基于确定学习理论的轴流压气机旋转失速建模与检测
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摘要
航空发动机被誉为飞机的“心脏”，没有高性能的航空发动机，就不会有先进的航空武器装备和具市场竞争力的民用客机。涡轮风扇（turbofan，简称涡扇）发动机是目前世界上军用和大型民用飞机最常用的动力装置。这种发动机的最主要特点是在高亚音速/超音速飞行条件下具有很高的效率。由于航空发动机的研发周期一般在15至20年左右，世界上航空发动机技术领先的国家都高度重视相关的基础和应用基础研究。高性能航空发动机是一个国家工业综合水平的重要标志。世界上主要发达国家长期以来一直将航空发动机列为优先发展产业，并高度重视与之相关的基础研究。我国是世界上具有航空发动机自主研制能力的少数国家之一，但与世界先进水平相比，在可靠性，稳定性和效率等方面还有明显差距，迫切需要我国在航空发动机领域加大投入、加快发展。喘振和旋转失速是航空涡扇发动机轴流压气机研究领域中重要而困难的问题。由于旋转失速一般被认为是喘振的先兆，因此对失速初始扰动的建模和检测对喘振和旋转失速的主动控制具有重要意义。鉴于旋转失速的建模与检测技术具有重要的理论研究意义和实际应用价值，本文对其进行了深入的研究，并基于确定学习理论，在前人研究的基础上进行了以下的研究和创新:
1、利用确定学习理论提出一个基于动力学分岔特性的轴流压气机旋转失速检测方法。基于简化后的Moore-Greitzer三阶压气机模型，分析了该系统中存在的分岔现象。选取跟喷管开度相关的γ参数作为分岔参数，分析表明随着γ从大到小变化，该系统中的Pitchfork分岔会先于Hopf分岔发生。Pitchfork分岔的出现对应于旋转失速的发生，所以预测Pitchfork的发生可以预测轴流压气机系统中的旋转失速的发生，从而提出预警并避免系统进入不稳定状态。利用基于确定学习理论方法，对压气机系统随着γ参数的变化出现的几种典型模态的相关系统动态进行辨识，表达和存储并建立相应的模式库。然后利用动态模式识别方法，提出一个针对Pitchfork分岔的快速检测机制。
2、利用确定学习理论提出一个基于高阶Mansoux模型的轴流压气机旋转失速检测方法。该方法分为两个阶段：训练阶段和测试阶段。在训练阶段，基于高阶离散化Mansoux模型，利用确定学习理论提出一个对旋转失速初始扰动的内在系统动态的近似准确建模方法。利用高阶有限维Mansoux模型，获得对压气机无穷维分布参数系统的有限维近似建模。在此基础上，研究Mansoux模型中的某个测量点的系统动态中由其本身状态和相邻2个测量点的状态表达的部分，并假设其它系统动态已知。进一步，利用在失速初始扰动阶段少数测量点信号，采用RBF神经网络和确定学习算法，对在失速初始扰动阶段每个测量点对应的未知内在系统动态进行辨识，获得对这些系统动态的常值RBF神经网络近似，并将之看作是对旋转失速初始扰动内在系统动态的近似建模。在检测阶段，利用以上通过确定学习获得的对旋转失速初始扰动的常值RBF神经网络全息特征表达，构建由常值RBF神经网络组成的旋转失速初始扰动模式库；然后基于这种失速初始扰动全息特征表达，构造一组嵌入了常值RBF神经网络的动态估计器，将这组动态估计器与被测模式比较得到一组残差信号；最后利用动态模式的相似性定义和最小残差准则，判断系统是否进入旋转失速初始扰动。
3、利用北京航空航天大学的低速轴流压气机试验台验证本文所提检测方法的有效性。通过沿周向布置的5个压力传感器获取压气机前缘壁面静压，对这些静压数据进行相应的转换，得到相应的流量脉动数据。利用以上所提的动态模式识别方法，对这些数据进行离线分析，离线分析包括两个环节，即先利用确定学习算法对这些数据进行近似准确建模，将得到的关于旋转失速初始扰动的内部系统动态知识以常值RBF神经网络存储。然后利用动态模式识别方法对被测数据进行快速检测。其次，利用LabVIEW软件对以上所提旋转失速检测算法进行在线实现，并利用该在线实现程序现场对旋转失速进行检测，充分的实验结果表明，本文所提方法能够对旋转失速进行快速准确检测。本文所提检测算法提取了压气机系统的流量信号与压力升信号，并对压气机系统的主要系统动态进行辨识，与传统检测方法相比，本文所用信息更加全面准确，以得到更为准确的旋转失速检测结果。
Aero-engine is known as the “heart” of aircraft. Without high-performance aircraftengines, there would be no advanced aviation weaponry and civil airplanes with power-ful market competitiveness. Turbofan (referred to as the vortex fan) engine is the mostcommonly used power unit of the military and large civil aircraft in the world. Themost notable feature of turbofan engine is that it works with high efciency at highsubsonic/supersonic fight conditions. Since the development of the aero-engine usuallytakes about15-20years, countries that lead in aero-engine technologies in the world at-tach great importance to the relevant basic and applied basic research. High-performanceaero-engine is an important symbol of a nation’s industrial level. Major developed coun-tries in the world, always take aero-engine