Research On Parameters Identification Methods Based On Wavelet Analysis For Linear Time Varying Structures

Structural dynamic parameters are the main parameters that are able to determine thedynamic characteristics of the mechanical structures, which could offer important reference tostructure finite element modeling, dynamic model updating, sensitivity analysis, vibration controland structural health monitoring, etc. The identification of dynamic parameters is always of primeimportance in vibration analysis. However by far studies on dynamic parameters identificationhave been mainly limited to linear time invariant structures and it has been being very difficult tomake progress in research on dynamic of time varying structure, because theoretically it has notgeneral solution up to now, especially the time varying parameters identification issue. But thereare a number of thus problems in engineering to solve urgently, for example, the stretchingdynamics of large spacecraft flexible structure, varying mass problem of supersonic rocket, bridgevibration caused by the high speed train, etc. Therefore the parameters identification methodsissue for time varying structures based on wavelet analysis are studied in this dissertation.The main contents of this dissertation are as follows:（1） in chapter two, the continuous wavelet transform based algorithm for functionalintegration is formulated and the continuous wavelet transform values of displacement andvelocity responses signals are calculated subsequently, only using the measurements ofacceleration responses signals. As a result, vibration differential equations of motion are betransformed into linear algebraic equations with wavelet-based coefficients. On the assumptionthat the time varying structural dynamic parameters are constant in a short period, the structurephysical parameters (mass, stiffness and damping coefficients) can be extracted by solving a leastsquare problem in every moment. Since the structural acceleration response data is just used toidentify the dynamic parameters, the proposed identification method has a strong practicability.（2） in chapter three, a wavelet-based state space time varying parameters identificationmethod is proposed based on the research results of wavelet scaling functional integrationproblem. For an arbitrary linear time varying system, the second order vibration differentialequations are first rewritten as the first order state equations using the state space theory. The statevectors are projected by using the Daubechies wavelet scaling functions and the first order statespace equations are transformed into simple linear equations based on the orthogonality of thewavelet scaling functions. This allows the time varying equivalent state space system matrices ateach moment to be identified directly via solving the linear equations on the assumption that thetime varying structural dynamic parameters are constant in a short period. The stiffness and damping matrices are determined by comparing the identified equivalent system matrices with thephysical system matrices on the premise of the system time varying mass characteristics areknown in advance. The system modal parameters are extracted though eigenvalue decompositionof the state space system matrices. The proposed algorithm is a development of Wavelet-Gelerkinmethod for time varying parameters identification as there is no need to calculate the second orderconnection coefficients of Daubechies wavelet during the identification procedure. Thisimprovement can supply a higher calculation speed.（3） in chapter four, the time varying auto regressive (T-AR) model has time dependent autoregressive coefficients which can be expanded by a set of orthogonal basis functions. Thisdissertation utilizes a time varying auto regressive model using B-spline wavelet on the interval asbasis function. The time varying auto regressive model’s coefficients are expanded with B-splinewavelet on the interval basis function first. Subsequently the system acceleration response signalsare utilized for structural instantaneous frequencies identification. Since the parameters are beextracted quickly and accurately, the proposed identification method is priority for the engineers.（4） in this dissertation, three proposed time varying parameters identification algorithmsabove are investigated with a number of different simulation models. The performance of theB-spline wavelet on the interval based T-AR method is illustrated using a cantilever beam withtime varying mass characteristics. The first three orders instantaneous frequencies of thecantilever beam are quickly and accurately identified only by using the measurement accelerationresponse signals. The test results demonstrate the good performance (the feasibility, effectiveness,and the anti-noise ability) of the T-AR identification method.