Simplification of ANFIS based on importance-confidence-similarity measures

In the classic approaches to design a fuzzy inference system, the fuzzy rules are determined by a domain expert a priori and then they are maintained unchanged during the learning. These fixed fuzzy rules may not be appropriate in real-time applications where the environment or model often meets unpredicted disturbances or damages. Hence, poor performance may be observed. In comparison to the conventional methods, fuzzy inference systems based on neural networks, called fuzzy-neural systems, have begun to exhibit great potential for adapting to the changes by utilizing the learning ability and adaptive capability of neural networks. Thus, a fuzzy inference system can be built using the standard structure of neural networks. Nevertheless, the determination of the number of fuzzy rules and the adjustment of the parameters in the if-then fuzzy rules are still open issues. A sequential adaptive fuzzy inference system (SAFIS) is developed to determine the number of fuzzy rules during learning and modify the parameters in fuzzy rules simultaneously. SAFIS uses the concept of influence of a fuzzy rule for adding and removing rules during learning. The influence of a fuzzy rule is defined as its contribution to the system output in a statistical sense when the input data is uniformly distributed. When there is no addition of fuzzy rules, only the parameters of the “closest” (in a Euclidean sense) rule are updated using an extended Kalman filter (EKF) scheme. The performance of SAFIS is evaluated based on some function approximation problems, via, nonlinear system identification problems and a chaotic time-series prediction problem. Results indicate that SAFIS produces similar or better accuracies with lesser number of rules compared to other algorithms.

In this paper, a hybrid meta-heuristic artificial intelligence (AI) method, named “ANFIS–PSOGA,” is developed for modeling the discharge coefficient of circular side orifices for the first time. For this purpose, the adaptive neuro fuzzy inference system (ANFIS) network is optimized by means of two robust optimization algorithms: the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm. Furthermore, the Monte Carlo simulations are utilized to enhance the performance of the AI hybrid model. Besides, the k-fold cross-validation method is employed in order to verify the numerical results. Initially, the performance of three fuzzy inference system (FIS) generations of the ANFIS model including grid partitioning, subtractive clustering and fuzzy C-means clustering are evaluated. After that, using the parameters affecting the discharge coefficient, eleven ANFIS models are defined and then the best ANFIS model and the most influencing input parameters are identified through the conduction of a sensitivity analysis. For the superior ANFIS model, mean absolute percentage error, root-mean-square error and the correlation coefficient (R) are obtained 0.021, 0.020 and 0.871, respectively. Also, the Froude number (Fr) is detected as the most effective input parameter. Moreover, the discharge coefficient of the circular side orifices and the flow field within main channels along the side orifices are simulated through the adoption of a computational fluid dynamics (CFD) model. Additionally, the flow field at three different cross sections (beginning, middle and end of orifice) along the side weir is evaluated. For instance, by advancing the flow toward the side orifice, the Froude number is reduced. Besides, at each cross section, the maximum shear stress is estimated to occur in the vicinity of the crest of the circular side orifice. According to the CFD results, the maximum lateral velocity is estimated near the circular side orifice. In addition, the results yielded by the ANFIS, ANFIS–PSO, ANFIS–PSOGA and CFD models are compared and an uncertainty analysis is carried out for the models. Based on the comparison, ANFIS–PSOGA has the best performance in simulating the discharge coefficient. Ultimately, a simple and practical computer code for the best model (ANFIS–PSOGA) is proposed which can be easily used by scholars and engineers in practical usages.

Wireless sensor network (WSN) brings an innovative model with embedded system with restrictions of computing ability, intercommunication, storage capacity, and energy resource which is applied for a high range of applications in the situations when constructing the network based on conventional infrastructure is not feasible. Clustering with WSN is a successful technique to reduce the rate of energy use of sensor node. The fuzzy logic calculates the cluster head (CH) selection probability depending on the node's earlier communication history to choose the CH. The set of rules applied to the fuzzified input is the fuzzy rule base. The output of the inference engine is changed to crisp output by defuzzification. Artificial bee colony (ABC) is an optimisation protocol owes its inspiration to the exploration behaviour of honey bees. It is a comparatively innovative optimisation algorithm which has proven to be on par with classical bio-inspired protocols. This work on ABC optimisation algorithm is suggested for selecting fuzzy rules. Rule selection methods combine different rules from fuzzy rule set to decrease the rules while maintaining the performance of the system. The rules that decrease the performance of the system are removed, to get a fuzzy rule set with improved performance.

