ABSTRACT
FIGURE 5.2: A schematic diagram of the NDE method for the detection of structural flaws. The sensor measures the surface temperature, and the measured temperature is different for the smooth versus the corroded surface.
problem for a heat diffusion system. From a physical point of view, the system state is the temperature distribution as a function of time and space, the boundary input represents the thermal source (for example, by a laser beam) and the output corresponds to the observation of the temperature distribution at the surface of the material (for example, by an infrared imager); see Figure 5.2 and [6] for more details. The problem is then of identifying, from input and output data, the geometrical structure of the boundary (i.e., the corroded surface). The mathematical model, which relates front surface temperature (the output data) and back surface “geometry,” is described by the heat equation with appropriate initial and boundary conditions (see [2] for a detailed description).
