Ellipsoidal Basis Function Research Articles

Multiobjective Optimization Design for a MR Damper Based on EBFNN and MOPSO

The structural parameters of the magnetorheological (MR) damper significantly affect the output damping force and dynamic range. This paper presents a design optimization method to improve the damping performance of a novel MR damper with a bended magnetic circuit and folded flow gap. The multiobjective optimization of the structural parameters of this MR damper was carried out based on the optimal Latin hypercube design (Opt LHD), ellipsoidal basis function neural network (EBFNN), and multiobjective particle swarm optimization (MOPSO). By using the Opt LHD and EBFNN, determination of the optimization variables on the structural parameters was conducted, and a prediction model was proposed for further optimization. Then, the MOPSO algorithm was adopted to obtain the optimal structure of the MR damper. The simulation and experimental results demonstrate that the damping performance indicators of the optimal MR damper were greatly improved. The simulation results show that the damping force increased from 4585 to 6917 N, and the gain was optimized by 50.8%. The dynamic range increased from 12.4 to 13.2, which was optimized by 6.4%. The experimental results show that the damping force and dynamic range of the optimal MR damper were increased to 7247 N and 13.8, respectively.

Nonlinear systems modelling based on self-organizing fuzzy neural network with hierarchical pruning scheme

In this paper, a self-organizing fuzzy neural network with hierarchical pruning scheme (SOFNN-HPS) is proposed for nonlinear systems modelling in industrial processes. In SOFNN-HPS, to strike the optimal balance between system accuracy and network complexity, an online self-organizing scheme for identifying the structure and parameters of the network simultaneously is developed. First, to enhance the characterization ability of the fuzzy rules for nonlinear systems, the asymmetric Gaussian functions that can partition the input space more flexibly are introduced as membership functions. Second, a hierarchical pruning scheme, which is designed by rule density and rule significance, is used to delete the redundant fuzzy rules while using the geometric growing criteria to generate fuzzy rules automatically, which can avoid the requirement of pre-setting the pruning threshold and prevent the mistaken deletion of significant rules. Third, an adaptive allocation strategy is adopted to set the antecedent parameters of the fuzzy rules in the learning process, which can not only adjust the region of generalized ellipsoidal basis functions for better local approximation, but also balance the accuracy of the system and the interpretability of the rule base obtained. Finally, to speed up the convergence of the estimation error, a modified recursive least square algorithm is used to update the consequent parameters of the resulting fuzzy rules online. In addition, the convergence proofs of the estimation error and the network linear parameters of SOFNN-HPS are given, and they are helpful in successfully applying the SOFNN-HPS in practical engineering. To verify the effectiveness of SOFNN-HPS, two benchmark test problems and a key water quality parameter prediction experiment in the wastewater treatment process are examined. The simulation results demonstrate that the proposed SOFNN-HPS algorithm can obtain a self-organizing fuzzy neural network with compact structure and powerful generalization performance. The source codes of SOFNN-HPS and other competitors can be downloaded from https://github.com/hyitzhb/SOFNN-HPS.

Collaborative optimization for ring-stiffened composite pressure hull of underwater vehicle based on lamination parameters

A Collaborative Optimization (CO) methodology for ring-stiffened composite material pressure hull of underwater vehicle is proposed. Structural stability and material strength are both examined. Lamination parameters of laminated plates are introduced to improve the optimization efficiency. Approximation models are established based on the Ellipsoidal Basis Function (EBF) neural network to replace the finite element analysis in layout optimizers. On the basis of a two-level optimization, the simultaneous structure material collaborative optimization for the pressure vessel is implemented. The optimal configuration of metal liner and frames and composite material is obtained with the comprehensive consideration of structure and material performances. The weight of the composite pressure hull decreases by 30.3% after optimization and the validation is carried out. Collaborative optimization based on the lamination parameters can optimize the composite pressure hull effectively, as well as provide a solution for low efficiency and non-convergence of direct optimization with design variables.

