detail Recovering Network for 3D Scanned Objects.

This article addresses the problem of mesh super-resolution such that the geometry details which are not well represented in the low-resolution models can be recovered and well represented in the generated high-quality models. The main challenges of this problem are the nonregularity of 3D mesh representation and the high complexity of 3D shapes. We propose a deep neural network called GDR-Net to solve this ill-posed problem, which resolves the two challenges simultaneously. First, to overcome the nonregularity, we regress a displacement in radial basis function parameter space instead of the vertex-wise coordinates in the euclidean space. Second, to overcome the high complexity, we apply the detail recovery process to small surface patches extracted from the input surface and obtain the overall high-quality mesh by fusing the refined surface patches. To train the network, we constructed a dataset composed of both real-world and synthetic scanned models, including high/low-quality pairs. Our experimental results demonstrate that GDR-Net works well for general models and outperforms previous methods for recovering geometric details.

Training RBF neural networks for the solution of elliptic boundary value problems

We propose a radial basis function (RBF) neural network method for solving two- and three–dimensional second and fourth order elliptic boundary value problems (BVPs). The neural network in question is trained by minimizing a nonlinear least squares functional, thus determining the optimal values of the various RBF parameters involved. The functional minimization is carried out using standard MATLAB® software efficiently. Several numerical experiments are presented to demonstrate the efficacy of the proposed method.

Chatter detection in milling process based on the combination of wavelet packet transform and PSO-SVM

Chatter is one of the biggest unfavorable factors during the high speed machining process of a machine tool. It severely affects the surface finish and geometric accuracy of the workpiece. To address this obstacle and improve the quality and efficiency of products, it is significantly essential to detect chatter during machining. Therefore, a multi-feature recognition system for chatter detection on the basis of the fusion technology of wavelet packet transform (WPT) and particle swarm optimization support vector machine (PSO-SVM) was proposed in this paper. Firstly, the original vibration signals collected from the acceleration sensor were processed through wavelet packet transform (WPT). The noise and the irrelevant information were remarkably decreased. In addition, the wavelet packets containing chatter-emerging information were chosen and reconstructed. The fourteen time–frequency domain characteristics of the reconstructed vibration signal were calculated and chosen as the multi-feature vectors of chatter detection. Finally, to obtain the optimal radial basis function parameter g and penalty parameter C of the SVM prediction model, the optimization algorithms of k-fold cross-validation (k-CV), genetic algorithm (GA), and particle swarm optimization (PSO) were employed in optimizing the model parameters of SVM. It was indicated that the PSO-SVM improved obviously the accuracy of chatter recognition than the others. In addition, we applied the optimized SVM prediction model by PSO for detecting chatter state in end milling machining. Chatter recognition results indicated that the model accurately predicted the slight chatter state in advance.

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.

A Method for Reconstruction of Boiler Combustion Temperature Field Based on Acoustic Tomography

Acoustic tomography (AT), as a noninvasive temperature measurement method, can achieve temperature field measurement in harsh environments. In order to achieve the measurement of the temperature distribution in the furnace and improve the accuracy of AT reconstruction, a temperature field reconstruction algorithm based on the radial basis function (RBF) interpolation method optimized by the evaluation function (EF-RBFI for short) is proposed. Based on a small amount of temperature data obtained by the least square method (LSM), the RBF is used for interpolation. And, the functional relationship between the parameter of RBF and the root-mean-square (RMS) error of the reconstruction results is established in this paper, which serves as the objective function for the effect evaluation, so as to determine the optimal parameter of RBF. The detailed temperature description of the entire measured temperature field is finally established. Through the reconstruction of three different types of temperature fields provided by Dongfang Boiler Works, the results and error analysis show that the EF-RBFI algorithm can describe the temperature distribution information of the measured combustion area globally and is able to reconstruct the temperature field with high precision.

Adaptive rapid neural observer-based sensors fault diagnosis and reconstruction of quadrotor unmanned aerial vehicle

