Sanhedrin 107a: David had asked Hashem why people say Elokei Avraham, and do not say Elokei David. Hashem said 'I tested him with 10 tests, and he passed all of them', like it says in Shabbos ¹ . David asked Hashem "test me!"

Radak: Like You find my heart, judge me.

Malbim: Test me regarding according to actions in purity. Actions that are not in purity, i.e. not done due to good, rather, for external motivations such as pride and flattery, he will not stand in them at the time of a test. If there is benefit in refraining from them, he will not do them. Acts of purity are different - "b'Sumi Halachti". They are purified silver without dross; they are tested in the furnace.

Radak: You will find (my kidneys and heart) like clean (refined) silver. The kidneys counsel, and the heart understands and thinks. Every thought I refined, without any dross. Even though sometimes my deeds are not good, my heart is always straight.

Malbim: This corresponds to "uva'Hashem Batachti" (verse 1) - trust in the heart.