Number Of Fuzzy Rules Research Articles

Prediction and control of surface roughness for end milling process using ANFIS

In this paper, we applied an Adaptive Neuro-Fuzzy Inference System (ANFIS) approach for prediction of the workpiece surface roughness for the end milling process. A small number of fuzzy rules were used for building ANFIS models with the help of Subtractive clustering method (ANFIS-Subtractive clustering model). The predicted values are found to be in excellent agreement with the experimental data with average error values in the range of 3.47-3.49%. Also, we compared the proposed ANFIS models to other Artificial intelligence (AI) approaches. Results show that the proposed model has high accuracy in comparison to other AI approaches in literature. Therefore, we can use ANFIS model to predict the workpiece surface roughness for the end milling process.

Dynamic-free robust adaptive intelligent fault-tolerant controller design with prescribed performance for stable motion of quadruped robots

In this article, a robust adaptive intelligent fault-tolerant controller with prescribed performance is proposed for an uncertain quadruped robot with actuator fault. The control system comprised of three terms: (1) a full-state feedback controller which includes the prescribed performance function, (2) an adaptive intelligent wavelet-based Takagi-Sugeno fuzzy network (TSFN), and (3) a robust control term. The proposed controller does not utilize the robot dynamic model. A wavelet-based TSFN is utilized to approximate adaptively the lumped nonlinear terms, parameter uncertainties, and defective torque signal. The wavelet block acts as a feature extractor, reduces the number of fuzzy rules, and also acts as a normalization function. The parameters of TSFN are tuned online by an adaptive law based on Lyapunov stability theory. The proposed controller guarantees the desired specification such as minimum speed of convergence, maximum steady-state error, overshoot concerning the position tracking error, and also bounded closed-loop signals. Numerical simulations on MATLAB/SimMechanics environment demonstrate the stable walking of the quadruped robot in the presence of the actuator faults and parameter uncertainties.

PERFORMANCE OF ARTIFICIAL NEURAL NETWORKS AND FUZZY INFERENCE SYSTEMS FOR PREDICTING CONCRETE COMPRESSIVE STRENGTH

Artificial neural networks (ANN) have been traditionally utilized for developing prediction models based on experimental data; however, fuzzy logic theory is a novel tool that could also be applied as well in this cases. The present study compares the performance of two different approaches; namely, ANN and fuzzy inference systems (FIS) for predicting concrete compressive strength. Adaptive neuro fuzzy inference systems (ANFIS) was the technique based on input – output experimental data that was used to create two Sugeno type fuzzy models for estimating concrete compressive strength and then compared with several ANN prediction models created through different methods. Subtractive clustering method was the clustering procedure for establishing the number of membership functions and fuzzy rules. Predicted data resulting from all models were presented in a comparative manner and validation analyses were conducted in order to observe the performance of ANN and ANFIS. The results indicate that both fuzzy models performed very well when estimating concrete compressive strength (i.e., all R2 values are greater than 90%) while for ANN, only one ANN method had an R2 value greater than 90%.

Decentralized Observer-Based Controller Synthesis for a Large-Scale Polynomial T-S Fuzzy System With Nonlinear Interconnection Terms.

This article proposes a novel approach to synthesize a decentralized observer-based controller for a large-scale nonlinear systems in which the interconnection terms are expressed in the nonlinear forms. The large-scale nonlinear system is modeled under the framework of the large-scale polynomial T-S fuzzy systems which can reduce the modeling error and the number of fuzzy rules. It is noted that the interconnection terms are arbitrary nonlinear functions and unnecessary to satisfy the bound constraints, while these constraints are mandatory in the previous studies. Therefore, the proposed method is more relaxed and applicable in practice. A new observer form based on an unknown input method is proposed to simultaneously estimate the unmeasurable states and interconnection terms, which has not been taken into consideration in any previous articles. The information of the unknown states and interconnection is fed back to the controller for stabilizing the system. With the support of the Lyapunov function, the sum-of-square (SOS) technique, the conditions for designing the observer and controller are derived. Finally, the two numerical examples are provided to prove the success and merit of the proposed method.

