调制信号分析在机械振动系统辨识和故障诊断中具有普遍性和重要性。对于复杂多分量任意时变调制信号，常规解调分析方法缺乏自适应性，难以准确全面地提取其中的丰富信息。以具有典型代表意义的转子、滚动轴承和行星齿轮机构为研究对象，针对振动信号的成分复杂性和时变调制特点，通过理论分析、仿真计算和实验研究等手段，研究基于广义能量算子的调制信号分析方法及其在机械振动系统辨识和故障诊断中的应用，包括高阶、多维、交叉等广义能量算子和Vold-Kalman时变滤波、生成微分方程等理论，以及动力学参数估计、宽带调制信号分析、多分量调制信号分析、时频分析和瞬态特征检测等方法。利用广义能量算子方法在分析任意时变调制信号方面的独特优势，克服常规方法的局限，有效分析复杂多分量任意时变调制信号中蕴含的丰富特征信息，提取幅值、频率、相位和阻尼比等关键动力学参数及其变化特征，全方位多角度揭示机械振动系统的健康状态和动力学特性。

Modulated signal analysis is a common yet important topic in mechanical vibration system identification and fault diagnosis. For complex multi-component modulated signals, most of the usual demodulation methods lack adaptability, thus are ineffective to fully extract the inherent meaningful information. The generalized energy operator provides a potentially effective approach to address this issue. In this project, with representative rotors, rolling element bearings and planetary gearboxes as the research targets, and regarding the complexity and the time-varying modulation feature of vibration signals, the modulated signal analysis method based on generalized energy operator and its application to mechanical vibration system identification and fault diagnosis will be investigated, by means of theoretical analysis, simulated validation and experimental test. This research includes the theories of higher order energy operator, multi-dimensional energy operator, cross energy operator, Vold-Kalman filter and signal generating differential equation, as well as the methods for dynamic parameter estimation, wide-band modulated signal analysis, multi-component modulated signal analysis, time-frequency analysis and transient feature detection. By exploiting the unique advantages of generalized energy operator in analyzing arbitrary time-varying modulated signals of complex multi-components, the limitations inherent with most of the usual demodulation methods will be overcome. Thus the rich characteristic information contained in modulated vibration signals (such as the fundamental yet key parameters like amplitude, frequency, phase, and damping ratio, as well as their instantaneous changes) is expected to be effectively extracted, and ultimately the health status and dynamic nature of mechanical vibration systems will be fully revealed and characterized.