Gradient-based parameter identification of fractional-order top-tensioned riser systems using analytical sensitivity

This study addresses parameter identification in a fractional-order viscoelastic top-tensioned riser system, where vortex-induced and parametric vibrations significantly influence fatigue life and structural safety. A key challenge lies in accurately identifying the fractional-order coefficient, which strongly governs the long-term memory effect and dynamic response of the system. To overcome this difficulty, an analytical sensitivity of the system response with respect to the fractional order is derived, providing exact and efficient gradient information and eliminating the dependence on finite-difference perturbations. Based on this analytical sensitivity, a reduced-order forward model incorporating Caputo fractional derivatives, non-dimensionalisation, modal reduction and wake oscillator-based fluid–structure interaction is formulated. The identification problem is then cast as a weighted nonlinear least-squares optimisation and solved using an enhanced response sensitivity method with Tikhonov regularisation and a consistency index to stabilise the iterative update. Numerical studies under periodic and quasi-periodic responses, various noise levels, initial guesses and measurement configurations demonstrate fast convergence and high identification accuracy. The results clearly show the superiority of the proposed analytical sensitivity over finite-difference schemes, particularly when the fractional order lies between zero and one.