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Overlapping of cooking behavior in high-rise residential buildings
Energy & Buildings 210 (2020) 109764
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Overlapping of cooking behavior in high-rise residential buildings Yirui Wang a, Jun Gao a,b,∗, Lingjie Zeng a, Leqi Tong a, Guodong Liu a, Changsheng Cao a a
Institute of HVAC Engineering, School of Mechanical Engineering, Tongji University, Shanghai 200092, China Key laboratory of Performance Evolution and Control for Engineering Structure of Ministry of Education, College of Civil Engineering, Tongji University, Shanghai 200092, China
b
a r t i c l e
i n f o
Article history: Received 11 October 2019 Revised 7 December 2019 Accepted 6 January 2020 Available online 10 January 2020 Keywords: Residential building Central shaft Cooking fume Coincidence factor Ventilation Energy conservation Cooking time
a b s t r a c t The design of a centralized cooking-fume exhaust system for high-rise residential buildings lacks the parameters related to cooking behavior, such as the coincidence factors. This study surveyed 12-, 14-, and 25-floor residential units by using a thermometer to obtain the continuous temperature profiles for study cooking behavior. Python was used to identify the breaks of temperature gradient, and continuous temperature profiles were transformed into a group of step signals consisting of only “0” and “1” while interfering fluctuations were eliminated and turning points were determined. The hourly overlapping rate of the residential unit after data processing is highly similar. The abstraction of cooking behavior is a mathematical statistical model that obeys normal distribution. A typical cooking behavior model based on normal distribution was established using the main cooking periods, kurtosis, and skewness values, the modeling step length, the peak value of the coincidence factors, and the time corresponding to the peak. Using different correction coefficients to correct the peak value of the coincidence factors can extend the application scope of the model to buildings of any height. In addition, the coincidence factor of 50% can be used as a design parameter for the flue cross section and fan selection parameters. Thus, the selected fan, which is fully loaded during cooking periods and has low load during non-cooking periods, has significant energy saving potential. © 2020 Elsevier B.V. All rights reserved.
1. Introduction The rapid urbanization of the developing countries has facilitated the construction of numerous high-rise residential buildings [1–3], especially in China [4–6]. This situation introduced the “design” requirement of the centralized exhaust system for each group of kitchens that distribute vertically in one high-rise unit and share one vertical shaft to discharge the cooling oil fumes (COFs) [7,8]. Such exhaust systems are used to effectively collect the cooking-generated airborne pollutants from each kitchen and prevent the cross contamination between the kitchens [9–12]. Two typical modes of the centralized exhaust system can be adopted according to the distributed or centralized fan power scheme (Fig. 1). The first mode consists of household range hoods with distributed fan power, one central shaft, and hose-branches that connect each range hood with the shaft. In such systems, the check valve is usually installed in each hose-branch to prevent cross contamination, and the distributed fan power assures the exhaust rate required for the discharge of COFs of each kitchen. For this system, the key “design” task is to determine the cross∗ Corresponding author at: Tongji University, 1239 Siping Road, Yangpu District, Shanghai 20 0 092, China. E-mail address: [email protected] (J. Gao).
https://doi.org/10.1016/j.enbuild.2020.109764 0378-7788/© 2020 Elsevier B.V. All rights reserved.
sectional area of the shaft by using the design flow rate in the shaft for ensuring the effective area of the kitchen space. Xu and Shen [13] proposed a trial algorithm to determine the cross-sectional area according to the exhaust volume, where the overlapping of cooking behaviors in one residential unit were considered. Chen and Gong [14] calculated the cross-sectional area of shaft according to a minimum exhaust volume with an assumed overlapping rate. The results showed that the cross-sectional area of the shaft is highly sensitized to the overlapping of the cooking behaviors. The second system mode has one central shaft, one centralized fan at the shaft outlet and hose-branches that connect each range hood (no fan power) with the shaft. For such systems, air leakage and cross contamination through the check valve is considerably reduced due to that the positive pressure in the shaft is effectively eliminated by the central fan. Tong et al. [15] studied the exhaust uniformity of such exhaust system and proposed a flow-guide device to regulate the distribution of exhaust volume. However, designing the cross-sectional area of the shaft is still difficult because of the unresolved overlapping rate of the cooking behavior. Determining the “design” working point of the central fan and the operating control scheme is also challenging. The overlapping of cooking behavior affects the design of the centralized exhaust system for the kitchens in high-rise residential buildings. However, the overlapping has not been well defined and
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
erature provide similar scenarios. Despite the significant difference in stochastics between building occupancy and cooking behavior, household cooking behaviors are still statistically significant and mostly occur within the specified time immediately before the home breakfast, lunch, and supper time. This study aims to provide the reasonable coincidence factors of cooking behavior as the key input for determining the design parameters of the centralized exhaust system for the kitchens in a high-rise residential unit. Measurements, which used thermographs to collect the real-time cooking temperature, were conducted to simultaneously record the real stochastic phenomenon of cooking behaviors. The recorded temperature data were processed and analyzed to detect the cooking time and duration for identifying the coincidence factors. Typical cooking periods and the maximum values of coincidence factor were extracted for the buildings studied. One statistically significant cooking rule was derived and then used to establish a typical cooking behavior model for the extensive predictions of coincidence factors. 2. Methodology 2.1. Measuring program
Fig. 1. Two modes of centralized exhaust system for the kitchens in high-rise residential buildings: (a) system type I of household range hoods with distributed fan power, one central shaft, and hose-branches that connect each range hood with the shaft; and (b) system type II with one central shaft, one centralized fan at the shaft outlet, and hose-branches that connect each range hood (no fan power) with the shaft.
parameterized because of the complexity and uncertainty of the random cooking behavior. Despite the centralized or distributed fan power, each range hood opens, runs, and closes separately and has no any mutual communication. Cooking duration and frequency vary by many family and social factors, such as the living habits, eating habits, family structure and size, and even the economic level. Therefore, the overlapping of cooking behaviors in one residential unit is difficult to directly calculate on the basis of family cooking rules. Here we define a concise coincidence factor of cooking behavior as the ratio of the number of household range hoods operating simultaneously to the total number, that is, the overlapping rate under a relatively high cumulative probability. Such definition provides possibility for reasonably determining the overlapping rate through statistical analysis without complicated bottom-up modeling. Similar definition has been found in computer-based building energy simulation. In building energy software, stochastic variables, such as occupancy, lighting, and plug load, greatly influence the energy-consumption results. The actual schedule, profile, or value of these variables is also difficult to obtain. Therefore, these variables are usually defined through the use of diversity factors. Diversity factors are defined as numbers between zero and one, and are used as multipliers of some user-defined peak loads [16]. If the energy use or waste due to human behavior in the spatiotemporal domain is concerned, then this factor is called building occupancy diversity factor [17]. Various methods using probabilistic or other models have been proposed to estimate the occupancy diversity in different building types [18–22]. A gap between the prediction models and measured results has often been observed and researchers are currently trying to bridge the gap through surveys, interviews, walkthrough inspections or sensors [23–25]. Existing studies have indirectly discussed the coincidence factors of cooking behavior in high-rise residential buildings. Modeling and measuring of occupancy behavior in building spaces in the lit-
The COF produced by cooking has strong adhesion, which can easily cause equipment failure or damage. Thus, conducting the cooking behavior measurement by using the methods used for occupancy, such as camera, passive infrared sensor, ultrasonic sensor, radio frequency signals, sensors fusion, WLAN, Bluetooth, and Wi-Fi, is inconvenient and non-economical [24]. This study proposed a much concise measuring method, which used a group of thermographs placed near gas cookers of each kitchen in one high-rise residential unit sharing one exhaust shaft. In the measurements, a significant temperature rise indicates the cooking initiation and a significant drop implies the cooking termination [26–28]. Pre-experiments of locating the temperature probe was conducted to detect the cooking period accurately. As shown in Fig. 2, three arrangements were tested under the consideration of safety and quick requirements. By comparing the opening and closing time of the gas cooker with the measured temperature data, the initiation and termination times for cooking can be determined through the two breaks of temperature gradient and the determined cooking period can be quite reliable. A measuring distance of 10 cm between the gas outer flame and probe is relatively acceptable because a small distance (e.g., 5 cm) leads to single risk of probe and a large distance (e.g. 15 cm) reduces identifiability of the cooking period. Three residential units with 12, 14, and 25 floors in three communities in Zhejiang Province, China were selected to measure the coincidence factors of cooking behaviors under different spatiotemporal conditions. All the selected residents used a gas cooker and applied Chinese-style cooking. The measurements lasted for four consecutive days, which included general weekdays and weekends, in February 2019. From the measured data, only three householders among all the 51 householders (51 represents the total number of households surveyed, which is the sum of 12, 14, and 25. The number can be converted into a proportion of 5.9%.) had no cooking activity within the 4 days, and 35 householders (68.6%) cooked daily during the survey. In addition, 43 households (84.3%) cooked on weekdays, and 40 households (78.4%) cooked on weekends. In the one flue unit, the residents occasionally did not cook. The proportion of non-cooked households in the total households affected the “design” value of coincidence factors for the centralized exhaust system. In the extreme use case of the flue, that is, when all households cooked daily, the coincidence factor of the one flue unit should be higher than the current survey value.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
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Fig. 2. Pre-experiments for the selection of temperature probe placement, (a) three locations of the probe, and (b) recorded temperature profiles during cooking.
