What is the various evaluation method to evaluate KM application? This is more so to evaluate the relevancy, usability and quality of the knowledge created for application.
In knowledge management research you'll often find case studies as the methods of choice as it is often highly qualitative research.
Since you ask for the "quality of knowledge" you may find the work on information/data quality an inspiring start as well.
Wang, R.Y. and Strong, D.M., 1996. Beyond accuracy: What data quality means to data consumers. Journal of management information systems, 12(4), pp.5-33.
Strong, D.M., Lee, Y.W. and Wang, R.Y., 1997. Data quality in context. Communications of the ACM, 40(5), pp.103-110.
Pipino, L.L., Lee, Y.W. and Wang, R.Y., 2002. Data quality assessment. Communications of the ACM, 45(4), pp.211-218.
Chen & Chen (2006) reviewed more than 100 papers and classified methods that have been used to measure and evaluation KM performance. I believe that this is still the most comprehensive report on the topic.
Try using the Logic Model to evaluate Knowledge Management Systems. The model is not necessarily meant for evaluating KMS but it can be adopted and adapted for your situation.
Information Management Model for Intellectual Capital of HEIs: Theoretical Quantitative Approach and Practical Results. J. of Information and Knowledge Management, 2018, Vol. 17, No. 1, pp.1-38. (World Scientific).