Dynamic saliency-driven associative memories based on network potential field

In this paper, we present a framework to construct a general class of recurrent neural networks (RNNs) as associative memories (AMs) for pattern storage and retrieval. Different from the traditional AM models that treat elements of a pattern equally, the proposed framework introduces visual saliency of a target pattern into the AM design process by encoding saliency values into the ellipsoidal basis function (EBF) kernel that calculates the weighted distance between the input and target patterns. Network potential fields (NPFs) are then constructed as the linear combination of EBF/radial basis function (RBF) kernels for auto-associative memories (AAMs) and hetero-associative memories (HAMs), respectively. Sparse and dynamic synapses for both the proposed AAMs and HAMs are determined according to the gradients of the NPFs with high efficiency and without the continuity assumptions of the RNN's activation function, which is usually required by traditional AMs. With the proposed method, the target patterns are assigned as fixed point attractors of the network and the AMs are proven to be able to converge to one of these attractors via Lyapunov analysis. The resulted AAMs and HAMs are demonstrated to have excellent tolerance and robustness to a variety of input noises and corruption via comparative experiments on retrieval and association of 2D color images.

Multiobjective optimization of injection molding process parameters based on Opt LHD, EBFNN, and MOPSO

The injection molding process parameters strongly affect plastic production quality, manufacturing cost, and molding efficiency. In this study, the effects of the process parameters, including the valve gate open timing, the molding temperature, the melt temperature, the injection time, the packing pressure, the packing time, and the cooling time, on the warpage of the plastic product and the clamping force during the injection molding process are analyzed using the analysis of variance method. A multiobjective optimization of the injection molding process parameters for a diesel engine oil cooler cover was carried out based on the optimal Latin hypercube design, ellipsoidal basis function neural network, and multiobjective particle swarm optimization. According to the calculated results using the optimal parameters, a structural optimization on the oil cooler cover cooling and a cooling channel improvement are proposed to further reduce the warpage. At last, a suite of overall tools are developed to treat the cooling deformation. As a result, the reduction on warpage is about 4 mm, the peak stress of the optimized plastic oil cooler cover is reduced by 60 MPa, and the stress distributes more evenly throughout the whole product. The peak clamping force is decreased from 760 to 470 t which makes the machine selection more flexible and reduces the production cost.

Data driven modeling based on dynamic parsimonious fuzzy neural network

In this paper, a novel fuzzy neural network termed as dynamic parsimonious fuzzy neural network (DPFNN) is proposed. DPFNN is a four layers network, which features coalescence between TSK (Takagi–Sugeno–Kang) fuzzy architecture and multivariate Gaussian kernels as membership functions. The training procedure is characterized by four aspects: (1) DPFNN may evolve fuzzy rules as new training datum arrives, which enables to cope with non-stationary processes. We propose two criteria for rule generation: system error and ε-completeness reflecting both a performance and sample coverage of an existing rule base. (2) Insignificant fuzzy rules observed over time based on their statistical contributions are pruned to truncate the rule base complexity and redundancy. (3) The extended self organizing map (ESOM) theory is employed to dynamically update the centers of the ellipsoidal basis functions in accordance with input training samples. (4) The optimal fuzzy consequent parameters are updated by time localized least square (TLLS) method that exploits a concept of sliding window in order to reduce the computational burden of the least squares (LS) method. The viability of the new method is intensively investigated based on real-world and artificial problems as it is shown that our method not only arguably delivers more compact and parsimonious network structures, but also achieves lower predictive errors than state-of-the-art approaches.

Online Adaptive Fuzzy Neural Identification of a Piezoelectric Tube Actuator System

A coupled actuator-flap-circuit system model and its online identification are presented. The coupled system consists of a piezoelectric tube actuator, a trailing-edge flap, and a series R-L-C circuit. The properties of the coupled system are examined using a Mach-scaled rotor simulation on hovering state. According to the high nonlinear hysteretic characteristics of the coupled system, the generalized dynamic fuzzy neural networks (GD-FNN) implementing Takagi-Sugeno-Kang (TSK) fuzzy systems based on extended ellipsoidal radial basis function (EBF) neural network is used to identify the coupled system. The structures and parameters are adaptive adjusted during the learning process, and don’t need too much expert experiences. Simulation studies show that the piezoelectric tube actuator has high authority with a broad frequency bandwidth, satisfies the requirements for helicopter vibration reduction; GD-FNN has a high learning speed, the final networks have a parsimonious network structure and generalize well, possessing broad application prospects in the helicopter vibration reduction.