Variable impedance control of finger exoskeleton for hand rehabilitation following stroke

PurposeThe purpose of this paper is to propose a variable impedance control method of finger exoskeleton for hand rehabilitation using the contact forces between the finger and the exoskeleton, making the output trajectory of finger exoskeleton comply with the natural flexion-extension (NFE) trajectory accurately and adaptively.Design/methodology/approachThis paper presents a variable impedance control method based on fuzzy neural network (FNN). The impedance control system sets the contact forces and joint angles collected by sensors as input. Then it uses the offline-trained FNN system to acquire the impedance parameters in real time, thus realizing tracking the NFE trajectory. K-means clustering method is applied to construct FNN, which can obtain the number of fuzzy rules automatically.FindingsThe results of simulations and experiments both show that the finger exoskeleton has an accurate output trajectory and an adaptive performance on three subjects with different physiological parameters. The variable impedance control system can drive the finger exoskeleton to comply with the NFE trajectory accurately and adaptively using the continuously changing contact forces.Originality/valueThe finger is regarded as a part of the control system to get the contact forces between finger and exoskeleton, and the impedance parameters can be updated in real time to make the output trajectory comply with the NFE trajectory accurately and adaptively during the rehabilitation.

A New Rule Reduction Method for Fuzzy Modeling

The Takagi–Sugeno fuzzy model (T–S fuzzy model) has been successfully applied to a wide range of problems due to its accurate modeling ability. However, its rule redundancy and dimension disaster remain an open and unsolved issue. In this article, a novel fuzzy modeling method is proposed to reduce the fuzzy rule number without a loss in modeling accuracy. It includes two novel mechanisms: the rule fusion mechanism and the space projection mechanism. The rule fusion mechanism is developed to merge several rules into one according to similarity. In this way, the number of rules will greatly decrease. After the rules are merged, the relationship of data is strongly nonlinear, which renders the local linear model ineffective. In order to alleviate this difficulty, the space projection mechanism is then proposed to project the low-dimensional feature space to a high-dimension space. In this high-dimension space, the relation of data is linear and easily represented by a linear model. In this way, the traditional fuzzy inference is still applicative. With the help of these two mechanisms, a fuzzy model with few rules is constructed, which enables reconstruction of the nonlinear system. A solving method is then developed to determine the optimal parameters of the fuzzy model. Additional analysis and proof show that the proposed method exhibits the uniform approximation ability for strongly nonlinear systems. Case studies not only demonstrate the effectiveness of the proposed method, but also demonstrate its superior modeling performance in comparison to several conventional fuzzy modeling methods, even with the use of fewer rules

Adaptive Fuzzy Tracking Control of Flexible-Joint Robots Based on Command Filtering

The precise tracking control problem for n -link flexible-joint (FJ) robotic systemsis addressed in this paper. A new adaptive fuzzy command filtered control strategy is presented, where fuzzy logic systems are utilized to approximate the unknown nonlinearities of FJ robot systems. Compared with existing backstepping-based methods, the proposed scheme can not only overcome the so-called “explosion of complexity” problem, but also reduce filter errors because of the introducing of an error compensation mechanism. Moreover, regardless of the number of fuzzy rules, only one parameter is required to be adjusted online, which reduces significantly the computational cost. The proposed scheme can guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The simulation results of a two-link robot system confirm our theoretical analysis and a comparison study demonstrates the advantages of the design method in comparison with existing results, such as the backstepping method and the dynamic surface control method.

