Type-2 Fuzzy Neural Network Research Articles

A data-knowledge-driven interval type-2 fuzzy neural network with interpretability and self-adaptive structure

Interval type-2 fuzzy neural networks (IT2FNNs) have gained sustainable attention and wide applications because of their power of adaptive fuzzy modeling. Although the existing models accurately simulate the relationships between inputs and outputs by various adaptive learning algorithms, the parameters and fuzzy rules characterizing the model behaviors no longer have explicit interpretations. To achieve good interpretability and generalization performance, this paper proposes a novel data-knowledge-driven IT2FNN (DKIT2FNN). Unlike accuracy-oriented model fitting, DKIT2FNN pioneers the use of famous association rule mining techniques to automatically explore the interpretable rule knowledge, which intuitively presents conditional relation patterns among features. Using the obtained knowledge, the DKIT2FNN model is accomplished in a single-hidden layer network framework, in which the antecedent structure of each fuzzy rule is determined by the relation patterns provided by rule knowledge. In addition, an adversarial incremental learning algorithm is proposed for the self-organizing modeling of DKIT2FNN. Besides automatically assembling a compact rule base, it integrates the label adversarial training to reinforce the model's capability against label noise. We validate the DKIT2FNN on classification benchmark datasets with label noise and compare it with state-of-the-art non-fuzzy and neuro-fuzzy methods. The results demonstrate that the proposed DKIT2FNN achieves robust classification performance and good interpretability.

Dynamic Analysis and Neural-Adaptive Prescribed-Time Control of the FO Memristive Magnetic-Field Electromechanical Transducer.

This article is concerned with dynamic analysis and neural-adaptive prescribed-time control of the magnetic-field electromechanical transducer incorporating a memristor. First, a fractional-order (FO) mathematical model is developed, which comprehensively characterizes fractional properties of various dielectrics and establishes the relationship between magnetic flux and electric charge. The dynamical analysis explores internal evolution and complexity performance concerning a single factor or double factors among the FO, system parameter, and memristor configuration by the Bifurcation diagram, sample entropy, and C0 complexity from multiple perspectives. Subsequently, a neural-adaptive prescribed-time control scheme is proposed to transform detrimental chaotic oscillations into orderly motions, achieve the pregiven tracking precision and accommodating both actuator fault and system uncertainty. The controller design consists of three key steps: 1) a deferred constraint function is imposed on the tracking error starting from anywhere to get assignable tracking precision within a specified time, ensuring collision avoidance; 2) a type-2 fuzzy wavelet neural network (FWNN) is utilized effectively to handle parameter perturbations and system uncertainties; and 3) a second-order FO tracking differentiator (TD) is utilized to address the "explosion of complexity" of traditional backstepping under actuator fault model. It is shown that the proposed scheme is able to ensure the boundness of all signals of the closed-loop system. Finally, extensive simulation experiments are conducted to validate the effectiveness and robustness of the rendered scheme.

Bayesian Optimization-Based Interval Type-2 Fuzzy Neural Network for Furnace Temperature Control

Bayesian Optimization-Based Interval Type-2 Fuzzy Neural Network for Furnace Temperature Control

Adaptive fuzzy sliding mode control of magnetic levitation system based on Interval Type-2 Fuzzy Neural Network Identification with an Extended Kalman–Bucy filter

