Type-2 Takagi-Sugeno-Kang Fuzzy Logic System and Uncertainty in Machining

RÉSUMÉ: Plusieurs méthodes permettent aujourd’hui d’analyser le comportement des écoulements qui régissent le fonctionnement de systèmes rencontrés dans l’industrie (véhicules aériens, marins et terrestres, génération d’énergie, etc.). Pour les écoulements transitoires ou turbulents, les méthodes expérimentales sont utilisées conjointement avec les simulations numériques (simulation directe ou faisant appel à des modèles) afin d’extraire le plus d’information possible. Dans les deux cas, les méthodes génèrent des quantités de données importantes qui doivent ensuite être traitées et analysées. Ce projet de recherche vise à améliorer notre capacité d’analyse pour l’étude des écoulements simulés numériquement et les écoulements obtenus à l’aide de méthodes de mesure (par exemple la vélocimétrie par image de particules PIV ). L’absence, jusqu’à aujourd’hui, d’une définition objective d’une structure tourbillonnaire a conduit à l’utilisation de plusieurs méthodes eulériennes (vorticité, critère Q, Lambda-2, etc.), souvent inadaptées, pour extraire les structures cohérentes des écoulements. L’exposant de Lyapunov, calculé sur un temps fini (appelé le FTLE), s’est révélé comme une alternative lagrangienne efficace à ces méthodes classiques. Cependant, la méthodologie de calcul actuelle du FTLE exige l’évaluation numérique d’un grand nombre de trajectoires sur une grille cartésienne qui est superposée aux champs de vitesse simulés ou mesurés. Le nombre de noeuds nécessaire pour représenter un champ FTLE d’un écoulement 3D instationnaire atteint facilement plusieurs millions, ce qui nécessite des ressources informatiques importantes pour une analyse adéquate. Dans ce projet, nous visons à améliorer l’efficacité du calcul du champ FTLE en proposant une méthode alternative au calcul classique des composantes du tenseur de déformation de Cauchy-Green. Un ensemble d’équations différentielles ordinaires (EDOs) est utilisé pour calculer simultanément les trajectoires des particules et les dérivées premières et secondes du champ de déplacement, ce qui se traduit par une amélioration de la précision nodale des composantes du tenseur. Les dérivées premières sont utilisées pour le calcul de l’exposant de Lyapunov et les dérivées secondes pour l’estimation de l’erreur d’interpolation. Les matrices hessiennes du champ de déplacement (deux matrices en 2D et trois matrices en 3D) nous permettent de construire une métrique optimale multi-échelle et de générer un maillage anisotrope non structuré de façon à distribuer efficacement les noeuds et à minimiser l’erreur d’interpolation.----------ABSTRACT: Several methods can help us to analyse the behavior of flows that govern the operation of fluid flow systems encountered in the industry (aerospace, marine and terrestrial transportation, power generation, etc..). For transient or turbulent flows, experimental methods are used in conjunction with numerical simulations ( direct simulation or based on models) to extract as much information as possible. In both cases, these methods generate massive amounts of data which must then be processed and analyzed. This research project aims to improve the post-processing algorithms to facilitate the study of numerically simulated flows and those obtained using measurement techniques (e.g. particle image velocimetry PIV ). The absence, even until today, of an objective definition of a vortex has led to the use of several Eulerian methods (vorticity, the Q and the Lambda-2 criteria, etc..), often unsuitable to extract the flow characteristics. The Lyapunov exponent, calculated on a finite time (the so-called FTLE), is an effective Lagrangian alternative to these standard methods. However, the computation methodology currently used to obtain the FTLE requires numerical evaluation of a large number of fluid particle trajectories on a Cartesian grid that is superimposed on the simulated or measured velocity fields. The number of nodes required to visualize a FTLE field of an unsteady 3D flow can easily reach several millions, which requires significant computing resources for an adequate analysis. In this project, we aim to improve the computational efficiency of the FTLE field by providing an alternative to the conventional calculation of the components of the Cauchy-Green deformation tensor. A set of ordinary differential equations (ODEs) is used to calculate the particle trajectories and simultaneously the first and the second derivatives of the displacement field, resulting in a highly improved accuracy of nodal tensor components. The first derivatives are used to calculate the Lyapunov exponent and the second derivatives to estimate the interpolation error. Hessian matrices of the displacement field (two matrices in 2D and three matrices in 3D) allow us to build a multi-scale optimal metric and generate an unstructured anisotropic mesh to efficiently distribute nodes and to minimize the interpolation error. The flexibility of anisotropic meshes allows to add and align nodes near the structures of the flow and to remove those in areas of low interest. The mesh adaptation is based on the intersection of the Hessian matrices of the displacement field and not on the FTLE field

