Nonlinear dynamic systems identification using recurrent interval type-2 TSK fuzzy neural network - A novel structure

Nonsingular Gradient Descent Algorithm for Interval Type-2 Fuzzy Neural Network

Interval type-2 fuzzy neural network (IT2FNN) is widely used to model nonlinear systems. Unfortunately, the gradient descent-based IT2FNN with uncertain variances always suffers from low convergence speed due to its inherent singularity. To cope with this problem, a nonsingular gradient descent algorithm (NSGDA) is developed to update IT2FNN in this article. First, the widths of type-2 fuzzy rules are transformed into root inverse variances (RIVs) that always satisfy the sufficient condition of differentiability. Second, the singular RIVs are reformulated by the nonsingular Shapley-based matrices associated with type-2 fuzzy rules. It averts the convergence stagnation caused by zero derivatives of singular RIVs, thereby sustaining the gradient convergence. Third, an integrated-form update strategy (IUS) is designed to obtain the derivatives of parameters, including RIVs, centers, weight coefficients, deviations, and proportionality coefficient of IT2FNN. These parameters are packed into multiple subvariable matrices, which are capable to accelerate gradient convergence using parallel calculation instead of sequence iteration. Finally, the experiments showcase that the proposed NSGDA-based IT2FNN can improve the convergence speed through the improved learning algorithm.

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.

Optimization of aluminum fluoride addition in aluminum electrolysis process based on pruned sparse fuzzy neural network

The aluminum fluoride (AF) addition in aluminum electrolysis process (AEP) can directly influence the current efficiency, energy consumption, and stability of the process. This paper proposes an optimization scheme for AF addition based on pruned sparse fuzzy neural network (PSFNN), aiming at providing an optimal AF addition for aluminum electrolysis cell under normal superheat degree (SD) condition. Firstly, a Gaussian mixture model (GMM) is introduced to identify SD conditions in which the operating modes of AEP are unknown. Then, PSFNN is proposed to establish the AF addition model under normal SD condition identified by GMM. Specifically, a sparse regularization term is designed in loss function of PSFNN to extract the sparse representation from nonlinear process data. A structure optimization strategy based on enhanced optimal brain surgeon (EOBS) algorithm is proposed to prune redundant neurons in the rule layer. Mini-batch gradient descent and AdaBound optimizer are then introduced to optimize the parameters of PSFNN. Finally, the performance is confirmed on the simulated Tennessee Eastman process (TEP) and real-world AEP. Experimental results demonstrate that the proposed scheme provides a satisfactory performance.

Multi-Model Adaptation Learning With Possibilistic Clustering Assumption for EEG-Based Emotion Recognition

In machine learning community, graph-based semi-supervised learning (GSSL) approaches have attracted more extensive research due to their elegant mathematical formulation and good performance. However, one of the reasons affecting the performance of the GSSL method is that the training data and test data need to be independently identically distributed (IID); any individual user may show a completely different encephalogram (EEG) data in the same situation. The EEG data may be non-IID. In addition, noise/outlier sensitiveness still exist in GSSL approaches. To these ends, we propose in this paper a novel clustering method based on structure risk minimization model, called multi-model adaptation learning with possibilistic clustering assumption for EEG-based emotion recognition (MA-PCA). It can effectively minimize the influence from the noise/outlier samples based on different EEG-based data distribution in some reproduced kernel Hilbert space. Our main ideas are as follows: (1) reducing the negative impact of noise/outlier patterns through fuzzy entropy regularization, (2) considering the training data and test data are IID and non-IID to obtain a better performance by multi-model adaptation learning, and (3) the algorithm implementation and convergence theorem are also given. A large number of experiments and deep analysis on real DEAP datasets and SEED datasets was carried out. The results show that the MA-PCA method has superior or comparable robustness and generalization performance to EEG-based emotion recognition.

Robust Latent Multi-Source Adaptation for Encephalogram-Based Emotion Recognition

In practical encephalogram (EEG)-based machine learning, different subjects can be represented by many different EEG patterns, which would, in some extent, degrade the performance of extant subject-independent classifiers obtained from cross-subjects datasets. To this end, in this paper, we present a robust Latent Multi-source Adaptation (LMA) framework for cross-subject/dataset emotion recognition with EEG signals by uncovering multiple domain-invariant latent subspaces. Specifically, by jointly aligning the statistical and semantic distribution discrepancies between each source and target pair, multiple domain-invariant classifiers can be trained collaboratively in a unified framework. This framework can fully utilize the correlated knowledge among multiple sources with a novel low-rank regularization term. Comprehensive experiments on DEAP and SEED datasets demonstrate the superior or comparable performance of LMA with the state of the art in the EEG-based emotion recognition.

