First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

Abstract

A novel efficient stochastic incremental dynamics methodology considering first-excursion probability for nonlinear structural systems subject to stochastic seismic excitations in alignment with contemporary aseismic codes provisions is developed. To this aim, an approximate nonlinear stochastic dynamics technique for conducting first-passage probability density function (PDF) based stochastic incremental dynamic analysis is developed. Firstly, an efficient stochastic iterative linearization methodology is devised achieving convergence of the equivalent system damping ratios with the damping premises of the excitation response spectrum leading to a coherent determination of a robust scalable intensity measure (IM) which bears direct relation to its damaging potential. Subsequently, utilizing the stochastically derived time-varying forced vibrational system properties in conjunction with a combination of deterministic and stochastic averaging treatment the first-excursion PDF is efficiently determined for each and every of the considered limit-state rules (LSs). Lastly, an incremental mechanization analogous to the one used in normal incremental dynamic analysis (IDA) is proposed to ensure the necessary compatibility for applications in the fields of structural and earthquake engineering. The back-and-forth twisting pattern of IDA curves which is related with the multiple points satisfaction of the very same limit-state rule encourages the study of the problem from a first-passage perspective considering timing in addition to the intensity of the excitation variable. The selected engineering demand parameter (EDP) of the firstexcursion time constitutes an excellent response related variable with twofold meaning; it performs structural behavior monitoring considering intensity and timing information whereas it is inherently coupled with limit-state requirements. The developed stochastic dynamics technique provides with reliable higher order statistics (i.e., PDF) of the chosen EDP. A structural system comprising the bilinear hysteretic model serves as a numerical example for demonstrating the reliability of the proposed first-excursion PDF-based stochastic incremental dynamics methodology. Nonlinear response time-history analysis involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

Probabilistic generation of hazard‐consistent suites of fully non‐stationary seismic records

“…If $$X_i(t)$$ is the obtained stochastic response process, the pseudo‐acceleration response spectrum is: $$$$\begin{equation} S_a^*(\omega _i,\zeta) = \eta _{X_i}\omega _i^2\sqrt {\lambda _{0,X_i}} \end{equation}$$$$where $$\eta _{X_i}$$ is the peak factor and $$\lambda _{0,X_i}$$ is the variance of the stochastic response process $$X_i(t)$$. The peak factor $$\eta _{X_i}$$ is the critical factor by which the standard deviation $$\sqrt {\lambda _{0,X_i}}$$ of the considered elastic oscillator response is multiplied to predict a level of spectral acceleration $$S_a^*(\omega _i,\zeta)$$ below which the peak response will remain in the interval of $$T_s$$, with probability $$p$$ 46 . The ”$$_s$$” in $$T_s$$ and …”

“…The peak factor 𝜂 𝑋 𝑖 is the critical factor by which the standard deviation √ 𝜆 0,𝑋 𝑖 of the considered elastic oscillator response is multiplied to predict a level of spectral acceleration 𝑆 * 𝑎 (𝜔 𝑖 , 𝜁) below which the peak response will remain in the interval of 𝑇 𝑠 , with probability 𝑝. 46 The " 𝑠 " in 𝑇 𝑠 and 𝐺 𝑠 (𝜔 𝑖 ) refers to stationarity. The evaluation of 𝜂 𝑋 𝑖 is related to the concept of the first-passage problem.…”

“…In the field of stochastic dynamics, power spectrum modeling techniques harness the potential of random vibration theory in order to provide efficient techniques for response determination and risk/reliability assessment at a low computational cost. 32,33,[43][44][45][46] These approaches use artificial accelerograms and they offer a straightforward implementation that relies on the power spectrum.…”

“…However, there are cases where the computational cost of these techniques can be prohibitive, therefore, alternative efficient approximate analytical/numerical techniques have been developed. In the field of stochastic dynamics, power spectrum modeling techniques harness the potential of random vibration theory in order to provide efficient techniques for response determination and risk/reliability assessment at a low computational cost 32,33,43–46 . These approaches use artificial accelerograms and they offer a straightforward implementation that relies on the power spectrum.…”

Stochastic Nonlinear Response of Structural Systems Endowed With Singular Matrices Subject to Combined Periodic and Stochastic Excitations

“…The stochastic component x s (t) of the system response is treated by resorting to the generalized statistical linearization methodology for systems with singular parameter matrices [12,13]; see also [16,17,18,19,20,21,22,23] for a broader perspective, as well as several examples pertaining to application of the method. First, the difference between the systems in Eqs.…”