0
Research Papers

Detection of Faults and Drifts in the Energy Performance of a Building Using Bayesian Networks

[+] Author and Article Information
David Bigaud

Laboratoire Angevin de Recherche en
Ingénierie des Systèmes (LARIS),
University of Angers,
62 Avenue Notre Dame du Lac,
Angers 49000, France
e-mail: david.bigaud@univ-angers.fr

Abderafi Charki

Laboratoire Angevin de Recherche en
Ingénierie des Systèmes (LARIS),
University of Angers,
62 Avenue Notre Dame du Lac,
Angers 49000, France
e-mail: abderafi.charki@univ-angers.fr

Antoine Caucheteux

Centre d'Etudes et d'expertise sur les Risques,
l'Environnement, la Mobilité et
l'Aménagement (CEREMA),
23 Avenue de l'Amiral Chauvin BP 20069,
Les Ponts-de-Cé 49136, France
e-mail: antoine.Caucheteux@cerema.fr

Fally Titikpina

Laboratoire Angevin de Recherche en
Ingénierie des Systèmes (LARIS),
University of Angers,
62 Avenue Notre Dame du Lac,
Angers 49000, France
e-mail: fally.titikpina@univ-angers.fr

Teodor Tiplica

Laboratoire Angevin de Recherche en
Ingénierie des Systèmes (LARIS),
University of Angers,
62 avenue Notre Dame du Lac,
Angers 49000, France
e-mail: teodor.tiplica@univ-angers.fr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 3, 2018; final manuscript received May 27, 2019; published online June 20, 2019. Assoc. Editor: Umesh Vaidya.

J. Dyn. Sys., Meas., Control 141(10), 101011 (Jun 20, 2019) (22 pages) Paper No: DS-18-1056; doi: 10.1115/1.4043922 History: Received February 03, 2018; Revised May 27, 2019

Despite improved commissioning practices, malfunctions or degradation of building systems still contribute to increase up to 20% the energy consumption. During operation and maintenance stage, project and building technical managers need appropriate methods for the detection and diagnosis of faults and drifts of energy performances in order to establish effective preventive maintenance strategies. This paper proposes a hybrid and multilevel fault detections and diagnosis (FDD) tool dedicated to the identification and prioritization of corrective maintenance actions helping to ensure the energy performance of buildings. For this purpose, we use dynamic Bayesian networks (DBN) to monitor the energy consumption and detect malfunctions of building equipment and systems by considering both measured occupancy and the weather conditions (number of persons on site, temperature, relative humidity (RH), etc.). The hybrid FDD approach developed makes possible the use of both measured and simulated data. The training of the Bayesian network for functional operating mode relies on on-site measurements. As far as dysfunctional operating modes are concerned, they rely mainly on knowledge extracted from dynamic thermal analysis simulating various operational faults and drifts. The methodology is applied to a real building and demonstrates the way in which the prioritization of most probable causes can be set for a fault affecting energy performance. The results have been obtained for a variety of simulated situations with faults deliberately injected, such as increase in heating preset temperature and deterioration of the transmission coefficient of the building's glazing. The limitations of the methodology are discussed and are translated in terms of the ability to optimize the experiment design, control period, or threshold adjustment on the control charts used.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

