What was found
AT CRUISE ALTITUDE EN ROUTE TO PDX, THE #1 ENGINE FIRE WARNING ILLUMINATED AND REMAINED ON. THE FLIGHT CREW PERFORMED AN IN FLIGHT ENGINE SHUTDOWN AND CALLED IN FOR AN EMERGENCY LANDING. THE AIRCRAFT ARRIVED TO PDX WITHOUT FURTHER ISSUES. MAINTENANCE INSPECTED THE AIRCRAFT ONCE IT WAS RELEASED FROM ARFF AND DETERMINED THAT THE FIRE WARNING INDICATION WAS FALSE AND THAT A DIRTY FIRE DETECTOR WAS THE CAUSE OF THE INDICATION AT CRUISE ALTITUDE. THE MAINTENANCE CREW INSPECTED ALL WIRING AND DETECTORS AND DETERMINED THAT NO OTHER DEFECTS WERE PRESENT. THE FIRE DETECTION SYSTEM WAS OPERATIONALLY CHECKED SUCCESSFULLY BEFORE THE AIRCRAFT WAS RETURNED TO SERVICE.