This paper investigates the problem of cycle detection in periodic noisy data sequences. Our approach is based on reinforcement learning principles. A constructive approach is used to devise a variable structure learning automaton (VSLA) that becomes capable of recognizing the potential cycles of the noisy input sequence. The constructive approach allows for VSLAs to analyze sequences not requiring a priori information about their cycle and noise. Consecutive tokens of the input sequence are presented to VSLA, one at a time, where VSLA uses data's syntactic property to construct itself from a single state at the beginning to a topology that is able to recognize an unknown cycle of the given data. The main strength of this approach is applicability in many fields and high recognition rates.