industry as the priority industry, and attachgreat importance to the associated basic research. Our country is one of the few countrieswith independent capability of aero-engine development in the world. However, comparedwith the world’s advanced level, there are still obvious gaps in terms of reliability, stabil-ity and efciency. Therefore, it is urgent for China to increase investment and acceleratethe development in the feld of aero-engine. Rotating stall and surge are important andchallenging problems in the area of axial compressors. For the reasons that, rotatingstall precedes surge in many machines, rotating stall has received much more attentionin both experimental and theoretical studies. To implement active control of rotatingstall and surge, it is essential to achieve accurate modeling and rapid detection of stallprecursors. Based on its strong points and importance both in theoretical research andpractical application, stall inception detection will be further studied based on the de-terministic learning theory in this dissertation. The main contribution and innovation ofthis dissertation are summarized as follows:
1. A precursor for Pitchfork bifurcation in axial compression system was proposed.Firstly, the bifurcation behavior of Moore-Greitzer model was analyzed: A Pitchforkbifurcation in this model is relevant to rotating stall; A Hoph bifurcation is associatedwith surge. The former bifurcation comes up before the latter one. Consequently, aprecursor for Pitchfork bifurcation can be treated as rotating stall. Secondly, based onthe bifurcation behavior of Moore-Greitzer model, a precursor for Pitchfork bifurcationwas proposed via deterministic learning, which was recently presented to learn unknownnonlinear system dynamics from uncertain dynamic environments. Specifcally:(i) severaltypical patterns in Moore-Greitzer model were identifed by deterministic learning, the obtained knowledge of the approximated system dynamics is stored in constant RBFnetworks;(ii) A bank of estimators are constructed using the constant RBF networksto represent the training patterns and previously learned system dynamics is embeddedin the estimators;(iii) By comparing the set of estimators with the test pattern, a setof recognition errors are generated, and the average L1norms of the errors are taken asthe similarity measure between the dynamics of the training patterns and the dynamicsof the test pattern. Therefore, the test pattern (Pitchfork bifurcation) similar to one ofthe training patterns can be rapidly recognized according to the smallest error principle.Simulations results illustrate the approach.
