تجزیه و تحلیل حساسیت جهانی برای مدل سازی ارتعاشات زمین تصادفی در ارزیابی لرزه ای خطر

Seismic risk assessment requires adoption of appropriate models for the earthquake hazard, the structural system and for its performance, and quantification of the uncertainties involved in these models through appropriate probability distributions. Characterization of the seismic hazard comprises undoubtedly the most critical component of this process, the one associated with the largest amount of uncertainty. For applications involving dynamic analysis this hazard is frequently characterized through stochastic ground motion models. This paper discusses a novel, global sensitivity analysis for the seismic risk with emphasis on such a stochastic ground motion modeling. This analysis aims to identify the overall (i.e. global) importance of each of the uncertain model parameters, or of groups of them, towards the total risk. The methodology is based on definition of an auxiliary density (distribution) function, proportional to the integrand of the integral quantifying seismic risk, and on comparison of this density to the initial probability distribution for the model parameters of interest. Uncertainty in the rest of the model parameters is explicitly addressed through integration of their joint auxiliary distribution to calculate the corresponding marginal distributions. The relative information entropy is used to quantify the difference between the compared density functions and an efficient approach based on stochastic sampling is introduced for estimating this entropy for all quantities of interest. The framework is illustrated in an example that adopts a source-based stochastic ground motion model, and valuable insight is provided for its implementation within structural engineering applications.

Description of seismic risk in structural engineering requires adoption of appropriate models for structural systems, for their performance quantification, and for the natural hazard itself, and characterization and propagation of the uncertainty (aleatoric or epistemic) related to these models. Undoubtedly the most important component of this process is the description of the earthquake hazard since significant variability is expected in future earthquake excitations. Moreover, for applications involving dynamic analysis, characterization of the entire ground motion history is needed. The growing interest in performance-based earthquake engineering (PBEE) in the last decade [1], [2] and [3] has intensified this need. PBEE addresses the entire spectrum of structural response, ranging from linear to grossly nonlinear, up to structural collapse, and this approach requires a realistic characterization of the earthquake acceleration time-history. Though numerous methodologies have been proposed for describing ground motion time histories for structural design applications (for example spectra and spectrum compatible approaches [4], [5] and [6] including extensions to describe spatial variability [7] and [8]), two are typically acknowledged [9] and [10] as the main approaches for accomplishing this task for probabilistic seismic risk assessment. The most common one relies on adoption of Intensity Measures (IMs) that represents the dominant features of the seismic excitation, and subsequent scaling/selection of ground motion records to different hazard levels (different IM values) [11] and [12], as prescribed by a probabilistic seismic hazard analysis. Though popular, this approach suffers, to some extent, from concerns regarding the validity for ground motion scaling [10] and [13] and from the fact that the inherent variability of the ground motions is somewhat arbitrarily addressed [9] by the exact selection of the ground motions, which does not necessarily correlate well with the true uncertainties for all sites. The alternative approach, which will be the topic of this study, is use of stochastic ground motion models [10], [14], [15] and [16]. These models are based on modulation of a stochastic sequence Z through functions that address spectral and temporal characteristics of the excitation. Their parameters can be related to earthquake (type of fault, moment magnitude and epicentral distance) and site characteristics (shear wave velocity, local site conditions) by appropriate predictive relationships [17] and [18]. Description of the uncertainty for the earthquake characteristics and the predictive relationships leads then to a complete probabilistic description of potential future ground-motion time-histories. Though concerns are also expressed for stochastic ground motion models, in particular that they cannot fully address physical characteristics of actual time histories, this modeling approach has gained increasing support within the structural engineering community [18], [19] and [20] since it provides a complete probabilistic characterization for seismic risk applications [9] within a modeling framework which is consistent with system-engineering (modeling of the earthquake process itself). Two types of stochastic ground motion models can be distinguished, ‘source-based’ models [14], [17] and [21] that describe the fault rupture at the source and propagation of seismic waves through the ground medium, and ‘site-based’ (or ‘record-based’) models that are developed by fitting a preselected mathematical model to a suite of recorded ground motions [10], [15], [16], [22] and [23]. Use of such stochastic ground motion models, accompanied by appropriate structural and performance evaluation models facilitates then the simulation-based, augmented model, illustrated in Fig. 1, for detailed estimation of the seismic response. Addressing the uncertainty in the properties of all components of this model, by appropriate probabilistic descriptions, leads to efficient seismic risk quantification, which can be defined as the expected value of the system performance [19], [20] and [24]. In this setting the uncertain model parameters can be considered as the risk factors, ultimately generating seismic risk. Full-size image (46 K) Fig. 1. Augmented model description for seismic risk characterization. Figure options The focus of the aforementioned studies has been, though, on the development of such stochastic ground motion models or on their implementation for describing seismic risk. Limited attention has been given to understanding the influence of such a seismic hazard characterization in the context of probabilistic seismic risk assessment. This paper directly focuses on this topic; it offers an innovative, global sensitivity analysis for quantifying the importance of the various risk factors or of groups of them towards the total seismic risk. Such an analysis identifies which of the model parameters contributed overall (i.e., globally) more to the estimated risk and can facilitate a better understanding of the correlation between the various risk factors and the risk itself, providing valuable insight for future research developments. A novel framework is discussed for this purpose, based on definition of an auxiliary density function and on comparison of this density to the initial probability distribution for each model parameter. The difference between the distributions is quantified through the relative information entropy and an approach based on stochastic sampling is introduced for efficiently estimating the latter. The framework is illustrated in an example considering the response of a Single Degree Of Freedom (SDOF) structural model; a source-based stochastic ground motion model is adopted for the acceleration time-history description [17] and the average structural response or reliability for rare events (1% probability of occurrence) are adopted for defining structural risk. The comparison to seismic risk defined in terms of peak ground-motion characteristics is also discussed. The illustrative study is limited here on linear structural response and on the specific ground motion model adopted, though the framework for sensitivity analysis is directly extendable to other cases.