de Wilde, P. , 2014, “ The Gap Between Predicted and Measured Energy Performance of Buildings: A Framework for Investigation,” Autom. Constr., 41, pp. 40–49. [CrossRef]
van Dronkelaar, C. , Dowson, M. , Spataru, C. , and Mumovic, D. , 2016, “ A Review of the Regulatory Energy Performance Gap and Its Underlying Causes in Non-Domestic Buildings,” Front. Mech. Eng., 1, p. 17. https://www.researchgate.net/publication/290478576_A_Review_of_the_Regulatory_Energy_Performance_Gap_and_Its_Underlying_Causes_in_Non-domestic_Buildings
Titikpina, F. , Caucheteux, A. , Charki, A. , and Bigaud, A. , 2015, “ Uncertainty Assessment in Building Energy Performance With a Simplified Model,” Int. J. Metrol. Qual. Eng., 6(3), p. 308. [CrossRef]
Katipamula, S. , and Brambley, M. R. , 2005, “ Review Article: Methods for Fault Detection, Diagnostics, and Prognostics for Building Systems—Part I: A Review,” HVACR Res., 11(1), pp. 3–25. [CrossRef]
Jing, R. , Wang, M. , Zhang, R. , Li, N. , and Zhao, Y. , 2017, “ A Study on Energy Performance of 30 Commercial Office Buildings in Hong Kong,” Energy Build., 144, pp. 117–128. [CrossRef]
Bynum, J. D. , Claridge, D. E. , and Curtin, J. M. , 2012, “ Development and Testing of an Automated Building Commissioning Analysis Tool (ABCAT),” Energy Build., 55, pp. 607–617. [CrossRef]
Wang, L. , 2012, “ Modeling and Simulation of HVAC Faulty Operations and Performance Degradation Due to Maintenance Issues,” Asia Conference of International Building Performance Simulation Association (ASIM'2012), Shangai, China, Nov. 27–29, p. 8. https://www.researchgate.net/publication/258246690_Modeling_and_Simulation_of_HVAC_Faulty_Operations_and_Performance_Degradation_due_to_Maintenance_Issues
Verhelst, J. , van Ham, G. , Saelens, D. , and Hensen, L. , 2017, “ Model Selection for Continuous Commissioning of HVAC-Systems in Office Buildings: A Review,” Renewable Sustainable Energy Rev., 76, pp. 673–686. [CrossRef]
Yu, Y. B. , Woradechjumroen, D. , and Yu, D. H. , 2014, “ A Review of Fault Detection and Diagnosis Methodologies on Air-Handling Units,” Energy Build., 82, pp. 550–562. [CrossRef]
Zhao, Y. , Wang, S. W. , and Xiao, F. , 2013, “ A Statistical Fault Detection and Diagnosis Method for Centrifugal Chillers Based on Exponentially-Weighted Moving Average Control Charts and Support Vector Regression,” Appl. Therm. Eng., 51(1–2), pp. 560–572. [CrossRef]
Verbert, K. , Babuška, R. , and De Schutter, B. , 2017, “ Combining Knowledge and Historical Data for System-Level Fault Diagnosis of HVAC Systems,” Eng. Appl. Artif. Intell., 59, pp. 260–273. [CrossRef]
Dong, B. , O'Neill, Z. , and Li, Z. , 2014, “ A BIM-Enabled Information Infrastructure for Building Energy Fault Detection and Diagnostics,” Autom. Constr., 44, pp. 197–211. [CrossRef]
Wall, J. , and Guo, Y. , 2018, “ RP1026: Evaluation of Next-Generation Automated Fault Detection & Diagnosis (FDD) Tools for Commercial Building Energy Efficiency—Part I: FDD Case Studies in Australia,” Low Carbon Living, CRC Press, Boca Raton, FL, p. 66.
Abdollahi, A. , Pattipati, K. R. , Kodali, A. , Singh, S. , Zhang, S. , and Luh, P. B. , 2016, “ Probabilistic Graphical Models for Fault Diagnosis in Complex Systems,” Principles of Performance Reliability Modeling and Evaluation—Essays in Honor of Kishor Trivedi on His 70th Birthday ( Springer Series in Reliability Engineering), L. Fiondella and A. Puliafito eds., Springer, Berlin, pp. 109–139.
Hao, J. , Kang, J. , Li, J. , and Zhao, Z. , 2012, “ A Physical Model Based Research for Fault Diagnosis of Gear Crack,” International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering, Chengdu, China, June 15–18, pp. 572–575.
Schein, J. , Bushby, S. T. , Castro, N. S. , and House, J. M. , 2006, “ A Rule-Based Fault Detection Method for Air Handling Units,” Energy Build., 38(12), pp. 1485–1492. [CrossRef]
Cai, B. , Huang, L. , and Xie, M. , 2017, “ Bayesian Networks in Fault Diagnosis,” IEEE Trans. Ind. Inf., 13(5), pp. 2227–2240. [CrossRef]
