A method for the detection of abnormal behavior in HVAC systems is presented. The method combines deterministic subspace identification for each zone independently to create a system model that produces the anticipated zone’s temperature and the sequential test CUSUM algorithm to detect drifts of the rate of change of the difference between the real and the anticipated measurements. Simulation results regarding the detection of infiltration heat losses and the detection of exogenous heat gains such as fire demonstrate the effectiveness of the proposed method.
Energy consumption control in buildings remains nowadays one of the most important issues in the total energy savings. About 40% of the total energy consumption is due to energy requirements for buildings and this percentage tends to be increasing from about 0.5% to 5% per year [
As the wireless sensor networks’ (WSNs) technology has been improved and widely applied, it has been also utilized in the HVAC systems contributing to more sophisticated control. A promising and effective way of implementing a HVAC system in a building area with respect to improved energy control is the multizone model approach. In such a model, each area of a heating/cooling space such as room, corridor, or others is treated as a single zone. With the use of a wireless node installed in each zone, a wireless network of scattered nodes (WSN) could be formed where each node would employ a variety of sensors for temperature, light, occupancy, and so forth. An appropriate utilization of a WSN would significantly contribute to the control of the energy consumption of the building. WSNs are easily installed and deployed allowing cost effective retrofits. The HVAC application requires a sensor network to process data cooperatively and combines information from multiple sources. In traditional centralized systems, measurements collected by sensor nodes are relayed to a central unit for further processing. In the decentralized or distributed systems, all wireless sensor nodes are autonomous and they perform their assigned task locally utilizing information from neighboring nodes.
A hybrid scheme of operation is used in the proposed algorithm. In a first phase, called “training phase,” the nodes installed in each room (zone) of the multizone system send their readings to a central computing unit. These readings are the measurements of the zone temperature as well as the current power of the heater that exists in each zone. Upon reception, the central unit arranges the received data to an input-output form in order to run a subspace identification (SID) process for each zone. The inputs, for each zone SID process, are the temperature measurements of its adjacent zones as well as the power profile of the heater of the zone. The output of the SID process is the zone’s temperature itself. The central unit identifies a linear state space system for each zone and its parameters are communicated back to the wireless sensor node that monitors the zone. After this point, the system enters in the second phase (detection phase) and the operation is turned to a decentralized mode. Each node collects temperature measurements by its surrounding sensor nodes and power measurements of the zone’s heater. Based on these measurements the identified state space subsystem predicts the temperature of the zone. A suitable detection algorithm is then applied to detect possible deviations of the predicted values from real measurements. Deviations may be due to high infiltration heat gains or other exogenous factors such as fire. The detection phase is spit into cycles and it utilizes the CUSUM algorithm to detect possible deviations from the normal operation.
The rest of the paper is organized as follows: Section
Several methods have been proposed for the detection of abnormal energy consumption or fault detection diagnosis (FDD) in HVAC systems and they are divided in two main categories: the statistical methods and the computational approaches. The statistical methods are mainly based on fault detection algorithms that compare data under normal operation conditions with the data under current conditions in order to detect any abnormal behavior. The authors in [
In the category of the computational approaches earlier works have introduced computer simulations as embedded mechanisms within the control methods of energy consumption of HVAC systems. In [
As it has been already mentioned, we consider a multizone system with a WSN deployed consisting of temperature sensor nodes. Each wireless node measures the temperature of the zone it covers and conveys this information to its neighboring nodes. Additionally, the nodes have the functionality to detect abnormal operation, for example, slower temperature rising than the anticipated one due to open windows during winter, or high temperature values due to the onset of a fire, and signal it to an operation center. The detection mechanism relies on knowledge of the surrounding zones’ temperatures and the dynamics of the covered zone. The dynamics of each zone are learned during a training period using the subspace identification procedure presented in the next subsection.
In general, the assumption is made that each zone is represented by a discrete model of the form
As it has already been stated, one of the most promising algorithms to sequentially detect the change is the CUSUM test. Gombay and Serban [
The test statistic
In what follows the assumption is made that all measurements
Drift of test statistic for
The only parameter needed to run the detection algorithm is
Each zone is treated separately and is represented by a discrete time, linear, time invariant, and state space model. That is,
Following the notation and the derivation in [
One method [
As it has been already stated deterministic subspace system identification and the CUSUM algorithm are the key ingredients in the proposed algorithm, which undergoes two phases: the training and the detection phase.
During the first phase (training) all the nodes in the structure report their measurements to a central computing system. These measurements consist of the temperature of the zone and the current power of a heater, if the sensor node is in charge of a heated zone, or only the temperature if the sensor node monitors an area immaterial to the detection process but relevant to other zones, that is, the exterior of a building. The training phase should be performed only once but under controlled conditions, for example, no extra sources of heating and closed windows. Moreover, the length of this period should be quite large in order that several variations in the input signals to excite the modes of the system are present. In the simulation part a training period of 24 h, that is, 86400 samples with sampling period 1 sec are considered. After receiving all the measurements, the central system arranges them to input-output data for each zone. For example, in the case of a zone named
Training phase steps of the algorithm.
