Normalized Radial Basis Function Research Articles

A Neural Network Model for Estimation of Maximum Next Day Energy Generation Capacity of a Hydropower Station: A Case Study from Turkey

Energy planning in a hydro power station (HPS) is essential for reservoir management, and to ensure efficient operation and financial usage. For robust energy planning, operators should estimate next day energy generation capacity correctly. This paper investigates use of a robust neural network model to estimate maximum next day energy generation capacity by using reservoir inflow rates for the previous four days, the current level of water in the reservoir, and the weather forecast for the Darıca-2 HPS in Ordu Province, Turkey. The generated energy in an HPS is directly dependent on the level of stored water in the reservoir, which depends on reservoir inflow. As the level of water in a reservoir varies during the year depending on climatic conditions, it is important to be able to estimate energy generation in an HPS to operate the HPS most effectively. This paper uses reservoir inflow data that has been collected daily during 2020 for the training phase of a neural network. The neural network is tested using a data set that has been collected daily during the first four months of 2021. Used neural network structure is called as LWNRBF (Linear Weighted Normalized Radial Basis Function) network, which is developed form of RBF network. In order to be able to be created valid model, LWNRBF network is trained with a two-pass hybrid training algorithm. After the training and testing stages, average training and testing error percentages have been obtained as 0.0012% and -0.0044% respectively.

An intelligent model for cost prediction in new product development projects

Precise cost prediction of new product development (NPD) projects has been a challenge for both academia and practitioners that often requires much effort and experience. In this paper, a combination of particle swarm optimization (PSO), cross validation (CV) and support vector regression (SVR) is proposed to predict the cost of NPD projects. SVR, a novel intelligent technique for time series analysis, can overcome some shortcomings in the conventional approaches; and PSO, a new evolutionary computation technique, is utilized to set the optimal parameters of the SVR. The proposed intelligent model avoids manual selection of these parameters. The PSO solves the difficulty of setting these parameters appropriately and enhances the efficiency and capability of cost prediction. In addition, the CV is employed to train the SVR and improve the reliability of model performance. Then a real dataset of a home appliances manufacturer is provided to illustrate the proposed model and demonstrate the high performance and applicability to cost prediction of the NPD project. Finally, the effectiveness of the support vector model is compared with well-known techniques including multilayer perceptron networks (MLP), normalized radial basis function (NRBF) neural network, and pure SVR in terms of the accuracy measures. Based on the real world dataset, it is observed that the proposed model outperforms other well-known techniques.

RETRACTED: Neural network based identification of meat spoilage using Fourier-transform infrared spectra

To address the rapid and non-destructive detection of meat spoilage microorganisms during aerobic storage at chill and abuse temperatures, Fourier transform infrared spectroscopy (FTIR) with the help of an intelligent-based identification system was attempted in this work. The objective of this study is to associate simultaneously spectral data with microbiological data (log counts), for Total Viable Counts, Pseudomonas spp., Brochothrix thermosphacta, Lactic Acid Bacteria and Enterobacteriaceae. The dual purpose of the proposed modelling scheme is not only to classify meat samples in the respective quality class (i.e. fresh, semi-fresh and spoiled), but also to predict their associated microbiological population directly from FTIR spectra. An Extended Normalised Radial Basis Function neural network has been implemented, and the Bayesian Ying-Yang Expectation Maximisation algorithm has been utilised together with novel splitting operations to determine network’s size and parameter set. The dimensionality reduction of spectral data has been addressed by the implementation of a fuzzy principal component algorithm. Results confirmed the superiority of the adopted methodology compared to other schemes such as multilayer perceptron and the partial least squares techniques and indicated that spectral information obtained by FTIR spectroscopy during beef spoilage, in combination with an efficient choice of a learning-based modelling scheme could be considered as an alternative methodology for the accurate evaluation of meat spoilage.

Annealed cooperative–competitive learning of Mahalanobis-NRBF neural modules for nonlinear and chaotic differential function approximation

This work explores annealed cooperative–competitive learning of multiple modules of Mahalanobis normalized radial basis functions (NRBF) with applications to nonlinear function approximation and chaotic differential function approximation. A multilayer neural network is extended to be composed of multiple Mahalanobis-NRBF modules. Each module activates normalized outputs of radial basis functions, determining Mahalanobis radial distances based on its own adaptable weight matrix. An essential cooperative scheme well decomposes learning a multi-module network to sub-tasks of learning individual modules. Adaptable network interconnections are asynchronously updated module-by-module based on annealed cooperative–competitive learning for function approximation under a physical-like mean-field annealing process. Numerical simulations show outstanding performance of annealed cooperative–competitive learning of a multi-module Mahalanobis-NRBF network for nonlinear function approximation and long term look-ahead prediction of chaotic time series.

