Stochastic Ground Motion Model Research Articles

Stochastic emulation with enhanced partial‐ and no‐replication strategies for seismic response distribution estimation

AbstractModern performance earthquake engineering practices frequently require a large number of time‐consuming non‐linear time‐history simulations to appropriately address excitation and structural uncertainties when estimating engineering demand parameter (EDP) distributions. Surrogate modeling techniques have emerged as an attractive tool for alleviating such high computational burden in similar engineering problems. A key challenge for the application of surrogate models in earthquake engineering context relates to the aleatoric variability associated with the seismic hazard. This variability is typically expressed as high‐dimensional or non‐parametric uncertainty, and so cannot be easily incorporated within standard surrogate modeling frameworks. Rather, a surrogate modeling approach that can directly approximate the full distribution of the response output is warranted for this application. This approach needs to additionally address the fact that the response variability may change as input parameter changes, yielding a heteroscedastic behavior. Stochastic emulation techniques have emerged as a viable solution to accurately capture aleatoric uncertainties in similar contexts, and recent work by the second author has established a framework to accommodate this for earthquake engineering applications, using Gaussian Process (GP) regression to predict the EDP response distribution. The established formulation requires for a portion of the training samples the replication of simulations for different descriptions of the aleatoric uncertainty. In particular, the replicated samples are used to build a secondary GP model to predict the heteroscedastic characteristics, and these predictions are then used to formulate the primary GP that produces the full EDP distribution. This practice, however, has two downsides: it always requires minimum replications when training the secondary GP, and the information from the non‐replicated samples is utilized only for the primary GP. This research adopts an alternative stochastic GP formulation that can address both limitations. To this end, the secondary GP is trained by measuring the square of sample deviations from the mean instead of the crude sample variances. To establish the primitive mean estimates, another auxiliary GP is introduced. This way, information from all replicated and non‐replicated samples is fully leveraged for estimating both the EDP distribution and the underlying heteroscedastic behavior, while formulation accommodates an implementation using no replications. The case study examples using three different stochastic ground motion models demonstrate that the proposed approach can address both aforementioned challenges.

Surrogate model‐aided global sensitivity analysis framework for seismic consequences estimation in buildings

AbstractSeismic consequences estimation for individual buildings is valuable for various stakeholders, including government entities, building owners, and insurers. The robustness of estimation results in the presence of incomplete input information can typically be investigated through sensitivity analysis. However, the estimation process's complexity and the sensitivity analysis's computational burden hinder its practical application, which requires a more efficient procedure to facilitate broader use. This paper proposes a novel framework for sensitivity analysis of seismic consequences estimation to improve the efficiency and reliability of such analysis. The proposed approach encompasses three key components: (1) stochastic ground motion modeling (SGMM)‐based seismic consequences estimation to evaluate the economic, environmental, and social consequences given specific buildings by considering different hazard levels, (2) the training of surrogate model (Gaussian process model) for structural analysis to reduce the computational cost of the evaluation process, and (3) variance‐based global sensitivity analysis to investigate the importance of parameters of concern in the estimation process. The entire procedure is implemented in Python, adhering to object‐oriented programming, and does not rely on external software. Then, the proposed methodology is applied to two distinct three‐story steel moment‐resistant frames (SMRFs) subjected to four different hazard levels to demonstrate its effectiveness. The SGMM method can generate specific ground motions for each hazard level, mitigating the potential for result bias from using ground motions with unrealistic characteristics. Furthermore, the SGMM method is particularly suitable for automated analysis processes reducing the laborious task of screening ground motions from the database. Comparative analysis with surrogate‐free estimation reveals that the surrogate‐based analysis delivers reliable results with significantly reduced computational cost. The results of analyzing different structures under varying hazard levels reflect the variability in sensitivity analysis of consequences estimation, highlighting the necessity of the proposed flexible and efficient framework. Furthermore, the proposed framework's advantages, limitations, and future research needs are discussed.

