A Proposal of Visualization Method for Interpretable Fuzzy Model on Fusion Axes

2006 ◽  
Vol 10 (1) ◽  
pp. 121-131 ◽  
Author(s):  
Kosuke Yamamoto ◽  
◽  
Tomohiro Yoshikawa ◽  
Takeshi Furuhashi
Keyword(s):  
Fuzzy Model ◽  
Visualization Method ◽  
Statistical Features ◽  
Artificial Data ◽  
Linear Combinations ◽  
Useful Knowledge ◽  
Fuzzy Models ◽  
Multiple Input ◽  
Input Variables ◽  
Interpretable Models

Interpretability of fuzzy models has become one of the major topics in the field of fuzzy modeling. Visualization that makes input-output relationships interpretable is effective in extracting useful knowledge from unknown data. This paper presents visualization method that considers the visibility of fuzzy models. This method identifies clusters that have different statistical features, and projects the data to the “fusion axes”, which are linear combinations of the multiple input variables, considering the distribution of each cluster in the projected space. This paper applies the proposed method to artificial data and also to collected data from the mobile robot, and shows that the proposed method can extract useful knowledge from the obtained visible and interpretable models.

Uneven Input Space Division and Balance of Generality and Conciseness of Submodels for Hierarchical Fuzzy Modeling

2000 ◽  
Vol 4 (2) ◽  
pp. 152-157
Author(s):  
Kanta Tachibana ◽  
◽  
Takeshi Furuhashi ◽  
Keyword(s):  
Fuzzy Neural Network ◽  
Fuzzy Model ◽  
Fuzzy Modeling ◽  
Performance Indices ◽  
Promising Technique ◽  
Input Space ◽  
Fuzzy Models ◽  
Multiple Input ◽  
Fuzzy Neural ◽  
Hierarchical Fuzzy Model

Hierarchical fuzzy modeling is a promising technique to describe input-output relationships of nonlinear systems with multiple input. This paper presents a new method of dividing input spaces for hierarchical fuzzy modeling using the Fuzzy Neural Network (FNN) and Genetic Algorithm (GA). Uneven division of input space for each submodel in the hierarchical fuzzy model can be achieved with the proposed method. The obtained hierarchical fuzzy models are likely more concise and more precise than those identified with conventional methods. Studies on effects of the weights on performance indices of generality and conciseness of the fuzzy model are also shown in this paper.

scholarly journals Streamflow forecasting by combining neural networks and fuzzy models using advanced methods of input variable selection

2017 ◽  
Vol 20 (2) ◽  
pp. 520-532 ◽  
Author(s):  
A. B. Dariane ◽  
Sh. Azimi
Keyword(s):  
Wavelet Transform ◽  
Multistep Method ◽  
Test Period ◽  
Fast Method ◽  
Streamflow Forecasting ◽  
Input Selection ◽  
Fuzzy Models ◽  
Monthly Streamflow ◽  
Input Variables ◽  
Learning Machine

Abstract In this paper the performance of extreme learning machine (ELM) training method of radial basis function artificial neural network (RBF-ANN) is evaluated using monthly hydrological data from Ajichai Basin. ELM is a newly introduced fast method and here we show a novel application of this method in monthly streamflow forecasting. ELM may not work well for a large number of input variables. Therefore, an input selection is applied to overcome this problem. The Nash–Sutcliffe efficiency (NSE) of ANN trained by backpropagation (BP) and ELM algorithm using initial input selection was found to be 0.66 and 0.72, respectively, for the test period. However, when wavelet transform, and then genetic algorithm (GA)-based input selection are applied, the test NSE increase to 0.76 and 0.86, respectively, for ANN-BP and ANN-ELM. Similarly, using singular spectral analysis (SSA) instead, the coefficients are found to be 0.88 and 0.90, respectively, for the test period. These results show the importance of input selection and superiority of ELM and SSA over BP and wavelet transform. Finally, a proposed multistep method shows an outstanding NSE value of 0.97, which is near perfect and well above the performance of the previous methods.

