Window opening behaviour modelled from measurements in Danish dwellings.doc

2.2. Measurements测量The following variables were measured continuously in all 15 dwellings. 下列变量在15个民居中被不断地测量。Indoor environment factors measured every 10 min室内环境因素每十分钟测量一次- Dry bulb temperature (C) - 干球温度（）- Relative humidity (RH) (%) - 相对湿度（RH）（%）- Illuminance (Lux) - 照度（Lux）- CO2 concentration (ppm) - CO2 浓度（ppm）Outdoor environment acquired from meteorological measuring stations in 10 min intervals 31 室外环境参数每十分钟从气象局得到- Air temperature () - 空气温度（）- RH (%) - 相对湿度（%） - Wind speed (m/s) - 风速（m/s）- Global Solar radiation (W/m2) - 总日照辐射（W/m2） - Sunshine hours (daily values) (Number of hours with sunshine(insolation higher than 120 W/m2) - 日照时间（每日值）（日照（辐射大于120W/m2）的小时数） Behaviour行为 Window position (open/closed)* 窗户状态（开/关） * In three of the dwellings, the actual opening angle of the window was measured . *在三家民居中，实际的开窗角度也被测量了。 Fig. 1 depicts some of the monitored windows.图1描述了一些被监测的窗户。 The indoor environment measurements were carried out with Hobo U12-012 data loggers 32. The CO2 concentration was measured using a Vaisala GMW22 sensor 33 connected to the Hobo logger as depicted in Fig. 2. Both the CO2 sensors and the Hobo data loggers were newly calibrated（校准） from the factory. The CO2 sensors were tested against a newly calibrated Innova multigas analyser both before and after the measuring period. The temperature sensors in the hobo data loggers were also tested before the measurements. The outdoor environmental variables were obtained from the Danish meteorological institute 31. Data from the meteorological station closest to each of the dwellings was used. The closest meteorological stations did not measure precipitation（降水量） and since local wind direction is very sensitive to local conditions it was decided not to include the direction of the wind . 室内环境参数由奥博U12-012数据记录器进行测量32。使用维萨拉GMW22传感器33连接到奥博记录器测量二氧化碳浓度，如图2中所示。二氧化碳传感器和奥博记录器都是从工厂那来的校准过的最新仪器。在测量期间的前后都把二氧化碳传感器与新校准的英诺华多气体多量程红外气体分析器进行了比较。奥博数据记录器中的温度传感器也在测量前被监测。室外环境参数变量从丹麦气象协会得到31。使用了距每个民居最近的气象站的数。最近的气象站并没有测量降水量，由于当地的风向对当地的条件的敏感性我们决定不考虑风向的影响。 The window position (open/closed) was measured using a Hobo U9 sensor 32. Three of the windows were hitched in the top and tilted（使倾斜） outwards when opening. In these cases the tilt was measured using an accelerometer （加速计）(HOBO UA-004-64 Pendant G) 32 attached to the window frame. In this way, the opening angle of the window was measured. 使用奥博U9传感器来测量窗户状态（开/关）。其中三个窗户安装在顶部的，并且打开的时候向室外倾斜。由于这样的原因，在窗户的框架上安装了加速计。通过这种方法，就可以测量窗户打开的角度了。 Generally, all measurements were carried out in the (main) living room and the (main) bedroom in each dwelling. The window sensors were installed on windows that inhabitants(居民） used most often when ventilating the dwelling. The number of operable（可操作的）windows varied between dwellings from 1 to 4 windows in the bedrooms and 3 to 6 windows in the living rooms. 一般所有住所的测量都在客厅(主要的)和卧室(主要的)中进行。窗户传感器被安装在居民住宅通风时最常使用的窗户上。民居中可操作的窗户的数量在卧室1-4面和客厅的3-6面之间。2.3. Place of measurement测量地点 Our measurements were limited to two rooms in each dwelling. Brundrett 34 found that open windows were most commonly found in the bedroom, particularly the main bedroom, while the sitting room, kitchen and the dining room had the lowest frequency（频率） of open windows. This was later supported by Dubrul 35 who found that bedrooms were the main ventilation zone, whereas（然而） the majority （大多）of windows which were never opened was in the living rooms. Furthermore, the percentage of open windows in kitchens and bathrooms was similar to that of living rooms. Based on these findings we chose to conduct the measurements in the main bedroom and in the main living room in each dwelling. This choice was made in an effort to（为了） select the rooms with the highest and lowest window opening frequency. 