2.2. Data processing and validity checking Cooking period was determined by the breaks of temperature gradient as shown in Fig. 2(b). The continuous temperature profiles were transformed into a group of step signals consisting of only “0” and “1” to determine the cooking behavior and duration. As described in Fig. 3, signal “0” indicated no cooking activity and “1” meant cooking was ongoing. Python was applied to identify the original data and to code them as 0 or 1. On the basis of the spatio-temporal distribution of cooking behaviors and the coded step signals in one residential unit, coincidence factors were calculated through the number of signal “1” at each time step to the total number of signals “0” and “1” at that time step. If the step signal was coded on a time metric of one hour, the hourly coincidence factor can be obtained. The temperature profiles were transformed into step signals. The turning point is generally determined according to the breaks of temperature gradient, such as turning points A and B in Fig. 3(a). The slope of two adjacent temperature profiles was
calculated and defined as the slope between two points. If the slope changes from a negative number or zero to a positive value, the time corresponding to the smaller temperature profile is the turning point of the cooking initiation. If the slope changes from 0 or a positive number to a negative number, the time corresponding to the larger temperature profile is the turning point of the cooking termination. However, the temperature profiles throughout the day are affected by the external environment with small fluctuations. Therefore, the turning point was determined by the slope between the two points and the multi-point slope in actual coding to eliminate the interference fluctuation from the temperature fluctuation caused by cooking and ensure the accuracy of the identification. With reference to the definition method of the slope between two points mentioned above, the slope between the first and last two points of the multiple temperature parameter points is defined as the multi-point slope. As shown in Fig. 4, the time interval between the two points was 5 s, and the time interval of the multi-point slope was 120 s. The starting point temperature parameters of Groups C, D, and E were 8.8 °C, 11.0 °C, and 45.6 °C,
Fig. 3. Extraction of cooking period from the original temperature data, (a) coded step signals for one cooking period, and (b) coded step signals for one day.
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764 Table 1 Standard deviations of the coincidence factors and the proportion. 25 floors-weekdays
25 floors-weekends
14 floors-weekdays
14 floors-weekends
12 floors-weekdays
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
0% 3% 6% 8% 11%
63% 27% 7% 3% 0%
0% 3% 6% 8%
61% 28% 9% 2%
0% 4% 7% 8% 11%
74% 21% 3% 2% 0%
0% 5% 10%
79% 17% 4%
0% 5% 8% 10% 13%
63% 26% 5% 4% 2%
12 floors-weekends
25 floors-all days
14 floors-all days
12 floors-all days
All
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
0% 6% 12%
78% 20% 3%
0% 1% 3% 4% 6% 7%
52% 25% 9% 6% 5% 3%
0% 1% 2% 3% 4% 5% 6% 7%
62% 5% 12% 16% 0% 3% 1% 1%
0% 1% 2% 3% 4% 5% 6% 7% 8%
57% 10% 12% 6% 7% 1% 4% 2% 1%
0% 1% 2% 3% 4%
39% 34% 15% 8% 4%
significance level reached 5%. The samples collected in this study are the coincidence factors of the same type of building during the main cooking period, and the standard deviation is calculated to reflect the discrete situation of the flue utilization distribution of this type of building. As shown in Table 1, the accumulated proportion of SD ≤ 3% is 86% for the 25-floor residential unit, 95% for the 14-floor residential unit, and 85% for the 12-floor residential unit, and the accumulated proportion of SD ≤ 8% is 100% for the three residential units. These results indicate that the coincidence factors detected from the measured data are significant. 2.3. Parameter independence test
Fig. 4. Slope of relative temperature over three periods (The original temperature parameters of Groups C, D, and E are from the three periods in Fig. 3(b) in the revised manuscript: 07:10:00–07:12:30, 11:10:00–11:12:30, 11:18:00–11:20:30. The black line represents the multi-point slope, and the red line represents the slope between two points.). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
respectively. For comparison of the slopes of the three groups, the temperature values of 31 points in each group were respectively subtracted from 8.8 °C, 11.0 °C, and 45.6 °C to obtain three sets of relative temperature values with 0 °C as the starting point. The treatment of temperature parameters does not affect the slope of each group. As shown in Fig. 4, the multi-point slope of the point where the slope between two points changed from negative or 0 to a positive value differed in the three groups. The multi-point slope of the turning point was much larger than the slope of the interference point. Therefore, the slope limit k0 can be set during data processing to distinguish between the two types. If the multi-point slope was less than the limit k0 , the interval was considered as an interfering fluctuation, such as the interfering points C in Fig. 3(b). As depicted in Fig. 3(b), coded step signals could not be clearly located when the temperature profiles show no obvious slope breaks because of the combined effect of the small thermal lag of the temperature probe and the frequent on/off of the gas cooker during a short period of time. Therefore, a validity check on the standard deviation (SD) of the coincidence factors and their proportion is necessary. The value of SD was calculated when the
For data processing, the time step length, data fusion time, and slope interval and limit significantly affected the detection of cooking durations and coincidence factors. The time step length is the unit for Python to extract the original temperature. If the step length is too long, the slope breaks of temperature profile cannot be correctly located. If it is too short, the recognition sensitivity and fluctuation increase and thus leads to high possibility of error. Data fusion time was selected to reduce the influence of the on/off process of the gas cooker, and it should not be too long or small. Taking points D and E as examples (Fig. 3(b)), three temperature rises and falls are noted between points D and E, and the time interval is within 2 min, which can be regarded as one cooking behavior. Therefore, the appropriate fusion time, slope interval, and slope limits must be selected to determine the cooking time clearly and accurately. The slope interval and limit correspond to the slope between multi-points mentioned in the data processing. Parameter independence test was performed for the step length, fusion time, and slope interval and slope limit. Residents of the 12-floors residential unit in the survey set up cameras in their homes to record cooking behavior continuously during the survey time. Measured data of the 12-floors residential unit on a certain day were randomly sampled, and the actual cooking behaviors were taken as indicators to test the parameter. Parameter independence test and the recommended values of step length, fusion time, and slope interval and slope limit are listed in Table 2. The slope value of the declining point is not limited because the declining point can be determined by referring to the determination method of the extremum of the curve to locate the maximum value in the interval. The processing results in the recommended values in Table 2 represent the actual cooking behavior used for comparison. The experimental groups with dif-
Table 2 Independence test for step length, fusion time, and slope interval and limit, and their recommended values. Fusion time (min)
Slope interval (min)
Slope limit
Processing results
5 10 30 60 90 120
10 10 10 10 10 10
6 6 6 6 6 6
0.05 0.05 0.05 0.05 0.05 0.05
3 3 3 3 3 3
0.1 0.1 0.1 0.35 0.8 0.8
−0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.35 −0.8 −0.8
4 4 4 4 4 4
2 2 2 2 2 2
2 2 4 4 2 2
6 6 6 4 6 4
6 6 6 6 6 6
2 2 2 2 2 2
2 2 2 2 2 2
2 2 2 2 2 2
0 0 0 0 0 0
2 2 2 2 2 2
4 4 4 4 4 4
4 4 4 4 4 4
10 10 10 10 10
2 5 10 15 20
4 4 4 4 4
0.05 0.05 0.05 0.05 0.05
3 3 3 3 3
0.1 0.1 0.1 0.1 0.1
−0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.08 −0.08
6 4 4 4 4
6 4 2 2 2
4 4 4 4 4
8 6 6 4 4
8 8 6 6 4
4 2 2 2 2
4 2 2 2 2
2 2 2 2 2
0 0 0 0 0
4 2 2 2 2
6 4 4 4 4
6 4 4 6 16
10 10 10 10 10
10 10 10 10 10
2 4 6 8 18
0.05 0.05 0.05 0.05 0.05
3 3 3 3 3
0.1 0.1 0.1 0.1 0.1
−0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.08 −0.08
10 4 4 4 2
6 2 2 2 2
6 4 2 2 2
8 6 6 6 6
16 6 6 6 6
8 2 2 2 2
4 2 2 2 2
4 2 2 2 2
2 0 0 0 0
4 2 2 2 2
8 4 4 4 4
8 4 4 4 4
10 10 10 10 10 10 10 10 10 10 10
10 10 10 10 10 10 10 10 10 10 10
4 4 4 4 4 4 4 4 4 4 4
0.05 0.05 0.05 0.05 0.05 0.4 0.5 0.4 0.4 0.4 0.4
1 0.5 1 1 1 1 1 1 1 1 1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.4 0.5
−0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −3 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−0.08 −0.08 −0.08 −0.08 −0.01 −0.01 −0.01 −0.01 −0.01 −0.01 −0.01
4 2 4 4 4 4 0 4 4 4 4
2 0 2 2 2 2 0 2 2 2 2
4 0 4 4 4 4 0 4 2 2 0
6 0 6 6 6 6 0 6 6 6 2
6 0 6 6 6 6 0 6 6 6 6
2 0 2 2 2 2 0 2 2 2 2
2 0 2 2 2 2 0 2 2 2 2
2 2 2 2 2 2 0 2 2 2 2
0 0 0 0 0 0 0 0 0 0 0
2 0 2 2 2 2 0 2 2 2 2
4 0 4 4 4 4 0 4 4 4 4
4 0 4 4 4 4 0 4 4 4 4
10s
10min
4-6min
0.05-0.4
1-3
-
4
2-4
2-4
6
6-8
2
2
2
0
2
4
4
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
Step length (s)
Recommended values 0.1
-
-
5
6
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
