建筑物动态能耗分析用气象仿真模型研究
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摘要
可持续发展给暖通工程师提出的要求是，设计合理、高效、优化的HVAC系统。HVAC系统的优化设计，以全年能耗分析为基础，而能耗分析必须输入可靠的气象数据。我国能耗分析用的气象数据非常欠缺，为推广先进的全年能耗分析方法，构成能耗分析用的气象数据是我国暖通界迫切的任务。
全年能耗分析用的全年气象数据，可以根据若干年的观测，按一定方法统计构成典型年，也可用数学模型模拟产生。论文选择数学模拟方法，因为该方法具有较少主观性、比较简洁，并且更适合我国现有气象观测客观条件的优点。论文主要以北京、西安、重庆和成都的数据为基础，辅以昆明和福州的少量数据进行分析。建模参数选择了对能耗分析最重要的三个要素，即辐射、气温和水汽压。根据我国目前逐日气象记录相对充分，而逐时观测稀少的客观条件，论文采用了分阶段建模和模拟的方法。即先模拟逐日气象参数，在此基础上再模拟逐时气象参数。
逐日气象参数包括日总辐射、日均气温、气温日较差、日均水汽压和水汽压日较差。逐日气象参数既有周期性变化趋势，又有随机特点，由于两者对能耗分析都有显著影响，因此对逐日气象参数建立了组合模型，即确定性模型+随机模型。确定性模型描述周期性变化，是由少量的显著频率构成的傅立叶级数。这些显著频率通过傅立叶变换及频谱分析确定。5个逐日气象参数的周期变化最多用显著频率0、1、2、3、4[周/年]来描述就足够了。
逐日气象参数分离确定项之后的随机项是均值平稳（零均值）、方差时变，并且存在互相关的非正态分布的随机序列。这些序列可以认为是分段（逐月）平稳的，因此用每个月的标准差进行标准化可得到方差也平稳的序列。本文对该标准序列采用误差函数成功进行了正态变换，这保证了模拟仿真数据与原始数据具有相同的分布。对平稳化正态化之后的随机序列，论文建立了多维满系数ARX模型即来进行模拟。模型以辐射序列为输入，模拟输出温湿度参数。模型阶数根据相关分析和FPE准则确定，参数估计采用了最小二乘法。ARX模型的残差通过了白噪声及正态检验。辐射作为相对独立的要素，单独建立一元AR（2）模型模拟。多元ARX模型与多元AR模型即相比的明显好处是，充分保证了随机序列之间的互相关，特别是0步互相关。因为多维ARX模型模拟温湿度参数时使用了同一时刻的辐射，而多维AR模型不可能用同一天的辐射计算温湿度。经检验ARX模型的模拟数据不但与建模数据具有相同的相关关系，还具有相同的分布特征。
论文的逐日气象组合模型形式，Fourier模型+ARX模型是国内首次提出，并首次进行了正态变换，模型在数据相关系数，分布特征方面也保持得最好。日散射或日直射没有与日总射同时进入随机模型，因为随机模拟时难以保证散射或直射不大
于日总射。故论文另外建立了一个日散射系数Kd多项式分离模型，在日总辐射已知的情况下估计日总辐射。该模型的估计数据与原始数据具有一致的月均值，对长期能耗分析具有足够的准确性。还建立了日散射概率密度模型。
逐时辐射模型采用了确定性模型。通过对原始逐时总辐射数据进行傅立叶变换，确定了显著频率，高频部分为1、2、3、4[周/日]及以上每个频率的4个旁瓣，低频部分为0、1、2、3、4[周/年]，用显著频率构成逐时总辐射的傅立叶级数模型。模拟时，该模型用日总辐射调整，以保证逐时值之和与日值相当。在逐日总射和逐时总射基础上，建立了逐时散射系数kd多项式模型。该逐时散射模型考虑了大气质量的影响，即不同大气质量下给出不同的拟合式，精度比笼统的拟合模型显著提高。
对昆明和福州的资料分析表明，逐时气温用日均气温和气温日较差进行标准化后，可以建立一个全年适用的傅立叶模型。该标准化逐时气温模型的显著频率是1、2[周/天]。就日均气温的计算而言，逐时资料和日4次定时值+最高最低值资料是一致的。因此对只有日4次定时值+最高最低值资料的北京、西安、成都和重庆，建立的逐时气温模型具有足够的准确性。本文按北京时间建立逐时气温模型，注意了最高最低气温的出现时间。
与逐时气温一样，逐时水汽压也进行了标准化处理。逐时资料和日4值资料计算的日均水汽压可以认为一致，但水汽压日较差有明显区别。我国大多数地区只有水汽压日4值资料，根据日4值资料建立逐时化模型存在先天不足，决定了任何复杂的模型都不可能准确。因此采用了简单组合模型：傅立叶模型+白噪声模型，其中白噪声标准差统一取0.28。为了保证随机模拟的水汽压不超过当时的饱和水汽压，建立了修正模型，该修正模型认为月均逐时相对湿度与月均逐时标准气温呈线性关系。
气象参数本质上是非平稳、非线性时间序列，论文除了用组合模型进行模拟外，还探讨了用线性神经网络和BP网络对其进行预报和模拟。研究表明，如果以一步预报为目的，神经网络比常规时间序列分析方法优越，因此可以用在HVAC系统的实时控制。但就随机模拟能耗分析用的全年气象数据而言，神经网络并不适合。因此，如果以能耗分析为目的，本文推荐采用组合逐日模型以及相应的逐时化模型，不推荐神经网络方法。
论文给出了气象组合模型模拟软件（suSim）的整体框架，以及北京、西安、重
HVAC engineers must design reasonable, high efficient and optimum HVAC systems to meat the trend of sustainable development. Only on the basis of annual energy analysis, would optimum design be archived. Energy analysis begins with cooling/heating loads calculation, which require climatic data as inputs. However, there isn't sufficient climatic data for energy analysis in China. So research work as to this aspect is emergent.
