WP5. Reliability assessment and calculation of vulnerability curves

Reliability analysis procedures will be implemented to calculate the vulnerability curves of typical industrial equipment structures. The target of this WP is to develop novel reliability analysis methods that allow the accurate estimation of vulnerability curves of typical industrial equipment structures as well as alternative simplified procedures that trade off accuracy for lower computational cost. The various approaches that will be implemented differ on the way that the seismic input is considered, on the analysis method adopted (static or dynamic) and on the number of simulations required. We will pinpoint the pros and cons of each method and recommend the most appropriate depending on the problem at hand.

Vulnerability analysis based on Incremental Dynamic Analysis (IDA) (Vamvatsikos & Cornell 2002) has the advantage that allows consistently handling the ground motion records in order to calculate the probabilities of exceedance, conditional on the intensity of the seismic event. Both the initial format of the method and also an alternative approach that utilizes synthetic ground motions will be applied. The use of the second approach avoids scaling the records and fully exploits our ability to produce synthetic ground motions of different magnitude and distance (Zacharenaki et al. 2009). IDA will be nested inside a Monte Carlo Simulation (MCS) where each sample will be a median IDA curve. This process allows for the calculation of the response statistics (median and dispersion) and the actual distribution of the demand parameters (Vamvatsikos & Fragiadakis 2011). 

Alternatively, Nonlinear Static Procedures (NSP) will be considered (Karakostas et al. 2006, Makarios et al. 2007, Moschonas et al., 2009). NSPs are able to provide estimates of ‘central’ (or ‘average’) values of the EDPs for different structural configurations, depending on the variation of the problem random variables. The shortcoming of typical NSP-based procedures is that they are not able to calculate the dispersion due to the record-to-record variably. To circumvent this problem, The SPO2IDA tool will be used (Fragiadakis & Vamvatsikos 2011). SPO2IDA is able to give estimates of the dispersion based on the results of the static pushover. Default dispersion values will be recommended for the future use of NSP procedures.

Approximate but cost-effective point estimate methods such as Rosenblueth’s 2K+1 and the FOSM method will be also used in conjunction with IDA or static pushover. In addition, properly trained Neural Networks (NN) will be used. NN have been successfully used in the past as meta-models in order to accelerate the computations required to produce the vulnerability curves (Lagaros & Fragiadakis 2007). The more rigorous MCS-based methods will provide the reference solutions in order to assess the performance of the approximate procedures. 

The responsibility for this WP belongs to the NTUA team that will collaborate with the ITSAK team. The NTUA team researchers have published several papers for the seismic reliability assessment of buildings (Papadrakakis et al. 1996, Lagaros & Fragiadakis 2007, Vamvatsikos & Cornell, 2002, Zacharenaki et al., 2009, Vamvatsikos & Fragiadakis 2011, Fragiadakis & Vamvatsikos 2011), while the ITSAK team has proposed methods for the vulnerability assessment of bridges using NSP-based procedures (Karakostas et al. 2006, Makarios et al. 2007, Moschonas et al., 2009).

Key intermediate goals: Calculation of vulnerability curves for typical industrial equipment structures, critical evaluation of alternative reliability and vulnerability analysis methods with respect to accuracy and computational efficiency.