二维稳态传热系统的模糊反演及其应用
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摘要
传热学反问题(Inverse Heat Transfer Problems,IHTP)是一类典型的反演课题,它是指根据研究对象内部或表面的温度信息反求如热物性参数、几何形状、边界条件以及源项等未知特征参量。各类传热学反问题广泛存在于科学研究以及航天、化工、材料加工处理、动力工程、冶金工程、无损探伤等工程领域,对其进行深入研究,具有十分重要的科学意义和工程意义。
模糊推理是建立在模糊集合理论基础上的一种较为典型的不确定推理方法和计算框架,对输入信息具有明显的抗干扰能力;能够有效利用不精确、不确定和不完备信息进行推理和决策;能够综合运用定性知识(包括经验知识)和定量知识完成推理过程,并具有较低的计算成本。本文研究了基于模糊推理的稳态传热过程的反演问题,主要研究工作与结果包括以下五个方面。
①以平板传热系统边界温度分布反演问题为例,建立了基于共轭梯度法(CGM)、Levenberg-Marquardt方法(L-MM)和遗传算法(GA)等常用最优化算法的传热学反问题模型。通过数值仿真试验,讨论了待反演参数的初始猜测值、温度测点数目以及温度测量误差等条件对反演结果的影响,在此基础上,总结了前述的求解传热学反问题常用方法存在的局限性。
②针对前述最优化算法求解传热反问题存在的局限性,提出了应用模糊逻辑理论研究传热学反问题的新思路;针对传热过程热边界条件反演问题测量信息与待反演信息所固有的空间分布特征,提出了一种适于传热学反问题的分散式模糊推理(Decentralized Fuzzy Inference,DFI)机制,建立了二维稳态传热学反问题的分散式模糊推理系统。该系统利用一组分散的模糊推理单元根据局部测量信息及相应的推理规则,通过模糊推理,产生与该局部信息对应的模糊推理分量;进一步,根据各待反演信息对于各局部测量信息影响程度进行综合协调,在综合考虑所有测量信息的前提下,获得各待反演参数的补偿量,实现传热系统的模糊反演。
③研究了分散式模糊推理(DFI)系统中分散推理结果的综合协调问题,提出了基于影响关系矩阵的传热学反问题分散式模糊推理系统的综合协调方法。对于规则区域导热系统热边界条件分布反演问题,提出通过传热过程定性分析确定影响关系矩阵方法,并以此方法建立了两类典型的规则区域导热系统的影响关系矩阵,形成了基于定性加权的分散模糊推理(QDFI)方法;对于一些相对复杂的非规则区域传热系统反演问题,提出采用灵敏度分析建立影响关系矩阵方法,形成基于灵敏度加权的分散模糊推理(SDFI)方法。利用DFI方法研究了典型的二维稳态传热系统边界温度分布和几何形状分布的反演问题,并与CGM的反演结果进行比较,证明了DFI方法求解传热学反问题的有效性。
④采用QDFI方法分别求解了连铸结晶器内壁热流分布估计以及工业窑炉内壁温度分布两类实际分布参数传热系统的反演问题;讨论了待反演参数的初始猜测值、温度测点数目及测量误差等因素对于热边界条件反演结果的影响,并CGM进行了比较。结果表明,相对CGM,DFI能够明显降低反演结果对测点数目的依赖程度以及对测量误的敏感程度,具有良好的抗不适定性。
⑤采用所建立的SDFI方法根据膜式水冷壁背火侧的局部可测壁温实现了水冷壁向火侧辐射热流、水冷壁管内汽水介质温度以及对流换热系数等传热边界条件的同时反演;讨论了不同反演条件对反演结果的影响,并与CGM的反演结果进行了对比,证明了SDFI具有较好的抗不适定性。研究表明,采用DFI方法能够更加有效地根据水冷壁背火侧的局部可测量壁温确定水冷壁传热边界条件以及向火侧温度分布及危险点位置等重要信息,为电站锅炉运行状态的分析与监测提供必要依据。
Inverse heat transfer problems (IHTP ) is a typical inverse subject, which involves the determination of thermophysical properties, geometric parameters, boundary conditions and source heat based on the internal or surface temperature of the object studied. IHTP is widely used in scientific research and the engineering filed such as aerospace, chemicals, materials processing, power engineering, metallurgical engineering, nondestructive testing, etc. It is of significant scientific and engineering value to further study the IHCP.
