hal-00779531
https://enpc.hal.science/hal-00779531
doi:10.1016/S0043-1354(98)00114-6
[SDE] Sciences De l'Environnement
[AGROPARISTECH] AgroParisTech
[ENPC] Ecole des Ponts ParisTech
[ENGREF] Ecole Nationale du Génie Rural des Eaux et des Forêts
[PARISTECH] ParisTech
[GIP-BE] GIP Bretagne Environnement
Estimation of settling velocities
Chancelier, J.P.
Chebbo, G.
Lucas-Aiguier, E.
[SDE] Environmental Sciences
ART
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.
1998
en
Water Research
IWA Publishing/Elsevier