基于矩阵论的供热管网阻力系数辨识研究
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摘要
集中供热系统是城市重要的基础设施,因其具有节能、环保和供热质量好等优点,在“节能减排”的大环境下将得到更广泛的应用。供热管网作为集中供热系统中的重要部分,具有规模大、结构复杂、投资巨大以及社会影响重大等特点,因此倍受关注。目前,供热管网水力工况计算、运行调度以及可靠性分析等几个方面的研究较多,而供热管网阻力特性辨识方面的研究较少。如果无法准确获得供热管网实际运行条件下的阻力系数,供热管网水力工况计算以及运行调度等研究大都只能停留在理论计算模拟与定性分析上。计算与分析的结果往往与实际运行情况不符,从而大大降低研究成果的实用价值。目前在为数不多的供热管网阻力系数辨识研究中,对供热管网辨识模型的研究还比较少,并且辨识方法单一,辨识准确程度不高、辨识计算耗时较大。因此,对供热管网阻力系数辨识问题开展深入研究有着重要的理论意义和实用价值。
本文针对供热管网阻力系数辨识问题进行了较为深入的研究,提出了一些行之有效的辨识研究方法。首先利用矩阵方程形式表达供热管网阻力系数辨识问题,并结合系统能观测性理论,指出供热管网节点压力均可观测是满足供热管网阻力系数辨识能观测性的必要条件。在此基础上提出多水力工况条件下满足供热管网阻力系数辨识能观测性的充分条件以及该条件下的辨识求解方法,为供热管网阻力系数辨识的理论研究及实验测试提供了一种新的研究途径。
考虑现有供热管网的实际观测条件一般不能满足辨识能观测性的要求,本文结合线性方程组的解分析理论和广义逆矩阵理论,提出基于广义逆矩阵理论辨识供热管网阻力系数的方法。该方法可以应用于一般观测条件下的供热管网阻力系数辨识问题的研究,其中利用逐步线性化的迭代方法求解辨识方程组的广义逆解,并以方程组解中的阻力系数值作为辨识结果,逼近供热管网阻力系数的实际值。而后,将基于广义逆矩阵理论辨识供热管网阻力系数的方法应用于辨识算例。
本文提出在可能获取更多的观测数据的条件下,可以利用部分管段(一般为一组链支管段)阻力系数初始值作为辨识的已知条件,辨识得到供热管网阻力系数。考虑到利用空间供热管网模型可以更直接地反映供热管网实际情况,利用分块矩阵表示空间供热管网阻力系数辨识问题,在求解辨识问题的同时结合空间供热管网的特点提出适用于空间供热管网阻力系数辨识的链支管段选择方案。
结合聚类分析理论提出了基于反映供热管网阻力系数变化的管段流量和节点压力观测点优化布置方法。基于矩阵论中的矩阵对矩阵微分运算法则以及供热管网阻力系数变化对管段流量和节点压力影响的线性分析结果,在上述研究基础上,提出利用管段流量和节点压力观测点相对灵敏度研究观测点优化布置问题,并且根据供热管网设计值计算相对灵敏度。
最后,利用供热系统多功能试验台及某集中供热管网观测数据进行供热管网阻力系数模拟辨识研究,说明不同供热管网观测条件下的阻力系数辨识方法的实现过程,表明本文所提出的辨识方法具有较高的辨识计算效率和较好的实际工程应用前景。
本文基于系统能观测性理论指出多水力工况条件下供热管网阻力系数辨识满足能观测性条件的可能性,在满足辨识能观测性的条件下可以直接求解阻力系数辨识问题。考虑到实际供热管网中压力和流量观测点的布置情况,提出基于广以逆矩阵理论辨识供热管网阻力系数的方法,以辨识方程组的广义逆解作为供热管网阻力系数辨识结果,该结果与实际值一般比较接近。在具备更加完善观测条件的情况下,可以利用基于一组链支管段阻力系数值的辨识方法得到更加接近实际值的供热管网阻力系数辨识结果。在上述研究基础上,可以依据观测点相对灵敏度选择合适的观测数据进行供热管网阻力系数辨识。本文的研究成果为进一步研究供热管网阻力系数辨识问题及实际工程应用奠定了理论基础,具有一定前导性。
Centralized heating systems have become important modern municipal infrastructures and will be applied widely when we focus on energy saving and emission reduction for those energy saving, environmental protection and good heating quality. Heat-supply network is an important part of centralized heating system, whose further study has drawn great attention because of its large scale, complicated structure, enormous investment and significant social impact. Nowadays the study of heat-supply networks focuses on hydraulic loading condition computation, reliability analysis, operation and regulation, but there is less study on pipe friction parameters identification of heat-supply networks. However, if actual pipe friction parameters can not be identified, the study mentioned above would just be theoretic simulation or qualitative analysis. In real-world engineering, theoretic simulation results can not always accord with practical operation conditions, so the application value could be reduced seriously. In the study of pipe friction parameters identification, there are a few identification models and identification methods of heat-supply networks pipe friction parameters. Identification accuracy is not high, and consuming time of identification computation is great. These deep reserarches of pipe friction parameters identification have theoretical significance and practical value.
