Granular Counterpart Research Articles

Granular transfer learning

Transfer learning is aimed at supporting the design of machine learning models in the target domain Dt, given that the knowledge (model) has already been constructed in the source domain Ds. The domains Dt and Ds (as well as the corresponding tasks Ts and Tt) are similar, yet not identical. As a result, the model transferred from Ds to Dt in this new environment exhibits its relevance (credibility) only to some limited extent. In this study, we develop an original approach, where we advocate that the knowledge transfer (model transfer) gives rise to a granular model where the level of information granularity associated with the produced results quantifies the relevance (quality or credibility) of the transferred model. In other words, we stress that the quality of knowledge transferred to Dt becomes captured through a granular generalization of the original numeric model. The overall systematic design process is elaborated on by focusing on the development process of granular neural networks carried out on a basis of the numeric neural networks coming from Ds. The key aspect of the design is to elevate the existing numeric neural network to its granular counterpart by admitting that the connections of the developed model come in the form of information granules, in particular intervals and fuzzy sets. The optimization process is guided by adjusting (optimizing) the level of information granularity being regarded as an essential design asset. The optimized performance index builds upon the descriptors of information granules commonly encountered in Granular Computing. In particular, coverage and specificity measures are treated as sound performance indicators of the quality of knowledge transfer (viz. the performance of the granular neural network expressed in the target domain). Several illustrative examples are provided to visualize the performance of the established design environment.

From Numeric to Granular Models: A Quest for Error and Performance Analysis.

In this study, we establish a new design methodology of granular models realized by augmenting the existing numeric models through analyzing and modeling their associated prediction error. Several novel approaches to the construction of granular architectures through augmenting existing numeric models by incorporating modeling errors are proposed in order to improve and quantify the numeric models' prediction abilities. The resulting construct arises as a granular model that produces granular outcomes generated as a result of the aggregation of the outputs produced by the numeric model (or its granular counterpart) and the corresponding error terms. Three different architectural developments are formulated and analyzed. In comparison with the numeric models, which strive to achieve the highest accuracy, granular models are developed in a way such that they produce comprehensive prediction outcomes realized as information granules. In virtue of the granular nature of results, the coverage and specificity of the constructed information granules express the quality of the results of prediction in a more descriptive and comprehensive manner. The performance of the granular constructs is evaluated using the criteria of coverage and specificity, which are pertinent to granular outputs produced by the granular models.

Deagglomeration of cohesive particles by turbulence

Abstract

Enskog kinetic theory for multicomponent granular suspensions.

The Navier-Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a normal solution to the set of Enskog equations is obtained by means of the Chapman-Enskog expansion around the local version of the homogeneous state. To first order in spatial gradients, the Chapman-Enskog solution allows us to identify the Navier-Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for dilute multicomponent granular suspensions [Khalil and Garzó, Phys. Rev. E 88, 052201 (2013)10.1103/PhysRevE.88.052201] to higher densities.

Transport coefficients for granular suspensions at moderate densities

The Enskog kinetic theory for moderately dense granular suspensions is considered as a model to determine the Navier–Stokes transport coefficients. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. The suspension model is solved by means of the Chapman–Enskog method conveniently adapted to dissipative dynamics. The momentum and heat fluxes as well as the cooling rate are obtained to first order in the deviations of the hydrodynamic field gradients from their values in the homogeneous steady state. Since the cooling terms (arising from collisional dissipation and viscous friction) cannot be compensated for by the energy gained by grains due to collisions with the interstitial gas, the reference distribution (zeroth-order approximation of the Chapman–Enskog solution) depends on time through its dependence on temperature. On the other hand, to simplify the analysis and given that we are interested in computing transport properties in the first order of deviations from the reference state, the steady-state conditions are considered. This simplification allows us to get explicit expressions for the Navier–Stokes transport coefficients. The present work extends previous results (Garzó et al 2013 Phys Rev. E 87 032201) since it incorporates two extra ingredients (an additional density dependence of the zeroth-order solution and the density dependence of the reduced friction coefficient) not accounted for by the previous theoretical attempt. While these two new ingredients do not affect the shear viscosity coefficient, the transport coefficients associated with the heat flux as well as the first-order contribution to the cooling rate are different from those obtained in the previous study. In addition, as expected, the results show that the dependence of the transport coefficients on both inelasticity and density is clearly different from that found in its granular counterpart (no gas phase). Finally, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state is performed. In contrast to the granular case (no gas-phase), no instabilities are found and hence, the homogeneous steady state is (linearly) stable.

