A study of chaotic searching paths for their application in an ultrasonic scanner

Most non-destructive ultrasonic automatic scanning tests are programmed with a complete systematic trajectory. However, when the location of a discontinuity (disturbance source) and the searching space are unknown, an exhaustive search can be time and computational inefficient. In this paper, the efficiency of chaotic trajectories to search for a discontinuity in an area with limited information is studied. The probability of detection and its relationship with topological properties of the proposed chaotic dynamic model is analyzed. The Pearson's random walk model is modified to substitute random for chaotic behavior by transferring the solutions of the chaotic dynamical model to the phase and modulus of the discrete path trajectories. This provides a simple description of the trajectories in a vector space where only magnitude and phase are required. Following this approach, the chaotic trajectories were generated in the working plane and then transferred to a Cartesian robotic ultrasonic system. The system was tested without human supervision on unknown environments for ultrasonic detection of hidden defects. The results show that the studied chaotic walk model provides efficient ultrasonic scanning trajectories for defect detection and can outperform systematic scanning when the geometry of the workspace is complex and unknown.