B-spline Membership Functions Research Articles

Adaptive Neural Network Q-Learning-Based Full Recurrent Adaptive NeuroFuzzy Nonlinear Control Paradigms for Bidirectional-Interlinking Converter in a Grid-Connected Hybrid AC-DC Microgrid

The stability of a hybrid AC-DC microgrid depends mainly upon the bidirectional interlinking converter (BIC), which is responsible for power transfer, power balance, voltage solidity, frequency and transients sanity. The varying generation from renewable resources, fluctuating loads, and bidirectional power flow from the utility grid, charging station, super-capacitor, and batteries produce various stability issues on hybrid microgrids, like net active-reactive power flow on the AC-bus, frequency oscillations, total harmonic distortion (THD), and voltage variations. Therefore, the control of BIC between AC and DC buses in grid-connected hybrid microgrid power systems is of great importance for the quality/smooth operation of power flow, power sharing and stability of the whole power system. In literature, various control schemes are suggested, like conventional droop control, communication-based control, model predictive control, etc., each addressing different stability issues of hybrid AC-DC microgrids. However, model dependence, single-point-failure (SPF), communication vulnerability, complex computations, and complicated multilayer structures motivated the authors to develop online adaptive neural network (NN) Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms for BIC in a grid-connected hybrid AC-DC microgrid. The proposed strategies successfully ensure the following: (i) frequency stabilization, (ii) THD reduction, (iii) voltage normalization and (iv) negligible net active-reactive power flow on the AC-bus. Three novel adaptive NN Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms are proposed for PQ-control of BIC in a grid-connected hybrid AC-DC microgrid. The control schemes are based on NN Q-learning and full recurrent adaptive neurofuzzy identifiers. Hybrid adaptive full recurrent Legendre wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, Hybrid adaptive full recurrent Mexican hat wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, and Hybrid adaptive full recurrent Morlet wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control are modeled and tested for the control of BIC. The controllers differ from each other, based on variants used in the antecedent part (Gaussian membership function and B-Spline membership function), and consequent part (Legendre wavelet, Mexican hat wavelet, and Morlet wavelet) of the full recurrent adaptive neurofuzzy identifiers. The performance of the proposed control schemes was validated for various quality and stability parameters, using a simulation testbench in MATLAB/Simulink. The simulation results were bench-marked against an aPID controller, and each proposed control scheme, for a simulation time of a complete solar day.

MIMO Adaptive Bspline-Based Wavelet NeuroFuzzy Control for Multi-Type FACTS

Motivated by the synergistic integration of soft computing paradigms this paper introduces a fully adaptive multiple-input-multiple-output NeuroFuzzy control for multi-type Flexible AC Transmission Systems (FACTS) to damp low frequency oscillations. The novel control strategy integrates the complementary features of locally controllable fuzzy Bspline membership functions and robust wavelet neural networks in NeuroFuzzy structure. The gradient decent based back-propagation mechanism used for parameters update has been optimized using online Adaptive Learning Rates (ALRs). The stability of the proposed algorithm has been ensured by deriving an upper bound on ALRs using Lyapunov stability criteria. The application of this controller to provide damping signals to various FACTS controllers like Static Synchronous Series Compensator (SSSC) and Static Synchronous Compensator (STATCOM) can effectively enhance the dynamic stability of the system. A benchmark multi-machine power system has been used for performance validation of the controller by applying various faults under different loading scenarios. Conventional Lead-Lag and NeuroFuzzy controls have been considered for comparative evaluation using nonlinear time and frequency domain techniques to reveal that the proposed control performs better in different operating regions. Furthermore, the graphical results obtained from time and frequency domain simulations have been quantified numerically using different performance indices and Energy Spectral Density (ESD), respectively. The temporal, spectral and numerical analysis confirms the superior performance of the proposed control scheme.

A novel Lyapunov stable higher order B-spline online adaptive control paradigm of photovoltaic systems

In this paper, research on the control of photovoltaic (PV) using a novel higher order B-spline online adaptive neuro-fuzzy paradigm considering high external uncertainties in weather and load demand is presented. We optimize the existing neuro-fuzzy technique by incorporating third order B-spline membership functions in its antecedent part, which we solve using an on-line learning gradient-decent back propagation method. We fit the system parameters online through adaptive fuzzy rules extracted from the maximum power point tracking (MPPT) error and its derivative. Unlike many existing neuro-fuzzy techniques, our method addresses the trapping in local minima. The proposed controller is demonstrated to be stable using Lyapunov stability analysis. The performance of our control philosophy is checked in terms of output power tracking, efficiency, and MPPT error. Finally, we validate via simulation the high robustness and the self-adaptation ability of the proposed method over other existing traditional and intelligent techniques.

