Beyond Control: Enabling Smart Thermostats For Leakage Detection

TL;DR

This paper introduces Greina, a novel system leveraging smart thermostats to detect refrigerant leaks early in retail cold-rooms, enabling proactive maintenance and energy savings.

Contribution

The paper presents Greina, a scalable leakage detection system that uses ambient data from thermostats to identify refrigerant leaks before manual detection methods.

Findings

Greina detects leaks up to a week early.

The system was evaluated on 74 retail outlets.

It improves early leak detection accuracy.

Abstract

Smart thermostats, with multiple sensory abilities, are becoming pervasive and ubiquitous, in both residential and commercial buildings. By analyzing occupants' behavior, adjusting set temperature automatically, and adapting to temporal and spatial changes in the atmosphere, smart thermostats can maximize both - energy savings and user comfort. In this paper, we study smart thermostats for refrigerant leakage detection. Retail outlets, such as milk-booths and quick service restaurants set up cold-rooms to store perishable items. In each room, a refrigeration unit (akin to air-conditioners) is used to maintain a suitable temperature for the stored products. Often, refrigerant leaks through the coils (or valves) of the refrigeration unit which slowly diminishes the cooling capacity of the refrigeration unit while allowing it to be functional. Such leaks waste significant energy, risk occupants' health, and impact the quality of stored perishable products. While store managers usually fail to sense the early symptoms of such leaks, current techniques to report refrigerant leakage are often not scalable. We propose Greina - to continuously monitor the readily available ambient information from the thermostat and timely report such leaks. We evaluate our approach on 74 outlets of a retail enterprise and results indicate that Greina can report the leakage a week in advance when compared to manual reporting.

Tables

Table 1. Table 1 . List of symbols used in the proposed thermal model

Symbol	Description	Unit
$\tau$	Sampling Interval	s
$r$	Thermal region $\in \{r_1,r_2,r_3\}$	$-$
${\eta }_r$	Thermal noise in region $r$	$-$
$Q_{oc}$	Cooling load due to occupants and their activities	$-$
$Q_{ac}$	Cooling capacity of AC	$kW$
$T_r^{\left(t\right)}$	Temperature in region $r$ at time instance $t$	${}_{}{}^{\circ }C$
$T_e^{\left(t\right)}$	External temperature at time instance $t$	${}_{}{}^{\circ }C$
$T_w^{\left(t\right)}$	Temperature of wall (facing outside) at time instance $t$	${}_{}{}^{\circ }C$
$C_r$	Thermal capacity of region $r$	$kJ/K$
$C_w$	Thermal capacity of wall (facing outside)	$kJ/K$
$K_w^r$	Heat transfer coefficient between wall (facing outside) and region $r$	$kW/K$
$K_e^r$	Heat transfer coefficient between external environment and region $r$	$kW/K$
$K_e^w$	Heat transfer coefficient between wall (facing outside) and weather	$kW/K$
$K_{r1}^{r2}$	Heat transfer coefficient between $r1$ and $r2$	$kW/K$
$K_{r2}^{r3}$	Heat transfer coefficient between $r2$ and $r3$	$kW/K$
$S_{ac}^{\left(t\right)}$	AC compressor state ($on$/$\mathrm{𝑜𝑓𝑓}$) at time instance $t$	$-$
$S_{oc}^{\left(t\right)}$	State of occupants at time instance $t$	$-$

Equations

$$\frac{(T_r^{(t+1)}-T_r^{(t)})\times C_r}{\tau }=K_e^r\times (T_e^{(t)}-T_r^{(t)})+(Q_{dr}\times S_{d_r}^{(t)})+(Q_{ru}\times S_{r{u}_r}^{(t)})+{\eta }_r$$

$$\begin{array}{rl}{\mu }_r=1-\frac{K_e^r\ast \tau }{C_r},& {\mu }_e=\frac{K_e^r\ast \tau }{C_r},{\mu }_{dr}=\frac{Q_{dr}\ast \tau }{C_r},\\ {\mu }_{ru}=\frac{Q_{ru}\ast \tau }{C_r},& {\eta }_r^{\prime }=\frac{{\eta }_r\ast \tau }{C_r}\end{array}$$

$$T_r^{(t+1)}={\mu }_r\times T_r^{(t)}+{\mu }_e\times T_e^{(t)}+{\mu }_{dr}\times S_{d_r}^{(t)}+{\mu }_{ru}\times S_{r{u}_r}^{(t)}+{\eta }_r^{\prime }$$

$$T_r^h=\frac{{\sum }_h{\mathbf{T}}_{\mathbf{r}}}{(3600/\tau )},{\tilde{T}}_r^h=\frac{{\sum }_h{\tilde{\mathbf{T}}}_{\mathbf{r}}}{(3600/\tau )}$$

$${\hat{T}}_r^h={\tilde{T}}_r^h+{\sigma }_r^h$$

$$e_h=\frac{{\sum }_h|{\tilde{T}}_r^{(t)}-T_r^{(t)}|}{(3600/\tau )}$$

$$r{d}_m=d{t}_m-d{t}_{s}r{d}_g=d{t}_g-d{t}_s$$

$$d_m^g=d{t}_g-d{t}_m$$

$$\begin{array}{r}\frac{(T_w^{(t+1)}-T_w^{(t)})\times C_w}{\tau }=K_e^w\times (T_e^{(t)}-T_w^{(t)})+\sum _{r=1}^{r_l}{K}_w^r\times (T_r^{(t)}-T_w^{(t)})\end{array}$$

$$\begin{array}{r}\frac{(T_{r_1}^{(t+1)}-T_{r_1}^{(t)})\times C_{r_1}}{\tau }=K_e^{r_1}\times (T_e^{(t)}-T_{r_1}^{(t)})+K_w^{r_1}\times (T_w^{(t)}-T_{r_1}^{(t)})+K_{r_1}^{r_2}\times (T_{r_2}^{(t)}-T_{r_1}^{(t)})\\ +Q_{ac}\times S_{ac}+{\eta }_{r_1}\end{array}$$

$$\begin{array}{r}\frac{(T_{r_2}^{(t+1)}-T_{r_2}^{(t)})\times C_{r_2}}{\tau }=K_e^{r_2}\times (T_e^{(t)}-T_{r_2}^{(t)})+K_w^{r_2}\times (T_w^{(t)}-T_{r_2}^{(t)})+K_{r_1}^{r_2}\times (T_{r_1}^{(t)}-T_{r_2}^{(t)})\\ +K_{r_2}^{r_3}\times (T_{r_3}^{(t)}-T_{r_2}^{(t)})+Q_{oc}\times S_{oc}+{\eta }_{r_2}\end{array}$$

$$\begin{array}{r}\frac{(T_{r_3}^{(t+1)}-T_{r_3}^{(t)})\times C_{r_3}}{\tau }=K_e^{r_3}\times (T_e^{(t)}-T_{r_3}^{(t)})+K_w^{r_3}\times (T_w^{(t)}-T_{r_3}^{(t)})+K_{r_2}^{r_3}\times (T_{r_3}^{(t)}-T_2^{(t)})+{\eta }_{r_3}\end{array}$$

$$\theta =\{C_w,C_{r_1},C_{r_2},C_{r_3},K_w^{r_1},K_w^{r_2},K_w^{r_3},K_e^{r_1},K_e^{r_2},K_e^{r_3},K_e^w,K_{r_1}^{r_2},K_{r_2}^{r_3},{\eta }_{r_1},{\eta }_{r_2},{\eta }_{r_3},Q_{ac},Q_{oc}\}$$

