Estimation of time-varying pollutant emission rates in a ventilated enclosure: inversion of a reduced model obtained by experimental application of the modal identification method

Abstract

A method is proposed for the estimation of time-varying emission rates of pollutant sources in a ventilated enclosure, through the resolution of an inverse forced convection problem. Unsteady transport-diffusion of the pollutant is considered, with the assumption of a stationary velocity field remaining unchanged during emission (passive contaminant). The pollutant transport equation is therefore linear with respect to concentration. The source's location is also supposed to be known. As the first step, a reduced model (RM) linking concentrations at a set of control points to emission rates of sources is identified from experimental data by using the modal identification method (MIM). This parameter estimation problem uses transient contaminant concentration measurements made at control points inside the ventilated enclosure, corresponding to increasing and decreasing steps of emission rates. Such experimental modelling allows us to avoid dealing with a CFD code involving turbulence modelling and to get rid of uncertainties about sensors position. In a second step, the identified RM is used to solve an inverse forced convection problem: from contaminant concentration measured at the same control points, rates of sources emitting simultaneously are estimated with a sequential in time algorithm using future time steps.

Estimation of position and time-varying intensity of a heat source using reduced models built with the Modal Identification Method

“…Hence there is no need for an initial guess for U(t). The sequential method that is used is described in detail in [5][6]. Once U(t) estimated, sensitivities of outputs with respect to x s are computed for x s * +∆x s and a new position is found.…”

“…As shown in [4][5][6], the MIM is a tool able to perform the identification of a RM of equations (3 a,b) for x s = x s * . This RM is written as:…”

“…It is not also a simple interpolation between some DM solutions. In the MIM, the RM is identified through an optimization procedure, described in [4][5][6], which consists of minimizing the quadratic residuals between DM solutions (or in-situ measurements) and RM solutions, when a known applied signal U(t) is applied to both models (or to the real system and to the RM). This means that the F i …”

“…These RMs can then be used to solve efficiently inverse problems with transient thermal loads. This approach has been used in [4] for an inverse heat conduction problem, and in [5] and [6] for inverse forced convection problems involving turbulent flows. Note also that experimental data have been used in [4] and [6].…”

“…• Secondly, to embed this RM in an optimisation procedure with either a reference detailed model outputs [5] or measurements at the same locations [6], for the estimation of both position and intensity of the source. For convenience, the approach is described in detail for 1D problems in section 2.…”