Method For The Identification Of Linear And Weak Nonlinear Structural Dynamic System Usingwavelet Transform

The identification of structural systems is very important when models for theprediction of systems performance are developed. In recent years, researchers inapplied mathematics, theoretical physics and signal processing have developed apowerful time-frequency signal-analysis tool, called wavelet transform, for themultiresolution analysis of signals. The continuous wavelet transform (CWT) of freedecay response signal of structural dynamic system concentrates the maximumamount of information contained in data near a series of ridges, which are directlylinked to the amplitude and phase of each component within the signal. From theextraction of the ridge and from the values of the CWT coefficients along the ridges,systemparameters can beidentified.In order to identify closely spaced modes, the traditional method for theestimation of modal parameters from free decay response of a linear system usingCWT isimproved. The CWT of free decay response is investigated especially for thecase when closely spaced modes need to be analyzed. Arobust iteratively reweightedleast-squares (IRLS) linear regression method is introduced to fit wavelet amplitudeand phase curves. The selection of the appropriate analyzing scale is proposed toimprove the modal parameter estimation of the system with poorly separated modes,which is performed by searching the locations of the local minima of fitting errorfunctions. The parameter selection of wavelet function achieved by minimizing thesum of the local minimum values of fitting error function is also presented forachieving modal separation and minimizing edge-effect. The results of a numericalsimulation on two 3dof damped systems shown that the improved method canprovide a more accurate estimation of the natural frequencies and damping ratios forthelinear system withcloselyspaced modes.Utilizing the amplitude and phase of CWT coefficients on ridge, weaknonlinearities on damping and stiffness are identified from the freedecay response ofa structural dynamic system. In order to eliminate the frequency-shift of CWTamplitude extreme, wavelet ridge is determined for each time by finding the scalewhere the normalized scalogram is a local maximum. The choice of the waveletfunction is not useful for the improvement of the sdof system identification accuracy.Theeffectiveness of the proposed method is demonstrated using numerical results for twosdof systems with nonlinearities on damping and stiffness.A wavelet ridge extraction method is proposed for efficient estimation ofinstantaneous frequency and amplitude of the asymptotic signal. Inequalities arederived to provide limitations on scale interval and sampling frequency. The optimalscale interval and sampling frequency at any given accuracy can be evaluated bysolving these inequalities and minimizing the computational complexity of CWT.After the CWT of the signal is completed with these optimal parameters, a morereliable ridge can be formed using only the discontinuity points on the ridgeextracted using the conventional method. The results of a weak nonlinear systemidentification simulation test performed to verify the efficiency of the proposedmethod indicate that the computational load of the proposed method is much lowerthanthat ofthe conventional method.At last, the technical parameters of self-developed high accuracy instrument formeasuring moment of inertia (MOI) are measured. The results show that theinstrument adopting the proposed technique for nonlinear system identification canimprove the measurement precision of MOI.