Journal of Energy

Volume 2015, Article ID 693749, 12 pages

http://dx.doi.org/10.1155/2015/693749

## A Subspace Identification Method for Detecting Abnormal Behavior in HVAC Systems

^{1}Department of Engineering and Design, Brunel University, Kingston Lane, Middlesex UB8 3PH, UK^{2}Department of Electronics, TEI of Athens, 12210 Egaleo Athens, Greece

Received 16 December 2014; Revised 16 February 2015; Accepted 18 February 2015

Academic Editor: Antonio Moreno-Munoz

Copyright © 2015 Dimitris Sklavounos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1]. Heat ventilation and air conditioning systems (HVAC) have become one of the main and widely equipped environmental technologies for the buildings. HVAC systems of the commercial and residential buildings consume about 57% of the required energy and they are wasting more than 20% of energy due to various faults, insufficient control, or improper positioning. Methods of faults detection (FDD) as well as abnormal situations detection are potentially able to save about 10–40% of the HVAC energy consumption [2]. Thus, sophisticated building automation systems, which utilize such methods of detection and improve the control mechanisms of HVAC systems, can significantly contribute to the total energy savings. To this end, the fault detection diagnosis as well as the detection of abnormal situations in the HVAC systems is a very challenging research area.

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 2 presents related work on the detection of faults and abnormalities as well as the use of SID to HVAC systems. Section 3 describes the system model and the subspace identification process as well as the CUSUM algorithm that is used to detect abnormal system operation. Section 4 contains simulation results and assesses the effectiveness of the proposed algorithm. Finally, Section 5 summarizes the paper and proposes research directions for future work.

#### 2. Prior Work

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 [3] proposed a method that is based on the principal component analysis (PCA) detection of sensor faults in air handling units (AHU). The -statistic method is used for the sensor fault detection, and in addition with the use of the contribution plot, the faulty sensors can be isolated. In [4], a statistical based method of detecting abnormal energy consumption in buildings is proposed, including the detection of HVAC abnormalities causing outliers. In a first stage, features like the average daily energy consumption or peak demands for a day are determined using data like the total energy consumption of the building. Then these features are sorted according to similar energy consumption and thus groups of days with similar energy consumption are formed. Thereafter, an outlier identifier is applied to determine features of the same day type with significant difference from the normal ones and if detected, a modified -score is used to determine the amount and direction of the variation. In [5], the authors estimated the appropriate power consumption by approximating the minimum cooling demands of a building (National Taiwan University) and comparing them with the real cooling supply. The results showed a high discrepancy and the authors proposed two types of statistical methods to reduce the energy consumption: polynomial regression and feature based regression are the methods used to model the behavior in the building and a Hampel identifier is applied to test the consistency of the data.

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 [6] the authors, based on the idea of encapsulating simulation programs within building energy management systems (BEMs), proposed a prototype simulation-assisted controller with an embedded simulation program in order to provide real time control decisions. In the same category also falls the work in [7], where a WSN was utilized for the abnormal situation detection. Each node of the WSN, covering a single zone, act as a controller (PI), tuning the heating supply to a predetermined temperature value. A lumped capacity model was used to predict the hypothetical normal operation and the CUSUM sequential algorithm detected possible divergences of the energy consumption from the anticipated one. In [8] a method using a multilevel fault detection diagnosis (FDD) algorithm is proposed, with an energy description of all units in a HVAC and a spatial temporal partition strategy, as the two main elements of the method. The energy performance signals of the HVAC units are becoming the inputs to the FDD algorithm, and possible hardware faults within the HVAC system are captured. The work in [9] proposes a method that detects actuator faults in a HVAC system. It is a software based fault detection diagnosis mechanism with a two-tiered detection approach. At the first tier, the method utilizes a quantitative model-based approach, which relies on a simple thermodynamic model and it does not require full knowledge of the system model. At the second tier, a qualitative model-based approach is utilized which, based on the air temperature, provides a quick decision whether an actuator is working properly or not. In [10] a Model Predictive Controller is presented which uses both weather forecasts as well as the thermal model of a building in order to maintain indoor temperature independent of the outdoor conditions. An accurate model of the building was indispensable and thus they created a simplified model of the crittall type ceiling of radiant heating and applied a subspace identification algorithm giving the appropriate inputs. In [11] a strategy is presented consisting of two schemes, the FDD of HVAC systems and the sensors fault detection. In the first scheme the indication of each system performance is taken by one or more performance indices (PIs) which they are validated from the actual measurements by the use of regression models. The detection and diagnosis of faulty sensors are achieved with the use of a PCA method. In [12] the authors have combined the benefits of the model predictive control (MPC) technique as well as building simulation software such as TRNSYS, Energy plus, and so forth, in order to create a physical model, as close as possible to a real building. To achieve this, they applied a subspace identification method which is appropriate to identify a multiple input multiple output (MIMO) system. In [13] the authors have focused on the preventive maintenance of the HVAC systems and they proposed a fault detection method that combines the model FDD method and a support vector machine classifier (SVM). The authors worked on the detection of components sensitive to faults. Using computer simulations they investigated three major faults such as recirculation damper stuck, the block of the cooling coil, and the decreasing of the supply fan.

