Basis Function Widths Research Articles

The Application and Research of Particle Swarm Optimization Radial Basis Function Network Driven by Edge Computing in Bogie Fault Diagnosis

The bogie system is a key system that affects the safety and quality of high-speed train operation. Constructing a fault diagnosis model for the bogie system can effectively improve the safety and comfort of high-speed train operation. The traditional modeling method uses the BP neural network to fit the temperature and other parameters of the bogie system. However, because the BP neural network is prone to fall into local minima, slow convergence and poor diagnostic accuracy, this paper proposes a radial basis function network bogie fault diagnosis model based on particle swarm optimization based on edge computing. The model combines edge computing and particle swarm optimization algorithm to improve the accuracy and real-time of bogie fault diagnosis. By implementing model training and inference on edge devices, data transmission latency has been reduced and diagnostic efficiency has been improved. A particle radial basis neural network (PSRB) was designed using a highly convergent particle swarm optimization algorithm, and the parameters of the radial basis neural network (RBF Neural Networks) were optimized using the Particle Swarm Optimization algorithm. Based on the complexity of the input parameters of the bogie system, determine the input and output parameters of the model, and use particle swarm optimization algorithm to search for the optimal values of the basis function center, width, and output layer weight threshold of the RBF neural network. The composite algorithm was applied to the fault diagnosis of the bogie system, and a particle radial basis neural network bogie fault diagnosis model was designed. The simulation and experimental results of the model show that the diagnostic model can effectively improve the identification accuracy of fault diagnosis, with a minimum error accuracy of 0.0255, saving computation time. The computation time is reduced to 2.9 seconds, eliminating the influence of non target parameters on the inversion results. This model can also be used in other systems of high-speed trains and has practical application value.

An enhanced artificial bee colony algorithm using radial bases function neural networks for color image segmentation

The aim of segmentation process is to partition the image into homogeneous regions or objects. The proposed segmentation algorithms using adaptive feature weighting to distinguish the significance of various features. To extract effective feature extraction could be used for establishing regions in region based image segmentation. The main goal of this exploration work is to segment objects that separating the foreground and background of the color images. The segmentation for color images is focused on the Enhanced Artificial Bee Colony segmentation algorithm that utilizes the Radial Basis Function (EABCRBF) neural network algorithm. This work arranges RBF neural networks to predict the end limits of the segmentation, which are formed from the artificial bee colony province made in the image histogram topography. The radial basis function initial parameters, for instance, centers and widths are automatically set upon the histogram peaks and minima. The proposed EABCRBF strategy is compared with two existing techniques of Artificial Bee Colony (ABC) and Fuzzy C-Means (FCM). The EABCRBF method gives great outcomes for color image segmentation as it extracts additional information from color images. The experimentation results are shown through Mat Lab R2013a.

Radial Basis Function Neural Network Model for Dissolved Oxygen Concentration Prediction Based on an Enhanced Clustering Algorithm and Adam

In fishery aquaculture, water quality directly determines the economic benefits of aquatic products, and dissolved oxygen is an important factor affecting water quality. To accurately grasp the trends of variation in dissolved oxygen, a dissolved oxygen concentration forecasting model based on an enhanced clustering algorithm and Adam with a radial basis function neural network (ECA-Adam-RBFNN) is proposed. An enhanced clustering algorithm (ECA) combining K-means with ant colony optimization is introduced in place of random selection to determine the center positions of the neural network hidden layer units. If the number of center points is too high, the neural network will be overfit, whereas if it is too low, sudden changes will appear in the results. Once the hidden layer centers have been determined, the radial basis function (RBF) width is calculated from the maximum center distance and the number of center points to avoid the two extreme cases of RBF that are too peaked or flat. The recursive least squares (RLS) algorithm is introduced to obtain the connection weights from the hidden layer to the output layer. The Adam algorithm is introduced to iteratively differentiate the objective function to adjust the center values, weights and width while adaptively varying the learning rates for these three types of parameters. Finally, the improved forecasting algorithm is applied for the prediction of the dissolved oxygen concentration in fishery aquaculture. The experimental results show that under identical conditions, compared with a long short-term memory (LSTM) network, a backpropagation neural network (BPNN), a traditional RBF neural network, a support vector regression (SVR) model, an autoregressive integrated moving average (ARIMA), K-MLPNN (K-means muhilayer perceptron neural networks), and SC-K-means-RBF model, the improved algorithm achieves significant reductions in the mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE) as model evaluation indicators.

