Using piezoelectric sensors embedded in an elastic infinite medium (2D problem-see attached sketch) subject to P incident wave. I would like to detect embedded damages in the form of circular voids. I intend to use statistical approaches to construct an image showing the approximate locations and approximate shape and size. In other words the image is a contour plot of the probability of the damage location and its rough shape. It should provide an initial guess of possible voids location and sizes. The statistical approach should be simple and non iterative (with few runs) based on comparing the sensor signal in free of damage with the damaged one. I have the solution to the direct problem i.e. I have sensor signals for the free of damage case. I can also provide sensor signals under a different loading frequency (different P wave frequency). Possible statistical methods assume the damage location would be closest to the sensor with the highest change in signal (similar to attached paper-no need to read all paper just section 3.2 to get the idea).
I prefer the program to be in Matlab.
I have few projects and this project is a seed project for others.
Sensor signals are a single volt value for each sensor for each loading frequency. For example the shown incident with voids has 5 sensors which means 5 volt values for each loading frequency. I am not looking for a complicated problem! 2 or 3 circular voids with 30 sensors to approximately identify. We will start with a single circular void with 5 sensors.