Multi-region System Modelling by using Genetic Programming to Extract Rule Consequent Functions in a TSK Fuzzy System

[EN] This paper aims to build a fuzzy system by means of genetic programming, which is used to extract the relevant function for each rule consequent through symbolic regression. The employed TSK fuzzy system is complemented with a variational Bayesian Gaussian mixture clustering method, which identifies the domain partition, simultaneously specifying the number of rules as well as the parameters in the fuzzy sets. The genetic programming approach is accompanied with an orthogonal least square algorithm, to extract robust rule consequent functions for the fuzzy system. The proposed model is validated with a synthetic surface, and then with real data from a gas turbine compressor map case, which is compared with an adaptive neuro-fuzzy inference system model. The results have demonstrated the efficacy of the proposed approach for modelling system with small data or bifurcating dynamics, where the analytical equations are not available, such as those in a typical industrial setting.Research supported by EPSRC Grant EVES (EP/R029741/1).Zhang, Y.; Martínez-García, M.; Serrano, J.; Latimer, A. (2019). Multi-region System Modelling by using Genetic Programming to Extract Rule Consequent Functions in a TSK Fuzzy System. IEEE. 987-992. https://doi.org/10.1109/ICARM.2019.8834163S98799

Neuro-Fuzzy Based Intelligent Approaches to Nonlinear System Identification and Forecasting

Nearly three decades back nonlinear system identification consisted of several ad-hoc approaches, which were restricted to a very limited class of systems. However, with the advent of the various soft computing methodologies like neural networks and the fuzzy logic combined with optimization techniques, a wider class of systems can be handled at present. Complex systems may be of diverse characteristics and nature. These systems may be linear or nonlinear, continuous or discrete, time varying or time invariant, static or dynamic, short term or long term, central or distributed, predictable or unpredictable, ill or well defined. Neurofuzzy hybrid modelling approaches have been developed as an ideal technique for utilising linguistic values and numerical data. This Thesis is focused on the development of advanced neurofuzzy modelling architectures and their application to real case studies. Three potential requirements have been identified as desirable characteristics for such design: A model needs to have minimum number of rules; a model needs to be generic acting either as Multi-Input-Single-Output (MISO) or Multi-Input-Multi-Output (MIMO) identification model; a model needs to have a versatile nonlinear membership function. Initially, a MIMO Adaptive Fuzzy Logic System (AFLS) model which incorporates a prototype defuzzification scheme, while utilising an efficient, compared to the Takagi–Sugeno–Kang (TSK) based systems, fuzzification layer has been developed for the detection of meat spoilage using Fourier transform infrared (FTIR) spectroscopy. The identification strategy involved not only the classification of beef fillet samples in their respective quality class (i.e. fresh, semi-fresh and spoiled), but also the simultaneous prediction of their associated microbiological population directly from FTIR spectra. In the case of AFLS, the number of memberships for each input variable was directly associated to the number of rules, hence, the “curse of dimensionality” problem was significantly reduced. Results confirmed the advantage of the proposed scheme against Adaptive Neurofuzzy Inference System (ANFIS), Multilayer Perceptron (MLP) and Partial Least Squares (PLS) techniques used in the same case study. In the case of MISO systems, the TSK based structure, has been utilized in many neurofuzzy systems, like ANFIS. At the next stage of research, an Adaptive Fuzzy Inference Neural Network (AFINN) has been developed for the monitoring the spoilage of minced beef utilising multispectral imaging information. This model, which follows the TSK structure, incorporates a clustering pre-processing stage for the definition of fuzzy rules, while its final fuzzy rule base is determined by competitive learning. In this specific case study, AFINN model was also able to predict for the first time in the literature, the beef’s temperature directly from imaging information. Results again proved the superiority of the adopted model. By extending the line of research and adopting specific design concepts from the previous case studies, the Asymmetric Gaussian Fuzzy Inference Neural Network (AGFINN) architecture has been developed. This architecture has been designed based on the above design principles. A clustering preprocessing scheme has been applied to minimise the number of fuzzy rules. AGFINN incorporates features from the AFLS concept, by having the same number of rules as well as fuzzy memberships. In spite of the extensive use of the standard symmetric Gaussian membership functions, AGFINN utilizes an asymmetric function acting as input linguistic node. Since the asymmetric Gaussian membership function’s variability and flexibility are higher than the traditional one, it can partition the input space more effectively. AGFINN can be built either as an MISO or as an MIMO system. In the MISO case, a TSK defuzzification scheme has been implemented, while two different learning algorithms have been implemented. AGFINN has been tested on real datasets related to electricity price forecasting for the ISO New England Power Distribution System. Its performance was compared against a number of alternative models, including ANFIS, AFLS, MLP and Wavelet Neural Network (WNN), and proved to be superior. The concept of asymmetric functions proved to be a valid hypothesis and certainly it can find application to other architectures, such as in Fuzzy Wavelet Neural Network models, by designing a suitable flexible wavelet membership function. AGFINN’s MIMO characteristics also make the proposed architecture suitable for a larger range of applications/problems

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

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Context dependent fuzzy modelling and its applications

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the meaning of the fuzzy terms. While efforts have been made to integrate contextual information into the representation of fuzzy sets, it remains the case that often the context model is very restrictive and/or problem specific. The work reported in this thesis is our attempt to create a practical frame work to integrate contextual information into the representation of fuzzy sets so as to improve the interpretability as well as the accuracy of the fuzzy system. Throughout this thesis, we have looked at the capability of the proposed context dependent fuzzy sets as a stand alone as well as in combination with other methods in various application scenarios ranging from time series forecasting to complicated car racing control systems. In all of the applications, the highly competitive performance nature of our approach has proven its effectiveness and efficiency compared with existing techniques in the literature

Intelligent Forecasting of Electricity Demand

In this paper, a number of approaches to the modelling of electricity demand, on a variety of time-scales, are considered. These approaches fall under the category of 'intelligent' systems engineering, where techniques such as neural networks, fuzzy logic and genetic algorithms are employed. The paper attempts to give some motivation for the employment of such techniques, while also making some effort to be realistic about the limitations of such methods, in particular a number of important caveats that should be borne in mind when utilising these techniques within the current application domain. In general, the electricity demand data is modelled as a time series, but one application considered involves application of linguistic modelling to capture operator expertise