Modeling the human perception of noise
As with any perceptual model, the answer is not exactly cut and dry.  In my research, I’ve found that many of the hearing models I’ve encountered are based on band pass filter banks.  These banks are numerous and tightly spaced.  The more adjacent banks that are stimulated, the ‘noiseyer’ the signal would sound.

There are examples of inharmonic signal analysis that take noise into account, such as: https://pdfs.semanticscholar.org/b5bf/98425051f47b0685e75da986ee166e41d6ec.pdf.  I’ve never tried to implement such a structure, but as I understand it, you analyze the peaks in the output of a frequency transform to create a ‘deterministic’ signal.  You then subtract the deterministic signal from the original to get the ‘residual’ noise.  You would then perform further analysis on the residual.  I assume that this isn’t exactly what you were looking for in terms of a model, but I figured it may be informative.