Afram, A. , Janabi-Sharifi, F. , Fung, A. S. , and Raahemifar, K. , 2017, “ Artificial Neural Network (ANN) Based Model Predictive Control (MPC) and Optimization of HVAC Systems: A State of the Art Review and Case Study of a Residential HVAC System,” Energy Build., 141, pp. 96–113. [CrossRef]
Li, G. , and Hu, Y. , 2019, “ An Enhanced PCA-Based Chiller Sensor Fault Detection Method Using Ensemble Empirical Mode Decomposition Based Denoising,” Energy Build., 183, pp. 311–324. [CrossRef]
Beghi, A. , Cecchinato, L. , Corazzol, C. , Rampazzo, M. , Simmini, F. , and Susto, G. A. , 2014, “ A One-Class SVM Based Tool for Machine Learning Novelty Detection in HVAC Chiller Systems,” IFAC Proc. Vol., 47(3), pp. 1953–1958. [CrossRef]
van Every, P. M. , Rodriguez, M. , Jones, C. B. , Mammoli, A. A. , and Martínez-Ramón, M. , 2017, “ Advanced Detection of HVAC Faults Using Unsupervised SVM Novelty Detection and Gaussian Process Models,” Energy Build., 149, pp. 216–224. [CrossRef]
He, S. , Zhiwei, W. , Zhanwei, W. , Xiaowei, G. , and Zengfeng, Y. , 2016, “ Fault Detection and Diagnosis of Chiller Using Bayesian Network Classifier With Probabilistic Boundary,” Appl. Therm. Eng., 107, pp. 37–47. [CrossRef]
Du, Z. , and Jin, X. , 2008, “ Multiple Faults Diagnosis for Sensors in Air Handling Unit Using Fisher Discriminant Analysis,” Energy Convers. Manage., 49(12), pp. 3654–3665. [CrossRef]
Kim, W. , and Katipamula, S. , 2018, “ A Review of Fault Detection and Diagnostics Methods for Building Systems,” Sci. Technol. Built Environ., 24(1), pp. 3–21. [CrossRef]
Uusitalo, L. , 2007, “ Advantages and Challenges of Bayesian Networks in Environmental Modelling,” Ecol. Modell., 203(3–4), pp. 312–318. [CrossRef]
Taal, A. , Itard, L. , and Zeiler, W. , 2018, “ A Reference Architecture for the Integration of Automated Energy Performance Fault Diagnosis Into HVAC Systems,” Energy Build., 179(15), pp. 144–155. [CrossRef]
Wang, Z. , Wang, Z. , Gu, X. , He, S. , and Yan, Z. , 2018, “ Feature Selection Based on Bayesian Network for Chiller Fault Diagnosis From the Perspective of Field Applications,” Appl. Therm. Eng., 129(25), pp. 674–683.
Zhao, Y. , Wen, J. , and Wang, S.-W. , 2015, “ Diagnostic Bayesian Networks for Diagnosing Air Handling Units Faults—Part II: Faults in Coils and Sensors,” Appl. Therm. Eng., 90(5), pp. 145–157. [CrossRef]
Zhao, Y. , Wen, J. , Xiao, F. , Yang, X. , and Wang, S.-W. , 2017, “ Diagnostic Bayesian Networks for Diagnosing Air Handling Units Faults—Part I: Faults in Dampers, Fans, Filters and Sensors,” Appl. Therm. Eng., 111(25), pp. 1272–1286. [CrossRef]
Cai, B. , Liu, Y. , Fan, Q. , Zhang, Y. , Liu, Z. , Yu, S. , and Ji, R. , 2014, “ Multi-Source Information Fusion Based Fault Diagnosis of Ground-Source Heat Pump Using Bayesian Network,” Appl. Energy, 114, pp. 1–9. [CrossRef]
Marvin, H. J. , Bouzembrak, Y. , Janssen, E. M. , van der Zande, M. , Murphy, F. , Sheehan, B. , Mullins, M. , and Bouwmeester, H. , 2017, “ Application of Bayesian Networks for Hazard Ranking of Nanomaterials to Support Human Health Risk Assessment,” Nanotoxicology, 11(1), pp. 123–133. [CrossRef] [PubMed]
Millán, E. , Descalço, L. , Castillo, G. , Oliveira, P. , and Diogo, S. , 2013, “ Using Bayesian Networks to Improve Knowledge Assessment,” Comput. Educ., 60(1), pp. 436–447. [CrossRef]
Shute, V. , and Wang, L. , 2016, “ Assessing and Supporting Hard-to-Measure Constructs in Video Games,” The Wiley Handbook of Cognition and Assessment: Frameworks, Methodologies, and Applications, Wiley, Hoboken, NJ, pp. 535–562.
Lyons, D. M. , Arkin, R. C. , Jiang, S. , O'Brien, M. , Tang, F. , and Tang, P. , 2017, “ Performance Verification for Robot Missions in Uncertain Environments,” Rob. Auton. Syst., 98, pp. 89–104. [CrossRef]
Ju, Z. , Ji, X. , Li, J. , and Liu, H. , 2017, “ An Integrative Framework of Human Hand Gesture Segmentation for Human-Robot Interaction,” IEEE Syst. J., 11(3), pp. 1326–1336. [CrossRef]