Site-specific stochastic ground motion model utilizing deterministic physics-informed simulations: A Bayesian approach

Limited availability of recorded ground motions poses a challenge for reliable probabilistic seismic-hazard analysis (PSHA), even in highly seismic regions like the Western United States. Stochastic ground motions are commonly employed to address this challenge. However, the stochastic ground motion models (GMMs) may not consistently generate ground motions compatible with the site hazard due to their calibration using global data, failing to capture site-specific characteristics adequately. In the absence of recorded motions, physics-informed simulations provide a viable alternative but are deterministic with limitations of their own that makes them challenging to support PSHA. This article introduces a Bayesian framework that combines prior knowledge from a stochastic GMM, calibrated with global data, with site-specific data obtained from deterministic physics-informed simulations. The proposed framework utilizes the Rezaeian–Der Kiureghian (2010) model as the stochastic GMM and incorporates site-specific data from the CyberShake 15.12 study. By updating the mean and variance of the predictive relationships, along with the marginal distribution of the model parameters, through Bayesian inference, this framework allows for the simulation of site-specific ground motions consistent with the site characteristics. The statistics of peak ground acceleration distributions, as well as both the median and variability of the elastic response spectra, obtained from the calibrated stochastic GMM, demonstrate consistency with those derived using GMMs based on the Next Generation Attenuation (NGA) database.

The assessment of probabilistic seismic risk using ground-motion simulations via a Monte Carlo approach

AbstractAccurately characterizing ground motions is crucial for estimating probabilistic seismic hazard and risk. The growing number of ground-motion models, and increased use of simulations in hazard and risk assessments, warrants a comparison between the different techniques available to predict ground motions. This research aims at investigating how the use of different ground-motion models can affect seismic hazard and risk estimates. For this purpose, a case study is considered with a circular seismic source zone and two line sources. A stochastic ground-motion model is used within a Monte Carlo analysis to create a benchmark hazard output. This approach allows the generation of many records, helping to capture details of the ground-motion median and variability, which a ground motion prediction equation may fail to properly model. A variety of ground-motion models are fitted to the simulated ground motion data, with fixed and magnitude-dependant standard deviations (sigmas) considered. These include classic ground motion prediction equations (with basic and more complex functional forms), and a model using an artificial neural network. Hazard is estimated from these models and then we extend the approach to a risk assessment for an inelastic single-degree-of-freedom-system. Only the artificial neural network produces accurate hazard results below an annual frequency of exceedance of 1 × 10–3 years−1. This has a direct impact on risk estimates—with ground motions from large, close-to-site events having more influence on results than expected. Finally, an alternative to ground-motion modelling is explored through an observational-based hazard assessment which uses recorded strong-motions to directly quantify hazard.

Utility of Stochastic Ground Motion Models in Conditional Spectrum-Based Selection Consistent with the Causal Earthquakes

ABSTRACT Conditional Spectrum (CS), characterized by a conditional mean and conditional standard deviation, serves as a target spectrum linking seismic hazard information to ground motion selection for seismic demand analysis. Current Ground Motion Selection and Modification (GMSM) methods aim to align with this target spectrum but face challenges due to the limited availability of recorded ground motions and potential modifications, leading to difficulties in ensuring selected ground motions accurately reflect site characteristics. Addressing this issue, the study presents an algorithm to select hazard-consistent CS-based records utilizing a stochastic ground motion model with a dual objective: (1) alleviate the need for scaling during the selection process, and (2) select records consistent with the target hazard and the contributing causal scenarios. To achieve both objectives, the study generates a database of hazard-targeted ground motions utilizing the kriging surrogate with scenarios sampled from the disaggregation matrix. Then, a postprocessing step explicitly considers causative parameters in the selection process. The algorithm’s potential to select site-specific ground motions is demonstrated using sites in the Western United States, providing insights into the computational cost and accuracy. Additionally, statistical comparisons are conducted to explore circumstances where similar hazard consistency can be achieved without the postprocessing step, reducing the overall computational cost. Finally, the selected ground motions are favorably compared to those selected through traditional conditional spectrum-based approaches based on their spectral shape and ground motion intensity measures.

