Vision-Based Measurement for the Transverse–Longitudinal–Rotational Displacement of Hoisting Rope by Modified Lucas–Kanade Algorithm

In the mine hoisting system, the hoisting rope generates transverse–longitudinal–rotational (TLR) motion due to external excitation and the structure of the hoisting rope. The motion parameters of the hoisting rope are the basis for the fault diagnosis and vibration control of the hoisting system. In this study, a modified Lucas–Kanade (LK) method is proposed to identify the TLR displacement of the hoisting rope, called TLR-LK algorithm. First, the longitudinal–rotational warp function for wire rope is constructed and the iterative calculation formula is derived. Then, a method of wire rope axis positioning and parameter identification is proposed based on projection minimization to obtain the transverse displacement and radial dimension of the rope. Finally, the performance and feasibility of the proposed TLR-LK algorithm are demonstrated by comparing the results with existing representative methods in the motion platform and a field experiment in colliery. Experimental results reveal that the proposed algorithm can obtain the transverse, longitudinal, and rotational parameters of the hoisting rope simultaneously with higher accuracy and efficiency.