Mayfly–Deep Learning Fusion for High-Dimensional Parameter Identification and Reinforcement of Historical Buildings

Structural health assessment of historic buildings frequently relies on finite element (FE) model updating, yet high-dimensional parameter identification under sparse, noise-contaminated modal data can reduce robustness and lead to prohibitive computational cost. This paper proposes an application-oriented integrated workflow that improves identification stability while accelerating the updating process. A multi-indicator objective function is formulated by combining residuals of natural frequencies and mode shapes with sensitivity-based consistency relations. The inverse problem is solved using the Mayfly Algorithm (MA), and a deep neural network (DNN) surrogate is introduced to replace repeated FE modal analyses during the optimization, thereby reducing the overall computational burden. The proposed workflow is demonstrated on the Christian Lutheran Church in Wuhan, China, constructed from 1923 to 1924, using operational modal testing data collected at 25 measurement points. A refined FE model is updated by identifying 24 grouped stiffness reduction coefficients that represent columns, beams, walls, and slabs across different floors. The updated model shows substantially improved agreement with the measured first four natural frequencies and corresponding mode shapes, enabling a quantitative diagnosis of stiffness degradation and supporting stiffness-oriented reinforcement planning. A stiffness enhancement target of 20% is adopted to guide intervention measures, and an analytical modal enhancement check is provided to relate the stiffness target to the expected frequency gain. The workflow offers a reproducible route for data-informed decision support in heritage building assessment and rehabilitation, while uncertainty quantification and post-intervention validation are identified as key priorities for future work. Under the available sparse modal information, the inverse problem is underdetermined; therefore, the reported stiffness-reduction coefficients should be interpreted as non-unique grouped solutions affected by modelling and measurement uncertainty, and the reinforcement measures are presented only as planning-level design proposals requiring post-intervention verification.