A NOVEL EFFICIENT LEARNING ALGORITHM FOR SELF-GENERATING FUZZY NEURAL NETWORK WITH APPLICATIONS

In this paper, a novel efficient learning algorithm towards self-generating fuzzy neural network (SGFNN) is proposed based on ellipsoidal basis function (EBF) and is functionally equivalent to a Takagi-Sugeno-Kang (TSK) fuzzy system. The proposed algorithm is simple and efficient and is able to generate a fuzzy neural network with high accuracy and compact structure. The structure learning algorithm of the proposed SGFNN combines criteria of fuzzy-rule generation with a pruning technology. The Kalman filter (KF) algorithm is used to adjust the consequent parameters of the SGFNN. The SGFNN is employed in a wide range of applications ranging from function approximation and nonlinear system identification to chaotic time-series prediction problem and real-world fuel consumption prediction problem. Simulation results and comparative studies with other algorithms demonstrate that a more compact architecture with high performance can be obtained by the proposed algorithm. In particular, this paper presents an adaptive modeling and control scheme for drug delivery system based on the proposed SGFNN. Simulation study demonstrates the ability of the proposed approach for estimating the drug's effect and regulating blood pressure at a prescribed level.

A Generalized Ellipsoidal Basis Function Based Online Self-constructing Fuzzy Neural Network

In this paper, we propose a Generalized ellipsoidal basis function based online self-constructing fuzzy neural network (GEBF-OSFNN) which extends the ellipsoidal basis function (EBF)-based fuzzy neural networks (FNNs) by permitting input variables to be modeled by dissymmetrical Gaussian functions (DGFs). Due to the flexibility and dissymmetry of left and right widths of the DGF, the partitioning made by DGFs in the input space is more flexible and more interpretable, and therefore results in a parsimonious FNN with high performance under the online learning algorithm. The geometric growing criteria and the error reduction ratio (ERR) method are used as growing and pruning strategies respectively to realize the structure learning algorithm which implements an optimal and compact network structure. The GEBF-OSFNN starts with no hidden neurons and does not need to partition the input space a priori. In addition, all free parameters in premises and consequents are adjusted online based on the ?-completeness of fuzzy rules and the linear least square (LLS) approach, respectively. The performance of the GEBF-OSFNN paradigm is compared with other well-known algorithms like RAN, RANEKF, MRAN, ANFIS, OLS, RBF-AFS, DFNN, GDFNN GGAP-RBF, OS-ELM, SOFNN and FAOS-PFNN, etc., on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification, chaotic time-series prediction and real-world benchmark problems. Simulation results demonstrate that the proposed GEBF-OSFNN approach can facilitate a more powerful and more parsimonious FNN with better performance of approximation and generalization.

Enhancing the Interactive Visualization of Procedurally Encoded Multifield Data with Ellipsoidal Basis Functions

Abstract Functional approximation of scattered data is a popular technique for compactly representing various types of datasets in computer graphics, including surface, volume, and vector datasets. Typically, sums of Gaussians or similar radial basis functions are used in the functional approximation and PC graphics hardware is used to quickly evaluate and render these datasets. Previously, researchers presented techniques for spatially‐limited spherical Gaussian radial basis function encoding and visualization of volumetric scalar, vector, and multifield datasets. While truncated radially symmetric basis functions are quick to evaluate and simple for encoding optimization, they are not the most appropriate choice for data that is not radially symmetric and are especially problematic for representing linear, planar, and many non‐spherical structures. Therefore, we have developed a volumetric approximation and visualization system using ellipsoidal Gaussian functions which provides greater compression, and visually more accurate encodings of volumetric scattered datasets. In this paper, we extend previous work to use ellipsoidal Gaussians as basis functions, create a rendering system to adapt these basis functions to graphics hardware rendering, and evaluate the encoding effectiveness and performance for both spherical Gaussians and ellipsoidal Gaussians. Categories and Subject Descriptors (according to ACMCCS): I.3.3 [Computer Graphics]: Scientific Visualization, Ellipsoidal Basis Functions, Functional Approximation, Texture Advection

