Uncertainty Propagation under Residual Disturbances: A Smart-Home Case Study

TL;DR

This paper introduces a data-driven method for uncertainty propagation in systems with unmeasured disturbances, validated on smart home data, using polynomial chaos and Chebyshev inequalities.

Contribution

It develops a causal, distributionally consistent stochastic predictor for residual disturbances, enabling efficient uncertainty quantification from data.

Findings

Validated method with real smart home data from Norway.

Achieved efficient uncertainty quantification using polynomial chaos.

Demonstrated the predictor's causality and distributional consistency.

Abstract

This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.