Reliability-based design optimization for seismic structures considering randomness associated with ground motions

When addressing the dynamic reliability analysis of structures, it becomes necessary to account for multiple limit state functions or their combinations. In scenarios where structures are subjected to random excitation, this can lead to intricate inter-dependencies among different limit states, and the computational workload can pose a substantial challenge in ensuring sufficient precision. Code-based design primarily ensures safety at the member level, while deterministic optimization fails to accommodate the inherent uncertainties associated with external excitation or the system as a whole. Therefore, in such cases, to address both the uncertainties in excitations and the presence of multiple limit states while mitigating computational challenges, equivalent extreme-value criteria are employed within the framework of the probability density evolution method to calculate the global reliability of the structure subjected to stochastic ground motions generated from the physically motivated stochastic ground motion model. Numerical optimization is subsequently conducted using genetic algorithms, aiming to minimize the cost of the superstructure while adhering to the design performance criteria related to the inter-story drift ratio and considering global reliability. Additionally, multi-objective optimization is carried out using NSGA-II, permitting the generation of multiple solutions, from which one can select the most suitable solution as needed. The numerical results illustrate the effectiveness of this technique in achieving an optimal balance between the cost of the structure and the consideration of global reliability, providing a comprehensive solution for dynamic reliability analysis and design optimization of structures under random excitations.

A non-ergodic spectral acceleration ground motion model for California developed with random vibration theory

A new approach for creating a non-ergodic pseudo-spectral acceleration (PSA) ground-motion model (GMM) is presented, which accounts for the magnitude dependence of the non-ergodic effects. In this approach, the average PSA scaling is controlled by an ergodic PSA GMM, and the non-ergodic effects are captured with non-ergodic PSA factors, which are the adjustment that needs to be applied to an ergodic PSA GMM to incorporate the non-ergodic effects. The non-ergodic PSA factors are based on the effective amplitude spectrum (EAS) non-ergodic effects and are converted to PSA through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through small-magnitude earthquakes. Due to the linear properties of the Fourier Transform, the EAS non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for PSA, as response spectra are controlled by a range of frequencies, making PSA non-ergodic effects dependent on the spectral shape, which in turn is magnitude-dependent. Two PSA non-ergodic GMMs are derived using the ASK14 (Abrahamson et al. in Earthq Spectra 30:1025–1055, 2014) and CY14 (Chiou and Youngs in Earthq Spectra 30:1117–1153, 2014) GMMs as backbone models, respectively. The non-ergodic EAS effects are estimated with the LAK21 (Lavrentiadis et al. in Bull Earthq Eng ) GMM. The RVT calculations are performed with the V75 (Vanmarcke in ASCE Mech Eng Mech Division 98:425–446, 1972) peak factor model, the D_{a0.05-0.85} estimate of AS96 (Abrahamson and Silva in Apendix A: empirical ground motion models, description and validation of the stochastic ground motion model. Tech. rep.,. Brookhaven National Laboratory, New York) for the ground-motion duration, and BT15 (Boore and Thompson in Bull Seismol Soc Am 105:1029–1041, 2015) oscillator-duration model. The California subset of the NGAWest2 database (Ancheta et al. in Earthq Spectra 30:989–1005, 2014) is used to fit both models. The total aleatory standard deviation of each of the two non-ergodic PSA GMMs is approximately 25% smaller than the total aleatory standard deviation of the corresponding ergodic PSA GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase in epistemic uncertainty.

Stochastic dynamic response and seismic fragility analysis for high concrete face rockfill dams considering earthquake and parameter uncertainties

The multiple uncertainties of soil properties and ground motions significantly affect the seismic response of high concrete face rockfill dams (CFRDs). Three types of randomness (the material parameter randomness, stochastic seismic excitation, and their coupling) are generated by stochastic ground motion model and generalized F-discrepancy (GF-discrepancy) method. The generalized probability density evolution method (GPDEM) is used to analyze the influence of randomness on the stochastic dynamic response and system reliability of high CFRDs. The limit state of CFRD is defined according to the crest subsidence and the stress of face-slab, and a performance-based reliability evaluation framework is established. The results show that the randomness of ground motions dominates stochastic dynamic response of the CFRD and the dynamic reliability at different safety thresholds can be obtained by the above methods. Moreover, the proposed seismic safety evaluation framework provides a significant guidance for designing and analyzing practical engineering projects.

