Antecedent Part Parameters Research Articles

Enhancing Positional Accuracy of the XY-Linear Stage Using Laser Tracker Feedback and IT2FLS

This paper proposes a calibration algorithm to improve the positional accuracies of an industrial XY-linear stage. Precision positioning of these linear stages is required to maintain highly accurate object handling and manipulation. However, due to imprecisions in linear motor stages and the gearbox, static and dynamic errors exist within these manipulators that cannot be adjusted internally. In this paper, to improve the positioning accuracy of these manipulators, measurements from a laser tracker are used within an interval type-2 fuzzy logic system. The laser tracker used in this experiment is an AT960-MR, which is a highly accurate noncontact coordinate metrology equipment capable of performing highly accurate robotic measurements. To perform calibration, we use an IT2FLS to find a nonlinear correcting relationship to compensate for position errors. The IT2FLS acts on the commands given to the move stage to find the accurate position of the move stage. To train the IT2FLS, we use particle swarm optimization (PSO) for the antecedent part parameters and Moore–Penrose generalized inverse to estimate the consequent part parameters. Data are split into train/test data to test the efficacy of the proposed algorithm. It is shown that by using the proposed IT2FLS-based calibration approach, the standard deviation of the position errors can be decreased from 86.1μm to 55.9μm, which is a 35.1% improvement. Comparison results with a multilayer perceptron neural network reveal that the proposed IT2FLS-based calibration algorithm outperforms multilayer perceptron neural network for positional calibration purposes.

Optimization of Interval Type-2 Fuzzy Logic System Using Grasshopper Optimization Algorithm

The estimation of the fuzzy membership function parameters for interval type 2 fuzzy logic system (IT2-FLS) is a challenging task in the presence of uncertainty and imprecision. Grasshopper optimization algorithm (GOA) is a fresh population based meta-heuristic algorithm that mimics the swarming behavior of grasshoppers in nature, which has good convergence ability towards optima. The main objective of this paper is to apply GOA to estimate the optimal parameters of the Gaussian membership function in an IT2-FLS. The antecedent part parameters (Gaussian membership function parameters) are encoded as a population of artificial swarm of grasshoppers and optimized using its algorithm. Tuning of the consequent part parameters are accomplished using extreme learning machine. The optimized IT2-FLS (GOAIT2FELM) obtained the optimal premise parameters based on tuned consequent part parameters and is then applied on the Australian national electricity market data for the forecasting of electricity loads and prices. The forecasting performance of the proposed model is compared with other population-based optimized IT2-FLS including genetic algorithm and artificial bee colony optimization algorithm. Analysis of the performance, on the same data-sets, reveals that the proposed GOAIT2FELM could be a better approach for improving the accuracy of the IT2-FLS as compared to other variants of the optimized IT2-FLS.

A HYBRID METHOD OF MODIFIED CAT SWARM OPTIMIZATION AND GRADIENT DESCENT ALGORITHM FOR TRAINING ANFIS

This paper introduces a novel approach for tuning the parameters of the adaptive network-based fuzzy inference system (ANFIS). In the commonly used training methods, the antecedent and consequent parameters of ANFIS are trained by gradient-based algorithms and recursive least square method, respectively. In this study, a new swarm-based meta-heuristic optimization algorithm, so-called "Cat Swarm Optimization", is used in order to train the antecedent part parameters and gradient descent algorithm is applied for training the consequent part parameters. Experimental results for prediction of Mackey–Glass model and identification of two nonlinear dynamic systems reveal that the performance of proposed algorithm is much better and it shows quite satisfactory results.

A Fuzzy System Constructed by Rule Generation and Iterative Linear SVR for Antecedent and Consequent Parameter Optimization

This paper proposes a new fuzzy regression model, i.e., the fuzzy system constructed by rule generation and iterative linear support vector regression (FS-RGLSVR) for structural risk minimization. The FS-RGLSVR is composed of Takagi-Sugeno (TS)-type fuzzy if-then rules. These rules are automatically constructed by a self-splitting rule generation algorithm that introduces the self-splitting technique to the k-means clustering algorithm. This new algorithm regards a cluster as a fuzzy rule, where no preassignment of the cluster (rule) number is necessary. The cost function for parameter learning is defined based on structural risk instead of empirical risk minimization in order to achieve generalizability. Tuning all of the free parameters in the FS-RGLSVR using linear support vector regression (SVR) is proposed to minimize the cost function. Each of the consequent and antecedent part parameters is expressed as a linear combination coefficient in a transformed input space so that the linear SVR is applicable. This paper introduces iterative linear SVR to tune antecedent and consequent parameters. This paper demonstrates the capabilities of FS-RGLSVR by two simulated and four practical regression examples. Comparisons with fuzzy systems with different types of learning algorithms verify the performance of the FS-RGLSVR.

Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input–output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input–output values are structured together in the regression matrix and named as “L-FBF”. Secondly, instead of using basis function, the membership values of the lagged input–output values are used in the regression matrix by using Gaussian membership functions, called “M-FBF”. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi-Sugeno-Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.

Identification using ANFIS with intelligent hybrid stable learning algorithm approaches and stability analysis of training methods

This paper proposes a novel hybrid learning algorithm with stable learning laws for Adaptive Network based Fuzzy Inference System (ANFIS) as a system identifier and studies the stability of this algorithm. The new hybrid learning algorithm is based on particle swarm optimization (PSO) for training the antecedent part and forgetting factor recursive least square (FFRLS) for training the conclusion part. Two famous training algorithms for ANFIS are the gradient descent (GD) to update antecedent part parameters and using GD or recursive least square (RLS) to update conclusion part parameters. Lyapunov stability theory is used to study the stability of the proposed algorithms. This paper, also studies the stability of PSO as an optimizer in training the identifier. Stable learning algorithms for the antecedent and consequent parts of fuzzy rules are proposed. Some constraints are obtained and simulation results are given to validate the results. It is shown that instability will not occur for the leaning rate and PSO factors in the presence of constraints. The learning rate can be calculated on-line and will provide an adaptive learning rate for the ANFIS structure. This new learning scheme employs adaptive learning rate that is determined by input–output data. Also, stable learning algorithms for two common methods are proposed based on Lyapunov stability theory and some constraints are obtained.

A Self-Evolving Interval Type-2 Fuzzy Neural Network for Nonlinear Systems Identification

Abstract This paper proposes a Self-Evolving Interval Type-2 Fuzzy Neural Network (SEIT2FNN) for nonlinear systems identification. The SEIT2FNN has both on-line structure and parameter learning abilities. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi-Sugeno-Kang (TSK) type. An on-line clustering method is proposed to generate fuzzy rules which flexibly partition the input space. For parameter learning, the consequent part parameters are tuned by a rule-ordered Kalman filter algorithm for high accuracy learning performance. The antecedent part parameters are learned by gradient descent algorithms. Comparisons with identification using other type-1 and type-2 fuzzy systems verify the performance of the SEIT2FNN.