ferent values of step length, fusion time, slope interval, and slope limit were set for data processing. The processing results that are very different from the actual cooking behavior are marked in red. By setting control groups, the parameter values of the experimental group whose processing results are close to the actual cooking behavior were selected as recommended values. The data processing results are better when the step length is 10 s, fusion time 10 min, slope interval 4–6 min, and slope limit k1 = 0.05–0.4, k2 = 1–3, k3 = 0.1, and k4 , k5 , k6 not limited, for most households. 3. Results 3.1. Averaged hourly coincidence factors Fig. 5 presents the real coincidence factors calculated using step length 10 s, fusion time 10 min, and slope interval 5 min, as recommended in Table 2. Fig. 6 shows the averaged coincidence factors, together with the SD values, of cooking behaviors for the 25-floor residential unit on weekdays and weekends, respectively. Three significant waves are observed in hourly coincidence factors, which are generated with the coincidence factors ≥5% and closely correspond to the time period immediately before home breakfast, lunch, and supper. Although SD exists with the averaged coincidence factors, three peak values, namely, 16% at 07:47, 22% at 11:59 and 32% at 17:32, are found on weekdays, and three other similar peaks are noted on weekends. Comparison of weekdays and weekends shows that the averaged profiles are close to each other, even in terms of peak coincidence factor and peak time. Despite the independent cooking behaviors among the 25 householders and the distinct individual activities between weekdays and weekends, the hourly overlapping rates of the residential units are highly similar. Fig. 7 presents the hourly coincidence factors for two other residential units with 14 and 12 floors and shows the small differences between weekdays and weekends. The first peak of coincidence factors on weekdays is slightly higher than that on weekends, and the other peaks are lower on weekends than on weekdays. We combined the coincidence factors of three residential units in one diagram and compared them with the averaged values to manifest the statistical significance of the overlapping of cooking behaviors. The coincidence factors of the three units are within the 95% confidence intervals of average on weekdays and weekends. The result indicates that the overlapping effect of cooking behaviors among the three surveyed residential units is of statistical significance, and more overlapping parameters such as “design” value of coincidence factor and cooking period can be proposed or modeled. 3.2. “Design” value of coincidence factors for the centralized exhaust system In the centralized exhaust system, the design parameters of the cross-sectional area of the flue and fan selection can be determined according to the maximum coincidence factors of the flue. Thus, how to determine the maximum coincidence factors, the “design” value, is the key to this section. As shown in Fig. 8, the coincidence factors of the three residential units have a high overlap ratio, and the waveform formed by averaged coincidence factors has three distinct peaks. The maximum value of the three peaks corresponding to the three buildings, that is, 32.0%, 21.4%, and 22.2% on weekdays, can be used as the design value. The statistical average is suitable for the overlapping effect of cooking behaviors, but not for determining the maximum overlap rate in actual use. The design value of the centralized exhaust system should refer to the cooking behavior under extreme operating
conditions to ensure that the system can meet the exhaust requirements under any operating conditions. The statistical average offsets the difference between the data when the number of samples is large, and it cannot reflect the extreme operating conditions well. Therefore, the peak value formed by the respective coincidence factors of the three buildings in mearing days as the maximum overlap ratio is appropriate, as shown in Fig. 5. Fig. 9 shows the maximum coincidence factors of the three buildings obtained by the above two methods. Comparison of the maximum overlap in mearing weekdays with the averaged coincidence factors shows that the averaging method slightly reduces the maximum that may occur during use. Using the maximum overlap in mearing weekdays as the design value is recommended. Not all households cooked three meals during the survey in the measuring program. To meet the actual need, we employed the correction coefficient to make up for the difference between the predicted and actual values, which can be used in modeling. The correction coefficient is equal to the total number of households in a building divided by the number of cooks during the survey. In this study, the correction coefficients are 1.19 on weekdays and 1.28 on weekends. 3.3. Typical cooking-behavior model The averaged hourly coincidence factors of the residential units are highly similar. The maximum overlapping rate in mearing weekdays with the correction coefficient provides a method for extending from a single model to different height buildings. The model must obey the probability distribution and modeling parameters to establish a typical cooking behavior model. 3.3.1. Probability distribution of the typical cooking behavior model The probability of a coincidence factor in a certain cooking period is approximate to the time proportion of the coincidence factor in that time. It is abstracted as a mathematical statistical problem, that is, event A: the probability distribution of the coincidence factors in this period is X. For the known terminal number N, this distribution is the probability distribution of the discrete random variable X. For the unknown terminal number N, the distribution can be approximated as the probability distribution of a continuous random variable X. In mathematical statistics, more than five influencing factors (at least three) exist, and the measured values can be regarded as a normal distribution [29]. With the assumption that the coincidence factors present a normal distribution in the cooking time period, the boxplot and normal curve graph of the all-day and three main time periods in the typical day flue are drawn Fig. 10. The figure shows that the distribution throughout the day presents heavy-tailed distribution, such as Pareto, Weibull, Gamma, Exponential, and Lognormal. The three main periods are close to a normal distribution with positive skewness and non-zero kurtosis. The z-score values of the skewness and kurtosis of the variables were calculated to test for normality [30,31]. The calculation process of kurtosis and skewness is shown in Formulas (1)–(4), and the result shows that event A follows a normal distribution (Table 3).
μ3 =
n
(xi − E (x˜) )3 f (xi )xi
(1)
i=1
γ3 =
μ3 (γ > 0 Positive skwness; γ3 < 0 negative skewness) σ3 3 (2)
μ4 =
n
(xi − E (x˜) )3 f (xi )xi
(3)
i=1
γ4 =
μ4 − 3(γ4 > 0Sharp; γ4 < 0 Flat) σ4
(4)
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
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Fig. 5. Continuous coincidence factors for the three residential units during full mearing days. Table 3 Normality test. Skewness
Breakfast Lunch Dinner
Kurtosis
Statistic
Standard error
Z-score
Statistic
Standard error
Z-score
0.051 0.264 0.318
0.168 0.168 0.168
0.304 1.571 1.893
0.542 −0.513 −0.657
0.334 0.334 0.334
1.623 −1.536 −1.967
If the Z-score is between +1.96 and −1.96, the variable can be considered to be normally distributed.
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
Fig. 6. Averaged hourly coincidence factors for the 25-floor residential unit (a) on weekdays and (b) on weekends.
Fig. 7. Averaged hourly coincidence factors for residential unit (a) with 14 floors and (b) with 12 floors.
Fig. 8. Averaged hourly coincidence factors of the three residential units (a) on weekdays, and (b) on weekends.
3.3.2. Basic parameters of the typical cooking-behavior model Basic parameters of modeling include three cooking periods, the skewness and kurtosis values of the probability distribution, maximum coincidence factors, and correction coefficients. A. Cooking period The recommended values of each parameter mentioned in Table 2 were then used to process the measured data of each
household and to obtain the daily cooking period and duration. Fig. 11 shows the calculated coincidence factors of the 25-floor residential unit on a certain weekday. Three cooking periods, namely, breakfast-B, lunch-L, and dinner-D are clearly observed. The time periods can be obtained by removing the time in which the factors are zero and eliminating extreme time.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
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Table 4 Cooking periods for residential units with 25, 14, and 12 floors on weekdays and weekends.
Breakfast Lunch Dinner
12 floors-weekdays
12 floors-weekends
14 floors-weekdays
14 floors-weekends
25 floors-weekdays
25 floors-weekends
07:00–08:30 11:00–12:30 16:40–18:40
08:00–09:30 11:00–13:00 17:00–18:30
07:00–07:30 11:00–12:30 16:00–18:00
07:20–07:40 11:00–12:00 16:30–18:00
07:00–08:30 11:00–12:30 17:00–18:30
08:00–09:30 10:00–12:30 15:30–19:00
Fig. 9. Maximum coincidence factors detected for the three residential units at different days (WD1 and WD2 are the maximum overlaps in mearing weekdays. WDAVG means averaged coincidence factors on weekdays. WE1 and WE2 are the maximum overlap on mearing weekends. WE-AVG means averaged coincidence factors on weekends.).