Seismic fragility analysis using stochastic polynomial chaos expansions

Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a set of selected intensity measures (IMs) that characterize the earthquake load. The-state-of-the art methods for fragility computation rely on full non-linear time–history analyses. Within this perimeter, there are two main approaches: the first relies on the selection and scaling of recorded ground motions; the second, based on random vibration theory, characterizes the seismic input with a parametric stochastic ground motion model (SGMM). The latter case has the great advantage that the problem of seismic risk analysis is framed as a forward uncertainty quantification problem. However, running classical full-scale Monte Carlo simulations is intractable because of the prohibitive computational cost of typical finite element models. Therefore, it is of great interest to define fragility models that link an EDP of interest with the SGMM parameters — which are regarded as IMs in this context. The computation of such fragility models is a challenge on its own and, despite a few recent studies, there is still an important research gap in this domain. This comes with no surprise as classical surrogate modeling techniques cannot be applied due to the stochastic nature of SGMM. This study tackles this computational challenge by using stochastic polynomial chaos expansions to represent the statistical dependence of EDP on IMs. More precisely, this surrogate model estimates the full conditional probability distribution of EDP conditioned on IMs. We compare the proposed approach with some state-of-the-art methods in two case studies. The numerical results show that the new method prevails over its competitors in estimating both the conditional distribution and the fragility functions.

Nonlinear Stochastic Seismic Response Analysis of Three-Dimensional Reinforced Concrete Piles

A reliable assessment and design of engineering structures requires appropriate estimation and consideration of different sources of uncertainty. The randomness of seismic ground motion is one major uncertainty that needs to be considered from the perspective of performance-based earthquake engineering. To properly account for this uncertainty and its corresponding effect on pile foundations, a stochastic seismic response analytical framework based on a probability density evolution method and a stochastic ground motion model is proposed for the nonlinear stochastic seismic response analysis of pile foundations. A three-dimensional finite element model of a reinforced concrete pile with a large diameter embedded in the soil foundation is firstly established and calibrated using the full-scale lateral load test results from the literature, in which the nonlinear behavior of soil, the soil–pile interaction, the concrete damaged plasticity, and the steel yielding of the pile are properly modeled. Then, the calibrated three-dimensional numerical model is employed as an illustrative example for the stochastic seismic response analysis using the proposed framework. The mean, standard deviation, and probability density function of pile settlement and the dynamic reliabilities of the pile concerning various performance requirements are obtained in the present study. The settlements of the pile show great variability under the excitation of various stochastic ground motions, and the maximum mean value of the pile settlements is about 8 mm. The changing shape of the settlement probability density functions in every moment demonstrates that it is unreasonable to use assumed probabilistic distribution models to characterize the seismic responses of pile foundations during a seismic reliability analysis. Based on the proposed method, it is found that the dynamic reliabilities of the selected reinforced concrete pile concerning four different performance levels are 0, 0.1293, 0.8247, and 1, respectively. The proposed stochastic seismic response analytical method in the present study can provide a proper and comprehensive way to quantify various uncertainties and their corresponding effects on the seismic performance of pile foundations. It can also be used to estimate the actual reliability level of pile foundations that are designed by the current codes when they are subjected to seismic loads.

Stochastic ground motion models to NGA‐West2 and NGA‐Sub databases using Bayesian neural network

AbstractGround motion models (GMMs) are traditionally developed from a frequentist approach. The Bayesian framework has received recent attention in developing nonergodic models, measuring uncertainty, or updating the model with additional data. However, no neural networks are developed to date in this framework to predict ground motion parameters or spectra. Hence, the present work develops a probabilistic Bayesian neural network (PBNN) to next‐generation attenuation – West2 and Subduction databases using variational inference with mean‐field assumption. Network inputs are magnitude, rupture distance, hypocentral depth, shear wave velocity, style of faulting, and region flags; outputs are peak ground values and response spectra. Both models have two hidden layers with seven neurons in each hidden layer. The models are verified for potential overfit, and their performance is validated through the parametric study by varying inputs. The output of a deterministic model is a point estimate. Considering probabilistic layers in hidden and output layers enables the model to capture within‐model epistemic uncertainty and aleatory variability. Obtained aleatory standard deviations are consistent with other models. Mean epistemic uncertainty and aleatory variability are in the range 0.07–0.10 and 0.62–0.78 (ln units) for NGA‐West2 and 0.09–0.16 and 0.67–0.95 for NGA‐Sub models, respectively. The correlation coefficients between recorded and overall mean predictions ranged from 0.94 to 0.97 for NGA‐the West2 model and from 0.91 to 0.95 for the NGA‐Sub models. Network performance for out‐of‐training inputs showed increased epistemic deviations with no effect on aleatory deviations.