Size Optimization Using Normalized Radial Basis Function and Bat Algorithm

This paper is intended to demonstrate the use of normalized radial basis function (NRBF) network and Bat Algorithm (BA) for size optimization of a mechanical part under static loading. The data needed for developing the NRBF model is generated simulating a parameterized CAD model in ANSYS Workbench 14.5. Plausible input data for the CAD model is created using Latin Hypercube Sampling (LHS) method. A torque arm is considered to proof the concept. The comparison between the result obtained from the proposed method and the solution from ANSYS Workbench itself shows that, the NRBF-BA model is indeed effective in providing a reasonable solution for a moderately complex problem.

Power load forecasting using extended normalised radial basis function networks

Neural networks are currently finding practical applications, ranging from 'soft' regulatory control in consumer products, to the accurate modelling of nonlinear systems. Load forecasting is an important component for power system energy management system. Precise load forecasting helps the electric utility to make unit commitment decisions, reduce spinning reserve capacity and schedule device maintenance plan properly. In this paper we analyse the problem of short term load forecasting and propose a novel neural network scheme based on the Extended Normalised Radial Basis Function network. The Bayesian Ying Yang Expectation Maximisation algorithm has been used with novel splitting operations to determine a network size and parameter set. The results, utilising data from Eastern Slovakian Energy Board, are then compared with that of an MLP neural network.

Prediction of magnetic field near power lines by normalized radial basis function network

Over the past several decades, concerns have been raised over the possibility that the exposure to extremely low frequency electromagnetic fields from power lines may have harmful effects on human and living organisms. This work involved the computation of the magnetic field generated by 110kV overhead power lines using a normalized radial basis function (NRBF) network. Training of the evolving NRBF network is achieved by using the data generated from the numerical simulation based on Charge Simulation method (CSM). Then, NRBF has been used to determine the magnetic field distribution in a new geometry differing from the geometries used for training. These test results show that proposed NRBF network can be used as useful tool to calculate the magnetic fields from power lines, alternative to the conventional methods.

Fuzzy Q-learning in continuous state and action space

An adaptive fuzzy Q-learning (AFQL) based on fuzzy inference systems (FIS) is proposed. The FIS realized by a normalized radial basis function (NRBF) neural network is used to approach Q-value function, whose input is composed of state and action. The rules of FIS are created incrementally according to the novelty of each element of the pair of state-action. Moreover the premise part and consequent part of the FIS are updated using extended Kalman filter (EKF). The action that impacts on environment is the one with maximum output of FIS in the current state and generated through optimization method. Simulation results in the wall-following task of mobile robots and the inverted pendulum balancing problem demonstrate that the superiority and applicability of the proposed AFQL method.

Application of wavelet packet transform based Normalised Radial Basis Function Network in a machining process

In this work, an attempt has been made to develop a drill wear prediction system. A Hall-effect current sensor has been used for acquiring motor current signals during drilling under different cutting conditions. Wavelet packet transform has been used on the acquired current signals to extract features. A normalised Radial Basis Function (RBF) neural network model has then been developed to correlate the extracted features with drill wear. The proposed network outperforms the standard RBF neural network in terms of training error and also in terms of prediction error.

Normalized RBF networks: application to a system of integral equations

Linear integral and integro-differential equations of Fredholm and Volterra types have been successfully treated using radial basis function (RBF) networks in previous works. This paper deals with the case of a system of integral equations of Fredholm and Volterra types with a normalized radial basis function (NRBF) network. A novel learning algorithm is developed for the training of NRBF networks in which the BFGS backpropagation (BFGS-BP) least-squares optimization method as a recursive model is used. In the approach presented here, a trial solution is given by an NRBF network of incremental architecture with a set of unknown parameters. Detailed learning algorithms and concrete examples are also included.

An experimental study of the extended NRBF regression model and its enhancement for classification problem

As an extension of the traditional normalized radial basis function (NRBF) model, the extended normalized RBF ( ENRBF) model was proposed by Xu [RBF nets, mixture experts, and Bayesian Ying-Yang learning, Neurocomputing 19 (1998) 223–257]. In this paper, we perform a supplementary study on ENRBF with several properly designed experiments and some further theoretical discussions. It is shown that ENRBF is able to efficiently improve the learning accuracies under some circumstances. Moreover, since the ENRBF model is initially proposed for the regression and function approximation problems, a further step is taken in this work to modify the ENRBF model to deal with the classification problems. Both the original ENRBF model and the new proposed ENRBF classifier (ENRBFC) can be viewed as the special cases of the mixture-of-experts (ME) model that is discussed in Xu et al. [An alternative model for mixtures of experts, in: Advances in Neural Information Processing Systems, MIT Press, Cambridge, MA, 1995]. Experimental results show the potentials of ENRBFC compared to some other related classifiers.

