On the achievable accuracy of structural system parameter estimates

摘要: Procedures to compute the statistical accuracy achievable in estimating natural frequency and damping parameters of randomly excited structural systems are demonstrated. Particular worked examples yield quantitative qualitative results. A regularly sampled stationary n degree-of-freedom differential equation model corresponding mixed autoregressive-moving average (AR-MA) time series order 2n that is known represent sample sequence assumed. The elements Fisher information matrix, second partial derivatives log-likelihood functional maximum likelihood estimates AR-MA parameters, computed from those parameters. matrix inverse asymptotically Cramer-Rao lower bound on covariance errors parameter estimates, result can be expressed terms AR results assumed system. It demonstrated cf cξ, respectively coefficient variation (the ratio standard deviation mean) 0·01 0·2 for N=1000 vibration observations theoretically values cξ have following properties: (a) inversely proportional N ; (b) essentially identical displacement velocity acceleration data taken at same observation point; (c) quite insensitive presence additive noise when estimation procedure used; (d) independent intensity correlation structure random excitation; (e) Ts, sampling interval; (f) a fixed any particular mode system, number modes system; (g) varies directly with an increase ξ.