Design-aware surrogate modeling for nonlinear energy consumption analysis using Gaussian process regression and kernel principal component analysis

Nonlinear load behavior, factor interactions, and high-dimensional variability in electrical systems make it challenging to model household power consumption accurately. This work presents a design-aware observational modeling framework that integrates statistical design principles with modern machine learning techniques to extract multivariate insights from household energy data. Unlike classical Design of Experiments (DOE), which relies on controlled interventions, the proposed methodology applies DOE-inspired analytical structure to observational datasets in order to improve interpretability and modeling robustness. The framework combines screening analysis (correlation and ANOVA), quadratic response surface modeling with canonical analysis, Mahalanobis-distance-based design space validation, Kernel Principal Component Analysis for nonlinear latent factor discovery, and Gaussian Process Regression as a probabilistic surrogate model with uncertainty quantification. Bayesian optimization using expected improvement is further employed to explore operating regimes in the modeled response landscape. Results demonstrate that while deterministic electrical relationships explain a large portion of power variability, the proposed framework enables structured analysis of nonlinear deviations, interaction effects, and boundary-region behavior in the energy system. The study provides a scalable statistical methodology for analyzing observational energy datasets and supporting design-informed analysis in future smart-grid environments.