Full text

Smart Thermostat; Refrigerant Gas Leakage; Ambient Sensing; Fault Detection; Refrigeration Unit

This work was done in collaboration with Zenatix Solutions Pvt. Ltd. We would like to thank TCS Innovation Lab for Ph.D. fellowship to the first author, the administration of the retail enterprise to allow us to collect data, and all the outlet managers and the technicians to help us during the data collection.

††copyright: usgovmixed††journal: IMWUT††journalyear: 2019††journalvolume: 3††journalnumber: 1††article: 1††publicationmonth: 3††doi: 0000001.0000001††ccs: Information systems Decision support systems††ccs: Human-centered computing Ubiquitous and mobile computing systems and tools††ccs: Applied computing Operations research

1. Introduction

Refrigerant leakage is a common mechanical fault in compressor based appliances which are primarily used for air-conditioning and refrigeration purposes (Brambley et al., 2005). The puncture hole often starts as a pinhole leak and becomes bigger when goes undetected. Due to the loss of refrigerant, compressor (a component within the RU) works with reduced efficiency and takes more time than the usual to cool the room; thus, wasting significant energy. In addition to that, the leakage exposes tenants to refrigerant which is extremely dangerous for their health (Assawamartbunlue and Brandemuehl, 2006). The consequences of refrigerant leakage are even worse for retail outlets who set up cold-rooms to preserve perishable food items (usually at $5^{\circ}$C-$8^{\circ}$C), and the stored product goes bad due to improper cooling by the RU during the leakage. Early detection of such leaks can benefit the retail enterprises in -

(1) increasing their profits by reducing the energy wastage,

(2) avoiding leakage of hazardous refrigerant in the open environment, and

(3) maintaining the product quality (Downey and Proctor, 2002; Dong et al., 2013; Francis et al., 2017; Davis and Gertler, 2015).

Unfortunately, store managers usually lack essential skills to sense the leakage at an early stage, and undetected leaks widen with time as RU remains functional during the leakage. At breakdown point, RU stops cooling followed by a complete shutdown of the outlet for several days. Figure 1 depicts one such scenario where store manager reported the problem when RU broke, and the store went out of operations. In addition to repairing cost, the owner also dealt with the staling of stored products and business loss owing to the downtime. Current techniques for leakage detection are either direct or indirect (Yoo et al., 2017). Direct methods, such as Halide leak detector, require an expert to use the device with certain precautions for on-spot leakage detection (Bender et al., 2003; Jeffers et al., 1984; Martell and Krcma, 1994). On the other hand, indirect techniques need specialized sensors to monitor temperature, pressure, and mass flow rate at multiple points inside the appliance (Fisera and Hrncar, 2012; Ren et al., 2008; Payne et al., 2015). As pressure and mass flow sensors are more expensive than temperature sensor, several studies focused on limiting the number of sensors for leakage detection (Fisera and Stluka, 2012; Yoo et al., 2017). However, even with the limited sensors, Yoo et al. (Yoo et al., 2017) required temperature sensors at five points inside the system -

(1) air inlet of indoor unit,

(2) air inlet of outdoor unit,

(3) evaporator midpoint,

(4) condenser midpoint, and

(5) compressor discharge point.

Such an extensive sensor installation (that too within the appliance) often limits indirect techniques to laboratory setup and considered as an expensive and unscalable solution to the problem.

In this paper, we reinforce smart thermostats with Greina111Greina  is an Icelandic word that means to identify. - a framework that observes deviations in the measured temperature from the estimated temperature to detect refrigerant leakage. The estimates come from a lumped parameter thermal model whose parameters are tuned to a particular room environment by the ambient information sensed by the thermostat. Smart thermostats are

(1) plug-n-play - no need of technician for installation,

(2) allow remote sensing of RU,

(3) never intervene in the daily routine of the store managers, and

(4) anticipated to increase by 400% in next couple of years (Knud Lasse Lueth, 2016).

Given the benefits, studies in the past explored smart thermostats for user feedback (Jain et al., 2016), occupancy detection (Kim et al., 2017), energy-efficient control (Lu et al., 2010), among many other applications. However, to the best of our knowledge, no one has studied smart thermostats for leakage detection. We believe enhancing smart thermostats for leakage detection presents a genuinely low-cost and scalable solution for the problem.

Despite all the benefits, one must also note that the overall problem is non-trivial and exhibits multiple challenges. Room temperature is sensitive to the actions of outlet manager (Figure 1) and outside weather conditions (Figure 1), and both these parameters differ significantly across the outlets. Even within a store, the daily routine of the manager, climatic conditions, and fitness level of an appliance change considerably with time. To consider both temporal and spatial variations, Greina  utilizes a first-order thermal model which simulates the room temperature while considering the influence of outlet manager and climate outside the room. Greina  collects weather data through a cloud-based weather service, and monitors user activity through a door sensor. With time, as the framework receives more and more clean data, it keeps updating the model parameters to accommodate temporal changes in the building’s thermal behavior. To gather clean data for the learning phase, Greina  does not consider those days which were identified as leaking while monitoring the RU. In the initial stages, when sufficient clean data is unavailable to tune the model parameters, Greina  benefits from transfer learning and uses the parameters of a contextually ‘similar’ outlet to simulate the room temperature. Transfer learning ensures that the proposed framework is ready-to-work from the day of installation. Eventually, Greina  compares the estimates from the tuned thermal model with sensor measurements and when the actual temperature is sufficiently above the estimate, the system raises a red flag.

