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Identifying temporal properties of building components and indoor environment for building performance assessment
Building and Environment 168 (2020) 106506
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Building and Environment journal homepage: http://www.elsevier.com/locate/buildenv
Identifying temporal properties of building components and indoor environment for building performance assessment Chirag Deb *, Mario Frei, Arno Schlueter Chair of Architecture and Building Systems, Institute of Technology in Architecture, ETH Zurich, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Temporal dynamics Building properties Wireless sensor network Time lag Data analytics Performance gap Energy saving
Buildings are dynamic thermal systems that require energy to maintain a comfortable indoor environment. Knowing these dynamics allows for identifying relevant building characteristics for assessing building energy performance. However, conventional building simulation programs take daily or monthly mean values for performance assessment. These often aggregate the errors and uncertainties between the theoretical and the actual building performance while missing the temporal dynamics on a minute or hourly basis. The objective of this study is to uncover the temporal aspects of building properties using data obtained by a wireless sensor network (WSN). Our analysis focuses on the following seven variables that are relevant for assessing building performance and retrofit measures: indoor air temperature, window opening instances, CO2 concentration, supply temperature from the heating system, outdoor air temperature, heat flux through the wall and the window. Using a singlefamily residence as a case study, we identify the temporal dynamics of these variables using polar plots on a high-resolution, 5-minute interval dataset. Following this, we define a set of conditional rules to study ‘expected’ and ‘unexpected’ impact of the six variables on the indoor air temperature. We observe strong temporal dynamics for certain building components, resulting in a large time lag. The conditional rule analysis also allows identi fying energy saving potentials and factors contributing to the performance gap. For example, we observe high indoor air temperatures and at times when no occupants are present. Finally, we discuss the benefits of this approach with respect to building retrofit and energy performance gap analysis.
1. Introduction It is widely known that building-related heating and cooling con sumes 40% of the final energy consumption in the European Union [1]. The building stock is also responsible for 36% of all the CO2 emissions. In view of this, the 2015 Paris Agreement on climate change requires consistent attention towards low greenhouse gas emissions and climate-resilient development [2]. Along with focusing on new sus tainable developments, it is important to focus on existing buildings as buildings have a long lifespan and 80% of today’s building stock will remain in place beyond 2050 [3,4]. In the context of Switzerland, a primary aim of the Swiss Energy Strategy 2050 is to reduce the energy consumption and promote energy efficiency in buildings, in the trans port sector and by electrical appliances [5]. Through the Building Pro gramme, the Federal Government and the cantons subsidize the cost of energy-saving renovation of buildings [6]. Although the importance of retrofitting existing buildings is clear,
the current rate of retrofit in Switzerland is only about 1–2% [7]. The low rate can be attributed to the many factors including the gap between the actual and the predicted energy use in pre- and post-retrofit condi tions, known as the ‘performance gap’ [8–10]. To address these gaps and barriers, recent research focuses on in-situ measurement of building variables using sensor networks [11–14]. There has also been efforts to develop co-incident low-cost sensors that capture holistic picture of building performance without significantly compromising information content [15]. The sensors provide accurate, near real-time information of building variables and operating conditions. These time series data can be used to develop and calibrate energy models for retrofit analysis as well as validate post-retrofit predictions [16]. For example, Lozinsky and Touchie measured window component infiltration rates to improve model calibration for a multi-unit residential building in Canada and noted that infiltration highly contributes to heating load of residential buildings [17]. Real-time data from sensors is also used for model pre dictive control (MPC) of building systems as well as forecasting [18]. In
* Corresponding author. E-mail address: [email protected] (C. Deb). https://doi.org/10.1016/j.buildenv.2019.106506 Received 22 May 2019; Received in revised form 25 September 2019; Accepted 26 October 2019 Available online 31 October 2019 0360-1323/© 2019 Elsevier Ltd. All rights reserved.
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both cases, there is either a white-box model which is calibrated using measured data or a black-box model which is developed from the dataset. The measured data is used to improve the model parameters rather than using it extensively to derive useful inferences on the existing building condition. This study is part of an endeavor aiming at developing a methodology to derive building and occupancy related inferences and related optimal retrofit measures using WSN data [13, 19]. In this work we utilize high-resolution measurement data to obtain an understanding of the temporal distribution of relevant variables and related energy saving potentials. Knowledge of temporal dynamics of variables describing the building as a thermal system also supports mitigating the retrofit performance gap. For this we formulate the following objectives of this study:
anomalies in energy consumption patterns [33]. Second, it is used in disaggregating energy consumption into its constituents [34]. As we see, most of the reviewed literature is based on datasets from already installed building management systems. There is a lack of investigation on residential buildings where hardly any data is readily available. This is because there are many challenges in setting up sensors in residences, including limited freedom on the number of sensors that can be deployed without hindering the privacy of the occupants. Therefore, our work contributes by presenting data and results from a measurement campaign in a single-family residence. The data gathered and the accompanying analysis can be used to understand building characteristics at a high-resolution, 5-min interval level. These will reveal the variation and mutual interaction between variables that are often missed while considering daily or monthly mean values for per formance assessment. The study of mutual interaction using conditioned rules will also help uncover instances of energy saving. The results can also be used to understand some aspects of the causes of the performance gap at the pre-retrofit stage.
1. To study the temporal aspects of building variables using highresolution measurement data obtained by a WSN and using a new form of polar plots. 2. To define conditional rules for ‘expected’ and ‘unexpected’ instances and study the influence of these variables on the indoor air temperature. 3. To uncover the instances of potential energy saving using the above rules.
2. Methods 2.1. Building case study and dataset The building under assessment is a single-family house located in the Canton of St. Gallen in Eastern Switzerland, which was part of a mea surement campaign of 10 buildings in total (Fig. 1). It was constructed in 1973 and has a heated floor area of 147 m2. The building is located in a sunny, unobstructed location and contains six rooms, occupied by a family of four with two adults and two children. It has three storeys with the façade consisting of cavity masonry and the floors made of concrete. The cavity masonry is made of two bricklayers, 12 cm each with a 5 cm rock wool layer between them. The estimated U-value of the masonry is 0.46 W/m2K. The windows have a wooden-metal frame with doubleglazing. The estimated U-value of the glass is 2.4 W/m2K. The base ment floor has a 7 cm concrete slab and polystyrene insulation with a thickness of 2 cm. The house has a pitched roof with paneling and a 5 cm thick mineral fiber insulation contained in one-sided laminated aluminum. The space heating system consists of an oil-based boiler and an underfloor heating network. It is fitted with a constant pressure pump for the underfloor network. The indoor temperature set point is at 23 � C. Based on the control settings, the heating system maintains an indoor air temperature of 23 � C during the day (5:30 to 22:00) and 17 � C during the night (22:00 to 5:30). The indoor set point can be changed through the thermostat in the living room. The loop for space heating also contains a mixing valve. The oil consumed in the boiler is used to heat water in the space heating loop as well as domestic hot water. The domestic hot water is stored in a storage tank and is consumed whenever required. The measurement campaign involves a wireless sensor network developed at the Chair of Architecture and Building Systems, ETH Zurich [19]. The sensor kit consists of sensor nodes, router nodes and a gateway. The sensor nodes collect data and transmit them through a communication module that is housed inside the sensor node. The data is transmitted to the gateway via the ZigBee communication protocol. The gateway, containing a SIM card, sends the data to a MySQL server. In cases where the sensor nodes are far from the gateway, router nodes are placed in between. The measurement campaign took place during the winter of 2016–17 but the period of analysis for this study is for two weeks between 13th and 27th March 2017. Measurements are recorded every 5 min. This gives a total of 288 points for each day per variable and 4032 points for two weeks. The data is preprocessed for timestamp synchronizing and removal of outliers. The outliers are removed by applying a smoothing technique with a moving average filter. The span window is taken at five, which means that each data point is replaced by an average of itself and two other points on each side of the data point.
1.1. Background There have been numerous studies in the domain of building assessment using measured data. The final goal for all these studies is to improve the energy situation of the building either by optimizing building systems and occupant behavior or by proposing retrofit stra tegies, in which case the measured data is used to calibrate the simu lation model [20–23]. A recent string of review articles highlights the importance of data mining and analytics for energy efficiency enhancement in buildings [24–26]. In this section, we review some of the recent research that uses sensor data to derive relevant inferences. Since the focus is on research methods and approach, we also include cases of non-residential buildings. Fan et al. are first to utilize time series data concerning building operation to discover gradual patterns [27]. The relationships between variables were defined as “the more/less A, the more/less B”. However, as their study was based on data from the building automation system of a large factory, the energy efficiency recommendations targeted the operation of the chiller system. Neither occupancy nor building prop erties such as of the façade were studied. Ahmadi-Karvigh et al. discussed energy saving potential through real-time activity recognition in a multi-occupancy office and two single occupancy apartments [28]. On average, they found an energy saving potential of 35.5% of an appliance or lighting system. Pena et al. pro posed a rule-based system to detect energy efficiency anomalies using a data mining approach in an office building with a glass curtain wall [29]. A similar study on temporal knowledge discovery was done by Fan et al. for a high rise office building [30]. They discovered motifs and temporal association rules as benchmarks for building operation. Bang et al. presented a real-time model-based fault detection method for the automatic identification of abnormal energy performance in building ventilation units [31]. The authors defined the threshold limits for detecting anomalies by a simple approach based on a percentage of the model predicted the performance of the ventilation systems. Fan et al. proposed an autoencoder-based unsupervised anomaly detection method for building energy data for an educational building [32]. They discovered various types of anomalies, including transient behaviors, operational faults, inefficient control strategies and atypical events. In addition to feature and motif extraction, the analysis of time stamps is very significant in building energy analysis and modelling. First, it is used in characterizing energy consumption patterns, as done by Capozolli et al. where a set of rules based on timestamps can identify 2
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Fig. 1. a) Southeast façade b) Southwest façade c) Air temperature sensor in the living room d) Heat flux sensor along with internal temperature probe e) Sensor probes measuring supply and return temperature of the heating system.
