Nonlinear Dynamical Systems Approach to Building Energy Prediction Problems

Given a time series data, model dynamical systems are built using a hierarchical Bayesian scheme with feedforward neural nets and then the models are compared in terms of marginal likelihood. The model with the highest marginal likelihood is used for predictions. The algorithm is applied to building air-conditioning load prediction. INTRODUCTION When nonlinearity is present, time series prediction becomes a di cult task. The problem is particularly di cult when no functional form (equation) is known of the dynamics. Given time series data, typically one constructs a model nonlinear dynamical system which ts to the given data, and makes predictions using the model. There are several important issues which need to be addressed: (i) Which class of models should be used; (ii) How should one estimate parameters associated with models without over tting. This paper models a non-autonomous nonlinear dynamical system by feedforward neural nets with a hierarchical Bayes scheme [1] and then applies the proposed algorithm to building airconditioning load prediction problem. Saving energy and reduction of CO2 emissions are becoming critical for conservation of global and regional environments. The cost of electricity during night hours is typically much less than that of the daytime. Therefore, in electrically operated HVAC (Heating, Ventilation, and AirConditioning) systems, introduction of thermal energy storage systems can help level o electricity demand throughout the day and thus increase the over all operation e ciency of the power plants run by utility companies. Thermal energy storage systems therefore contribute to avoid construction of additional power plants and stability of power systems. However, in reality thermal energy storage systems are often found not operating as e ciently as expected at the design stage. Typical reasons for this are: excessive storage of thermal energy leads to signi cant heat loss through tank surroundings; and peak hour operation of energy plants becomes necessary because stored energy is completely discharged early in a day. In order to overcome these problems, very good prediction algorithms are needed for predicting air-conditioning loads. A prediction competition was organized by SHASE (Society of Heating, Air-conditioning, and Sanitary Engineers in Japan) [4] which we participated. The results are on those real data provided by the competition organizer. Achilles heel of Bayesian method is its dependency on prior. Hierarchical Bayes considers a family of prior distributions parameterized by hyperparameters instead of a single prior. One can estimate hyperparameters given data and then one estimates the parameters in question. This way hierarchical Bayes approach enables algorithms less dependent on a particular prior. Hierarchical Bayes approach is also endowed with a natural structure for model comparisons which is extremely important.