Slanzi, D. , and Poli, I. , 2014, “ Evolutionary Bayesian Network Design for High Dimensional Experiments,” Chemom. Intell. Lab. Syst., 135(15), pp. 172–182. [CrossRef]
Taylor, D. , Biedermann, A. , Hicks, T. , and Champod, C. , 2018, “ A Template for Constructing Bayesian Networks in Forensic Biology Cases When Considering Activity Level Propositions,” Forensic Sci. Int.: Genet., 3, pp. 136–146. [CrossRef]
Szkuta, B. , Ballantyne, K. N. , Kokshoorn, B. , and van Oorscho, R. A. H. , 2018, “ Transfer and Persistence of Non-Self DNA on Hands Over Time: Using Empirical Data to Evaluate DNA Evidence Given Activity Level Propositions,” Forensic Sci. Int.: Genet., 33, pp. 84–97. [CrossRef] [PubMed]
Bae, S.-C. , and Lee, Y. H. , 2018, “ Comparative Efficacy and Tolerability of Monotherapy With Leflunomide or Tacrolimus for the Treatment of Rheumatoid Arthritis: A Bayesian Network Meta-Analysis of Randomized Controlled Trials,” Clin. Rheumatol., 37(2), pp. 323–330. [CrossRef] [PubMed]
Chiremsel, Z. , Nait Said, R. , and Chiremsel, R. , 2016, “ Probabilistic Fault Diagnosis of Safety Instrumented Systems Based on Fault Tree Analysis and Bayesian Network,” J. Failure Anal. Prev., 16(5), pp. 747–760. [CrossRef]
Sousa, H. S. , Prieto-Castrillo, F. , Matos, J. C. , Branco, J. M. , and Lourenço, P. B. , 2018, “ Combination of Expert Decision and Learned Based Bayesian Networks for Multi-Scale Mechanical Analysis of Timber Elements,” Expert Syst. Appl., 93(1), pp. 156–168. [CrossRef]
Bishop, C. M. , 2006, Pattern Recognition and Machine Learning, Springer, Berlin, p. 738.
Dondelinger, F. , Lèbre, S. , and Husmeier, D. , 2013, “ Non-Homogeneous Dynamic Bayesian Networks With Bayesian Regularization for Inferring Gene Regulatory Networks With Gradually Time-Varying Structure,” Mach. Learn., 90(2), pp. 191–230. [CrossRef]
Kwisthout, J. , 2018, “ Approximate Inference in Bayesian Networks: Parameterized Complexity Results,” Int. J. Approximate Reasoning, 93, pp. 119–131. [CrossRef]
Wu, P. P.-Y. , Julian Caley, M. , Kendrick, G. A. , McMahon, K. , and Mengersen, K. , 2018, “ Dynamic Bayesian Network Inferencing for Non-Homogeneous Complex Systems,” J. R. Stat. Soc. Ser. C: Appl. Stat., 67(2), pp. 417–434. [CrossRef]
Black, A. , Korb, K. B. , and Nicholson, A. E. , 2014, “ Intrinsic Learning of Dynamic Bayesian Networks,” PRICAI 2014: Trends in Artificial Intelligence ( Lecture Notes in Computer Science, Vol. 8862), Springer, Berlin, pp. 256–269.
Hu, M. , Chen, H. , Shen, L. , Li, G. , Guo, Y. , Li, H. , Li, J. , and Hu, W. , 2018, “ A Machine Learning Bayesian Network for Refrigerant Charge Faults of Variable Refrigerant Flow Air Conditioning System,” Energy Build., 158, pp. 668–676. [CrossRef]
Lin, S. , Chen, X. , and Wang, Q. , 2018, “ Fault Diagnosis Model Based on Bayesian Network Considering Information Uncertainty and Its Application in Traction Power Supply System,” IEEJ Trans. Electr. Electron. Eng., 13(5), pp. 671–680. [CrossRef]
Verron, S. , 2007, “ Diagnosis and Monitoring of Complex Processes Via Bayesian Networks,” Ph.D. thesis, University of Angers, Angers, France.
Pillet, M. , Boukar, A. , Pairel, E. , Rizzon, B. , Boudaoud, N. , and Cherfi, Z. , 2013, “ Multivariate SPC for Total Inertial Tolerancing,” Int. J. Metrol. Qual. Eng., 4(3), pp. 169–175. [CrossRef]
Caucheteux, A. , Sabar, A. E. , and Boucher, V. , 2013, “ Occupancy Measurement in Building: A Literature Review, Application on an Energy Efficiency Research Demonstration Building,” Int. J. Metrol. Qual. Eng., 4(2), pp. 135–144. [CrossRef]
ASHRAE, 2014, “ ASHRAE Guideline 14 for Measurement of Energy and Demand Savings,” American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, GA.
EVO, 2012, “ International Performance Measurement and Verification Protocol: Concepts and Options for Determining Energy and Water Savings,” Efficiency Valuation Organization, Toronto, ON, Canada, Report No. EVO 10000 − 1:2012.