Fig. 10. Boxplot and normal curve of a weekday.
The above method was used to determine the cooking period of the three residential units on weekdays and weekends, as shown in Table 4. B. Skewness and kurtosis The kurtosis and skewness of the probability distribution of the three residential units on weekdays and weekends were calculated, as shown in Table 5. With the same building height and the same cooking period, the probability distribution of the 0%–20% coincidence factor increases on weekends. With the same building height, on weekdays or weekends, the function of the distribution curve is directly affected by the dining time (B or L or D). For the same cooking period (B or L or D) on weekdays or weekends, the peak value of probability distribution and the value range of the independent variables are different. The probability distribution is the most affected by the height of the building, followed by the dining time (B or L or D), and finally, whether the day is a weekday or a weekend.
Fig. 11. Hourly coincidence factors for residential unit with 25 floors in a weekday.
C. Other parameters In addition to the above parameters, the modeling step length is determined as 1 min, and the peak value of the coincidence factors is usually at the midpoint of cooking periods. To make the established model more secure and reliable, we selected the sustainability coincidence factors for the three residential units during full mearing days as a comparison to model the cooking behavior of the residential units on weekdays and weekends. 3.3.3. Model validation Modeling is as follows. First, the common cooking period was determined based on Table 4. Second, the function of the coincidence factors and time was calculated according to the kurtosis, skewness and peak time of the normal distribution. Third, the factors outside the cooking period were set to 0 on weekdays and 4% on weekends. The model of the coincidence factors had a good coincidence degree with the survey results (Fig. 12). Different from the model, small factors outside the cooking periods exert minimal, influence on the design parameters of the flue. The maximum overlapping rate was calculated with the surveyed data and the correction coefficient. The “design” values must be modified with different correction factors, and the above method can be used to establish a cooking-behavior model of any height building, thereby designing the cross-sectional area of share shaft and selecting a fan. 4. Discussion 4.1. Design of sectional area of share shaft The maximum coincidence factors are the “design” value for the centralized exhaust system. This survey was conducted in February 2019 in China, just after the Chinese New Year. Chinese people celebrate the festival together. Thus, the factors are higher regardless of weekdays or weekends, indicating that the coincidence factors of high-rise residential buildings should be lower than 50%. The maximum factor of 50% was selected as the design parameter, and
10
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764 Table 5 Skewness and kurtosis in different scenarios. 25 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.569 −0.059
0.61 0.032
0.561 −0.558
−0.026 −1.034
0.364 −0.657
1.391 1.998
14 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.251 −0.86
0.289 −1.126
0.797 −0.197
−0.084 −1.27
1.105 1.086
0.041 −0.811
12 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.892 0.019
0.751 −0.368
0.751 −0.368
0.374 −0.839
0.695 0.583
−0.03 −0.668
Fig. 12. Model validation of three buildings (a) on weekdays and (b) on weekends (25, 14, and 12 indicates the number of floors in the residential unit. WD1 and WD2 represent two working days of the survey. WE1 and WE2 represent two days of the weekend).
the airflow rate in the flue can be determined by referring to the national standard to determine the cross-sectional area of the flue.
Thus, if centralized power is used for smoke extraction in high-rise residential buildings, the fan has great potential for energy saving.
4.2. Selection of centralized exhaust fan 4.3. Research limitations and potential extension In addition to using the model to determine the design parameters, the power consumption of roof fans used in the centralized power exhaust system can be predicted and the fan configuration can be determined through the hourly coincidence factors on weekdays and weekends. An example is given below. In a 25-floor residential building, a roof fan is used to exhaust cooking oil fumes. The exhaust volume of each kitchen is assumed to be 500 m3 /h, and the corresponding fan energy consumption is calculated according to the following three schemes. a: Fan operates at full load for 24 h; b: The fan is selected according to the factor of 60% and the fan operates at full load all day [13,32]; c: The fan is selected according to the factor of 50% and the fan operates at full load during the cooking period and operates at a 10% load in the rest of the period; d: The fan is the same as scheme c, and the energy consumption is calculated according to the hourly coincidence factors of the model. The calculation shows that the power consumption of scheme a is 91.67 kWh /day, that of b is 50.44 kWh /day, that of c is 12.01 kWh /day, and that of d is 1.38 kWh /day (weekday) and 1.95 kWh /day (weekend). Compared with that of scheme a, the energy saving of scheme c is 86.90%, the energy saving of scheme d is 98.49% (weekday) and 97.24% (weekend). Compared with that of scheme b, the energy saving of scheme c is 76.19%, and the energy saving of scheme d is 97.87% (weekday) and 96.13% (weekend).
This paper provides a reasonable “design” value of coincidence factors for a centralized exhaust system by studying the overlapping of high-rise residential cooking behavior. This research is beneficial to the popularization and use of the centralized power exhaust system in high-rise buildings. The equipment is installed in the household of one residential unit to monitor the cooking behavior and obtain the coincidence factor of the flue, and the model is established based on the data analysis. This research method can be used as a reference for the study of similar problems. The research method in this paper has no limitations in areas and research objects, and subsequent research will be conducted in buildings with different heights in different regions. The problem of centralized exhaust mostly occurs in high-rise residential buildings. Therefore, high-rise residential buildings with different heights are selected as the research object in this study. Comparison of the overlapping of cooking behaviors in the three buildings on weekdays and weekends shows that the coincidence factors of flues with different heights in a small area have a high consistency on weekdays and weekends. Cooking behavior is closely related to the eating habits and daily life of people. Thus, the time of extreme overlapping in different provinces must be different. For example, dinner time is different in the south and north. The maximum overlap rate cannot be determined to be geographically related.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
This research is dedicated to optimizing the design of centralized exhaust systems for high-rise buildings. The research results show that the larger the high-rise buildings, the more significant the energy-saving effect obtained by using the proposed method. The research results need not be used for flue reconstruction because of the good operation status of low-rise building exhaust systems and the small number of households.
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CRediT authorship contribution statement Yirui Wang: Conceptualization, Investigation, Formal analysis, Writing - original draft. Jun Gao: Funding acquisition, Supervision. Lingjie Zeng: Writing - review & editing. Leqi Tong: Data curation. Guodong Liu: Data curation. Changsheng Cao: Data curation. Acknowledgment
5. Conclusions A four-day survey was conducted on 12-, 14-, and 25-floor high-rise residential buildings in Zhejiang Province, China. The real stochastic phenomenon of cooking behaviors was recorded simultaneously by placing automatic thermographs 10 cm away from the pot of residents sharing one vertical shaft. Python was used to identify the breaks of temperature gradient and transformed the continuous temperature profiles into a group of step signals consisting of only “0” and “1”. By eliminating interfering fluctuations, the turning point can be more accurately identified when the step length is 10 s, fusion time 10 min, slope interval 4–6 min, and slope limit k1 = 0.05–0.4, k2 = 1–3, k3 = 0.1, and k4, k5, k6 not limited, for most households. The hourly coincidence factor of the different buildings was obtained though data processing and validity checking. The four-day overlapping cooking behaviors of the three residential units were compared, and coincidence factors consisted of three significant waves, namely, breakfast, lunch, and dinner represented by B, L, and D, respectively. Despite the independent cooking behaviors among the householders and the distinct individual activities between weekdays and weekends, the hourly overlapping rates of the residential units are highly similar. Thus, overlapping parameters, such as the “design” value of coincidence factor and cooking period, are proposed or modeled. To determine the maximum coincidence factors, we implemented the “design” value, two parameter extraction methods. Results show that the averaging method slightly reduces the maximum that may occur during use compared with the maximum overlap in mearing weekdays. Using the maximum overlap in mearing weekdays as the design value is recommended, with the correction coefficients of 1.19 on weekdays and 1.28 on weekends. The abstraction of cooking behavior is a mathematical statistical model obeying the normal distribution, and the kurtosis and skewness values describing its characteristics were determined. A typical cooking behavior model was established by extracting the main cooking period from hourly coincidence factors, combining the modeling step length determined as 1 min, the peak value of the coincidence factors, and the time corresponding to the peak. Using different correction coefficients to correct the peak value of the coincidence factors can extend the application scope of the model to buildings of any height. In addition, according to the hourly coincidence factors, the factor of 50% can be used as a design parameter for the flue cross section and fan selection parameters. The power consumption of roof fans used in the centralized power exhaust system can be predicted and the fan configuration can be determined through the hourly coincidence factors on weekdays and weekends. Compared with the scheme of 24-hour operation at full load, the energy saving rate of the model is over 95%.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Contents lists available at ScienceDirect
Energy & Buildings journal homepage: www.elsevier.com/locate/enbuild
Overlapping of cooking behavior in high-rise residential buildings Yirui Wang a, Jun Gao a,b,∗, Lingjie Zeng a, Leqi Tong a, Guodong Liu a, Changsheng Cao a a
Institute of HVAC Engineering, School of Mechanical Engineering, Tongji University, Shanghai 200092, China Key laboratory of Performance Evolution and Control for Engineering Structure of Ministry of Education, College of Civil Engineering, Tongji University, Shanghai 200092, China
b
a r t i c l e
i n f o
Article history: Received 11 October 2019 Revised 7 December 2019 Accepted 6 January 2020 Available online 10 January 2020 Keywords: Residential building Central shaft Cooking fume Coincidence factor Ventilation Energy conservation Cooking time
a b s t r a c t The design of a centralized cooking-fume exhaust system for high-rise residential buildings lacks the parameters related to cooking behavior, such as the coincidence factors. This study surveyed 12-, 14-, and 25-floor residential units by using a thermometer to obtain the continuous temperature profiles for study cooking behavior. Python was used to identify the breaks of temperature gradient, and continuous temperature profiles were transformed into a group of step signals consisting of only “0” and “1” while interfering fluctuations were eliminated and turning points were determined. The hourly overlapping rate of the residential unit after data processing is highly similar. The abstraction of cooking behavior is a mathematical statistical model that obeys normal distribution. A typical cooking behavior model based on normal distribution was established using the main cooking periods, kurtosis, and skewness values, the modeling step length, the peak value of the coincidence factors, and the time corresponding to the peak. Using different correction coefficients to correct the peak value of the coincidence factors can extend the application scope of the model to buildings of any height. In addition, the coincidence factor of 50% can be used as a design parameter for the flue cross section and fan selection parameters. Thus, the selected fan, which is fully loaded during cooking periods and has low load during non-cooking periods, has significant energy saving potential. © 2020 Elsevier B.V. All rights reserved.