An on-line algorithm for creating self-organizing fuzzy neural networks

This paper presents a new on-line algorithm for creating a self-organizing fuzzy neural network (SOFNN) from sample patterns to implement a singleton or Takagi-Sugeno (TS) type fuzzy model. The SOFNN is based on ellipsoidal basis function (EBF) neurons consisting of a center vector and a width vector. New methods of the structure learning and the parameter learning, based on new adding and pruning techniques and a recursive on-line learning algorithm, are proposed and developed. A proof of the convergence of both the estimation error and the linear network parameters is also given in the paper. The proposed methods are very simple and effective and generate a fuzzy neural model with a high accuracy and compact structure. Simulation work shows that the SOFNN has the capability of self-organization to determine the structure and parameters of the network automatically.

An approach for on-line extraction of fuzzy rules using a self-organising fuzzy neural network

This paper presents a hybrid neural network, called the self-organising fuzzy neural network (SOFNN), to extract fuzzy rules from the training data. The first hidden layer of this network consists of ellipsoidal basis function (EBF) neurons. Every EBF neuron in the SOFNN has both a centre vector and a width vector. Neurons are organised by the network itself. The methods of the structure and parameter learning, based on new adding and pruning techniques and a recursive learning algorithm, are simple and effective, with a high accuracy and a compact structure. Simulations show that the SOFNN has the capability to encode fuzzy rules in the resulting network.

Artificial neural networks for fault detection in large-scale data acquisition systems

In this paper, a fault detection scheme for application to large-scale data acquisition systems is presented. The detection scheme has to process up to several hundreds of different measurements at a time and check them for consistency. The fault detection scheme works in three steps: First, principal component analysis of training data is used to determine non-sparse areas of the measurement space. Fault detection is accomplished by checking whether a new data record lies in a cluster of training data or not. Therefore, in a second step the distribution function of the available data is estimated using kernel regression techniques. In order to reduce the degrees of freedom and to determine clusters of data efficiently, in a third step the distribution function is approximated by a neural network. In order to use as few basis functions as possible a new training algorithm for ellipsoidal basis function networks is presented: New neurons are placed such that they approximate the distribution function in the vicinity of their centers up to the second order. This is accomplished by adapting the spread parameters using Taylor's theorem. Thus, the amount of necessary parameters and the computational effort for online supervision can be reduced dramatically. An important requirement for the fault detection scheme is that it is able to automatically adapt itself to new data. The present paper also addresses this feature. It is demonstrated how a gradient optimization with algebraic constraints can be applied to adapt a pre-existing network to new data points. Numerical examples with real data show that the proposed method produces excellent results.

A fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks

A fast approach for automatically generating fuzzy rules from sample patterns using generalized dynamic fuzzy neural networks (GD-FNNs) is presented. The GD-FNN is built based on ellipsoidal basis functions and functionally is equivalent to a Takagi-Sugeno-Kang fuzzy system. The salient characteristics of the GD-FNN are: (1) structure identification and parameters estimation are performed automatically and simultaneously without partitioning input space and selecting initial parameters a priori; (2) fuzzy rules can be recruited or deleted dynamically; (3) fuzzy rules can be generated quickly without resorting to the backpropagation (BP) iteration learning, a common approach adopted by many existing methods. The GD-FNN is employed in a wide range of applications ranging from static function approximation and nonlinear system identification to time-varying drug delivery system and multilink robot control. Simulation results demonstrate that a compact and high-performance fuzzy rule-base can be constructed. Comprehensive comparisons with other latest approaches show that the proposed approach is superior in terms of learning efficiency and performance.