Forecasting Stock Market with Social Media Sentiment Based on Adaptive Network Fuzzy Inference System

The Adaptive Neuro Fuzzy Inference System (ANFIS), based on fuzzy inference system, describes the process of human logical reasoning by establishing a number of fuzzy rules. It has a good ability to deal with uncertain and imprecise systems and is suitable for application in stock market forecasting. In this paper, the model inputs are chosen based on multiple feature combinations with multiple experiments, and social media is added as part of the features. Gaussian membership function was selected as the main constraint and triangle function was the result optimizer. The experiments using data from both social media and stock markets—the Sina Weibo and the Shanghai Stock Market—to train and evaluate the change in trend for the next trading day, with the ‘‘buy and hold” strategy and several other timing trading strategies. The empirical results show that our proposed method outperforms the ANFIS with only technical index as input.

A novel fuzzy extended state observer

In designing the extended state observer (ESO), one of the most challenging issues is its performance improvement. In this paper, a simple fuzzy system is proposed to improve the performance of ESO and changes this observer into fuzzy extended state observer (FESO). This FESO is an intelligent linear form of the ESO. The fuzzy system, which is applied to tune the observer gains in an intelligent manner, directs the observer to deliver an appropriate estimation performance. To design this fuzzy system, a simple input–output form is applied to reduce the number of fuzzy rules. The linear form of FESO simplifies the convergence analysis of this observer, which is analyzed through a Lyapunov function. The performance of FESO in the fields of fault diagnosis and active disturbance rejection control (ADRC) are shown by simulation examples and compared with traditional forms of ESO. In this paper, it is revealed that this new proposed ESO embodies advantages of the simple linear structure and provides a good performance, confirmed by its results.

T–S Fuzzy Model Identification with Sparse Bayesian Techniques

This paper introduces a novel method for fuzzy modeling based on sparse Bayesian techniques. The sparse representation problems in the Takagi–Sugeno (T–S) fuzzy system identification are studied, which is to establish a T–S fuzzy system with a adaptive number of fuzzy rules and simultaneously have a minimal number of nonzero consequent parameters. The proposed method is called sparse Bayesian fuzzy inference systems (B-sparseFIS). There are two main procedures in the paper. Firstly, initial fuzzy rule of antecedent part is extracted automatically by an AP clustering method. By using the algorithm of adaptive block orthogonal matching pursuit, the number of rules is computed statistically then the main important fuzzy rules can be selected. In the algorithm, the redundant rules are eliminated for better model accuracy and generalization performance; secondly, an adaptive B-sparseFIS is exploited. The consequence of fuzzy system is identified and simplified with sparse Bayesian techniques such that many consequent parameters will approximate to zero. Four examples are provided to illustrate the effectiveness of the proposed algorithm. Furthermore, the performances of the algorithm are validated through the results of statistical analyses including parameter estimate error, MSE, NRMSE, etc.

An Efficient Optimization Method for Improving Generalization Performance of Fuzzy Neural Networks

Fuzzy neural networks (FNNs), with suitable structures, have been demonstrated to be an effective tool in approximating nonlinearity between input and output variables. However, it is time-consuming to construct an FNN with appropriate number of fuzzy rules to ensure its generalization ability. To solve this problem, an efficient optimization technique is introduced in this paper. First, a self-adaptive structural optimal algorithm (SASOA) is developed to minimize the structural risk of an FNN, leading to an improved generalization performance. Second, with the proposed SASOA, the fuzzy rules of SASOA-based FNN (SASOA-FNN) are generated or pruned systematically. This SASOA-FNN is able to organize the structure and adjust the parameters simultaneously in the learning process. Third, the convergence of SASOA-FNN is proved in the cases with fixed and updated structures, and the guidelines for selecting the parameters are given. Finally, experimental studies of the proposed SASOA-FNN have been performed on several nonlinear systems to verify the effectiveness. The comparison with other existing methods has been made, and it demonstrates that the proposed SASOA-FNN is of better performance.

