Video Quality Assessment (No-Reference)
Freely available video quality of experience tools are quite rare and probably aren't going to work for your use case out of the box. The Netflix VMAF algorithm recently became available as an FFmpeg filter. The MSU VQMT is one of the more mature tools, but is only free for non-commercial use.

There are several (and some even good) commercial QoE monitoring systems available, if you have the budget.