Preliminary Study On Symbolic Space Method Of Dynamic Structure Estimation

The study on the whole state estimation of the structural dynamics which does not rely on accurate mathematical model is a hot area of the vibration and control. Lempel-Ziv Complexity (LZC) and symbolic dynamics theory are used in this paper to estimate the initial state of the structure dynamic behavior in the symbolic space that is constructed by the acceleration response of the measuring point. Some significant conclusions have been got.(1)The symbolic space reconstruction of the vibration response series and the characteristics of symbolic dynamics shift are researched. Through analyzing the simulated decay sequence, the relationship between its inherent characteristics and the embedding dimension, the shift step and the reconstruction vectors distance are obtained. The selection rules of reconstruction parameter are summarized and the criteria for the sequence reconstruction is determined.(2)These methods are used to analysis some typical engineering and experimental sequence. The results show that the shifting and phase space reconstruction can reflect the nature of the sequence. Their evolution laws are well correlated to its intensity . The method and results depend and reflect the strength of the signals. There are very practical value for system monitoring.(3)The LZ complexity of typical project measured responses is studied. The responses are translated into symbolic sequences by coarse-grained method, and its phase space are reconstructed, then the shift map and the LZ complexity analysis are proceeded. The relations between LZC and symbolic parameters and the nature are worked over. The results show that the LZC is sensitive to the nonlinear factor and it is suitable for the engineering.(4)The discreteness of the LZC of the elastomer is verified. With T-shaped plate, for example, through calculating the LZC of the 240 points near the center point, it is shown that LZC does not change the discreteness of the elastomer. This result lays the foundation for the combination of FEM, LZC and the symbolic space method.(5)The symbolic space is constructed by the response of the measured points. The new method of initial state estimation is described in the symbolic space. The cavitation status of a centrifugal pump are estimated in this new method. The results show that its cost is low and the process is simple compared with traditional methods. The method is effective.The initial state estimation to structure dynamics based on the symbolic space have some advantages to the nonlinear structure which is difficult to accurately model. The study is important to the structure dynamic performance monitoring, state control and so on. There is a broad research space for the parameters of the state description, the state estimation accuracy issues, sensitivity issues and control issues.