Fuzzy inference is a typical uncertain reasoning method and calculation framework on the basis of the fuzzy set theory. It has the low computational cost and the strong capacity of resisting disturbance to input information and can effectively use the imprecise and incomplete information for reasoning and decision-making. What’s more, qualitative knowledge (including experience knowledge) and quantitative knowledge can both be applied in fuzzy inference process. In this paper the inverse problem of steady heat transfer process is studied based on the fuzzy inference, the main works include the following five parts:
①Take the problem of estimating the flat boundary temperature for example, the inverse model of heat transfer process is established on the typical optimal algorithms such as CGM, L-MM and GA. Through numerical simulation experiments, the influence of different initial guesses of the estimated parameters, the number of temperature measuring points and measurement errors on the inversion results are discussed, and the limitation of the before-mentioned method used for solving the inverse heat transfer problems are summarized.
②For the limitation of the optimization algorithm used for solving the inverse heat transfer problems, a new idea based on fuzzy logical theory is presented to study the inverse heat transfer problem, and for the inherent spatial distribution characteristics among measured information and the estimated information of the inverse thermal boundary conditions problem, the decentralized fuzzy inference (DFI) strategy tending to solve the inverse heat transfer problems is proposed. And then the decentralized fuzzy inference system is set up based on DFI strategy for two-dimensional inverse steady heat transfer problem. According to the local measured information and the fuzzy inference rules, the system utilizes a set of decentralized fuzzy inference units to produce the fuzzy inference components which are corresponding to the local measured information. Further, depending on the importance of the estimated information for local measured information, the fuzzy inference components are synthesized. And under the premise of considering all the measured information, the compensations of estimated information are gained, and the estimation is achieved.
③The synthetic issue on the fuzzy inference results in the DFI system is studied, and the synthesized method based on influence relation matrix for DFI system is presented. For the inverse heat transfer problem to estimate thermal boundary conditions of heat transfer system on regular domain, the influence relation matrix is gained by the qualitative analysis of the heat transfer process, by which the influence relation matrix of two typical heat transfer system on regular domain is established, and the qualitative weighting decentralized fuzzy inference (QDFI) method is formed. For some complicated inverse heat transfer problem on irregular domain, the sensitivity analysis is used to build the influence relation matrix, and the sensitivity weighting decentralized fuzzy inference (SDFI) is formed. The DFI is performed to estimate the temperature boundary of a flat and the geometry of a tube inner surface, and the results are compared with the CGM to show its validity.
④The heat flux distribution at the metal-mold interface and the temperature distribution at furnace inner surface are solved by QDFI method respectively, and the influence of initial guesses of the inverse parameters, the number of measuring points and measurement errors on thermal boundary conditions results are discussed. From the results, it can be concluded that DFI compared to CGM can reduce the dependence of results on the number of measuring points and weaken the effect of measurement errors on the results. The DFI is of a good anti ill-posed characteristic for solving inverse problem of the actual distribution parameters heat transfer system.
⑤The thermal boundary conditions of membrane water wall, which are comprised of the radiation heat flux at the fireside, the temperature of the working steam-water-mixtures and the convective heat transfer coefficient in the water wall tubes, are estimated in the same time by the SDFI method based on the local measured temperatures on the back of membrane water wall, and the influence of the different inverse conditions on the results are discussed. In comparison with CGM, it is concluded that SDFI is of a good anti ill-posed characteristic. The study shows that DFI can determine the thermal boundary conditions of membrane water wall, the temperature distribution of the fireside and the positions of the dangerous points more effectively based on the local measured temperatures on the back of membrane water wall. It would provide necessary basis for the operation state analysis and monitoring of power plant boilers.