A new Neuro-Fuzzy Inference System with Dynamic Neurons (NFIS-DN) for system identification and time series forecasting

A new Neuro-Fuzzy Inference System with Dynamic Neurons or NFIS-DN is presented here for discrete time dynamic system identification and time series forecasting problems. The proposed dynamic system based neuron, referred to as Dynamic Neuron (DN) is realized by a discrete-time nonlinear state-space model. The DN is designed such way, that the output considers only the effect of finite past instances, enabling the system with finite memory. The NFIS-DN model has five layers, and DNs are employed only in the layers handling crisp values. The antecedent and the consequent parameters of NFIS-DN are updated using a self-regulated backpropagation through time learning algorithm. The performance evaluation of NFIS-DN has been carried-out using benchmark problems in the areas of nonlinear system identification and time series forecasting. The results are compared with the state-of-the-art method on the neural fuzzy networks. The obtained results clearly suggest that the NFIS-DN performs significantly better while using a smaller or similar number of fuzzy rules. Finally the practical application of the NFIS-DN has been demonstrated using two real-world problems.

Fuzzy logic‐based adaptive equaliser for non‐linear perpendicular magnetic recording channels

This paper proposes the fuzzy logic equaliser (FLE) for the detection of non-linear perpendicular magnetic recording (PMR) channels. The multi-objective genetic algorithm (MOGA) is utilised to optimise all of the fuzzy parameters and reduce the complexity while maintaining the accuracy. By means of this optimisation, the total number of fuzzy rules is significantly reduced about 44%. The bit error rate (BER) performance of the proposed FLEs are compared with those of the conventional detector and traditional non-linear equalisers for Volterra channel, in presence of non-linear amplitude distortions in high-density PMR channels. The proposed FLE outperforms existing detectors by 1 to 12 dB SNR gains. Furthermore, the complexity in terms of multiplication counts per execution and reliability of detectors with regard to the number of system parameters through the Akaike's information criterion (AIC) are assessed to verify the effectiveness of the proposed FLEs. An extension to PMR channel with jitter noise proves the robustness of the proposed FLEs.

Concise Fuzzy System Modeling Integrating Soft Subspace Clustering and Sparse Learning

The superior interpretability and uncertainty modeling ability of Takagi-Sugeno-Kang fuzzy system (TSK FS) make it possible to describe complex nonlinear systems intuitively and efficiently. However, classical TSK FS usually adopts the whole feature space of the data for model construction, which can result in lengthy rules for high-dimensional data and lead to degeneration in interpretability. Furthermore, for highly nonlinear modeling task, it is usually necessary to use a large number of rules which further weakens the clarity and interpretability of TSK FS. To address these issues, a concise zero-order TSK FS construction method, called ESSC-SL-CTSK-FS, is proposed in this paper by integrating the techniques of enhanced soft subspace clustering (ESSC) and sparse learning (SL). In this method, ESSC is used to generate the antecedents and various sparse subspace for different fuzzy rules, whereas SL is used to optimize the consequent parameters of the fuzzy rules, based on which the number of fuzzy rules can be effectively reduced. Finally, the proposed ESSC-SL-CTSK-FS method is used to construct con-cise zero-order TSK FS that can explain the scenes in high-dimensional data modeling more clearly and easily. Experiments are conducted on various real-world datasets to confirm the advantages.

New adaptive fuzzy sliding mode scheme for speed control of linear switched reluctance motor

This study presents a new control system for a linear switched reluctance motor (LSRM). Type-2 Takati-Sugeno fuzzy system is used for the motor approximation. The uncertain parameters of the motor are described by the lower and upper membership functions. By constructing an integral sliding mode surface, an adaptive sliding mode controller is designed and dynamic stability of the sliding motion is verified using the Lyapunov function. The design of the proposed sliding mode surface is independent of the number of fuzzy rules and thus, computational complexity is significantly decreased. The control system is implemented on a double-sided four-phase LSRM and its performance is demonstrated by means of modelling and experimental results.

