Subdomain cointegration method for early damage warning of bridges considering nonlinear and nonstationary modal variabilities

Modal frequencies are widely utilized as damage-sensitive features in vibration-based bridge damage warning. However, nonlinear and nonstationary modal variabilities induced by environmental fluctuations, compounded by improper selection of modal orders, may obscure damage sensitivity and degrade warning accuracy. Therefore, a subdomain cointegration (Sub-CI) method for environment-tolerant and early damage warning of bridges is proposed. The proposed method initially partitions the multimodal training data into local subsets that capture local variation information using the Dirichlet process K-means cluster. Subsequently, an implicit cointegration model with immunity to environmental effects within each cluster is established. Then, two types of damage indexes are considered separately, namely the robust Mahalanobis squared distance for multivariate cointegration and the Johnson transformation-based one-dimensional residual for bivariate cointegration. After that, the dynamic thresholds are derived from each Sub-CI model to assess the health status of in-service bridges. Results demonstrate that the proposed method mitigates modal variabilities induced by latent periodic temperature changes and overcomes larger damage prediction errors and higher false alarm rates in comparison to classical linear cointegration.