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A Framework for Probabilistic Building Energy Modeling
- 1. A Framework for Probabilistic Building Energy Modeling Lukas Lundström Doctoral thesis defense 2020-09-10 Opponent: Angela Sasic Kalagasidis (Chalmers) Evaluation board: Joakim Widén (UU), Natasa Nord (NTNU), Sture Holmberg (KTH) and reserve Ning Xiong (MDH) Supervisors: Erik Dahlquist, Fredrik Wallin and Jan Akander
- 2. Content 2 Background & data Gap & research questions Methods Case studies Contribution, conclusions & future work
- 3. • More efficient energy use and a larger share of renewables are needed to mitigate global warming • Existing buildings play a key role in this transition • They stand for about 40% of the global energy use • More flexible energy use could enable a larger share of intermittent energy supply from renewables 3 Background
- 4. Heat balance of a Swedish multifamily building 4 Solar heat gains Internal gains Heating system Space heating Ventilation Transmission Internal mass Infiltration Manual venting AHU Thermal bridges Roof Windows External walls Ground floor
- 5. Total heat supply 5 District heating Solar heat gains Internal gains Heating system Internal DHWC Space heating Ventilation Transmission Pipe network Internal mass Infiltration Manual venting AHU Thermal bridges Roof Windows External walls Ground floor DHW
- 6. 6 Data
- 7. 7 Numerical weather prediction Forecasting and historical (re-analysis) • External air temperature • Wind • Sky temperature • Soil temperatures • Albedo • Solar irradiance Copernicus ERA5 global climate re-analysis
- 8. 8 SN W E Winter Summer Ground Space Pixel 1 Pixel 2 Remote sensing Satellite-based solar irradiance
- 9. 9 Source: https://doi.org/10.3390/s17030621 Remote sensing II 3D-shapes from aerial surveying (photogrammetry / LiDAR)
- 10. 10 Source: https://doi.org/10.3390/s17030621 Remote sensing 3D-shapes from aerial surveying (photogrammetry / LiDAR)
- 11. 11 Utility billing metering District heating and cold-water metering
- 12. 12 Metering from within the building Domestic-hot-water use, indoor temperature Flow meter Communication unit
- 13. Data within a context increase our understanding 13 Data Understanding Context
- 14. Data within a context increase our understanding 14Understanding Data InformationRelations Context
- 16. Data tuned decision making 16Understanding Data Information Knowledge Wisdom Relations Patterns Insights Context
- 17. Focus on the machinery of creating data calibrated knowledge 17 Wisdom Context Understanding Information Knowledge Relations Patterns Data Insights
- 18. Two approaches to BEM (Building Energy Modeling) 18Complexity Simulation software, e.g. IDA ICE Grey-box models data-driven / inverse law-driven / forward
- 19. Detailed models potentially provide more insights 19Complexity <-LessMore-> Insights Simulation software, e.g. IDA ICE Grey-box models
- 20. Issues with identifiability 20Complexity <-LessMore-> Insights Identifiable / Directly calibratable Simulation software, e.g. IDA ICE Grey-box models
- 21. A calibrated model provides more trustworthy insights 21Complexity <-LessMore-> Identifiable / Directly calibratable Insights Simulation software, e.g. IDA ICE Grey-box models
- 22. Identified gap 22Complexity <-LessMore-> Identifiable / Directly calibratable Insights Simulation software, e.g. IDA ICE Grey-box models
- 23. Push the limit of directly calibratable BEM 23Complexity <-LessMore-> Identifiable / Directly calibratable Insights Simulation software, e.g. IDA ICE Grey-box models Proposed BEM
