With regard to the word “PREMIUM”, from your situation we would advise to file for the mark “Double A logo” without the word “PREMIUM”.
For your concern relating to the non-use cancellation, since the term “PREMIUM” is rather ‘descriptive’ or directly refers to the quality of the products, should a third party try to invalidate your mark based on non-use, we are of the opinion that there are rooms for us to argue that the word “PREMIUM” is a minor component of the mark and is descriptive. Anyone can incorporate such term to his/her trademark in order to convey the message that the goods are of excellent quality. Therefore, the use of the mark “Double A logo” with or without the word “PREMIUM” does not affect the entire character of the mark.