scholarly journals A Control Approach Based on Observers of State and Uncertainty for a Class of Takagi–Sugeno Fuzzy Models

2021 ◽  
Vol 25 (3) ◽  
pp. 317-325
Author(s):  
Jun Zhao ◽  
Hugang Han ◽  
◽  
Keyword(s):  
Control System ◽  
Control Systems ◽  
Fuzzy Model ◽  
State Observer ◽  
The State ◽  
State Information ◽  
Control Approach ◽  
Fuzzy Models ◽  
Takagi Sugeno ◽  
Stable Control

Although the Takagi–Sugeno fuzzy model is effective for representing the dynamics of a plant to be controlled, two main questions arise when using it just as other models: 1) how to deal with the gap, which is referred to as uncertainty in this study, between the model and the concerned plant, and how to estimate the state information when it cannot be obtained directly, especially with the existence of uncertainty; 2) how to design a controller that guarantees a stable control system where only the estimated state is available and an uncertainty exists. While the existing studies cannot effectively observe the state and the resulting control systems can only be managed to be uniformly stable, this study first presents a state observer capable of precisely estimating the state regardless of the existence of uncertainty. Then, based on the state observer, an uncertainty observer is derived, which can track the trajectory of uncertainty whenever it occurs in a real system. Finally, a controller based on both observers is presented, which guarantees the asymptotic stability of the resulting control system.

scholarly journals Prediction of dissolved oxygen in reservoirs using adaptive network-based fuzzy inference system

2011 ◽  
Vol 14 (1) ◽  
pp. 167-179 ◽  
Author(s):  
Vesna Ranković ◽  
Jasna Radulović ◽  
Ivana Radojević ◽  
Aleksandar Ostojić ◽  
Ljiljana Čomić
Keyword(s):  
Experimental Data ◽  
Water Quality ◽  
Dissolved Oxygen ◽  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Adaptive Network ◽  
Inference System ◽  
Fuzzy Models ◽  
Highly Nonlinear ◽  
Input Variables

Predicting water quality is the key factor in the water quality management of reservoirs. Since a large number of factors affect the water quality, traditional data processing methods are no longer good enough for solving the problem. The dissolved oxygen (DO) level is a measure of the health of the aquatic system and its prediction is very important. DO dynamics are highly nonlinear and artificial intelligence techniques are capable of modelling this complex system. The objective of this study was to develop an adaptive network-based fuzzy inference system (ANFIS) to predict the DO in the Gruža Reservoir, Serbia. The fuzzy model was developed using experimental data which were collected during a 3-year period. The input variables analysed in this paper are: water pH, water temperature, total phosphate, nitrites, ammonia, iron, manganese and electrical conductivity. The selection of an appropriate set of input variables is based on the building of ANFIS models for each possible combination of input variables. Results of fuzzy models are compared with measured data on the basis of correlation coefficient, mean absolute error and mean square error. Comparing the predicted values by ANFIS with the experimental data indicates that fuzzy models provide accurate results.

Decay rate performance approach for stabilization continuous fuzzy models using their discretized forms

2015 ◽  
Vol 8 (4) ◽  
pp. 383-400
Author(s):  
Ameni Ellouze ◽  
François Delmotte ◽  
Jimmy Lauber ◽  
Mohamed Chtourou ◽  
Mohamed Ksantini
Keyword(s):  
Decay Rate ◽  
Discrete Model ◽  
Fuzzy Model ◽  
Performance Criterion ◽  
Rate Performance ◽  
Content Type ◽  
Ts Fuzzy Model ◽  
Fuzzy Models ◽  
Discretization Step ◽  
The Stability

Purpose – The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno (TS) fuzzy models using their discretized forms based on the decay rate performance approach. Design/methodology/approach – This approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. The discretized model is obtained from the Euler approximation method which is used for several orders. Second, based on the decay rate stabilization conditions, the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined. Third by keeping the values of the gains, the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold. Findings – The proposed idea lead to compare the performance continuous stability results with the literature. The comparison is, also, taken between the quadratic and non-quadratic cases. Originality/value – Therefore, the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models. In this case, the effect of the discretization step on the performances of the continuous TS fuzzy models is studied. The usefulness of this approach is shown through two examples.