Of course, not every red flag is a leakage flag. Room temperature can be higher than the estimates even when RU is working fine (false positive), and vice-a-versa, the framework might confuse the initial symptoms of leakage with the noise generated from manual interventions (false negative). For instance, in Figure 1, the room temperature is in the range of $8^{\circ}$C-$10^{\circ}$C in the initial stages of the refrigerant leak, akin to temperature variations due to tenants’ activities in Figure 1. If misclassification is a false negative (misinformed that RU is fine), then repairing will get delayed until the outlet manager identifies the leakage. However, if misclassification is a false positive (misinformed that RU broke), then the company might end up paying a significant amount to their maintenance contractor for the unnecessary visits. While such visits are immoderate, they are annoying for the store manager and disruptive to the daily operations. Henceforth, Greina  employs CUSUM (Cumulative Sum Control) technique to ensure that the user gets notified only when the system is confident about the leakage.

We evaluate Greina  using the data collected from 74 outlets of a retail enterprise for one year. For ground truth verification, we use fault logs as reported by the servicing company after addressing the fault. Our results indicate that Greina  is comparable or better than manual reporting. The proposed framework can reduce average reporting delay by 5-6 days, when compared to manual reporting. In other words, even if outlet managers could use the leakage detectors (such as Halide leak detector), they would have delayed the repairing by almost a week. We couldn’t compare Greina  with indirect methods (of leakage detection) because proposed techniques require specialized sensors to monitor temperature at multiple points within the RU.

Given the energy-saving features and other advancements, smart thermostats are anyways going to replace traditional thermostats very soon. As of now, thermostats can monitor room temperature, tenants’ daily activities 222Though, in this study, we used door sensor to monitor human activities, Appendix A discusses an extended thermal model which replaces door sensor with the motion sensor of the smart thermostat., and even upload the sensed information to the cloud. Location-based detailed weather information is readily available from several cloud-based climate monitoring applications. By combining the two pieces of information, we can use Greina  for leakage detection without instrumenting the appliance. In addition to being scalable, the proposed approach is reliable enough to maintain food quality and generate minimal false alarms. Finally, Greina  requires minimal (or no) intervention from the store manager and ensures non-interruptive working hours. Currently, in collaboration with an energy-analytics based venture, we are working on the deployment of proposed thermostats across all the 74 outlets which were considered as part of this study.

2. Related Work

Anomaly detection is an active area of research with extensive literature in numerous domains and applications (Chandola et al., 2009; Kim and Katipamula, 2018). One such problem is fault detection and diagnosis (FDD) where the objective is first to identify a malfunctioned appliance followed by a root-cause analysis to diagnose the problem (Gertler, 2013; Isermann, 2011). Usually, the partial or complete failure of the hardware (present in the equipment) brings down the whole system. Though the literature on fault detection in mechanical units is considerably extensive, we will limit the scope of this survey only to compressor-based appliances.

2.1. Fault Detection Frameworks

Typically, fault detection frameworks for compressor-based appliances are designed either for Refrigeration Units (Behfar et al., 2017; Thybo and Izadi-Zamanabadi, 2004) or Heating, Ventilation, and Air Conditioning Units (HVAC) (Wirz, 2017; Brambley et al., 2005; Diagnostics, 2005; Yu et al., 2014). Irrespective of the type of appliance, most fault detection engines are based on a conventional design - simulate a baseline and compare with the measured signal (mostly energy) to mark any deviations due to the fault (Du et al., 2007; Meng et al., 2006; Narayanaswamy et al., 2014; Ganu et al., 2014; Palani et al., 2014; Chen and Braun, 2001). O’Neil et al. (O’Neill et al., 2014) simulated the energy consumption through a building simulation framework, EnergyPlus (Crawley et al., 2000), and compared with actual energy consumption data to identify unacceptable performance. Mavromatidis et al. (Mavromatidis et al., 2013) computed baseline energy consumption through an artificial neural network model and used the baseline to detect faults in supermarket refrigerators. Li et al. (Li et al., 2014) studied the correlation between electrical signals and the common faults for roof-top air conditioners by conducting a series of experiments. Srinivasan et al. (Srinivasan et al., 2015) proposed an energy model to pick anomalies in the power signature of supermarket refrigerators.

Studies also monitored different other parameters to develop a black box model for fault detection (Yang et al., 2011a, b; Han et al., 2010). Keres et al. (Keres et al., 2016) observed compressor frequency to identify a faulty refrigerant unit. Porter et al. (Porter et al., 2008) collected actual operating parameters from a set of microsystem sensors installed throughout the refrigeration and compared with ideal conditions of the system for fault detection. Payne et al. (Payne et al., 2015, 2018) monitored temperature at nine points within an air-conditioner for a self-trained fault-free model and then a data-clustering approach to segregate faulty instances. Similarly, Kulkarni et al. (Kulkarni et al., 2018) designed a random forest binary classifier to detect issues in refrigeration cases by observing temperature and defrost state within supermarket refrigeration cases. While most of the above-mentioned studies focused only on detecting ‘abrupt’ faults, none of them looked into the problem of refrigerant leakage. Though such a fault detection engine would confirm the presence of a fault, the engine won’t label the fault. In the absence of labeling, we couldn’t compare Greina with any of the above-mentioned generic fault detection frameworks333If we would have considered all anomaly instances as leakage, our analysis would have shown high false alarm rate for any generic fault detection framework. Therefore, though we had data to implement some of these techniques, we couldn’t compare the performance of any generic fault detection framework with Greina in our evaluation (Section 4)..

2.2. Leakage Detection Frameworks

Specifically for leakage detection, exiting systems are typically categorized as direct and indirect methods.

2.2.1. Direct Methods

In direct methods, typically a technician visits the site and uses a leakage detector (Bender et al., 2003; Martell and Krcma, 1994) to confirm the leak. Hailey detector (Jeffers et al., 1984) is one such widely used leak detector in which flame changes the color when the refrigerant is present in the environment. Parekh (Parekh, 1992) proposed composition of fluorescent, alkyl substituted perylene-dye, and a polyhalogenated hydrocarbon refrigerant to visually detect refrigerant leakage. Though these detectors are accurate, one must use them with certain precautions. For instance, we cannot use Hailey detector with hydrocarbon refrigerants. Moreover, the effectiveness of direct methods primarily relies on manager’s ability in timely detecting the leakage.

2.2.2. Indirect Methods

Alternatively, in indirect methods, studies often monitor multiple parameters at different points within the appliance for leakage detection (Jeong, 2005; Tassou and Grace, 2005; Rinehart, 2004; Kadle and Ghodbane, 2014; Dube, 2009; Morrow, 1994; Morrow and White, 1996). Taylor et al. (Taylor and Corne, 2004) designed a neural network to analyze data from multiple monitoring alarms to predict refrigerant leakage. Rossi et al. (Rossi and Braun, 1997) proposed a statistical rule-based leakage detection technique which could detect 5% loss of refrigerant through extensive instrumentation. Breuker et al. (Breuker and Braun, 1998) studied temperature at nine different locations and relative humidity to characterize soft faults (such as loss of refrigerant) and their impact on the operations of rooftop air conditioners. Since the majority of leakage detection studies (Li, 2004; Navarro-Esbri et al., 2006; Grace et al., 2005) assume steady-state, Kim et al. (Kim et al., 2008) proposed a methodology for developing a steady-state detector for any generic vapor-compression system. Steady-state in itself is a misleading term because parameters of a vapor-compression system are dynamic in real-world (Kim et al., 2008). Therefore, the study recommended inclusion of all leakage detection features (for best results) which makes the overall approach expensive due to extensive instrumentation of the appliance.