2. We present an approach for approximately accurate modeling and rapid detectionof stall precursors. Firstly, a method of modeling the system dynamics corresponding tostall precursor is presented:(i) The Mansoux model, which is a high-dimensional ODEmodel used to approximate the axial compressor, is considered as the approximation ofthe model describing stall precursors.(ii) By analyzing the properties of the Mansouxmodel, for a measurement point, the system dynamics represented by states at this pointand other two adjacent points are supposed to be unknown. The other system dynamicsare assumed to be known.(iii) By using RBF neural networks (NN) and the deterministiclearning algorithms, approximately-accurate modeling of the dominant system dynamicscorresponding to stall precursors is achieved. The obtained knowledge of system dynamicsis stored in constant RBF networks, and is considered as the locally accurate approxima-tion of the model describing stall precursors. Secondly, a scheme for rapid detection ofa stall precursor is proposed:(i) By using the constant RBF networks obtained above,a bank of estimators are constructed corresponding to trained stall precursors.(ii) Bycomparing the set of estimators with the test monitored system, a set of residuals aregenerated.(iii) Based on dynamical pattern recognition, the occurrence of stall precursorcan be rapidly detected according to the smallest residual principle. Simulation studiesare included to show the efectiveness of the approach.
3. A low-speed axial fow compressor test rig of Beijing University of Aeronau-tics and Astronautics is employed to verify the efectiveness of the proposed detectionmethod. Five ftting seats are evenly placed in the circumferential direction of the com-pressor. Respectively, fve high response transducers, which are used for dynamic pressuremeasurement for the fow feld between the rotor and stator, are spaced at each fttingseats. The data sampled by the pressure transducers located was saved as voltage values.The voltage values are transformed to axial velocity coefcients by linear transformation.Firstly, by employing the dynamic pattern recognition algorithm proposed in this disser- tation, the data acquired are processed of-line. The general process for the of-line dataprocessing consists of two phases: the identifcation phase and the recognition phase. Inthe training phase, locally-accurate identifcation of the stall inception system dynamicsis achieved by using radial basis function (RBF) neural networks (NNs) through deter-ministic learning. The obtained knowledge of the approximated gait system dynamicsis stored in constant RBF networks. A bank of estimators are constructed using con-stant RBF networks to represent the training stall inception patterns. In the recognitionphase, by comparing the set of estimators with the test stall inception pattern, a set ofrecognition errors are generated, and the average L1norms of the errors are taken as thesimilarity measure between the dynamics of the training stall inception patterns and thedynamics of the test stall inception pattern. Therefore, the test stall inception patternsimilar to one of the training gait patterns can be rapidly recognized according to thesmallest error principle. Secondly, the online programs for stall inception detection arerealized by LabVIEW. Sufcient online experiments were carried out to demonstrate theefciency of the algorithm proposed in this dissertation. Experimental results shows thepossible value of the stall inception detection method in engineering. In this dissertation,information about fow rate and pressure rise in the compressor is employed to identifythe internal system dynamics corresponding to stall inception. Compared to other de-tection methods in the literature, much more information are exploited to achieve moreaccurate detection results.
1、利用确定学习理论提出一个基于动力学分岔特性的轴流压气机旋转失速检测方法。基于简化后的Moore-Greitzer三阶压气机模型，分析了该系统中存在的分岔现象。选取跟喷管开度相关的γ参数作为分岔参数，分析表明随着γ从大到小变化，该系统中的Pitchfork分岔会先于Hopf分岔发生。Pitchfork分岔的出现对应于旋转失速的发生，所以预测Pitchfork的发生可以预测轴流压气机系统中的旋转失速的发生，从而提出预警并避免系统进入不稳定状态。利用基于确定学习理论方法，对压气机系统随着γ参数的变化出现的几种典型模态的相关系统动态进行辨识，表达和存储并建立相应的模式库。然后利用动态模式识别方法，提出一个针对Pitchfork分岔的快速检测机制。
