Sensor network design for the estimation of spatially distributed processes
International Journal of Applied Mathematics and Computer Science
| Hi-index | 0.00 |
A critical first step in responding to an airborne chemical or biological attack is determining the location of the source of the toxin. We have formulated the mathematical description of source location as an inverse problem constrained by the partial differential equation (PDE) that describes the toxin's transport. This transport is advection-dominated, but takes place in a flow field that in realistic settings will be turbulent, thereby inducing an effective diffusivity tensor in the transport model. We model the turbulent flow using a Reynolds-averaged Navier--Stokes (RANS) approach, which can be solved offline for an arbitrary building of interest. The inversion problem then consists of finding the (regularized) source distribution that best reproduces a set of sensor measurements, subject to the transport model constraint relating the source to the concentration at the sensor positions. Though individual toxin sources are likely to be point sources, we cannot make any assumptions about the number of such sources. Hence, because multiple sources are a possibility, we assume a spatially continuous source distribution, thus eliminiating any need to impose assumptions about the number and nature of the sources. The operational context for this problem implies certain practical requirements. In particular, it is critical to reduce the time for inversion and the number of sensors required for an accurate determination of the source field. A particular focus of this paper is the exploration of the degree to which we can economize on computational effort through adaptive mesh coarsening tailored to preserve the essential features of the flow field. We have found that location of multiple sources is well accommodated by this method, and have shown that it is possible to reduce significantly the computational time through flow-tailored mesh adaptation without adverse impact on the accuracy of the source location. Finally, we have done a preliminary study of the number of sensors required for useful inversion. These conclusions will be of considerable use in developing sensor deployment strategies.