To minimize the number of sensors and sensing points, Fisera et al. (Fisera and Hrncar, 2012; Fisera and Stluka, 2012) developed an energy consumption model by monitoring nine parameters (including relative humidity and carbon-dioxide level) to distinguish anomalous and degradation events. In a patented technology, Suzuki et al. (Suzuki et al., 2004) compared theoretical heat dissipation of the condenser with the actual temperature difference (in the condenser) for leakage detection. In the same direction, Yoo et al. (Yoo et al., 2017) monitored temperature difference between inlet air and midpoint of the heat exchanger to detect the refrigerant charge level. Though stated approaches require less number of sensing points, invasive sensing often limits their evaluation to a controlled environment. Consequently, the efficacy relies on the validity of assumptions from the controlled environment to a real-world scenario.

3. Approach

In Greina, every outlet goes through a two-step process -

(1) learn the normal behavior, and

(2) monitor refrigeration unit for leakage,

as shown in Figure 2.

3.1. Learn Normal Behaviour

In a typical room $r$, the change in temperature, in a given time interval $\tau$ (in seconds), primarily depends on the heat transferred by the weather outside the room, the heat added by the open door, and the heat extracted by the refrigeration unit (Equation 1).

[TABLE]

Here, $T_{r}^{(t)}$ and $T_{e}^{(t)}$ denote the average room and external temperature in the last time interval $\tau$ (between $t$ and $t-1$), respectively. $C_{r}$ is the thermal capacity of the room, and $K^{r}_{e}$ is the heat transfer coefficient between room and external weather conditions. We derived the model from Bacher et al. (Bacher and Madsen, 2011).

When supply in the front runs out, the manager opens the room to get the fresh stock and $S^{(t)}_{d_{r}}$ denotes the state of door (open/close) at time $t$. Given that RU is a two-state appliance -

(1) compressor on, and

(2) compressor off,

where compressor is the major power consuming component of RU, $S^{(t)}_{ru_{r}}$ is the state of RU at time $t$. Correspondingly, $Q_{dr}$ and $Q_{ru}$ denote the amount of heat added through the door, and heat extracted by the refrigeration unit, respectively. $\eta_{r}$ is the thermal noise introduced by the random events.

[TABLE]

In state space representation, we can lump the parameters (as shown in Equation 2) and rewrite the thermal model as Equation 3. Greina  learns the model parameters ($\theta=<\mu_{r},\mu_{e},\mu_{dr},\mu_{ru},\eta^{\prime}_{r}>$) through linear regression while using the data streams of room temperature ($\mathbf{T_{r}}$), external temperature ($\mathbf{T_{e}}$), door status ($\mathbf{S_{d_{r}}}$), and RU status ($\mathbf{S_{ru_{r}}}$). Tuning the parameters of a physics-based thermal model by using the real-world data is called Grey Box Modelling and widely practised by the researchers in several domains (Dewson et al., 1993). As tuning involves sensor data, the model with adjusted parameters represents an approximate thermal behaviour of the room.

[TABLE]

Greina  tunes model parameters every month through Stochastic Gradient Descent (Pedregosa et al., 2011). The online learning ensures that model adapts to recent changes occurring in the environment, without forgetting the existing knowledge. Now, to tune the model parameters, the proposed framework require clean data - data when the refrigeration unit was working fine. To gather clean data for the learning phase, Greina  does not consider those days which were identified as leaking during the monitoring phase. For instance, if Greina  labeled refrigeration unit as Refrigerant Leaking for five days in the last month, the learning module won’t consider data from those five days to tune the model parameters. The rationale behind this is that if RU was unable to keep room temperature within limits for more than 36 hours consecutively, it was not an ideal situation and there was a problem. During those five days, the problem could have been Refrigerant Leakage (true positive), or an ongoing maintenance (false positive); either way, those days are not ideal (or regular) days for the training. Thus, we discard those from the learning data and only use clean data.

Initially, we specified two key features of Greina  -

(1) it uses readily available information from the smart thermostat, and

(2) it can start monitoring the RU without waiting for the sensor data for a long time.

Though the proposed framework can collect room temperature ($\mathbf{T_{r}}$) and door status ($\mathbf{S_{d_{r}}}$) information from the thermostat, and external temperature ($\mathbf{T_{e}}$) from any third-party weather server, the refrigeration state ($\mathbf{S_{ru_{r}}}$), which typically requires appliance-level monitoring is unavailable to the framework. In addition to that, waiting for clean data for a long time in the initial stages of deployment can significantly delay the monitoring process. Greina  leverages domain advancements to fulfill these requirements.

3.1.1. State of Refrigeration Unit

Jain et. al. (Jain et al., 2016), proposed a classification based algorithm to determine compressor state from the room temperature. The intuition was to first identify compressor on and off events from the temperature data followed by event sequencing to estimate the state vector for RU. When compressor turns on, the room temperature quickly goes down due to the addition of cold air, and when compressor turns off, the room temperature shoots up due to thermal leakage. The estimation algorithm (EA) uses k-means to segregate sudden increase and sudden decrease in room temperature (in $\tau$ time) from normal variations. On the segregated events, the algorithm applies sequencing and recreates the compressor cycles of the refrigeration unit. We employ estimation algorithm to represent RU state as a function of room temperature ($\mathbf{S_{ru_{r}}}=EA(\mathbf{T_{r}})$) and learn the model parameters. One must note that Greina  estimates state vector only when RU is working fine because learning requires clean data.