PurposeThe objective of this research is to investigate various neural network (NN) observer techniques for sensors fault identification and diagnosis of nonlinear system in consideration of numerous faults, failures, uncertainties and disturbances. For the importunity of increasing the faults diagnosis and reconstruction preciseness, a new technique is used for modifying the weight parameters of NNs without enhancement of computational complexities.Design/methodology/approachVarious techniques such as adaptive radial basis functions (ARBF), conventional radial basis functions, adaptive multi-layer perceptron, conventional multi-layer perceptron and extended state observer are presented. For increasing the fault detection preciseness, a new technique is used for updating the weight parameters of radial basis functions and multi-layer perceptron (MLP) without enhancement of computational complexities. Lyapunov stability theory and sliding-mode surface concepts are used for the weight-updating parameters. Based on the combination of these two concepts, the weight parameters of NNs are updated adaptively. The key purpose of utilization of adaptive weight is to enhance the detection of faults with high accuracy. Because of the online adaptation, the ARBF can detect various kinds of faults and failures such as simultaneous, incipient, intermittent and abrupt faults effectively. Results depict that the suggested algorithm (ARBF) demonstrates more confrontation to unknown disturbances, faults and system dynamics compared with other investigated techniques and techniques used in the literature. The proposed algorithms are investigated by the utilization of quadrotor unmanned aerial vehicle dynamics, which authenticate the efficiency of the suggested algorithm.FindingsThe proposed Lyapunov function theory and sliding-mode surface-based strategy are studied, which shows more efficiency to unknown faults, failures, uncertainties and disturbances compared with conventional approaches as well as techniques used in the literature.Practical implicationsFor improvement of the system safety and for avoiding failure and damage, the rapid fault detection and isolation has a great significance; the proposed approaches in this research work guarantee the detection and reconstruction of unknown faults, which has a great significance for practical life.Originality/valueIn this research, two strategies such Lyapunov function theory and sliding-mode surface concept are used in combination for tuning the weight parameters of NNs adaptively. The main purpose of these strategies is the fault diagnosis and reconstruction with high accuracy in terms of shape as well as the magnitude of unknown faults. Results depict that the proposed strategy is more effective compared with techniques used in the literature.

Railway dangerous goods transportation system risk identification: Comparisons among SVM, PSO-SVM, GA-SVM and GS-SVM

In this paper, three algorithms are applied to obtain the parameters of Radial Basis Function (RBF) kernels of Support Vector Machines (SVM), which include: PSO (Particle Swarm Optimization), GA (Genetic Algorithm) and GS (Grid Search). The three improved SVM approaches are applied to identify the risk of railway dangerous goods transportation system (RDGTS). The statistical occurrence frequency of each sub-risk indicator of the happened RDGTS accidents is used as the basis of experts’ scores, the experts’ scores are presented in interval numbers form, which are used as the inputs of the four approaches. The accuracy rate, optimization time consuming, Mean Square Error (MSE), Receiver Operating Characteristic Curve (ROC) and Area Under Curve (AUC) are used as the evaluation indexes of the identification results. The comparison studies are conducted by using SVM with linear kernel (SVM-L) and SVM with polynomial kernel (SVM-P), respectively. By using such new methodology, the risk identification problem (evaluation problem) is transferred into a classification problem with faster identification speed, higher identification efficiency and higher accuracy. The identification results show that: GS-SVM is the optimal approach to identify the risk factors of Human; SVM is the optimal approach to identify the risk factors of Machine, Materials, Environment and Management. SVM has the shortest optimization time consuming, GA-SVM has the highest accuracy, hence, SVM and GA-SVM are better to applied to identify the risk of RDGTS. The optimization time consuming of all models is no more than 5 s, which means the RDGTS risk identification results could be obtained fast and high-efficiently and the mental strength for researchers can be reduced by using the SVM and improved SVM models. For the risk identification results considering MSE and AUC, GS-SVM is the most accurate and best classification algorithm, and the results based on SVM-P is better than the results based on SVM-L. The results based on PSO-SVM, GA-SVM and GS-SVM have better accuracy and reliability than that based on SVM-L or SVM-P, which means the PSO-SVM, GA-SVM and GS-SVM based risk identification approaches are practicable.

Short-term Traffic Flow Forecast Based on DE-RBF Fussion Model

The road traffic system is a time-varying, complex nonlinear system. Real-time and accurate road short-term traffic flow prediction is the key to realizing the traffic flow guidance system. In order to improve the prediction accuracy of short-term traffic flow, this paper proposes an algorithm based on the fusion model of differential evolution algorithm (DE) and radial basis function (RBF). This method takes the fitness function as the measurement standard, and uses the DE algorithm to optimize the RBF parameters to obtain the optimal short-term traffic flow prediction value. Through MATLAB simulation experiments, a relatively accurate prediction of the short-term traffic flow of the DE-RBF fusion model is realized. The mean square error (MSE) and the average absolute error percentage of actual and predicted values (MAPE) analysis index are introduced as the evaluation index of the prediction model. After comparing with the two prediction network models of radial basis function (RBF) and wavelet function (WNN), the results show that the DE-RBF fusion model proposed in this paper is effective and feasible for short-term traffic flow prediction.