Augmentation of rule-based models with a granular quantification of results

This study is concerned with the augmentation of rule-based models or fuzzy rule-based models by associating the numeric results produced by them with granular characterization in the form of prediction intervals. The role of prediction intervals encountered in regression analysis is well emphasized in the literature, especially for “monolithic” models such as linear regression or neural networks. However, there have not been comprehensive and algorithmically complete studies devoted to the conceptualization and determination of prediction intervals for rule-based models, Boolean (two-valued) and fuzzy ones. While the results generated by rule-based models are formed by aggregating partial outcomes resulting from the individual rules, the prediction intervals adhere to the same way of aggregation. In this sense, one can regard the rule-based model augmented by the associated prediction intervals as a granular rule-based model. The construction of rule-based models is, in a nutshell, the optimization process being commonly guided by the sum of squared errors (say, RMSE or alike), and the quality of the granular counterpart of the rule-based models is assessed by looking at the quality of prediction intervals and introducing the two pertinent quality measures focused on the granular nature of the obtained results, namely coverage and specificity along with their combined index. In this study, we analyze an impact of the rules and the parameters of fuzzy clustering on the quality of the numeric and granular performance of the models. A series of experimental results is presented to help quantify the performance of granular outputs (prediction intervals) constructed for rule-based models.

The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series

The Sugeno-type fuzzy models are used frequently in system modeling. The idea of information granulation inherently arises in the design process of Sugeno-type fuzzy model, whereas information granulation is closely related with the developed information granules. In this paper, the design method of Sugeno-type granular model is proposed on a basis of an optimal allocation of information granularity. The overall design process initiates with a well-established Sugeno-type numeric fuzzy model (the original Sugeno-type model). Through assigning soundly information granularity to the related parameters of the antecedents and the conclusions of fuzzy rules of the original Sugeno-type model (i.e. granulate these parameters in the way of optimal allocation of information granularity becomes realized), the original Sugeno-type model is extended to its granular counterpart (granular model). Several protocols of optimal allocation of information granularity are also discussed. The obtained granular model is applied to forecast three real-world time series. The experimental results show that the method of designing Sugeno-type granular model offers some advantages yielding models of good prediction capabilities. Furthermore, those also show merits of the Sugeno-type granular model: (1) the output of the model is an information granule (interval granule) rather than the specific numeric entity, which facilitates further interpretation; (2) the model can provide much more flexibility than the original Sugeno-type model; (3) the constructing approach of the model is of general nature as it could be applied to various fuzzy models and realized by invoking different formalisms of information granules.

Impact of collisional versus viscous dissipation on flow instabilities in gas–solid systems

AbstractFlow instabilities encountered in the homogeneous cooling of a gas–solid system are considered via lattice-Boltzmann simulations. Unlike previous efforts, the relative contribution of the two mechanisms leading to instabilities is explored: viscous dissipation (fluid-phase effects) and collisional dissipation (particle-phase effects). The results indicate that the instabilities encountered in the gas–solid system mimic those previously observed in their granular (no fluid) counterparts, namely a velocity vortex instability that precedes in time a clustering instability. We further observe that the onset of the instabilities is quicker in more dissipative systems, regardless of the source of the dissipation. Somewhat surprisingly however, a cross-over of the kinetic energy levels is observed during the evolution of the instability. Specifically, the kinetic energy of the gas–solid system is seen to become greater than that of its granular counterpart (i.e. same restitution coefficient) after the vortex instability sets in. This cross-over of kinetic energy levels between a more dissipative system (gas–solid) and a less dissipative system (granular) can be explained by the alignment of particle motion found in a vortex. Such alignment leads to a reduction in both collisional and viscous energy dissipation due to the more glancing nature of collisions.

