Ojas Pradhan is a doctoral student in the Building Science and Engineering Group (BSEG) at Drexel University, Philadelphia, PA. Jin Wen, Ph.D. is a Professor
in the Department of Civil, Architectural, and Environmental Engineering department at Drexel University, Philadelphia, PA. Yimin Chen, Ph.D. is a Senior
Scientific Engineering Associate in the Building Technology & Urban Systems Division at Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA. Teresa
Wu, Ph.D. is a Professor of Industrial Engineering, School of Computing, Informatics, Decision Systems Engineering at Arizona State University, Tempe, AZ.
Zheng O’Neill, Ph.D. is an Associate Professor in the Department of Mechanical Engineering at Texas A&M University at College Station, TX.
Dynamic Bayesian Network for Fault Diagnosis
Ojas Pradhan Jin Wen, PhD Yimin Chen, PhD Teresa Wu, PhD Zheng O’Neill, PhD
A comparative study between using a dynamic Bayesian network (DBN) against using a static Bayesian network (BN) for building heating ventilating,
and air conditioning fault diagnosis (HVAC) is presented. Contrarily to a static BN, DBN method incorporates temporal dependencies between fault
nodes between timesteps using temporal conditional probabilities. This allows fault beliefs to accumulate over time and hence improves the diagnosis accuracy.
The two methods are evaluated using real building data obtained from a campus building. Overall, the DBN showed improved fault belief when diagnosing
and isolating faults across various components and sub-systems. Sensitivity tests on the temporal conditional probabilities for DBN showed that the model
Studies and field practices have shown that applying automated fault detection and diagnosis (AFDD) tools in
HVAC systems, followed up with service and corrections, can help reduce the energy waste, improve occupant comfort
and extend equipment lifecycle (Piette et al. 2001). Within the AFDD framework, the process of locating and isolating
the fault root causess has been challenging since a detailed and accurate reasoning of the HVAC system and its control
strategies is required (Zhao et al. 2015, 2017). Several inference and classification approaches have been developed and
used as a fault diagnosis tool in the field. Among them, Bayesian networks (BN) based on the probability inference
theorem that infers the fault causes based on a set of observations have been popular. The BN models have performed
well even when complete information about the system is not available (Mirnaghi et al. 2020).
Successfully implemented BNs for fault diagnosis for different HVAC components have been reported in existing
literature for both component-level and whole building fault diagnosis. For instance, Zhao et al. proposed a component-
level diagnostic BN for 28 different faults in air handling units (AHUs) in (Zhao et al. 2015, 2017), and for intelligent
chiller FDD in (Zhao et al. 2013). Similarly, Xiao et al. (2014) developed a BN based FDD strategy for diagnosis typical
VAV terminal unit faults. For whole building fault diagnosis, Chen et al. (2018) developed a BN model using expert and
physical knowledge using weather and schedule information-based pattern matching (WPM). Although the existing
studies demonstrate good potentials of BNs for both component-level and whole building fault diagnosis, the BN
structure model used are event-based, time-invariant models (i.e., information from the previous time steps are not
carried over to the next time step). Instead, a DBN model is more suitable for a continuous-time engineering system
such as a building HVAC system (Murphy 2002). The main advantage is that a DBN carries over past information
which allows fault belief to accumulate over time. Therefore, a DBN increases diagnosis accuracy by eliminating
measurement errors and only retain faults that are persistent over time.
Given the lack of a comprehensive comparison study between the conventional BN and a DBN, in this study, the
WPM-BN model developed by Chen et al. (2018) is cssonverted to a DBN for whole building fault diagnosis. Fault free
and artificially implemented fault data from a real campus building are used to evaluate the effectiveness of the DBN.
Dynamic Bayesian Network
Bayesian networks used for fault diagnosis are directed acyclic network in which the nodes represent the faults
and symptoms (evidences) from measurements and observations, and the arcs represent the direct probabilistic
dependencies among the connected nodes. The probability of a fault based on observed symptoms, defined as the
posterior probability, P(F|S) can be calculated using the Bayes’ theorem as (Murphy 2012):
Where, P(F) is the prior probability of a fault occurring, P(S|F) is the conditional probability of a symptom
occurring given the fault state, and P(S) is the observation of symptom states.
A DBN is an extension of the conventional static BN which can represent temporal relationships of the fault and
symptom nodes between different time steps. Figure 1 shows the difference between a BN and a DBN with one fault
and one symptom node for n-time steps. In a static BN, the probability of a fault node (Ft+1) only depends on the
corresponding symptom node (St+1), whereas, in a DBN, the probability of node Ft+1 depends on its symptom nodes
St+1 and its own values at the previous time step Ft.
Figure 1. Schematics of a static BN (left) and a dynamic BN (right)
The additional dependency on the fault node from the previous time step requires a temporal conditional
probability table (CPT) between P(Ft+1|F), to define the relationship. The temporal CPTs carry over posterior
probabilities from the previous to the current time step.
