Steps to finding out what part of my fridge is tripping its GFCI outlet?

My Kenmore fridge kept tripping the circuit breaker in the GPCI once every 10 hours or so. I have had the fridge for almost 9 years now, and the problem started a month ago. What I tried so far is that I plugged the fridge to another GPCI outlet with nothing else plugged-in and the problem persisted.

The manual says nothing about this problem. Having a Kenmore technician come and try diagnose for the problem costs $129 with no result guaranteed. So I thought I should try doing diagnosis on the fridge myself. But where can I start (e.g., how do I know if it's the compressor drawing too much current or something else that needs replacement)?

Any guidance or reference to tutorial would be helpful. Appreciate it.