Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems

In this paper, adaptive meshfree methods using local nodes and radial basis functions (RBFs) which based on strong-form formulation is presented. In this present formulation, radial basis functions are used in the function approximation for the discretization of the governing system equations. Regularization techniques are suggested and examined to stabilize the solutions in order to obtain stable and accurate results. Different schemes for constructing regularization matrix are compared and discussed. As stability is restored, meshfree strong-form method using local nodes and RBFs can facilitate an easier implementation for adaptive analysis to achieve desired accuracy. Residual based error indicator is devised in the adaptive scheme. A simple and practical node refinement procedure is presented for node insertion at each adaptive step.

Our work provides an effective feature based method for analyzing both steady state and short duration non-stationary power signal disturbances using a Local Linear Radial Basis Function Neural Network (LLRBFNN). In contrast to the normalized probabilistic neural network (PNN), the proposed LLRBFNN is an excellent approximation network, which performs the classification task with minimal amount of computational power than probabilistic neural network (PNN). The difference of the LLRBFNN with conventional Radial Basis Function Neural Network (RBFNN) is that a local linear model replaces the connection of weights between the hidden layer and output layer of conventional RBFNN. Both normalized time domain and frequency domain features are used for the training purpose. It is noticed that spectral entropy is an effective frequency domain feature for non-stationary power signal classification. Moreover the local linear model provides a robust model for network learning, which is not prone to local linear points. This is supported by the observation that both the LLRBFNN model and the global search optimization techniques like Genetic algorithm provide similar results.

Unsteady mixed convective heat transfer flow past an inclined square cylinder is numerically investigated using a local multi-quadric radial basis function (MQRBF) interpolation. The blockage parameter (ratio of square cylinder length d to height of the computational domain H) varies from 0.025 to 0.2. Air is considered as the working fluid and Prandtl number is fixed at 0.71. Richardson number generally affects the heat transfer efficiency ranging from 0 to 20. Inclined angle of square cylinder ranges from 0° to 45°. The inlet flow is assumed to be laminar and uniform. At the outlet of the computational domain, a convective boundary condition is compared with a traditional Neumann condition. A study of the shape parameter of MQRBF which is sensitive to the distribution of inhomogeneous supporting nodes is provided. The representative streamlines, vortex structures and isotherm patterns are presented and discussed. In addition, the overall lift and drag coefficients, average Nusselt number and Strouhal number for unsteady flow are analyzed for various Reynolds number and Richardson number.

In this paper the development and application of a dynamic neural network called the dynamic neural processor (DNP) are discussed. The DNP is developed based on the neuro-physiological evidence that neural activity of any complexity depends upon the interaction of assembly of cells called neural subpopulations. A single subpopulation of neurons is assumed to consist of a number of similar neurons that lie in close proximity. For simplicity, live neural subpopulations, namely excitatory and inhibitory, are assumed to exist in a neural population. The DNP consists of two dynamic neurons configured to function as excitatory and inhibitory neurons. A learning algorithm to adapt the weights of the subpopulation and the connecting weights between the subpopulations is developed. The efficacy of the DNP structure is demonstrated for the direct adaptive control of unknown nonlinear systems. >

The local radial basis function (RBF) method is a promising solver for variable‐order time fractional diffusion equation (TFDE), as it overcomes the computational burden of the traditional global method. Application of the local RBF method is limited to Fickian diffusion, while real‐world diffusion is usually non‐Fickian in multiple dimensions. This article is the first to extend the application of the local RBF method to two‐dimensional, variable‐order, time fractional diffusion equation in complex shaped domains. One of the main advantages of the local RBF method is that only the nodes located in the subdomain, surrounding the local point, need to be considered when calculating the numerical solution at this point. This approach can perform well with large scale problems and can also mitigate otherwise ill‐conditioned problems. The proposed numerical approach is checked against two examples with curved boundaries and known analytical solutions. Shape parameter and subdomain node number are investigated for their influence on the accuracy of the local RBF solution. Furthermore, quantitative analysis, based on root‐mean‐square error, maximum absolute error, and maximum error of the partial derivative indicates that the local RBF method is accurate and effective in approximating the variable‐order TFDE in two‐dimensional irregular domains.

Nonlinear classifiers, e.g., support vector machines (SVMs) with radial basis function (RBF) kernels, have been used widely for automatic diagnosis of diseases because of their high accuracies. However, it is difficult to visualize the classifiers, and thus difficult to provide intuitive interpretation of results to physicians. We developed a new nonlinear kernel, the localized radial basis function (LRBF) kernel, and new visualization system visualization for risk factor analysis (VRIFA) that applies a nomogram and LRBF kernel to visualize the results of nonlinear SVMs and improve the interpretability of results while maintaining high prediction accuracy. Three representative medical datasets from the University of California, Irvine repository and Statlog dataset-breast cancer, diabetes, and heart disease datasets-were used to evaluate the system. The results showed that the classification performance of the LRBF is comparable with that of the RBF, and the LRBF is easy to visualize via a nomogram. Our study also showed that the LRBF kernel is less sensitive to noise features than the RBF kernel, whereas the LRBF kernel degrades the prediction accuracy more when important features are eliminated. We demonstrated the VRIFA system, which visualizes the results of linear and nonlinear SVMs with LRBF kernels, on the three datasets.

