Check the rated current usage of the led strip of lights. The 3528 strip I have says 3 amps and the 5050 strip says 5 amps. Both strips draw less than that when measured. Both strips are designed to run off of a 12v dc power source.
If your AC input is 18volt then your 16volt capacitor is way under rated and may be passing too much ripple current. Increase the cap rating to 35 v rating and add some caps until the ripple decreases. Your bridge may need to be heat sinked if you have substantial current going thru it.
Adding inductors would help as well.
The wall wart that came with my strip gets warm after a while.
You could always add a volt regulator ckt with cooling.
I am planning to use a computer power supply to power my strips. It has readily available high current 12v sources.
