With the increase of hydropower units and installed capacity in China,the fault problem during the transient process occurs frequently.The signal analysis method is widely used to deal with the problem.The variational mode decomposition (VMD) method,a relatively new self-adaptive method for processing non-linear and non-stationary signals,was adopted to investigate the vibration signals during the transient process of a hydropower unit in the Gezhouba power plant.The first step was to use VMD to analyze the simulated vibration signals of the transient process,and to verify the effectiveness of the VMD method in dealing with non-linear and unstable signals.The Hilbert-Huang transform (HHT) was then used to calculate the instantaneous frequency of each intrinsic mode functions (IMF) decomposed by VMD to obtain the corresponding Hilbert spectrum.These results were compared with those from empirical mode decomposition (EMD) method.From the final vibration signal analysis,the IMF decomposed by VMD could be divided into three parts.The first part was the trend of signal development.The second part was the basic decomposition of the signal with a strong regularity of "spindle" signal reflecting the change law of the transient process.The third part was high-frequency characteristic signals mainly caused by interference noise or unit failure.The corresponding Hilbert spectrum had the characteristics of small fluctuation and stable amplitude.The results showed good consistency between the frequency change of each component and the time-dependent rule of the rotational speed.This suggested that VMD was capable of extracting characteristic frequencies to facilitate the analysis of vibration characteristics.Compared with EMD,the VMD outperformed in self-adaptivity.It provided more accurate and effective analysis results and a better representation of the vibration rule during the transient process of the hydropower unit.

Rigid body guidance synthesis is a typical problem in mechanism design.In order to avoid the defects by traditional synthesis methods based on Burmester kinematic geometry theory,such as the limitation of mechanism structure type and the uncertainty of mechanism function,a generalized function oriented geometric synthesis method based on similarity transformation of the mechanism function modules was discussed.Since the standard mechanism modules were considered as basic design units for this method,the structure type of guidance mechanism modules need to be extended for a larger solution space,thereforethe geared linkage structure that can generate complex motion patterns was taken into account,aiming at the establishment of corresponding function module through kinematic analysis.At first,the transformation and mapping method between transmission function and guidance function were obtained through the configuration analysis of geared linkage,thus converting the transmission mechanism to the guidance mechanism through changing the rotation center of output gear.Secondly,the complex vector method was introduced for the kinematic analysis to obtain the guidance function,after that the geared linkage function module with full topology information was established,which included the transmission characteristics as well as the guidance characteristics,i.e. the relative dimensional parameters,the guidance angle performance, the guidance point trajectory and the motion geometric identifier.Then,in order to obtain the method for adjusting dimensional parameters of the preselected function module,a bidirectional mapping rule between relative dimensions and achievable guidance functions was revealed.At last,a practical guidance mechanism design task for powder production with partial parallel guidance function requirement was given, the similarity transformation of geometric identifier between geared linkage function module and the guidance task was presented, then the actual solution mechanism size and position parameters which meet the technical requirements were obtained. Finally the validity and practicability of the proposed generalized synthesis method were verified by the analysis of design results.