How can I estimate the noise of an elastic non-deformable ball that hits an elastic plate that is simply supported?
Try to figure out the change in the kinetic energy of the ball after the bounce. Here I am assuming that the elastic plate remanis motionless. Now this change in kinteic energy is the energy that has been either dissipated as heat, or stored in the deformation of the ball (or plate) or (finally) transferred into the energy of a sound wave.
Now I am assuming that by "estimating the noise", you mean the "estimating the loudness of noise". Also I assume that you want the loudness in decibels ($dB$). The decibel scale works like this (I am not getting into its details as it would be quite off-topic).
So back to the question. The change in kinetic energy would give you an approximate value of the intensity of the "noise" produced. And on the decibel scale, the loudness will vary logarithmically with the intensity. You will get quite precise results, only if you manage to get a ball and a plate that do not store any energy in their deformations and there is no friction between them and you can measure the change in kinetic energy correctly and there is no dissipation of energy during the collision due to the drag force of the surrounding medium and...
As you can see, practically you are never going to get any precise results.