AIR CARGO ACFT CROSSES RWY CLRED TO AND LINES UP WITH WRONG RWY AT MIA.

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ACFT WAS TAXIING ON 'Q' AT MIA INTL PREPARING FOR TKOF ON RWY 27L. SWITCHED TO TWR AND WAS CLRED FOR TKOF ON RWY 27. AN MLG WAS PARKED AT THE APCH END OF RWY 27. OUR ACFT TURNED INSIDE OF MLG; INADVERTENTLY CROSSED RWY 27 AND LINED UP ON RWY 30 AT MIA. WE REALIZED THE MISTAKE; INFORMED TWR AND HELD OUR POS. WE WERE SUBSEQUENTLY CLRED FOR TKOF ON RWY 30. FATIGUE; CONFUSING RWY SIGNS; UNFAMILIAR WITH ARPT ALL PLAYED A ROLE IN THE ERROR. TWR PERSONNEL HANDLED MY MISTAKE VERY PROFESSIONALLY AND NO CONFLICT WITH ANY OTHER ACFT WAS EXPERIENCED. LESSON: TAKE MORE TIME; BE EXTRA CAUTIONS WHEN UNFAMILIAR WITH ARPT; ESPECIALLY WHEN INTERSECTING RWYS ARE SO NEAR TO EACH OTHER. APPARENTLY NO HARM DONE; BUT VIOLATION OF RWY INCURSION MAKES YOU FEEL LIKE AN IDIOT! UNPROFESSIONAL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THIS WAS A STUPID PLT ERROR. (HE MADE NO EXCUSES.) WITH SOME QUESTIONING; HOWEVER; HE STATED THIS WAS A MOST UNUSUAL DEP. USUALLY 12 OR 9 RWYS IN USE AT NIGHT FOR NOISE ABATEMENT. FATIGUE ALSO FACTOR; 8TH DAY OF 8 DAY SCHEDULE. TWO JUMPSEAT RIDERS ADDED DISTR. SIDE RAMP AREA; AT NIGHT DIFFICULT TO DETERMINE RWY AS TAXI LINE CROSSES 27.