In this paper online monitoring issues for infrastructure disaster preparedness was analyzed taking into account the difficulties in monitoring due to ill-posed inverse problems. For this case of real-time sensing followed by online inverse problem solving was investigated. Difficulties resulting from the ill-posed problem of estimation of internal variables of a distributed parameters system from local measurements on the boundary of the system will be analyzed using a generic simulator developed for such problems. The paper illustrates these issues by focusing on monitoring explosions to be sensed in real-time using distance temperature sensing, away from explosion location and online reconstruction of the explosion parameter