The electromagnet levitation control system (EMS) is the core component of the magnetic levitation train. However, its nature is characterized by an inherent instability and strongly nonlinear dynamic. Additionally, modeling uncertainties and numerous exogenous perturbations make the design of the controller even more difficult for this system. To overcome these limitations, a Fuzzy Sliding Mode Control based on Interval Type-2 Fuzzy Neural Network Identification (FSMCF2NN) is designed for the EMS system. The suggested controller has a unique feature that allows the sliding surface and controller effort to be designed by using model-free techniques. As a result, the drawbacks of the conventional SMC schemes, such as the chattering effect, requiring prior knowledge of the system’s uncertainties bounds, and selection of the appropriate control gains, are eliminated. Also, the FSMCF2NN method, since it is designed based on intelligence methods not only minimizes the accumulation of state errors, but also generates the optimum control efforts of the EMS system to ensure stability in different situations. Furthermore, since the measurement of all EMS states is not achievable in reality, a qualified observer is needed to estimate unmeasured states. For this purpose, the Extended Kalman-Bucy filter (EKBF) is selected because of its superiority in managing disturbances for nonlinear systems. Furthermore, to confirm the robustness of the FSMCF2NN scheme in different scenarios, the results of the controller based on Linear Matrix Inequality (LMI), Linear Quadratic Regulation (LQR) controller, and the conventional Sliding Mode Controller (SMC) are compared with the proposed controller. Analyzing the results of simulation demonstrates that maintaining the levitated object is achievable with the proposed control scheme, effectively. At the same time, it attempts to adequately compensate for the uncertainties and disturbances present in the EMS structure.

Anti-lock braking control using an interval type-2 fuzzy neural network scheme for electric vehicles

Control precision and robustness can be regarded as essential challenges of slip ratio control because of the external uncertainties of road conditions and the internal delay response of braking actuators. In addition, it is difficult to obtain a trade-off between braking energy recovery efficiency and braking safety under some extreme braking conditions. To synchronously improve both slip ratio control and braking energy recovery efficiency for different road conditions, an anti-lock braking system (ABS) using a novel interval type-2 fuzzy neural network (IT2FNN) control scheme is proposed for electrohydraulic braking systems. The novel IT2FNN control scheme with five layers is designed to calculate the commanded braking torque. The membership function layer utilizes type-2 fuzzy sets to describe the slip ratio error degree, which enhances the scheme’s anti-interference ability, and the enhanced Karnik-Mendel (EKM) algorithm is used in the type-reduction layer to accelerate computation. Additionally, the network adjusts the parameters of the membership function and rules by decreasing the performance function value corresponding to the braking torque error to improve slip ratio control and enhance the self-adaptation capacity. Simulations showed that IT2FNN control can not only improve slip ratio control performance and decrease the braking torque error but also enhance the energy recovery efficiency of regenerative braking on different road surfaces.

A Comprehensively Improved Interval Type-2 Fuzzy Neural Network for NOx Emissions Prediction in MSWI Process

The accurate and timely prediction of nitrogen oxides (NOx) emissions ensures eco-friendly and efficient operations for municipal solid waste incineration (MSWI) plants. Due to the high nonlinearity and uncertainty in MSWI processes, constructing an efficient prediction model remains challenging. This work proposes a comprehensively improved interval type-2 fuzzy neural network (CI-IT2FNN) for NOx emissions prediction. First, the neighborhood rough set (NRS) is introduced to determine the structure of this fuzzy neural network automatically, including the number of fuzzy rules and their corresponding consequent parameters. Second, an adaptive shape factor is added to the fuzzy membership function to better cope with the uncertainty, which can help to improve the generalization ability of network. Furthermore, to reduce the computational complexity, the Begian-Melek-Mendel (BMM) method is utilized as the defuzzification method in this study. Then, by integrating the linear least square estimation (LSE) and gradient decent (GD), a hierarchical learning algorithm is applied to adjust the network parameters to further enhance the learning efficiency and accuracy. Finally, after being evaluated by a benchmark simulation, the proposed CI-IT2FNN demonstrates its effectiveness and superiority on NOx emissions prediction.

Mode transition prescribed performance control of connected hybrid electric vehicles based on driver intention fuzzy prediction

A novel hierarchical mode transition control (NHMTC) algorithm utilizing traffic information is investigated for realizing a superior dynamic and ride comfort performance of a connected hybrid electric vehicle (CHEV). The upper level includes the target vehicle velocity planning by model predictive control (MPC) considering less vehicle jerk based on the vehicle-to-infrastructure (V2I) information and the driving intention prediction by a type-2 fuzzy neural network (T2FNN) model using the planned target velocity. The lower level involves the automatic clutch system’s prescribed performance fixed-time controller (PPFTC) design and the desired velocity of the clutch engagement calculated by the predicted driving intention to improve the clutch position trajectory’s tracking accuracy and stability under the actual mode transition process. The comparison results with existing schemes under a co-simulation environment demonstrate the advantage and effectiveness of the designed NHMTC method.

