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

2. 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
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3. 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.
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4. 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
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5. 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
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6. 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:
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7. 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
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8. 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)
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9. 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%
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10. Mixed Training Mode
temperature under control period, with nonzero cooling or heating load
temperature floating period, heating or cooling load is zero
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11. 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
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12. 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
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13. 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
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14. 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 °C with a fixed transmittance and °C with a linear transmittance correlation
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15. 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
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16. 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
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