Metamodel-based approaches to reliability analysis, e.g., adaptive Kriging, are computationally challenged by the complexity of reliability problems, thus limiting the application of these methods to ...problems that are low-dimensional or not rare. Here, we propose a reliability analysis approach via a deep integration of subset simulation and adaptive kriging (RASA) for an unbiased estimation of failure probabilities of high-dimensional or rare event problems. Concepts of conditional failure probability curves and dynamic learning function are introduced to decompose the original problem to subreliability problems and adaptively identify intermediate failure thresholds of limit state functions corresponding to the subreliability problems. The reliability decomposition and the establishment of target intermediate failure thresholds are guided by the available computational capacity, thus, enabling RASA to control the computational cost associated with the estimation of the intermediate failure thresholds in each subset and consequently to analyze the reliability of medium to high-dimensional problems or rare events. Three numerical examples are investigated as benchmark to explore the performance of the proposed method. Results indicate that the proposed method has high accuracy and has the ability to adjust to available computational resources.
A significant challenge with reliability-based design optimization (RBDO) is the high computational cost associated with the double-loop structure that entails a large number of function calls for ...both the optimization process and reliability analysis. Several decoupling methods have been developed to improve the efficiency of RBDO. In addition, surrogate models have been used to replace the original time-consuming models and improve the computational efficiency. This paper proposes a novel quantile-based sequential RBDO method using Kriging surrogate models for problems with independent constraint functions. An error-controlled adaptive Kriging scheme is integrated to derive accuracy information of surrogate models and develop a strategy that facilitates independent training of the models for the performance function. The proposed independent training avoids unnecessary performance function evaluations while ensuring the accuracy of reliability estimates. Moreover, a new sampling approach is proposed that allows refinement of surrogate models for both deterministic and probabilistic constraints. Five numerical examples are carried out to demonstrate the performance of the proposed method. It is observed that the proposed method is able to converge to the optimum design with significantly fewer function evaluations than the state-of-the-art methods based on surrogate models given the constraint functions are independent.
•A new highly efficient Bayesian updating method called BUAK is proposed.•Simple Rejection Sampling with Multiple Auxiliary Random Variables is introduced.•SRS-MARV features improved acceptance rates ...for decomposed limit state functions.•Adaptive Kriging-based reliability analysis is deeply integrated into BUAK.•BUAK reduces the computational demand by 1 to 3 orders of magnitude compared to BUS.
Bayesian updating offers a powerful tool for probabilistic calibration and uncertainty quantification of models as new observations become available. By reformulating Bayesian updating into a structural reliability problem via introducing an auxiliary random variable, the state-of-the-art Bayesian updating with structural reliability method (BUS) has showcased large potential to achieve higher accuracy and efficiency compared with conventional approaches based on Markov Chain Monte Carlo simulations. However, BUS faces a number of limitations. The transformed reliability problem often involves a very rare event especially when the number of observations increases. This along with the fact that conventional reliability analysis techniques are not efficient, and often not capable of accurately estimating the probability of rare events, unavoidably lead to a very large number of evaluations of the likelihood function and simultaneously insufficient accuracy of the derived posterior distributions. To overcome these limitations, we propose Simple Rejection Sampling with Multiple Auxiliary Random Variables (SRS-MARV), where the limit state function in BUS is decomposed into a system reliability problem with multiple limit state functions. The main advantage of this approach is that the acceptance rate of each decomposed limit state function is significantly improved, which facilitates effective integration of adaptive Kriging-based reliability analysis into SRS-MARV. Moreover, a new stopping criterion is proposed for efficient, adaptive training of the Kriging model. The proposed method called BUAK is shown to be highly computationally efficient and accurate based on results of comprehensive investigations for three diverse benchmark problems. Compared to the state-of-the-art methods, BUAK substantially reduces the computational demand by one to three orders of magnitude, therefore, facilitating the application of Bayesian updating to computationally very intensive models.
Seismic intensity measures (IMs) perform a pivotal role in probabilistic seismic demand modeling. Many studies investigated appropriate IMs for structures without considering soil liquefaction ...potential. In particular, optimal IMs for probabilistic seismic demand modeling of bridges in liquefied and laterally spreading ground are not comprehensively studied. In this paper, a coupled-bridge-soil-foundation model is adopted to perform an in-depth investigation of optimal IMs among 26 IMs found in the literature. Uncertainties in structural and geotechnical material properties and geometric parameters of bridges are considered in the model to produce comprehensive scenarios. Metrics such as efficiency, practicality, proficiency, sufficiency and hazard computability are assessed for different demand parameters. Moreover, an information theory based approach is adopted to evaluate the relative sufficiency among the studied IMs. Results indicate the superiority of velocity-related IMs compared to acceleration, displacement and time-related ones. In particular, Housner spectrum intensity (
HI
), spectral acceleration at 2.0 s (
S
a
-20
), peak ground velocity (
PGV
), cumulative absolute velocity (
CAV
) and its modified version (
CAV
5
) are the optimal IMs. Conversely, Arias intensity (
I
a
) and shaking intensity rate (
SIR
) which are measures often used in liquefaction evaluation or related structural demand assessment demonstrate very low correlations with the demand parameters. Besides, the geometric parameters do not evidently affect the choice of optimal IMs. In addition, the information theory based sufficiency ranking of IMs shows an identical result to that with the correlation measure based on coefficient of determination (
R
2
). This means that
R
2
can be used to preliminarily assess the relative sufficiency of IMs.