Fractional order sliding mode control for an omni-directional mobile robot based on self-organizing interval type-2 fuzzy neural network

Four-wheeled omnidirectional mobile robots (FM-OMR) are widely used in various fields due to their excellent steering ability and adaptability. As application scenarios expand, higher requirements are placed on their trajectory tracking capabilities. FM-OMR is highly complex and difficult to model accurately, and the system contains uncertainties. Therefore, achieving accurate trajectory tracking in the presence of system uncertainty is a pressing problem. Traditional control methods struggle to accurately estimate uncertainty, and existing controllers often rely on model parameters, resulting in poor transferability. To address this issue, this paper proposes a new control method based on an online self-organizing interval type II fuzzy neural network (SOIT2FNNFSMC). This method employs an online self-organizing algorithm to dynamically compensate for uncertainty, providing greater flexibility and accuracy compared to traditional approximation networks in terms of network construction and approximation performance. A new combined reaching law is proposed based on the characteristics of traditional reaching laws, resulting in improved chattering reduction. Additionally, fractional calculus is introduced to enhance the dynamic characteristics of the controller. Simulation and experimental results demonstrate the effectiveness of this method in achieving precise trajectory tracking while handling uncertainty and not relying on model parameter features. The self-organizing algorithm proposed in this method also provides a reference for the application of SOIT2FNN in FM-OMR.

A smoothing Group Lasso based interval type-2 fuzzy neural network for simultaneous feature selection and system identification

Inspired by the life philosophy, an ingenious gate (membership) function, which can mimic the open and close of the gate in the real world, is proposed to realize feature selection (FS) for interval type-2 fuzzy neural network. Based on the widths of gate functions, a smoothing integrated learning strategy is designed, and in the regularized FS error function the gate widths corresponding to one feature are grouped as one Group Lasso (GL) regularization term. During the training procedure of feature selection, all the group terms with respect to bad features will be punished, but for the good features the corresponding group terms converge to different nonzero values. When feature selection is finished, using the selected features, the interpretable clustering algorithm based initial interval type-2 rule generation method is detailedly introduced firstly, then a simple and efficient memory-based gradient method is presented for the tuning of rule structure parameters. Lastly, employing the simulation results of four regression problems and four classification problems, the effectiveness on simultaneous feature selection and system identification of our proposed model, i.e., the smoothing Group Lasso based interval type-2 fuzzy neural network (SGLIT2FNN), is proved, which illustrates that SGLIT2FNN not only simplifies the model structure by deleting the bad features, but also maintains the performance.

A hybrid control combining an advanced sliding mode control law with a proportional-derivative control by applying on vibration suppression

A hybrid controller is proposed to control the vibration of a cantilever structure. The hybrid adaptive controller combines sliding mode controller (SMC) and proportional-derivative (PD) controller. Meanwhile, a type-2 fuzzy neural network (T2FNN) with a zero-order consequent part and certain center is applied to SMC due to the unknown of the controlled object. The initial parameters of T2FNN are obtained through the identification by an SMC-theory based T2FNN. The adaption laws of the controller and T2FNN are given through Lyapunov stability. The state space equation of the beam is established for simulation. The proposed controller is applied to vibration control of a cantilever beam bonded with piezoelectric actuator to verify its effectiveness. The simulation and experiment results show excellent control performance of disturbance rejection and vibration suppression of the proposed controller.

Self-Organizing Interval Type-2 Fuzzy Neural Network Using Information Aggregation Method.