scholarly journals Development Multiple Neuro-Fuzzy System Using Back-propagation Algorithm

2013 ◽  
Vol 6 (2) ◽  
pp. 794-804
Author(s):  
Dr. Imad S. Alshawi ◽  
Haider Khalaf Allamy ◽  
Dr. Rafiqul Zaman Khan
Keyword(s):  
Fuzzy System ◽  
Back Propagation ◽  
Fuzzy Model ◽  
Back Propagation Algorithm ◽  
New Approach ◽  
Training Time ◽  
Propagation Algorithm ◽  
Neuro Fuzzy ◽  
Highly Nonlinear ◽  
Input Variables

When fuzzy systems are highly nonlinear or include a large number of input variables, the number of fuzzy rules constituting the underlying model is usually large. Dealing with a large-size fuzzy model may face many practical problems in terms of training time, ease of updating, generalizing ability and interpretability. Multiple Fuzzy System (MFS) is one of effective methods to reduce the number of rules, increase the speed to obtain good results. This paper is therefore proposes another approach call Multiple Neuro-Fuzzy System (MNFS) which can further enhance the performance of the MFS approach. The new approach is used Back-propagation algorithm in the learning process. The performance of the proposed approach evaluates and compares with MFS by three experiments on nonlinear functions. Simulation results demonstrate the effectiveness of the new approach than MFS with regards to enhancement of the accuracy of the results.  

scholarly journals A Novel Ultra-Short-Term PV Power Forecasting Method Based on DBN-Based Takagi-Sugeno Fuzzy Model

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6447
Author(s):  
Ling Liu ◽  
Fang Liu ◽  
Yuling Zheng
Keyword(s):  
Power Generation ◽  
Fuzzy Model ◽  
Redundant Information ◽  
Short Term ◽  
Forecasting Method ◽  
Input Variables ◽  
Takagi Sugeno ◽  
Pv Power Generation ◽  
Fuzzy Subsets ◽  
Power Forecasting

Forecasting uncertainties limit the development of photovoltaic (PV) power generation. New forecasting technologies are urgently needed to improve the accuracy of power generation forecasting. In this paper, a novel ultra-short-term PV power forecasting method is proposed based on a deep belief network (DBN)-based Takagi-Sugeno (T-S) fuzzy model. Firstly, the correlation analysis is used to filter redundant information. Furthermore, a T-S fuzzy model, which integrates fuzzy c-means (FCM) for the fuzzy division of input variables and DBN for fuzzy subsets forecasting, is developed. Finally, the proposed method is compared to a benchmark DBN method and the T-S fuzzy model in case studies. The numerical results show the feasibility and flexibility of the proposed ultra-short-term PV power forecasting approach.

scholarly journals A Study on the Application of Sensitivity Analysis for Ship Hydrodynamic Coefficients

2018 ◽  
Vol 7 (4.36) ◽  
pp. 953
Author(s):  
Khanh Toan Tran ◽  
. .
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Mathematics Model ◽  
Hydrodynamic Coefficients ◽  
Ship Manoeuvring ◽  
Multiple Input ◽  
Sensitivity Analysis Method ◽  
Ship Hydrodynamic ◽  
Input Variables ◽  
The Mathematical Model

In the mathematical model with multiple input variables, the sensitivity analysis of the input variables is an important step to ensure the reliability of the mathematical model. In order to optimize the ship manoeuvring simulation, in particular the optimization of the trajectory ship, the sensitivity analysis should be performed in the mathematical model to select the group of the most sensitive hydrodynamic coefficients. In this paper, the author applied the sensitivity analysis method in mathematics model of ship manoeuvring programming in order to optimize the ship trajectory of Esso Bernicia 193000DWT tanker model.  

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

Sign in / Sign up

Export Citation Format

Share Document