The realm of investigation is the living room of the building. We hypothesize that the thermal characteristics obtained from measure ments of the living room can be transferred to other parts of the building and to the entire house. Although the measurement campaign involved the installation of 16 sensors, we utilize only 7 sensors from this set that relate to the living room. These are indoor air temperature, window open time, CO2 concentration, supply temperature from the heating system, outdoor air temperature, heat flux through the wall, and heat flux through the window. The heat flux sensors were mounted on the inside surface of the wall and window. The corresponding indoor and outdoor air temperature were measured on the same height as the heat flux and approximately 5 cm away from the surface of the wall or win dow. The placement and details of these sensors are shown in Fig. 2. The scatter plot between the six variables and the indoor air temperature is shown in Fig. A1. Further details on the design and configuration of the sensors can be found in Ref. [19].
conditional rules between each pair. The description of cross-correlation and defined rules is provided in the following sections. 2.2.1. U-value calculations The U-value calculations based on measured data are done using the method from the ISO 9869–1:2014 standard [35]. This standard pre scribes an average method that assumes that the U-value can be ob tained by dividing the mean density of heat flow rate by the mean temperature difference, the average being taken over a long enough time period. The following text in italics is directly taken from the standard. The calculated U-value is obtained as, Pn j¼1 qj � U ¼ Pn (1) Tej j¼1 Tij where, U is the U-value of the element, q is the density of heat flow rate into the element (W/m2), Ti and Te are the internal and external surface tem perature across the element (K). The calculation procedure is separated for ‘light’ and ‘heavy’ building elements. For light elements (like window glass), which have a specific heat capacity per unit area of less than 20 kJ/(m2.K), it is recommended that the analysis is carried out only on data acquired at night (from 1 h after sunset until sunrise), to avoid the effects of solar radiation. The test may be stopped when the results after three subsequent nights do not differ by more than �5%. Otherwise, it shall be continued. Whereas, for heavier elements, which have a specific heat per unit area of more than 20 kJ/ (m2.K), the analysis shall be carried out over a period which is an integer multiple of 24 h. The test shall be ended only when the following conditions are fulfilled:
2.2. The approach In order to achieve the first objective, we explored the most conve nient ways of representing temporal distribution in the context of building operation. Analyzing the time series data, it was evident that there is a diurnal variation in all variables. Keeping this in mind, we selected polar plots to represent the daily distribution of variables. The polar axis is transformed into a 24-h coordinate system and the measured values are represented on the radial axis. We call these transformed polar plots as ‘clock plots’. An example using outdoor air temperature is shown in Fig. 3. Most of the analysis in the first part of this study is done by combining clock plots with histogram analysis. To achieve the second objective, we first study the cross-correlation of the 6 selected variables with indoor air temperature. The cross-correlation gives the lag time between a pair of variables. Once we obtain the lag times, we look at the slopes of the variables at every 5-min and define
a) the duration of the test exceeds 72 h; b) the R-value obtained at the end of the test does not deviate by more than �5% from the value obtained 24 h before; c) the R-value obtained by analyzing the data from the first time period during INT(2 x DT/3) d does not deviate by more than � 5% from the 3
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Fig. 2. Floor plan showing the placement of the sensors in the living room as well as the three main components of the sensor kit.
values obtained from the data of the last time period of the same duration. DT is the duration of the test in days; INT is the integer part; d) if the change in heat stored in the wall is more than 5% of the heat passing through the wall over the test period, further analysis based on ISO 9869–1:2014, section 7.2 or Annex B shall be done.
The results of this analysis are presented in section 3.2. Since we did not have the means to obtain the heat stored in the wall, we neglect rule d) from the standard. However, we assume that the change in heat stored in the wall is not more than 5% of the heat passing through the wall over the test period since the temperature difference between in ternal and external temperatures did not vary much. In addition, the ISO standard states that the heat flux measurements should not be exposed to solar radiation. In our measurements, the heat flux is placed on the internal surface on the wall facing north which does not receive any direct solar radiation.
Since the calculation method for heavier building elements is more detailed, we use them for our analysis for calculating the U-values for the wall and the window. In addition, we perform a sensitivity analysis to see the effect of the length of measurement duration on the calculated Uvalues. This is done in the following steps:
2.2.2. Cross-correlation analysis The cross-correlation function (XCF) measures the similarity be tween a time series and lagged versions of another time series as a function of the lag. XCF starts with the estimation of the sample crosscovariance function. Cross-correlation is implemented through a sam ple cross-correlation function between two univariate time series [36]. This phenomena with respect to building variables is well known as demonstrated by Lim and Kim who studied time-lag phenomenon be tween the external environment and thermal load of a building [37]. We believe that such lags exist in each pair consisting of indoor air tem perature and the six selected variables. The cross-correlation analysis is computed using the following equations. Consider the time series y1t and y2t and lags k ¼ 0, �1, �2, …For data pairs (y11,y21), (y12,y22), …,(y1T, y2T), an estimate of the lag k cross-covariance, Cy1y2 is.
a) Divide the 2-week period data into periods of 24 h (14 days); b) Fix 72 h (3 days) as the minimum period of measurement (based on rule a) of the ISO standard). Generate analysis periods based on the selected number of days. For example, selecting 3 as the number of days will generate 4 periods for the 2-week duration. Similarly, selecting 4, 5 and 6 days will generate 3, 2 and 2 periods respectively; c) Get the U-value using heat flux and temperature measurements at the end of each period. We call this as ‘U-final’; d) Check this value against the one obtained 24 h before (based on ISO rule b)). We call it as ‘U-final 2’. The error between U-final and Ufinal 2 should be within 5%. We call this ‘Error condition 1’; e) Check the U-values at first 2/3 and last 2/3 time periods (based on ISO rule c)). We call these as ‘U2-final’ and ‘U3-final’ respectively. The error between U2-final and U3-final should be within 5%. We call this ‘Error condition 2’; f) Select U-values in which both the error conditions are fulfilled.
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Fig. 3. Steps to transform a general time series into polar coordinates with outdoor air temperature as an example. Such polar plots are used for the rest of the study.
8 > > < cy1 y2 ðkÞ ¼
T k 1X ðy1t T T¼1
> T k > :1 X ðy2t T T¼1
y1 Þ y2;tþk
y2 Þ y1;t
� y2 ; �
k
y1 ;
The cross-correlation, ry1y2 is estimated by.
k ¼ 0; 1; 2; … (2)
ry1y2 ðkÞ ¼
k ¼ 0; 1; 2; …
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi cy2y2 ð0Þ; where cy2y2 ð0Þ ¼ Varðy2 Þ
(5)
By knowing the time lag, we get an enhanced understanding of the time it takes for change in one variable to influence the other. This will assist in formulating the conditional rules in the next section. Based on these rules, we can quantify the simultaneous change in a pair of vari ables. A simple correlation plot for the pair of the six variables is shown in Fig. A2. The results of the cross-correlation analysis are plotted in Figure A 2.
where ȳ1 and ȳ2 are the sample means of the series. The sample standard deviations Sy1 and Sy2 of the series are. qffiffiffiffiffiffiffiffiffiffiffiffiffiffi sy1 ¼ cy1y1 ð0Þ; where cy1y1 ð0Þ ¼ Varðy1 Þand (3) sy2 ¼
cy1y2 ðkÞ ; k ¼ 0; � 1; �2; … sy1 sy2
(4)
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Table 1 Conditional rules for the six pair of variables. Variable 1:
Window opening time CO2 concentration Supply temperature Outdoor temperature Heat flux through the wall Heat flux through the window
Variable 2: Indoor air temperature Rule 1
Rule 2
Rule 3
Rule 4
Increase/ Decrease
Decrease/ Decrease
Increase/ Increase
Decrease/ Increase
E
U
U
E
U U
E E
E E
U U
E
U
U
E
E
U
U
E
E
U
U
E
Table legend: E –Expected, U – Unexpected.
2.2.3. Conditional rules To study the simultaneous change in a pair of variables, we first take each time series and perform differencing. Differencing provides us with instances when the variable has a positive, negative or no slope between a unit time interval, which in this case is 5-min. By knowing instances of increase and decrease in variable values, we can look into simultaneous changes in pairs of variables. Although this will not necessarily indicate a causal relationship, it will tell us the instances when a pair of variables behave similarly. We define a set of conditional rules to study the individual influence of the six variables on the indoor air temperature. As an example, consider the pair including heat flux through the window and indoor air temperature. Our first proposed rule for this pair states that if heat flux through the window (from inside to the outside) increases, the indoor temperature decreases. The second rule states that if the heat flux de creases, the indoor temperature also decreases. The third rule states that if heat flux increases, the indoor temperature also increases and the fourth rule states that if the heat flux decreases, the indoor temperature increases. From these rules, we derive the instances for ‘expected’ and ‘unexpected’ behavior. For example, we know that if the heat loss through the window increases, the indoor temperature shall drop down and vice versa. Such instances are labelled as ‘expected’ instances. On the other hand, if the heat loss through the window increases and the indoor temperature also increases, we consider such instances as ‘un expected’. Even though, the increase in indoor temperature may be due to the rise in hot water supplied by the heating system. Nevertheless, considering just the pair of heat flux loss through the window and indoor air temperature, we consider contradicting instances as unexpected. This is because we are interested in instances of ‘expected’ and ‘unex pected’ behavior between a pair of variables. Since our analysis is based on data from a heating period, the rules defined also consider the operation and settings of the heating system. Therefore, based on the settings of the heating system, when the outdoor temperature drops, the heating system regulates the indoor temperature by increasing it. Once we obtain the pair-wise results, we rank the variables according to their degree of correlation on the change in indoor air temperature. To stay within the scope of this study, we limit the rules to two variables, i.e. a pair-wise relation. A summary of rules involving all six pairs is listed in Table 1.