Glass fiber reinforced polyester (GFRP) composite materials are widely used in various applications. The prediction of wear values for composite materials is very complex and nonlinear phenomena. Artificial intelligence methods (AI) and expert systems such as artificial neural networks (ANNs) and fuzzy inference systems (FIS) have a series of properties on modeling nonlinear systems. In some situations, ANNs are insufficient under abrupt changes in input variables. Adaptive Neuro Fuzzy Inference System (ANFIS) is capable of integrating the linguistic expressions of FIS with the adaptation and learning skills of the ANNs. The aim of this study is to determine the optimum material content and working conditions in terms of wear resistance. This study proposes an ANFIS sub-clustering based prediction model for estimation of wear behavior of GFRP composites within various concentrations of materials and under diverse loads and speeds. Proposed ANFIS model extracted optimum concentrations and operating parameters to obtain the minimum wear rate. Due to the wear rate estimation model, optimum wear rate value is reached to 25.0013 (mm3/Nm)*10−6 at CaCO3, polystyrene, glass fiber, glass bead, alumina, load and speed values of 49%, 0%, 11%, 10%, 0.8%, 10 N and 100 rpm respectively. A high estimation capability (R2 = 0.964) has been achieved using ANFIS Model.

The accurate rotor position information is very important for high performance operation of switched reluctance motor (SRM). Traditionally, there is a mechanical rotor position sensor. But this reduces the reliability and increases cost and size of SRM. In order to overcome the disadvantage of mechanical rotor position sensor, a sensorless operation method of SRM based on adaptive network based fuzzy inference system (ANFIS) is developed in this paper. The rotor position can be estimated by using the unique relationship between rotor position, flux linkage and phase current. In this paper, the ANFIS is used to map this relationship. Among the sensorless position estimation method, approach based on fuzzy neural network (FNN) is one of the promising methods. By combining the benefits of artificial neural network (ANN) and fuzzy inference system (FIS) in a single model, the ANFIS shows characteristics of fast and accurate learning, the ability of using both linguistic information and data information and good generalization capability. For its antecedents are fuzzy sets, the noise in the input signals can be restrained. This approach shows a characteristic of robustness. For its consequent is in linear function of input variables, it has a simple structure and low computation complexity. So, it is well suited to be applied on-line. Applying it to the rotor position estimation, a high accuracy and robust sensorless rotor position estimator is presented. The experimental results proved the effectiveness of the proposed method.

In this article, adaptive‐network‐based fuzzy inference system (ANFIS) models are proposed to compute the characteristic impedances of air‐suspended trapezoidal‐shaped microshield lines (AS‐TSMLs) and air‐suspended rectangular‐shaped microshield lines (AS‐RSMLs). The ANFIS is a fuzzy inference system implemented within the architecture and optimization procedure of adaptive networks. Four optimization algorithms, hybrid learning, simulated annealing, genetic, and least‐squares, are used to determine optimally the design parameters of ANFIS. The characteristic impedance results of ANFIS models are in very good agreement with the results available in the literature. When the performances of ANFIS models are compared with each other, the best results are obtained from the ANFIS model trained by the hybrid learning algorithm. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 20–24, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24829

In this work we propose an immune approach for learning neurofuzzy systems, namely Adaptive-Network-based Fuzzy Inference System (ANFIS). ANFIS is proved to be universal approximator of nonlinear functions. But in case of great number of input variables ANFIS structure grows essentially and the dimensionality of learning task becomes a problem. Existing methods of ANFIS learning allow only to identify parameters of ANFIS without modifying its structure. We propose an immune approach for ANFIS learning based on clonal selection and immune network theories. It allows not only to identify ANFIS parameters but also to reduce number of neurons in hidden layers of ANFIS. These tasks are performed simultaneously using the model of adaptive multiantibody.