Performance Analysis of a Wind Turbine Pitch Neurocontroller with Unsupervised Learning

In this work, a neural controller for wind turbine pitch control is presented. The controller is based on a radial basis function (RBF) network with unsupervised learning algorithm. The RBF network uses the error between the output power and the rated power and its derivative as inputs, while the integral of the error feeds the learning algorithm. A performance analysis of this neurocontrol strategy is carried out, showing the influence of the RBF parameters, wind speed, learning parameters, and control period, on the system response. The neurocontroller has been compared with a proportional-integral-derivative (PID) regulator for the same small wind turbine, obtaining better results. Simulation results show how the learning algorithm allows the neural network to adjust the proper control law to stabilize the output power around the rated power and reduce the mean squared error (MSE) over time.

Research on Regional Logistics Demand Forecast Based on Improved Support Vector Machine: A Case Study of Qingdao City under the New Free Trade Zone Strategy

Based on the analysis on the influencing factors of urban logistics demand, this paper, taking into account the logistics demand with non-linear and small sample modeling characteristics from the perspective of urban freight volume, introduces the ant colony algorithm into the modeling process to optimize the penalty parameter “c” and “g” parameter of Radial Basis Function in support vector machine, and has made a prediction to the logistics demand of Qingdao with the optimized support vector machine model. The experimental results show that the prediction results of the improved support vector machine can bring the prediction closer to the reality with their more accuracy, stronger stability and less error rate, thus providing a guarantee for the logistics demand forecast of Qingdao.

A joint optimization QSAR model of fathead minnow acute toxicity based on a radial basis function neural network and its consensus modeling.

Acute toxicity of the fathead minnow (Pimephales promelas) is an important indicator to evaluate the hazards and risks of compounds in aquatic environments. The aim of our study is to explore the predictive power of the quantitative structure–activity relationship (QSAR) model based on a radial basis function (RBF) neural network with the joint optimization method to study the acute toxicity mechanism, and to develop a potential acute toxicity prediction model, for fathead minnow. To ensure the symmetry and fairness of the data splitting and to generate multiple chemically diverse training and validation sets, we used a self-organizing mapping (SOM) neural network to split the modeling dataset (containing 955 compounds) characterized by PaDEL-descriptors. After preliminary selection of descriptors via the mean decrease impurity method, a hybrid quantum particle swarm optimization (HQPSO) algorithm was used to jointly optimize the parameters of RBF and select the key descriptors. We established 20 RBF-based QSAR models, and the statistical results showed that the 10-fold cross-validation results (Rcv102) and the adjusted coefficients of determination (Radj2) were all great than 0.7 and 0.8, respectively. The Qext2 of these models was between 0.6480 and 0.7317, and the Rext2 was between 0.6563 and 0.7318. Combined with the frequency and importance of the descriptors used in RBF-based models, and the correlation between the descriptors and acute toxicity, we concluded that the water distribution coefficient, molar refractivity, and first ionization potential are important factors affecting the acute toxicity of fathead minnow. A consensus QSAR model with RBF-based models was established; this model showed good performance with R2 = 0.9118, Rcv102 = 0.7632, and Qext2 = 0.7430. A frequency weighted and distance (FWD)-based application domain (AD) definition method was proposed, and the outliers were analyzed carefully. Compared with previous studies the method proposed in this paper has obvious advantages and its robustness and external predictive power are also better than Xgboost-based model. It is an effective QSAR modeling method.

Finding a good shape parameter of RBF to solve PDEs based on the particle swarm optimization algorithm

The present study aims at integrating the Particle Swarm Optimization (PSO) algorithm with Kansa’s method based on meshless collocation methods in order to determine a good shape parameter of Radial Basis Function (RBF) for solving partial differential equations (PDEs). For this purpose, we use a two-staged experimental design. While in the first stage, PSO algorithm was used to determine an optimal shape parameter for the related RBFs, in the second stage, we employed Kansa’s method to estimate the RMS error for specifying approximate solutions. To study the performance of the proposed algorithm, we offer numerical results for two examples of partial differential equations and show the effectiveness of the proposed method. Numerical results demonstrated the performance superiority of the new algorithm model. The findings also indicated that the evolutionary algorithm model is more effective than the golden section search algorithm in finding a good shape parameter of RBF.

