A Novel Tree-Based Hybrid Kernelized Regressor for Predicting Modal Frequencies of Timber Buildings Using Weakly Correlated Data

Prediction of the dynamic behavior of civil structures, particularly multi-story timber buildings, offers valuable opportunities to reduce reliance on extensive field measurements. Although environmental parameters such as relative humidity, temperature and moisture content significantly influence timber structures, regression-based prediction becomes particularly challenging when available environmental data are either limited or weakly correlated. Limited dynamic response data (e.g., modal frequencies from short-term monitoring programs) and weak environmental-response correlations often prevent traditional regression methods from establishing accurate, robust predictive relationships, resulting in poor predictive reliability. To address these challenges, this study proposes a novel tree-based hybrid kernelized regression approach, termed Decision Tree Residual-embedded Gaussian Process (DTRGP). This method innovatively integrates decision tree regression (DTR) with a tree learning mechanism and Gaussian process regression (GPR) based on the concept of probabilistic kernel learning framework. The proposed method leverages advanced machine learning algorithms such as residual learning and hybrid modeling to develop a robust regressor for weakly correlated environmental-response relationships. Initially, a DTR model per each response is constructed using available and measured data. Residuals between measured and DTR-predicted responses are then determined to extract latent environmental patterns, which can supplement the originally measured environmental data. Both measured environmental and residual-augmented data are combined to form an enhanced predictor dataset for training a GPR model. The proposed DTRGP method is validated using the identified modal frequency data from an eight-story cross-laminated timber building alongside with real environmental data from a nearby weather station. Results demonstrate that the proposed method substantially improves prediction accuracy of the building modal frequencies, even under conditions of limited response data and weakly correlated environmental-response relationships.