Open chess board

I seem to have a fairly good grasp (relatively speaking) when most or all of the pawns are on the board. Games are generally about favorale pawn structures, playing for breaks and generally getting your pieces in place to support and capitalize on those breaks. Owning the only or few open and semi open files is critical. 

But when many pawns are gone from both sides and heavy pieces remain, I struggle. When I analyze games using a computer afterward, almost none of my moves are optimal. There is less structure (or it seems so to a patzer like me) and I flounder.

Are there principles to playing on a more open board? Any methods to understand this type of game better?

Well, you could familiarize yourself with the more "important" pieces, but really knowing what it means to out number the opponent with pawns is a necessary skill. Try using your pawns together more, not using only big pieces to protect them (this is sometimes the problem). Also, don't rely to much on the pawns in battle, even though those guys win games. Always, always, always keep trying.

Thank you for your input.

Everything is relative. My online chess rating is good because I take my time with every game and have found that half of my opponents don't take the opening seriously and leave themselves in a weak position. Then it becomes a case of grinding out the win. I am using online chess to improve my opening understanding which is quite weak.

Nonetheless, I have found there are some positions which I simply do not understand... it is like there is a missing formula or missing lesson in my understanding.

In positions with only a couple of missing pawns, I find that I pick the best or near best move according to Fritz in the vast majority of cases (given a lot of time as I do with online chess). This means I understand the position, but may not be efficient at reaching conclusion. Put me in a wide open board and I will miss the optimal or near optimal move in the majority of cases. Again, somewhere I am missing a fundamental understanding.

Thanks, though, for your kind words :)