Fig. 4. Time series plot of the indoor and outdoor air temperature, heat flux and the resultant U-value of the wall.
see that the U-values converge to an asymptotical value. We further perform a sensitivity study to analyze the influence of length of mea surements on the U-value calculations. The associated methodology is discussed in section 2.2.1. Table 2 shows the results for the sensitivity analysis for the window U-value. We see that most of the values fulfil both the error conditions. The mean U-value of the data used for the sensitivity analysis is found to be 2.5 W/m2.K whereas the one obtained by considering the entire data is found to be 2.45 W/m2.K. We also see that these values are very close to the estimated value of this element, which is at 2.4 W/m2.K. The close proximity of all the values shows the robustness of the sensor data as well as the calculation methods. We also see that a measurement period of 3 days is enough for calculating the Uvalue of the window. The results for the U-value calculation for the wall show that there are only few values that fulfil both the error conditions (Table 3). We see that the duration of 3 days is not enough and the error conditions are likely to be fulfilled when higher number of days are considered. The mean U-value of the wall for the entire sensitivity analysis is found to be 0.72 W/m2.K, whereas the one obtained by considering the entire data is found to be 0.65 W/m2. K. We also see that these values deviate from the estimated value of this element, which is at 0.46 W/m2. K. The deviation of this value to the one calculated using the entire data is 29%. Although this may be attributed to the thermal storage effect, which we do not measure, the deviation from the theoretical value is high. The minimum U-value from the entire sensitivity analysis is found to be 0.59 which is still at a deviation of 22%. Such deviations might lead to the perfor mance gap which is often observed in results of simulations based on theoretical values. To elaborate on the deviation within the measured values, the results are also plotted as a boxplot (Fig. 5). Here, we see the absolute deviation for both the wall and the window as well as the percentage deviation of the measured U-values. Within the sensitivity analysis, the highest deviation for the window is at 5.4% whereas for the wall it is at 9.4%. The corresponding theoretical U-values are also shown in the plot with absolute values.
3. Results 3.1. Measured U-values Fig. 4 shows the internal and external temperature, the heat flux through the wall and the resultant U-value during the 2-week mea surement period. Since equation (1) entails cumulative calculations, we 6
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Table 2 Results of sensitivity analysis for the measured U-value (W/m2.K) of the window. Days
Periods
U-final
U-final 2
U2-final
U3-final
3
1 2 3 4 1 2 3 1 2 1 2 1
2.515 2.672 2.395 2.524 2.519 2.601 2.474 2.531 2.537 2.587 2.464 2.456
2.520 2.561 2.440 2.543 2.515 2.661 2.470 2.519 2.528 2.531 2.459 2.508
2.520 2.561 2.440 2.543 2.482 2.652 2.418 2.535 2.609 2.519 2.447 2.535
2.518 2.751 2.368 2.497 2.493 2.562 2.504 2.568 2.468 2.627 2.474 2.426
4 5 6 12 days (all data)
Both conditions should be fulfilled Error condition 1 (less than 0.05)
Error condition 2 (less than 0.05)
0.002 0.042 0.019 0.007 0.002 0.023 0.002 0.005 0.004 0.022 0.002 0.021
0.001 0.069 0.031 0.018 0.004 0.035 0.034 0.013 0.057 0.041 0.011 0.045
Bold signifies that the values are less than the error threshold, that is, less than 0.05. Table 3 Results of sensitivity analysis for the measured U-value (W/m2.K) of the wall. Days 3
4 5 6 12 days (all data)
Periods 1 2 3 4 1 2 3 1 2 1 2 1
U final 0.796 0.658 0.719 0.659 0.768 0.700 0.656 0.788 0.599 0.732 0.686 0.702
U final 2 0.818 0.775 0.758 0.718 0.796 0.688 0.695 0.768 0.642 0.788 0.718 0.708
U2 final 0.818 0.775 0.758 0.718 0.792 0.670 0.639 0.741 0.617 0.768 0.640 0.712
U3 final 0.772 0.647 0.690 0.780 0.787 0.689 0.704 0.765 0.623 0.682 0.655 0.658
Both conditions should be fulfilled Error condition 1 (less than 0.05)
Error condition 2 (less than 0.05)
0.028 0.177 0.055 0.090 0.036 0.017 0.060 0.026 0.072 0.077 0.046 0.007
0.060 0.198 0.099 0.080 0.006 0.028 0.091 0.031 0.010 0.126 0.023 0.082
Fig. 5. Results of the sensitivity analysis for the measured U-values of the window and the wall a) in absolute values and b) in percentage deviation from the means of results from the sensitivity analysis.
3.2. Temporal distribution
(Fig. 6). The periods of highest value are between 13:00 and 17:00. We can see that the indoor air temperature during the night (00:00 to 6:00) is between 23 and 24 � C. Since this is a living room, there is no occu pancy during the night. However, the high temperature shows that either the floor heating system is actively heating during this period or the thermal insulation of the house is extremely good such that there is no significant heat loss during the night. We explore these factors while discussing the distribution of other variables like the supply temperature of the heating system and heat flux through the wall and window.
In this section, we discuss the temporal distribution of variables using a combination of clock plots and histogram analysis. For this, the time-series measurement of each variable is distributed into bins. The width of bins is fixed by considering that there are a substantial number of points in each bin. We perform the analysis separately for weekdays and weekends for the two-week period. As seen in the results, the indoor air temperature during weekdays is more than 23 � C for 87% of the time 7
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Fig. 6. Temporal distribution of variables on a polar ‘clock’ plot. In the figure, the unit for the indoor and the outdoor air temperature and the supply temperature of the heating system is � C, the unit for the heat flux through the wall and the window is W/m2 , and the unit for the CO2 concentration is ppm.
During weekends, we see the indoor temperature being higher during day hours but lower during the night. This is due to the high natural ventilation during this time. This ventilation aspect is also visible in the CO2 plot when the concentration during the weekend is much lower for early morning hours. The CO2 concentration is higher during late hours in the weekend showing that there were more occupants which likely
has influenced the ventilation behavior. This is also supported by the high indoor air temperature observed during this time. In general, the CO2 concentration is higher during weekends for known reasons of oc cupants being present in the living room. The CO2 concentration is highest for both weekdays and weekends during late evening hours (between 18:00 and 23:00). 8
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Fig. 6. (continued).
The heating system of this residence is configured to maintain a temperature of 23 � C between 5:30 and 22:30 during weekdays. As seen in the clock plot for supply temperature, the operation matches well with the settings. We also see that there is some heating even beyond these hours when the supply temperature is maintained between 30 and 34 � C. Based on the settings, the indoor temperature to be maintained
during this period is 17 � C. We clearly see that the heating system is operating outside of this desired requirement. This leads to a rather high indoor air temperature in the living room during the night. The high indoor temperature is also due to heat being given back to the room from the thermal mass of the inner layer of brick walls as well as the hot water in the heating pipes. The insulation within the wall also prevents heat 9
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from dissipating to the cooler exterior. We observe that the air tem perature in the living room never goes below 17 � C. It is also reflected in the data for the weekends, the supply temperature is greater than 34 � C for 43% of the time. This is also reflected in the clock plot for CO2 concentration. The outdoor air temperature during this two-week period is contin uously below 12 � C for 85% of the time. One of the weekends witnessed
a rather cool and stagnant period. This is reflected in the clock plot for the weekends when the outdoor temperature is between 4 and 12 � C for 90% of the time. From the measurements, we observe that the heat flux through the northeast wall of the living room is highest between 11:00 and 17:00. The difference between the indoor and outdoor temperature is low during this time, therefore, the high heat flux during this period can be
Fig. 7. Results from the conditional rule analysis for the six pair of variables. 10
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Fig. 7. (continued).
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attributed to the high thermal mass of the wall. The periods of least heat flux are observed between 23:00 and 9:00. It is almost half of what is measured during the day and is true for both weekdays and weekends. The heat flux is less than 10 W/m2 for 53% and 66% of the time during weekdays and weekends respectively. The heat flux through the window is highest during the night and least during late afternoon, which co incides with the low outdoor temperatures during night and higher ones during the day. This shows the direct proportionality between the heat flux through the window and difference between indoor and outdoor temperature (as indoor temperature operates at a narrow range). This is attributed to the low thermal mass of the window, showing that the window has a very low heat content.
5:00. These correspond to rule 1 which refers to an increase in supply temperature and a decrease in indoor air temperature. This is also observed in the conditioned rules for outdoor and indoor air tempera ture. The percentage of expected instances for weekdays, in this case, is 37 and 44 for weekends. Most of the unexpected instances related to rule 3 occur between 8:00 and 12:00. This is the period when the outdoor temperature rises but the indoor temperature in the living room also rises. This is the period when the supply temperature of the heating system is also the highest. Since the increase and decrease in outdoor and the indoor temperature are relative to each variable, we cannot conclude any energy saving potential for this pair. For example, although the outdoor temperature increases, it may still be at a much lower temperature when compared to the indoor temperature. While discussing conditional rules from the building envelope, we look at heat flux values. The result for the pair between heat flux through the wall and indoor air temperature shows that the percentage of ex pected instances is 40 for weekdays and 45 for weekends. Most of the unexpected instances are between 6:00 and 13:00 and again between 22:00 and 3:00. There are also a reasonable number of unexpected in stances between 14:00 and 18:00. The corresponding rules 2 and 3 are instances when both these variables simultaneously increase or decrease. Rule 3 concerns a simultaneous increase in both variables. It is interesting to observe that an increase in indoor air temperature also increases the heat flux lost through the wall envelope, although the outdoor temperature also rises during this period. This is most likely due to the high thermal mass of the wall and the high lag time that is noted between heat flux and indoor air temperature. A similar distribution is seen for the weekends as well. The result for the pair between heat flux through the window and indoor air temperature shows that the percentage of expected instances is 54 for weekdays and 49 for weekends. In contrast to the heat loss through the wall, we see that the heat flux through window decreases between 7:00 and 8:00 and the indoor air temperature increases. This is due to the increase in outdoor air temperature during this period, resulting in a lower temperature difference between indoor and outdoor. This reduction in temperature difference is reflected sooner in the heat flux through the window than through the wall.
