Development of a Relaxed Stationary Power Spectrum using Imprecise Probabilities with Application to High-rise Buildings

Modern approaches to solve dynamic problems, where random vibrations are the governing excitations, are in most cases based on the concept of the power spectrum as the core model for the representation of excitation and response processes. This is partly due to the practical applicability of spectral models for frequency domain analysis. In addition, compatible time-domain samples can easily be generated. Such samples can be used for numerical performance evaluation of systems or structures represented by complex non-linear models.The development of spectral estimation methods that use ensemble statistics to generate a single or finite number of deterministic spectra results in spectral models that can be applied directly in structural analysis. However, the properties of the measured environmental process are still lost.In order to produce reliable and realistic power spectra for the application to systems, in most cases not enough real data sets are available. To capture the epistemic uncertainties of the model by taking into account inherent statistical differences that exist across real data sets, an approach for a stochastic representation of the loads can be used. In this work, the epistemic uncertainties in the spectral density of the process are captured by using an interval approach which, in combination with the stochastic nature of the process, leads to an imprecise probability model. From all the available power spectra of the ensemble, one power spectrum is identified on which the resulting relaxed power spectrum is based. To relax the power spectrum, interval parameters are implemented, thereby forming an enveloping boundary for all estimated power spectra. In order to capture the epistemic uncertainties and to present this information effectively, imprecise probabilities are used in this newly developed load representation.The relaxed power spectrum is validated by application to a single-degree-of-freedom system and a multiple-degree-of-freedom system by determining and analysing the response spectra of the systems.