模糊推理是建立在模糊集合理论基础上的一种较为典型的不确定推理方法和计算框架,对输入信息具有明显的抗干扰能力;能够有效利用不精确、不确定和不完备信息进行推理和决策;能够综合运用定性知识(包括经验知识)和定量知识完成推理过程,并具有较低的计算成本。本文研究了基于模糊推理的稳态传热过程的反演问题,主要研究工作与结果包括以下五个方面。
①以平板传热系统边界温度分布反演问题为例,建立了基于共轭梯度法(CGM)、Levenberg-Marquardt方法(L-MM)和遗传算法(GA)等常用最优化算法的传热学反问题模型。通过数值仿真试验,讨论了待反演参数的初始猜测值、温度测点数目以及温度测量误差等条件对反演结果的影响,在此基础上,总结了前述的求解传热学反问题常用方法存在的局限性。
②针对前述最优化算法求解传热反问题存在的局限性,提出了应用模糊逻辑理论研究传热学反问题的新思路;针对传热过程热边界条件反演问题测量信息与待反演信息所固有的空间分布特征,提出了一种适于传热学反问题的分散式模糊推理(Decentralized Fuzzy Inference,DFI)机制,建立了二维稳态传热学反问题的分散式模糊推理系统。该系统利用一组分散的模糊推理单元根据局部测量信息及相应的推理规则,通过模糊推理,产生与该局部信息对应的模糊推理分量;进一步,根据各待反演信息对于各局部测量信息影响程度进行综合协调,在综合考虑所有测量信息的前提下,获得各待反演参数的补偿量,实现传热系统的模糊反演。
③研究了分散式模糊推理(DFI)系统中分散推理结果的综合协调问题,提出了基于影响关系矩阵的传热学反问题分散式模糊推理系统的综合协调方法。对于规则区域导热系统热边界条件分布反演问题,提出通过传热过程定性分析确定影响关系矩阵方法,并以此方法建立了两类典型的规则区域导热系统的影响关系矩阵,形成了基于定性加权的分散模糊推理(QDFI)方法;对于一些相对复杂的非规则区域传热系统反演问题,提出采用灵敏度分析建立影响关系矩阵方法,形成基于灵敏度加权的分散模糊推理(SDFI)方法。利用DFI方法研究了典型的二维稳态传热系统边界温度分布和几何形状分布的反演问题,并与CGM的反演结果进行比较,证明了DFI方法求解传热学反问题的有效性。
④采用QDFI方法分别求解了连铸结晶器内壁热流分布估计以及工业窑炉内壁温度分布两类实际分布参数传热系统的反演问题;讨论了待反演参数的初始猜测值、温度测点数目及测量误差等因素对于热边界条件反演结果的影响,并CGM进行了比较。结果表明,相对CGM,DFI能够明显降低反演结果对测点数目的依赖程度以及对测量误的敏感程度,具有良好的抗不适定性。
⑤采用所建立的SDFI方法根据膜式水冷壁背火侧的局部可测壁温实现了水冷壁向火侧辐射热流、水冷壁管内汽水介质温度以及对流换热系数等传热边界条件的同时反演;讨论了不同反演条件对反演结果的影响,并与CGM的反演结果进行了对比,证明了SDFI具有较好的抗不适定性。研究表明,采用DFI方法能够更加有效地根据水冷壁背火侧的局部可测量壁温确定水冷壁传热边界条件以及向火侧温度分布及危险点位置等重要信息,为电站锅炉运行状态的分析与监测提供必要依据。
Inverse heat transfer problems (IHTP ) is a typical inverse subject, which involves the determination of thermophysical properties, geometric parameters, boundary conditions and source heat based on the internal or surface temperature of the object studied. IHTP is widely used in scientific research and the engineering filed such as aerospace, chemicals, materials processing, power engineering, metallurgical engineering, nondestructive testing, etc. It is of significant scientific and engineering value to further study the IHCP.