- 24. Research questions 24 Q2. What level of detail is required to obtain a BEM that can provide actionable insights on the building’s actual energy performance, yet allow calibration in a scalable way? VI Q1. What information from meteorological reanalysis, remote sensing and on-site metering data sources can be utilized for BEM calibration in a scalable way? IV, VI Q3. What are the advantages and disadvantages of using a probabilistic BEM calibration approach? II- VI
- 25. 25 Included publications Heat Demand Profiles of Energy Conservation Measures in Buildings and Their Impact on a District Heating System (Lundström L., Wallin F.) Mesoscale Climate Datasets for Building Modelling and Simulation (Lundström L.) Adaptive Weather Correction of Energy Consumption Data (Lundström L.) Development of a Space Heating Model Suitable for Automated Model Generation of Existing Multifamily Buildings (Lundström L., Akander J., Zambrano J.) Bayesian Calibration with Augmented Stochastic State-Space Models of District- Heated Multifamily Buildings (Lundström L., Akander J.,) Uncertainty in Hourly Readings from District Heat Billing Meters (Lundström L., Dahlquist E.) Applied Energy 2016 Proceedings CLIMA 2016 I II III IV V VI Energies 2019 Energies 2019 Proceedings SIMS 2019 Proceedings ICAE 2016
- 26. Bayesian calibration Probability density distribution encoding prior knowledge 26 𝜋(𝜽) Prior 0.0 0.20 0.4 0.6 W/K,m2
- 27. Bayesian calibration Evidence in the data 27 I n p u t u 𝜋(𝒚|𝜽, 𝒖) Likelihood 𝜋(𝜽) Prior 0.0 0.20 0.4 0.6 W/K,m2
- 28. Bayesian calibration Joint probability 28 𝜋(𝜽|𝒚, 𝒖) Posterior I n p u t u 𝜋(𝒚|𝜽, 𝒖) Likelihood 𝜋(𝜽) Prior ×∝ 0.0 0.20 0.4 0.6 W/K,m2
- 29. Bayesian calibration Bayes’ theorem 29 I n p u t u 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽
- 30. Prediction 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Bayesian calibration 30 Stochastic state-space model
- 31. Deterministic BEM 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction 31
- 32. 32 Deterministic BEM • Dynamic and physics-based • Modelling district-heated multifamily buildings 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction eat meter lo meter return supply ipe net orold ater supply adiators aps
- 33. 33 Thermal space • A resistance-capacitance (RC) network • Lumped version of ISO 52016:2017 eat meter lo meter return supply ipe net orold ater supply adiators aps
- 34. rew rf rew rf rew rf rew rf rew rf rrf rew rimrgf External walls Ground floor Roof Internal mass 34 Thermal network • A resistance-capacitance (RC) network • Lumped version of ISO 52016:2017 • Building geometry represented with 5 elements • 14 temperature nodes (states) External walls Windows Ground floor Roof Internal mass
- 35. 35 Thermal network • A resistance-capacitance (RC) network • Lumped version of ISO 52016:2017 • Building geometry represented with 5 elements • 14 temperature nodes (states) External walls Windows Ground floor Roof Internal mass
- 36. System of differential equations 36 A = - x = 𝑑𝒙 𝑡 = 𝑨𝒕 𝒙 𝒕 + 𝑩 𝒕 𝒖 𝒕 𝑑𝑡 External walls Windows Ground floor Roof Internal mass
