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Estimation of settling velocities

Abstract : This paper deals with settling velocities estimation, which is of major importance as settling velocities estimation is a prerequisite for properly dimensioning settling ranks. Several measurement procedures are presented and analyzed here. A general framework for identification which includes modelisation of the settlers and identification techniques is developed here-in. In this paper, we demonstrate that for a parametric set of settling density functions ?(dv) = S(i)(N)= (l)?(i)?(i)(dv) the mathematical relation between the measures M(t(i))(i) = l,N and the unknown quantities (0(i))(i) = (l,N) take the following linear form M(t(i)) = S(k)(N) = (l)0(k)?RØx(t(i),v)?(k)(dv). This relation makes it possible to have access to statistical errors in settling velocity estimates (0(i)) in assuming that a statistical model of measurement errors (M(t(i))) exists. The consequences of the choice of sampling times (t(i))(i) = (l,N) on the quality of the estimation are also investigated.This paper deals with settling velocities estimation, which is of major importance as settling velocities estimation is a prerequisite for properly dimensioning settling tanks. Several measurement procedures are presented and analyzed here. A general framework for identification which includes modelization of the settlers and identification techniques is developed here-in. In this paper, we demonstrate that for a parametric set of settling density functions ?(dv) = ?i = 1N?i?i(dv) the mathematical relation between the measures M(ti)i = 1,N and the unknown quantities (?i)i = 1,N take the following linear form M(ti) = ?k = 1N?k?Rfx(ti, v)?k(dv). This relation makes it possible to have access to statistical errors in settling velocity estimates (?i) in assuming that a statistical model of measurement errors (M(ti)) exists. The consequences of the choice of sampling times (ti)i = 1,N on the quality of the estimation are also investigated.
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Soumis le : mardi 22 janvier 2013 - 14:34:09
Dernière modification le : samedi 7 avril 2018 - 01:18:08

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J.P. Chancelier, G. Chebbo, E. Lucas-Aiguier. Estimation of settling velocities. Water Research, IWA Publishing, 1998, 32 (11), pp.3461. ⟨10.1016/S0043-1354(98)00114-6⟩. ⟨hal-00779531⟩

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