Hybrid adaptive neuro-fuzzy B-spline--based SSSC damping control paradigm using online system identification

B-spline membership functions have produced promising results in the field of signal processing and control due to their local control property. This work explores the potential of B-spline--based adaptive neuro-fuzzy wavelet control to damp low frequency power system oscillations using a static synchronous series compensator (SSSC). A comparison of direct and indirect adaptive control based on hybrid adaptive B-spline wavelet control (ABSWC) is presented by introducing the online identification block. ABSWC with identification (ABSWCI) provides the sensitivity information of the plant needed to control the system. The parameters of the control and identification block are updated online using a gradient descent-based backpropagation algorithm. The stability and convergence of the proposed control system is discussed based on Lyapunov stability criteria. The robustness of the proposed control algorithm has been evaluated for local and interarea modes of oscillations using different faults. The nonlinear time-domain simulations have been analyzed on the basis of different performance indices and time-frequency representation, showing that ABSWC effectively damps low-frequency oscillations and incorporation of online identification optimizes the control system performance in terms of control effort, which reduces the switching losses of the converter.

Fuzzy inference system based on B-spline membership function

It is hard to determine the membership function and inference rules in fuzzy reasoning.By studying the fuzzy reasoning process and the characteristics of B-spline function,the reasoning method on the application of B-spline function fitting to fuzzy membership function was improved.Through the calculation and selection of the extreme points of error and the extreme point of curvature,the B-spline function data points were obtained.After obtaining the control points by inversing data points,the curve fitting of the membership function was increased and the B-spline membership function fitting problem was solved on the curve of the B-spline by increasing the control points.B-spline inference rule was established and B-spline inference system was constructed,and then the final result of the system was calculated as a B-spline hypersurface.Finally,the experimental results validate the effectiveness and feasibility of this method.

On-line genetic algorithm-based fuzzy-neural sliding mode controller using improved adaptive bound reduced-form genetic algorithm

In this article, a novel on-line genetic algorithm-based fuzzy-neural sliding mode controller trained by an improved adaptive bound reduced-form genetic algorithm is developed to guarantee robust stability and good tracking performance for a robot manipulator with uncertainties and external disturbances. A general sliding manifold, which can be non-linear or time varying, is used to construct a sliding surface and reduce control law chattering. In this article, the sliding surface is used to derive a genetic algorithm-based fuzzy-neural sliding mode controller. To identify structured system dynamics, a B-spline membership function fuzzy-neural network, which is trained by the improved genetic algorithm, is used to approximate the regressor of the robot manipulator. The sliding mode control with a general sliding surface plays the role of a compensator when the fuzzy-neural network does not approximate the dynamics regressor of the robot manipulator well in the transient period. The adjustable parameters of the fuzzy-neural network are tuned by the improved genetic algorithm, which, with the use of the sequential-search-based crossover point method and the single gene crossover, converges quickly to near-optimal parameter values. Simulation results show that the proposed genetic algorithm-based fuzzy-neural sliding mode controller is effective and yields superior tracking performance for robot manipulators.

RGA-based on-line tuning of BMF fuzzy-neural networks for adaptive control of uncertain nonlinear systems

In this paper, an RGA-based indirect adaptive fuzzy-neural controller (RIAFC) for uncertain nonlinear systems is proposed by using a reduced-form genetic algorithm (RGA). Both the control points of B-spline membership functions (BMFs) and the weighting factors of the adaptive fuzzy-neural controller are tuned on-line via the RGA approach. Each gene represents an adjustable parameter of the BMF fuzzy-neural network with real number components. For the purpose of on-line tuning these parameters and evaluating the stability of the closed-loop system, a special fitness function is included in the RGA approach. In addition, in order to guarantee that the system states are confined to the safe region, a supervisory controller is incorporated into the RIAFC. To illustrate the feasibility and applicability of the proposed method, two examples of nonlinear systems controlled by the RIAFC are demonstrated.

Soft Computing for Battery State-of-Charge (BSOC) Estimation in Battery String Systems

In this paper, a soft computing technique for estimating battery state-of-charge of individual batteries in a battery string is proposed. The soft computing approach uses a fusion of a fuzzy neural network (FNN) with B-spline membership functions (BMFs) and a reduced-form genetic algorithm (RGA). The algorithm is employed to tune both control points of the BMFs and the weights of the FNNs. The traditional multiple-input multiple-output FNN (MIMOFNN) cannot directly be used in this paper. The main reason is that there are too many free parameters in the MIMOFNN to be trained if many inputs are required. In this paper, a merged multiple-input single-output (MISO) FNN is proposed and can be trained by the RGA optimization approach. The merged MISO FNN with RGA (FNNRGA) can achieve faster convergence and lower estimation error than neural networks with the back propagation method. From experimental results, the proposed merged MISO FNNRGA is superior, more robust than the traditional method, and the overfitting suppression features are significantly improved.