Addressing the different sources of excitation variability in seismic response distribution estimation using kriging metamodeling

AbstractThis paper investigates the impact of the different sources of excitation variability within the stochastic kriging framework recently developed by the authors for the estimation of the distribution of engineering demand parameters (EDPs) in applications that the seismic hazard is described through stochastic ground motion models. For a given seismic event, described by seismicity characteristics such as the moment magnitude and the distance to source, one can distinguish two type of uncertainties in the excitation description: (g.i) the stochastic sequence utilized within the excitation model; (g.ii) the predictive models relating the ground motion parameters, such as significant duration, arias intensity, or frequency properties of seismic waves, to the seismicity characteristics. The original formulation of the authors treats (g.i) as aleatoric uncertainty and (g.ii) as parametric uncertainty, including the latter in the model parameters for the risk characterization, representing the metamodel input. Implementation establishes the EDP distribution approximation by utilizing a database of EDP estimates for a set of different input parameters, considering replications of these estimates for different stochastic sequences for some small part of this database. The database with replications is first leveraged to approximate the heteroscedastic behavior with respect to the aleatoric uncertainty, and the entire database is subsequently used, coupled with the previous heteroscedasticity approximation, to establish the stochastic kriging predictions for the EDP distribution. For excitation models with a large number of ground motion parameters, the original formulation leads to a significant increase of the input dimensionality for the metamodel development, requiring a larger database for facilitating accurate EDP approximations. Here, an alternative formulation is investigated, considering some (or perhaps even all) of the ground motion parameters to be part of the aleatoric uncertainty of the excitation description. It is shown that careful selection is needed for the exact ground motion parameters that can be treated as part of this aleatoric uncertainty, to accommodate an accurate overall EDP approximation. Similarities are discussed for applications that consider the description of the seismic hazard through the selection of ground motions based on intensity measures. An extensive validation of this new approach is presented considering two different stochastic ground motion models.

Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra

Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T0)-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.

Stochastic Dynamic Response Analysis of the 3D Slopes of Rockfill Dams Based on the Coupling Randomness of Strength Parameters and Seismic Ground Motion

Because rockfill strength and seismic ground motion are dominant factors affecting the slope stability of rockfill dams, it is very important to accurately characterize the distribution of rockfill strength parameters, develop a stochastic ground motion model suitable for rockfill dam engineering, and effectively couple strength parameters and seismic ground motion to precisely evaluate the dynamic reliability of the three-dimensional (3D) slope stability of rockfill dams. In this study, a joint probability distribution model for rockfill strength based on the copula function and a stochastic ground motion model based on the improved Clough-Penzien spectral model were built; the strength parameters and the seismic ground motion were coupled using the GF-discrepancy method, a method for the analysis of dynamic reliability of the 3D slope stability of rockfill dams was proposed based on the generalized probability density evolution method (GPDEM), and the effectiveness of the proposed method was verified. Moreover, the effect of different joint distribution models on the dynamic reliability of the slope stability of rockfill dams was revealed, the effect of the copula function type on the dynamic reliability of the slope stability was analysed, and the differences in the dynamic reliability of the slope stability under parameter randomness, seismic ground motion randomness, and coupling randomness of parameters and seismic ground motion were systematically determined. The results were as follows: the traditional joint distribution models ignored related nonnormal distribution characteristics of rockfill strength parameters, which led to excessively low calculated failure probabilities and overestimations of the reliability of the slope stability; in practice, we found that the optimal copula function should be selected to build the joint probability distribution model, and seismic ground motion randomness must be addressed in addition to parameter randomness.