This thesis focuses on pipe friction parameters identification of heat-supply networks, and proposes some effective identification methods. Pipe friction parameters identification is expressed as matrix equations. Combined with system observability theory, it is proposed that a necessary condition for observability of pipe friction parameters which is all the nodes pressure heads values are available. Then, a sufficient condition for observability of pipe friction parameters is proposed under multiple hydraulic loading conditions, which provides a new approach to theoretic analysis and field measurement of pipe friction parameters.
Considering the observability conditions of pipe friction parameters identification can not be satisfied under common measured conditions, based on solution analysis and pseudo-inverse matrix theories of linear equations, an identification method based on pseudo-inverse matrix theory is proposed. This identification method can be applied under the common measured conditions. This thesis presents a progressive linearization iteration methodology for solving the pseudo-inverse solution of the identification equations, and considers the pipe friction parameters values in the pseudo-inverse solution as the identification results which are approximate to real pipe friction parameters values. Then, this identification method is applied in a case study.
Furthermore, if more known operational parameters of heat-supply networks can be obtained, a method by using the initial values of some pipe friction parameters (a group of link pipe friction parameters generally) can be used in pipe friction parameters identification. Considering spacial heat-supply network models can represent heat-supply networks more accurately, we presents pipe friction parameters identification problem of spacial heat-supply networks by the form of partitioned matrixes. In the identification process, combined with characteristics of spacial heat-supply networks, an option method of link pipes which is suitable for spacial heat-supply networks is proposed.
Combined with clustering theory, it is proposed that an optimal arrangement method of pipe flow measured points and node pressure head measured points based on reflecting the change of pipe friction parameters. By using matrix differential calculation method, the linear results of pipe flows and node pressure heads reflected by the change of pipe friction parameters can be studied. Then, measured points optimal arrangement is studied by pipe flows and node pressure heads relative sensitivity which can be expressed by design values of heat-supply networks.
Finally, the pipe friction parameters identification methods are applied on a multi-function experiment platform and a centralized heating system. By using field measured values, the identification processes are introduced under different field measured conditions, which can show the identification method has higher efficiency and better prospect of real-world engineering.
It is proposed that pipe friction parameters identification of heat-supply networks may satisfy observability conditions under multiple hydraulic loading conditions based on system observability theory. When pipe friction parameters observability conditions can be satisfied, a new approach for solving pipe friction parameters identification directly is proposed. Considering the real-world nodes pressure heads and pipes flows measured conditions, an identification method based on pseudo-inverse matrix theory is proposed, which can be used in real-world pipe friction parameters identification in heat-supply networks. We consider the pipe friction parameters values in the pseudo-inverse solution as the identification results which are approximate to real pipe friction parameters values. When more known operational parameters of heat-supply networks can be obtained, we could calculate pipe friction parameters which are more closed to their real values by using a group of link pipe friction parameters initial values. On this basis, some measured values with high relative sensitivity can be used. The research results of the thesis which can be used in future study are theoretical foundation of heat-supply network pipe friction parameters identification and real-world application.
本文针对供热管网阻力系数辨识问题进行了较为深入的研究,提出了一些行之有效的辨识研究方法。首先利用矩阵方程形式表达供热管网阻力系数辨识问题,并结合系统能观测性理论,指出供热管网节点压力均可观测是满足供热管网阻力系数辨识能观测性的必要条件。在此基础上提出多水力工况条件下满足供热管网阻力系数辨识能观测性的充分条件以及该条件下的辨识求解方法,为供热管网阻力系数辨识的理论研究及实验测试提供了一种新的研究途径。
考虑现有供热管网的实际观测条件一般不能满足辨识能观测性的要求,本文结合线性方程组的解分析理论和广义逆矩阵理论,提出基于广义逆矩阵理论辨识供热管网阻力系数的方法。该方法可以应用于一般观测条件下的供热管网阻力系数辨识问题的研究,其中利用逐步线性化的迭代方法求解辨识方程组的广义逆解,并以方程组解中的阻力系数值作为辨识结果,逼近供热管网阻力系数的实际值。而后,将基于广义逆矩阵理论辨识供热管网阻力系数的方法应用于辨识算例。
本文提出在可能获取更多的观测数据的条件下,可以利用部分管段(一般为一组链支管段)阻力系数初始值作为辨识的已知条件,辨识得到供热管网阻力系数。考虑到利用空间供热管网模型可以更直接地反映供热管网实际情况,利用分块矩阵表示空间供热管网阻力系数辨识问题,在求解辨识问题的同时结合空间供热管网的特点提出适用于空间供热管网阻力系数辨识的链支管段选择方案。
结合聚类分析理论提出了基于反映供热管网阻力系数变化的管段流量和节点压力观测点优化布置方法。基于矩阵论中的矩阵对矩阵微分运算法则以及供热管网阻力系数变化对管段流量和节点压力影响的线性分析结果,在上述研究基础上,提出利用管段流量和节点压力观测点相对灵敏度研究观测点优化布置问题,并且根据供热管网设计值计算相对灵敏度。
最后,利用供热系统多功能试验台及某集中供热管网观测数据进行供热管网阻力系数模拟辨识研究,说明不同供热管网观测条件下的阻力系数辨识方法的实现过程,表明本文所提出的辨识方法具有较高的辨识计算效率和较好的实际工程应用前景。
本文基于系统能观测性理论指出多水力工况条件下供热管网阻力系数辨识满足能观测性条件的可能性,在满足辨识能观测性的条件下可以直接求解阻力系数辨识问题。考虑到实际供热管网中压力和流量观测点的布置情况,提出基于广以逆矩阵理论辨识供热管网阻力系数的方法,以辨识方程组的广义逆解作为供热管网阻力系数辨识结果,该结果与实际值一般比较接近。在具备更加完善观测条件的情况下,可以利用基于一组链支管段阻力系数值的辨识方法得到更加接近实际值的供热管网阻力系数辨识结果。在上述研究基础上,可以依据观测点相对灵敏度选择合适的观测数据进行供热管网阻力系数辨识。本文的研究成果为进一步研究供热管网阻力系数辨识问题及实际工程应用奠定了理论基础,具有一定前导性。
