Least squares estimates of structural system parameters using covariance function data

A statistically efficient and computationally economical two-stage least squares procedure for the estimation of the natural frequencies and damping parameters of structural systems under stationary random vibration conditions is considered. The structural system is represented by the system of ordinary differential equations that is characteristic of lumped mass-spring-damper systems with a random forcing function. Emphasis is placed on the problem corresponding to the observation of the top story vibrations of a tall building under random wind excitation. In that case, the random excitation can be approximated by a white noise and the regularly sampled vibration record can be represented as a mixed autoregressive-moving average (ARMA) time series. The ARMA time series parameters are estimated by a two-stage least squares method using only the covariance function of the top story vibrations. The natural frequency and damping parameters of the structural system can be expressed in terms of the AR parameters. Estimates of the coefficient of variation of the structural system parameter estimates are expressed in terms of the ARMA parameter estimates. The numerical results of the least squares and maximum likelihood parameter estimation procedures worked on a real vibration data example are shown.

[1]  Will Gersch,et al.  Estimation of the autoregressive parameters of a mixed autoregressive moving-average time series , 1970 .

[2]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[3]  James Durbin,et al.  The fitting of time series models , 1960 .

[4]  W. Gersch,et al.  Estimation of power spectra with finite-order autoregressive models , 1973 .

[5]  Peter E. Caines,et al.  Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[6]  W. Gersch.  On the achievable accuracy of structural system parameter estimates , 1974 .

[7]  E. Robinson,et al.  Recursive solution to the multichannel filtering problem , 1965 .

[8]  A. M. Walker.  Note on a Generalization of the Large Sample Goodness of Fit Test for Linear Autoregressive Schemes , 1950 .

[9]  Hirotugu Akaike,et al.  Maximum likelihood estimation of structural parameters from random vibration data , 1973 .

[10]  E. Vanmarcke.  Properties of Spectral Moments with Applications to Random Vibration , 1972 .

[11]  M. Bartlett.  On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[12]  Will Gersch,et al.  Discrete Time Series Synthesis of Randomly Excited Structural System Response , 1972 .

[13]  Karl Johan Åström,et al.  On the Achievable Accuracy in Identification Problems , 1967 .

[14]  W Gersch.  A note on trapezoidal digital filter design. , 1973, Computers and biomedical research, an international journal.

[15]  H. Akaike.  Block Toeplitz Matrix Inversion , 1973 .