Seismic Collapse Risk Assessment of Braced Frames under Near-Fault Earthquakes

Special concentrically braced frames (SCBFs) located in regions close to earthquake faults may be subjected to near-fault ground motions, often characterized by pulses with long periods. These near-fault pulses could impose additional seismic demands on structures and increase the risk for structural collapse. Currently, there is limited research on the seismic collapse risk of SCBFs under near-fault earthquakes. This paper uses a general simulation-based framework to assess the seismic collapse risk of SCBFs under near-fault earthquakes. To quantify the large variability and uncertainty associated with the seismic hazard, a stochastic ground motion (SGM) model is used where the near-fault pulse characteristics are explicitly incorporated. The uncertainties in the SGM model parameters (including the near-fault pulse characteristics) are addressed through appropriate selection of probability distribution functions. To accurately predict the occurrence of collapse, numerical models capable of capturing the nonlinear and collapse behavior are established and used. Efficient stochastic simulation approaches are proposed to estimate the seismic collapse risk with or without considering the near-fault pulse. As an illustration, the seismic collapse risks of two SCBFs are investigated and compared. Probabilistic sensitivity analysis is also carried out to investigate the importance of uncertain model parameters within the SGM towards the seismic collapse risk.

Kriging metamodeling for seismic response distribution estimation

AbstractThis paper revisits the implementation of surrogate modeling (metamodeling) techniques within seismic risk assessment, for applications that the seismic hazard is described through stochastic ground motion models. Emphasis is placed on how to efficiently address the aleatoric uncertainty in the ground motions, stemming in this case from the stochastic sequence utilized within the excitation model. Previous work has accommodated this uncertainty by approximating the statistics of the engineering demand parameters (EDPs), something that required a large number of replication simulations (for different stochastic sequences) for each training point that was used to inform the metamodel calibration. Using kriging (Gaussian Process regression) as surrogate model, an alternative formulation is discussed here, aiming to minimize the replications for each training point. This is achieved by approximating directly the EDP distribution. It is shown that accommodating heteroscedastic behavior with respect to the aleatoric uncertainty is absolutely critical for achieving an accurate approximation, and two different approaches are presented for establishing this objective. The first approach adopts a stochastic kriging formulation, utilizing a small number of replications for judicially selected inputs, leveraging a secondary surrogate model over the latter inputs to address the heteroscedastic behavior. The second approach uses no replications, establishing a heteroscedastic nugget formulation to accommodate the EDP distribution estimation. A functional relationship is introduced between the nugget and the excitation intensity features to approximate the heteroscedastic behavior. This relationship is explicitly optimized during the metamodel calibration.

Seismic fragility analysis of a coupled tank-piping system based on artificial ground motions and surrogate modeling

The catastrophic consequences of recent NaTech events triggered by earthquakes highlighted the inadequacy of standard approaches to seismic risk assessment of chemical process plants. To date, the risk assessment of such facilities mainly relies on historical data and focuses on uncoupled process components. As a consequence, the dynamic interaction between process equipment is neglected. In response to this gap, researchers started a progressive integration of the Pacific Earthquake Engineering Research Center (PEER) Performance-Based Earthquake Engineering (PBEE) risk assessment framework. However, a few limitations still prevent a systematic implementation of this framework to chemical process plants. The most significant are: (i) the computational cost of system-level simulations accounting for coupling between process equipment; (ii) the experimental cost for component-level model validation; (iii) a reduced number of hazard-consistent site-specific ground motion records for time history analyses.In response to these challenges, this paper proposes a recently developed uncertainty quantification-based framework to perform seismic fragility assessments of chemical process plants. The framework employs three key elements: (i) a stochastic ground-motion model to supplement scarcity of real records; (ii) surrogate modeling to reduce the computational cost of system-level simulations; (iii) a component-level model validation based on cost-effective hybrid simulation tests. In order to demonstrate the potential of the framework, two fragility functions are computed for a pipe elbow of a coupled tank-piping system.

Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations

In practical geotechnical engineering of slopes, it is well-known that the uncertainty of soil properties and ground motions need to be considered for the safety of the project. The effect of uncertain parameters and stochastic ground motions on seismic responses as well as dynamic failure probabilities of slopes are analyzed and discussed in this study. A recently proposed generalized probability density evolution method (GPDEM) is formulated to investigate the system reliability of complex slopes with consideration to uncertainty in multiple slope parameters and in ground motions. Firstly, the fundamental theory of dynamic stability, GPDEM, dynamic system reliability, generation of random samples and stochastic ground motion model are described. Then, the efficiency and accuracy of proposed GPDEM are verified and a novel evaluating index is presented. Four complex slopes, each with multi-parameter uncertainties, are examined in separate study cases. Each study case uses GPDEM to study the random dynamic responses as well as probability responses of slopes while considering deterministic ground motion. The efficiency and accuracy of GPDEM used in complex slopes are validated by comparing with the Monte Carlo method (MCM). In addition, a novel evaluating index called the average large failure probability Pff, is proposed to describe the failure probability of the slopes, and can take the probability time histories intoaccount. Finally, the seismic system reliability of complex slopes is evaluated using the time-history method, and randomness in earthquakes, parameters and their coupling are investigated. The stochastic dynamic responses and probability responses of deterministic parameters subjected to stochastic earthquake excitations, and random parameters subjected to stochastic earthquake excitations are also discussed and are compared based on study case 3. The results demonstrate the high accuracy and validity of the GPDEM. Furthermore, the probability of failure and the degree of safety for the slopes can be directly estimated through probability analysis. In addition, the results also indicate that randomness in ground motions have a much larger influence than randomness in slope parameters, but randomness in slope parameters cannot be completely neglected.

Evaluation of Kriging-NARX Modeling for Uncertainty Quantification of Nonlinear SDOF Systems with Degradation

Structural assessment for collapse is commonly approached by observing the failure or collapse of systems fully incorporating degradation. Challenges however exist in the performance indicator or damage measure due to compound impacts of uncertainties of external (seismic excitation) and internal (structural properties) characteristics with degradation behavior. To account for the impacts of uncertainties, the state-of-the-art kriging nonlinear autoregressive with exogenous (NARX) model is explored in this study to replicate the response of nonlinear single-degree-of-freedom systems. The generalized hysteretic Bouc-Wen model with internal uncertainties is selected to emulate the stiffness and strength degradation. A probabilistic stochastic ground motion model is introduced to represent the external uncertainties. The global terms of NARX model are selected by least-angle regression algorithm and the kriging model is utilized to surrogate uncertain parameters into corresponding NARX model coefficients. The predictions of kriging NARX models are further compared with that of the polynomial chaos nonlinear autoregressive with exogenous input form model as well as Monte Carlo simulation. The comparisons show that kriging NARX model presents an effective and efficient meta-model technique for uncertainty quantification of systems with degradation.

Two Empirical Double-Corner-Frequency Source Spectra and Their Physical Implications

ABSTRACTWe introduce double-corner-frequency (DCF) source spectral models JA19 and JA19_2S, which, in conjunction with a stochastic ground-motion model, can reproduce the mean peak ground acceleration (PGA) and mean peak ground velocity (PGV) of the Next Generation Attenuation-West 2 database for magnitudes 3.3–7.3. Their displacement amplitude spectrum remains constant for frequencies less than fc1, decays as f−1 between fc1 and fc2, and decays as f−2 for frequencies greater than fc2. The model JA19 is self-similar. Its two corner frequencies fc1 and fc2 scale with moment magnitude (M) as (1) log(fc1(M))=1.754−0.5M and (2) log(fc2(M))=3.250−0.5M. We find that relation (1) is consistent with the known self-similar scaling relations of the rupture duration (Td), in which Td=1/(πfc1). Relation (2) may reflect the scaling relation of the average rise time (TR), where TR∼0.8/(fc2). Stochastic simulations of ground motion using JA19 cannot reproduce the sharp change in magnitude dependence of PGA and PGV at M 5.3, suggesting a breakdown of self-similarity. The magnitude dependence of PGA and PGV and this change in slope is well explained by JA19_2S, which results from perturbing the fc1 scaling relationship in JA19. For JA19_2S: log(fc1(M))=1.474−0.415M for M≤5.3; log(fc1(M))=2.375−0.585M for M>5.3. The scaling relation for fc2 is unchanged. When fc1≪fc2, the scaled energy (ratio of radiated energy and seismic moment) scales with M0fc12fc2. The scaled energy of JA19 is 2.2×10−5, independent of magnitude. Because JA19_2S is not self-similar, its scaled energy is 2.2–4.7×10−5, increasing 2.2 times, when magnitude increases from 3.3 to 5.3, and, subsequently decreasing 2.2 times, as magnitude further increases from 5.3 to 7.3. Both agree with the global average (∼3×10−5) reported previously. Using our proposed empirical models, the standard deviation of average static stress drop from seismological studies can be significantly greater than the standard deviation of the stress parameter used to estimate PGA and PGV.