Structure Vibration Analysis Based On Quaternion Theory

When structure state changes, the structural dynamic characteristics will change in a certain extent, these changes will be reflected in the vibration response. Under natural conditions, the complicated excitation, longitudinal temperature force, complicated operation conditions and weak damage will make the state identification based on vibration analysis more difficult. In this paper, the "high-speed rail experiment platform" was used as the research object and the quaternion theory was applied to the three channels vibration analysis.We discussed and studied the several problems in three-channel vibration signal processing with quaternion Fourier transform, quaternion convolution, quaternion matrix singular value decomposition, K-L transformation, quaternion rotation theory and other signal processing method, such as spectrum analysis, analysis of frequency response functions analysis and transmissibility functions, etc. The main work is as follows:(1) Verified the availability of the denoising method by quaternion singular value decomposition theory through the simulation signal.(2) Constructed the quaternion vibration response signal based on the quaternion theory and make the three-channel vibration signal spectrum analysis of the simulated and measured vibration signal of the rail, and then make a comparison with the traditional single channel signal spectrum analysis. The analysis results show that three-channel vibration signal spectrum analysis based on the quaternion theory could contain all three channels frequency domain information.(3) Constructed and studied the transmissibility functions based on the quaternion theory. It was proved that excitation only provide energy in situation of single point driven, it doesn’t participate in the calculation of transmissibility function. The transmissibility function is a function of frequency response function (FRF). It is determined by the location of the excitation and the characteristics of the structure itself, which is of great significance in the state detection.(4) Simulated different rail states by loosing different rail fastener one by one. The rail was excited by hammer and the response signals were acquired using two three axis sensor. The amplitude spectrum of quaternion transmissibility function was calculated, based on which the database sample and test sample were constructed. And then the state recognition experiment was carried out using K-L transformation to get the feature vector and a satisfactory result was also achieved. (5) Two three axis sensors are fixed in the same installation position but with different installation orientation. Then the quaternion transmissibility function was analyzed. It was proved that the quaternion transmissibility between two fixed sampling points has nothing to do with the direction of the sensors.