2、利用确定学习理论提出一个基于高阶Mansoux模型的轴流压气机旋转失速检测方法。该方法分为两个阶段：训练阶段和测试阶段。在训练阶段，基于高阶离散化Mansoux模型，利用确定学习理论提出一个对旋转失速初始扰动的内在系统动态的近似准确建模方法。利用高阶有限维Mansoux模型，获得对压气机无穷维分布参数系统的有限维近似建模。在此基础上，研究Mansoux模型中的某个测量点的系统动态中由其本身状态和相邻2个测量点的状态表达的部分，并假设其它系统动态已知。进一步，利用在失速初始扰动阶段少数测量点信号，采用RBF神经网络和确定学习算法，对在失速初始扰动阶段每个测量点对应的未知内在系统动态进行辨识，获得对这些系统动态的常值RBF神经网络近似，并将之看作是对旋转失速初始扰动内在系统动态的近似建模。在检测阶段，利用以上通过确定学习获得的对旋转失速初始扰动的常值RBF神经网络全息特征表达，构建由常值RBF神经网络组成的旋转失速初始扰动模式库；然后基于这种失速初始扰动全息特征表达，构造一组嵌入了常值RBF神经网络的动态估计器，将这组动态估计器与被测模式比较得到一组残差信号；最后利用动态模式的相似性定义和最小残差准则，判断系统是否进入旋转失速初始扰动。
3、利用北京航空航天大学的低速轴流压气机试验台验证本文所提检测方法的有效性。通过沿周向布置的5个压力传感器获取压气机前缘壁面静压，对这些静压数据进行相应的转换，得到相应的流量脉动数据。利用以上所提的动态模式识别方法，对这些数据进行离线分析，离线分析包括两个环节，即先利用确定学习算法对这些数据进行近似准确建模，将得到的关于旋转失速初始扰动的内部系统动态知识以常值RBF神经网络存储。然后利用动态模式识别方法对被测数据进行快速检测。其次，利用LabVIEW软件对以上所提旋转失速检测算法进行在线实现，并利用该在线实现程序现场对旋转失速进行检测，充分的实验结果表明，本文所提方法能够对旋转失速进行快速准确检测。本文所提检测算法提取了压气机系统的流量信号与压力升信号，并对压气机系统的主要系统动态进行辨识，与传统检测方法相比，本文所用信息更加全面准确，以得到更为准确的旋转失速检测结果。
Aero-engine is known as the “heart” of aircraft. Without high-performance aircraftengines, there would be no advanced aviation weaponry and civil airplanes with power-ful market competitiveness. Turbofan (referred to as the vortex fan) engine is the mostcommonly used power unit of the military and large civil aircraft in the world. Themost notable feature of turbofan engine is that it works with high efciency at highsubsonic/supersonic fight conditions. Since the development of the aero-engine usuallytakes about15-20years, countries that lead in aero-engine technologies in the world at-tach great importance to the relevant basic and applied basic research. High-performanceaero-engine is an important symbol of a nation’s industrial level. Major developed coun-tries in the world, always take aero-engine industry as the priority industry, and attachgreat importance to the associated basic research. Our country is one of the few countrieswith independent capability of aero-engine development in the world. However, comparedwith the world’s advanced level, there are still obvious gaps in terms of reliability, stabil-ity and efciency. Therefore, it is urgent for China to increase investment and acceleratethe development in the feld of aero-engine. Rotating stall and surge are important andchallenging problems in the area of axial compressors. For the reasons that, rotatingstall precedes surge in many machines, rotating stall has received much more attentionin both experimental and theoretical studies. To implement active control of rotatingstall and surge, it is essential to achieve accurate modeling and rapid detection of stallprecursors. Based on its strong points and importance both in theoretical research andpractical application, stall inception detection will be further studied based on the de-terministic learning theory in this dissertation. The main contribution and innovation ofthis dissertation are summarized as follows:
1. A precursor for Pitchfork bifurcation in axial compression system was proposed.Firstly, the bifurcation behavior of Moore-Greitzer model was analyzed: A Pitchforkbifurcation in this model is relevant to rotating stall; A Hoph bifurcation is associatedwith surge. The former bifurcation comes up before the latter one. Consequently, aprecursor for Pitchfork bifurcation can be treated as rotating stall. Secondly, based onthe bifurcation behavior of Moore-Greitzer model, a precursor for Pitchfork bifurcationwas proposed via deterministic learning, which was recently presented to learn unknownnonlinear system dynamics from uncertain dynamic environments. Specifcally:(i) severaltypical patterns in Moore-Greitzer model were identifed by deterministic learning, the obtained knowledge of the approximated system dynamics is stored in constant RBFnetworks;(ii) A bank of estimators are constructed using the constant RBF networksto represent the training patterns and previously learned system dynamics is embeddedin the estimators;(iii) By comparing the set of estimators with the test pattern, a setof recognition errors are generated, and the average L1norms of the errors are taken asthe similarity measure between the dynamics of the training patterns and the dynamicsof the test pattern. Therefore, the test pattern (Pitchfork bifurcation) similar to one ofthe training patterns can be rapidly recognized according to the smallest error principle.Simulations results illustrate the approach.