A Novel Intelligent Method for Predicting the Penetration Rate of the Tunnel Boring Machine in Rocks

In the construction of rock tunnels, the penetration rate of the tunnel boring machine (TBM) is influenced by many factors (e.g., geomechanical parameters), some of which are highly uncertain. It is difficult to establish a precise model for predicting the penetration rate on the basis of the influencing factors. Thus, this work proposed a useful method, based on the relevance vector machine (RVM) and particle swarm optimization (PSO), for the prediction of the TBM penetration rate. In this method, the RVM played a vital role in establishing a nonlinear mapping relationship between the penetration rate and its influencing factors through training-related samples. Then, the penetration rate could be predicted using some collected data of the influencing factors. As for the PSO, it helped to find the optimum value of a key parameter (called the basis function width) that was needed in the RVM model. Subsequently, the validity of the proposed RVM-PSO method was checked with the data monitored from a rock tunnel. The results showed that the RVM-PSO method could estimate the penetration rate of the TBM, and it proved superior to the back-propagation artificial neural network, the least-squares support vector machine, and the conventional RVM methods, in terms of the prediction performance. Moreover, the proposed RVM-PSO method could be applied to identify the difference in the importance of the various factors affecting the TBM penetration rate prediction for a tunnel.

Surrogate based optimization of functionally graded plates using radial basis functions

This work presents an efficient methodology for optimum design of functionally graded plates. Isogeometric analysis is used to evaluate the structural responses and the material gradation is described using B-Splines to enhance design flexibility. A constraint is included in the optimization model to ensure a smooth material gradation. In order to improve the computational efficiency of the optimization process, a surrogate model based on Radial Basis Functions is used to accurately approximate the structural responses. Different methods to define the width of basis functions based on analytical and cross-validation techniques are adopted and compared. Two infill criteria based on the expected improvement technique are used to continuously improve the surrogate model accuracy by balancing both the local and global searches. The accuracy and efficiency of the proposed approaches are assessed through a set of problems involving the maximization of the buckling load and the fundamental frequency of functionally graded plates, showing excellent results.

Improved broadband performance of an adjoint shape optimized waveguide crossing using a Levenberg-Marquardt update.

We derive an adjoint shape optimization algorithm with a compound figure of merit and demonstrate its use with both gradient descent and Levenberg-Marquart updates for the case of SiO2-buried SOI coplanar waveguide crossings. We show that a smoothing parameter, basis function width, can be used to eliminate small feature sizes with a small cost to device performance. The Levenberg-Marquardt update produces devices with larger bandwidth. A waveguide crossing with simulated performance values of > 60 dB cross power extinction ratio and > -0.08 dB through power over the 1500-1600 nm band is presented. A fabricated device is measured to have a maximum of -0.06 dB through power and a 50 dB cross power extinction ratio.

An Adaptive Policy Evaluation Network Based on Recursive Least Squares Temporal Difference With Gradient Correction

Reinforcement learning (RL) is an important machine learning paradigm that can be used for learning from the data obtained by the human–computer interface and the interaction in human-centered smart systems. One of the essential problems in RL algorithms is the value functions. Value functions are usually estimated via linearly parameterized value functions. Prior RL algorithms that generalize in this way required learning times tuning the linear weights leaving out the basis function. In fact, basis functions in value function approximation also have a significant influence on the performance. In this paper, a new adaptive policy evaluation network based on recursive least squares temporal difference (TD) with gradient correction (adaptive RC network) is proposed. Basis functions in the proposed algorithm were adaptive optimized, mainly aiming at the widths. In the proposed algorithm, TD error and value function were estimated by RC algorithm and value function approximation. The gradient derived from the squares of TD error was used to update the widths of basis functions. Therefore, the RC network can adjust its network parameters in an adaptive way with a self-organizing approach according to the progress in learning. Empirical results based on the three RL benchmarks show the performance and applicability of the proposed adaptive RC network.