3.3. Conditional rules As mentioned earlier, we perform the conditional rule analysis for each pair separately. We begin with analyzing window opening duration and indoor air temperature. We see from Table 1 that rule 1 for this pair corresponds to expected situations and rules 2, 3 and 4 represent un expected situations. It is to be noted that we are looking into the intake of outdoor air through the window when it is open. Rule 1 is based on the instance when the window is open and the indoor air temperature decreases. This is termed as ‘expected’ as any mixing of outdoor air will reduce the indoor air temperature. Rules 2 and 3 are for instances when the window is closed but the air temperature decreases and when the window is open but the air temperature increases. These are termed as ‘unexpected’ instances as the heat loss due to intake of outdoor air is expected when the window is open and not expected when it is closed. Similarly, rule 4 is based on instances of when the window is closed but the indoor air temperature increases and is termed as ‘expected’. The results for this pair of variable shows that the duration of the window being opened has a small influence on variation in indoor temperature (Fig. 7). This is because this window is opened only for 3% of the time during the entire measurement period. During weekends, the total opening duration for this window increases from 3 to 7%. Although the window is responsible for heat loss through conduction, we see that its influence on reducing indoor air temperature through the intake of outdoor air, in this specific case, is insignificant. The aspect of conduc tive heat loss is discussed while analyzing heat flux through the window. The results of conditioned rules for CO2 show that 63% of instances are expected and 37% are unexpected. Most of the unexpected instances are between 8:00 and 15:00. This is also the time period when the supply temperature of the heating system is high and the resulting indoor air temperature is high. During this time period, the CO2 concentration is very low, indicating that there are no occupants present. The window being closed during this time does not allow any mixing with outdoor air which would lower the CO2 concentration. This also tells us that there is some potential for energy saving related to this time period, for example by lowering the heating supply temperature or mass flow to reduce heating input. The percentage of expected instances increases during weekends and is calculated to be 78%. This shows that in terms of occupant presence and operation of the heating system, the current setpoint configuration fits better for weekends than weekdays, due to longer absences of the occupants. We see that most ‘unexpected’ in stances between 8:00 and 15:00 are replaced by ‘expected’ instances during weekends. The results for conditioned rules for the supply temperature of the heating system show that there are 48% of expected instances. The unexpected instances are distributed between 23:00 and 11:00. The supply temperature increases between 23:00 and 5:00, whereas the in door air temperature decreases. This is due to the high heat loss through the building envelope because of the high-temperature difference be tween indoor and outdoor. We also note from Fig. 4 that the indoor air temperature is maintained between 23 and 24 � C during this entire period, which offers additional energy savings potential. There is a significant number of unexpected instances every day between 4:00 and
4. Discussion The temporal analysis of individual variables shows that none of the seven variables is static and each has a good variation at a 5-min in terval. A normalized time series plot for all the variables is provided in Fig. 8. As an example, we observe that the indoor air temperature in this space is higher than 23 � C for more than 87% of the time and for 32% higher than 24 � C. This is higher than the standard value of 20 � C that is taken as the design indoor temperature for residences according to the Swiss standard, SIA 380/1 [38]. Furthermore, for building simulation or heat balance models, the indoor temperature is taken as constant. Using standard values, the temperature difference to the outdoor temperature would be offset by 4 � C and therefore, the estimated heat loss will be higher. This will increase the calculated heating energy demand and thus result in the pre-retrofit performance gap, also known as the pre-bound effect and potentially more drastic retrofit measures on the envelope than necessary. Another parameter contributing to the performance gap is the dif ference in estimated and measured U-values of the wall and window. In addition to this variation, we also observe that the measured U-value of the wall and window are 0.72 and 2.5 W/m2K when compared to their theoretical values of 0.46 and 2.4 W/m2K respectively. We see the applicability of the ISO 9869-1 2014 method in determining the U-value of the building elements. The sensitivity analysis for U-value measure ments show that a minimum of 3 days is required in order to adhere to the ISO guidelines for measuring the U-value of the window. It is to be noted that the measurement error of the sensor is �3% The standard acknowledges such measurement errors and along with procedural 12
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Fig. 8. Time series plot at 5-min interval for the seven variables over a typical weekday.
errors, it mentions that the measured U-values should be expected with an uncertainty of 14–28%. The temporal analysis also indicates time periods of occupantpresence as well as occupant-behavior such as instances of opening windows. Not only is this information useful for building modelling, but we also analyze their effect on change in indoor air temperature. The cross-correlation analysis shows that, for this building, the two occupant-related variables window opening and CO2 concentration do not have a significant influence on the change in indoor air temperature. Other occupant-related variables like thermostat settings also influence indoor air temperature, however, it is not recorded as part of the current WSN campaign. We conclude that the variation in indoor air tempera ture is rather governed by the settings of the heating system and the gradual heat loss process through the wall and window. The highest correlation to a change in indoor air temperature is observed for heat flux through the wall. This is perhaps due to the larger area of the wall compared to the window. The second highest correlation to a change in indoor air temperature is the outdoor air temperature. This is under standable as a change in outdoor air temperature governs the heat loss from the building, and therefore the indoor air temperature. The cor responding lag period of 150 min shows that it takes about 2 h and 30 min for a change in outdoor temperature to be reflected in indoor temperature. However, analyzing the conditional rules for the two occupantrelated variables, we see that there are instances when no occupant is present but the indoor air temperature is still high. These instances occur between 8:00 and 15:00 during weekdays. This information can be readily used for heating system control. The same does not apply during weekends when there is significant occupant-presence during this time. Another case of saving energy is identified with respect to heating sys tem supply temperature and indoor air temperature. We observe that every day between 23:00 and 5:00, the heat supplied to the building is
high, whereas there are many instances of indoor air temperature decreasing during this time. This is due to the high heat loss through the building envelope during the night. Perhaps, such heating can be avoi ded as there is no occupancy in the living room at this period, although heating is required to maintain the required indoor air temperature. The functioning of the heating system at this time is related to the thermostat control in the living room. As can be seen, the heating system maintains an indoor temperature of 23 � C during this time as against 17 � C for which the heating system control was originally programmed for. We also identify high thermal mass of the wall. The influence of heat loss from the wall on indoor air temperature is highest at a lag of 10 h. The conditional rule analysis shows that the period of heat loss is highest during day hours. This is the period when the outdoor air temperature Table 4 Summary of results from conditional rule analysis. Variable 1 Window open duration CO2 concentration Heating supply temperature Outdoor air temperature Heat flux through the wall Heat flux through the window
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Variable 2
Expected instances
Unexpected instances
Weekday
Weekend
Weekday
Weekend
3%
7%
97%
93%
63%
78%
37%
22%
48%
50%
52%
50%
Indoor air temperature Indoor air temperature
37%
44%
63%
56%
40%
45%
60%
54%
Indoor air temperature
54%
49%
46%
51%
Indoor air temperature Indoor air temperature Indoor air temperature
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rises. Therefore, if we neglect this time lag and consider heat loss from the wall based on instant temperature difference between the indoor and outdoor, we are bound to produce an error. Such errors may balance out while considering the mean daily or monthly values, but these do not provide an accurate assessment of the heat loss phenomena. Apart from window open duration, which hardly has any correlation with changes in indoor air temperature, we see that outdoor air tem perature also has a lower correlation with instances of change in indoor air temperature. This is very reasonable as occupants have a preferred temperature range, and thereby we see daily periods when the outdoor and indoor temperature are not in sync. We see that a simple correlation does not tell as much as conditioned rules with reasoning. Next to outdoor temperature, we see the highest percentage for unexpected behavior is for heat flux through the wall. As explained earlier, this is due to the thermal mass of the wall. It will be interesting to see the variation of this variable with added wall insulation. This variable is followed by heating supply temperature and heat flux through the window. The instances of an unexpected situation for heating supply temperature will be much less if the mixing valve data was available. Lastly, we see that CO2 monitoring also indicates periods of high heating with no occupant present. How ever, in terms of a percentage value, the unexpected instances corre sponding to this situation are the least. At the same time, this could be seen as the simplest step in the retrofit recommendation as it deals with re-programming of the heating control. A summary of the results from the conditional rule analysis is shown in Table 4.
5. Conclusions This study investigates the temporal distribution of building vari ables and their instances of variation. It is observed that a more refined and dynamic assessment of building properties reveal relevant insights for building performance assessment and retrofitting. The findings of this study are based on a case study of a single-family residence, where a wireless sensor network is deployed. We see the importance of in-situ measurements that generate high-resolution datasets of not only in door environmental conditions but also building properties. These measurements allow for the calculation of U-values of the walls and windows using the method prescribed by the ISO 9869-1 standard. We observe that the U-value for the window glass is close to its estimated value, while the same is not true for the wall. The difference in estimated and measured U-value of the wall is attributed to the thermal mass of the wall, which was apparent from the measurement data. It took a mini mum of 3 days of measurements to adhere to all the guidelines of the standard for measuring the U-value of the window. The conditional rule analysis allows to investigate the mutual vari ation of pairs of variables. This helps to identify simple steps towards energy saving. For example, we identify instances of high indoor air temperature and supply temperature while no occupants are present in the space. Although these findings are very specific to the building studied, these can be extended to other single-family residences. The simple rules defined in this approach should hold true to other studies as well, although the details might differ. In terms of thermal modelling of buildings, the temporal analysis clearly shows the dynamics on a highresolution time domain in contrast to conventional approaches that consider only daily or monthly mean values. We can also readily identify time periods of expected and unexpected instances and treat these pe riods differently for calibrating thermal models of buildings. We also see the importance of heat capacity of the wall along with transmittance values (U-values), although only the latter is usually considered for thermal analysis. Finally, the proposed approach supports a thorough understanding of variable distribution and interaction to the different stakeholders and occupants.
4.1. Limitations One of the limitations of this study is that we measure the supply temperature only on the outlet from the heating system, before the mixing valve. Therefore, we do not capture the direct relationship be tween supply temperature from the heating system and the indoor air temperature. We also did not measure the space heating demand as the flow meter was not installed. Otherwise, the study of the influence of energy consumption on indoor air temperature would have provided interesting insights. We try to uncover this using only the supply tem perature from the heating system and intend to include flow meters in future measurements. Our analysis is limited to the functioning of the living room, although the WSN was deployed in the entire house. We take the living room as a sample room so that the pairwise analysis between the six variables and indoor air temperature can be performed. It is to be noted that the focus is neither on a holistic building analysis nor on a comparison between different spaces within the building, although the methodology can be easily extended to other spaces or to the entire building. We also neglect the influence of incoming solar radiation and suspect that it will not hamper the results too much as the window faces northeast. Although there is a complex interaction between many variables and a combined influence of these on the indoor air temperature, we only look into individual relationships. This is to get a simplified under standing of the influence of individual variables on indoor air temperature.
Declaration of competing interest The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consul tancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Acknowledgment This research project is supported by the Swiss Innovation Agency Innosuisse and is part of the Swiss Competence Center for Energy Research SCCER FEEB&D. This work is also supported by the Office for Water and Energy of the Canton St. Gallen (AWE), Switzerland.
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Appendix
Fig. A1. Scatter plot at hourly interval for the six pair of variables.
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Fig. A2. Cross-correlation plots for the six variables with indoor air temperature. The sample cross correlation at lag 0 represents the correlation coefficient when the two time series are in complete sync.