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

Adaptive Super-Twisting Sliding Mode Control of Active Power Filter Using Interval Type-2-Fuzzy Neural Networks

Aiming at the unknown uncertainty of an active power filter system in practical operation, combining the advantages of self-feedback structure, interval type-2 fuzzy neural network, and super-twisting sliding mode, an adaptive super-twisting sliding mode control method of interval type-2 fuzzy neural network with self-feedback recursive structure (IT2FNN-SFR STSMC) is proposed in this paper. IT2FNN has an uncertain membership function, which can enhance the nonlinear ability and robustness of the network. The historical information will be stored and utilized by the self-feedback recursive structure (SFR) at runtime. Therefore, the novel IT2FNN-SFR is designed to improve the dynamic approximation effect of the neural network and reduce the dependence of the controller on the actual mathematical model. The adaptive rate of each weight of the neural network is designed by the Lyapunov method and gradient descent (GD) algorithm to ensure the convergence and stability of the system. Super-twisting sliding mode control (STSMC) has strong robustness, which can effectively reduce system chattering, and improve control accuracy and system performance. The gain of the integral term in the STSMC is set as a constant, and the other gain is changed adaptively whose adaptive rate is deduced through the stability proof of the neural network, which greatly reduces the difficulty of parameter adjustment. The harmonic suppression ability of the designed control strategy is verified by simulation experiments.

Recurrent general type-2 fuzzy neural networks for nonlinear dynamic systems identification

This paper introduces a recurrent general type-2 Takagi–Sugeno–Kang fuzzy neural network (RGT2-TSKFNN) for the identification of nonlinear systems. In the proposed structure, the general type-2 fuzzy set (GT2FS) and a recurrent fuzzy neural network (RFNN) are combined to obviate the data uncertainties. The fuzzy firing strengths in the developed structure are returned to the network input as internal variables. In the proposed structure, GT2FS is utilized to characterize the antecedent parts while the consequent parts are performed using TSK type. The issues of constructing a RGT2-TSKFNN involve type reduction, structure learning as well as parameter learning. An efficient strategy is developed by utilizing alpha-cuts to decompose a GT2FS into several interval type-2 fuzzy sets (IT2FSs). In order to solve the computation time of the type-reduction issue, a direct defuzzification method is used instead of iterative nature of Karnik–Mendel​ (KM) algorithm. Type-2 fuzzy clustering and Lyapunov criteria are utilized for online structure learning as well as the antecedent and consequent parameters, respectively for reducing the number of rules and guaranteeing the stability of the proposed RGT2-TSKFNN. The reported comparative analysis of the simulation results is utilized to estimate the performance of the proposed RGT2-TSKFNN with respect to other popular type-2 FNNs (T2FNNs) methodologies.

Fourier-based type-2 fuzzy neural network: Simple and effective for high dimensional problems

The main contribution of this study is to introduce a simple and effective deep learning Fourier-based type-2 fuzzy neural network for high-dimensional problems. The rules are directly constructed by fast Fourier transformation. The input matrix/vector is segmented, and each segment represents a fuzzy rule. The upper/lower bounds of rule firings are obtained by the Fourier transformation approach. The output is computed by a simple type-reduction method. All antecedent and consequent parameters are optimized by simple gradient descent and fuzzy correntropy-based extended Kalman filter. The kernel size of a conventional correntropy-based filters is determined by a fuzzy system. The convergence of the learning method is proved by the Lyapunov method. The effectiveness of the suggested approach is verified by the face recognition problem (1024 input variables), English handwriting digit recognition (1024 input variables), and modeling problem with real-world data set (32 input variables). The simulations and comparisons demonstrate the superiority of the introduced scheme.

Prediction the Effect of Tensile and Elongation Properties of Dry and Wet Cotton Fibre on the Fabric Wrinkle Grade Based on Polynomial Type2 Fuzzy Neural Network Modelling

Prediction the Effect of Tensile and Elongation Properties of Dry and Wet Cotton Fibre on the Fabric Wrinkle Grade Based on Polynomial Type2 Fuzzy Neural Network Modelling

Refined fault tolerant tracking control of fixed-wing UAVs via fractional calculus and interval type-2 fuzzy neural network under event-triggered communication

The refined fault tolerant tracking control (FTTC) scheme is developed for multiple fixed-wing unmanned aerial vehicles (UAVs) against actuator faults and wind effects under event-triggered communication. To decrease the communication overload caused by the continuous information transmissions among neighboring UAVs, an event-triggered communication mechanism is incorporated to dynamically reduce and increase the triggering frequency at the pre-fault and post-fault phases, respectively, thus reducing the communication burden while ensuring the synchronization tracking performance of faulty UAVs. Moreover, refined FTTC performance with event-triggered communications can be achieved by skillfully invoking fractional-order calculus. Furthermore, interval type-2 fuzzy neural networks with fractional-order adaptive modulation factors are constructed to compensate for the unknown nonlinearities. Lyapunov stability analysis has revealed that all attitudes can synchronously track their references. Simulation results are presented to demonstrate that communication resource-saving refined FTTC performance can be guaranteed with different fractional-order operators.