AbstractPopulation growth, economic development, and rapid urbanization in many areas have led to increased exposure and vulnerability of structural and infrastructure systems to hazards. Thus, ...developing risk-based assessment and management tools is crucial for stakeholders and the general public to make informed decisions on prehazard planning and posthazard recovery. To this end, structural risk and resilience assessment has been an ongoing research topic in the past 20 years. Recently, machine learning (ML) techniques have been shown as promising tools for advancing the risk and resilience assessment of structure and infrastructure systems. To date, however, there is a lack of a holistic review on ML progress across various branches of structural engineering; an in-depth analysis of literature that can provide a timely evaluation of risk and resilience assessment methods of the built environment, where different types of structural and infrastructure facilities are interconnected. For this reason, this study conducted a comprehensive review on ML for risk and resilience assessment in four main branches of structural engineering (buildings, bridges, pipelines, and electric power systems). To cover the crucial modules in the prevailing risk and resilience assessment frameworks, existing literature is thoroughly examined and characterized in terms of six attributes of ML, including method, task type, data source, analysis scale, event type, and topic area. Moreover, limitations and challenges are identified, and future research needs are highlighted to move forward the frontiers of ML for structural risk and resilience assessment.
Power distribution systems in the US are commonly supported by wood utility poles. These assets require regular maintenance to enhance the reliability of power delivery to support many dependent ...functions of the society. Limitations in budget, however, warrant efficient allocation of limited resources based on optimal preventive maintenance plans. A few studies have developed risk-based metrics to support risk-informed decision making in preventive maintenance planning for power distribution systems. However, integration of risk-based metrics and optimization for enhancing the life-cycle resilience of distribution systems has not been explored. To address this gap, this paper proposes a mixed-integer nonlinear programming (MINLP) model to maximize the life-cycle resilience of aging power distribution systems subject to multi-occurrences of hurricane events using an optimal risk-based maintenance planning. For this purpose, a risk-based index called the Expected Outages is proposed and integrated into the optimization problem to minimize the total expected number of power outages in the entire planning horizon. Various uncertainties in the performance of poles under stochastic occurrences of hazards are taken into account through advanced fragility models and an efficient recursive formulation that models the uncertainty of precedent pole failures. The proposed approach is applied to a large, realistic power distribution system for long-term maintenance planning given a total budget limit and different levels of periodic budget constraints. The resulting optimization problems are solved through the branch and bound algorithm. Results indicate that applying the presented methodology leads to a significant enhancement of the life-cycle resilience of distribution systems compared to the commonly implemented strength-based maintenance strategy set by National Electric Safety Code.
An appropriate seismic intensity measure (IM) for response prediction is central to reliable probabilistic seismic demand modeling of structures and subsequently, risk and resilience quantification. ...Bridges in liquefiable and laterally spreading ground may undergo nonlinear responses with large uncertainties when subjected to earthquakes. These issues often lead to low-confidence demand models based on traditional IMs. Fractional order IMs have shown the potential to yield improved demand models in recent studies. To further increase confidence in demand models, this study proposes Fractional Order Spectrum intensity considering Integral period and Damping ratio (named
FOSID
). The viability of
FOSID
for use in probabilistic seismic demand modeling of structures is evaluated in the context of extended pile-shaft-supported bridges against liquefaction-induced lateral spreading. The performance of
FOSID
is systematically assessed by comparisons to an existing fractional order spectrum intensity (
SI
r,α
), Housner intensity (
HI
)—an optimal traditional IM for these structures, and the average spectral acceleration (
Sa
avg
)—a state-of-the-art non-fractional-order IM. Multiple metrics for characterizing an optimal IM are adopted, including practicality, efficiency, proficiency, sufficiency, and relative sufficiency. Optimal variables of integral period, damping ratio, and fractional order for
FOSID
are identified for different demand parameters such as peak and residual column-drift-ratios. Results show that
FOSID
is generally more practical, efficient, proficient and sufficient than
SI
r,α
,
HI
and
Sa
avg
. In particular,
FOSID
significantly outperforms
HI
by improving the proficiency by nearly 40% and 20% for the peak and residual column-drift-ratios, respectively. With respect to
SI
r,α
,
FOSID
improves the proficiency by 20% and 15% on average. When compared with
Sa
avg
, such improvements are as large as 13% and 24% on average for the peak and residual column-drift-ratios, respectively.