Climatic data may be constructed to form TRY/TMY by statistic methods or synthesized by stochastic models. Stochastic models are chosen because they have the advantages of conciseness and less subjective, and are more suitable for the original data in China. Analysis is carried out on the data base of Beijing, Xi'an; Chongqing and Chengdu. Part data of Kunming and Fuzhou is also employed. Three climatic factors including solar radiation, temperature and humidity are considered, to which building energy analysis is most sensitive. Conditioned by the fact that daily records are sufficient while hourly records are insufficient, two-stage models are supposed. That means that models do not generate hourly variables directly. Daily variables would be simulated at first and then hourly variables would be simulated on basis of daily data.
Daily variables including daily total solar radiation, daily mean and range of temperature, daily mean and range of water-vapor pressure are modeled. Daily climatic variables consist in deterministic and stochastic components, both of which have important impacts on energy analysis. Thus combination models :deterministic models + stochastic models are established. Deterministic models describe the periodic variation and are Fourier series with only significant cycles. Significant cycles are identified by Fourier transfer and spectrum analysis. The most significant frequencies of daily climatic variables are 0,1,2,3,4 cycles/day.
Stochastic components formed by subtracting deterministic components from the original data are non-normal, cross-related series with stationary means and time-varying variances. The series become weak stationary after standardized with monthly variance. Normal transfers are performed on the standard series, which ensure that simulated data
have the same distributions of the original data. The normal series are described by multivariate ARX model, of which input is solar variable and outputs are temperature and water-vapor pressure variables. The orders are determined by correlation analysis and FPE criteria, and parameters are estimated by least square mean technique. The stochastic solar variables are separately modeled by univariate AR(2). The supposed multivariate ARX models have the advantage of keeping the same cross-correlation among daily variables over the common multivariate AR model. The reason is that the solar variable of the n'th day comes into effect when simulating temperature and water-vapor pressure variables of the n'th day by ARX.