Self-Organizing Interval Type-2 Fuzzy Neural Network With Adaptive Discriminative Strategy

Covariate shift is a critical issue of interval type-2 fuzzy neural networks (IT2FNNs) due to the distribution discrepancy between training and testing samples. In this situation, IT2FNNs usually struggle to identify potential features from samples with explicit inductive biases. To address this problem, a self-organizing IT2FNN with an adaptive discriminative strategy (ADS-SOIT2FNN) is developed to maintain the identification performance in the presence of covariate shift. First, a granularity-based metric (GM), using higher-order statistics of local samples, is designed to distinguish the distribution discrepancy caused by covariate shift. The multiple kernels incorporated into GM are able to cover the sample features of the whole Hilbert space. Second, a self-organizing strategy, associated with GM-based discriminative information, is presented to alleviate the structural bias by growing and pruning fuzzy rules. Then, a compact structure of ADS-SOIT2FNN is achieved to adapt to the covariate shift of samples and further strengthen its inductive ability. Third, an adaptive risk mitigation learning algorithm (RMLA) is introduced to update the parameters of ADS-SOIT2FNN. RMLA can regulate the derivatives of parameters with arbitrary distribution samples, which is beneficial for maintaining the global accuracy by relieving the risk of parameter biases. Finally, the effectiveness of ADS-SOIT2FNN is verified by some experiments for identifying nonlinear systems with covariate shift.

Self-Organizing Interval Type-2 Fuzzy Neural Network Compensation Control Based on Real-Time Data Information Entropy and Its Application in n-DOF Manipulator.

In order to solve the high-precision motion control problem of the n-degree-of-freedom (n-DOF) manipulator driven by large amount of real-time data, a motion control algorithm based on self-organizing interval type-2 fuzzy neural network error compensation (SOT2-FNNEC) is proposed. The proposed control framework can effectively suppress various types of interference such as base jitter, signal interference, time delay, etc., during the movement of the manipulator. The fuzzy neural network structure and self-organization method are used to realize the online self-organization of fuzzy rules based on control data. The stability of the closed-loop control systems are proved by Lyapunov stability theory. Simulations show that the algorithm is superior to a self-organizing fuzzy error compensation network and conventional sliding mode variable structure control methods in control performance.

Dynamic Analysis and Fuzzy Fixed-Time Optimal Synchronization Control of Unidirectionally Coupled FO Permanent Magnet Synchronous Generator System

This paper focuses on dynamic analysis and the fuzzy fixed-time optimal synchronization control problem of unidirectionally coupled fractional-order (FO) permanent magnet synchronous generator (PMSG) system. The synchronization model between FO master and slave PMSGs with capacitive and resistive couplings is built. The dynamic analysis fully reveals its abundant dynamical behaviors including chaotic oscillations and gives stability/instability boundaries with the designed numerical method. In controller design, the hierarchical type-2 fuzzy neural network (HT2FNN) with a transformation is designed to approximate unknown functions, the fixed-time command filter matched up with the compensating signal is proposed to achieve precise estimate and fast convergence, and a fixed-time preconfigured performance function integrated with a smooth and invertible function is built to realize fixed-time convergence and performance constraint. Then a fuzzy fixed-time optimal synchronization control scheme fusing with the HT2FNN, filter, performance function and optimal control is developed under the FO backstepping theory. The stability analysis proves that all signals of the closed-loop system are bounded along with the cost function being minimized. Finally, numerical simulation results verify the feasibility and advantages of our scheme.

Neuroadaptive Optimal Fixed-Time Synchronization and its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems.

This article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme.