The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed.
Bibliographical noteFunding Information:
This publication is partly based on work supported by Award no. UK-c0020 , made by King Abdullah University of Science and Technology (KAUST) . Furthermore, the authors acknowledge support from the Munich Center of Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) of the Technische Universität München. Extensive research reports related to buckling experiments in I-sections have been kindly provided by Prof. Kim Rasmussen from the University of Sydney and Dr. Andreas Lechner from the Technical University of Graz. Furthermore, Prof. Kai-Uwe Bletzinger and Michael Fischer from the Technische Universität München provided access to the research code Carat++ for benchmarking some of the Nastran results. Their assistance is also gratefully acknowledged.
- Evolutionary power spectrum estimation
- Method of separation
- Non-stationary stochastic processes and random fields
- Spectral representation
- Stochastic buckling analysis