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.

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation.

We present a framework for the identification of spatiotemporal linear dynamical systems. We use a state-space model representation that has the following attributes: 1) the number of spatial observation locations are decoupled from the model order; 2) the model allows for spatial heterogeneity; 3) the model representation is continuous over space; and 4) the model parameters can be identified in a simple and sparse estimation procedure. The model identification procedure we propose has four steps: 1) decomposition of the continuous spatial field using a finite set of basis functions where spatial frequency analysis is used to determine basis function width and spacing, such that the main spatial frequency contents of the underlying field can be captured; 2) initialization of states in closed form; 3) initialization of state-transition and input matrix model parameters using sparse regression-the least absolute shrinkage and selection operator method; and 4) joint state and parameter estimation using an iterative Kalman-filter/sparse-regression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model.

Improving the effect of fuzzy clustering on RBF network’s performance in terms of particle swarm optimization

This paper proposes a novel training algorithm for radial basis function neural networks based on fuzzy clustering and particle swarm optimization. So far, fuzzy clustering has proven to be a very efficient tool in designing such kind of networks. The motivation of the current work is to quantify the exact effect of fuzzy cluster analysis on the network’s performance and use it in order to substantially improve this performance. There are two key theoretical findings resulting from the present work. First, it is analytically proved that when the standard fuzzy c-means algorithm is used to generate the input space fuzzy partition, the main effect this partition imposes to the network’s square error (i.e. performance index) can be written down in terms of a distortion function that measures the ability of the partition to recreate the original data. Second, using the aforementioned distortion function, an upper bound of the network’s square error can be constructed. Then, the particle swarm optimization (PSO) is put in place to minimize the above upper bound and determine the network’s parameters. To further improve the accuracy, the basis function widths and the connection weights are fine-tuned by employing a steepest descent approach. The main experimental findings are: (a) the implementation of the PSO obtains a significant reduction of the square error while exhibiting a smooth dynamic behavior, (b) although the steepest descent further decreases the error it finally obtains smaller reduction rates, meaning that the strongest impact on the error reduction is provided by the PSO, and (c) the improved performance of the proposed network is demonstrated through an extensive comparison with other related methods using a 10-fold cross-validation analysis.

The advantage of flexible neuronal tunings in neural network models for motor learning

Human motor adaptation to novel environments is often modeled by a basis function network that transforms desired movement properties into estimated forces. This network employs a layer of nodes that have fixed broad tunings that generalize across the input domain. Learning is achieved by updating the weights of these nodes in response to training experience. This conventional model is unable to account for rapid flexibility observed in human spatial generalization during motor adaptation. However, added plasticity in the widths of the basis function tunings can achieve this flexibility, and several neurophysiological experiments have revealed flexibility in tunings of sensorimotor neurons. We found a model, Locally Weighted Projection Regression (LWPR), which uniquely possesses the structure of a basis function network in which both the weights and tuning widths of the nodes are updated incrementally during adaptation. We presented this LWPR model with training functions of different spatial complexities and monitored incremental updates to receptive field widths. An inverse pattern of dependence of receptive field adaptation on experienced error became evident, underlying both a relationship between generalization and complexity, and a unique behavior in which generalization always narrows after a sudden switch in environmental complexity. These results implicate a model that is flexible in both basis function widths and weights, like LWPR, as a viable alternative model for human motor adaptation that can account for previously observed plasticity in spatial generalization. This theory can be tested by using the behaviors observed in our experiments as novel hypotheses in human studies.