#### 3. System Modeling

##### 3.1. Detection of Abnormal System Behavior

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 formwhere is the state vector at discrete time , is a vector of external inputs, is the predicted zone temperature, and , are specific parameters to the systems and , respectively. Knowing the dynamics of the system and the external inputs , the node is able to predict the temperature of the zone . The inputs in this case are the temperatures of the surrounding zones, the outdoor temperature, and the power of heaters located in the zone. Comparing the predicted values to the actual ones, as measured by the temperature sensors, possible changes in the dynamics of the system can be detected, which signal an abnormal operation. Optimal detection theory deals with the problem of detection of changes in the distribution of measurement data. Control charts [14] and the CUSUM algorithm [15] are some of the simplest and most applied solutions. Alternatively, the subsystem model can be periodically reidentified looking for possible changes in the parameter space . However, such a detection process is computationally demanding and overloads the wireless nodes. Moreover, more data are needed to be processed to draw safe conclusions and thus large delays are unavoidable. Shewhart charts cannot detect small shifts; that is, the probability of detecting small shifts is rather small. On the contrary CUSUM charts can detect easily small systematic shifts but their response to large shifts is relatively slow. For all these reasons, in this work, the CUSUM technique is used as the basic change detection algorithm since even small deviations from strict operating requirements should be detected. The detection process will be based on the rate of variation of the prediction error between the real and the predicted temperature. To this end the sequence of prediction errors is defined where denotes the predicted temperature process and is the “real” temperature process of the zone. The derivative of this discrete process is the random variable , whereThe assumption is made that have density for and density for where the parameter is known (or it is estimated) and and are generally unknown. The time index signals an event that changes the distribution of the measurements. In terms of the proposed algorithm, is the mean of the rate of the prediction error in normal operation and is the variance of the rate due to uncertainties of the measurement devices. is a nuisance parameter and it is generally unknown. The parameter denotes the mean of the rate of the prediction error in case of an abnormal situation, and it is considered unknown. The parameter is the time index when a change of densities occurs and sequential tests deal with the detection of this change. Although, is in general a function of time , the detection algorithm will be applied using the random variables . Thus, under normal operation (null hypothesis) has a constant mean value equal to 0, whereas under the alternative hypothesis has a nonzero unknown mean value . Note that the measurement noise is only due to the sensors and not due to exogenous factors such as lamps and the presence of people that may influence the detection process. These sources of noise affect both the estimate of , the mean of the rate of the prediction error on normal operation, and the drift of the test statistic (see below) so that one cannot draw safe conclusions about an abnormal situation. Nevertheless, in the simulation section, we include an experiment with such noise processes modeled, primarily to demonstrate the effectiveness of the SID method and to provide directions for future research.

As it has already been stated, one of the most promising algorithms to sequentially detect the change is the CUSUM test. Gombay and Serban [16] adapted Page’s CUSUM test for change detection in the presence of nuisance parameters. Gombay proposed statistics based on the efficient score (Rao’s statistics), on the maximum likelihood estimator (Wald’s statistics), or on the log likelihood ratio. The efficient score vector is defined asAs it can be proved, if the density belongs to the exponential family, that is, Gaussian, then if some regularity conditions hold under the null hypothesis (normal operation), there exists a Wiener process that approximateswhere is the maximum likelihood estimation of and is the Fisher information matrix.

The test statistic in (4) can be used to check if a change in densities has occurred at some time instant . Under the alternative hypothesis (abnormal behavior) this statistic drifts for with the size of the drift proportional to the rate at which the test statistic moves in the direction of the alternative density. Moreover, in order to make decisions after observations have been obtained, the following result is used (Darling and Erdös [17])whereTo make use of this result a false alarm rate is set, that is, , where and the threshold is computedThen, the alternative hypothesis (abnormal operation) is supported by the data at the first , whenIf no such exists for the hypothesis of normal operation is not rejected. For (that is 5 min with sampling period 1 sec) and the two indicative values of and and are obtained, respectively.

In what follows the assumption is made that all measurements , , are independent random variables. In this case the test statistic in (4) takes the formUnder the alternative, the drift of after change is Figure 1 shows the drift for , , , (blue), (green), and (red). As it is observed the greater the excess difference of the means of the rates the largest the slope of the drift.