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The fault resistance is the key factor to affect the travelling waves and the performance of travelling-wave-based protections on HVDC transmission lines. In order to explain accurately the impacts of the fault resistance to travelling waves in theory and improve computational efficiency on the existing data of the travelling waves at given fault conditions, this paper proposed a global-sensitivity-based method to fast predict the new travelling waves with any other fault resistance. This method was built on the actual HVDC project topology and its frequency-dependent nature, and derived by the infinite-Taylor series in the phase and frequency domain, and then realized by a rational fitting technique with an order estimation scheme for the conversion to the time domain, which would overcome three limitations compared with conventional sensitivity methods. Numerical examples show that the proposed method has a huge advantage in saving CPU time to predict travelling waves in the network with any fault resistance increment over traditional simulations.