2. We present an approach for approximately accurate modeling and rapid detectionof stall precursors. Firstly, a method of modeling the system dynamics corresponding tostall precursor is presented:(i) The Mansoux model, which is a high-dimensional ODEmodel used to approximate the axial compressor, is considered as the approximation ofthe model describing stall precursors.(ii) By analyzing the properties of the Mansouxmodel, for a measurement point, the system dynamics represented by states at this pointand other two adjacent points are supposed to be unknown. The other system dynamicsare assumed to be known.(iii) By using RBF neural networks (NN) and the deterministiclearning algorithms, approximately-accurate modeling of the dominant system dynamicscorresponding to stall precursors is achieved. The obtained knowledge of system dynamicsis stored in constant RBF networks, and is considered as the locally accurate approxima-tion of the model describing stall precursors. Secondly, a scheme for rapid detection ofa stall precursor is proposed:(i) By using the constant RBF networks obtained above,a bank of estimators are constructed corresponding to trained stall precursors.(ii) Bycomparing the set of estimators with the test monitored system, a set of residuals aregenerated.(iii) Based on dynamical pattern recognition, the occurrence of stall precursorcan be rapidly detected according to the smallest residual principle. Simulation studiesare included to show the efectiveness of the approach.
3. A low-speed axial fow compressor test rig of Beijing University of Aeronau-tics and Astronautics is employed to verify the efectiveness of the proposed detectionmethod. Five ftting seats are evenly placed in the circumferential direction of the com-pressor. Respectively, fve high response transducers, which are used for dynamic pressuremeasurement for the fow feld between the rotor and stator, are spaced at each fttingseats. The data sampled by the pressure transducers located was saved as voltage values.The voltage values are transformed to axial velocity coefcients by linear transformation.Firstly, by employing the dynamic pattern recognition algorithm proposed in this disser- tation, the data acquired are processed of-line. The general process for the of-line dataprocessing consists of two phases: the identifcation phase and the recognition phase. Inthe training phase, locally-accurate identifcation of the stall inception system dynamicsis achieved by using radial basis function (RBF) neural networks (NNs) through deter-ministic learning. The obtained knowledge of the approximated gait system dynamicsis stored in constant RBF networks. A bank of estimators are constructed using con-stant RBF networks to represent the training stall inception patterns. In the recognitionphase, by comparing the set of estimators with the test stall inception pattern, a set ofrecognition errors are generated, and the average L1norms of the errors are taken as thesimilarity measure between the dynamics of the training stall inception patterns and thedynamics of the test stall inception pattern. Therefore, the test stall inception patternsimilar to one of the training gait patterns can be rapidly recognized according to thesmallest error principle. Secondly, the online programs for stall inception detection arerealized by LabVIEW. Sufcient online experiments were carried out to demonstrate theefciency of the algorithm proposed in this dissertation. Experimental results shows thepossible value of the stall inception detection method in engineering. In this dissertation,information about fow rate and pressure rise in the compressor is employed to identifythe internal system dynamics corresponding to stall inception. Compared to other de-tection methods in the literature, much more information are exploited to achieve moreaccurate detection results.
引文
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