IRG2016: RBF-based regional geoid model of Iran

The aim of this research is the optimal determination of the regional geoid model of Iran based on radial basis functions (RBFs). In this case, the type and number of RBFs, their horizontal positions, depths, and unknown coefficients must be properly determined. The quality of calculations strongly depends on the correct choice of these unknown parameters. Given the precise geocentric position of any point on the Earth’s surface with the beginning of the global navigation satellite system (GNSS), the surface gravity disturbances were used to calculate the height anomaly according to Molodensky’s theory. The residual surface gravity disturbances derived by subtracting the global gravitational model EIGEN-6C4 up to degree and order 360 were applied to determine the unknown RBF parameters using the stabilized orthogonal matching pursuit (SOMP) algorithm. Based on this iterative sparse approach, non-zero components of unknown RBF parameters having the maximum recoverable energy for the desired signal were found at each iteration. The SOMP algorithm was applied for optimal determination of the proper basis functions since each unknown RBF coefficient is related to a specific basis function. Only the RBFs representing the best solution to the problem were selected at each iteration, then several new RBFs were added at suitable positions to enhance the calculation result. The new RBF-based regional geoid model entitled IRG2016 was calculated by applying the geoid-to-quasigeoid corrections to the height anomaly. The IRG2016 was fitted to 1288 GNSS/levelling control points over Iran, by applying the polynomial corrector surface. Relying on this new strategy, the calculated height reference surface shows an RMS value of approximately 0.23 m for the difference in geoidal height at the independent control points, which is comparable with the last Stokes-based geoid model.

Equivalent magnetic vector potential model for low-frequency magnetic exposure assessment

In this paper, a novel source model based on a magnetic vector potential for the assessment of induced electric field strength in a human body exposed to the low-frequency (LF) magnetic field of an electrical appliance is presented. The construction of the vector potential model requires only a single-component magnetic field to be measured close to the appliance under test, hence relieving considerable practical measurement effort—the radial basis functions (RBFs) are adopted for the interpolation of discrete measurements; the magnetic vector potential model can then be directly constructed by summing a set of simple algebraic functions of RBF parameters. The vector potentials are then incorporated into numerical calculations as the equivalent source for evaluations of the induced electric field in the human body model. The accuracy and effectiveness of the proposed model are demonstrated by comparing the induced electric field in a human model to that of the full-wave simulation. This study presents a simple and effective approach for modelling the LF magnetic source. The result of this study could simplify the compliance test procedure for assessing an electrical appliance regarding LF magnetic exposure.

Combined mesh free method and mode matching approach for transmission loss predictions of expansion chamber silencers

A coupled method (abbreviated here as the MFMM method) that combines the mesh free (MF) method and mode matching (MM) approach is introduced to predict the transmission loss (TL) of expansion chamber silencers. The Hermite radial point interpolation collocation (HRPIC) method is employed to solve the 2-D eigen equation of silencer sections. Then the mode matching method is used to calculate the transmission loss. The eigenvalues predictions of circular cross section from the present method exhibit desirable precision comparison with analytical results. Additionally, the effects of size of influence domain, number of computational nodes and shape parameters of radial basis functions on the calculation accuracy are evaluated. TL calculations of four typical expansion chambers with extended inlet and outlet are presented to valid the computational accuracy and efficiency of the proposed combined method.

Anomaly Detection for Aviation Safety Based on an Improved KPCA Algorithm

Thousands of flights datasets should be analyzed per day for a moderate sized fleet; therefore, flight datasets are very large. In this paper, an improved kernel principal component analysis (KPCA) method is proposed to search for signatures of anomalies in flight datasets through the squared prediction error statistics, in which the number of principal components and the confidence for the confidence limit are automatically determined by OpenMP-based K-fold cross-validation algorithm and the parameter in the radial basis function (RBF) is optimized by GPU-based kernel learning method. Performed on Nvidia GeForce GTX 660, the computation of the proposed GPU-based RBF parameter is 112.9 times (average 82.6 times) faster than that of sequential CPU task execution. The OpenMP-based K-fold cross-validation process for training KPCA anomaly detection model becomes 2.4 times (average 1.5 times) faster than that of sequential CPU task execution. Experiments show that the proposed approach can effectively detect the anomalies with the accuracy of 93.57% and false positive alarm rate of 1.11%.

Cooperative learning for radial basis function networks using particle swarm optimization

This paper presents a new evolutionary cooperative learning scheme, able to solve function approximation and classification problems with improved accuracy and generalization capabilities. The proposed method optimizes the construction of radial basis function (RBF) networks, based on a cooperative particle swarm optimization (CPSO) framework. It allows for using variable-width basis functions, which increase the flexibility of the produced models, while performing full network optimization by concurrently determining the rest of the RBF parameters, namely center locations, synaptic weights and network size. To avoid the excessive number of design variables, which hinders the optimization task, a compact representation scheme is introduced, using two distinct swarms. The first swarm applies the non-symmetric fuzzy means algorithm to calculate the network structure and RBF kernel center coordinates, while the second encodes the basis function widths by introducing a modified neighbor coverage heuristic. The two swarms work together in a cooperative way, by exchanging information towards discovering improved RBF network configurations, whereas a suitably tailored reset operation is incorporated to help avoid stagnation. The superiority of the proposed scheme is illustrated through implementation in a wide range of benchmark problems, and comparison with alternative approaches.