Centralized heating systems have become important modern municipal infrastructures and will be applied widely when we focus on energy saving and emission reduction for those energy saving, environmental protection and good heating quality. Heat-supply network is an important part of centralized heating system, whose further study has drawn great attention because of its large scale, complicated structure, enormous investment and significant social impact. Nowadays the study of heat-supply networks focuses on hydraulic loading condition computation, reliability analysis, operation and regulation, but there is less study on pipe friction parameters identification of heat-supply networks. However, if actual pipe friction parameters can not be identified, the study mentioned above would just be theoretic simulation or qualitative analysis. In real-world engineering, theoretic simulation results can not always accord with practical operation conditions, so the application value could be reduced seriously. In the study of pipe friction parameters identification, there are a few identification models and identification methods of heat-supply networks pipe friction parameters. Identification accuracy is not high, and consuming time of identification computation is great. These deep reserarches of pipe friction parameters identification have theoretical significance and practical value.
This thesis focuses on pipe friction parameters identification of heat-supply networks, and proposes some effective identification methods. Pipe friction parameters identification is expressed as matrix equations. Combined with system observability theory, it is proposed that a necessary condition for observability of pipe friction parameters which is all the nodes pressure heads values are available. Then, a sufficient condition for observability of pipe friction parameters is proposed under multiple hydraulic loading conditions, which provides a new approach to theoretic analysis and field measurement of pipe friction parameters.
Considering the observability conditions of pipe friction parameters identification can not be satisfied under common measured conditions, based on solution analysis and pseudo-inverse matrix theories of linear equations, an identification method based on pseudo-inverse matrix theory is proposed. This identification method can be applied under the common measured conditions. This thesis presents a progressive linearization iteration methodology for solving the pseudo-inverse solution of the identification equations, and considers the pipe friction parameters values in the pseudo-inverse solution as the identification results which are approximate to real pipe friction parameters values. Then, this identification method is applied in a case study.
Furthermore, if more known operational parameters of heat-supply networks can be obtained, a method by using the initial values of some pipe friction parameters (a group of link pipe friction parameters generally) can be used in pipe friction parameters identification. Considering spacial heat-supply network models can represent heat-supply networks more accurately, we presents pipe friction parameters identification problem of spacial heat-supply networks by the form of partitioned matrixes. In the identification process, combined with characteristics of spacial heat-supply networks, an option method of link pipes which is suitable for spacial heat-supply networks is proposed.
Combined with clustering theory, it is proposed that an optimal arrangement method of pipe flow measured points and node pressure head measured points based on reflecting the change of pipe friction parameters. By using matrix differential calculation method, the linear results of pipe flows and node pressure heads reflected by the change of pipe friction parameters can be studied. Then, measured points optimal arrangement is studied by pipe flows and node pressure heads relative sensitivity which can be expressed by design values of heat-supply networks.
Finally, the pipe friction parameters identification methods are applied on a multi-function experiment platform and a centralized heating system. By using field measured values, the identification processes are introduced under different field measured conditions, which can show the identification method has higher efficiency and better prospect of real-world engineering.
It is proposed that pipe friction parameters identification of heat-supply networks may satisfy observability conditions under multiple hydraulic loading conditions based on system observability theory. When pipe friction parameters observability conditions can be satisfied, a new approach for solving pipe friction parameters identification directly is proposed. Considering the real-world nodes pressure heads and pipes flows measured conditions, an identification method based on pseudo-inverse matrix theory is proposed, which can be used in real-world pipe friction parameters identification in heat-supply networks. We consider the pipe friction parameters values in the pseudo-inverse solution as the identification results which are approximate to real pipe friction parameters values. When more known operational parameters of heat-supply networks can be obtained, we could calculate pipe friction parameters which are more closed to their real values by using a group of link pipe friction parameters initial values. On this basis, some measured values with high relative sensitivity can be used. The research results of the thesis which can be used in future study are theoretical foundation of heat-supply network pipe friction parameters identification and real-world application.
引文
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