The form of Fourier model plus ARX model is employed first time in China, and have the best performance of keeping cross-correlation and distribution. Daily diffuse radiation wasn't included in combination model, because stochastic model can not ensure that daily diffuse radiation is not more than daily total radiation. Polynomial models are built to estimate daily diffuse radiation from daily total radiation. A probability density model has been supposed also.
Models for hourly solar radiation are deterministic ones. Hourly total radiation models are Fourier series models with significant frequencies determined by Fourier transfer,which include 1,2,3,4 cycles/day and 4 bandsides of every frequency above and frequencies of 0,1,2,3,4 cycles/year . The Fourier models should be adjusted by daily values generated by combination models. Polynomial models separating hourly diffuse radiation from hourly total are built under different air mass. Polynomial fits under different air mass are more accurate than general model for the whole day.
Fourier models with freq
全年能耗分析用的全年气象数据，可以根据若干年的观测，按一定方法统计构成典型年，也可用数学模型模拟产生。论文选择数学模拟方法，因为该方法具有较少主观性、比较简洁，并且更适合我国现有气象观测客观条件的优点。论文主要以北京、西安、重庆和成都的数据为基础，辅以昆明和福州的少量数据进行分析。建模参数选择了对能耗分析最重要的三个要素，即辐射、气温和水汽压。根据我国目前逐日气象记录相对充分，而逐时观测稀少的客观条件，论文采用了分阶段建模和模拟的方法。即先模拟逐日气象参数，在此基础上再模拟逐时气象参数。
逐日气象参数包括日总辐射、日均气温、气温日较差、日均水汽压和水汽压日较差。逐日气象参数既有周期性变化趋势，又有随机特点，由于两者对能耗分析都有显著影响，因此对逐日气象参数建立了组合模型，即确定性模型+随机模型。确定性模型描述周期性变化，是由少量的显著频率构成的傅立叶级数。这些显著频率通过傅立叶变换及频谱分析确定。5个逐日气象参数的周期变化最多用显著频率0、1、2、3、4[周/年]来描述就足够了。
逐日气象参数分离确定项之后的随机项是均值平稳（零均值）、方差时变，并且存在互相关的非正态分布的随机序列。这些序列可以认为是分段（逐月）平稳的，因此用每个月的标准差进行标准化可得到方差也平稳的序列。本文对该标准序列采用误差函数成功进行了正态变换，这保证了模拟仿真数据与原始数据具有相同的分布。对平稳化正态化之后的随机序列，论文建立了多维满系数ARX模型即来进行模拟。模型以辐射序列为输入，模拟输出温湿度参数。模型阶数根据相关分析和FPE准则确定，参数估计采用了最小二乘法。ARX模型的残差通过了白噪声及正态检验。辐射作为相对独立的要素，单独建立一元AR（2）模型模拟。多元ARX模型与多元AR模型即相比的明显好处是，充分保证了随机序列之间的互相关，特别是0步互相关。因为多维ARX模型模拟温湿度参数时使用了同一时刻的辐射，而多维AR模型不可能用同一天的辐射计算温湿度。经检验ARX模型的模拟数据不但与建模数据具有相同的相关关系，还具有相同的分布特征。
论文的逐日气象组合模型形式，Fourier模型+ARX模型是国内首次提出，并首次进行了正态变换，模型在数据相关系数，分布特征方面也保持得最好。日散射或日直射没有与日总射同时进入随机模型，因为随机模拟时难以保证散射或直射不大
于日总射。故论文另外建立了一个日散射系数Kd多项式分离模型，在日总辐射已知的情况下估计日总辐射。该模型的估计数据与原始数据具有一致的月均值，对长期能耗分析具有足够的准确性。还建立了日散射概率密度模型。
逐时辐射模型采用了确定性模型。通过对原始逐时总辐射数据进行傅立叶变换，确定了显著频率，高频部分为1、2、3、4[周/日]及以上每个频率的4个旁瓣，低频部分为0、1、2、3、4[周/年]，用显著频率构成逐时总辐射的傅立叶级数模型。模拟时，该模型用日总辐射调整，以保证逐时值之和与日值相当。在逐日总射和逐时总射基础上，建立了逐时散射系数kd多项式模型。该逐时散射模型考虑了大气质量的影响，即不同大气质量下给出不同的拟合式，精度比笼统的拟合模型显著提高。
