Not a teacher.
Complex: The noise increased as the day advanced.
Simple: a) The noise increased with the advancement of the day.
b) The day having been advanced, the noise increased.
c) The day advancing, the noise increased.
d) The day being advanced, the noise increased.
Are a), b), c), d) grammatically correct?
In my opinion, the complex sentence is most natural.
Otherwise, I would use TEECHAR's proposition, "as the day unfolded..."
Completely unnatural sentences are crossed out.
Complex: The noise increased as the day advanced. (Okay)
The noise increased as the day
unfolded. (Also okay.)
Simple: a) The noise increased with the
unfolding of the day. (Poetic...)
a) The noise increased with the advancement of the day. (It's a little strange but I would say it's okay.)
[STRIKE]b) The day
having been unfolded, the noise increased.[/STRIKE]
[STRIKE]b) The day
having been advanced, the noise increased.[/STRIKE]Nope. It is confusing.
c) The day
unfolding, the noise increased. (also poetic, but somewhat unnatural)
c) The day
advancing, the noise increased. (It seems a little strange.)
[STRIKE]d) The day
being unfolded, the noise increased. [/STRIKE]
[STRIKE]d) The day
being advanced, the noise increased.[/STRIKE] Nope. Actually, the meaning of this grammar is different from the original meaning. It means that the day already unfolded or advanced, meaning it is evening or the day has (almost?) ended, yet it seems like you are trying to use a progression of time with the second phrase. It doesn't work together.
It seems like the use of "being" or "been" is not okay in this context.