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Extra resources for Computational Methods and Experimental Measurements: Proceedings of the International Conference, Washington D.C., July 1982
Thus the problem formulation reads: estimation of system parameters taking into account a priori knowledge of the computational model. In the same way the following formulation holds true: system parameter adjustment of the computational model using identified values. Estimation methods have to be applied in order to treat measurement noise. With regard to statistical distributed parameters, see the annotation in section 4. 19 3. PARAMETER ESTIMATION BY EXTENDED WEIGHTED LEAST SQUARES (WLS) Because of the author's own experience, and for simplicity, the WLS should be considered.
According to Wedig (1981), the response process x(t) is separated into a positive signal p(t) and a negative one n(t) as it is shown in the right side of Fig. 10. The left side represents the analogue simulation of the cracked bending oscillator. 10: Separation of the reponse process After the separation, both different processes p(t) and n(t) are analysed in two correlators, separately. The results are given in Fig. 11. RP(~) denotes the correlation function of the positive-valued process and Rn(~) belongs to n(t).
If we associate a covariance matrix fxx with the difference ~:= ~ - ~ 0 , the choice Qa = f~x expresses this confidence in the computational model. & The minimization of the aim functional is done with the necessary conditions (;)J(g_) . -! uaj (4) and a positive definite Hessian matrix /Eykhoff, P. (1974)/. They lead to a system of algebraic equations in the desired estimated parameters ti. This system of equations may be linear or nonlinear in the unknowns. In the linear case it can be advantageous with Ga = 0 to apply the orthogonalization method for solving the system of equations.