Axial dynamic load identification of hydraulic turbine based on Chebyshev orthogonal polynomial approximation

Abstract

An analysis method is proposed to identify axial dynamic loads acting on the Francis turbine based on Chebyshev orthogonal polynomial expansion theory. Dynamic loads are expressed as functions of time and polynomial coefficients. The dynamic load identification model is constructed through discretized integral convolution of the loads, such as the Duhamel integral. However, the discretized numerical integral has a time-cumulative error problem that decreases the recognition accuracy of the dynamic load. Compared with the traditional method, the algorithm proposed in this paper constructs the relationship between the modal displacement and force using polynomial orthogonality and derivative relation between displacement and velocity or acceleration. The new method could avoid the Duhamel integral and time-cumulative error problem. This algorithm not only requires less measuring point information, but is also highly efficient. Compared with genetic algorithm identification, orthogonal polynomial algorithm is not easy falling into local convergence, and does not require multiple repetitions positive analysis trial to evaluate individual fitness value. Numerical simulations demonstrate that the identification and assessment of dynamic loads are effective and consistent when the proposed method is used.