A Multi-Agent Architecture for the Design of Hierarchical Interval Type-2 Beta Fuzzy System

This paper presents a new methodology for building and evolving hierarchical fuzzy systems. For the system design, a tree-based encoding method is adopted to hierarchically link low dimensional fuzzy systems. Such tree structural representation has by nature a flexible design offering more adjustable and modifiable structures. The proposed hierarchical structure employs a type-2 beta fuzzy system to cope with the faced uncertainties, and the resulting system is called the Hierarchical Interval Type-2 Beta Fuzzy System (HT2BFS). For the system optimization, two main tasks of structure learning and parameter tuning are applied. The structure learning phase aims to evolve and learn the structures of a population of HT2BFS in a multiobjective context taking into account the optimization of both the accuracy and the interpretability metrics. The parameter tuning phase is applied to refine and adjust the parameters of the system. To accomplish these two tasks in the most optimal and faster way, we further employ a multi-agent architecture to provide both a distributed and a cooperative management of the optimization tasks. Agents are divided into two different types based on their functions: a structure agent and a parameter agent. The main function of the structure agent is to perform a multi-objective evolutionary structure learning step by means of the Multi-Objective Immune Programming algorithm (MOIP). The parameter agents have the function of managing different hierarchical structures simultaneously to refine their parameters by means of the Hybrid Harmony Search algorithm (HHS). In this architecture, agents use cooperation and communication concepts to create high-performance HT2BFSs. The performance of the proposed system is evaluated by several comparisons with various state of art approaches on noise-free and noisy time series prediction data sets and regression problems. The results clearly demonstrate a great improvement in the accuracy rate, the convergence speed and the number of used rules as compared with other existing approaches

Application of Neuro-Fuzzy system to solve Traveling Salesman Problem

This paper presents the application of adaptive neuro-fuzzy inference system (ANFIS) in solving the traveling salesman problem. Takagi-Sugeno-Kang neuro-fuzzy architecture model is used for this purpose. TSP, although, simple to describ

Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique

Development of Neurofuzzy Architectures for Electricity Price Forecasting

In 20th century, many countries have liberalized their electricity market. This power markets liberalization has directed generation companies as well as wholesale buyers to undertake a greater intense risk exposure compared to the old centralized framework. In this framework, electricity price prediction has become crucial for any market player in their decision‐making process as well as strategic planning. In this study, a prototype asymmetric‐based neuro‐fuzzy network (AGFINN) architecture has been implemented for short‐term electricity prices forecasting for ISO New England market. AGFINN framework has been designed through two different defuzzification schemes. Fuzzy clustering has been explored as an initial step for defining the fuzzy rules while an asymmetric Gaussian membership function has been utilized in the fuzzification part of the model. Results related to the minimum and maximum electricity prices for ISO New England, emphasize the superiority of the proposed model over well‐established learning‐based models

Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf

SIGNIFICANT WAVE HEIGHT FORECASTING BY USING TYPE-2 FUZZY

ignificant wave height parameter plays an important role in ocean and coastal activities. However, the forecasting process of this parameter involved with uncertainty due to the nature of data. In past decades, fuzzy logic was introduced by Zadeh that enables a computer system to reason with uncertainty. This theory had widely applied in many applications, including wave parameter forecasting. Currently, wave height forecasting techniques were focusing on using Type-1 fuzzy method. This technique has a limitation in handling and minimizing uncertainties 'which affect the accuracy ofthe forecasting result. Therefore, this research is aimed to propose a method on forecasting significant wave height by using Type-2 fuzzy

Improving the cost model development process using fuzzy logic

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Frbs: Fuzzy Rule-Based Systems for Classification and Regression in R

Fuzzy rule-based systems (FRBSs) are a well-known method family within soft computing. They are based on fuzzy concepts to address complex real-world problems. We present the R package frbs which implements the most widely used FRBS models, namely, Mamdani and Takagi Sugeno Kang (TSK) ones, as well as some common variants. In addition a host of learning methods for FRBSs, where the models are constructed from data, are implemented. In this way, accurate and interpretable systems can be built for data analysis and modeling tasks. In this paper, we also provide some examples on the usage of the package and a comparison with other common classification and regression methods available in R.This work was supported in part by the Spanish Ministry of Science and Innovation (MICINN) under Projects TIN2009-14575, TIN2011-28488, TIN2013-47210-P, and P10-TIC-06858. Bergmeir held a scholarship from the Spanish Ministry of Education (MEC) of the \Programa de Formación del Profesorado Universitario (FPU)"