The detection phase is split into cycles of possibly unequal lengths. In the beginning of each cycle the value
Note that a positive drift of the test statistic (
Detection phase steps of the algorithm.
In this paper a multizone system consisting of a squared arrangement of rooms (zones) is simulated where each room (zone) is equipped with a wireless sensor node as shown in Figure
Multizone model.
In Figure
Empirical estimation of
Isolating a single zone of the multizone system its dynamics can be expressed using a lumped capacity model.
The assumption is made that the zone temperature distribution is uniform and therefore a single sensor is capable of providing the zone temperature values (Figure
Single zone model consisting of a heat source and a wireless node.
The parameters used in the previous equations are as follows:
The zone model parameter values are taken from [
Equations (
The discrete version of the model, with sampling period
Note that for the multizone system of Figure
For the deterministic subsystem identification 86400 samples are used with sampling period
Training and testing parameters for outer temperature model and heat gain.
Walter’s model | Heat gain | |||
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Phase |
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Training | 13 | 2 | 7 | 600 |
Testing | 16 | 1 | 6 | 700 |
Training and testing zones’ target temperature.
Target temperatures | |||||||||
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Zone | I | II | III | IV | V | VI | VII | VIII | IX |
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Training | 16 | 18 | 13 | 15 | 14 | 13 | 12 | 16 | 14 |
Testing | 17 | 20 | 17 | 17 | 17 | 14 | 18 | 19 | 21 |
Having collected the data over the period of 24 hours, the measurements of the zones’ temperature, the outer temperature, and the heat gains of each zone are arranged into input-output data for the subsystem identification process. For example, for zone I, the outer temperature, the heating gain of zone I, and the temperatures of zones II and IV are the input data to the identification process whereas the temperature of the zone I itself is the output data. Note that the number of input signals differs from zone to zone. Zones I, III, VII, and IX use 4 input signals whereas the rest of the zones use 5 input signals. Based on the input-output data the matrices
Singular values of zones I and V.
Next a test is run on the obtained state space models. The outer temperature parameters are set as in the second row of Table
Real and predicted temperature of zone I.
To demonstrate the detection capabilities of the algorithm two scenarios are used. In the first scenario, there is heat leakage, possibly due to an open window. To take into account the infiltration gain the term is added
Real and predicted temperature of zone I, with a heat leakage starting at
As it is observed the predicted values deviate from the real ones after time index 8000. In fact the predicted values do not stay in the zone
Drift of the test statistic for scenario I, under no change and a heat leakage starting at
The CUSUM algorithm started at time 7000 and 60 samples were used to estimate
Real and predicted temperature of zone I, with an extra heat source powered on at
As it is observed, the predicted values in this case fall below the zone
Drift of the test statistic for scenario II, under no change and an extra heat source powered on at
It should be noticed at this point that the “original” simulated system (42 state space model) is also linear and thus the use of linear subspace identification may be questionable for more complex and possibly nonlinear systems. As the simulation results indicate although the dynamics of each zone are more complex (including the roof temperature for example) a low dimensionality subsystem of order 2 can capture its behaviour.
For more complex systems the order of the identified subsystem can be chosen high enough. For nonlinear systems the identification of a time varying system is possible using a recursive update of the model.
Next, the SID method is tested when an exogenous heat noise is present. This noise is modeled as
Exogenous heat noise profile.
The real and predicted temperature values for this case are shown in Figure
Real and predicted temperature of zone I, with an exogenous heat noise depicted in Figure
A method for the detection of abnormal behaviour in HVAC systems based on the multizone principle is proposed. The method uses deterministic subspace identification to obtain state space system models that will provide the reference temperatures for each zone. As it is shown using simulations, simple state space models of order 2 are able to capture the dynamics of each zone and to produce predicted temperature profiles that closely follow real measurements. The CUSUM algorithm is used next to detect possible divergences of the rate of change of the difference between the real and the reference values. The method was tested using two different scenarios, that is, heat leakage due to infiltration losses and heat gains due to an exogenous source, that is, the onset of a fire. In both cases, the abnormal operation is detected within 5 min with a small false alarm rate equal to 0.001.
Two directions are foreseen for future work: in the first direction, investigating the use of sophisticated classifiers such as SVM or Neural Nets incorporating more features of the reference signals in the decision process for the early detection of abnormal behaviour and in the second direction, focusing on utilizing heterogeneous sensors (temperature, occupancy) in the WSN aiming at optimizing the energy consumption at each zone while in parallel maintaining the comfort conditions of the occupants. To this end, combining the powerful subspace identification process should be combined with results from Optimal Stopping Theory.
The authors declare that there is no conflict of interests regarding the publication of this paper.