3.1.2. Parameter Initialization

When a store comes under monitoring, there exists no data to learn the model parameters for the particular outlet. In such a scenario, Greina  uses the parameters of a contextually ‘similar’ store to monitor the refrigeration unit for leakage detection until sufficient clean data from the new outlet is available to update the model parameters. To find ’similar’ outlet, we compare the average daily routine of managers in each store. We do not use room temperature directly to measure ‘similarity’ because it is possible that RU is faulty at the time of installation. The rationale for using daily schedule is that out of all the factors, room temperature is most sensitive to managers’ activities. While the efficiency of the refrigeration unit, building insulation, and other building characteristics are static and change over a long span of time (in months or years), the schedule of any manager is stochastic. Therefore, if the managers of two outlets have ‘similar’ routine, there are high chances that the hourly temperature profile will also be ‘similar’ for those outlets (Figure 3). Our ranking algorithm (Algorithm 1) then sorts all the available stores based on the ‘similarity’ in the daily routine of their respective managers. We use $l2$-norm to measure the similarity. When there exists no ‘similar’ outlet, the monitoring module (of Greina) uses $10^{\circ}$C as a default threshold 444The refrigeration units are supposed to maintain a temperature range of $5^{\circ}$C-$8^{\circ}$C in the cold-rooms. Typically, temperature remains higher (than the limits) during the working hours, and within the limits during the non-working hours. The $10^{\circ}$C is the median value for both working and non-working hours..

3.2. Monitor for Leakage Detection

At the end of each hour, the tuned thermal model estimates typical temperature profile of the room ($\mathbf{\tilde{T}_{r}}$), for the framework to look for refrigerant leakage. However, it is infeasible to estimate the temperature profile which perfectly aligns with the actual temperature profile, and the reason lies in the control strategy embedded within the internal thermostat of a typical refrigeration unit. The inbuilt thermostat of an RU uses on hysteresis as an upper threshold and off hysteresis as a lower threshold. When room temperature goes beyond the on hysteresis, the thermostat turns on the compressor, and the room temperature starts decreasing. Subsequently, when the room temperature reaches the off hysteresis, the thermostat turns off the compressor and allows room temperature to increase up to on hysteresis. However, in real-world, the temperature readings from the inbuilt thermostat of RU differs significantly from the deployed sensor measurements. As it is difficult for the external temperature sensor to match the temperature readings as sensed by the inbuilt sensor, it is also hard to accurately predict room temperature at every time instance. If we observe deviations in the raw temperature profiles ($\mathbf{T_{r}}$ and $\mathbf{\tilde{T}_{r}}$) for anomaly detection, the misalignments will lead to false conclusions 555We discuss misalignment in detail in Section 5 - Discussions.

Instead, Greina  analyses hourly mean temperature to mark if the RU in a particular hour is anomalous or not. In any hour, the thermostat tries to achieving a temperature which is the average of on and off hysteresis. For instance, in the current scenario, outlets use 5∘C as off hysteresis and 8∘C as $on$ hysteresis to maintain an average temperature of 6.5∘C in the room. Though the temperature at any time instance may misalign, the average temperature in that hour should remain close to 6.5∘C. Thus, Greina  first computes mean actual ($T_{r}^{h}$) and estimated ($\tilde{T}_{r}^{h}$) temperature in Equation 4 followed by decision boundary for leakage detection in Equation 5.

[TABLE]

[TABLE]

Here, $\tilde{T}^{h}_{r}$ is the estimated mean temperature, $\sigma^{h}_{r}$ is the standard deviation in $\mathbf{T_{r}}$ in an hour $h$, and $\hat{T}^{h}_{r}$ denotes the estimated decision boundary for the particular hour $h$ and room $r$. If the sensed mean temperature ($T^{h}_{r}$) is beyond the estimate ($\hat{T}^{h}_{r}$), then we mark that specific hour anomalous (Algorithm 2). Furthermore, to gain confidence that deviations are due to leakage, Greina  applies CUSUM (Cumulative Sum) control strategy (Wikipedia contributors, 2017) and maintains a bucket variable ($b_{r}$) to monitor consecutive such anomalous instances. Whenever room temperature goes beyond the decision boundary, the monitoring module increments the $b_{r}$ value by one (Algorithm 2). For every consecutive hour, when room temperature is within the estimated limits, $b_{r}$ decreases by one unit. If room temperature stays below the decision boundary for consecutive $h_{mon}$ hours, Greina  assumes RU is working fine and resets the bucket. In case of missing information, $b_{r}$ remains unchanged.

3.2.1. Label the Refrigeration Unit

In the final step, Greina  labels the refrigeration unit based on its bucket value ($b_{r}$) in the particular hour $h$. Our analysis indicates that if the room temperature is beyond the estimated decision boundary for consecutively 36 hours, then there are maximum chances of refrigerant leakage. Though we learned the current transition thresholds from the data, we can always adjust these settings based on user requirements.

4. Evaluation

For the study, we deployed a customized thermostat and power meter across 74 outlets of a retail enterprise. From July 2016 until June 2017, thermostats collected room temperature and door information from the cold-rooms, and energy meters gathered appliance level power consumption. Every cold room is $9$ ft wide, $9$ ft long, and $8$ ft high. With thick walls and doors, these highly insulated cold rooms can maintain storage temperature anywhere between $-2^{\circ}$C and $5^{\circ}$C. We keep thermostats close to the blower fan (of the RU), because that allows Greina  to focus more on the output of refrigeration unit and less on the thermal noises in the environment. We monitored weather conditions (in the region) through an API of a cloud-based weather service (TWC Product and Technology, 2014). The outlets were located in a city where outside temperature usually stays between $21^{\circ}$C and $37^{\circ}$C, all around the year. The retail enterprise maintains a log of calls from the store managers regarding the complaint in their cold-rooms. We used the fault logs for ground truth verification. During the study period, repair person identified 42 cases of refrigerant leakage across 39 outlets, in addition to several other defects. In remaining 35 stores, neither manager nor repair person mentioned any instance of refrigerant leakage in the logs during the study period. In one instance, the outlet manager called a local repair person instead of reporting the fault to the authorised maintenance contractor.

4.1. Evaluation Metrics

We evaluate Greina  primarily on two aspects -

(1) model accuracy in estimating the decision boundary ($\mathbf{\hat{T}_{r}}$), and

(2) minimising the delay in reporting refrigerant leakage.

4.1.1. Modelling Error

For each hour, we compute mean absolute deviation (denoted by $e_{h}$) in measured ($\mathbf{T_{r}}$) and estimated temperature ($\mathbf{\tilde{T}_{r}}$) to quantify the accuracy of model parameters in simulating the room temperature in an hour $h$ (Equation 6).

[TABLE]

[TABLE]

4.1.2. Delay in Reporting the Leakage

We labelled all the leakage instances by start date ($dt_{s}$) - when symptoms became visible in the data, and end date ($dt_{e}$) - when repair person repaired the leak. Reporting delay is the number of days between the start and the leakage reporting dates. Equation 6 computes reporting delay for store manager ($rd_{m}$) and Greina ($rd_{g}$). Here, $dt_{m}$ and $dt_{g}$ are the dates when the manager and Greina  reported the leaks, respectively.

