Structural health monitoring commonly uses natural frequency analysis to assess structural conditions, but direct frequency shifts are often insensitive to minor damage and susceptible to environmental influences like temperature variations. Traditional methods, whether based on absolute frequency changes or theoretical models like PCA and GMM, face challenges in robustness and reliance on model selection. These limitations highlight the need for a more adaptive and data-driven approach to capturing the intrinsic nonlinear correlations among multi-order modal frequencies. This study proposes a novel approach that leverages the nonlinear correlations among multi-order natural frequencies, which are more sensitive to structural state changes. A deep learning framework integrating CNN-BiLSTM-Attention is designed to capture the spatiotemporal dependencies of multi-order frequency data, enabling the precise modeling of intrinsic correlations. The model was trained exclusively on healthy-state frequency data and validated on both healthy and damaged conditions. A probabilistic modeling approach, incorporating Gaussian distribution and cumulative probability functions, was used to evaluate the estimation accuracy and detect correlation shifts indicative of structural damage. To enhance the robustness, a moving average smoothing technique was applied to reduce random noise interference, and damage identification rates over extended time segments were calculated to mitigate transient false alarms. Validation experiments on a mass-spring system and the Z24 bridge dataset demonstrated that the proposed method achieved over 95% damage detection accuracy while maintaining a false alarm rate below 5%. The results validate the ability of the CNN-BiLSTM-Attention framework to effectively capture both structural and environmental nonlinearities, reducing the dependency on explicit theoretical models. By leveraging multi-order frequency correlations, the proposed method provides a robust and highly sensitive approach to structural damage identification. These findings confirm the practical applicability of deep learning in damage identification during the operational phase of structures.

Structural Health Monitoring relies on accurate modal identification and effective damage detection to assess structural performance and safety. However, traditional sensor placement methods struggle to balance modal identification uncertainty, which arises from limited sensor coverage and measurement noise and damage detection sensitivity, which requires sensors to be optimally positioned to capture structural stiffness variations. To address this challenge, this study proposes a multi-objective sensor placement optimization method based on the Non-Dominated Sorting Genetic Algorithm. The method introduces two key objective functions: minimizing modal identification uncertainty by leveraging Bayesian modal identification theory and information entropy and maximizing damage detection sensitivity by incorporating an entropy-based measure to quantify the uncertainty in stiffness variation estimation. By formulating the problem as Pareto-based multi-objective optimization, the method efficiently explores a trade-off between the two competing objectives and provides a diverse set of optimal sensor placement solutions. The proposed approach is validated through numerical experiments on a simply supported beam and a benchmark bridge structure, demonstrating that different optimization objectives lead to distinct sensor placement patterns. The results show that solutions prioritizing modal identification distribute sensors across the structure to improve global response estimation, while solutions favoring damage detection concentrate sensors in critical areas to enhance sensitivity. The proposed method significantly improves sensor placement strategies by offering a systematic and flexible framework for SHM applications, enabling engineers to tailor monitoring strategies based on specific structural assessment needs.

In structural health monitoring, effectively eliminating the influence of variable environmental conditions on modal frequencies remains a critical challenge for accurate damage identification. Nonstationary and nonlinear variations in modal frequencies, commonly induced by environmental changes, tend to overshadow the effects caused by structural damage. An improved Gaussian mixture model (GMM) is proposed in this paper to normalize nonlinear and nonstationary frequency data, enabling effective structural damage detection under variable environmental conditions. As the effectiveness of the GMM is highly influenced by the initial parameter values used in the expectation-maximization (EM) algorithm, a subdomain division strategy is first presented to determine the unique initial values of the GMM parameters. Through the application of the EM algorithm, the GMM is constructed simply and efficiently through the determined initial parameters. Next, on the basis of the constructed GMM, the modal frequency data are normalized to extract damage features that remain unaffected by environmental variations. Subsequently, Hotelling’s T2 statistic and its cumulative form are calculated for the damage features and designated as the damage indicators; meanwhile, the corresponding damage thresholds are also calculated according to the kernel density estimation technique. To validate the proposed method, two case studies are conducted: one with a numerical mass-spring system and the other with a real bridge structure. Results show that environmental influences no longer impact the normalized frequency data, and the cumulative statistic demonstrates outstanding accuracy in identifying structural damage.