1. Introduction The rapid urbanization of the developing countries has facilitated the construction of numerous high-rise residential buildings [1–3], especially in China [4–6]. This situation introduced the “design” requirement of the centralized exhaust system for each group of kitchens that distribute vertically in one high-rise unit and share one vertical shaft to discharge the cooling oil fumes (COFs) [7,8]. Such exhaust systems are used to effectively collect the cooking-generated airborne pollutants from each kitchen and prevent the cross contamination between the kitchens [9–12]. Two typical modes of the centralized exhaust system can be adopted according to the distributed or centralized fan power scheme (Fig. 1). The first mode consists of household range hoods with distributed fan power, one central shaft, and hose-branches that connect each range hood with the shaft. In such systems, the check valve is usually installed in each hose-branch to prevent cross contamination, and the distributed fan power assures the exhaust rate required for the discharge of COFs of each kitchen. For this system, the key “design” task is to determine the cross∗ Corresponding author at: Tongji University, 1239 Siping Road, Yangpu District, Shanghai 20 0 092, China. E-mail address: [email protected] (J. Gao).
https://doi.org/10.1016/j.enbuild.2020.109764 0378-7788/© 2020 Elsevier B.V. All rights reserved.
sectional area of the shaft by using the design flow rate in the shaft for ensuring the effective area of the kitchen space. Xu and Shen [13] proposed a trial algorithm to determine the cross-sectional area according to the exhaust volume, where the overlapping of cooking behaviors in one residential unit were considered. Chen and Gong [14] calculated the cross-sectional area of shaft according to a minimum exhaust volume with an assumed overlapping rate. The results showed that the cross-sectional area of the shaft is highly sensitized to the overlapping of the cooking behaviors. The second system mode has one central shaft, one centralized fan at the shaft outlet and hose-branches that connect each range hood (no fan power) with the shaft. For such systems, air leakage and cross contamination through the check valve is considerably reduced due to that the positive pressure in the shaft is effectively eliminated by the central fan. Tong et al. [15] studied the exhaust uniformity of such exhaust system and proposed a flow-guide device to regulate the distribution of exhaust volume. However, designing the cross-sectional area of the shaft is still difficult because of the unresolved overlapping rate of the cooking behavior. Determining the “design” working point of the central fan and the operating control scheme is also challenging. The overlapping of cooking behavior affects the design of the centralized exhaust system for the kitchens in high-rise residential buildings. However, the overlapping has not been well defined and
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
erature provide similar scenarios. Despite the significant difference in stochastics between building occupancy and cooking behavior, household cooking behaviors are still statistically significant and mostly occur within the specified time immediately before the home breakfast, lunch, and supper time. This study aims to provide the reasonable coincidence factors of cooking behavior as the key input for determining the design parameters of the centralized exhaust system for the kitchens in a high-rise residential unit. Measurements, which used thermographs to collect the real-time cooking temperature, were conducted to simultaneously record the real stochastic phenomenon of cooking behaviors. The recorded temperature data were processed and analyzed to detect the cooking time and duration for identifying the coincidence factors. Typical cooking periods and the maximum values of coincidence factor were extracted for the buildings studied. One statistically significant cooking rule was derived and then used to establish a typical cooking behavior model for the extensive predictions of coincidence factors. 2. Methodology 2.1. Measuring program
Fig. 1. Two modes of centralized exhaust system for the kitchens in high-rise residential buildings: (a) system type I of household range hoods with distributed fan power, one central shaft, and hose-branches that connect each range hood with the shaft; and (b) system type II with one central shaft, one centralized fan at the shaft outlet, and hose-branches that connect each range hood (no fan power) with the shaft.
parameterized because of the complexity and uncertainty of the random cooking behavior. Despite the centralized or distributed fan power, each range hood opens, runs, and closes separately and has no any mutual communication. Cooking duration and frequency vary by many family and social factors, such as the living habits, eating habits, family structure and size, and even the economic level. Therefore, the overlapping of cooking behaviors in one residential unit is difficult to directly calculate on the basis of family cooking rules. Here we define a concise coincidence factor of cooking behavior as the ratio of the number of household range hoods operating simultaneously to the total number, that is, the overlapping rate under a relatively high cumulative probability. Such definition provides possibility for reasonably determining the overlapping rate through statistical analysis without complicated bottom-up modeling. Similar definition has been found in computer-based building energy simulation. In building energy software, stochastic variables, such as occupancy, lighting, and plug load, greatly influence the energy-consumption results. The actual schedule, profile, or value of these variables is also difficult to obtain. Therefore, these variables are usually defined through the use of diversity factors. Diversity factors are defined as numbers between zero and one, and are used as multipliers of some user-defined peak loads [16]. If the energy use or waste due to human behavior in the spatiotemporal domain is concerned, then this factor is called building occupancy diversity factor [17]. Various methods using probabilistic or other models have been proposed to estimate the occupancy diversity in different building types [18–22]. A gap between the prediction models and measured results has often been observed and researchers are currently trying to bridge the gap through surveys, interviews, walkthrough inspections or sensors [23–25]. Existing studies have indirectly discussed the coincidence factors of cooking behavior in high-rise residential buildings. Modeling and measuring of occupancy behavior in building spaces in the lit-
The COF produced by cooking has strong adhesion, which can easily cause equipment failure or damage. Thus, conducting the cooking behavior measurement by using the methods used for occupancy, such as camera, passive infrared sensor, ultrasonic sensor, radio frequency signals, sensors fusion, WLAN, Bluetooth, and Wi-Fi, is inconvenient and non-economical [24]. This study proposed a much concise measuring method, which used a group of thermographs placed near gas cookers of each kitchen in one high-rise residential unit sharing one exhaust shaft. In the measurements, a significant temperature rise indicates the cooking initiation and a significant drop implies the cooking termination [26–28]. Pre-experiments of locating the temperature probe was conducted to detect the cooking period accurately. As shown in Fig. 2, three arrangements were tested under the consideration of safety and quick requirements. By comparing the opening and closing time of the gas cooker with the measured temperature data, the initiation and termination times for cooking can be determined through the two breaks of temperature gradient and the determined cooking period can be quite reliable. A measuring distance of 10 cm between the gas outer flame and probe is relatively acceptable because a small distance (e.g., 5 cm) leads to single risk of probe and a large distance (e.g. 15 cm) reduces identifiability of the cooking period. Three residential units with 12, 14, and 25 floors in three communities in Zhejiang Province, China were selected to measure the coincidence factors of cooking behaviors under different spatiotemporal conditions. All the selected residents used a gas cooker and applied Chinese-style cooking. The measurements lasted for four consecutive days, which included general weekdays and weekends, in February 2019. From the measured data, only three householders among all the 51 householders (51 represents the total number of households surveyed, which is the sum of 12, 14, and 25. The number can be converted into a proportion of 5.9%.) had no cooking activity within the 4 days, and 35 householders (68.6%) cooked daily during the survey. In addition, 43 households (84.3%) cooked on weekdays, and 40 households (78.4%) cooked on weekends. In the one flue unit, the residents occasionally did not cook. The proportion of non-cooked households in the total households affected the “design” value of coincidence factors for the centralized exhaust system. In the extreme use case of the flue, that is, when all households cooked daily, the coincidence factor of the one flue unit should be higher than the current survey value.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
3
Fig. 2. Pre-experiments for the selection of temperature probe placement, (a) three locations of the probe, and (b) recorded temperature profiles during cooking.
