In some cases“觉得”means a feeling,such as"我觉得冷"，in other cases it means a thought:"我觉得你是个好人"equal to"我认为你是个好人"，but"认为"is more logical,I think.
"以为"means"I thought xxx,but I was wrong",such as"我以为天气冷，但其实天气很暖和"，and"我以为你是个好人，但你不是".
But long ago in ancient time we used"以为"as"认为"，"吾以为，此事必有蹊跷"that means"我认为,这件事很可疑".
That's my opinion.