Identification of 72 phytoplankton species by radial basis function neural network analysis of flow cytometric data

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 195:47-59 (2000) - doi:10.3354/meps195047 Identification of 72 phytoplankton species by radial basis function neural network analysis of flow cytometric data Lynne Boddy1,*, C. W. Morris2, M. F. Wilkins1, Luan Al-Haddad2, G. A. Tarran3, R. R. Jonker4, P. H. Burkill3 1Cardiff School of Biosciences, University of Cardiff, Cardiff CF1 3TL, United Kingdom 2School of Computing, University of Glamorgan, Pontypridd, United Kingdom 3Centre for Coastal and Marine Sciences, Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth PL1 3DH, United Kingdom 4AquaSense Lab, Kruislaan 411, 1090 HC Amsterdam, The Netherlands *E-mail: boddyl@cardiff.ac.uk ABSTRACT: Radial basis function artificial neural networks (ANNs) were trained to discriminate between phytoplankton species based on 7 flow cytometric parameters measured on axenic cultures. Comparison was made between the performance of networks restricted to using radially-symmetric basis functions and networks using more general arbitrarily oriented ellipsoidal basis functions, with the latter proving significantly superior in performance. ANNs trained on 62, 54 and 72 taxa identified them with respectively 77, 73 and 70% overall success. As well as high success in identification, high confidence of correct identification was also achieved. Misidentifications resulted from overlap of character distributions. Improved overall identification success can be achieved by grouping together species with similar character distributions. This can be done within genera or based on groupings indicated in dendrograms constructed for the data on all species. When an ANN trained on 1 data set was tested with data on cells grown under different light conditions, overall successful identification was low (<20%), but when an ANN was trained on a combined data set identification success was high (>70%). Clearly it is essential to include data on cells covering the whole spectrum of biological variation. Ways of obtaining data for training ANNs to identify phytoplankton from field samples are discussed. KEY WORDS: Radial basis functions · Neural networks · Principal component analysis · Dinoflagellates · Prymnesiomonads · Flagellates · Cryptomonads · Diatoms Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 195. Publication date: March 31, 2000 Print ISSN:0171-8630; Online ISSN:1616-1599 Copyright © 2000 Inter-Research.

Neurofuzzy modeling of chemical process systems with ellipsoidal radial basis function neural networks and genetic algorithms

Non-parametric methods for the construction of empirical process models have been used successfully in a variety of contexts in the field of process engineering. Despite their ability to form accurate representations of chemical process systems, non-parametric models are usually difficult to interpret. This is a serious hindrance where a premium is placed on model reliability and transparency. In this paper it is shown that by making use of radial basis function neural networks with arbitrarily oriented ellipsoidal basis functions, more parsimonious process models can be constructed. As with other radial basis function neural networks, the radial basis kernels also lend themselves to the construction of fuzzy rules. The methodology is illustrated by means of a case study on induced aeration in agitated vessels.

The ellipsoidal Gaussian basis in molecular orbital theory

The ellipsoidal Gaussian basis function used in a minimal valence atomic orbital representation is compared with the double-zeta spherical Gaussian basis orbital representation for some seventeen molecules made up of first row atoms and hydrogen. Except for acetylene the double-zeta basis gives consistently better total electronic energies and generally better property values than the optimized ellipsoidal single zeta basis. Difference molecular density contour maps comparing the two basis sets, as well as other one-electron property values, indicate that the ellipsoidal basis exaggerates the transfer of charge from the atomic regions to the interatomic and lone pair regions of molecules. Apparently, the forced complete elliptization of the valence atomic orbital in the single-zeta representation does not allow the basis set sufficient flexibility to simultaneously represent both the basically spherical atomic part of these orbitals and the non-spherical molecular bond formation. Other properties and aspects of the ellipsoidal Gaussian basis are also discussed.