This paper presents a learning approach called adaptive coherence scheme (CAS) that adaptively reduces information on input patterns in hidden layer(s) of a neural network. The hidden units in a neural network store information continuously during training session. As a result the network becomes extremely familiar with every details of input patterns. This is not desirable in training. Therefore, we attempt to limit this information automatically with a regularization function consisting of activations of hidden units. We proposed standard coherence learning (SCL) where a constant coherence strength was used in order to solve the problem. Here, we attempt to develop a coherence adaptation scheme in order to maintain small amount of information in the network automatically. We have applied the algorithm to the breast cancer classification and Mackey-Glass chaotic time series prediction problems with single and double hidden layered networks. The results show that the network maintains small amount of information with good classification and prediction accuracies.

In this paper, we compare and analyze the prediction performance of existing ANFIS (Adaptive Neuro Fuzzy Inference System) models. The ANFIS model is a fusion of neural networks with learning ability, adaptability, and computational ability, and a fuzzy system with human-like thinking ability and reasoning ability. In this paper, we analyze the prediction performance of ANFIS models using different input space partitioning methods. ANFIS 1 uses SC (Subtractive Clustering), a clustering method based on the density of data, to calculate the center of the cluster by calculating potential values inversely proportional to the distances of the different inputs. ANFIS 2 uses Fuzzy C-Means (FCM) clustering, which is a clustering method based on degree of belonging to data, and classifies each data belonging to each cluster according to degree of affiliation. ANFIS 3 is a method of using Context based Fuzzy C-Means (CFCM) clustering, which is a clustering method considering characteristics of input and output space based on FCM clustering. It creates clusters for each context generated according to characteristics of output space, to classify the data. To evaluate these ANFIS models, we use short term electricity price forecasting data and Boston housing data. The prediction performance is based on the Root Mean Squared Error (RMSE) method. Experimental results show that the prediction performance of the ANFIS model is different depending on the characteristics of each data. Furthermore, we confirmed that the prediction performance of ANFIS model using CFCM clustering method is constant.

Genetic Reinforcement Learning Algorithms for On-line Fuzzy Inference System Tuning Application to Mobile Robotic"

In the dynamic realm of Automatic Voltage Regulation (AVR), the pursuit of robust transient response, adaptability, and stability drives researchers to explore novel avenues. This study introduces a groundbreaking approach—the Hybrid Intelligent Fractional Order Proportional Derivative2+Integral (FOPDD+I) controller—leveraging the power of the Adaptive Neuro-Fuzzy Inference System (ANFIS). The novelty lies in the comparative analysis of three scenarios: the AVR system without a controller, with a traditional PID controller, and with the proposed FOPDD+I-based ANFIS. By fusing ANFIS with a hybrid controller, we forge a unique path toward optimized AVR performance. The hybrid controller, based on FOPID (Fractional Order Proportional Integral Derivative) principles, synergizes individual integral factors with ANFIS, augmenting them with a doubled derivative factor. The ANFIS design employs a hybrid optimization learning scheme to fine-tune the Fuzzy Inference System (FIS) parameters governing the AVR system. To train the fuzzy inference system, we utilize a Proportional-Integral-Derivative (PID) simulation of the entire AVR system, capturing essential data over approximately seven seconds. Our simulations, conducted in MATLAB/Simulink, reveal impressive performance metrics for the FOPDD+I-ANFIS approach: Rise time: 1.1162 seconds, settling time: 0.5531 seconds, Overshoot: 0%, Steady-state error: 0.00272, These results position our novel approach favorably against existing works, underscoring the transformative potential of intelligent creation in AVR control.

In the present study, the adaptive neuro-fuzzy inference system (ANFIS) is developed for the prediction of effective thermal conductivity (ETC) of different fillers filled in polymer matrixes. The ANFIS uses a hybrid learning algorithm. The ANFIS is a class of adaptive networks that is functionally equivalent to fuzzy inference systems (FIS). The ANFIS is based on neuro-fuzzy model, trained with data collected from various sources of literature. ETC is predicted using ANFIS with volume fraction and thermal conductivities of fillers and matrixes as input parameters, respectively. The predicted results by ANFIS are in good agreements with experimental values. The predicted results also show the supremacy of ANFIS in comparison with other earlier developed models.