A Merged Fuzzy Neural Network and Its Applications in Battery State-of-Charge Estimation

To solve learning problems with vast number of inputs, this paper proposes a novel learning structure merging a number of small fuzzy neural networks (FNNs) into a hierarchical learning structure called a merged-FNN. In this paper, the merged-FNN is proved to be a universal approximator. This computing approach uses a fusion of FNNs using B-spline membership functions (BMFs) with a reduced-form genetic algorithm (RGA). RGA is employed to tune all free parameters of the merged-FNN, including both the control points of the BMFs and the weights of the small FNNs. The merged-FNN can approximate a continuous nonlinear function to any desired degree of accuracy. For a practical application, a battery state-of-charge (BSOC) estimator, which is a twelve input, one output system, in a lithium-ion battery string is proposed to verify the effectiveness of the merged-FNN. From experimental results, the learning ability of the newly proposed merged-FNN with RGA is superior to that of the traditional neural networks with back-propagation learning.

On-line modeling and control via T-S fuzzy models for nonaffine nonlinear systems using a second type adaptive fuzzy approach

This paper proposes a novel method for on-line modeling and robust adaptive control via Takagi-Sugeno (T-S) fuzzy models for nonaffine nonlinear systems, with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way. The so-called second type adaptive law is adopted, where not only the consequent part (the weighting factors) of fuzzy implications but also the antecedent part (the membership functions) of fuzzy implications are adjusted. Fuzzy B-spline membership functions (BMFs) are used for on-line tuning. Furthermore, the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated by a fuzzy error compensator which is also constructed from the T-S fuzzy model. In this paper, we can prove that the closed-loop system which is controlled by the proposed controller is stable and the tracking error will converge to zero. Three examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.

Evolutionary learning of bmf fuzzy-neural networks using a reduced-form genetic algorithm

In this paper, a novel approach to adjust both the control points of B-spline membership functions (BMFs) and the weightings of fuzzy-neural networks using a reduced-form genetic algorithm (RGA) is proposed. Fuzzy-neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, genetic algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional genetic algorithms is not desirable. Such conventional genetic algorithms are inherently incapable of dealing with a vast number (over 100) of adjustable parameters in the fuzzy-neural networks. In this paper, the RGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed, serving as a single gene crossover operation. Chromosomes consisting of both, the control points of BMFs and the weightings of the fuzzy-neural network are coded as an adjustable vector with real number components that are searched by the RGA. Simulation results have shown that faster convergence of the evolution process searching for an optimal fuzzy-neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy-neural network via the RGA are demonstrated to illustrate the effectiveness of the proposed method.

Fuzzy System and CMAC Network with B-Spline Membership/Basis Functions can Approximate A Smooth Function and its Derivatives

In control and other modeling applications, fuzzy system with B-spline membership functions and CMAC neural network with B-spline basis functions are sometimes desired to approximate not only the assigned smooth function as well as its derivatives. In this paper, by designing the fuzzy system and CMAC neural network with B-spline basis functions, we prove that such a fuzzy system and CMAC can universally approximate a smooth function and its derivatives, that is to say, for a given accuracy, we can approximate an arbitrary smooth function by such fuzzy system and CMAC that not only the function is approximated within this accuracy, but its derivatives are approximated as well. The conclusions here provide solid theoretical foundation for their extensive applications.

Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators

Due to their universal approximation, fuzzy system with B-spline membership functions and CMAC neural network with B-spline basis functions have been extensively used in control. In many practical applications, they are desired to approximate not only the assigned smooth function as well as its derivatives. In this paper, by designing a fuzzy system and CMAC neural network with B-spline basis functions, we prove that such a fuzzy system and CMAC can universally approximate a smooth function and its derivatives, i.e, for a given accuracy, we can approximate an arbitrary smooth function by such a fuzzy system and CMAC that not only the function is approximate within this accuracy, but its derivatives are approximated as well. The conclusions here provide solid theoretical foundation for their extensive applications.

Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems

A robust adaptive fuzzy-neural controller for a class of unknown nonlinear dynamic systems with external disturbances is proposed. The fuzzy-neural approximator is established to approximate an unknown nonlinear dynamic system in a linearized way. The fuzzy B-spline membership function (BMF) which possesses a fixed number of control points is developed for online tuning. The concept of tuning the adjustable vectors, which include membership functions and weighting factors, is described to derive the update laws of the robust adaptive fuzzy-neural controller. Furthermore, the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated by the error compensator which is also constructed by fuzzy-neural inference. We prove that the closed-loop system which is controlled by the robust adaptive fuzzy-neural controller is stable and the tracking error will converge to zero under mild assumptions. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods.

Modelling the probabilistic behaviour of function point analysis

Function point analysis is one of the most popular methods for estimating software size and, sometimes, development effort. However, accuracy for the result of estimation by using this method has not been ascertained significantly. Depending on human professional subjective judgement is one major reason that causes this problem. Subjective judgement may lead to inconsistency and inaccuracy in the estimation process. Fuzzified function point analysis model (FFPA) is proposed (C. Yau and R.H.L. Tsoi, Assessing the fuzziness of general system characteristics for estimating software size, ANZIIS Conference, Brisbane, Australia, Nov. 1994; C. Yau and R.H.L. Tsoi, A fuzzified approach to overcome the imprecisions of software sizing, IEEE SICICI '95, Singapore, July 1995.) to help software size estimators express their judgement in a more realistic manner. Surely, arangements given by FFPA will provide more information and can reflect the real life situation, but it does not show the confidence interval. Therefore, it is no way to assess the confidence level of the estimate. This paper will discuss the way to use fuzzy B-spline membership function (BMF) to derive the assessment values for 14 system characteristics of FFPA model. At the end of this paper, an empirical case study will show the merits of using confidence level in the estimate. These results imply that there may be potential for improving the way of using the estimation's result in different application environments.

On-line tuning of fuzzy-neural network for adaptive control of nonlinear dynamical systems

The adaptive fuzzy-neural controllers tuned online for a class of unknown nonlinear dynamical systems are proposed. To approximate the unknown nonlinear dynamical systems, the fuzzy-neural approximator is established. Furthermore, the control law and update law to tune on-line both the B-spline membership functions and the weighting factors of the adaptive fuzzy-neural controller are derived. Therefore, the control performance of the controller is improved. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.

Function approximation using fuzzy neural networks with robust learning algorithm

The paper describes a novel application of the B-spline membership functions (BMF's) and the fuzzy neural network to the function approximation with outliers in training data. According to the robust objective function, we use gradient descent method to derive the new learning rules of the weighting values and BMF's of the fuzzy neural network for robust function approximation. In this paper, the robust learning algorithm is derived. During the learning process, the robust objective function comes into effect and the approximated function will gradually be unaffected by the erroneous training data. As a result, the robust function approximation can rapidly converge to the desired tolerable error scope. In other words, the learning iterations will decrease greatly. We realize the function approximation not only in one dimension (curves), but also in two dimension (surfaces). Several examples are simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.

Neuro-fuzzy ID3: a method of inducing fuzzy decision trees with linear programming for maximizing entropy and an algebraic method for incremental learning

ID3 is a popular and efficient method of making a decision tree for classification from symbolic data without much computation. Fuzzy reasoning rules in the form of a decision tree, which can be viewed as a fuzzy partition, are obtained by fuzzy ID3. The aims of this paper are: (1) Not only the learning from examples but also the interview with domain specialists are needed for knowledge acquisition in expert systems. In order to avoid dangerous simplification of the tree by discarding partial knowledge of the experts, a measure of uncertainty with maximizing entropy is applied to fuzzy ID3. (2) Basically the tree based learning is nonincremental or single step. An algebraic method to facilitate incremental learning like the neural nets is adapted and the fuzzy decision tree which consists of B-spline membership function is regarded as three layered neural network. (3) Prototypes of expert system for estimation of wheel wear characteristics and surface roughness in abrasive cut-off are developed.

Fuzzy B-spline membership function (BMF) and its applications in fuzzy-neural control

A general methodology for constructing fuzzy membership functions via B-spline curves is proposed. By using the method of least-squares, the authors translate the empirical data into the form of the control points of B-spline curves to construct fuzzy membership functions. This unified form of fuzzy membership functions is called a B-spline membership function (BMF). By using the local control property of a B-spline curve, the BMFs can be tuned locally during the learning process. For the control of a model car through fuzzy-neural networks, it is shown that the local tuning of BMFs can indeed reduce the number of iterations tremendously. This fuzzy-neural control of a model car is presented to illustrate the performance and applicability of the proposed method. >