我们测量仅限于每个住宅的两个房间。布伦德里特34发现开窗在卧室最常见,尤其是主卧室,而客厅,厨房和餐厅开窗的频率是最低的。这个现象后来由杜布鲁35证实发现,卧室是主要的通风区,而在客厅的大多数的窗户是没有被打开的。此外,在厨房和浴室开窗的百分比是类似于客厅的。基于这些调查结果，我们选择在每家民居的主卧室和主客厅测量。这个选择是为了挑选出最高和最低开窗频率的房间。3. Processing and preparation of data The indoor environment sensors were placed on internal（内部的）walls at a height of roughly 1.8 m above the floor with a minimum distance of one metre to the closest radiator/convector.We attempted to place the sensors so they would not be hit by direct sunlight. In eight of the dwellings, this was not always possible due to acceptance of the occupants in the dwellings and other practicalities(可行性). In the cases when direct sunlight fell on the sensors, the temperature measurements were corrected for the heating of the sensor. This was done in periods when the measured illuminance was larger than 1000 lux. In these cases the temperature was corrected by linear(线性的)interpolation(插入) between temperature measurements 30 min prior to and one hour after direct sunlight fell on the sensor. In the eight dwellings, between 1% and 2% of the temperature measurements were corrected for direct solar radiation. 室内环境传感器被放置在室内墙上距地板高度约1.8米处并且距离最近的散热器/对流加热器最小一米的距离。我们尽量把传感器安装在不会受到阳光直射的地方。在8个民宅中,鉴于居民的接受程度和其他可行性这并不总是可能的。在阳光直射到传感器的情况下,温度的测量会因为传感器被加热而经修正。当照度超过1000勒克斯测量时这样做的。在这些情况下，在温度测量的30分钟前和阳光直射在传感器1个小时后测温值之间采用线性插值法修正。在8间住宅中,1%至2%的温度测量因太阳直射辐射而被修正。 The CO2 concentration was used as an indicator of the occupancy of the rooms where the measurements took place. If the CO2 concentration was below 420 ppm and the window was closed the room was classified as being unoccupied. Furthermore, if the CO2 concentration was higher than 420 ppm, but decreased and continued to decrease until reaching values below 420 ppm and the window was closed in the entire period, the room was classified as unoccupied during the period of concentration decay（衰减）. 二氧化碳的浓度作为房间入住并开始测量的指标。若二氧化碳浓度低于420ppm并且窗口被关闭则房间被列为闲置。此外,如果二氧化碳浓度高于420 ppm,但浓度持续下降到低于420 ppm并且整个下降期间窗口被关闭,房间在浓度衰减期间被归类为闲置。 The value of 420 ppm was chosen since earlier observations had shown that the outdoor concentrations might reach levels of up to 400 ppm. To ensure that long unoccupied periods were not classified as occupied an uncertainty range of 20 ppm was added to the highest observed outdoor concentration. 由于早起的观察研究发现室外的浓度能达到400ppm，所以选择420ppm为评判指标。为确保长期闲置的时段没有被误归为有人员在室，在所观测到最大的室外浓度的基础上加20ppm的不确定值。 The room was classified as occupied if the window was open. This classification was based on a questionnaire survey conducted by Andersen et al. 36 who found that the statement “I had to leave the dwelling” was mentioned amongst（在中） the most common reasons for closing windows. 如果窗户被打开则房间被划分为有人员在室。这种分类是基于安徒生等人所进行的问卷调查36，他们发现“我不得不离开住宅”这样的陈述在关窗的最普遍提及的原因中。 If the bedroom and the living room were both unoccupied, the dwelling was classified as unoccupied. Periods when the dwelling was unoccupied were not taken into consideration in the analysis. 如果卧室和客厅都是没人的则住宅被分为闲置。无人居住的时段没有做考虑分析。 