Correct preposition? Understanding of and based on

When writing a sentence how can one select the correct preposition?

For instance, in the following sentence, I fell it should be “of “when thinking the “understanding of” but again when consider the “above aspects” I feel it should be “on” the above aspects.

So which will be the most correct?

  1. Accordingly, we hope to extend our understanding of the above aspects
  2. Accordingly, we hope to extend our understanding on the above aspects

suppose we cant use

  1. Accordingly, we hope to extend our understanding based on the above aspects

Which should be more considerable before word or the after word which respect to the preposition?

Have a nice day

Thank you
Nakamura

.
#1 is the correct choice. #3 carries a different meaning. An alternative to #1:

Accordingly, we hope to extend our understanding with regard to / concerning the above aspects.

Dear Micawber

Thank you so much. You always help me.

“Arigathogosaimasu”

Nakamura

.
Dou itashimashite.
.