The automatic model selection and variable kernel width for RBF neural networks

The Orthogonal Least Squares (OLS) algorithm has been extensively used in basis selection for RBF networks, but it is unable to perform model selection automatically because the tolerance ρ must be specified manually. This introduces noise and it is difficult to implement in the parametric complexity of real-time system. Therefore, a generic criterion that detects the optimum number of its basis functions is proposed. In this paper, not only the Bayesian Information Criterion (BIC) method, used for fitness calculation, is incorporated into the basis function selection process of the OLS algorithm for assigning its appropriate number, but also a new method is developed to optimize the widths of the Gaussian functions in order to improve the generalization performance. The augmented algorithm is employed to the Radial Basis Function Neural Networks (RBFNN) for known and unknown noise nonlinear dynamic systems and its performance is compared with the standard OLS; experimental results show that both the efficacy of BIC for fitness calculation and the importance of proper choice of basis function widths are significant.

Machine learning approach to automatic exudate detection in retinal images from diabetic patients

Exudates are among the preliminary signs of diabetic retinopathy, a major cause of vision loss in diabetic patients. Early detection of exudates could improve patients’ chances to avoid blindness. In this paper, we present a series of experiments on feature selection and exudates classification using naive Bayes and support vector machine (SVM) classifiers. We first fit the naive Bayes model to a training set consisting of 15 features extracted from each of 115,867 positive examples of exudate pixels and an equal number of negative examples. We then perform feature selection on the naive Bayes model, repeatedly removing features from the classifier, one by one, until classification performance stops improving. To find the best SVM, we begin with the best feature set from the naive Bayes classifier, and repeatedly add the previously-removed features to the classifier. For each combination of features, we perform a grid search to determine the best combination of hyperparameters ν (tolerance for training errors) and γ (radial basis function width). We compare the best naive Bayes and SVM classifiers to a baseline nearest neighbour (NN) classifier using the best feature sets from both classifiers. We find that the naive Bayes and SVM classifiers perform better than the NN classifier. The overall best sensitivity, specificity, precision, and accuracy are 92.28%, 98.52%, 53.05%, and 98.41%, respectively.

Modelling of the Automatic Depth Control Electrohydraulic System Using RBF Neural Network and Genetic Algorithm

The automatic depth control electrohydraulic system of a certain minesweeping tank is complex nonlinear system, and it is difficult for the linear model obtained by first principle method to represent the intrinsic nonlinear characteristics of such complex system. This paper proposes an approach to construct accurate model of the electrohydraulic system with RBF neural network trained by genetic algorithm‐based technique. In order to improve accuracy of the designed model, a genetic algorithm is used to optimize centers of RBF neural network. The maximum distance measure is adopted to determine widths of radial basis functions, and the least square method is utilized to calculate weights of RBF neural network; thus, computational burden of the proposed technique is relieved. The proposed technique is applied to the modelling of the electrohydraulic system, and the results clearly indicate that the obtained RBF neural network can emulate the complex dynamic characteristics of the electrohydraulic system satisfactorily. The comparison results also show that the proposed algorithm performs better than the traditional clustering‐based method.

Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model

Solid oxide fuel cell (SOFC) is a kind of nonlinear, multi-input–multi-output (MIMO) system that is hard to model by the traditional methodologies. For the purpose of dynamic simulation and control, this paper reports a dynamic modeling study of SOFC stack using a Hammerstein model. The static nonlinear part of the Hammerstein model is modeled by a radial basis function neural network (RBFNN), and the linear part is modeled by an autoregressive with exogenous input (ARX) model. To estimate the hidden centers, the radial basis function widths and the connection weights of the RBFNN, a new gradient descent algorithm is derived in the study. On the other hand, the least squares (LS) algorithm and Akaike Information Criteria (AIC) are used to estimate the parameters and the orders of the ARX model, respectively. The applicability of the proposed Hammerstein model in modeling the nonlinear dynamic properties of the SOFC is illustrated by the simulation. At the same time, the experimental comparisons between the Hammerstein model and the RBFNN model are provided which show a substantially better performance for the Hammerstein model. Furthermore, based on this Hammerstein model, some control schemes such as predictive control, robust control can be developed.