4.2. Model Validation

Across all the outlets, our analysis indicates that the model tuned with clean data (when RU was fit) can simulate the room temperature with a mean absolute error of 2∘C (with $\sigma$ = 0.9∘C), as shown in (Figure 4). Estimation error is primarily due to misalignment and noise due to random events - such as leaving the door open, refilling the food products at a higher temperature. For the same reason, the error is usually higher during the operational hours, as also evident from the bumps. Erroneous estimations might mislead Greina  that room temperature is above the estimated temperature, but adding standard deviation in Equation 5 minimises such instances.

4.3. Results and Analysis

In the study period, we noted 42 instances in the logs where either the store manager or the repair person mentioned the keywords - gas666local people often use the word ‘gas’ to refer refrigerant and leakage. In 4 cases, though the records had the gas keyword, no leakage occurred in the refrigeration unit at that time, as validated by the store manager and the data. Furthermore, refrigerant leakage shows physical symptoms, such as water dripping and ice formation, which are visible before any leakage pattern in the temperature data. In 3 such instances, outlet managers quickly intimated the maintenance contractor to fix the refrigeration unit and Greina  had no data to analyse the symptoms for leakage detection. In remaining 35 instances, the proposed framework correctly identified 25 leaks and failed to detect leakage in the remaining scenarios. While few of them were genuine system failures, others happened due to ungovernable circumstances -

1. (1)

Too Early to Detect: During the learning phase, Greina  borrows model parameters from a ‘similar’ outlet. While Greina  successfully identified six leaks when knowledge transferred from one store to another, it failed twice. 2. (2)

Improper Learning: Outlet managers generate significant thermal noise in the room through their dynamic and random activities. While the model can deal with such noise with a substantial amount of data, Greina  incorrectly learns the model parameters when the data is insufficient. As the occupants’ behaviour differs significantly across the outlets, there exists no definite way to compute - How much data will suffice to train the model correctly? 3. (3)

Noisy Sensor: In two cases, we noticed that a faulty sensor was providing incorrect temperature readings which resulted in false negative. However, we believe that these issues are solvable with better governance around the deployment. 4. (4)

Low on Refrigerant: Quite often, a refrigeration unit is actually low on refrigerant (due to heavy usage), and there exists no leakage. In such scenarios, though temperature remains in a higher range as RU is not running at the full capacity, but differs from the temperature patterns as in the case of refrigerant leakage. Therefore, when RU was low on refrigerant in 3 such instances, the technician mentioned gas top up in the log; however, Greina  failed to find the symptoms of refrigerant leakage.

Furthermore, Greina  reported only 6 instances of false positives - marked RU as leaking while it was working fine. In four out of six cases, either store manager or technician shut down the refrigeration unit for construction and the repairing work. As the shutdown was unexpected, Greina  confused the rise in room temperature with leakage and marked the refrigeration unit as leaking. In remaining two instances, RU broke abruptly due to an electrical fault and stayed down until a technician came to fix it. Consequently, room temperature went high and Greina  raised a refrigerant leakage flag. As the company, maintenance contractor, and the outlet managers are usually aware of these situations; we believe these flags are harmless. In addition to this, Greina  also pinpointed a case of refrigerant leakage where store manager called an unauthorised technician to repair the RU and didn’t notify the enterprise. Though such cases are rare, they are a serious concern for the company.

Beyond Accuracy

Though accuracy is essential, minimisation of reporting delay is a more significant concern for the stakeholders because the delay is directly proportional to energy wastage, health hazards, and product wastage. In our analysis, we noted an average reporting delay of seven days for Greina, while managers had a mean reporting delay of 12 days (Figure 5). In 19 out of 25 instances, Greina  detected leakage before the store manager (Figure 5). In eight cases, the difference was as high as 10-30 days. The early detection of leakage exhibits several benefits.

Minimise Energy Wastage

In Section 1, we presented a scenario (Figure 1) when refrigeration unit had a gas leakage, and outlet manager kept using the RU for more than a week. While such situations are common across all the stores, we noticed significant energy wastage in doing so. Figure 6 compares hourly energy consumption during the normal operations with faulty operations, when RU has a leakage. There are two essential takeaways -

(1) energy consumption increases significantly during the working hours (almost $4x$), and

(2) energy consumption is very high when refrigeration unit is leaking (around $7x$ during the non-working hours).

[TABLE]

While the activities (or routine) of store managers are hard to change, Greina  seems robust enough to minimise the energy wastage due to gas leakage. Figure 6 compares the hourly energy wasted in the $d_{m}^{g}$ period - the number of days between the reporting dates of manager and Greina (Equation 8). Our analysis indicates that if central maintenance team had taken the recommendations from Greina, they might have saved 5-10 $kWh$ energy every day (when RU was faulty) which is twice the typical daily power consumption of RU (Figure 6). The negative wastage depicted those scenarios when RU stopped working, and the outlet ended up consuming less energy in comparison to normal operations.

Minimising Risk to Product Quality

Next, we observed that room temperature remains significantly high during the gas leakage (Figure 6). High temperature risks the product quality and impacts the store operations. The average room temperature increased by 2∘C-3∘C in both working and non-working hours. When we analysed across all the 19 instances where Greina  reported before the store manager, we noted a median increase of 6∘C during the $d_{t}^{g}$ period for each hour of the day, across different outlets (Figure 6). If maintenance team had taken the recommendations from Greina, they could have kept the rooms 5∘C-6∘C colder every day (when RU was faulty), by timely repairing the RU (Figure 6).

Even though store managers have a benefit of observing the physical symptoms of leakage, Greina  identified 19 out of 25 leakages before the store manager. Though in two instances, Greina  couldn’t detect the leakage before manager; we also noted that in remaining three cases, it occurred due to the negligence of the maintenance contractor. While outlet manager timely reported the leakage to the maintenance team, the maintenance contractor didn’t take any action for several days. Consequently, the symptoms became visible and Greina  detected the leakage even though store manager repeatedly complained about the leakage.

Beyond Leakage

Though we designed Greina  for refrigerant leakage, we observed that the proposed framework also identified other common time-varying faults.

Ice Formation

Dirty air filters, defective evaporator or condenser fans, lack of refrigerant often results in the formation of ice in the refrigeration unit. The ice obstructs the path of cold air and the refrigeration unit works at a reduced efficiency. Though the symptoms of ice formation in temperature data may depend on the fault, Figure 7 depicts one scenario where the increase in temperature is akin to refrigerant leakage (Figure 1). If the ice forms due to heavy usage or a dirty filter, store managers usually clean the filters, however, if the ice forms due to a fault, ice keeps on forming even after cleaning and manager needs to call the technician to repair the RU. Greina  identified 18 such instances where ice formed due to dirty air filter or defective fans.