Fuzzy inference is a typical uncertain reasoning method and calculation framework on the basis of the fuzzy set theory. It has the low computational cost and the strong capacity of resisting disturbance to input information and can effectively use the imprecise and incomplete information for reasoning and decision-making. What’s more, qualitative knowledge (including experience knowledge) and quantitative knowledge can both be applied in fuzzy inference process. In this paper the inverse problem of steady heat transfer process is studied based on the fuzzy inference, the main works include the following five parts:
①Take the problem of estimating the flat boundary temperature for example, the inverse model of heat transfer process is established on the typical optimal algorithms such as CGM, L-MM and GA. Through numerical simulation experiments, the influence of different initial guesses of the estimated parameters, the number of temperature measuring points and measurement errors on the inversion results are discussed, and the limitation of the before-mentioned method used for solving the inverse heat transfer problems are summarized.
②For the limitation of the optimization algorithm used for solving the inverse heat transfer problems, a new idea based on fuzzy logical theory is presented to study the inverse heat transfer problem, and for the inherent spatial distribution characteristics among measured information and the estimated information of the inverse thermal boundary conditions problem, the decentralized fuzzy inference (DFI) strategy tending to solve the inverse heat transfer problems is proposed. And then the decentralized fuzzy inference system is set up based on DFI strategy for two-dimensional inverse steady heat transfer problem. According to the local measured information and the fuzzy inference rules, the system utilizes a set of decentralized fuzzy inference units to produce the fuzzy inference components which are corresponding to the local measured information. Further, depending on the importance of the estimated information for local measured information, the fuzzy inference components are synthesized. And under the premise of considering all the measured information, the compensations of estimated information are gained, and the estimation is achieved.
③The synthetic issue on the fuzzy inference results in the DFI system is studied, and the synthesized method based on influence relation matrix for DFI system is presented. For the inverse heat transfer problem to estimate thermal boundary conditions of heat transfer system on regular domain, the influence relation matrix is gained by the qualitative analysis of the heat transfer process, by which the influence relation matrix of two typical heat transfer system on regular domain is established, and the qualitative weighting decentralized fuzzy inference (QDFI) method is formed. For some complicated inverse heat transfer problem on irregular domain, the sensitivity analysis is used to build the influence relation matrix, and the sensitivity weighting decentralized fuzzy inference (SDFI) is formed. The DFI is performed to estimate the temperature boundary of a flat and the geometry of a tube inner surface, and the results are compared with the CGM to show its validity.
④The heat flux distribution at the metal-mold interface and the temperature distribution at furnace inner surface are solved by QDFI method respectively, and the influence of initial guesses of the inverse parameters, the number of measuring points and measurement errors on thermal boundary conditions results are discussed. From the results, it can be concluded that DFI compared to CGM can reduce the dependence of results on the number of measuring points and weaken the effect of measurement errors on the results. The DFI is of a good anti ill-posed characteristic for solving inverse problem of the actual distribution parameters heat transfer system.
⑤The thermal boundary conditions of membrane water wall, which are comprised of the radiation heat flux at the fireside, the temperature of the working steam-water-mixtures and the convective heat transfer coefficient in the water wall tubes, are estimated in the same time by the SDFI method based on the local measured temperatures on the back of membrane water wall, and the influence of the different inverse conditions on the results are discussed. In comparison with CGM, it is concluded that SDFI is of a good anti ill-posed characteristic. The study shows that DFI can determine the thermal boundary conditions of membrane water wall, the temperature distribution of the fireside and the positions of the dangerous points more effectively based on the local measured temperatures on the back of membrane water wall. It would provide necessary basis for the operation state analysis and monitoring of power plant boilers.
引文
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