A system is disclosed, including: a plurality of Bragg gratings distributed in positions transversely to the direction of flow of an exhaust gas in an exhaust gas channel of the device; an optical wave guide structure including at least one optical wave guide and in which the Bragg gratings are embodied; a heating device arranged adjacently to the Bragg gratings and through which the Bragg gratings are subjected to heat, or a cooling device arranged adjacently to the Bragg gratings, through which the Bragg gratings are subjected to cold; at least one light source for irradiating light into the optical wave guide structure; and at least one signal processing device which determines, from light backscattered from Bragg gratings in the optical wave guide structure against its original direction of diffusion, the speed of the flow of the exhaust gas.