随着科学技术与现代工业的发展，对于旋转机械高速、高效、重载的需求迫使动静件间隙减小而诱发转子碰摩失稳响应。即使初始设计处于正常工况，装备也可能在长期运行下产生部件老化这样参数慢变而导致系统内在动力学结构改变的情况，促使系统向干摩擦反向涡动这一危险的全局分岔失稳响应过渡。立足于工业大数据状态响应数据充足但预警信息匮乏的现状，对系统非线性全局动力学分析可以揭示系统在失稳响应发生前的全局结构属性，有效识别系统失稳的前兆信号，并结合数据驱动技术为潜在的运行失稳风险提供切实可靠的早期预警方法。因此，基于全局动力学特征的转子/定子碰摩失稳响应早期预警方法的研究具有重要的工程实际意义。本研究主要内容如下：

       首先，对转子/定子碰摩系统开展全局动力学分析，研究了系统在全局分岔点前后内在动力学结构和响应的关系，其全局动态特性呈现出无碰周期一运动和干摩擦反向涡动准周期运动双稳态共存以及随参数变化稳定解个数发生改变的全局分岔行为。结合非线性分岔理论，在转子/定子碰摩系统状态空间内揭示了响应临界慢化现象。结果表明：靠近分岔点的无碰吸引域尺寸比远离临界点情况更小，其吸引子的稳定性和吸引性更弱，且受微小扰动后恢复至平衡点的时间会更长，短时间恢复速率则更小。

       其次，在认识系统全局动力学特性的基础上，综合考虑相空间动力学和临界慢化现象，提出了转子系统从稳定运行到失稳响应的一系列早期预警关键指标体系。在早期预警信号的有效性分析中，考虑外部扰动和采样周期因素进行多样化数值模拟，通过划分正负类样本对预警信号进行比较，发现正类样本相较于负类样本其预警特征呈现明显的上升趋势。同时，通过设置多级预警机制及肯德尔秩相关系数量化发展趋势，以便于更全面地评估预警指标的效能，进一步验证了预警信号的有效性，为构建故障预警模型提供了高质量特征集。

       最后，将前述早期预警特征作为深度学习框架的输入数据，系统是否发生失稳作为输出标签，以此构建数据驱动的失稳响应早期预警模型，并进行超参数调优和模型拟合度检测，得到较为精确且具有良好泛化能力的预警模型。此外，通过滑动窗口方式实现了对响应失稳概率的动态预测，并基于3σ统计准则设置动态阈值自学习来进行分级故障预报。同时，通过分析预警信号提前周期数分布来评估数据驱动早期预警方法的时效性，以期在工程实际中能够及时发现系统失稳迹象，为实现转子碰摩失稳响应早期预警提供了理论和方法支持。

       综上所述，本研究通过结合全局动力学特征和深度学习框架，提出了有效的转子/定子碰摩失稳响应的早期预警方法，不仅在理论上深化了对转子/定子碰摩失稳响应机理的全局认识，而且在实践方面提供了数据驱动的早期预警手段，为工程实践的故障预警和预测性维修提供重要的方法支持，具有重要的学术和工程意义。

      With the advancement of science, technology, and modern industry, the demand for high-speed, high-efficiency, and heavy-load rotating machinery has led to a reduction in the clearance between the rotor and stator, triggering rotor rub-induced instability responses. Long-term operation of equipment can cause component aging, even under normal operating conditions, resulting in slow changes in intrinsic dynamic parameters of systems. This prompts the system to transition towards dangerous global bifurcation, such as instability responses for dry friction backward whirl. In the current state of rich state response data but limited early warning information within industrial big data fields, nonlinear global dynamic analysis of systems can effectively identify precursor signals of system instability by revealing the global structural attributes prior to instability responses occurring. Additionally, merging data-driven approaches provides practical and reliable early warning methods for potential instability responses. Therefore, there is significant engineering practical value to research on early warning methods for rotor/stator rubbing instability responses based on global dynamic characteristics. The main research contributions of this thesis are as follows:

      Firstly, a global dynamical analysis of the rotor/stator rub system is conducted, investigating the relationship between the intrinsic dynamical structure and response of the system before and after global bifurcation points. The global dynamic characteristics exhibit the coexistence of motion without rub periods and quasi-periodic motion with dry friction backward whirl, as well as global bifurcation behavior where the number of stable solutions changes with parameter variations. Combining nonlinear bifurcation theory, critical slowing down phenomenon is revealed within the state space of rotor/stator rub system: the no-rub basin of attraction near the bifurcation point is smaller compared to situations farther from the critical point, with weaker stability and basin of attractors, and longer recovery times to equilibrium solutions under small perturbations, indicating slower rates of returning to equilibrium points in a short time frame.

      Secondly, taking into account both phase space dynamics and critical slowing down phenomena, a set of early warning indications for the rotor system's shift from stable operation to unstable response are given, based on the understanding of global dynamical properties. Various numerical simulations are carried out taking into account external disturbances and sampling intervals in order to analyze the efficacy of early warning signals. When positive and negative samples are separated, it is evident that the positive samples' early warning characteristics are trending increasing in comparison to the negative samples. The effectiveness of warning indicators is thoroughly assessed by creating a multi-level warning mechanism and quantifying the development trend using Kendall’s tau rank correlation coefficients. This further validates the efficacy of warning signals and offers a superior feature set for creating fault warning models.

      Finally, the aforementioned early warning features are used as input data for deep learning algorithms, with the occurrence of system instability as the output label, to construct a data-driven early warning model for instability response. Hyperparameter tuning and model fit testing are conducted to obtain a more accurate and well-generalized warning model. Additionally, dynamic prediction of the probability of instability in response data is achieved through a sliding window approach, and a dynamic threshold based on the 3σ statistical criterion is set for self-learning to perform graded fault prediction. Furthermore, the timeliness of the data-driven early warning method is evaluated by analyzing the distribution of lead time of graded warning signals, aiming to promptly detect signs of system instability in engineering practice and provide theoretical and methodological support for achieving early warning of instability response.

      In summary, this thesis proposes an effective early warning method for rotor/stator rub-induced instability by integrating global dynamical characteristics and deep learning algorithms. It not only deepens the global understanding of the mechanism of rotor/stator rub-induced instability response theoretically but also provides data-driven early warning means in practice, offering important methodological support for fault warning and predictive maintenance in engineering practice, with significant academic and engineering implications.

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