LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Dr Jitender Deogu

Edwards statistical mechanics for jammed granular matter

International audienc

Nonlinear rheology of granular matter

A tremendous amount of upheaval and rethinking of "free-volume" theories to describe granular systems have made staggering progress. However, owing to a plethora of macroscopically equivalent yet microscopically distinct metastable states, the average free volume density does not fully describe the complex dynamics of granular systems. The nonlinear rheology of grains and powders is filled with an assortment of such micro-macro processes interrupted by shear bands or decorated with inhomogeneous force chain networks, obscuring their “true” physical interpretation. By combining FT-rheology with Chebyshev polynomials, we quantified these nonlinearities and revealed that the viscoelastic features of granular matter at different length scales are governed by an intensive property known as the “noise temperature” (a non-thermodynamic parameter), resembling the constitutive law for soft glasses. Furthermore, upon confinement, dry grains followed compaction-like dynamics, while wet grains were unpacked into a dilatant-like fluid.Die Theorien des "freien Volumens" zur Beschreibung granularer Systeme haben einen enormen Umbruch und ein Umdenken bewirkt. Aufgrund einer Fülle makroskopisch gleichwertiger, aber mikroskopisch unterschiedlicher metastabiler Zustände wird die durchschnittliche Dichte des freien Volumens (ein einziger makroskopischer Freiheitsgrad) der komplexen Dynamik granularer Systeme jedoch nicht gerecht. Die nichtlineare Rheologie von Körnern und Pulvern ist mit einer Vielzahl solcher Mikro-Makro-Prozesse gefüllt, die durch Scherbänder unterbrochen oder mit filamentären Kraftkettennetzwerken ausgestattet sind, was eine homogene Reaktion verhindert und damit die Vorhersage ihrer physikalischen Interpretation erschwert. Das Modell, das sowohl die räumliche Heterogenität als auch die intermittierende Dynamik berücksichtigt, ist eine verallgemeinerte Version des "Fallen"- Modells, das Modell der weichen glasartigen Rheologie (engl. soft glassy rheology, SGR). Obwohl es absichtlich zur Untersuchung von Glasbildnern eingesetzt wird, ist der entscheidende Bestandteil hier die "Rauschtemperatur", die den Konfigurationszustand eines Systems berücksichtigt und Glasübergang, Alterung, Verjüngung und nichtlineare Rheologie berücksichtigt. In dieser Arbeit untersuchen wir eine spezielle Klasse von athermischen Materialien, die in den Anwendungsbereich dieses konstitutiven Modells fallen

Numerical and experimental investigation of dry particle coating

Dry particle coating is an emerging field in the industries that deal with particulate products and powder processing. Compared to the widely reported experimental studies of the dry particle coating, the theoretical modeling of such processes is found to be less comprehensive. The work presented in this thesis is an attempt to fill this gap. The first part of the dissertation aims at the numerical investigation of the hybridization system (Nara Machinery, Tokyo, Japan). The flow behavior of different materials processed in this device is analyzed using three-dimensional Discrete Element Method (DEM) as well as the computational fluid dynamics (CFD) models. The particulate motion is directly simulated using the D EM c ode, which incorporates the effect of the fluid drag force, computed through the CFD models. The diagnostic investigation includes various aspects pertinent to the effectiveness of the hybridizer system in the coating process. Inter-particle collisions and particle-wall collisions as well as the normal and tangential forces between the particles are estimated which play an important role in the surface modification process of a powder. Experimentally measured velocities in the mixing chamber are in good agreement with the computed velocities. CFD results show that the flow field is not significantly affected as the volume fraction of particles is varied from 3 to 10 percent. Overall, it is found that the combined DEM-CFD model appears to be an adequate approximation of the behavior of the fluid-particle system in the hybridizer. The experimental part of this dissertation presents an investigation of different powder processing devices such as the Hybridizer, Mechanofusion and Magnetically Assisted Impaction Coating (MAIC) devices for a specific application of improving the humidity resistance of the ground magnesium powder through the dry particle coating technique. It is shown that coating by wax (1 percent by weight) is sufficient to increase the humidity resistance of ground magnesium to a level almost as good as the atomized magnesium powder. The last part of the dissertation deals with a related, yet different type of numerical study, carried out using the DEM approach, of the granular flows and mixing behavior in the oscillating sectorial containers. Mixing patterns are observed for a wide range of frequencies of oscillation as well as different operating conditions such as the powder loading, the coefficient of friction, and the coefficient of restitution. It is observed that the flow patterns follow a particular trend and there exists a critical frequency at which the mixing rate is very small

