摘要
现代工程系统所表现出来的构成复杂和大动态范围的特点使得变量信号的随机过程不再符合平稳性假设,而是非平稳随机过程,这给系统的状态监测任务带来了新的困难。广泛使用的基于信号分析的监测方法由于分析对象往往是单个信号,因此不能够对系统整体状态进行综合监测,而基于模型的方法又存在着系统模型难以建立的困难。对此本课题创新地借鉴了计量经济学领域的协整理论,基于该理论的基本概念和方法对上述类型的工程系统开展了基于模型的状态监测方法研究。
计量经济学中的协整理论认为,系统中的非平稳变量之间可能存在着长期的动态均衡关系。即各个变量围绕着一个共同的长期趋势随机波动,而与各自的非平稳性质无关。这个长期均衡关系就是协整关系。协整关系是由变量所处系统所决定的,描述了变量之间内在本质的相互关系。根据这样的理论观点,如果能够建立起工程系统变量之间的协整关系模型,那么当系统发生故障而造成变量之间关系被改变时,相应的信息便会反映在模型残差(新息变量)中。因此通过模型残差分析,便可以得到故障特征和系统状态信息。
就此,本课题研究中利用协整理论的基本概念和协整关系的检验方法,并结合工程系统状态监测任务的需要,对工程系统状态监测方法进行了研究。在系统状态监测模型的构建技术上,本课题采用了基于最大特征值所对应的协整关系向量模型和基于最大熵准则的多个协整关系向量线性组合模型两种方法,并对其分别进行了研究和对比。而对模型残差的分析,研究中分别从时域统计分析角度和频域特征分析的角度对多种系统状态下的监测模型残差进行了分析讨论。
研究结果表明,根据协整理论建立的系统状态监测模型,其残差在正常状态下是围绕零值附近波动的平稳序列。而当故障发生时残差序列的动态特征会发生明显改变。并且不同故障类型下的模型残差在时域和频域都有着不同的特征模式。从而证实了基于协整理论的状态监测方法的有效性。
在本课题的研究中,采用了液压舵面伺服控制系统仿真模型作为符合复杂动态工程系统特征的应用对象。该仿真模型为状态监测方法研究提供了必需的系统过程变量数据和模型验证的平台,是本课题研究的重要组成。
The complex structure and dynamic feature of modern engineering system cause more trouble for the condition monitoring (CM) task than ever. This is because those well developed monitoring method based on signal analysis techniques can not provide the status information of whole system since they usually deal with single variable. And those strategies based on system model face the difficulty of building an accurate model to characterize the system behavior. To achieve the CM task of complex engineering systems, this paper creatively applies the cointegraton theory which is form econometrics to the CM task.
According to the cointegration theory, there could be a long-run equilibrium between the nonstationary system variables. In that case, these stochastic variables follow a long term common trend in despite of individual nonstationarity. The deviation of variable level from this common trend is stationary. This equilibrium is called cointegration relation, and can be described as a simple linear combination form. The cointegraton relation is determined by the system’s inherent mechanism. Consequently, if the cointegration relation can be found between the engineering system variables, the cointegration model residuals (innovations) then are able to detect the relation change caused by system faults.
Based on this idea, this paper explores a new CM method based on basic cointegration concept and test method. For the building of CM model, two different methods are researched. One is building CM model based on single cointegrating vector which is according to the maximum eigenvalue. And the other one is building CM model through linear combination of multi cointegrating vectors under maximum entropy criterion. Subsequently, CM model residuals are analyzed both in time domain statistically and in frequency domain for signal signature.
The analysis results show that, when the system condition is normal, the CM model residuals fluctuate around mean zero randomly. But when faults occur, the CM model residual’s dynamic characters change obviously. Furthermore, each type of system fault shows a unique pattern of influence on the model residuals. These evidences prove that the cointegration based method is feasible for complex engineering system’s CM task.
During this research, a hydraulic flap servo control system is designed and simulated. This simulation model is employed to play the role of a complex engineering system which the CM method is applied to. The simulation model provides not only the system process variable data to build the CM model, but also a platform to test it. Therefore, the hydraulic simulation model is also an important part of this research project.
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