INVERSE BUILDING MODELING Jie Cai and James E. Braun Ray W. Herrick Laboratory Purdue University, US

Outlines Envelope inverse modeling Backup topics Introduction Model structure Parameter estimation Multi-start search Mixed training mode Seasonal effect estimation Single zone case study Backup topics Multi-zone decoupled training DX unit inverse model TSRA Seminar

Inverse Model Inverse model VS forward model Suitable applications Inverse model: data-driven modeling approach, not in the control sense. Forward model: detailed physical-based model, e.g., TRNSYS. Suitable applications To model existing buildings and equipments. Can be used for optimal control development. Can be used for retrofit analysis. Physics-preserved ROM. TSRA Seminar

Introduction Introduction: Extends previous work on inverse building modeling with the following new elements: Includes seasonal variation of window transmittance Mixed training mode Multi-start search scheme Advantages of inverse modeling Only an approximate building description is needed in the model setup phase (no need for detailed parameters) Computationally efficient due to the simplified model structure; suitable for online applications Uncertainties in the building parameters can be well captured TSRA Seminar

Model Structure State space representation Model calculation x= nodal temperatures u= ambient conditions and internal heat gains y= zone air temperature or load Model calculation Efficient methodology for calculating coefficient matrices proposed by Seem et al. (1989) is used TSRA Seminar

Parameter Estimation Estimator structure Parameters to be estimated: resistances and capacitances in the thermal network; other coefficients Cost function: RMSE of outputs between baseline and simplified model Estimator formulation: TSRA Seminar

Global-Local Search Global search: systematic search algorithm developed by Aird and Rice (1977) Local search: Levenburg-Marquardt algorithm (Madsen et al., 2004) (a) Small search region (b) Large search region, in which the number of point evaluations is increased to maintain the same level of gridding TSRA Seminar

Multi-Start Search Multi-start search: several points are generated pseudo-randomly regression is performed for each generated point parameter values with best performance are chosen as final solution Suitable for large-scale estimation problems (Aster et al., 2005) TSRA Seminar

Multi-Start Search Table 1: Comparison of performances of global-local and multi-start search algorithms Global-local Search Multi-start Search Search region lower bound: 10% of nominal parameter values 5% of nominal parameter values Search region upper bound: 300% of nominal parameter values 400% of nominal parameter values Training time: >30 min 45s Testing case RMSE: >10% 0.24% TSRA Seminar

Mixed Training Mode temperature under control period, with nonzero cooling or heating load temperature floating period, heating or cooling load is zero TSRA Seminar

Mixed Training Mode Table 2: Performance of different training mode approaches in terms of prediction errors (P is percentage of the training period where the zone temperature was under controlled conditions) Mixed training Training using load Training using temperature P=23% Zone Temperature (RMSE °C) 0.33 1.05 0.298 Zone Load (% RMSE) 2.73 3.0 2.70 P=65% 0.207 0.38 0.273 2.82 4.03 3.42 P=86% 0.913 0.313 0.283 6.65 2.51 2.56 TSRA Seminar

Window Transmittance Variation Primary seasonal effects can be captured with following transmittance correlation: = transmittance = solar incidence angle = correlation coefficients that need to be estimated via training = correlation power TSRA Seminar

Window Transmittance Variation Estimation was embedded in entire zone training process Linear correlation was found to provide accurate predictions Estimated value of btrans was within the range of 6.2 to 6.5 for all cases TSRA Seminar

Window Transmittance Variation Summer data (hour 5300 to 5500) was used for training and winter data (hour 1500 to 2200) was used for testing Testing RMSE was 0.501 °C with a fixed transmittance and 0.185 °C with a linear transmittance correlation TSRA Seminar

Case Study N Geometry of zone: Construction information: Zone size: 10 by 10 by 10 (m) Window size: 7 by 7 (m) on south wall Internal wall size: 7 by 7 (m) Construction information: Wall (including all walls, ceiling and ground) material: concrete Wall (including all walls, ceiling and ground) thickness: 0.2 (m) Window: INS2_KR_3 from library WINDOW 4.1; insulating glazing with Krypton as gas fill Other information: Weather location: Madison, Wisconsin Control strategy: precool Training period: hour 5300 to 5500 from TMY2 N TSRA Seminar

Temperature Prediction RMSE (C) Load Prediction Relative RMSE (%) Case Study Test Period Temperature Prediction RMSE (C) Load Prediction Relative RMSE (%) Hr 5080 to 5250 0.37 2.8 TSRA Seminar