Parallel interval algorithm for parameter identification in the frequency domain

Abstract

An interval analytical approach to parameter identification in the frequency domain of mathematical models for linear elasto-mechanical systems is described. Experimental resources, such as prior parameter information, also called parameter start box, measurement errors and unmeasurable output components, are enclosed by real and complex intervals. The parameter start box is reduced by a parallel sequence of Gauss-Seidel steps. Gauss-Seidel iteration is a common technique in Verified Computing to improve interval solutions of linear equation systems. For this purpose we investigate the overdetermined linear system of equations-with-out the WLS ¹ Gauss transformation-derived from input measurement residuals. The resulting parameter box thus obtained encloses the global minimizer of the nonlinear weighted least squares aim functional, which is based on output measurement residuals. The global optimization of this aim functional on the shrunk parameter search space is performed in a last step ² . Subsystem identification and sub-model synthesis can be applied to realistic models with a large number (⩾ 100) of degrees of freedom. Parallelization of the algorithm with respect to subsystems can be performed for large structures to reduce the amount of memory and to speed up computation. The paper finishes with the presentation and discussion of an illustrative benchmark result for a 27 degree of freedom test structure.

Keywords:

• System identification
• Interval algorithm
• Enclosures for global minima
• Model updating

¹WLS = weighted least squares.

²Global optimation is not discussed in this paper.

¹WLS = weighted least squares.

²Global optimation is not discussed in this paper.

Notes

¹WLS = weighted least squares.

²Global optimation is not discussed in this paper.