2.2. Data processing and validity checking Cooking period was determined by the breaks of temperature gradient as shown in Fig. 2(b). The continuous temperature profiles were transformed into a group of step signals consisting of only “0” and “1” to determine the cooking behavior and duration. As described in Fig. 3, signal “0” indicated no cooking activity and “1” meant cooking was ongoing. Python was applied to identify the original data and to code them as 0 or 1. On the basis of the spatio-temporal distribution of cooking behaviors and the coded step signals in one residential unit, coincidence factors were calculated through the number of signal “1” at each time step to the total number of signals “0” and “1” at that time step. If the step signal was coded on a time metric of one hour, the hourly coincidence factor can be obtained. The temperature profiles were transformed into step signals. The turning point is generally determined according to the breaks of temperature gradient, such as turning points A and B in Fig. 3(a). The slope of two adjacent temperature profiles was
calculated and defined as the slope between two points. If the slope changes from a negative number or zero to a positive value, the time corresponding to the smaller temperature profile is the turning point of the cooking initiation. If the slope changes from 0 or a positive number to a negative number, the time corresponding to the larger temperature profile is the turning point of the cooking termination. However, the temperature profiles throughout the day are affected by the external environment with small fluctuations. Therefore, the turning point was determined by the slope between the two points and the multi-point slope in actual coding to eliminate the interference fluctuation from the temperature fluctuation caused by cooking and ensure the accuracy of the identification. With reference to the definition method of the slope between two points mentioned above, the slope between the first and last two points of the multiple temperature parameter points is defined as the multi-point slope. As shown in Fig. 4, the time interval between the two points was 5 s, and the time interval of the multi-point slope was 120 s. The starting point temperature parameters of Groups C, D, and E were 8.8 °C, 11.0 °C, and 45.6 °C,
Fig. 3. Extraction of cooking period from the original temperature data, (a) coded step signals for one cooking period, and (b) coded step signals for one day.
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764 Table 1 Standard deviations of the coincidence factors and the proportion. 25 floors-weekdays
25 floors-weekends
14 floors-weekdays
14 floors-weekends
12 floors-weekdays
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
0% 3% 6% 8% 11%
63% 27% 7% 3% 0%
0% 3% 6% 8%
61% 28% 9% 2%
0% 4% 7% 8% 11%
74% 21% 3% 2% 0%
0% 5% 10%
79% 17% 4%
0% 5% 8% 10% 13%
63% 26% 5% 4% 2%
12 floors-weekends
25 floors-all days
14 floors-all days
12 floors-all days
All
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
SD
Proportion
0% 6% 12%
78% 20% 3%
0% 1% 3% 4% 6% 7%
52% 25% 9% 6% 5% 3%
0% 1% 2% 3% 4% 5% 6% 7%
62% 5% 12% 16% 0% 3% 1% 1%
0% 1% 2% 3% 4% 5% 6% 7% 8%
57% 10% 12% 6% 7% 1% 4% 2% 1%
0% 1% 2% 3% 4%
39% 34% 15% 8% 4%
significance level reached 5%. The samples collected in this study are the coincidence factors of the same type of building during the main cooking period, and the standard deviation is calculated to reflect the discrete situation of the flue utilization distribution of this type of building. As shown in Table 1, the accumulated proportion of SD ≤ 3% is 86% for the 25-floor residential unit, 95% for the 14-floor residential unit, and 85% for the 12-floor residential unit, and the accumulated proportion of SD ≤ 8% is 100% for the three residential units. These results indicate that the coincidence factors detected from the measured data are significant. 2.3. Parameter independence test
Fig. 4. Slope of relative temperature over three periods (The original temperature parameters of Groups C, D, and E are from the three periods in Fig. 3(b) in the revised manuscript: 07:10:00–07:12:30, 11:10:00–11:12:30, 11:18:00–11:20:30. The black line represents the multi-point slope, and the red line represents the slope between two points.). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
respectively. For comparison of the slopes of the three groups, the temperature values of 31 points in each group were respectively subtracted from 8.8 °C, 11.0 °C, and 45.6 °C to obtain three sets of relative temperature values with 0 °C as the starting point. The treatment of temperature parameters does not affect the slope of each group. As shown in Fig. 4, the multi-point slope of the point where the slope between two points changed from negative or 0 to a positive value differed in the three groups. The multi-point slope of the turning point was much larger than the slope of the interference point. Therefore, the slope limit k0 can be set during data processing to distinguish between the two types. If the multi-point slope was less than the limit k0 , the interval was considered as an interfering fluctuation, such as the interfering points C in Fig. 3(b). As depicted in Fig. 3(b), coded step signals could not be clearly located when the temperature profiles show no obvious slope breaks because of the combined effect of the small thermal lag of the temperature probe and the frequent on/off of the gas cooker during a short period of time. Therefore, a validity check on the standard deviation (SD) of the coincidence factors and their proportion is necessary. The value of SD was calculated when the
For data processing, the time step length, data fusion time, and slope interval and limit significantly affected the detection of cooking durations and coincidence factors. The time step length is the unit for Python to extract the original temperature. If the step length is too long, the slope breaks of temperature profile cannot be correctly located. If it is too short, the recognition sensitivity and fluctuation increase and thus leads to high possibility of error. Data fusion time was selected to reduce the influence of the on/off process of the gas cooker, and it should not be too long or small. Taking points D and E as examples (Fig. 3(b)), three temperature rises and falls are noted between points D and E, and the time interval is within 2 min, which can be regarded as one cooking behavior. Therefore, the appropriate fusion time, slope interval, and slope limits must be selected to determine the cooking time clearly and accurately. The slope interval and limit correspond to the slope between multi-points mentioned in the data processing. Parameter independence test was performed for the step length, fusion time, and slope interval and slope limit. Residents of the 12-floors residential unit in the survey set up cameras in their homes to record cooking behavior continuously during the survey time. Measured data of the 12-floors residential unit on a certain day were randomly sampled, and the actual cooking behaviors were taken as indicators to test the parameter. Parameter independence test and the recommended values of step length, fusion time, and slope interval and slope limit are listed in Table 2. The slope value of the declining point is not limited because the declining point can be determined by referring to the determination method of the extremum of the curve to locate the maximum value in the interval. The processing results in the recommended values in Table 2 represent the actual cooking behavior used for comparison. The experimental groups with dif-
Table 2 Independence test for step length, fusion time, and slope interval and limit, and their recommended values. Fusion time (min)
Slope interval (min)
Slope limit
Processing results
5 10 30 60 90 120
10 10 10 10 10 10
6 6 6 6 6 6
0.05 0.05 0.05 0.05 0.05 0.05
3 3 3 3 3 3
0.1 0.1 0.1 0.35 0.8 0.8
−0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.35 −0.8 −0.8
4 4 4 4 4 4
2 2 2 2 2 2
2 2 4 4 2 2
6 6 6 4 6 4
6 6 6 6 6 6
2 2 2 2 2 2
2 2 2 2 2 2
2 2 2 2 2 2
0 0 0 0 0 0
2 2 2 2 2 2
4 4 4 4 4 4
4 4 4 4 4 4
10 10 10 10 10
2 5 10 15 20
4 4 4 4 4
0.05 0.05 0.05 0.05 0.05
3 3 3 3 3
0.1 0.1 0.1 0.1 0.1
−0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.08 −0.08
6 4 4 4 4
6 4 2 2 2
4 4 4 4 4
8 6 6 4 4
8 8 6 6 4
4 2 2 2 2
4 2 2 2 2
2 2 2 2 2
0 0 0 0 0
4 2 2 2 2
6 4 4 4 4
6 4 4 6 16
10 10 10 10 10
10 10 10 10 10
2 4 6 8 18
0.05 0.05 0.05 0.05 0.05
3 3 3 3 3
0.1 0.1 0.1 0.1 0.1
−0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −5 −5 −5
−0.08 −0.08 −0.08 −0.08 −0.08
10 4 4 4 2
6 2 2 2 2
6 4 2 2 2
8 6 6 6 6
16 6 6 6 6
8 2 2 2 2
4 2 2 2 2
4 2 2 2 2
2 0 0 0 0
4 2 2 2 2
8 4 4 4 4
8 4 4 4 4
10 10 10 10 10 10 10 10 10 10 10
10 10 10 10 10 10 10 10 10 10 10
4 4 4 4 4 4 4 4 4 4 4
0.05 0.05 0.05 0.05 0.05 0.4 0.5 0.4 0.4 0.4 0.4
1 0.5 1 1 1 1 1 1 1 1 1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.4 0.5
−0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−5 −5 −3 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05 −0.05
−0.08 −0.08 −0.08 −0.08 −0.01 −0.01 −0.01 −0.01 −0.01 −0.01 −0.01
4 2 4 4 4 4 0 4 4 4 4
2 0 2 2 2 2 0 2 2 2 2
4 0 4 4 4 4 0 4 2 2 0
6 0 6 6 6 6 0 6 6 6 2
6 0 6 6 6 6 0 6 6 6 6
2 0 2 2 2 2 0 2 2 2 2
2 0 2 2 2 2 0 2 2 2 2
2 2 2 2 2 2 0 2 2 2 2
0 0 0 0 0 0 0 0 0 0 0
2 0 2 2 2 2 0 2 2 2 2
4 0 4 4 4 4 0 4 4 4 4
4 0 4 4 4 4 0 4 4 4 4
10s
10min
4-6min
0.05-0.4
1-3
-
4
2-4
2-4
6
6-8
2
2
2
0
2
4
4
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
Step length (s)
Recommended values 0.1
-
-
5
6