Knowledge transfer in system modeling and its realization through an optimal allocation of information granularity

In this study, we introduce and discuss a concept of knowledge transfer in system modeling. In a nutshell, knowledge transfer is about forming ways on how a source of knowledge (namely, an existing model) can be used in presence of new, very limited experimental evidence. In virtue of the nature of the problem at hand (a situation encountered quite commonly, e.g. in project cost estimation), new data could be very limited and this scarcity of data makes it insufficient to construct a new model. At the same time, the new data originate from a similar (but not the same) phenomenon (process) for which the original model has been constructed so the existing model, even though it could applied, has to be treated with a certain level of reservation. Such situations can be encountered, e.g. in software engineering where in spite existing similarities, each project, process, or product exhibits its own unique characteristics. Taking this into consideration, the existing model is generalized (abstracted) by forming its granular counterpart – granular model where its parameters are regarded as information granules rather than numeric entities, viz. their non-numeric (granular) version is formed based on the values of the numeric parameters present in the original model. The results produced by the granular model are also granular and in this manner they become reflective of the differences existing between the current phenomenon and the process for which the previous model has been formed.In the study on knowledge transfer and reusability, information granularity is viewed as an important design asset and as such it is subject to optimization. We formulate an optimal information granularity allocation problem: assuming a certain level of granularity, distribute it optimally among the parameters of the model (making them granular) so that a certain data coverage criterion is maximized. While the underlying concept is general and applicable to a variety of models, in this study, we discuss its use to fuzzy neural networks with intent to clearly visualize the advantages of the approach and emphasize various ways of forming granular versions of the weights (parameters) of the connections of the network. Several granularity allocation protocols (ranging from a uniform distribution of granularity, symmetric and asymmetric schemes of allocation) are discussed and the effectiveness of each of them is quantified. The use of Particle Swarm Optimization (PSO) as the underlying optimization tool to realize optimal granularity allocation is discussed.

Statistical mechanics for static granular media: open questions

The theoretical description of granular materials, or assemblies of macroscopic particles, is a formidable task. Not only are granular materials out of thermal equilibrium, but they are also characterized by dissipative interactions and by static friction. Following a suggestion by S. F. Edwards, researchers have investigated the possible existence of a statistical mechanics of static granular systems, which would permit the description of macroscopic properties of mechanically stable granular assemblies from just a few parameters. The formulation and the validity of such an approach is still a matter of debate. This “emerging area” focuses on three important questions concerning such a statistical mechanics approach. First, we consider how the phase space of interest is affected by the requirement of mechanical stability. Second, we explore how the intensive parameters analogous to temperature can be determined from experimental or numerical data. Finally, we contrast different ways to express the granular counterpart to the classical Hamiltonian, known as the volume function.

A characterization of electrocardiogram signals through optimal allocation of information granularity

We propose and develop a concept of a granular representation of a collection of signals (patterns) where a prototype (representative) of such numeric signals is formed as a certain information granule (say, a set, fuzzy set, rough set, and alike) instead of a single numeric entity. As being more abstract, the granular format of the representative of the family of signals is more in rapport with the nature of the representation task itself. It is instrumental in quantifying the diversity of data and capture their inherent distribution characteristics. In the realization of the granular representation of the signals, we introduce a certain level of granularity (supplied in advance), which in the construction of the granular representative is regarded as an essential important modeling asset. A two-phase design is developed whose ultimate goal is to optimally allocate (distribute) the predefined level of granularity to the individual elements of the universe of discourse over which the signals are described. Given the nature of the required optimization, the ensuing optimization problem is solved by engaging a machinery of population-based optimization, namely Particle Swarm Optimization (PSO). Furthermore a number of information granularity distribution protocols are proposed. The numerical experiments completed for synthetic data and ECG MIT-BIH database signals are used to demonstrate the performance of the overall optimization algorithm and quantify the effectiveness of the allocation of information granularity realized by the PSO. An area under curve (AUC) criterion is proposed as a measure to express the quality of the overall optimization framework. For both synthetic as well as ECG signals, it is shown that the method endowed with the PSO identifies the best prototype and spans the lower and upper bounds of its granular counterpart. In addition to the numeric quantification of the best (optimized) granular prototype, the method helps visualizing its bounds. The relative difference in mapping performance between the best and the weakest granular prototypes is in the range of 18% (for normal ECG complexes) and over 26% in case of complexes of premature ventricular contraction. A complete algorithm of the construction of granular prototypes is presented. Treating the granular prototype as a template of a given class of electrocardiogram (ECG) signals, a matching process is facilitated and used as a basis for the design of signal classification algorithms. Various realizations of granular prototypes can be completed with the use of fuzzy sets or rough sets.

