Shape estimation of a deformed cylinder via fiber optic strain sensors in triple helices

Abstract

This study proposes the use of strain sensors in a triple-helix configuration to measure the bending and twist deformation in a cylinder. The method consists of two steps: first to determine the local deformation coefficients from the surface strains, and second to reconstruct the overall deflected shape of the cylinder from the local deformation coefficients. I derived an exact analytical formula for the surface strain on a bent and twisted cylinder according to the deformation coefficients based on my original superhelix model, in which the deformed cylinder segment is regarded as a helical coil and the sensors bound upon it as segments of superhelices. The local deformation coefficients are iteratively computed by the Newton-Raphson method using the surface strain formula. I incorporate the local deformation coefficients into the Helical Extension Method, which is an exact solution to the Frenet-Serret formulas, to reconstruct the overall deflected shape of the cylinder. From the simulations, the proposed method was shown to determine the overall deformation state of a cylindrical body with remarkable precision. The position errors decreased rapidly with shorter spatial intervals of strain sensing and lower default rates of the spin of the sensors, showing a strong trend of convergence. The accuracy depended strongly on the rotational angle of the strain sensing interval in the case with the midpoint strain method, while the dependence was much weaker in the same cases but solved by the arc length method. A brief description of the procedures of two preliminary experiments I have conducted for further validation is given. This study demonstrates a potential for general applicability to various fields, especially for the shape sensing of multicore optical fibers.