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
ferent values of step length, fusion time, slope interval, and slope limit were set for data processing. The processing results that are very different from the actual cooking behavior are marked in red. By setting control groups, the parameter values of the experimental group whose processing results are close to the actual cooking behavior were selected as recommended values. The data processing results are better when the step length is 10 s, fusion time 10 min, slope interval 4–6 min, and slope limit k1 = 0.05–0.4, k2 = 1–3, k3 = 0.1, and k4 , k5 , k6 not limited, for most households. 3. Results 3.1. Averaged hourly coincidence factors Fig. 5 presents the real coincidence factors calculated using step length 10 s, fusion time 10 min, and slope interval 5 min, as recommended in Table 2. Fig. 6 shows the averaged coincidence factors, together with the SD values, of cooking behaviors for the 25-floor residential unit on weekdays and weekends, respectively. Three significant waves are observed in hourly coincidence factors, which are generated with the coincidence factors ≥5% and closely correspond to the time period immediately before home breakfast, lunch, and supper. Although SD exists with the averaged coincidence factors, three peak values, namely, 16% at 07:47, 22% at 11:59 and 32% at 17:32, are found on weekdays, and three other similar peaks are noted on weekends. Comparison of weekdays and weekends shows that the averaged profiles are close to each other, even in terms of peak coincidence factor and peak time. Despite the independent cooking behaviors among the 25 householders and the distinct individual activities between weekdays and weekends, the hourly overlapping rates of the residential units are highly similar. Fig. 7 presents the hourly coincidence factors for two other residential units with 14 and 12 floors and shows the small differences between weekdays and weekends. The first peak of coincidence factors on weekdays is slightly higher than that on weekends, and the other peaks are lower on weekends than on weekdays. We combined the coincidence factors of three residential units in one diagram and compared them with the averaged values to manifest the statistical significance of the overlapping of cooking behaviors. The coincidence factors of the three units are within the 95% confidence intervals of average on weekdays and weekends. The result indicates that the overlapping effect of cooking behaviors among the three surveyed residential units is of statistical significance, and more overlapping parameters such as “design” value of coincidence factor and cooking period can be proposed or modeled. 3.2. “Design” value of coincidence factors for the centralized exhaust system In the centralized exhaust system, the design parameters of the cross-sectional area of the flue and fan selection can be determined according to the maximum coincidence factors of the flue. Thus, how to determine the maximum coincidence factors, the “design” value, is the key to this section. As shown in Fig. 8, the coincidence factors of the three residential units have a high overlap ratio, and the waveform formed by averaged coincidence factors has three distinct peaks. The maximum value of the three peaks corresponding to the three buildings, that is, 32.0%, 21.4%, and 22.2% on weekdays, can be used as the design value. The statistical average is suitable for the overlapping effect of cooking behaviors, but not for determining the maximum overlap rate in actual use. The design value of the centralized exhaust system should refer to the cooking behavior under extreme operating
conditions to ensure that the system can meet the exhaust requirements under any operating conditions. The statistical average offsets the difference between the data when the number of samples is large, and it cannot reflect the extreme operating conditions well. Therefore, the peak value formed by the respective coincidence factors of the three buildings in mearing days as the maximum overlap ratio is appropriate, as shown in Fig. 5. Fig. 9 shows the maximum coincidence factors of the three buildings obtained by the above two methods. Comparison of the maximum overlap in mearing weekdays with the averaged coincidence factors shows that the averaging method slightly reduces the maximum that may occur during use. Using the maximum overlap in mearing weekdays as the design value is recommended. Not all households cooked three meals during the survey in the measuring program. To meet the actual need, we employed the correction coefficient to make up for the difference between the predicted and actual values, which can be used in modeling. The correction coefficient is equal to the total number of households in a building divided by the number of cooks during the survey. In this study, the correction coefficients are 1.19 on weekdays and 1.28 on weekends. 3.3. Typical cooking-behavior model The averaged hourly coincidence factors of the residential units are highly similar. The maximum overlapping rate in mearing weekdays with the correction coefficient provides a method for extending from a single model to different height buildings. The model must obey the probability distribution and modeling parameters to establish a typical cooking behavior model. 3.3.1. Probability distribution of the typical cooking behavior model The probability of a coincidence factor in a certain cooking period is approximate to the time proportion of the coincidence factor in that time. It is abstracted as a mathematical statistical problem, that is, event A: the probability distribution of the coincidence factors in this period is X. For the known terminal number N, this distribution is the probability distribution of the discrete random variable X. For the unknown terminal number N, the distribution can be approximated as the probability distribution of a continuous random variable X. In mathematical statistics, more than five influencing factors (at least three) exist, and the measured values can be regarded as a normal distribution [29]. With the assumption that the coincidence factors present a normal distribution in the cooking time period, the boxplot and normal curve graph of the all-day and three main time periods in the typical day flue are drawn Fig. 10. The figure shows that the distribution throughout the day presents heavy-tailed distribution, such as Pareto, Weibull, Gamma, Exponential, and Lognormal. The three main periods are close to a normal distribution with positive skewness and non-zero kurtosis. The z-score values of the skewness and kurtosis of the variables were calculated to test for normality [30,31]. The calculation process of kurtosis and skewness is shown in Formulas (1)–(4), and the result shows that event A follows a normal distribution (Table 3).
μ3 =
n
(xi − E (x˜) )3 f (xi )xi
(1)
i=1
γ3 =
μ3 (γ > 0 Positive skwness; γ3 < 0 negative skewness) σ3 3 (2)
μ4 =
n
(xi − E (x˜) )3 f (xi )xi
(3)
i=1
γ4 =
μ4 − 3(γ4 > 0Sharp; γ4 < 0 Flat) σ4
(4)
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
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Fig. 5. Continuous coincidence factors for the three residential units during full mearing days. Table 3 Normality test. Skewness
Breakfast Lunch Dinner
Kurtosis
Statistic
Standard error
Z-score
Statistic
Standard error
Z-score
0.051 0.264 0.318
0.168 0.168 0.168
0.304 1.571 1.893
0.542 −0.513 −0.657
0.334 0.334 0.334
1.623 −1.536 −1.967
If the Z-score is between +1.96 and −1.96, the variable can be considered to be normally distributed.
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
Fig. 6. Averaged hourly coincidence factors for the 25-floor residential unit (a) on weekdays and (b) on weekends.
Fig. 7. Averaged hourly coincidence factors for residential unit (a) with 14 floors and (b) with 12 floors.
Fig. 8. Averaged hourly coincidence factors of the three residential units (a) on weekdays, and (b) on weekends.
3.3.2. Basic parameters of the typical cooking-behavior model Basic parameters of modeling include three cooking periods, the skewness and kurtosis values of the probability distribution, maximum coincidence factors, and correction coefficients. A. Cooking period The recommended values of each parameter mentioned in Table 2 were then used to process the measured data of each
household and to obtain the daily cooking period and duration. Fig. 11 shows the calculated coincidence factors of the 25-floor residential unit on a certain weekday. Three cooking periods, namely, breakfast-B, lunch-L, and dinner-D are clearly observed. The time periods can be obtained by removing the time in which the factors are zero and eliminating extreme time.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
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Table 4 Cooking periods for residential units with 25, 14, and 12 floors on weekdays and weekends.
Breakfast Lunch Dinner
12 floors-weekdays
12 floors-weekends
14 floors-weekdays
14 floors-weekends
25 floors-weekdays
25 floors-weekends
07:00–08:30 11:00–12:30 16:40–18:40
08:00–09:30 11:00–13:00 17:00–18:30
07:00–07:30 11:00–12:30 16:00–18:00
07:20–07:40 11:00–12:00 16:30–18:00
07:00–08:30 11:00–12:30 17:00–18:30
08:00–09:30 10:00–12:30 15:30–19:00
Fig. 9. Maximum coincidence factors detected for the three residential units at different days (WD1 and WD2 are the maximum overlaps in mearing weekdays. WDAVG means averaged coincidence factors on weekdays. WE1 and WE2 are the maximum overlap on mearing weekends. WE-AVG means averaged coincidence factors on weekends.).