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Contents lists available at ScienceDirect
Building and Environment journal homepage: http://www.elsevier.com/locate/buildenv
Identifying temporal properties of building components and indoor environment for building performance assessment Chirag Deb *, Mario Frei, Arno Schlueter Chair of Architecture and Building Systems, Institute of Technology in Architecture, ETH Zurich, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Temporal dynamics Building properties Wireless sensor network Time lag Data analytics Performance gap Energy saving
Buildings are dynamic thermal systems that require energy to maintain a comfortable indoor environment. Knowing these dynamics allows for identifying relevant building characteristics for assessing building energy performance. However, conventional building simulation programs take daily or monthly mean values for performance assessment. These often aggregate the errors and uncertainties between the theoretical and the actual building performance while missing the temporal dynamics on a minute or hourly basis. The objective of this study is to uncover the temporal aspects of building properties using data obtained by a wireless sensor network (WSN). Our analysis focuses on the following seven variables that are relevant for assessing building performance and retrofit measures: indoor air temperature, window opening instances, CO2 concentration, supply temperature from the heating system, outdoor air temperature, heat flux through the wall and the window. Using a singlefamily residence as a case study, we identify the temporal dynamics of these variables using polar plots on a high-resolution, 5-minute interval dataset. Following this, we define a set of conditional rules to study ‘expected’ and ‘unexpected’ impact of the six variables on the indoor air temperature. We observe strong temporal dynamics for certain building components, resulting in a large time lag. The conditional rule analysis also allows identi fying energy saving potentials and factors contributing to the performance gap. For example, we observe high indoor air temperatures and at times when no occupants are present. Finally, we discuss the benefits of this approach with respect to building retrofit and energy performance gap analysis.
1. Introduction It is widely known that building-related heating and cooling con sumes 40% of the final energy consumption in the European Union [1]. The building stock is also responsible for 36% of all the CO2 emissions. In view of this, the 2015 Paris Agreement on climate change requires consistent attention towards low greenhouse gas emissions and climate-resilient development [2]. Along with focusing on new sus tainable developments, it is important to focus on existing buildings as buildings have a long lifespan and 80% of today’s building stock will remain in place beyond 2050 [3,4]. In the context of Switzerland, a primary aim of the Swiss Energy Strategy 2050 is to reduce the energy consumption and promote energy efficiency in buildings, in the trans port sector and by electrical appliances [5]. Through the Building Pro gramme, the Federal Government and the cantons subsidize the cost of energy-saving renovation of buildings [6]. Although the importance of retrofitting existing buildings is clear,
the current rate of retrofit in Switzerland is only about 1–2% [7]. The low rate can be attributed to the many factors including the gap between the actual and the predicted energy use in pre- and post-retrofit condi tions, known as the ‘performance gap’ [8–10]. To address these gaps and barriers, recent research focuses on in-situ measurement of building variables using sensor networks [11–14]. There has also been efforts to develop co-incident low-cost sensors that capture holistic picture of building performance without significantly compromising information content [15]. The sensors provide accurate, near real-time information of building variables and operating conditions. These time series data can be used to develop and calibrate energy models for retrofit analysis as well as validate post-retrofit predictions [16]. For example, Lozinsky and Touchie measured window component infiltration rates to improve model calibration for a multi-unit residential building in Canada and noted that infiltration highly contributes to heating load of residential buildings [17]. Real-time data from sensors is also used for model pre dictive control (MPC) of building systems as well as forecasting [18]. In
* Corresponding author. E-mail address: [email protected] (C. Deb). https://doi.org/10.1016/j.buildenv.2019.106506 Received 22 May 2019; Received in revised form 25 September 2019; Accepted 26 October 2019 Available online 31 October 2019 0360-1323/© 2019 Elsevier Ltd. All rights reserved.
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both cases, there is either a white-box model which is calibrated using measured data or a black-box model which is developed from the dataset. The measured data is used to improve the model parameters rather than using it extensively to derive useful inferences on the existing building condition. This study is part of an endeavor aiming at developing a methodology to derive building and occupancy related inferences and related optimal retrofit measures using WSN data [13, 19]. In this work we utilize high-resolution measurement data to obtain an understanding of the temporal distribution of relevant variables and related energy saving potentials. Knowledge of temporal dynamics of variables describing the building as a thermal system also supports mitigating the retrofit performance gap. For this we formulate the following objectives of this study:
anomalies in energy consumption patterns [33]. Second, it is used in disaggregating energy consumption into its constituents [34]. As we see, most of the reviewed literature is based on datasets from already installed building management systems. There is a lack of investigation on residential buildings where hardly any data is readily available. This is because there are many challenges in setting up sensors in residences, including limited freedom on the number of sensors that can be deployed without hindering the privacy of the occupants. Therefore, our work contributes by presenting data and results from a measurement campaign in a single-family residence. The data gathered and the accompanying analysis can be used to understand building characteristics at a high-resolution, 5-min interval level. These will reveal the variation and mutual interaction between variables that are often missed while considering daily or monthly mean values for per formance assessment. The study of mutual interaction using conditioned rules will also help uncover instances of energy saving. The results can also be used to understand some aspects of the causes of the performance gap at the pre-retrofit stage.
1. To study the temporal aspects of building variables using highresolution measurement data obtained by a WSN and using a new form of polar plots. 2. To define conditional rules for ‘expected’ and ‘unexpected’ instances and study the influence of these variables on the indoor air temperature. 3. To uncover the instances of potential energy saving using the above rules.
2. Methods 2.1. Building case study and dataset The building under assessment is a single-family house located in the Canton of St. Gallen in Eastern Switzerland, which was part of a mea surement campaign of 10 buildings in total (Fig. 1). It was constructed in 1973 and has a heated floor area of 147 m2. The building is located in a sunny, unobstructed location and contains six rooms, occupied by a family of four with two adults and two children. It has three storeys with the façade consisting of cavity masonry and the floors made of concrete. The cavity masonry is made of two bricklayers, 12 cm each with a 5 cm rock wool layer between them. The estimated U-value of the masonry is 0.46 W/m2K. The windows have a wooden-metal frame with doubleglazing. The estimated U-value of the glass is 2.4 W/m2K. The base ment floor has a 7 cm concrete slab and polystyrene insulation with a thickness of 2 cm. The house has a pitched roof with paneling and a 5 cm thick mineral fiber insulation contained in one-sided laminated aluminum. The space heating system consists of an oil-based boiler and an underfloor heating network. It is fitted with a constant pressure pump for the underfloor network. The indoor temperature set point is at 23 � C. Based on the control settings, the heating system maintains an indoor air temperature of 23 � C during the day (5:30 to 22:00) and 17 � C during the night (22:00 to 5:30). The indoor set point can be changed through the thermostat in the living room. The loop for space heating also contains a mixing valve. The oil consumed in the boiler is used to heat water in the space heating loop as well as domestic hot water. The domestic hot water is stored in a storage tank and is consumed whenever required. The measurement campaign involves a wireless sensor network developed at the Chair of Architecture and Building Systems, ETH Zurich [19]. The sensor kit consists of sensor nodes, router nodes and a gateway. The sensor nodes collect data and transmit them through a communication module that is housed inside the sensor node. The data is transmitted to the gateway via the ZigBee communication protocol. The gateway, containing a SIM card, sends the data to a MySQL server. In cases where the sensor nodes are far from the gateway, router nodes are placed in between. The measurement campaign took place during the winter of 2016–17 but the period of analysis for this study is for two weeks between 13th and 27th March 2017. Measurements are recorded every 5 min. This gives a total of 288 points for each day per variable and 4032 points for two weeks. The data is preprocessed for timestamp synchronizing and removal of outliers. The outliers are removed by applying a smoothing technique with a moving average filter. The span window is taken at five, which means that each data point is replaced by an average of itself and two other points on each side of the data point.
1.1. Background There have been numerous studies in the domain of building assessment using measured data. The final goal for all these studies is to improve the energy situation of the building either by optimizing building systems and occupant behavior or by proposing retrofit stra tegies, in which case the measured data is used to calibrate the simu lation model [20–23]. A recent string of review articles highlights the importance of data mining and analytics for energy efficiency enhancement in buildings [24–26]. In this section, we review some of the recent research that uses sensor data to derive relevant inferences. Since the focus is on research methods and approach, we also include cases of non-residential buildings. Fan et al. are first to utilize time series data concerning building operation to discover gradual patterns [27]. The relationships between variables were defined as “the more/less A, the more/less B”. However, as their study was based on data from the building automation system of a large factory, the energy efficiency recommendations targeted the operation of the chiller system. Neither occupancy nor building prop erties such as of the façade were studied. Ahmadi-Karvigh et al. discussed energy saving potential through real-time activity recognition in a multi-occupancy office and two single occupancy apartments [28]. On average, they found an energy saving potential of 35.5% of an appliance or lighting system. Pena et al. pro posed a rule-based system to detect energy efficiency anomalies using a data mining approach in an office building with a glass curtain wall [29]. A similar study on temporal knowledge discovery was done by Fan et al. for a high rise office building [30]. They discovered motifs and temporal association rules as benchmarks for building operation. Bang et al. presented a real-time model-based fault detection method for the automatic identification of abnormal energy performance in building ventilation units [31]. The authors defined the threshold limits for detecting anomalies by a simple approach based on a percentage of the model predicted the performance of the ventilation systems. Fan et al. proposed an autoencoder-based unsupervised anomaly detection method for building energy data for an educational building [32]. They discovered various types of anomalies, including transient behaviors, operational faults, inefficient control strategies and atypical events. In addition to feature and motif extraction, the analysis of time stamps is very significant in building energy analysis and modelling. First, it is used in characterizing energy consumption patterns, as done by Capozolli et al. where a set of rules based on timestamps can identify 2
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Fig. 1. a) Southeast façade b) Southwest façade c) Air temperature sensor in the living room d) Heat flux sensor along with internal temperature probe e) Sensor probes measuring supply and return temperature of the heating system.