对昆明和福州的资料分析表明，逐时气温用日均气温和气温日较差进行标准化后，可以建立一个全年适用的傅立叶模型。该标准化逐时气温模型的显著频率是1、2[周/天]。就日均气温的计算而言，逐时资料和日4次定时值+最高最低值资料是一致的。因此对只有日4次定时值+最高最低值资料的北京、西安、成都和重庆，建立的逐时气温模型具有足够的准确性。本文按北京时间建立逐时气温模型，注意了最高最低气温的出现时间。
与逐时气温一样，逐时水汽压也进行了标准化处理。逐时资料和日4值资料计算的日均水汽压可以认为一致，但水汽压日较差有明显区别。我国大多数地区只有水汽压日4值资料，根据日4值资料建立逐时化模型存在先天不足，决定了任何复杂的模型都不可能准确。因此采用了简单组合模型：傅立叶模型+白噪声模型，其中白噪声标准差统一取0.28。为了保证随机模拟的水汽压不超过当时的饱和水汽压，建立了修正模型，该修正模型认为月均逐时相对湿度与月均逐时标准气温呈线性关系。
气象参数本质上是非平稳、非线性时间序列，论文除了用组合模型进行模拟外，还探讨了用线性神经网络和BP网络对其进行预报和模拟。研究表明，如果以一步预报为目的，神经网络比常规时间序列分析方法优越，因此可以用在HVAC系统的实时控制。但就随机模拟能耗分析用的全年气象数据而言，神经网络并不适合。因此，如果以能耗分析为目的，本文推荐采用组合逐日模型以及相应的逐时化模型，不推荐神经网络方法。
论文给出了气象组合模型模拟软件（suSim）的整体框架，以及北京、西安、重
HVAC engineers must design reasonable, high efficient and optimum HVAC systems to meat the trend of sustainable development. Only on the basis of annual energy analysis, would optimum design be archived. Energy analysis begins with cooling/heating loads calculation, which require climatic data as inputs. However, there isn't sufficient climatic data for energy analysis in China. So research work as to this aspect is emergent.
Climatic data may be constructed to form TRY/TMY by statistic methods or synthesized by stochastic models. Stochastic models are chosen because they have the advantages of conciseness and less subjective, and are more suitable for the original data in China. Analysis is carried out on the data base of Beijing, Xi'an; Chongqing and Chengdu. Part data of Kunming and Fuzhou is also employed. Three climatic factors including solar radiation, temperature and humidity are considered, to which building energy analysis is most sensitive. Conditioned by the fact that daily records are sufficient while hourly records are insufficient, two-stage models are supposed. That means that models do not generate hourly variables directly. Daily variables would be simulated at first and then hourly variables would be simulated on basis of daily data.
Daily variables including daily total solar radiation, daily mean and range of temperature, daily mean and range of water-vapor pressure are modeled. Daily climatic variables consist in deterministic and stochastic components, both of which have important impacts on energy analysis. Thus combination models :deterministic models + stochastic models are established. Deterministic models describe the periodic variation and are Fourier series with only significant cycles. Significant cycles are identified by Fourier transfer and spectrum analysis. The most significant frequencies of daily climatic variables are 0,1,2,3,4 cycles/day.