Fig. 10. Boxplot and normal curve of a weekday.
The above method was used to determine the cooking period of the three residential units on weekdays and weekends, as shown in Table 4. B. Skewness and kurtosis The kurtosis and skewness of the probability distribution of the three residential units on weekdays and weekends were calculated, as shown in Table 5. With the same building height and the same cooking period, the probability distribution of the 0%–20% coincidence factor increases on weekends. With the same building height, on weekdays or weekends, the function of the distribution curve is directly affected by the dining time (B or L or D). For the same cooking period (B or L or D) on weekdays or weekends, the peak value of probability distribution and the value range of the independent variables are different. The probability distribution is the most affected by the height of the building, followed by the dining time (B or L or D), and finally, whether the day is a weekday or a weekend.
Fig. 11. Hourly coincidence factors for residential unit with 25 floors in a weekday.
C. Other parameters In addition to the above parameters, the modeling step length is determined as 1 min, and the peak value of the coincidence factors is usually at the midpoint of cooking periods. To make the established model more secure and reliable, we selected the sustainability coincidence factors for the three residential units during full mearing days as a comparison to model the cooking behavior of the residential units on weekdays and weekends. 3.3.3. Model validation Modeling is as follows. First, the common cooking period was determined based on Table 4. Second, the function of the coincidence factors and time was calculated according to the kurtosis, skewness and peak time of the normal distribution. Third, the factors outside the cooking period were set to 0 on weekdays and 4% on weekends. The model of the coincidence factors had a good coincidence degree with the survey results (Fig. 12). Different from the model, small factors outside the cooking periods exert minimal, influence on the design parameters of the flue. The maximum overlapping rate was calculated with the surveyed data and the correction coefficient. The “design” values must be modified with different correction factors, and the above method can be used to establish a cooking-behavior model of any height building, thereby designing the cross-sectional area of share shaft and selecting a fan. 4. Discussion 4.1. Design of sectional area of share shaft The maximum coincidence factors are the “design” value for the centralized exhaust system. This survey was conducted in February 2019 in China, just after the Chinese New Year. Chinese people celebrate the festival together. Thus, the factors are higher regardless of weekdays or weekends, indicating that the coincidence factors of high-rise residential buildings should be lower than 50%. The maximum factor of 50% was selected as the design parameter, and
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Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764 Table 5 Skewness and kurtosis in different scenarios. 25 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.569 −0.059
0.61 0.032
0.561 −0.558
−0.026 −1.034
0.364 −0.657
1.391 1.998
14 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.251 −0.86
0.289 −1.126
0.797 −0.197
−0.084 −1.27
1.105 1.086
0.041 −0.811
12 floors
weekdays-breakfast
weekends-breakfast
weekdays-lunch
weekends-lunch
weekdays-dinner
weekends-dinner
γ3 γ4
0.892 0.019
0.751 −0.368
0.751 −0.368
0.374 −0.839
0.695 0.583
−0.03 −0.668
Fig. 12. Model validation of three buildings (a) on weekdays and (b) on weekends (25, 14, and 12 indicates the number of floors in the residential unit. WD1 and WD2 represent two working days of the survey. WE1 and WE2 represent two days of the weekend).
the airflow rate in the flue can be determined by referring to the national standard to determine the cross-sectional area of the flue.
Thus, if centralized power is used for smoke extraction in high-rise residential buildings, the fan has great potential for energy saving.
4.2. Selection of centralized exhaust fan 4.3. Research limitations and potential extension In addition to using the model to determine the design parameters, the power consumption of roof fans used in the centralized power exhaust system can be predicted and the fan configuration can be determined through the hourly coincidence factors on weekdays and weekends. An example is given below. In a 25-floor residential building, a roof fan is used to exhaust cooking oil fumes. The exhaust volume of each kitchen is assumed to be 500 m3 /h, and the corresponding fan energy consumption is calculated according to the following three schemes. a: Fan operates at full load for 24 h; b: The fan is selected according to the factor of 60% and the fan operates at full load all day [13,32]; c: The fan is selected according to the factor of 50% and the fan operates at full load during the cooking period and operates at a 10% load in the rest of the period; d: The fan is the same as scheme c, and the energy consumption is calculated according to the hourly coincidence factors of the model. The calculation shows that the power consumption of scheme a is 91.67 kWh /day, that of b is 50.44 kWh /day, that of c is 12.01 kWh /day, and that of d is 1.38 kWh /day (weekday) and 1.95 kWh /day (weekend). Compared with that of scheme a, the energy saving of scheme c is 86.90%, the energy saving of scheme d is 98.49% (weekday) and 97.24% (weekend). Compared with that of scheme b, the energy saving of scheme c is 76.19%, and the energy saving of scheme d is 97.87% (weekday) and 96.13% (weekend).
This paper provides a reasonable “design” value of coincidence factors for a centralized exhaust system by studying the overlapping of high-rise residential cooking behavior. This research is beneficial to the popularization and use of the centralized power exhaust system in high-rise buildings. The equipment is installed in the household of one residential unit to monitor the cooking behavior and obtain the coincidence factor of the flue, and the model is established based on the data analysis. This research method can be used as a reference for the study of similar problems. The research method in this paper has no limitations in areas and research objects, and subsequent research will be conducted in buildings with different heights in different regions. The problem of centralized exhaust mostly occurs in high-rise residential buildings. Therefore, high-rise residential buildings with different heights are selected as the research object in this study. Comparison of the overlapping of cooking behaviors in the three buildings on weekdays and weekends shows that the coincidence factors of flues with different heights in a small area have a high consistency on weekdays and weekends. Cooking behavior is closely related to the eating habits and daily life of people. Thus, the time of extreme overlapping in different provinces must be different. For example, dinner time is different in the south and north. The maximum overlap rate cannot be determined to be geographically related.
Y. Wang, J. Gao and L. Zeng et al. / Energy & Buildings 210 (2020) 109764
This research is dedicated to optimizing the design of centralized exhaust systems for high-rise buildings. The research results show that the larger the high-rise buildings, the more significant the energy-saving effect obtained by using the proposed method. The research results need not be used for flue reconstruction because of the good operation status of low-rise building exhaust systems and the small number of households.
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CRediT authorship contribution statement Yirui Wang: Conceptualization, Investigation, Formal analysis, Writing - original draft. Jun Gao: Funding acquisition, Supervision. Lingjie Zeng: Writing - review & editing. Leqi Tong: Data curation. Guodong Liu: Data curation. Changsheng Cao: Data curation. Acknowledgment
5. Conclusions A four-day survey was conducted on 12-, 14-, and 25-floor high-rise residential buildings in Zhejiang Province, China. The real stochastic phenomenon of cooking behaviors was recorded simultaneously by placing automatic thermographs 10 cm away from the pot of residents sharing one vertical shaft. Python was used to identify the breaks of temperature gradient and transformed the continuous temperature profiles into a group of step signals consisting of only “0” and “1”. By eliminating interfering fluctuations, the turning point can be more accurately identified when the step length is 10 s, fusion time 10 min, slope interval 4–6 min, and slope limit k1 = 0.05–0.4, k2 = 1–3, k3 = 0.1, and k4, k5, k6 not limited, for most households. The hourly coincidence factor of the different buildings was obtained though data processing and validity checking. The four-day overlapping cooking behaviors of the three residential units were compared, and coincidence factors consisted of three significant waves, namely, breakfast, lunch, and dinner represented by B, L, and D, respectively. Despite the independent cooking behaviors among the householders and the distinct individual activities between weekdays and weekends, the hourly overlapping rates of the residential units are highly similar. Thus, overlapping parameters, such as the “design” value of coincidence factor and cooking period, are proposed or modeled. To determine the maximum coincidence factors, we implemented the “design” value, two parameter extraction methods. Results show that the averaging method slightly reduces the maximum that may occur during use compared with the maximum overlap in mearing weekdays. Using the maximum overlap in mearing weekdays as the design value is recommended, with the correction coefficients of 1.19 on weekdays and 1.28 on weekends. The abstraction of cooking behavior is a mathematical statistical model obeying the normal distribution, and the kurtosis and skewness values describing its characteristics were determined. A typical cooking behavior model was established by extracting the main cooking period from hourly coincidence factors, combining the modeling step length determined as 1 min, the peak value of the coincidence factors, and the time corresponding to the peak. Using different correction coefficients to correct the peak value of the coincidence factors can extend the application scope of the model to buildings of any height. In addition, according to the hourly coincidence factors, the factor of 50% can be used as a design parameter for the flue cross section and fan selection parameters. The power consumption of roof fans used in the centralized power exhaust system can be predicted and the fan configuration can be determined through the hourly coincidence factors on weekdays and weekends. Compared with the scheme of 24-hour operation at full load, the energy saving rate of the model is over 95%.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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