A multivariable hyperstable robust adaptive decoupling control algorithm based on a neural network is presented for the control of nonlinear multivariable coupled systems with unknown parameters and structure. The Popov theorem is used in the design of the controller. The modelling errors, coupling action and other uncertainties of the system are identified on-line by a neural network. The identified results are taken as compensation signals such that the robust adaptive control of nonlinear systems is realised. Simulation results are given.

Improved localized radial basis functions with fitting factor for dominated convection-diffusion differential equations

Localized BF-Type Networks for Identification and Adaptive Control of Discrete-Time Nonlinear Systems

A novel brain shift tracking protocol is introduced in this paper which utilizes laser range scan (LRS) data and 2D deformable image registration. This protocol builds on previous efforts to incorporate intra-operative LRS data into a model-updated image guided surgery paradigm for brain shift compensation. The shift tracking method employs the use of a LRS system capable of capturing textures of the intra-operative scene during range data acquisition. Textures from serial range images are then registered using a 2D deformable registration approach that uses local support radial basis functions and mutual information. Given the deformation field provided by the registration, 3D points in serial LRS datasets can then be tracked. Results from this paper indicate that the error associated with tracking brain movement is 1.1mm on average given brain shifts of approximately 20.5mm. Equally important, a strategy is presented to rapidly acquire intra-operative measurements of shift which are compatible with model-based strategies for brain deformation compensation.

Soil management is an essential concern in protecting soil properties, in enhancing appropriate soil quality for plant growth and agricultural productivity, and in preventing soil erosion. Soil scientists and decision makers require accurate and well-distributed spatially continuous soil data across a region for risk assessment and for effectively monitoring and managing soils. Recently, spatial interpolation approaches have been utilized in various disciplines including soil sciences for analysing, predicting and mapping distribution and surface modelling of environmental factors such as soil properties. The study area selected in this research is Tuz Lake Basin in Turkey bearing ecological and economic importance. Fertile soil plays a significant role in agricultural activities, which is one of the main industries having great impact on economy of the region. Loss of trees and bushes due to intense agricultural activities in some parts of the basin lead to soil erosion. Besides, soil salinization due to both human-induced activities and natural factors has exacerbated its condition regarding agricultural land development. This study aims to compare capability of Local Polynomial Interpolation (LPI) and Radial Basis Functions (RBF) as two interpolation methods for mapping spatial pattern of soil properties including organic matter, phosphorus, lime and boron. Both LPI and RBF methods demonstrated promising results for predicting lime, organic matter, phosphorous and boron. Soil samples collected in the field were used for interpolation analysis in which approximately 80% of data was used for interpolation modelling whereas the remaining for validation of the predicted results. Relationship between validation points and their corresponding estimated values in the same location is examined by conducting linear regression analysis. Eight prediction maps generated from two different interpolation methods for soil organic matter, phosphorus, lime and boron parameters were examined based on R2 and RMSE values. The outcomes indicate that RBF performance in predicting lime, organic matter and boron put forth better results than LPI. However, LPI shows better results for predicting phosphorus.

Natural convection in a pentagonal house with a protruding cooler for summer is numerically investigated. The sloping roof is subjected to constant heat flux, and the cooler maintains at a uniform cold temperature. The remaining walls of the house are insulated. Local multi-quadratic radial basis function (LMQRBF) method is applied in solution of Navier–Stokes equations in stream function-vorticity form. The working fluid in the house is air with Pr = 0.71. The effects of Rayleigh number (103 ≤ Ra ≤ 106), heat flux of the roof (0.1 ≤ q ≤ 2.0), and the cooler’s vertical position (0.65 ≤ H/L ≤ 0.85) are explored. Streamlines, isotherms, velocity profiles, and the distribution of Nusselt number are displayed. Numerical results indicate that for the top and right wall of the cooler, the heat transfer is stronger than that for the bottom wall. It reveals that all the governing parameters efficiently impact the generation and evolution of the secondary and tertiary vortex in the gable roof. It is also observed that the variation of average Nusselt number on the right wall with Rayleigh number is under the combined influence of the heat flux and the cooler’s vertical position.

Simulation of electromagnetic wave propagations in negative index materials by the localized RBF-collocation method

This work presents a new technique for the identification of multiple power quality disturbances in industrial power systems. This new technique is developed based on change detection filter (CDF) and machine intelligence techniques like the local linear radial basis function neural network (LLRBFNN) and decision tree (DT). The proposed change detection filter has been designed in one cycle back fashion for the multiple non–stationary transient power signal disturbances for localisation, and feature extraction. The extracted features are fed as inputs to either a LLRBFNN or a decision tree–based classifier (DTC) for characterisation of the power quality events. The performance of LLRBFNN and DTC are evaluated and compared with local linear wavelet neural network (LLWNN), wavelet neural network (WNN), radial basis function neural network (RBFNN), etc., to highlight the superior performance of the proposed classifiers.

Despite the remarkable progress in silicon-based integration technology, there is still no clear consensus on how to exploit efficiently this technology for massively parallel neural network hardware implementation. In the following some of the key implementational issues will be considered and microelectronic implementations developed in our research group will be sketched. Especially, the question of resource-efficient implementations will be discussed.The chips presented are model-specific integrated circuits for neural associative memories, self-organizing feature maps, local cluster neural networks and radial basis function networks, respectively. These chips are embedded in our VMEbus environment for large scale simulation as well as into the micro-robot Khepera for resource-efficient real-time application.