The realm of investigation is the living room of the building. We hypothesize that the thermal characteristics obtained from measure ments of the living room can be transferred to other parts of the building and to the entire house. Although the measurement campaign involved the installation of 16 sensors, we utilize only 7 sensors from this set that relate to the living room. These are indoor air temperature, window open time, CO2 concentration, supply temperature from the heating system, outdoor air temperature, heat flux through the wall, and heat flux through the window. The heat flux sensors were mounted on the inside surface of the wall and window. The corresponding indoor and outdoor air temperature were measured on the same height as the heat flux and approximately 5 cm away from the surface of the wall or win dow. The placement and details of these sensors are shown in Fig. 2. The scatter plot between the six variables and the indoor air temperature is shown in Fig. A1. Further details on the design and configuration of the sensors can be found in Ref. [19].
conditional rules between each pair. The description of cross-correlation and defined rules is provided in the following sections. 2.2.1. U-value calculations The U-value calculations based on measured data are done using the method from the ISO 9869–1:2014 standard [35]. This standard pre scribes an average method that assumes that the U-value can be ob tained by dividing the mean density of heat flow rate by the mean temperature difference, the average being taken over a long enough time period. The following text in italics is directly taken from the standard. The calculated U-value is obtained as, Pn j¼1 qj � U ¼ Pn (1) Tej j¼1 Tij where, U is the U-value of the element, q is the density of heat flow rate into the element (W/m2), Ti and Te are the internal and external surface tem perature across the element (K). The calculation procedure is separated for ‘light’ and ‘heavy’ building elements. For light elements (like window glass), which have a specific heat capacity per unit area of less than 20 kJ/(m2.K), it is recommended that the analysis is carried out only on data acquired at night (from 1 h after sunset until sunrise), to avoid the effects of solar radiation. The test may be stopped when the results after three subsequent nights do not differ by more than �5%. Otherwise, it shall be continued. Whereas, for heavier elements, which have a specific heat per unit area of more than 20 kJ/ (m2.K), the analysis shall be carried out over a period which is an integer multiple of 24 h. The test shall be ended only when the following conditions are fulfilled:
2.2. The approach In order to achieve the first objective, we explored the most conve nient ways of representing temporal distribution in the context of building operation. Analyzing the time series data, it was evident that there is a diurnal variation in all variables. Keeping this in mind, we selected polar plots to represent the daily distribution of variables. The polar axis is transformed into a 24-h coordinate system and the measured values are represented on the radial axis. We call these transformed polar plots as ‘clock plots’. An example using outdoor air temperature is shown in Fig. 3. Most of the analysis in the first part of this study is done by combining clock plots with histogram analysis. To achieve the second objective, we first study the cross-correlation of the 6 selected variables with indoor air temperature. The cross-correlation gives the lag time between a pair of variables. Once we obtain the lag times, we look at the slopes of the variables at every 5-min and define
a) the duration of the test exceeds 72 h; b) the R-value obtained at the end of the test does not deviate by more than �5% from the value obtained 24 h before; c) the R-value obtained by analyzing the data from the first time period during INT(2 x DT/3) d does not deviate by more than � 5% from the 3
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Fig. 2. Floor plan showing the placement of the sensors in the living room as well as the three main components of the sensor kit.
values obtained from the data of the last time period of the same duration. DT is the duration of the test in days; INT is the integer part; d) if the change in heat stored in the wall is more than 5% of the heat passing through the wall over the test period, further analysis based on ISO 9869–1:2014, section 7.2 or Annex B shall be done.
The results of this analysis are presented in section 3.2. Since we did not have the means to obtain the heat stored in the wall, we neglect rule d) from the standard. However, we assume that the change in heat stored in the wall is not more than 5% of the heat passing through the wall over the test period since the temperature difference between in ternal and external temperatures did not vary much. In addition, the ISO standard states that the heat flux measurements should not be exposed to solar radiation. In our measurements, the heat flux is placed on the internal surface on the wall facing north which does not receive any direct solar radiation.
Since the calculation method for heavier building elements is more detailed, we use them for our analysis for calculating the U-values for the wall and the window. In addition, we perform a sensitivity analysis to see the effect of the length of measurement duration on the calculated Uvalues. This is done in the following steps:
2.2.2. Cross-correlation analysis The cross-correlation function (XCF) measures the similarity be tween a time series and lagged versions of another time series as a function of the lag. XCF starts with the estimation of the sample crosscovariance function. Cross-correlation is implemented through a sam ple cross-correlation function between two univariate time series [36]. This phenomena with respect to building variables is well known as demonstrated by Lim and Kim who studied time-lag phenomenon be tween the external environment and thermal load of a building [37]. We believe that such lags exist in each pair consisting of indoor air tem perature and the six selected variables. The cross-correlation analysis is computed using the following equations. Consider the time series y1t and y2t and lags k ¼ 0, �1, �2, …For data pairs (y11,y21), (y12,y22), …,(y1T, y2T), an estimate of the lag k cross-covariance, Cy1y2 is.
a) Divide the 2-week period data into periods of 24 h (14 days); b) Fix 72 h (3 days) as the minimum period of measurement (based on rule a) of the ISO standard). Generate analysis periods based on the selected number of days. For example, selecting 3 as the number of days will generate 4 periods for the 2-week duration. Similarly, selecting 4, 5 and 6 days will generate 3, 2 and 2 periods respectively; c) Get the U-value using heat flux and temperature measurements at the end of each period. We call this as ‘U-final’; d) Check this value against the one obtained 24 h before (based on ISO rule b)). We call it as ‘U-final 2’. The error between U-final and Ufinal 2 should be within 5%. We call this ‘Error condition 1’; e) Check the U-values at first 2/3 and last 2/3 time periods (based on ISO rule c)). We call these as ‘U2-final’ and ‘U3-final’ respectively. The error between U2-final and U3-final should be within 5%. We call this ‘Error condition 2’; f) Select U-values in which both the error conditions are fulfilled.
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Fig. 3. Steps to transform a general time series into polar coordinates with outdoor air temperature as an example. Such polar plots are used for the rest of the study.
8 > > < cy1 y2 ðkÞ ¼
T k 1X ðy1t T T¼1
> T k > :1 X ðy2t T T¼1
y1 Þ y2;tþk
y2 Þ y1;t
� y2 ; �
k
y1 ;
The cross-correlation, ry1y2 is estimated by.
k ¼ 0; 1; 2; … (2)
ry1y2 ðkÞ ¼
k ¼ 0; 1; 2; …
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi cy2y2 ð0Þ; where cy2y2 ð0Þ ¼ Varðy2 Þ
(5)
By knowing the time lag, we get an enhanced understanding of the time it takes for change in one variable to influence the other. This will assist in formulating the conditional rules in the next section. Based on these rules, we can quantify the simultaneous change in a pair of vari ables. A simple correlation plot for the pair of the six variables is shown in Fig. A2. The results of the cross-correlation analysis are plotted in Figure A 2.
where ȳ1 and ȳ2 are the sample means of the series. The sample standard deviations Sy1 and Sy2 of the series are. qffiffiffiffiffiffiffiffiffiffiffiffiffiffi sy1 ¼ cy1y1 ð0Þ; where cy1y1 ð0Þ ¼ Varðy1 Þand (3) sy2 ¼
cy1y2 ðkÞ ; k ¼ 0; � 1; �2; … sy1 sy2
(4)
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Table 1 Conditional rules for the six pair of variables. Variable 1:
Window opening time CO2 concentration Supply temperature Outdoor temperature Heat flux through the wall Heat flux through the window
Variable 2: Indoor air temperature Rule 1
Rule 2
Rule 3
Rule 4
Increase/ Decrease
Decrease/ Decrease
Increase/ Increase
Decrease/ Increase
E
U
U
E
U U
E E
E E
U U
E
U
U
E
E
U
U
E
E
U
U
E
Table legend: E –Expected, U – Unexpected.
2.2.3. Conditional rules To study the simultaneous change in a pair of variables, we first take each time series and perform differencing. Differencing provides us with instances when the variable has a positive, negative or no slope between a unit time interval, which in this case is 5-min. By knowing instances of increase and decrease in variable values, we can look into simultaneous changes in pairs of variables. Although this will not necessarily indicate a causal relationship, it will tell us the instances when a pair of variables behave similarly. We define a set of conditional rules to study the individual influence of the six variables on the indoor air temperature. As an example, consider the pair including heat flux through the window and indoor air temperature. Our first proposed rule for this pair states that if heat flux through the window (from inside to the outside) increases, the indoor temperature decreases. The second rule states that if the heat flux de creases, the indoor temperature also decreases. The third rule states that if heat flux increases, the indoor temperature also increases and the fourth rule states that if the heat flux decreases, the indoor temperature increases. From these rules, we derive the instances for ‘expected’ and ‘unexpected’ behavior. For example, we know that if the heat loss through the window increases, the indoor temperature shall drop down and vice versa. Such instances are labelled as ‘expected’ instances. On the other hand, if the heat loss through the window increases and the indoor temperature also increases, we consider such instances as ‘un expected’. Even though, the increase in indoor temperature may be due to the rise in hot water supplied by the heating system. Nevertheless, considering just the pair of heat flux loss through the window and indoor air temperature, we consider contradicting instances as unexpected. This is because we are interested in instances of ‘expected’ and ‘unex pected’ behavior between a pair of variables. Since our analysis is based on data from a heating period, the rules defined also consider the operation and settings of the heating system. Therefore, based on the settings of the heating system, when the outdoor temperature drops, the heating system regulates the indoor temperature by increasing it. Once we obtain the pair-wise results, we rank the variables according to their degree of correlation on the change in indoor air temperature. To stay within the scope of this study, we limit the rules to two variables, i.e. a pair-wise relation. A summary of rules involving all six pairs is listed in Table 1.