- 37. ϕhyd θgr ϕint θsky θe Heat transfer Radiative heat transfer c1rf c2rf c3rf c1ew c2ew c3ew c1gl c2gl c1im c2im c1gf c2gf c3gf Cint 37 x1rf hserf+h1rf -h1rf 0 0 0 0 0 0 0 0 0 0 0 0 x2rf f -h1rf h1rf+h2rf -h2rf 0 0 0 0 0 0 0 0 0 0 0 x3rf f 0 -h2rf h2rf+hsirf 0 0 -frf‧hriew 0 -frf‧hrigl 0 -frf‧hriim 0 0 -frf‧hrigf -rrf‧hcirf x1ew 0 0 0 hseew+h1e w -h1ew 0 0 0 0 0 0 0 0 0 x2ew F 0 0 0 -h1ew h1ew+h2ew -h2ew 0 0 0 0 0 0 0 0 x3ew F 0 0 -few‧hrirf 0 -h2ew h2ew+hsiew 0 -few‧hrigl 0 -few‧hriim 0 0 -few‧hrigf -rew‧hciew x1gl f 0 0 0 0 0 0 hsegl+h1gl -h1gl 0 0 0 0 0 0 x2gl F 0 0 -fgl‧hrirf 0 0 -fgl‧hriew -h1gl h1gl+hsigl 0 -fgl‧hriim 0 0 -fgl‧hrigf -rgl‧hcigl x1im F 0 0 0 0 0 0 0 0 h1im -h1im 0 0 0 0 x2im F 0 0 -fim‧hrirf 0 0 -fim‧hriew 0 -fim‧hrig -h1im h1im+hsiim 0 0 -fim‧hrigf -rim‧hciim x1gf f 0 0 0 0 0 0 0 0 0 0 hsegf+h1gf -h1gf 0 0 x2gf F 0 0 0 0 0 0 0 0 0 0 -h1gf h1gf+h2gf -h2gf 0 x3gf F 0 0 -fgf‧hrirf 0 0 -fgf‧hriew 0 -fgf‧hrig 0 -fgf‧hriim 0 -h2gf h2gf+hsigf -rgf‧hcigf xint f 0 0 hcirf 0 0 hciew 0 hcigl 0 hciim 0 0 hcigf x = Hve Htb ϕsol rrf‧hcirf + rew‧hciew + rgl‧hcigl + rim‧hciim + rgf‧hcigf + Htb System of differential equations 𝑑𝒙 𝑡 = 𝑨𝒕 𝒙 𝒕 + 𝑩 𝒕 𝒖 𝒕 𝑑𝑡 A = - External walls Windows Ground floor Roof Internal mass
- 38. Discretized state-space model 𝒙 𝑘 𝜃 = 𝑭 𝑘 𝜃 𝒙 𝑘−1 + 𝑮 𝑘 𝜃 𝒖 𝑘 where 𝑭 𝑘 𝜃 = 𝑒 𝑨 𝑡Δ𝑡 𝑮 𝑘 𝜃 = 𝑒 𝑨 𝑡Δ𝑡 −𝑰 𝑨 𝑡 −1 𝑩 𝑡 38 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction
- 39. Prediction The probabilistic part 39 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽
- 40. Stochastic state-space model 𝒙 𝑘 = 𝑭 𝑘 𝒙 𝑘−1 + 𝑮 𝑘 𝒖 𝑘−1 + 𝒩 0 𝑸 𝑘 𝒚 𝑘 = 𝑯 𝑘 𝒙 𝑘 + 𝒩 0 𝑹 𝑘 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Output y, with noise R Filtering 40
- 41. State augmentation to make also inputs stochastic 𝒙 𝑘 = 𝑭 𝑘 𝒙 𝑘−1 + 𝑮 𝑘 𝒖 𝑘−1 + 𝒩 0 𝑸 𝑘 𝒚 𝑘 = 𝑯 𝑘 𝒙 𝑘 + 𝒩 0 𝑹 𝑘 Where 𝒙 𝑘 = 𝒙 𝑘 𝜃 𝒙 𝑘 𝜙 𝑭 𝑘 = 𝑭 𝑘 𝜃 𝑮 𝑘 𝜙 0 𝟎 𝑰 0 0 0 0 where 𝑮 𝑘 𝜙 ⊂ 𝑮 𝑘 𝜃 𝑮 𝑘 = 𝑮 𝑘 𝜃 0 𝟎 0 0 1 𝑸 𝑘 = diag 𝝈 𝜃 𝝈 𝑘 𝜙 2 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Uncertainty in input 𝝈 𝑢 Augmented process noise Q 41
- 42. Case study Paper IV Comparison with IDA ICE • Replicates heat & temperatures patterns well 42 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction
- 43. Case study Comparison with IDA ICE • Replicates heat & temperatures patterns well • Fast: ~50 whole-year simulations per second 43 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction
- 44. Case study Comparison with IDA ICE • Replicates heat & temperatures patterns well • Fast: ~50 whole-year simulations per second • pre-processing • lumping • discretization scheme for time-varying matrices • floor area normalization, less precision required • linear algebra when possible (Eigen C++) • KF only on a subset of the system • automatic differentiation 44 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽 Prediction
- 45. Prediction Case study Paper VI: probabilistic calibration with actual buildings 45 𝜽 𝜋 𝜽 𝒚 𝒖 𝜋 𝒚 𝜽 𝒖 𝜋 𝜽
- 46. Case study Location of unknown parameters θ District heating Solar heat gains Internal gains Heating system Internal DHWC Space heating Ventilation Pipe network Internal mass Infiltration Manual venting AHU DHW Fint ggl Hhyd, θset Urf κrf Uew κew Ugf κgf qV;ahu Cinf Uwi Htb Fdhw Φdhwc Ψp Htot Ctot, Htr Hve Thermal bridges Roof Transmission Windows External walls Ground floorκim 46
- 47. Case study: Heat transfer coefficient for transmission (Htr) Htr Thermal bridges Roof Transmission Windows External walls Ground floor 47
- 48. Case study Probability density distribution 0.4 0.5 MLE HMC Prior W/K,mfl 2 Htr Thermal bridges Roof Transmission Windows External walls Ground floor 48
- 49. Case study Prior set at lowest level, pushed forward 0.4 0.5 MLE HMC Prior Uew 0.2 0.4 Ugl 1.0 1.5 2.0 Ugf 0.2 0.4 0.6 Htb 0.04 0.06 0.08 Urf 0.10 0.1 W/K,mfl 2 Htr Thermal bridges Roof Transmission Windows External walls Ground floor 49
