Statistical and deep learning techniques applied to ambient vibration-based monitoring of an historical Peruvian building

Structural Health Monitoring (SHM) plays a crucial role in assessing the integrity of historic buildings. This work focuses on the development of machine learning models to analyze the dynamic response of the San Cristobal Church in Cusco, Peru, a 17th century World Heritage Site instrumented with a seismic sensor. The study is carried out within the framework of the IRD-funded ARCHIVES project. The main objective of this research is to model the resonant frequency of the church using environmental parameters such as temperature, humidity, and atmospheric pressure. Three key tasks are explored: (1) developing a predictive model of resonant frequency based on weather conditions, (2) using explanatory techniques to assess the impact of individual weather variables, and (3) performing anomaly detection to identify unusual structural responses, particularly after earthquakes. The Experimental Results section presents a systematic evaluation of various regression and deep learning models. Ridge regression is first used as a baseline, utilizing rolling window feature engineering to account for time-dependent effects. This analysis reveals the critical influence of past rainfall accumulation on the resonant frequency, which is consistent with the moisture absorption properties of adobe materials. However, linear models struggle to fully capture peak variations, motivating the transition to more complex approaches. Deep learning architectures, including Feedforward Neural Networks (FNNs) and Temporal Convolutional Networks (TCNs), are then introduced. The TCN model outperforms other approaches, achieving the lowest Root Mean Squared Error (RMSE) and demonstrating superior generalization on test data. SHAP analysis confirms the non-linear contributions of humidity and precipitation to frequency shifts, validating the physical hypotheses underlying the study. For anomaly detection, Bai-Perron structural break test is applied to both the raw environmental features and the latent feature space of the neural networks. The results of the TCN model provide the most reliable estimate of the post-earthquake recovery period, refining the initial conservative assumptions made by visual inspection. This finding highlights the potential of machine learning in SHM applications, particularly for non-invasive monitoring of historic structures.