Confronting Grand Challenges in Environmental Fluid Dynamics

Environmental fluid dynamics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that need to be tackled, ranging from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing, to applied studies of pollution transport in the ocean, atmosphere and urban environments. A workshop was organized in the Les Houches School of Physics in France in January 2019 with the objective of gathering leading figures in the field to produce a road map for the scientific community. Five subject areas were addressed: multiphase flow, stratified flow, ocean transport, atmospheric and urban transport, and weather and climate prediction. This article summarizes the discussions and outcomes of the meeting, with the intent of providing a resource for the community going forward

Dense granular flow in rotating drums: a computational investigation of constitutive equations

The constitutive laws of dense granular flow are investigated. Simulations of a drum, with periodic boundary conditions, rotating at varying speeds are performed. From the resulting data, kinematic and kinetic fields are extracted and used to investigate the validity of constitutive relations proposed in the literature. Two key constitutive assumptions are (a) isotropy and (b) incompressibility. The rotating drum system is found to be largely isotropic for high rotational speeds. For low rotational speeds, anisotropy is observed in the bottom part of the system, where the particles are flowing upwards. A small degree of compressibility is observed in the downward-flowing layer. The friction coefficient for the granular constitutive relations is also investigated. An empirically-derived friction law has a better fit to the data when compared to other friction laws proposed in the literature. Lastly, two scaling laws are investigated: the scaling between the scaled flow-rate (flux) and the thickness of the downward- flowing layer and the scaling between the dynamic angle of repose of the bed and the flux through the downward- flowing layer. The thickness-flux scaling is measured by interpolating the flux over a number of slices through the flowing layer, this is done in a number of different ways. The size of the measured section through the flowing layer is varied. The orientation of the slices is also varied. Also investigated is whether the total velocity or the tangential velocity produce the same scaling. The size of the section of the flowing layer significantly changes the scaling, this shows that the scaling is not constant throughout the flowing layer. The dynamic angle of repose is determined using two methods, one which is determined unambiguously as the repose angle of the ellipse fitted to the equilibrium surface and the other which is the changing angle of the tangent to the equilibrium surface or free surface. The first repose angle is found to be highly dependent on the flux even in the limit of infinite drum length, which is modelled using axial periodic boundary conditions. The second definition results in two sets of repose angles with complex behaviour that may be due to inertial effects. An instability in the system is observed, this is conjectured to be due to a frictional threshold that is breached as the rotational speed of the drum increases. Algorithms for calculating field variables and features of the charge are presented

