PEAQ is an algorithm and scoring system that takes psychoacoustic modeling into account. When I looked into this more than ten years ago, I managed to find a command line utility called pqevalaudio or something that I could just use to assign a score to a file.
The README was pretty sparse and I wanted to read more about what was actually going on, so I poked around a bit. First of all, wikipedia article if you just want a birds eye view [0].
The website the README links to as the original isn’t secure, but you can read the paper talking about this particular way of measuring perceptual audio quality here if you don’t mind living a little dangerously[1]. I also found this paper, which I haven’t had a chance to read yet, but it gives a “zoomed out” view, looking at a bunch of different perceptual audio quality measures [2].
[0] https://en.wikipedia.org/wiki/Perceptual_Evaluation_of_Audio...
[1] https://www-mmsp.ece.mcgill.ca/Documents/Reports/2002/KabalR...
[2] https://dl.acm.org/doi/pdf/10.1109/TASLP.2021.3069302 https://en.wikipedia.org/wiki/Perceptual_Evaluation_of_Audio...