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• A novel hybrid strategy (HJDEA) based on Jaya and differential evolution algorithm is proposed. • A noise insensitive objective function is established based on adjacent acceleration correlation function. • An attractive combination of HJDEA and gradient search method is proposed to further improve performance. • Alterations of both stiffness and mass parameters are considered in the damage model. • Studies on shear-type frame, cantilever beam and ASCE benchmark structure are conducted to verify the effectiveness of the proposed methods. To solve the optimization-based structural damage identification problem, a novel hybrid algorithm based on Jaya and differential evolution algorithm (HJDEA) is proposed to detect, locate and quantify structural damages by effectively incorporating the powerful local exploitation capacity of Jaya algorithm and global exploration capability of differential evolution. Meanwhile, Hammersley sequence initialization and Lévy flight search mechanism are introduced into HJDEA to further improve convergence rate and refining the quality of the best solution. Four different algorithms, genetic algorithm, particle swarm optimization, Jaya and the proposed HJDEA are employed for comparative study. In addition, the objective function is established by adjacent acceleration correlation function so as to avoid false identification caused by defining improper reference point. The performance of the proposed damage identification strategy based on HJDEA and adjacent acceleration correlation function is investigated with numerical examples involving an 8-DOF lumped mass model and a cantilever beam, as well as an experimental study of the ASCE benchmark structure under white noise excitation. Results show that the proposed hybrid identification method is accurate, efficient and robust in the identification of the damage existence, location and severity of stiffness and mass parameters even with partial output-only responses and 20% noise-polluted measurements. [ABSTRACT FROM AUTHOR]