Safety Assessment Method for Cracks in Ancient Timber Structures Based on an Improved Entropy Weight–Fuzzy Matter-Element Model

Ancient timber structures are important carriers of valuable cultural heritage, and their structural safety directly determines whether historic buildings can remain in safe service over time. Cracks represent one of the most widespread and important forms of damage in ancient timber structures. They can directly lead to cross-sectional weakening of structural members, degradation of load-bearing capacity, and the gradual development of overall structural safety risks. To address the limitations of existing crack assessment methods, such as strong subjectivity in weight determination, insufficient accuracy in grade boundary discrimination, and inadequate coupling with mechanical performance, this study proposes a crack safety assessment method for ancient timber structures based on an improved entropy–fuzzy matter-element model. A multi-dimensional evaluation index system is established, incorporating crack geometric characteristics, structural load-bearing capacity, and service time effects. A mechanically driven load-carrying capacity degradation index is introduced to quantitatively characterize the influence mechanism of crack propagation on structural performance deterioration. The entropy weight method is employed to objectively determine the weights of each indicator, and an asymmetric closeness degree is introduced to improve the traditional fuzzy matter-element model, thereby enhancing the stability and accuracy of safety grade classification. A case study of the Bawang Academy, Shenyang Jianzhu University, is conducted. Crack parameters are obtained using image recognition and three-dimensional laser scanning techniques, and a comprehensive structural safety assessment is performed. The results indicate that the proposed method can accurately reflect the actual damage distribution and deterioration level of the structure, providing a reliable theoretical basis and technical support for crack safety evaluation and preventive conservation of ancient timber structures.