A probabilistic global sensitivity analysis for seismic risk was discussed in this paper with emphasis on the impact of stochastic ground motion models for description of the seismic hazard. Such models characterize the entire ground motion time-history by modulating a white noise stochastic sequence through functions that depend on the regional seismicity characteristics (moment magnitude, epicentral distance, fault type) and on predictive relationships that relate ground motion properties (frequency content and temporal properties) to these characteristics. For assessing seismic risk both the regional seismicity as well as the ground motion properties need to be considered as uncertain and assigned appropriate probability distributions. The proposed sensitivity analysis aims to identify which of these parameters have higher contribution towards the overall risk. The methodology discussed is based on the definition of an auxiliary density function, proportional to the integrand of the risk integral, and on the comparison of this density to the initial probability models through their relative information entropy. A sampling-based approach was discussed for efficient computation of this entropy for each of the model parameters whereas an analysis using stochastic simulation was proposed for similar computation for the stochastic sequence used in the ground motion modeling. The framework was illustrated in an example considering a linear SDOF structure and a source-based stochastic ground motion model. The average response and the reliability for rare events were adopted for defining structural risk whereas an additional comparison to seismic risk defined in terms of peak ground response was also presented. The sensitivity analysis was performed with respect to the model parameters of the stochastic ground motion model as well with respect to the seismic hazard characteristics (moment magnitude and epicentral distance). When considered as uncertain these characteristics were identified as the most important parameters influencing seismic risk. The group of model parameters related to temporal variation of the ground motion was found to have a small only importance towards the total risk, with primary contribution coming from the excitation-duration, whereas model parameters related to local site diminution were identified to have a negligible influence. Uncertainty in their description can be, thus neglected, with a minor only impact on the estimated risk. The group of model parameters related to the source spectrum, especially the parameter related to high-frequency content, was found to have a considerable contribution towards the seismic risk. This indicates that uncertainty in their characterization is important and warrants further attention. Dependence of the sensitivity analysis results on the seismic hazard and on the response selection for quantifying risk was also illustrated. The moment magnitude was shown to have an overall stronger impact on the sensitivity of the rest of the excitation model parameters. This stresses the importance of an appropriate description for it when quantifying seismic hazard. For lower magnitude events or regions with low seismicity, it was shown that the white noise sequence actually becomes the dominant risk factor with the excitation duration also having a comparatively increased importance. For stronger seismic events, though, the exact characteristics of the source spectrum were shown to have the highest impact on the estimated risk. The overall study shows the benefits stemming from the proposed global sensitivity analysis for investigating the impact of stochastic ground motion modeling on the seismic risk, for efficiently identifying the underlying trends and potential correlations for the model parameters, and for providing guidance for future research efforts.