When analysing the window opening data the database was divided depending on the state of the window (open/closed) to infer the probability of opening and closing the window (change from one state to another) separately. The 15 dwellings were divided into four groups based on ownership (owner-occupied or rental) and ventilation type (natural ventilation or mechanical ventilation) (Table 2). This division was based on the findings in Andersen et al. (2009) 26 and an assumed effect of ventilation principle on window opening behaviour. Table 3 shows how the dwellings were divided in the four groups.在分析开窗数据时依据窗口的状态(开启/关闭)将源数据划分来分别推断开窗和关窗(从一个状态变化到另一个)的概率。15个住处基于所有权(自有或租赁)和通风类型(自然通风或机械通风)被分成四组(表2)。这样的划分基于安徒生等人的发现(2009)26和通风原理对开窗影响的假设。表3显示如何将住宅被分为四组。3.1. Statistical analysis Multivariate logistic regression with interactions between selected variables was used to infer the probability of a window opening and closing event. The method relies on the probability function described in formula (1). 由于选变量之间的相互作用，使用多元逻辑回归来推断一个窗口打开和关闭事件的概率。这种方法所依靠的概率函数如公式(1)所示。 Where式中p is the probability of an opening/closing event a is the intercept b1-n are coefficients x1-n are explanatory variables such as temperature，CO2 concentration etc. p 为开关窗的概率a 为拦截系数b1-n为回归系数x1-n为解释系数如温度，CO2浓度等 However, the probability might depend differently on x1 at one level of x2 as compared to another level of x2 (e.g. an increase in temperature might increase the probability of opening a window in the bedroom, whereas the same increase might result in a lower probability in the living room). An example like the one described above would not be well described by a model based on equation (1). Equation (2) deals with interactions between variables by adding interaction terms to the model.然而，可能由于x1值相对于不同x2值有差异地决定着开窗概率（例如一定的温升可能提高卧室的开窗概率，而同样的温升可能降低客厅的开窗概率。）上述案例可能不能用公式（1）很好的表述。公式（2）的建模通过加入相互作用项解决了变量之间的相互作用。 Equation (2) was used to infer the probability of windows being opened or closed. The Akaike information criterion (AIC) was used as a basis for forward and backward selection of variables in the regression models 37. Each individual variable was first fitted(拟合) to the measured window opening data and then AIC was calculated for each fit. The variable with the lowest AIC was selected and the remaining variables were then tested one by one on a bivariate(二元的) level, to see if any of the bivariate models resulted in a lower AIC. If this was the case, the remaining variables were tested in a model with three variables and so on (forward selection). At each step, the AIC was also calculated for models, where each of the selected variables was removed from the models (backward selection). In this way, the final model included variables and interaction terms that resulted in the lowest AIC. To limit the complexity of the model, only interaction terms between continuous and nominal(名义的) variables, e.g. indoor temperature and day of week were included in the analyses. Table 4 lists all explanatory variables used in the inference of the window opening and closing models. 方程(2)被用来推断窗户被打开或关闭的概率。在做回归模型的前向逆向变量选择时以赤池信息量准则(AIC)为标准37。首先每个变量对测量的开窗数据进行拟合,然后AIC为每个拟合值进行估算。挑选AIC最低的变量然后将其余变量依次在二元层面上测试,以查看是否有任一个二元模式会导致更低的AIC。如果这样的话,剩下的变量进行三个变量的模型测试(向前选择)。在每一步中,同样用AIC为模型进行估算,其中每个所选变量将从模型中移除(逆向选择)。通过这种方法,最终的模型包括变量和造成最低AIC的相互作用项。为了简化复杂的模型，连续变量和名义变量之间只考虑相互作用项,如室内温度和周几被包含在分析中,表4列出了所有影响开关窗模型的名义可变因素。 