Extraction of supervisory building control rules from model predictive control of windows in a mixed mode building

Abstract

Rule extraction is a promising technique for developing or fine-tuning supervisory control strategies in buildings. Three data mining techniques are examined that extract rules from offline model predictive control (MPC) results for a mixed mode building operated during the cooling season: generalized linear models (GLM), classification and regression trees (CART), and adaptive boosting. All rules were able to recover approximately 90% of the original optimizer energy savings under open loop tests, but the GLM-based rules saw significant performance degradation under simulated tests. CART and boost rules only degraded in performance by a few percentage points, still retaining the vast majority of optimizer savings (84% and 93% for the CART and boost rules, respectively). The results demonstrate that the proposed rule extraction techniques may allow building automation systems to achieve near-optimal supervisory control strategies without online MPC systems, although further research is required to broadly test applicability to more complex cases.

Keywords:

• model predictive control
• rule extraction
• mixed mode buildings
• generalized linear models
• classification and regression trees
• adaptive boosting

Acknowledgements

This research was funded by the United States Green Building Council under a research project entitled ‘HVAC Control Algorithms for Mixed Mode Buildings.’ The authors would also like to thank Colin Jones (EPFL Lausanne) and Alexander Domahidi (ETH Zurich) for their sharing and discussion of unpublished work during the preparation of this manuscript. These conversations were extremely useful in arriving at some common nomenclature around testing processes.

Notes

When implemented as a supervisory control rule, the exponential term could be approximated with a Taylor series expansion if the BAS does not directly support transcendental functions like e_x .

Energy savings are only counted during the cross-validation period, not the entire simulation period.

Random numbers were binomially distributed with a mean equal to the probability of open windows from the MPC solution (27%).

Ultimately a l(0 | 1):l(1 | 0) ratio of 1:1.75 was arrived at after a series of manual trials. This does not represent an ‘optimal’ value, nor would this type of weighting apply to all cases. We merely use an asymmetrical weighting to demonstrate that small performance improvements can be achieved.

In this case, both competing and surrogate splits were included in the importance measure. See (Breiman 1984) for further clarification on CART importance measures.