Granular computing approach for intelligent classifier design

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.Granular computing facilitates dealing with information by providing a theoretical framework to deal with information as granules at different levels of granularity (different levels of specificity/abstraction). It aims to provide an abstract explainable description of the data by forming granules that represent the features or the underlying structure of corresponding subsets of the data. In this thesis, a granular computing approach to the design of intelligent classification systems is proposed. The proposed approach is employed for different classification systems to investigate its efficiency. Fuzzy inference systems, neural networks, neuro-fuzzy systems and classifier ensembles are considered to evaluate the efficiency of the proposed approach. Each of the considered systems is designed using the proposed approach and classification performance is evaluated and compared to that of the standard system. The proposed approach is based on constructing information granules from data at multiple levels of granularity. The granulation process is performed using a modified fuzzy c-means algorithm that takes classification problem into account. Clustering is followed by a coarsening process that involves merging small clusters into large ones to form a lower granularity level. The resulted granules are used to build each of the considered binary classifiers in different settings and approaches. Granules produced by the proposed granulation method are used to build a fuzzy classifier for each granulation level or set of levels. The performance of the classifiers is evaluated using real life data sets and measured by two classification performance measures: accuracy and area under receiver operating characteristic curve. Experimental results show that fuzzy systems constructed using the proposed method achieved better classification performance. In addition, the proposed approach is used for the design of neural network classifiers. Resulted granules from one or more granulation levels are used to train the classifiers at different levels of specificity/abstraction. Using this approach, the classification problem is broken down into the modelling of classification rules represented by the information granules resulting in more interpretable system. Experimental results show that neural network classifiers trained using the proposed approach have better classification performance for most of the data sets. In a similar manner, the proposed approach is used for the training of neuro-fuzzy systems resulting in similar improvement in classification performance. Lastly, neural networks built using the proposed approach are used to construct a classifier ensemble. Information granules are used to generate and train the base classifiers. The final ensemble output is produced by a weighted sum combiner. Based on the experimental results, the proposed approach has improved the classification performance of the base classifiers for most of the data sets. Furthermore, a genetic algorithm is used to determine the combiner weights automatically.Higher Committee for Education Development in Iraq (HCED

Regime analysis of the rheology of spherical and non-spherical particles

In the early stages of granular rheology, the majority of analytical studies were based on granular assembly consisting of spherical particles. This was due to geometric simplicity and feasibility when calculating dynamic variables. Furthermore system limitation emerged as a problem when investigating more complex and realistic considerations. However, in the contemporary research field, with the steadily increasing ability to perform more complex computations and with available resources, attention has focused on non-spherical particles because of their deeper relevance to practical applications. In this work, a 3D shear cell model is developed based on the Discrete Element Method using the commercial software platform “PFC” to study non-spherical particles’ flow characteristics. A comparison is made with those of spherical assemblies. Firstly, the simulation model of annular shear cell consisting of spherical particles is tested with PFC and this agreed well with previous results, thus justifying the use of this tool to analyse the nonspherical level. Then the effect of platen roughness is investigated on spherical particle assembly from the microdynamic perspective, in order to establish a correlation between platen roughness and granular flow dynamics. This is undertaken in terms of particle size that is used to construct the platens. It is found that linearity and non-linearity of gradient profile across several important parameters are distinguishing features affected by variations in platen texture. The externally applied load is the most important aspect that bridges studies where gravity is considered and yet often overlooked. This point is established through in-depth investigation of granular flow in presence and absence of gravity where comparison of an number of flow characteristics is presented. Following this, the effects of particle shape are microdynamically investigated with reference to aspect ratio of non-spherical (ellipsoidal) particles and compared with spherical particles. The following key properties - particle linear velocity, angular velocity, contact normal force, contact shear force, total contact force, total contact moment and porosity - are 4 analysed to explain the effect of variation of the above-mentioned geometric properties on each of these parameters. Then, macrodynamic analysis is performed in a comparative study between spherical particles and ellipsoidal particles of varying aspect ratios with focus on the variables that are important in general constitutive model such as velocity, density and stress tensors. Physics underlying the observation is discussed to highlight effect of particle aspect ratio. Finally and most importantly, regime transition of ellipsoidal particle assembly is contrasted with the findings for spherical particles. In this study, the techniques that are generally used to identify regime transition for granular rheology of spherical particles are tested on flow of non-spherical (ellipsoidal) particles of varying shapes (aspect ratios). This includes correlation between elastically scaled force, kinetically scaled force, coordination number, apparent coefficient of friction and porosity. Some observations are found to be similar and useful for non-spherical particles while others found not suitable for nonspherical particles