A regularized minimum cross-entropy algorithm on mixtures of experts for time series prediction and curve detection

The well-known mixtures of experts (ME) model has been used in many different areas to account for nonlinearities and other complexities in the data, such as time series prediction. We usually train ME model by expectation maximization (EM) algorithm for maximum likelihood learning. However, the number of experts has to be determined first, which is often hardly known. Derived from regularization theory, a regularized minimum cross-entropy (RMCE) algorithm is proposed to train ME model, which can automatically make model selection. When time series is modeled by ME, it is demonstrated by some climate prediction experiments that RMCE algorithm outperforms EM algorithm. We also compare RMCE algorithm with other regression methods such as back-propagation (BP) and normalized radial basis function (NRBF) networks, and find that RMCE algorithm shows promising results. Moreover, we investigate curve detection problem by ME model with RMCE algorithm, which can detect curves (straight lines or circles) from a binary image. Some simulations and image experiments show that RMCE algorithm can automatically determine the number of straight lines or circles during parameter learning against noise, and in this way our algorithm does better than Hough transform (HT).

THE USE OF GAS-SENSOR ARRAYS TO DIAGNOSE URINARY TRACT INFECTIONS

Sensorial analysis based on the utilisation of human senses, is one of the most important and straightforward investigation methods in food and chemical analysis. An electronic nose has been used to detect in vivo Urinary Tract Infections from 45 suspected cases that were sent for analysis in a UK Health Laboratory environment. These samples were analysed by incubation in a volatile generation test tube system for 4-5 h. The volatile production patterns were then analysed using an electronic nose system with 14 conducting polymer sensors. An intelligent model consisting of an odour generation mechanism, rapid volatile delivery and recovery system, and a classifier system based on learning techniques has been considered. The implementation of an Extended Normalised Radial Basis Function network with advanced features for determining its size and parameters and the concept of fusion of multiple classifiers dedicated to specific feature parameters has been also adopted in this study. The proposed scheme achieved a very high classification rate of the testing dataset, demonstrating in this way the efficiency of the proposed scheme compared with other approaches. This study has shown the potential for early detection of microbial contaminants in urine samples using electronic nose technology.

Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth—active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure.

Online identification of the electrically stimulated quadriceps muscle group

In this paper, a new approach for estimating a nonlinear model of the electrically stimulated quadriceps muscle group under non-isometric conditions is investigated. In order to identify the muscle dynamics (stimulation pulse width-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shankquadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM). and passive joint properties form the time-invariant part. The actuator. i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time non linear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously.

RBF nets, mixture experts, and Bayesian Ying–Yang learning

The connections of the alternative model for mixture of experts (ME) to the normalized radial basis function (NRBF) nets and extended normalized RBF (ENRBF) nets are established, and the well-known expectation-maximization (EM) algorithm for maximum likelihood learning is suggested to the two types of RBF nets. This new learning technique determines the parameters of the input layer (including the covariance matrices or so-called receptive fields) and the parameters of the output layer in the RBF nets globally, instead of separately training the input layer by the K-means algorithm and the output layer by the least-squares learning as done in most of the existing RBF learning methods. In addition, coordinated competitive learning (CCL) and adaptive algorithms are proposed to approximate the EM algorithm for considerably speeding up the learning of the original and alternative ME models as well as the NRBF and ENRBF nets. Furthermore, the two ME models are linked to the recent proposed Bayesian Ying–Yang (BYY) learning system and theory such that not only the architecture of ME and RBF nets is shown to be more preferred than multilayer architecture, but also a new model selection criterion has been obtained to determine the number of experts and basis functions. A number of experiments are made on the prediction of foreign exchange rate and trading investment as well as piecewise nonlinear regression and piecewise line fitting. As shown in these experiments, the EM algorithm for NRBF nets and ENRBF nets obviously outperforms the conventional RBF learning technique, CCL speeds up the learning considerably with only a slight sacrifice on performance accuracy, the adaptive algorithm gives significant improvements on financial predication and trading investment, as well as that the proposed criterion can select the number of basis functions successfully. In addition, the ENRBF net and the alternative ME model are also shown to be able to implement curve fitting and detection.

Mixture of experts regression modeling by deterministic annealing

We propose a new learning algorithm for regression modeling. The method is especially suitable for optimizing neural network structures that are amenable to a statistical description as mixture models. These include mixture of experts, hierarchical mixture of experts (HME), and normalized radial basis functions (NRBF). Unlike recent maximum likelihood (ML) approaches, we directly minimize the (squared) regression error. We use the probabilistic framework as means to define an optimization method that avoids many shallow local minima on the complex cost surface. Our method is based on deterministic annealing (DA), where the entropy of the system is gradually reduced, with the expected regression cost (energy) minimized at each entropy level. The corresponding Lagrangian is the system's free-energy, and this annealing process is controlled by variation of the Lagrange multiplier, which acts as a temperature parameter. The new method consistently and substantially outperformed the competing methods for training NRBF and HME regression functions over a variety of benchmark regression examples.