Abstract: One or more systems, devices, and techniques for heating a structure using boiler water stored by a boiler are described herein. For example, a method includes obtaining gas consumption data for a heat source that is heating a structure and obtaining zone and ambient temperature data while the structure is being heated. Additionally, the method includes estimating unknown parameters of elements of a dynamic heat loss model as part of a model predictive control (MPC) model for the structure using inverse modeling as a function of the obtained gas consumption data and zone and ambient data.

Abstract: Parameters are estimated for continuous time linear gray-box models using a fast sensitivity evaluation, which is a measure of how output of the model changes with changes in parameters. A two-step parameter estimation of non-linear models, such as a steady-state model and dynamical model, is performed. A parameter estimation algorithm is employed for estimation of non-linear model parameters via local approximation at different system operating levels or operating set-points. The parameter estimation task is improved by an efficient parameter estimation of linear, continuous-time, stochastic, gray-box models. It is further improved by using a two-step parameter estimation of non-linear, continuous-time, gray-box models. It is still further improved by employing the efficient parameter estimation algorithm for the non-linear gray-box models.

Abstract: A method includes obtaining gas consumption data for a heat source that is heating a structure, obtaining zone and ambient temperature data while the structure is being heated, and estimating unknown parameters of elements of a dynamic heat loss model as part of a model predictive control (MPC) model for the structure using inverse modeling as a function of the obtained gas consumption data and zone and ambient data.

Abstract: A method includes using first principles and engineering knowledge to define a continuous time nonlinear gray-box model of a system performing a process, defining a numerically tractable optimization problem for parameter estimation of the nonlinear gray-box model, tuning a vector of parameters of a static model of the nonlinear gray-box model, and extending the vector of parameters of the static model to a dynamic model by fitting measured transient data from the process.