Cardinal Interpolation

A Bayesian probability density for an interpolating function is developed, and its desirable properties and practical potential are demonstrated. This density has an often needed but previously unachieved property, here called cardinal interpolation, which ensures extrapolation to the density of the least squares linear model. In particular, the mean of the cardinal interpolation density is a smooth function that intersects given (x, y) points and which extrapolates to their least squares line, and the variance of this density is a smooth function that is zero at the point x values, that increases with distance from the nearest point x value, and that extrapolates to the well-known quadratic variance function for the least squares line. The new cardinal interpolation density is developed for Gaussian radial basis interpolators using fully Bayesian methods that optimize interpolator smoothness. This optimization determines the basis function widths and yields an interpolating density that is non-Gaussian except for large magnitude x and which is therefore not the outcome of a Gaussian process. Further new development shows that the salient property of extrapolation to the density of the least squares linear model can be achieved for more general approximating (not just interpolating) functions.

Genetic optimization of GRNN for pattern recognition without feature extraction

This paper describes an approach for pattern recognition using genetic algorithm and general regression neural network (GRNN). The designed system can be used for both 3D object recognition from 2D poses of the object and handwritten digit recognition applications. The system does not require any preprocessing and feature extraction stage before the recognition. In GRNN, placement of centers has significant effect on the performance of the network. The centers and widths of the hidden layer neuron basis functions are coded in a chromosome and these two critical parameters are determined by the optimization using genetic algorithms. Experimental results show that the optimized GRNN provides higher recognition ability compared with that of unoptimized GRNN.

Inter-Residue Spatial Distance Map Prediction by Using Integrating Ga with Rbfnn

The spatial ordering information of amino acid residue in protein primary sequence is an important determinant of protein three-dimensional structure. In this paper, we describe a radial basis function neural network (RBFNN), whose hidden centers and basis function widths are optimized by a genetic algorithm (GA), for the purpose of predicting three dimensional spatial distance location from primary sequence information. Experimental evidence on soybean protein sequences indicates the utility of this approach.

Prediction of inter-residue contacts map based on genetic algorithm optimized radial basis function neural network and binary input encoding scheme

Inter-residue contacts map prediction is one of the most important intermediate steps to the protein folding problem. In this paper, we focus on the problem of protein inter-residue contacts map prediction based on neural network technique. Firstly, we use a genetic algorithm (GA) to optimize the radial basis function widths and hidden centers of a radial basis function neural network (RBFNN), then a novel binary encoding scheme is employed to train the network for the purpose of learning and predicting the inter-residue contacts patterns of protein sequences got from the protein data bank (PDB). The experimental evidence indicates the utility of our proposed encoding strategy and GA optimized RBFNN. Moreover, the simulation results demonstrate that the network got a better performance for these proteins, whose residue length falls into the area of (100, 300), and the predicted accuracy with a contact threshold of 7 Angstroms scores higher than the other 3 values with 5, 6, and 8 Angstroms.

On the Kernel Widths in Radial-Basis Function Networks

RBFN (Radial-Basis Function Networks) represent an attractive alternative to other neural network models. Their learning is usually split into an unsupervised part, where center and widths of the basis functions are set, and a linear supervised part for weight computation. Although available literature on RBFN learning widely covers how basis function centers and weights must be set, little effort has been devoted to the learning of basis function widths. This paper addresses this topic: it shows the importance of a proper choice of basis function widths, and how inadequate values can dramatically influence the approximation performances of the RBFN. It also suggests a one-dimensional searching procedure as a compromise between an exhaustive search on all basis function widths, and a non-optimal a priori choice.