- 50. Case study Evidence from data pushed back Uew 0.2 0.4 Ugl 1.0 1.5 2.0 Ugf 0.2 0.4 0.6 Htb 0.04 0.06 0.08 Urf 0.10 0.15 0.4 0.5 MLE HMC Prior W/K,mfl 2 Htr Thermal bridges Roof Transmission Windows External walls Ground floor 50
- 51. Case study Full picture Urf κrf Uew κew Ugf κgf Uwi Htb Thermal bridges Roof Transmission Windows External walls Ground floor Ventilation AHU District heating Solar heat gains Internal gains Heating system Internal DHWC Space heating Pipe network Internal mass Infiltration Manual venting DHW Fint ggl Hhyd, θset qV;ahu Cinf Fdhw Φdhwc Ψp Htot Ctot, Htr Hve κim 51
- 52. 52 Contribution to Knowledge A dynamic physics-based BEM that is detailed enough to provide actionable insights, yet directly calibratable Methods and tools to incorporate information from meteorological reanalysis, remote sensing and on-site metering data sources A fully probabilistic BEM calibration framework that make also inputs probabilistic, enables data and knowledge fusion and propagates uncertainty Framework BEM Data
- 53. Conclusions I – data • Reanalysis and satellite-based solar irradiance data are homogenous, consistent and provide variables that are seldom metered locally • Aerial surveying scales well, provides information on geometry and shading/sheltering • District-heating billing metering scales well, but still quality issues • Domestic-hot-water metering is not available in a systematic way, domestic-cold-water metering has potential as as a substitute • Indoor temperature readings carry much information, but scalable methods cannot relay on such data being available Q1. What information from meteorological reanalysis, remote sensing and on-site metering data sources can be utilized for BEM calibration in a scalable way? 53
- 54. Conclusions II – Building Energy Model • Proposed model fills a gap • More detailed and realistic than the grey-box models commonly used in literature • Yet, directly calibratable • Parameters are interpretable (which also allow incorporation of prior knowledge) • Automatic differentiation is essential for computing the likelihood in a scalable way Q2. What level of detail is required to obtain a BEM that can emulate reality sufficiently well to gain actionable insights, yet allow calibration in a scalable way? 54
- 55. Conclusions – framework • The uncertainty of the resulting estimates is acknowledged. But requires quantifying the uncertainty -> can be laborious and unfamiliar • Full Bayesian inference requires compute-intensive sampling. However, used BEM is well approximated with the much faster penalized optimization • The prior model provides the necessary regulation to identify the relatively complex model, while also enabling information and knowledge fusion • Kalman filtering enables data fusion on time-series level • State augmentation enable treating also inputs as probabilistic • more implicit knowledge ca be codified into explicit information • smarter learning as more weight is put on periods of lower uncertainty Q3. What are the advantages and disadvantages of using a fully probabilistic BEM calibration approach? 55
- 56. Future work • More information from aerial surveys (shading, sheltering, heat island) and building management systems • A seamless utilization of both metering- and model-based time-series • Improve the modelling of the indoor temperature (the between apartment variations) • Building archetype modeling approach to incorporate more information from databases (e.g. building codes) and allow information pooling between models 56
- 57. Thank you for listening! 57