Probabilistic modeling of particle movement through a gravity separator

Abstract

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Particle Movement and Separation Phenomena for a Gravity Separator: II. Experimental Data and Performance of Distance-Transition Markov Models.

“…A better test is to examine performance for prediction of particle distributions over a number of transition periods. See Balascio (1985) for a more detailed discussion.…”

“…In equations [1] and [la] the carets {^) over the vectors on the left sides of the equations indicate that those quantities are estimates. Note also that the superscript on the transition probability matrix P in equation la denotes the power t of the matrix P. Note that equations [1] and [la] are nonlinear; estimates obtained by use of equations [1] or [la] cannot be analyzed with any simple statistical test. Lee et al (1977) proposed the use of a statistic, which they claim is approximately x^ distributed, to test for stationarity of the Markov process.…”

“…We can compute estimated values of y^Ct) by using the definition of /(t) given by equation [1]. Therefore, coordinates of the estimated mass centroid pathway are given by:…”

“…The deck is rectangular over approximately the last 84 cm of its length. Balascio (1985) used a nonstationary Markov model based on geometrical parameters to describe particle movement in the nonrectangular portion of the deck.…”

“…Note that transition probabilities from states along the high side of the deck to states along the low side are generally greater in the second matrix P (9 to 15) than the first P(l to 8). Balascio (1985) fitted nonstationary models to the data of experiments a through e. The variable transition probabilities were correlated with parameters such as:…”