In the interpretation(解释) of the coefficients, the sign, the size and the scale of the corresponding variable have to be taken into account. For example, a coefficient for solar hours of 0.057 might seem to impact the probability more than an outdoor relative humidity coefficient of 0.029 (group 4, opening model). However, the scales of the two variables (solar hours: 0 to 16.1, outdoor RH: 28%-100%) should be taken into account: Schweiker et al. 39 suggested to multiply the scale of the variable with the coefficient, to get an indication(指示) of the magnitude(量级，大小) of the impact from each variable. In the example described above the magnitude of the impact was 0.057(16.1-0) = 0.91 and 0.029(100-28) = 2.08 for the solar hours and the outdoor relative humidity respectively, revealing(揭示，显示) that the outdoor RH had a higher impact on the probability than the solar hours. 回归系数,符号,大小和变量的数值范围的解释必须给予考虑。例如,日照时间的回归系数0.057可能看上去比室外相对湿度的回归系数0.029更加影响开窗概率(第四组,开窗模型)。然而,需要考虑到两者的数值范围(日照时间:0-16.1,室外相对湿度：16.1)：史威克等人39建议变量回归系数乘以数值范围,得到一个变量各自影响大小的指标。上述例子中表述的日照时间和室外相对湿度的影响大小分别是 0.057(16.1-0) = 0.91和0.029(100-28) = 2.08，显示出相对湿度比日照时间更加影响开窗概率。 When using logistic regression, it is required that all variables are independent. Since the data was obtained in 15 dwellings with different physical properties and different inhabitants, all variables could not be assumed a priori(先验) to be independent of the dwelling it was obtained from. Variable independency was tested by assigning an index to each of the dwellings, which was used as a factor in the analyses. If an interaction term between a variable and the dwelling index was retained in the model, it was taken as an indication of dependence and the variable was removed from the model. Variables that did not interact with the dwelling index were assumed to be independent of the individual dwelling.使用罗辑回归时要求所有的变量都是独立的。由于15个不同住户中得到不同居民的不同物性参数，使用逻辑回归时,要求所有的变量是独立的。由于数据得到15个不同的物理性质和不同的居民住宅,所有住宅中获得的变量不能直接假定是相互独立的。每间民居通过设定一个在分析中使用的因素指标来验证变量独立性。若在变量和民居指标之间的一个相互作用项保留在模型中,它被认为是不独立的并从模型中删除。变量与民宅指标之间没有相互作用则被认为相互独立的。 Correlations(相关性) between explanatory variables may result in inflation(膨胀) of the estimated(估计) variance(不一致) (估计方差)of the inferred coefficient, which in turn will result in too wide confidence intervals(置信区间). To estimate the size of the inflation due to correlations between all explanatory variables (multicolinearity), generalized variance(广义方差) inflation factors (GVIF) were calculated for coefficients of all continuous explanatory variables. The GVIF estimates the inflation of the variance, due to multicolinearity as compared to no multicolinearity. Since the GVIF is an estimate of the inflation of the variance, the GVIF1/(2Df) is an estimate of the factor by which the standard error and confidence interval is inflated due to multicolinearity between explanatory variables. 解释变量之间的相关性可能造成估计回归系数的方差膨胀,进而会导致过大的置信区间。为了估计因所有解释变量两两间的相关性( 多重共线性)所导致的膨胀大小，为连续的解释变量计算广义方差膨胀因子(GVIF)。由于多重共线性与非多重共线性得比较，GVIF可以估计方差的膨胀大小。因为GVIF是方差膨胀大小的估计，又由于解释变量的多重共线性，通过GVIF1/(2Df)可以估计标准差和置信区间膨胀的。 Prior to the regression analyses, four variables were transformed to obtain a better distribution. Table 5 describes how the variables were transformed. 回归分析之前,四个变量经转换以获得一个更好的定位。表5描述了变量是如何转换的。 The statistical analyses were conducted using the statistical software “R” and the models were inferred using the step function in R 38. 使用数据分析软件R进行了数据分析并使用R中的step功能推测了模型38。4. Results In this section, the main results of the statistical analysis are presented. Table 6 presents descriptive statistics of all measured variables in each of the four groups. 在本节中,给出了统计分析的主要结果。表6给出了四组数据每组中的所有测量变量的描述性统计。 All results from group 1 are presented in this section, while tables with inferred coefficients and results from the VIF analyses from groups 2, 3 and 4 are presented in Appendix 1. 