Residual-informed deep meta regressor for predicting modal frequencies of historical masonry buildings under environmental and operational data scarcity

• A novel framework for predicting modal frequencies of historical masonry buildings under limited monitoring data. • Development of a residual-informed deep meta regressor based on advanced machine learning strategies. • Integration of statistical regressors and a deep LSTM network within a hybrid meta -learning framework. • Utilization of the prediction errors of base regressors to capture hidden effects of unmeasured factors. • Validation on a full-scale historical masonry building with high prediction accuracy. Dynamic monitoring of historical masonry buildings is essential for preserving architectural heritage and ensuring structural safety under varying operational and environmental conditions. Field measurements for dynamic monitoring, while invaluable, often face significant limitations including high costs, logistical challenges of masonry buildings, limited sensor coverage, and sensor malfunctions. Although machine learning-based predictive models offer promising alternatives to complement or replace in-situ monitoring, their performance is often degraded by unmeasured environmental and operational factors, resulting in reduced accuracy and uncertainty in dynamic response prediction. To address these challenges, this study proposes a novel predictive method called Residual-informed Deep Meta Regressor (RiDMR) designed to forecast dynamic responses (modal frequencies) of heritage masonry buildings under partially observed environmental and/or operational conditions. The proposed RiDMR model is developed from a long short-term memory (LSTM) neural network trained on a meta dataset. This meta dataset is constructed by combining measured data with residuals (prediction errors) extracted from some baseline regression models, thereby capturing hidden information of unmeasured but influential environmental/operational variables. The major innovation of this research lies in the development of a residual-informed meta learning framework that integrates statistical and deep learning models by leveraging residual learning to capture unmeasured influences, meta learning to enhance generalization under uncertainty, and hybrid learning to combine the strengths of multiple predictive approaches. Validation on a real-world historical masonry building demonstrates that the proposed RiDMR method significantly enhances prediction accuracy and generalization under unobservable and evolving environmental or operational conditions.