Nonlinear Dynamic Models With Uncertainties Measured by Fuzzy Sets for Radiator-Heated Buildings

Dynamic models are indispensable for the optimization, prediction, and control of thermal comfort in buildings. This article proposes a new method for modeling the nonlinear dynamics of radiator-heated buildings and measuring model uncertainties. Specifically, a nonlinear dynamic model is established according to the heat conservation between independent heat storage units in heating buildings. The model uncertainties are measured based on the fuzzy set theory by a number of sub-optimal parameter vectors that reproduce certain measured outputs and approach the optimal value of a modeling objective function. These sub-optimal parameter vectors can describe the uncertainties in the presence of model structure deviations and unknown noise distributions, without making restrictive assumptions that the noise follows a Gaussian distribution as in existing methods. The proposed method is validated by practical examples in a radiator-heated residential building. The examples illustrate that the proposed method can provide more accurate measurements of the model uncertainties than the Markov Chain Monte Carlo method.