Similar to the faulty-symptom CPTs or the prior probability, temporal CPTs can be estimated either from historical
process data or from expert knowledge. Maximum likelihood estimation (MLE) and Bayesian estimation (BE) are some
of the techniques used to estimate the unknown probabilities (Amin et al. 2019). However, utilizing statistical techniques
to obtain the probability distributions is a major challenge for building system data since (i) ground truth data that
confirms the root fault causes of natural-occurring faults are hard to obtain, and (ii) even if the ground truth data exists
for a specific building, the probability distributions learned from data in that specific building system are usually not
scalable to other building systems (Chen et al. 2018). Hence, in this study, the temporal CPT are also developed using
expert knowledge and sensitivity analysis is performed to evaluate the impact of the temporal CPT values in the fault
The development of the DBN methodology is divided into seven sub-tasks. First, a dynamic baseline method is
developed to automatically generate a baseline for each incoming snapshot building system data. Pattern matching
method as described by Chen et al. (2017) is used to identify, from a historical baseline data pool, those building data
that have similar weather and schedule information. The purpose of this is to compare incoming snapshot data with
historical baseline data that are under similar weather and internal load conditions. Following this, the DBN structure
which includes the nodes for fault and evidence, and the causal relation between them based on expert knowledge is
developed. Various probability distributions for each fault node and evidence node, including the LEAK distribution is
calculated and assigned in the parameter model. Next, code to generate the evidence event is developed to compare the
incoming snapshot data with the baseline. An evidence event is classified to be abnormal if the incoming data is
significantly different from the baseline, i.e., is higher than the statistical threshold. Based on the judgment in this step,
the Bayesian inference is trigged, and the posterior probabilities of each fault node is calculated based on the Bayes’
theorem. Finally, the posterior probabilities are ranked, and the root fault is isolated based on pre-defined rules.
The DBN structure model is based on 13 fault nodes that represent faults in the whole building as described by
Chen et al. (2018). 15 evidence nodes that represent the observable fault symptoms are developed for the faults. The
evidence nodes are established from two sources: direct measurements and virtual measurements (combination of direct
measurements). To connect the fault nodes with the evidence nodes, causal relations based on expert knowledge are
developed for each fault case that indicate the probability set of evidence along with the severity level and direction
(positive or negative) of the evidence.
The method is evaluated using a campus building at Drexel University. This building is a seven-story, mixed use
commercial building that includes classrooms, laboratory space and offices. The HVAC system configuration consists
of one chiller, two steam-to-hot water heat exchange systems (for hot water and VAV reheat) and 3 AHUs. All the
HVAC equipment is controlled and monitored in a BAS through which faults can be implemented remotely.
14 faults were artificially implemented in the test building. Data were collected for the periods when the faults
were implemented. Data that represented baseline conditions were also collected. Both data were used to evaluate the
developed DBN. It was found that when applying static BN or DBN for fault diagnosis, both methods correctly
diagnosed 11 out of the 14 cases, i.e., identified the root causes of the faults. For two of the three reminding cases,
both methods ranked the implemented faults and some other faults as root causes. A closer manual inspection of the
data revealed that nature faults have occurred during these two cases and the ground thruth was unclear. For the other
reminding case, the implemented fault did not yield any symptom.
Although both methods perform similiarly, the major benefit of using a DBN is seen when analyzing the time
series plots for posterior probabilities of the fault nodes. For example, on 9/7/2016, a supply air temperature sensor
negative bias fault has been artificially implemented on AHU-2 in the building. According to the diagnosis results, the
fault belief (posterior probabilities) obtained for AHU2-SA-Temp-Bias-N node is stronger when using a DBN than a
static BN. Figure 2 presents the posterior probability of the top 3 ranked faults using a static BN and a DBN,
respectively. The AHU2-SA-Temp-Bias-N fault node (shown in blue) is observed to be consistently high inside the fault
window when using a DBN. Since a DBN allows evidence to accumulate over time, whereas only evidence from a single
time step is considered for inference in a static BN, the fault belief is often limited to a lower value when using a static
BN. Similar trends are seen across rest of the fault cases evaluated in this section.
Figure 2. Time series posterior probability result using a static and dynamic BN for top three fault nodes (2016/09/07)
A parameter sensitivity test is performed to evaluate the impact of the temporal conditional probabilities on the
diagnosis accuracy. It is seen that the posterior probability values of some fault nodes change, however, the fault isolation
accuracy is not affected and does not change the fault ranking. Therefore, the developed DBN framework is robust
against the change in temporal conditional probabilities and can successfully diagnose faults with a stronger fault belief
than a static BN.
Amin M.T., F. Khan and S. Imtiaz. 2019. Fault detection and pathway analysis using a dynamic Bayesian network, Chemical
Engineering Science. 195: 777–790
Chen Y. and J. Wen. 2017. A Whole Building Fault Detection Using Weather Based Pattern Matching and Feature Based
PCA Method. IEEE International Conference on Big Data (BIGDATA).
Chen Y., J. Wen, T. Chen and O. Pradhan. 2018. Bayesian Networks for Whole Building Level Fault Diagnosis and Isolation.
5th International High Performance Buildings Conference at Purdue.
Mirnaghi M.S., and F. Haghighat. 2020. Fault detection and diagnosis of large-scale HVAC systems in buildings using data-
driven methods: A comprehensive review, Energy and Buildings.
Murphy, K.P. 2002. Dynamic Bayesian Networks: Representation, Inference and Learning.
Murphy, K.P. 2012. Machine Learning: A Probabilistic Perspective, Chapter 2, Probability. MIT press.
Piette M.A., S.K. Kinney and P. Haves. 2001. Analysis of an information monitoring and diagnostic system to improve
building operations, Energy and Buildings.
Xiao, F., Y. Zhao , J. Wen and S. Wang. 2014. Bayesian network based FDD strategy for variable air volume terminals,
Automation in Construction.
Zhao Y., F. Xiao and S. Wang. 2013. An intelligent chiller fault detection and diagnosis methodology using Bayesian belief
network, Energy and Buildings.
Zhao Y., J. Wen and S. Wang. 2017. Diagnostic Bayesian networks for diagnosing air handling units faults - Part II: Faults in
coils and sensors, Applied Thermal Engineering. 90: 145–157.
Zhao Y., J. Wen, F. Xiao, X. Yang and S. Wang. 2015. Diagnostic Bayesian networks for diagnosing air handling units faults
– Part I: Faults in dampers, fans, filters and sensors, Applied Thermal Engineering. 111: 1272–1286.