•A new adaptive Kriging-based reliability analysis algorithm called REAK is proposed.•A maximum error rate for failure probability is derived via Central Limit Theorem.•Effective Sampling Region is ...proposed for efficient generation of training samples.•REAK reduces computational demands by as high as 50% compared to AK-MCS and ISKRA.•REAK enables establishing balance between the accuracy and computational demand.
As models in various fields are becoming more complex, associated computational demands have been increasing significantly. Reliability analysis for these systems when failure probabilities are small is very challenging, requiring a large number of costly simulations. To address this challenge, this paper introduces Reliability analysis through Error rate-based Adaptive Kriging (REAK). An extension of the Central Limit Theorem based on Lindeberg condition is adopted here to derive the distribution of the number of design samples with wrong sign estimate and subsequently determine the maximum error rate for failure probability estimates. This error rate enables optimal establishment of effective sampling regions at each stage of an adaptive scheme for strategic generation of design samples. Moreover, it facilitates setting a target accuracy for failure probability estimation, which is used as the stopping criterion for reliability analysis. These capabilities together can significantly reduce the number of calls to sophisticated, computationally demanding models. The application of REAK for four examples with varying extent of nonlinearity and dimension is presented. Results indicate that REAK is able to reduce the computational demand by as high as 50% compared to the state-of-the-art methods of Adaptive Kriging with Monte Carlo Simulation (AK-MCS) and Improved Sequential Kriging Reliability Analysis (ISKRA).
The ever-increasing complexity of numerical models and associated computational demands have challenged classical reliability analysis methods. Surrogate model-based reliability analysis techniques, ...and in particular those using kriging meta-model, have gained considerable attention recently for their ability to achieve high accuracy and computational efficiency. However, existing stopping criteria, which are used to terminate the training of surrogate models, do not directly relate to the error in estimated failure probabilities. This limitation can lead to high computational demands because of unnecessary calls to costly performance functions (e.g., involving finite element models) or potentially inaccurate estimates of failure probability due to premature termination of the training process. Here, we propose the error-based stopping criterion (
ESC
) to address these limitations. First, it is shown that the total number of wrong sign estimation of the performance function for candidate design samples by kriging,
S
, follows a Poisson binomial distribution. This finding is subsequently used to estimate the lower and upper bounds of
S
for a given confidence level for sets of candidate design samples classified by kriging as safe and unsafe. An upper bound of error of the estimated failure probability is subsequently derived according to the probabilistic properties of Poisson binomial distribution. The proposed upper bound is implemented in the kriging-based reliability analysis method as the stopping criterion. The efficiency and robustness of
ESC
are investigated here using five benchmark reliability analysis problems. Results indicate that the proposed method achieves the set accuracy target and substantially reduces the computational demand, in some cases by over 50%.
In performance-based earthquake engineering, probabilistic seismic demand models of structures are essential components that provide probabilistic estimates of earthquake-induced demands as a ...function of a variable(s) called the ground motion intensity measure (IM). Uncertainties in these models are often dependent on the IM used. Extending from traditional integer order IMs, this study assesses the performance of fractional order (FO, order of α) IMs on the probabilistic seismic demand modeling of extended pile-shaft supported bridges sited in liquefiable and laterally spreading ground. Uncertainties in structural and geotechnical material properties as well as geometric parameters of the bridges are considered in finite element models to achieve comprehensive scenarios. The FO IMs considered include peak ground response (PGRα), cumulative absolute response (CARα) and its modified version (CAR5α), spectral acceleration at 2.0 s for a fractionally damped single degree of freedom (SDF) system (Sad-20α) and for a conventional SDF system with fractional response (Sar-20α), spectrum intensity for a fractionally damped SDF system (SIdα), as well as for a conventional SDF system with fractional response (SIrα). Metrics such as efficiency, practicality, proficiency and sufficiency are measured to assess the optimal α with respect to different demand parameters. Results show the advantages of FO IMs as they increase confidence in demand models compared to traditional integer order IMs. In particular, the proposed fractional spectrum intensities (SIdα and SIrα) with their optimal α values produce significant improvements in practicality, efficiency and proficiency, while maintaining sufficiency. Therefore, FO IMs can provide more reliable demand models for probabilistic seismic demand analysis of extended pile-shaft supported bridges in liquefiable and laterally spreading ground.
•Novel fractional order (FO) seismic intensity measures (IMs) are proposed.•A coupled bridge-soil-foundation model considering lateral spreading is developed.•The proposed FO IMs show significant advantages compared to traditional IMs.•Optimal fractional orders for the FO IMs are stable for various modeling scenarios.
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