WMO, 2008, Guide to Meteorological Instruments and Methods of Observation, 7th ed., World Meteorological Organization, Geneva, Switzerland.
ASHRAE, 2017, “ Thermal Environmental Conditions for Human Occupancy,” American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, GA, Standard No. 55.
Caucheteux, A. , Gautier, A. , and Lahrech, R. , 2016, “ A Metamodel-Based Methodology for an Energy Savings Uncertainty Assessment of Building Retrofitting,” Int. J. Metrol. Qual. Eng., 7(4), p. 402. [CrossRef]
Calì, D. , Matthes, P. , Huchtemann, K. , Streblow, R. , and Müller, D. , 2015, “ CO2 Based Occupancy Detection Algorithm: Experimental Analysis and Validation for Office and Residential Buildings,” Building Environ., 86, pp. 39–49. [CrossRef]
Ansanay-Alex, G. , Abdelouadoud, Y. , and Schetelat, P. , 2016, “ Statistical and Stochastic Modelling of French Households and Their Energy Consuming Activities,” 12th REHVA World Congress-CLIMA, Aalborg, Denmark, May 22–25, Paper No. 385. https://www.researchgate.net/publication/301684851_Statistical_and_Stochastic_Modelling_of_French_Households_and_Their_Energy_Consuming_Activities
Yan, D. , O'Brien, W. , Hong, T. , Feng, X. , Gunay, H. B. , Tahmasebi, F. , and Mahdavi, A. , 2015, “ Occupant Behavior Modeling for Building Performance Simulation: Current State and Future Challenges,” Energy Build., 107, pp. 264–278. [CrossRef]
Murphy, K. , 2001, “ The Bayesian Network Toolbox for Matlab,” University of California, Berkeley, CA, accessed Dec. 18, 2018, https://www.cs.ubc.ca/~murphyk/Papers/bnt.pdf
Lauritzen, S. L. , 1992, “ Propagation of Probabilities, Means and Variances in Mixed Graphical Association Models,” J. Am. Stat. Assoc., 87(420), pp. 1098–1108. [CrossRef]
Lauritzen, S. L. , and Jensen, F. , 2001, “ Stable Local Computation With Conditional Gaussian Distributions,” Stat. Comput., 11(2), pp. 191–203. [CrossRef]
Sachs, K. , Perez, O. , Pe'er, D. , Lauffenburger, D. A. , and Nolan, G. P. , 2005, “ Causal Protein-Signaling Networks Derived From Multiparameter Single-Cell Data,” Science, 308(5721), pp. 523–529. [CrossRef] [PubMed]
Claeskens, G. , and Hjort, N. L. , 2008, Model Selection and Model Averaging (Part of Cambridge Series in Statistical and Probabilistic Mathematics), Cambridge Press, Cambridge, UK, p. 332.
Ghahramani, Z. , 2001, “ An Introduction to Hidden Markov Models and Bayesian Networks,” Int. J. Pattern Recognit. Artif. Intell., 15(1), pp. 9–42. [CrossRef]
Vlachopoulou, M. , Chin, G. , Fulle, J. , and Lu, S. , 2014, “ Aggregated Residential Load Modeling Using Dynamic Bayesian Networks,” IEEE International Conference on Smart Grid Communications (SmartGridComm), Venice, Italy, Nov. 3–6, pp. 818–823.
Ghahramani, A. , Tang, C. , Yang, Z. , and Becerik-Gerber, B. , 2015, “ A Study of Time-Dependent Variations in Personal Thermal Comfort Via a Dynamic Bayesian Network,” First International Symposium on Sustainable Human-Building Ecosystems, Pittsburgh, PA, Oct. 5–6, pp. 99–107. https://www.researchgate.net/publication/283083710_A_Study_of_Time-Dependent_Variations_in_Personal_Thermal_Comfort_via_a_Dynamic_Bayesian_Network
Markovic, R. , Wolf, S. , Cao, J. , Spinnräker, E. , Wölki, D. , Frisch, J. , and van Treeck, C. , 2017, “ Comparison of Different Classification Algorithms for the Detection of User's Interaction With Windows in Office Buildings,” International Conference on Future Buildings and Districts—Energy Efficiency From Nano to Urban Scale (CISBAT), Lausanne, Switzerland, Sept. 6–8, pp. 337–342. http://orbit.dtu.dk/ws/files/139843510/1_s2.0_S1876610217329375_main.pdf
Cai, B. , Liu, Y. , Ma, Y. , Huang, L. , and Liu, Z. , 2015, “ A Framework for the Reliability Evaluation of Grid-Connected Photovoltaic Systems in the Presence of Intermittent Faults,” Energy, 93, pp. 1308–1320. [CrossRef]
Hastie, T. , Efron, B. , 2012, “ Lars: Least Angle Regression, Lasso and Forward Stage Wise. R Package Version 1.1,” Stanford, CA, accessed June 8, 2019, https://cran.r-project.org/web/packages/lars/index.html