ANFIS-Based Signal Reconstruction for Nonlinear Multifunctional Sensor

In this paper, one approach based on adaptive network-based fuzzy inference system is designed to reconstruct signal for nonlinear multifunctional sensor used in multifunctional sensing technique. Before training, fuzzy rule number is automatically obtained through subtractive clustering to simplify the model structure. Simulation results for an analog circuit model which simulates a nonlinear multifunctional sensor system demonstrate the effectiveness of the designed approach in reconstructing signal. Application of processing real-life data reveals performance of the proposed method is evidently promoted by combining with fuzzy c-means clustering.

Dissipativity-Preserving Model Reduction for Takagi–Sugeno Fuzzy Systems

This paper is concerned with the dissipativity-preserving model reduction problem for Takagi–Sugeno (T–S) fuzzy systems. The principal goal is to approximate the high-order T–S model with a dissipative reduced-order T–S model. The number of fuzzy rules and the membership functions of the reduced-order T–S model are chosen freely to enhance design flexibility. To this end, an $H_{\infty }$ performance index is used to describe the approximation error. Meanwhile, dissipativity of the reduced-order model is guaranteed by satisfying a dissipation inequality. With the aid of fuzzy-basis-dependent Lyapunov functions and slack variable techniques, less conservative design conditions for reduced-order models are derived. An algorithm is proposed to calculate a desired reduced-order model. A rail traction control system is given to illustrate the effectiveness of the proposed method and the advantages over the existing methods.

General controllability and observability tests for Takagi-Sugeno fuzzy systems

An approach for investigating controllability and observability properties in Takagi-Sugeno (TS) fuzzy systems is given. The proposed method is independent of the number of fuzzy rules acting at the same instant and independent of the number of inputs and outputs included in the TS fuzzy model. Therefore, it can be applied to a wide class of fuzzy systems. The analysis relies on the solution of a set of symbolic simultaneous equations with the fuzzy weights as the unknowns of such equations.

Stability analysis and dynamic output feedback controller design of T–S fuzzy systems with time-varying delays and external disturbances

This paper investigates the stability analysis and Takagi–Sugeno (T–S) fuzzy dynamic output feedback control for a class of T–S fuzzy systems with multiple time-varying delays and unmatched disturbances. Firstly, the T–S fuzzy model is employed to represent the system based on the system input matrix and output matrix. Secondly, the T–S fuzzy dynamic output feedback controller is designed based on the T–S fuzzy model. Thirdly, the line-integral fuzzy Lyapunov functional is employed and the boundary information of membership functions is considered in the stability analysis. Compared with previous works, the multiple time-varying delays and unmatched disturbances are considered in the T–S fuzzy system. The T–S fuzzy dynamic output feedback controller and T–S fuzzy system employ the same number of fuzzy rules but different membership functions to relax the control design conditions. The line-integral fuzzy Lyapunov functional is employed and the boundary information of membership functions is considered to obtain the less conservative stability conditions. Finally, two simulation examples are performed and some comparison figures/results are presented to show the effectiveness and advantage of proposed method, respectively.

Polynomial Controller Synthesis for Uncertain Large-Scale Polynomial T-S Fuzzy Systems.

This paper proposes a novel method to synthesize a controller for stabilizing the nonlinear large-scale system which is represented by a large-scale polynomial Takagi-Sugeno (T-S) fuzzy system. The large-scale system consists of a set of the uncertain polynomial T-S fuzzy system with interconnection terms. Modeling the large-scale nonlinear system under the framework of the polynomial form will decrease both the modeling errors and the number of fuzzy rules with respect to the conventional large-scale T-S fuzzy system. In addition, because of the existence of uncertainties, the synthesizing controller for the large-scale polynomial fuzzy system becomes much more challenging and has not been investigated in the previous studies. In this paper, a controller is synthesized to simultaneously eliminate the impact of the uncertainties and stabilize the system. With the aid of Lyapunov theory, sum-of-square technique, and S-procedure, the conditions for controller synthesis are derived in the main theorems. Finally, two examples are illustrated to show the effectiveness and merit of the proposed method.