Identification of a thermal building model by learning the dynamics of the solar flux

This article deals with the identification of a dynamic building model from on-site input-output records. In practice, the solar gains, a key input, are often unobserved due to the cost of the associated sensor. We suggest here to replace this sensor by a cheap outdoor temperature sensor, exposed to the sun. Our assumption is that the temperature bias between this sensor and a second sheltered sensor is an indirect observation of the solar flux. We derive a novel state-space model for the outdoor temperature bias, with sudden changes in the weather conditions accounted for by occasional high variance increments of the hidden state. The magnitude of the high values and the times at which they occur are estimated with an ℓ₁-regularized maximum likelihood approach. Finally, this model is appended to a thermal building model based on an equivalent RC network, forming a conditionally linear Gaussian state-space system. We apply the Expectation-Maximization algorithm with Rao-Blackwellised particle smoothing in order to learn the thermal model. We are able, despite the indirect observation of the solar flux, to correctly estimate the physical parameters of the building, in particular the static coefficients and the fast time constant.