An aerodynamically shaped profile member for aircraft and wind power stations includes, for example, phased-array ultrasonic generator arrangement arranged therein. During operation of the profile member, the ultrasonic generator emits ultrasonic waves in a targeted manner in multiple directions to determine a profile of the thickness of an ice layer on the surface of the aerodynamic profile. The structure may be, for example, a composite fiber material arranged around a foam core, with the ultrasonic generator arrangement being laminated into the composite fiber material. For measurement of the ice thickness, ultrasonic waves are transmitted in a targeted manner to different positions of the surface of the aerodynamic profile, and the ultrasonic waves reflected on the interfaces of the ice layer are detected. At least one region of the surface is scanned by means of the targeted ultrasonic waves, to determine an ice thickness profile.