Stochastic components formed by subtracting deterministic components from the original data are non-normal, cross-related series with stationary means and time-varying variances. The series become weak stationary after standardized with monthly variance. Normal transfers are performed on the standard series, which ensure that simulated data
have the same distributions of the original data. The normal series are described by multivariate ARX model, of which input is solar variable and outputs are temperature and water-vapor pressure variables. The orders are determined by correlation analysis and FPE criteria, and parameters are estimated by least square mean technique. The stochastic solar variables are separately modeled by univariate AR(2). The supposed multivariate ARX models have the advantage of keeping the same cross-correlation among daily variables over the common multivariate AR model. The reason is that the solar variable of the n'th day comes into effect when simulating temperature and water-vapor pressure variables of the n'th day by ARX.
The form of Fourier model plus ARX model is employed first time in China, and have the best performance of keeping cross-correlation and distribution. Daily diffuse radiation wasn't included in combination model, because stochastic model can not ensure that daily diffuse radiation is not more than daily total radiation. Polynomial models are built to estimate daily diffuse radiation from daily total radiation. A probability density model has been supposed also.
Models for hourly solar radiation are deterministic ones. Hourly total radiation models are Fourier series models with significant frequencies determined by Fourier transfer,which include 1,2,3,4 cycles/day and 4 bandsides of every frequency above and frequencies of 0,1,2,3,4 cycles/year . The Fourier models should be adjusted by daily values generated by combination models. Polynomial models separating hourly diffuse radiation from hourly total are built under different air mass. Polynomial fits under different air mass are more accurate than general model for the whole day.
Fourier models with freq
引文
前 言
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第6章
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第8章
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[2]. 江亿.空调负荷计算用随机气象模型.制冷学报. 1981.NO.3，P45-55
[3]. 张素宁，田胜元.建筑能耗分析用逐日气象数学模型的建立.暖通空调. 2000.Vol.30，No.3，P64-66
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[2]. 周淑珍主编.气象学与气候学.北京.高等教育出版社.1997年7月第3版
[3]. 张家诚主编.中国气候总论.北京.气象出版社.1991年12月
[4]. 邓必鑫编著.信号分析基础.北京.北京理工大学出版社.1994年4月
[5]. 杨位钦等编著.时间序列分析与动态数据建模.北京.北京工业学院出版社.1986年12月
[6]. 田胜元等编著.实验设计与数据处理.北京.中国建筑出版社.1988年11月
[7]. 汪荣鑫著.数理统计.西安.西安交通大学出版社.1986年10月
[8]. 杨凤翔等编著.数值分析.天津.天津大学出版社.1996年6月
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6. David E. Knebel. ASHRAE technical committee 4.7 development of simplified energy analysis procedures.ASHRAE Transactions.1995（1）P869-881
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[2]. 张家诚主编.中国气候总论.北京：气象出版社.1991年12月
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第3章
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第7章
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第8章
[1]. John Boland. Time series analysis of climatic variables. Solar Energy. 1995.Vol.55,No.5,P377-388
[2]. 江亿.空调负荷计算用随机气象模型.制冷学报. 1981.NO.3，P45-55
[3]. 张素宁，田胜元.建筑能耗分析用逐日气象数学模型的建立.暖通空调. 2000.Vol.30，No.3，P64-66
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第9章
[1]. 江亿.空调负荷计算用随机气象模型.制冷学报.1981（3）.P45-55
[2]. 周淑珍主编.气象学与气候学.北京.高等教育出版社.1997年7月第3版
[3]. 张家诚主编.中国气候总论.北京.气象出版社.1991年12月
[4]. 邓必鑫编著.信号分析基础.北京.北京理工大学出版社.1994年4月
[5]. 杨位钦等编著.时间序列分析与动态数据建模.北京.北京工业学院出版社.1986年12月
[6]. 田胜元等编著.实验设计与数据处理.北京.中国建筑出版社.1988年11月
[7]. 汪荣鑫著.数理统计.西安.西安交通大学出版社.1986年10月
[8]. 杨凤翔等编著.数值分析.天津.天津大学出版社.1996年6月
第10章
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