Abstract: Although the field of parametric Pattern Recognition (PR) has been thoroughly studied for over five decades, the use of the Order Statistics (OS) of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. This must be contrasted with the Bayesian paradigm in which, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal strategy would be to achieve this based on the (Mahalanobis) distance from the corresponding central points, for example, the means. In [2], we showed that the results could be extended for a few symmetric distributions within the exponential family. In this paper, we attempt to extend these results significantly by considering asymmetric distributions within the exponential family, for some of which even the closed form expressions of the cumulative distribution functions are not available. These distributions include the Rayleigh, Gamma and certain Beta distributions. As in [1] and [2], the new scheme, referred to as Classification by Moments of Order Statistics (CMOS), attains an accuracy very close to the optimal Bayes’ bound, as has been shown both theoretically and by rigorous experimental testing.
Abstract: The influence of eccentric discharge of stored solids in
squat silos has been highly valued by many researchers. However,
calculation method of lateral pressure under eccentric flowing still
needs to be deeply studied. In particular, the lateral pressure
distribution on vertical wall could not be accurately recognized
mainly because of its asymmetry. In order to build mechanical model
of lateral pressure, flow channel and flow pattern of stored solids in
squat silo are studied. In this passage, based on Janssen-s theory, the
method for calculating lateral static pressure in squat silos after
eccentric discharge is proposed. Calculative formulae are deduced for
each of three possible cases. This method is also focusing on
unsymmetrical distribution characteristic of silo wall normal
pressure. Finite element model is used to analysis and compare the
results of lateral pressure and the numerical results illustrate the
practicability of the theoretical method.