Characterization of poly(2,6-diphenyl- p-phenylene oxide) films as adsorbent for microfabricated preconcentrators

This work aims at evaluating poly(2,6-diphenyl- p-phenylene oxide) (Tenax TA), in the form of thin films, as an adsorbent material for various analytical applications. The physical properties of the polymer were studied with regard to surface topography, crystal structure, and thermal stability. Films deposited from solution at different substrate temperatures were studied and compared to the granular form of the polymer. It was found that Tenax TA deposited from solution have a different topography compared to their granular counterpart. The films possess a complex phase composition that includes crystalline and amorphous phases. The films showed high thermal stability (400 °C) similar to the granular form. The adsorption performance of the polymer compared to other possible adsorbent films such as polydimethylsiloxane (PDMS) and layer-by-layer assembled gold nanoparticles (GNPs) were also investigated. Representative volatile organic compound samples were used to compare the adsorption properties of Tenax TA films to that of the granules.

Toward a simple method for the fabrication of 1D or 3D nanostructures of polyaniline

We present a one-step chemical method for the fabrication and isolation of conjugated polymer nanostructures, in particular, polyanilines (PANIs), either in the pernigraniline or emeraldine oxidation state. The polymerization is initiated by the addition of a solid oxidant into an unstirred anilinium hydrochloride solution. This step allows a slow release of the oxidant, via its solubilization and diffusion into the undisturbed solution. The formation of visible macroscopic heterogeneous seeds promotes the homogeneous polymerization and growth of bulk nanostructures in solution. The shape of the first formed heterogeneous seeds was found to be dependent on the solubility/diffusion of the oxidant, allowing the prediction and control of the nanomorphology (1D vs. 3D or granular) of the bulk polyanilines. X-ray analyses of the as-prepared nanostructured PANIs showed that, compared to the literature data, the crystallite growth in the present study is significantly enhanced, with the 1D fibrillar morphology exhibiting a higher crystallinity per volume of nanostructure than that of a 3D granular counterpart. The electrical conductivity ( σ ) of pelletized HCl doped PANIs or emeraldine salts (ES) showed significant differences depending on the fibrillar or granular morphology, but a close relationship among number of unit cells, crystallite size and electrical conductivity is evidenced.

Carbon Monoliths: A Comparison with Granular Materials

An activated carbon monolith synthesized from a phenolic resin precursor provides capacity and kinetic properties which compare most favourably with the same mass of its granular counterpart. Experimental data have been obtained using a dynamic, flow apparatus. The comparative performances are readily explained by an analysis of internal and external mass transfer coefficients. The effect of axial dispersion is neglected. Internal mass transfer coefficients are based on the linear driving force assumption, being approximated for the monolith by a geometric transformation from the square channel to a hollow cylinder impervious to mass at its outer radius. The monolith is predicted to have a pressure drop which is less than 6% of that of its equivalent granular system.

A granular counterpart to the gradient operator

We introduce the linguistic gradient operator, a granular counterpart to the gradient operator in classical calculus. A multiple-input single-output Mamdani fuzzy rulebase is treated as a function in a linguistic state space, defined by the Cartesian product of the antecedent linguistic variables in the rulebase. The value of the consequent linguistic variable is treated as a function in this space, and thus represents the fuzzy rulebase. The linguistic gradient operator takes the consequent function and produces an N-vector of linguistic values, which are approximations to the N first partial derivatives of the consequent function. This vector points in the direction of the greatest local increase of the consequent function, and thus shows how a rule relates to its “neighboring” rules in rule space. Two Examples demonstrate that the linguistic gradient is a linguistic analogue of the classical gradient operator.

Insecticide Performance Against First-Generation European Corn Borer—Liquids Vs Granules, 1991

Abstract Granules are generally recommended over liquids for first-generation ECB. The comparative efficacy of liquid and granular insecticides was evaluated against an artificial ECB infestation established in a commercial corn field at the University of Minnesota, St. Paul, MN. Plots, measuring 1 row (76-cm centers) X 9.1 m, were infested in the late whorl stage; the middle 15 plants received 3 egg masses, 1 each on 18 Jul, 19 Jul, and 20 Jul. Whenever possible, granular and liquid formulations of the same active ingredient were used plus several standards lacking a granular or liquid counterpart. Treatments were arranged in a randomized complete block design with 4 replications. Granules were banded over the row on 22 Jul pm with a 1-row Gandy granular applicator. Liquids were banded over the row on 23 Jul am with a C02-powered backpack sprayer delivering 217 liters/ha using 8002 nozzles. Efficacy was evaluated from 27 Aug to 4 Sep by dissecting the 15 infested plants from each plot and counting both tunnels and larvae.