Figures

Grahic Jump Location
Fig. 1

The Markov Blanket. The shaded nodes (parents, co-parents, children nodes) are inside the Markov Blanket of node “A.” The white ones are outside the blanket.

Grahic Jump Location
Fig. 2

Three stages of the proposed approach: (a) modeling principle for functional mode—inductive stage to establish “baseline” of behavior in functional (nonfaulty) mode, (b) modeling principle for dysfunctional mode—inductive stage to characterize effects of faults, and (c) modeling principle for dysfunctional mode—deductive stage to identify and hierarchize causes of performance drift

Grahic Jump Location
Fig. 3

Modeling using Sketchup 3D® of CEREMA building

Grahic Jump Location
Fig. 4

Positioning of different sensors installed by CEREMA

Grahic Jump Location
Fig. 5

Comparisons between the results obtained from DES model and actual data: (a) Variation of the required HQ (for the whole surface area of 105 m²) as a function of the difference between indoor and OTs for both simulated and actual data, (b) variation of the difference between indoor and OTs as a function of time, and (c) variation of the required daily HQ (for the whole surface area of 105 m²) as a function of time

Grahic Jump Location
Fig. 6

Bayesian network for operational mode solely for Office #5 (with hourly measurements over a period of a year)

Grahic Jump Location
Fig. 7

Bayesian network for operational mode for whole floor (with hourly measurements over a period of a year)

Grahic Jump Location
Fig. 8

Bayesian network for operational mode for whole floor (using hourly measurements during period of heating only)

Grahic Jump Location
Fig. 9

Bayesian network for whole floor (using daily measurements over a period of a year). Implementation of a T² Hotelling multivariate control chart to detect drifts of the energy needs is also illustrated.

Grahic Jump Location
Fig. 10

The Bayesian network for whole floor (using daily measurements over a period of a year) with continuous nodes

Grahic Jump Location
Fig. 11

Illustrations of a dynamic Bayesian network with two different levels of significance: (a) Relationships between variables at (t − 1) and (t) for a level of significance p-value < 0.01 and (b) relationships between variables at (t − 1) and (t) for a level of significance p-value < 0.001

Grahic Jump Location
Fig. 12

Energy needs (or HQ) of office #6 (HQ_office#6)

Grahic Jump Location
Fig. 13

Simulation of consumption deviations for an increase in preset temperature (case_1)

Grahic Jump Location
Fig. 14

Simulation of consumption deviations for a deterioration in glazing transmission coefficient (case_2)

Grahic Jump Location
Fig. 15

Probability of being under SC after an increase in the preset temperature (case_1) or a decrease in the glazing transmission coefficient (case_2)

Grahic Jump Location
Fig. 16

Statistical distributions of detection times after an increase in the preset temperature (case_1) or a decrease in the glazing transmission coefficient (case_2)

Grahic Jump Location
Fig. 17

Influence of the preset temperature drift amplitude on the probability of process being under SC

Grahic Jump Location
Fig. 18

Principle of the fault characterization moving time-window

Grahic Jump Location
Fig. 19

Simulations of consumption deviations for the case with two simultaneous faults (IT and Uwi)

Grahic Jump Location
Fig. 20

Simulations of consumption deviations for the case with two simultaneous faults (IT and Uwi)

Grahic Jump Location
Fig. 21

Probability of process being under SC for a case with two faults appearing simultaneously (IT and Uwi)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In