Fig. 4. Time series plot of the indoor and outdoor air temperature, heat flux and the resultant U-value of the wall.
see that the U-values converge to an asymptotical value. We further perform a sensitivity study to analyze the influence of length of mea surements on the U-value calculations. The associated methodology is discussed in section 2.2.1. Table 2 shows the results for the sensitivity analysis for the window U-value. We see that most of the values fulfil both the error conditions. The mean U-value of the data used for the sensitivity analysis is found to be 2.5 W/m2.K whereas the one obtained by considering the entire data is found to be 2.45 W/m2.K. We also see that these values are very close to the estimated value of this element, which is at 2.4 W/m2.K. The close proximity of all the values shows the robustness of the sensor data as well as the calculation methods. We also see that a measurement period of 3 days is enough for calculating the Uvalue of the window. The results for the U-value calculation for the wall show that there are only few values that fulfil both the error conditions (Table 3). We see that the duration of 3 days is not enough and the error conditions are likely to be fulfilled when higher number of days are considered. The mean U-value of the wall for the entire sensitivity analysis is found to be 0.72 W/m2.K, whereas the one obtained by considering the entire data is found to be 0.65 W/m2. K. We also see that these values deviate from the estimated value of this element, which is at 0.46 W/m2. K. The deviation of this value to the one calculated using the entire data is 29%. Although this may be attributed to the thermal storage effect, which we do not measure, the deviation from the theoretical value is high. The minimum U-value from the entire sensitivity analysis is found to be 0.59 which is still at a deviation of 22%. Such deviations might lead to the perfor mance gap which is often observed in results of simulations based on theoretical values. To elaborate on the deviation within the measured values, the results are also plotted as a boxplot (Fig. 5). Here, we see the absolute deviation for both the wall and the window as well as the percentage deviation of the measured U-values. Within the sensitivity analysis, the highest deviation for the window is at 5.4% whereas for the wall it is at 9.4%. The corresponding theoretical U-values are also shown in the plot with absolute values.
3. Results 3.1. Measured U-values Fig. 4 shows the internal and external temperature, the heat flux through the wall and the resultant U-value during the 2-week mea surement period. Since equation (1) entails cumulative calculations, we 6
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Table 2 Results of sensitivity analysis for the measured U-value (W/m2.K) of the window. Days
Periods
U-final
U-final 2
U2-final
U3-final
3
1 2 3 4 1 2 3 1 2 1 2 1
2.515 2.672 2.395 2.524 2.519 2.601 2.474 2.531 2.537 2.587 2.464 2.456
2.520 2.561 2.440 2.543 2.515 2.661 2.470 2.519 2.528 2.531 2.459 2.508
2.520 2.561 2.440 2.543 2.482 2.652 2.418 2.535 2.609 2.519 2.447 2.535
2.518 2.751 2.368 2.497 2.493 2.562 2.504 2.568 2.468 2.627 2.474 2.426
4 5 6 12 days (all data)
Both conditions should be fulfilled Error condition 1 (less than 0.05)
Error condition 2 (less than 0.05)
0.002 0.042 0.019 0.007 0.002 0.023 0.002 0.005 0.004 0.022 0.002 0.021
0.001 0.069 0.031 0.018 0.004 0.035 0.034 0.013 0.057 0.041 0.011 0.045
Bold signifies that the values are less than the error threshold, that is, less than 0.05. Table 3 Results of sensitivity analysis for the measured U-value (W/m2.K) of the wall. Days 3
4 5 6 12 days (all data)
Periods 1 2 3 4 1 2 3 1 2 1 2 1
U final 0.796 0.658 0.719 0.659 0.768 0.700 0.656 0.788 0.599 0.732 0.686 0.702
U final 2 0.818 0.775 0.758 0.718 0.796 0.688 0.695 0.768 0.642 0.788 0.718 0.708
U2 final 0.818 0.775 0.758 0.718 0.792 0.670 0.639 0.741 0.617 0.768 0.640 0.712
U3 final 0.772 0.647 0.690 0.780 0.787 0.689 0.704 0.765 0.623 0.682 0.655 0.658
Both conditions should be fulfilled Error condition 1 (less than 0.05)
Error condition 2 (less than 0.05)
0.028 0.177 0.055 0.090 0.036 0.017 0.060 0.026 0.072 0.077 0.046 0.007
0.060 0.198 0.099 0.080 0.006 0.028 0.091 0.031 0.010 0.126 0.023 0.082
Fig. 5. Results of the sensitivity analysis for the measured U-values of the window and the wall a) in absolute values and b) in percentage deviation from the means of results from the sensitivity analysis.
3.2. Temporal distribution
(Fig. 6). The periods of highest value are between 13:00 and 17:00. We can see that the indoor air temperature during the night (00:00 to 6:00) is between 23 and 24 � C. Since this is a living room, there is no occu pancy during the night. However, the high temperature shows that either the floor heating system is actively heating during this period or the thermal insulation of the house is extremely good such that there is no significant heat loss during the night. We explore these factors while discussing the distribution of other variables like the supply temperature of the heating system and heat flux through the wall and window.
In this section, we discuss the temporal distribution of variables using a combination of clock plots and histogram analysis. For this, the time-series measurement of each variable is distributed into bins. The width of bins is fixed by considering that there are a substantial number of points in each bin. We perform the analysis separately for weekdays and weekends for the two-week period. As seen in the results, the indoor air temperature during weekdays is more than 23 � C for 87% of the time 7
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Fig. 6. Temporal distribution of variables on a polar ‘clock’ plot. In the figure, the unit for the indoor and the outdoor air temperature and the supply temperature of the heating system is � C, the unit for the heat flux through the wall and the window is W/m2 , and the unit for the CO2 concentration is ppm.
During weekends, we see the indoor temperature being higher during day hours but lower during the night. This is due to the high natural ventilation during this time. This ventilation aspect is also visible in the CO2 plot when the concentration during the weekend is much lower for early morning hours. The CO2 concentration is higher during late hours in the weekend showing that there were more occupants which likely
has influenced the ventilation behavior. This is also supported by the high indoor air temperature observed during this time. In general, the CO2 concentration is higher during weekends for known reasons of oc cupants being present in the living room. The CO2 concentration is highest for both weekdays and weekends during late evening hours (between 18:00 and 23:00). 8
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Fig. 6. (continued).
The heating system of this residence is configured to maintain a temperature of 23 � C between 5:30 and 22:30 during weekdays. As seen in the clock plot for supply temperature, the operation matches well with the settings. We also see that there is some heating even beyond these hours when the supply temperature is maintained between 30 and 34 � C. Based on the settings, the indoor temperature to be maintained
during this period is 17 � C. We clearly see that the heating system is operating outside of this desired requirement. This leads to a rather high indoor air temperature in the living room during the night. The high indoor temperature is also due to heat being given back to the room from the thermal mass of the inner layer of brick walls as well as the hot water in the heating pipes. The insulation within the wall also prevents heat 9
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from dissipating to the cooler exterior. We observe that the air tem perature in the living room never goes below 17 � C. It is also reflected in the data for the weekends, the supply temperature is greater than 34 � C for 43% of the time. This is also reflected in the clock plot for CO2 concentration. The outdoor air temperature during this two-week period is contin uously below 12 � C for 85% of the time. One of the weekends witnessed
a rather cool and stagnant period. This is reflected in the clock plot for the weekends when the outdoor temperature is between 4 and 12 � C for 90% of the time. From the measurements, we observe that the heat flux through the northeast wall of the living room is highest between 11:00 and 17:00. The difference between the indoor and outdoor temperature is low during this time, therefore, the high heat flux during this period can be
Fig. 7. Results from the conditional rule analysis for the six pair of variables. 10
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Fig. 7. (continued).
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attributed to the high thermal mass of the wall. The periods of least heat flux are observed between 23:00 and 9:00. It is almost half of what is measured during the day and is true for both weekdays and weekends. The heat flux is less than 10 W/m2 for 53% and 66% of the time during weekdays and weekends respectively. The heat flux through the window is highest during the night and least during late afternoon, which co incides with the low outdoor temperatures during night and higher ones during the day. This shows the direct proportionality between the heat flux through the window and difference between indoor and outdoor temperature (as indoor temperature operates at a narrow range). This is attributed to the low thermal mass of the window, showing that the window has a very low heat content.
5:00. These correspond to rule 1 which refers to an increase in supply temperature and a decrease in indoor air temperature. This is also observed in the conditioned rules for outdoor and indoor air tempera ture. The percentage of expected instances for weekdays, in this case, is 37 and 44 for weekends. Most of the unexpected instances related to rule 3 occur between 8:00 and 12:00. This is the period when the outdoor temperature rises but the indoor temperature in the living room also rises. This is the period when the supply temperature of the heating system is also the highest. Since the increase and decrease in outdoor and the indoor temperature are relative to each variable, we cannot conclude any energy saving potential for this pair. For example, although the outdoor temperature increases, it may still be at a much lower temperature when compared to the indoor temperature. While discussing conditional rules from the building envelope, we look at heat flux values. The result for the pair between heat flux through the wall and indoor air temperature shows that the percentage of ex pected instances is 40 for weekdays and 45 for weekends. Most of the unexpected instances are between 6:00 and 13:00 and again between 22:00 and 3:00. There are also a reasonable number of unexpected in stances between 14:00 and 18:00. The corresponding rules 2 and 3 are instances when both these variables simultaneously increase or decrease. Rule 3 concerns a simultaneous increase in both variables. It is interesting to observe that an increase in indoor air temperature also increases the heat flux lost through the wall envelope, although the outdoor temperature also rises during this period. This is most likely due to the high thermal mass of the wall and the high lag time that is noted between heat flux and indoor air temperature. A similar distribution is seen for the weekends as well. The result for the pair between heat flux through the window and indoor air temperature shows that the percentage of expected instances is 54 for weekdays and 49 for weekends. In contrast to the heat loss through the wall, we see that the heat flux through window decreases between 7:00 and 8:00 and the indoor air temperature increases. This is due to the increase in outdoor air temperature during this period, resulting in a lower temperature difference between indoor and outdoor. This reduction in temperature difference is reflected sooner in the heat flux through the window than through the wall.
