Is the tribulation of a believer either for the raising of ranks or for the expiation of sins only, or can it be a punishment for a sin, or a tribulation that does not fall under the expiation of sins or the raising of ranks?

Distinguishing whether an affliction is a punishment or for elevating one's rank is a matter of the unseen, known only to Allah. Allah tests His servants with ease and hardship, either to raise their ranks or because of sins. All of this is for a wisdom, and the believer should be grateful in ease and patient in hardship, for all of it is good for him.