Machine learning methods such as Adaptive Network-Based Fuzzy Inference System (ANFIS) have been widely employed in intelligent urban storm water disaster warning for the purpose of smart city. However, there exists lack of research proposed for applying ANFIS and mobile application (App) to reach the purpose of smart city. In order to accomplish the goal, the study integrates ANFIS and Qt Framework to develop a Typhoon Rainfall Forecasting System to real-time typhoon rainfall forecast via a mobile device. The Service is first built by applying cluster analysis to typhoon data (Tamsui Weather Station of Taiwan) during June 1967 and November 2020 to classify the data into four groups and then applying the ANFIS to construct the Service with data in each group. The fuzzy rule of ANFIS is established by grid partition method. Both the Service and App employ Qt Framework as the cross-operating development tool, and the App is transformed to a smart mobile device App of different platforms. The simulated results show the following: (1) Taking the example of typhoon Nakri in group 1, the lowest root mean square error (7.898 mm) and the lowest computation time (178 sec) were obtained for training with 1000 steps and three membership functions. (2) Using the optimal parameters of the typhoon belonging to that group can obtain better prediction results. The developed typhoon rainfall forecasting system App in the supplementary information demonstrates that the user can use the smart mobile device for real-time typhoon forecasting at the most three hours ahead easily.

In this paper, an approach in predicting surface roughness of Titanium Aluminum Nitrite (TiN) coatings using Adaptive Network Based Fuzzy Inference System (ANFIS) is implemented. The TiN coatings were coated on tungsten carbide (WC) using Physical Vapor Deposition (PVD) magnetron sputtering process. The N2 pressure, argon pressure and turntable speed were selected as the input parameters and the surface roughness as an output of the process. Response Surface Methodology (RSM) was used to design the matrix in collecting the experimental data. In the ANFIS structure, triangular, trapezoidal, bell and Gaussian shapes were used for as input membership function (MFs). The collected experimental data was used to train the ANFIS model. Then, the ANFIS model were validated with the actual testing data and compared with regression model in terms of the residual error and model accuracy. The result indicated that the ANFIS model using three bell shapes MFs obtained better result compared to the polynomial regression model. The number of MFs showed significant influence to the ANFIS model performance. The result also indicated that the limited experimental data could be used in training the ANFIS model and resulting accurate predictive result.

Bubbly flow behavior simulation in two-phase chemical reactors such bubble column type reactors is widely employed for chemical industry purposes. The computational fluid dynamics (CFD) approach has been employed by engineers and researchers for modeling these types of chemical reactors. In spite of the CFD robustness for simulating transport phenomena and chemical reactions in these reactors, this approach has been known as expensive for modeling such turbulent complex flows. Artificial intelligence (AI) algorithm of the adaptive network-based fuzzy inference system (ANFIS) are largely understood and utilized for the CFD approach optimization. In this hybrid approach, the CFD findings are learned by AI algorithms like ANFIS to save computational time and expenses. Once the pattern of the CFD results have been captured by the AI model, this hybrid model can be then used for process simulation and optimization. As such, there is no need for further simulations of new conditions. The objective of this paper is to obviate the need for expensive CFD computations for two-phase flows in chemical reactors via coupling CFD data to an AI algorithm, i.e., differential evolution based fuzzy inference system (DEFIS). To do so, air velocity as the output and the values of the x, and y coordinates, water velocity, and time step as the inputs are inputted the AI model for learning the flow pattern. The effects of cross over as the DE parameter and also the number of inputs on the best intelligence are investigated. Indeed, DEFIS correlates the air velocity to the nodes coordinates, time, and liquid velocity and then after the CFD modeling could be replaced with the simple correlation. For the first time, a comparison is made between the ANFIS and the DEFIS performances in terms of the prediction capability of the gas (air) velocity. The results released that both ANFIS and DEFIS could accurately predict the CFD pattern. The prediction times of both methods were obtained to be equal. However, the learning time of the DEFIS was fourfold of ANFIS.