Clustering methods need to be robust if they are to be useful in practice. In this paper, we analyze several popular robust clustering methods and show that they have much in common. We also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least-squares (LS) technique, the M estimator, the minimum volume ellipsoid (MVE) algorithm, cooperative robust estimation (CRE), minimization of probability of randomness (MINPRAN), and the epsilon contamination model. By gleaning the common principles upon which the methods proposed in the literature are based, we arrive at a unified view of robust clustering methods. We define several general concepts that are useful in robust clustering, state the robust clustering problem in terms of the defined concepts, and propose generic algorithms and guidelines for clustering noisy data. We also discuss why the generalized Hough transform is a suboptimal solution to the robust clustering problem.

An experimental study is conducted to determine the effect of different types of nanoparticles on the gas fluidization characteristics of nanoparticle agglomerates. Taking advantage of the extremely high porosity of the bed, optical techniques are used to visualize the flow behavior, as well as to measure the sizes of the fluidized nanoparticle agglomerates at the bed surface. Upon fluidizing 11 different nanoparticle materials, two types of nanoparticle fluidization behavior, agglomerate particulate fluidization (APF) and agglomerate bubbling fluidization (ABF), are observed and systematically investigated. A simple analytical model is developed to predict the agglomerate sizes for APF nanoparticles, and the results agree fairly well with the optical measurements. Using the Ergun equation, the experimentally measured pressure drop and bed height, and the average agglomerate size and voidage at minimum fluidization predicted by the model, the minimum fluidization velocities for APF nanoparticles are calculated and also agree well with the experimental values. Other important fluidization features such as bed expansion, bed pressure drop, and hysteresis effects, and the effects of the primary particle size and material properties are also described. © 2005 American Institute of Chemical EngineersAIChE J, 51: 426 -439, 2005 Keywords: fluidization, nanoparticles, agglomerates, pressure drop, bed expansion IntroductionGas fluidization of small solid particles has been widely used in a variety of industrial applications because of its unusual capability of continuous powder handling, good mixing, large gas-solid contact area, and very high rates of heat and mass transfer. Extensive research has been done in the area of gas fluidization, and the fluidization behavior of classical powders in the size range of 30 to 1000 m (Geldart group A and B powders) is relatively well understood. However, the fluidization behavior of ultrafine particles, including nanoparticles, is much more complex and has received relatively little attention in the literature.Because of their unique properties arising from their very small primary particle size and very large surface area per unit mass, nanostructured materials are already being used in the manufacture of drugs, cosmetics, foods, plastics, catalysts, energetic and biomaterials, and in mechatronics and microelectro-mechanical systems (MEMS). Therefore, it is necessary to develop processing technologies that can handle large quantities of nanosized particles, such as mixing, transporting, modifying the surface properties (coating), and downstream processing of nanoparticles to form nanocomposites. Before processing of nanostructured materials can take place, however, the nanosized particles have to be well dispersed. Gas fluidization is one of the best techniques available to disperse Correspondence concerning this article should be addressed to R. Pfeffer at pfeffer@adm.njit.edu. © 2005 American Institute of Chemical Engineers PARTICLE TECHNOLOGY AND FLUIDIZATION 426AIChE Journa...

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Vigorous homogeneous fluidization of 12‐nm silica particles was easily achieved by coupling aeration with vibration. Vibration (with frequency in the range of 30 to 200 Hz, and vibrational acceleration in the range of 0 to 5 g) was found to be necessary to achieve smooth fluidization. The minimum fluidization velocity, defined as the lowest gas velocity at which the pressure drop across the bed reaches a plateau, was approximately 0.3–0.4 cm/s, and essentially independent of the vibrational acceleration. However, the bed expanded almost immediately after the air was turned on, reaching bed expansions of three times the initial bed height or higher. Thus the bed appeared to exhibit a fluidlike behavior at velocities much lower than the minimum fluidization velocity. Fluidization of nanoparticles was achieved as a result of the formation of stable, relatively large, and very porous agglomerates. Practically no bubbles or elutriation of particles was observed. A fractal analysis combined with a modified Richardson–Zaki approach is proposed for prediction of agglomerate size and voidage. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1776–1785, 2004

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