3.3. Conditional rules As mentioned earlier, we perform the conditional rule analysis for each pair separately. We begin with analyzing window opening duration and indoor air temperature. We see from Table 1 that rule 1 for this pair corresponds to expected situations and rules 2, 3 and 4 represent un expected situations. It is to be noted that we are looking into the intake of outdoor air through the window when it is open. Rule 1 is based on the instance when the window is open and the indoor air temperature decreases. This is termed as ‘expected’ as any mixing of outdoor air will reduce the indoor air temperature. Rules 2 and 3 are for instances when the window is closed but the air temperature decreases and when the window is open but the air temperature increases. These are termed as ‘unexpected’ instances as the heat loss due to intake of outdoor air is expected when the window is open and not expected when it is closed. Similarly, rule 4 is based on instances of when the window is closed but the indoor air temperature increases and is termed as ‘expected’. The results for this pair of variable shows that the duration of the window being opened has a small influence on variation in indoor temperature (Fig. 7). This is because this window is opened only for 3% of the time during the entire measurement period. During weekends, the total opening duration for this window increases from 3 to 7%. Although the window is responsible for heat loss through conduction, we see that its influence on reducing indoor air temperature through the intake of outdoor air, in this specific case, is insignificant. The aspect of conduc tive heat loss is discussed while analyzing heat flux through the window. The results of conditioned rules for CO2 show that 63% of instances are expected and 37% are unexpected. Most of the unexpected instances are between 8:00 and 15:00. This is also the time period when the supply temperature of the heating system is high and the resulting indoor air temperature is high. During this time period, the CO2 concentration is very low, indicating that there are no occupants present. The window being closed during this time does not allow any mixing with outdoor air which would lower the CO2 concentration. This also tells us that there is some potential for energy saving related to this time period, for example by lowering the heating supply temperature or mass flow to reduce heating input. The percentage of expected instances increases during weekends and is calculated to be 78%. This shows that in terms of occupant presence and operation of the heating system, the current setpoint configuration fits better for weekends than weekdays, due to longer absences of the occupants. We see that most ‘unexpected’ in stances between 8:00 and 15:00 are replaced by ‘expected’ instances during weekends. The results for conditioned rules for the supply temperature of the heating system show that there are 48% of expected instances. The unexpected instances are distributed between 23:00 and 11:00. The supply temperature increases between 23:00 and 5:00, whereas the in door air temperature decreases. This is due to the high heat loss through the building envelope because of the high-temperature difference be tween indoor and outdoor. We also note from Fig. 4 that the indoor air temperature is maintained between 23 and 24 � C during this entire period, which offers additional energy savings potential. There is a significant number of unexpected instances every day between 4:00 and
4. Discussion The temporal analysis of individual variables shows that none of the seven variables is static and each has a good variation at a 5-min in terval. A normalized time series plot for all the variables is provided in Fig. 8. As an example, we observe that the indoor air temperature in this space is higher than 23 � C for more than 87% of the time and for 32% higher than 24 � C. This is higher than the standard value of 20 � C that is taken as the design indoor temperature for residences according to the Swiss standard, SIA 380/1 [38]. Furthermore, for building simulation or heat balance models, the indoor temperature is taken as constant. Using standard values, the temperature difference to the outdoor temperature would be offset by 4 � C and therefore, the estimated heat loss will be higher. This will increase the calculated heating energy demand and thus result in the pre-retrofit performance gap, also known as the pre-bound effect and potentially more drastic retrofit measures on the envelope than necessary. Another parameter contributing to the performance gap is the dif ference in estimated and measured U-values of the wall and window. In addition to this variation, we also observe that the measured U-value of the wall and window are 0.72 and 2.5 W/m2K when compared to their theoretical values of 0.46 and 2.4 W/m2K respectively. We see the applicability of the ISO 9869-1 2014 method in determining the U-value of the building elements. The sensitivity analysis for U-value measure ments show that a minimum of 3 days is required in order to adhere to the ISO guidelines for measuring the U-value of the window. It is to be noted that the measurement error of the sensor is �3% The standard acknowledges such measurement errors and along with procedural 12
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Fig. 8. Time series plot at 5-min interval for the seven variables over a typical weekday.
errors, it mentions that the measured U-values should be expected with an uncertainty of 14–28%. The temporal analysis also indicates time periods of occupantpresence as well as occupant-behavior such as instances of opening windows. Not only is this information useful for building modelling, but we also analyze their effect on change in indoor air temperature. The cross-correlation analysis shows that, for this building, the two occupant-related variables window opening and CO2 concentration do not have a significant influence on the change in indoor air temperature. Other occupant-related variables like thermostat settings also influence indoor air temperature, however, it is not recorded as part of the current WSN campaign. We conclude that the variation in indoor air tempera ture is rather governed by the settings of the heating system and the gradual heat loss process through the wall and window. The highest correlation to a change in indoor air temperature is observed for heat flux through the wall. This is perhaps due to the larger area of the wall compared to the window. The second highest correlation to a change in indoor air temperature is the outdoor air temperature. This is under standable as a change in outdoor air temperature governs the heat loss from the building, and therefore the indoor air temperature. The cor responding lag period of 150 min shows that it takes about 2 h and 30 min for a change in outdoor temperature to be reflected in indoor temperature. However, analyzing the conditional rules for the two occupantrelated variables, we see that there are instances when no occupant is present but the indoor air temperature is still high. These instances occur between 8:00 and 15:00 during weekdays. This information can be readily used for heating system control. The same does not apply during weekends when there is significant occupant-presence during this time. Another case of saving energy is identified with respect to heating sys tem supply temperature and indoor air temperature. We observe that every day between 23:00 and 5:00, the heat supplied to the building is
high, whereas there are many instances of indoor air temperature decreasing during this time. This is due to the high heat loss through the building envelope during the night. Perhaps, such heating can be avoi ded as there is no occupancy in the living room at this period, although heating is required to maintain the required indoor air temperature. The functioning of the heating system at this time is related to the thermostat control in the living room. As can be seen, the heating system maintains an indoor temperature of 23 � C during this time as against 17 � C for which the heating system control was originally programmed for. We also identify high thermal mass of the wall. The influence of heat loss from the wall on indoor air temperature is highest at a lag of 10 h. The conditional rule analysis shows that the period of heat loss is highest during day hours. This is the period when the outdoor air temperature Table 4 Summary of results from conditional rule analysis. Variable 1 Window open duration CO2 concentration Heating supply temperature Outdoor air temperature Heat flux through the wall Heat flux through the window
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Variable 2
Expected instances
Unexpected instances
Weekday
Weekend
Weekday
Weekend
3%
7%
97%
93%
63%
78%
37%
22%
48%
50%
52%
50%
Indoor air temperature Indoor air temperature
37%
44%
63%
56%
40%
45%
60%
54%
Indoor air temperature
54%
49%
46%
51%
Indoor air temperature Indoor air temperature Indoor air temperature
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rises. Therefore, if we neglect this time lag and consider heat loss from the wall based on instant temperature difference between the indoor and outdoor, we are bound to produce an error. Such errors may balance out while considering the mean daily or monthly values, but these do not provide an accurate assessment of the heat loss phenomena. Apart from window open duration, which hardly has any correlation with changes in indoor air temperature, we see that outdoor air tem perature also has a lower correlation with instances of change in indoor air temperature. This is very reasonable as occupants have a preferred temperature range, and thereby we see daily periods when the outdoor and indoor temperature are not in sync. We see that a simple correlation does not tell as much as conditioned rules with reasoning. Next to outdoor temperature, we see the highest percentage for unexpected behavior is for heat flux through the wall. As explained earlier, this is due to the thermal mass of the wall. It will be interesting to see the variation of this variable with added wall insulation. This variable is followed by heating supply temperature and heat flux through the window. The instances of an unexpected situation for heating supply temperature will be much less if the mixing valve data was available. Lastly, we see that CO2 monitoring also indicates periods of high heating with no occupant present. How ever, in terms of a percentage value, the unexpected instances corre sponding to this situation are the least. At the same time, this could be seen as the simplest step in the retrofit recommendation as it deals with re-programming of the heating control. A summary of the results from the conditional rule analysis is shown in Table 4.
5. Conclusions This study investigates the temporal distribution of building vari ables and their instances of variation. It is observed that a more refined and dynamic assessment of building properties reveal relevant insights for building performance assessment and retrofitting. The findings of this study are based on a case study of a single-family residence, where a wireless sensor network is deployed. We see the importance of in-situ measurements that generate high-resolution datasets of not only in door environmental conditions but also building properties. These measurements allow for the calculation of U-values of the walls and windows using the method prescribed by the ISO 9869-1 standard. We observe that the U-value for the window glass is close to its estimated value, while the same is not true for the wall. The difference in estimated and measured U-value of the wall is attributed to the thermal mass of the wall, which was apparent from the measurement data. It took a mini mum of 3 days of measurements to adhere to all the guidelines of the standard for measuring the U-value of the window. The conditional rule analysis allows to investigate the mutual vari ation of pairs of variables. This helps to identify simple steps towards energy saving. For example, we identify instances of high indoor air temperature and supply temperature while no occupants are present in the space. Although these findings are very specific to the building studied, these can be extended to other single-family residences. The simple rules defined in this approach should hold true to other studies as well, although the details might differ. In terms of thermal modelling of buildings, the temporal analysis clearly shows the dynamics on a highresolution time domain in contrast to conventional approaches that consider only daily or monthly mean values. We can also readily identify time periods of expected and unexpected instances and treat these pe riods differently for calibrating thermal models of buildings. We also see the importance of heat capacity of the wall along with transmittance values (U-values), although only the latter is usually considered for thermal analysis. Finally, the proposed approach supports a thorough understanding of variable distribution and interaction to the different stakeholders and occupants.
4.1. Limitations One of the limitations of this study is that we measure the supply temperature only on the outlet from the heating system, before the mixing valve. Therefore, we do not capture the direct relationship be tween supply temperature from the heating system and the indoor air temperature. We also did not measure the space heating demand as the flow meter was not installed. Otherwise, the study of the influence of energy consumption on indoor air temperature would have provided interesting insights. We try to uncover this using only the supply tem perature from the heating system and intend to include flow meters in future measurements. Our analysis is limited to the functioning of the living room, although the WSN was deployed in the entire house. We take the living room as a sample room so that the pairwise analysis between the six variables and indoor air temperature can be performed. It is to be noted that the focus is neither on a holistic building analysis nor on a comparison between different spaces within the building, although the methodology can be easily extended to other spaces or to the entire building. We also neglect the influence of incoming solar radiation and suspect that it will not hamper the results too much as the window faces northeast. Although there is a complex interaction between many variables and a combined influence of these on the indoor air temperature, we only look into individual relationships. This is to get a simplified under standing of the influence of individual variables on indoor air temperature.
Declaration of competing interest The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consul tancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Acknowledgment This research project is supported by the Swiss Innovation Agency Innosuisse and is part of the Swiss Competence Center for Energy Research SCCER FEEB&D. This work is also supported by the Office for Water and Energy of the Canton St. Gallen (AWE), Switzerland.
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Appendix
Fig. A1. Scatter plot at hourly interval for the six pair of variables.
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Fig. A2. Cross-correlation plots for the six variables with indoor air temperature. The sample cross correlation at lag 0 represents the correlation coefficient when the two time series are in complete sync.
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