在这一章节给出了组1的所有结论,而附录1中写出了组2、3和4由VIF分析等到的推断回归系数和结论。 The dwelling index affected the impact of some of the explanatory variables as concerns(就而言) the probability of opening and closing a window. This indicates different habits in the different dwellings included in the four groups, which were not described by the measured variables. For example, the CO2 concentration interacted with the dwelling index in the model for closing windows in group 3, indicating that the windows were closed at different (but distinct) concentrations of CO2 in each dwelling. The variables that interacted with the dwelling index were removed from the models where the interaction occurred. In the further analyses, the dwelling index was not included, since we were not interested in the behaviour in each single dwelling, but in the overall behaviour in all of the surveyed dwellings.就开关窗概率而言，住宅指标会影响解释变量的效果。这表明测量变量没有表示四组民居中不同民居中的不同行为习惯。例如，在组3的关窗模型中C02浓度与建筑指标的相互作用显示出每间民居的窗户在不同（但很明显）的CO2浓度时被关闭。当变量在建筑指标相互作用时出现了交互作用，则该变量就被一出模型，在接下来的研究中，建筑指标也不包含在内，因为我们不关心每间民居的单一人行为而是所有被研究的民居的所有人行为。 Table 7 shows a list of variables that were removed from the models due to interactions with the dwelling index.表7列出了由于民居指标存在交互作用而从模型中移除的变量。4.1. Group 1: owner-occupied, naturally ventilated dwellings4.1. 组1：私有，自然通风 As expected, CO2 concentration, indoor temperature and solar radiation were positively correlated with the probability of opening the window, while Outdoor Temperature was negative correlated with （与相关）the probability of closing windows. In the bedroom, the CO2 concentration was the most important variable for the probability of opening windows, while it did not have a significant effect in the living room (the confidence interval for the coefficient contains the number 0). The indoor relative humidity had the biggest effect on the closing probability in the living room, but did not have a significant effect in the bedroom. Both the opening and closing probabilities were influenced by the season and by the time of day.正如预期所想，CO2浓度，室外温度和太阳辐射强度和与开窗概率是正相关的，与此同时，室外温度和关窗概率是负相关的。在卧室中，CO2浓度对开窗概率来说是最重要的，而它对客厅关窗概率并没有很大影响(回归系数区间包含数字0)。室内相对湿度对客厅的关窗概率影响最大，但对卧室关窗概率影响并不大。开关窗概率同时受到季节和当时或当前的情况的影响。 Since no windowwere opened during the winter time, the seasonal effects only take spring and summer into account. During winter, the inferred probability of opening a window was 0. 由于在冬天没有窗户被打开，所以季节影响仅考虑春天和夏天。在冬季，推测的开窗概率为0。 The coefficients and intercepts listed in Table 8 constitute the opening and closing model for group 1. The two formulas （公式）below are examples of the logistic regression equation （ 方程式）for opening probability for a morning in spring in the living room (3) and bedroom (4): 组成组1开关窗模型的回归系数和拦截系数如表8所示。如下是两个春季早上客厅(3)和卧室(4)开窗概率的回归方程式的例子。Where, p is the probability of opening a window within the next 10 min, CO2 is the CO2 concentration in ppm, ti is the indoor temperature in C and Rad in the solar radiation in W/m2. 式中，p是下一个10分钟开窗的概率，CO2是以ppm为单位的CO2浓度，ti是以表示的室外空气温度，Rad是以W/m2为单位的太阳辐射强度。 The results in Table 9 indicate that the confidence intervals of some variables may be inflated due to multicolinearity (the GVIF1/(2Df) is a measure of inflation due to multicolinearity). Especially the standard error （标准差）of the categorical （分类的，绝对的）variable Room and the interaction terms were inflated due to multicolinearity. This indicates that some variables were biased by(与有偏差) the room in which they were measured. 表9中的结论表明了由于多重共线性一些变量的置信区间膨胀了(GVIF1/(2Df)衡量由