Modeling Renewable Energy Systems by a Self-Evolving Nonlinear Consequent Part Recurrent Type-2 Fuzzy System for Power Prediction

A novel Nonlinear Consequent Part Recurrent Type-2 Fuzzy System (NCPRT2FS) is presented for the modeling of renewable energy systems. Not only does this paper present a new architecture of the type-2 fuzzy system (T2FS) for identification and behavior prognostication of an experimental solar cell set and a wind turbine, but also, it introduces an exquisite technique to acquire an optimal number of membership functions (MFs) and their corresponding rules. Using nonlinear functions in the “Then” part of fuzzy rules, introducing a new mechanism in structure learning, using an adaptive learning rate and performing convergence analysis of the learning algorithm are the innovations of this paper. Another novel innovation is using optimization techniques (including pruning fuzzy rules, initial adjustment of MFs). Next, a solar photovoltaic cell and a wind turbine are deemed as case studies. The experimental data are exploited and the consequent yields emerge as convincing. The root-mean-square-error (RMSE) is less than 0.006 and the number of fuzzy rules is equal to or less than four rules, which indicates the very good performance of the presented fuzzy neural network. Finally, the obtained model is used for the first time for a geographical area to examine the feasibility of renewable energies.

A novel fuzzy Wiener-based nonlinear modelling for engineering applications

This study proposes a novel fuzzy Wiener structure for identifying engineering systems. The proposed model has a cascade structure; a nonlinear static part preceded by a linear dynamic part. The nonlinear static part is represented by an interval type-2 fuzzy Takagi-Sugeno-Kang (IT2TSK) system in which the antecedents of the rules are described by interval type-2 fuzzy sets (IT2FSs) and a TSK-type system describes the consequents. An autoregressive moving average (ARMA) model is developed for representing the linear dynamic part. The proposed structure parameters including the ARMA, antecedent and consequent parameters are updated using the Lyapunov function to ensure the model stability. The simulation results confirm that the proposed Wiener structure can successfully model nonlinear engineering applications in the existence of system uncertainties and noisy measurement data. Moreover, the proposed model consistently achieves higher fitness (FIT) and smaller root mean square error (RMSE) values than other existing schemes.

Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults

In this paper, a robust attitude and position control of a novel modified quadrotor unmanned aerial vehicles (UAV) which has higher drive capability as well as greater robustness against actuator faults than conventional quad-rotor UAV has been developed. A robust backstepping controller with adaptive interval type-2 fuzzy logic is proposed to control the attitude and position of the modified quadrotor under actuator faults. Besides globally stabilizing the system amid other disturbances, the insensitivity to the model errors and parametric uncertainties are the asset of the backstepping approach. The adaptive interval type-2 fuzzy logic as fault observer can effectively estimate the lumped faults without the knowledge of their bounds for the modified quadrotor UAV. Additionally, the type-2 fuzzy systems are utilized to approximate the local nonlinearities of each subsystem under actuator faults, next and in order to achieve the expected tracking performance, we used Lyapunov theory stability and convergence analysis to online adjust adaptive laws. As a result, the uniformly ultimate stability of the modified quadrotor system is proved. Finally, the performances of the proposed control method are evaluated by simulation and the results demonstrate the effectiveness of the proposed control strategy for the modified quadrotor in vertical flights in presence of actuator faults.

Soft sensor modeling of chemical process based on self-organizing recurrent interval type-2 fuzzy neural network

This study introduces a novel self-organizing recurrent interval type-2 fuzzy neural network (SRIT2FNN) for the construction of a soft sensor model for a complex chemical process. The proposed SRIT2FNN combines interval type-2 fuzzy logic systems (IT2FLSs) and recurrent neural networks (RNNs) to improve the modeling precision. The Gaussian interval type-2 membership function is used to describe the antecedent part of the SRIT2FNN fuzzy rule, and the consequent part is of the Mamdani type with an interval random number. An adaptive optimal clustering number of fuzzy kernel clustering algorithm based on a Gaussian kernel validity index (GKVI-AOCN-FKCM) is developed to determine the structure of the SRIT2FNN and fuzzy rule antecedent parameters, and the parameter learning of SRIT2FNN used the gradient descent method. Finally, the proposed SRIT2FNN is applied to the soft sensor modeling of ethylene cracking furnace yield in a typical chemical process. Comparisons between the SRIT2FNN and conventional fuzzy neural network (FNN) and interval type-2 fuzzy neural network (IT2FNN) are made via simulation experiments. The results show that the proposed SRIT2FNN performs better than the conventional FNN and IT2FNN.