Condenser Motor Failure

The job of the condenser is to cool the high-pressure refrigerant gas received from the compressor by moving outside air across the condenser coils. Through condensation, the high-pressure, high-temperature refrigerant gas changes to low-temperature liquid refrigerant. However, due to wear and tear, and high temperature during the summers, the condenser fan motor usually fails and RU stops cooling the room. In an attempt to cool the room during the motor failure, RU starts drawing more current which increases the peak power consumption of RU and heats up the system further (Figure 7). Eventually, RU breaks down, and manager calls a technician to repair the motor. Greina  detected ten such instances of motor failure and raised the alarm 1-2 days before complete shutdown of the RU.

To conclude, our analysis on a reasonably rich dataset collected from actual field deployments, indicates that Greina  possesses the power to timely identify the refrigerant leakage instances. Beyond being accurate, on an average, Greina  also proved to reduce the reporting delay by five to six days. The improvement in reporting delay can minimize the energy wastage and maintain desired temperature for the stored items. Interestingly, to achieve these benefits, the company needs to only upgrade their traditional thermostat to a smart thermostat with Greina  running in the cloud and leveraging the data collected from the thermostat. Our study indicates that with smart thermostats, the simple yet powerful framework, Greina  is easily scalable.

5. Discussion

In this paper, we proposed a leakage detection framework Greina  for smart thermostats and validated its efficacy on a year-long field data collected from 74 outlets of a retail enterprise. In collaboration with an energy-analytic firm, we are currently deploying Greina  across all the 74 outlets. In this section, we discuss three possible dimensions to extend the proposed framework.

5.1. Modelling Error

We rely on our thermal model to first learn a decision boundary for Greina  to monitor the RU for any leakage on a daily basis. Though current model estimates room temperature with a mean absolute error of $2^{\circ}$C (with $\sigma$ = $0.9^{\circ}$C), the reader should also be mindful of the fact that the model is a replaceable module of the whole framework. In Appendix A, we discuss one such extension of the current thermal model which can estimate room temperature with an RMSE of $2.85^{\circ}$C (with $\sigma=1.3^{\circ}$C) even in a highly noisy environment of residential apartments. In our analysis, we noticed that Misalignment and Constant Thermal Noise are the primary sources of error.

Misalignment

When we turn on the RU (also applicable on AC), the compressor turns on and starts putting cold air into the room. Due to the flow of cold air, room temperature drops up to a certain level - off hysteresis and compressor turns off (as depicted in Figure 8). At this point, RU allows room temperature to increase up to a certain level - on hysteresis. As temperature reaches the on hysteresis, compressor turns on again and starts cooling the space.

The control algorithm of RU decides compressor state based on the return air temperature which is measured inside the RU, near the filters. Let’s call it $T_{\mathit{rat}}$. On the other hand, we install temperature sensor just outside the RU, near the fan. Now, let’s say $T_{r}$ represents room temperature as measured by the sensor and $\tilde{T}_{r}$ depicts the estimated room temperature. As per the control logic, the controller will turn off the compressor when $T_{\mathit{rat}}\geq T_{\mathit{off}}$. However, given the complex non-linear thermodynamics, it is impractical to precisely estimate $T_{\mathit{rat}}$ or $T_{r}$ at any time instance; thus, $T_{\mathit{rat}}-T_{\mathit{off}}$ and $T_{\mathit{rat}}-T_{\mathit{on}}$. As a result, $T_{\mathit{rat}}-T_{\mathit{off}}\neq\tilde{T}_{r}-T_{\mathit{off}}$ and $T_{\mathit{rat}}-T_{\mathit{on}}\neq\tilde{T}_{r}-T_{\mathit{on}}$. As a result, though the estimated room temperature will follow the pattern, it will fail to align perfectly with the measured room temperature. As depicted in Figure 8 also, the actual (hard black line) and estimated (dashed black line) temperature signals are misaligned. To minimize the effect of error due to misalignment, we consider hourly mean temperature and add standard deviation to monitor the RU for refrigerant leakage.

Constant Thermal Noise

Another primary reason is the thermal noise due to multiple dynamic activities at the same time. In current implementation (Equation 1 and Equation 9-12), we assume that the thermal noise is constant at any time. However, if the noise is coming from multiple sources, the impact of noise on room temperature will vary with time. For instance, consider Figure 8 where initially noise is coming through two activities (window open and ceiling fan running), however, later noise is coming only through an open door. As the current model is unaware of time-varying noise, it will compute room temperature with time-independent noise learned from the data; thus inflating the error. While constant noise makes little impact on room temperature estimation in cold rooms (space is highly insulated and activities are limited), it causes a significant estimation error for residential apartments. One way to handle time-varying noise is to first identify the activity (based on temperature, occupancy, and time of the day), and then compute thermal noise for that particular time instance. At this point, we repeat that the model is a replaceable module of the whole framework; thus, the community is encouraged to explore other such variants of the current model to enhance Greina’s performance.

5.2. False Negatives & Positives

We discussed multiple scenarios when Greina  generated both, false negatives and false positives. After scrutinizing those situations, we noted that we could avoid many of those instances through user-friendly and interactive interfaces (or advanced notification systems). Basically, by involving users, we can empower Greina  with two-way communication with the outlet managers for accurate estimation of the refrigerant leakage. In several instances, managers spotted unusual events, such as high temperature or ice formation. If they could have notified Greina  through a device, Greina  would have used the information to detect the leak, even early. Similarly, we discussed multiple cases where store manager timely reported the leakage, but the repair person (or the maintenance contractor) only refilled the gas instead of fixing the leakage. Consequently, refrigeration unit again went down in a couple of weeks and company had to suffer from the business loss, in addition to typical consequences of refrigeration leakage. If Greina  could validate the existence of unusual pattern even after the corrective action, the maintenance company could reassess the appliance. Not only the two-way communication would minimize such instances, but it will also develop a sense of trust for the system.

However, one must also remember that user attention is costly. When users are involved, the line between a useful system and an annoying system is typically very thin. User input is valuable only if the system is designed while considering -

1. (1)

How frequently user should input the information? 2. (2)

How much time does it take the user to input the information? 3. (3)

How frequently system should notify the users? 4. (4)

Is the interface intuitive and user-friendly?

For the same reason, the new frontiers opening in the domain of smart and ambient notification and attention management systems, the design of web and mobile application, and many such factors can significantly influence the outcome of this study. In the future, we plan to implement the proposed framework (along with the user feedback) to critically evaluate the effectiveness of Greina  in achieving the desired goals at a much larger scale.

5.3. Beyond Temperature Signal

From data, we noticed that power consumption data provides better visibility of leakage than the room temperature because it is less sensitive to thermal noise in the environment and occupants’ dynamic activities. We believe, for the same reason, technicians analyze electrical component such as input/output voltage and supply current for fault detection. Moreover, with the advent of advanced techniques to estimate usage and operating conditions of the appliance through NILM (Non-Intrusive Load Monitoring) (Batra et al., 2016, 2017) and EMI (Electromagnetic Interference) signatures (Chen et al., 2015; Gupta et al., 2010; Sense, 2018; Gulati et al., 2014), the use of energy signal for fault detection is worthwhile. However, even though the power signal is useful for fault detection, power signal alone won’t allow us to monitor the consequences777When a fault occurs, the power signal cannot tell if the appliance is maintaining a suitable temperature for the occupants (if the aim is maintain user comfort), or the stored products (when using for refrigeration).. Although, a smart thermostat together with appliance-level power consumption monitoring could provide best of both the worlds; one must also note that the duo could significantly impact the scalability of Greina. Until now, Greina  only needed a smart thermostat, however, to realize the pair, the home must either have a smart plug to monitor AC power consumption, or a smart meter to get AC power consumption profile by disaggregating meter-level data through NILM algorithms.

If we first look at smart plugs, besides cost, significant variation in supply voltage, type of socket, and power quality across countries challenge the ubiquity of smart plugs. For instance, domestic appliances in India works at 230 V at 50 Hz frequency, however, in United States, 120 V power is supplied at 60 Hz for domestic use. In addition to that, voltage fluctuations, frequency variation, generation of spikes, high earth current leaking are some of the many power quality issues (especially in developing economies) that further hinders the ubiquity of smart plugs. On the other hand, if we consider smart meter data, the effectiveness of the duo would rely on the accuracy of disaggregation algorithm in capturing the AC power consumption signal. If we look at power consumption data (blue curve) in Figure 1, refrigerant leakage mainly impacts peak power consumption (decreases with time) and the duration of each cycle (increases with time). Since peak power consumption is critical for leakage detection, the disaggregation algorithm should ensure that we correctly capture the drop in peak value, and not confuse with the power consumption of small appliances. Though there are challenges, we believe that a study exploring the effectiveness of smart thermostats along with smart meter/plug for fault detection could significantly enhance the performance of Greina  without impacting its scalability.

5.4. Beyond Refrigeration

Beauty of Greina  lies in its modular and systematic architecture, especially the replaceable thermal model and ability to work on top of smart thermostats. While Greina  can benefit from readily available information from the thermostat (temperature, occupancy), we can adapt it to diverse environments by tweaking the proposed thermal model. In Appendix A, we discuss one such extension to a noisy home environment. Poor thermal insulation and time-varying stochastic activities of people are the primary two bases of thermal noise in residential apartments. In a separate analysis across five apartments for a month, we found that a non-linear thermal model can estimate room temperature with an RMSE of $2.85^{\circ}$C (with $\sigma=1.3^{\circ}$C).

Though it is feasible to extend Greina  for the home environment, the real challenge lies in evaluating the efficacy of the proposed framework in such an environment. In residential apartments, tenants call local technicians, and typically no fault logs are available. Ground truth data collection (at a large scale) demands enormous support from tenants and the technicians in sharing the information whenever there is a fault. For the same reason, several studies in the past have either evaluated their approach in theory, or in a controlled environment. We believe a comprehensive evaluation of Greina  across residential apartments can bring up additional intriguing insights about both, the environment and the system.

6. Conclusion

In this paper, we discussed an unsupervised self-learning framework, Greina  that senses ambient information from smart thermostat for leakage detection. The proposed technique employs Grey-Box Modelling to estimate a decision boundary and later uses the estimates for leakage monitoring. The performance evaluation of Greina  on data from 74 stores (from a city in India) testifies that the simple yet powerful framework can reduce the reporting delay by a week with best of around 20-30 days in few instances. During these days, the retail enterprise could have saved twice the energy RU consumes on a typical day. Moreover, by timely repairing the refrigeration unit, they could have kept the rooms 5∘C-10∘C colder every day when refrigerant was leaking. In the future, we plan to deploy the retrofitted thermostats across multiple outlets and study various other challenges, as discussed in the paper.

Appendix A Extension to Home Environment

A residential apartment differs from a cold room in two major aspects:

1. (1)

Poor Insulation - Typically, thermal insulation in a residential apartment is substandard as compared to a cold room. Often, heat leaks through walls, gaps around doors and windows, and multiple such sources. 2. (2)

Noisy Occupants - In cold room, loss of cooling only happens (given superior insulation) when manager opens the door for cleaning or shifting the goods. However, significant amount of cooling is consumed by the occupants in a residential apartment.

Thus, we need a high order thermal model to capture the non-linearity and estimate the room temperature in a residential apartment. Equation 9-12 depict one such thermal model derived from Bacher et al. (Bacher and Madsen, 2011).

[TABLE]

[TABLE]

[TABLE]

[TABLE]

Here, the first region ($r_{1}$) is the area in proximity of the AC, thus facing direct and the maximal impact of cold air coming from the AC. The second region, $r_{2}$ is the region where occupants stay, and the region receives indirect cooling from $r_{1}$ region where AC is present. $r_{3}$ indicates corner spaces in the room. The thermal model in Equation 1 is a special case of above mentioned model where whole room is considered as single region and manager’s activities are monitored through a door sensor. Table 1 describes all the notations used in the extended thermal model.

The idea is to logically divide the room into multiple thermal regions and capture heat transfer at region level. In the model, we assume that thermostat is installed closer to the AC and each region is considered to be separated by a thin layer of air having negligible thermal mass. To evaluate the model, we installed smart thermostat in the bedrooms of five residential apartments, and collected temperature and occupancy data for a month. In parallel, we gathered weather information from a cloud based weather service. Leave p-out cross validation (with $p=10$) indicates that even in such a noisy environment, the extended model can estimate room temperature with a mean RMSE of $2.85^{\circ}$C (with $\sigma=1.3^{\circ}$C).

[TABLE]

One must note that we only used temperature in $r_{1}$ ($\mathbf{T_{r_{1}}}$), outside temperature ($\mathbf{T_{e}}$), and occupancy information ($\mathbf{S_{oc}}$) to learn the parameter set $\theta$ (Equation 13). While temperature and motion data can certainly be captured from a smart thermostat, climatic conditions are readily available from cloud based weather services. Once Greina  learns the model parameters, it will simulate temperature in $r_{1}$ and compare with actual temperature data for leakage detection. Details for monitoring stage remain same as specified in Section 3. We believe, an interchangeable thermal model empowers Greina  to be genuinely pervasive and ubiquitous. Depending upon the design requirements, researchers can explore different variants of the thermal model for diverse scenarios.