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• Delta formulations provide objective functions for action and information value prediction and optimisation. • Delta formulations facilitate consistent decision identification and value quantification. • Principal mechanisms and conditions of a positive information value are identified. • Delta formulations for predicted information value lead to a reduction of computational effort. This paper contains decision analytical approaches, conditions and models for the quantification of decision values for built environment systems. Specifically, (1) delta formulations of objective functions for decision value quantification are introduced, (2) conditions for decision value are identified and (3) action value analysis formulations are further developed. The delta objective functions are formulated with differences in utility, cost, and probabilities for consistent decision identification by expected utility and value. The delta formulations facilitate the direct calculation of action and information values and the explication of conditions for a positive decision value. Action value objective functions are derived in delta formulation for the action types of utility and system state actions and with action implementation states and action uncertainty models. The delta formulations are exemplified for predicted information and predicted actions values. The paper closes with a synthesis and discussion of decision values and with findings encompassing a computational effort reduction and the identification of predicted information value mechanisms. [ABSTRACT FROM AUTHOR]

• The paper aims at the setting up of a probabilistic procedure to be applied for Steel MRFs equipped with FREEDAM joints. • The uncertainty of the properties of the FREEDAM connections and of the yield stress of the material have been considered. • The probabilistic procedure is based on the combination of the First Order Reliability Method with the Bimodal Bounds. • The achievement of the design goal with a target reliability is assured using overstrength factors opportunely calibrated. • A mathematical relation is proposed to estimate the overstrength to apply to deterministic version of the TPMC. In this work, the Theory of Plastic Mechanism Control (TPMC) is combined with a probabilistic method to account for the influence of random material variability. Reference is made to steel Moment Resisting Frames (MRFs) equipped with FREEDAM connections. FREEDAM connections are beam-to-column connections equipped with friction dampers to dissipate the seismic input energy. TPMC is used to guarantee that in case of destructive seismic events the structural members such as beams and columns remain undamaged. To this scope, the structure is designed to assure a collapse mechanism characterized by the activation of all the friction dampers of the beam ends and the formation of plastic hinges at the base of the first storey columns only. From the probabilistic point of view, the random uncertainties are given by the static friction coefficient of the contact surfaces and the preloading of the bolts of the friction dampers as well as the yielding resistance of the steel members. The failure domain is related to all the possible failure events, where the term "failure" concerns the development of an undesired mechanism different from the global one. Generally, the design conditions to prevent undesired collapse mechanisms are stochastic events within the framework of the kinematic theorem of plastic collapse. The limit state function corresponding to each event can be represented by a hyperplane in the space of random variables. Consequently, the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states of each single failure event. Since dissipative zones (member ends or friction dampers) in the frame members are common to many different mechanisms, the single limit state functions are correlated. Therefore, the probability of failure can be evaluated by means of the Bimodal or Ditlevsen bounds by assuming that the failure events are located in series. The output of the work is a simple relationship which provides the overstrength factor of FREEDAM connections to be considered in the column design phase to account for random material variability thus assuring a given level of reliability in the application of TPMC. [ABSTRACT FROM AUTHOR]

• ISO 2394:2015 introduced pT (maximum acceptable Pf) to limit cost optimized Pf. • VSL based metrics may fail to place independent constraints on monetary optimization. • pT is derived from LQI based SWTP in marginal lifesaving cost constraint. • Like SWTP, pT is governed by the reciprocal of per capita GDP (g). • pT not consistent with ALARP framework unless applied to nations with high g. The idea of coupling economics and safety into one optimization exercise, and hence deriving target reliabilities explicitly from socio-economic consequences of limit state violation, appeared in the JCSS Probabilistic Model Code around the turn of the century; the effort culminated in the form of a Life Quality Index (LQI)-based marginal lifesaving costs (MLSC) methodology in ISO 2394:2015 for determining maximum acceptable failure probabilities, p T , in life safety limit states for civil engineering structures across all nations. Unfortunately, while the methodology does yield adequate levels of safety when applied to structures in the developed countries, the recommended values of p T turn out to be one to two orders of magnitude higher, and unacceptable to every known standard in the world including its own earlier edition (ISO 2394:1998) when applied to structures in the developing world (exemplified by India) with identical functions and expected fatalities. This arises from two shortcomings: (1) an MLSC approach is generally unable to provide an independent constraint on monetary optimization, and (2) the LQI-based measure of MLSC constraint is strongly dependent on a country's per capita GDP (g) and the resultant p T is effectively governed by the reciprocal of g. This paper recommends continuing with the absolute − not marginal − consequences of violating life safety limit states, and setting constraints on monetary optimization that are consistent with fatality risks from engineering activities more universally accepted to be safe. [ABSTRACT FROM AUTHOR]

• The proposed tropical cyclone model is completely driven by a set of environmental variables. • This model reproduces the spatial and temporal characteristics of observed tropical cyclones. • The model achieves remarkable balance between computational complexity and efficiency. • This model will provide decision-makers with valuable information regarding potential wind-induced hazards. • When future climate data are fed into this model, the impact of climate change on tropical cyclones can be evaluated. This paper presents an environment-driven tropical cyclone (TC) model for the Western North Pacific basin, which comprises a revised Poisson regression genesis model, a tailored beta-advection track model, and a fast intensity model. The TC model reproduces the temporal and spatial distributions of genesis events, the motion pattern of tracks, as well as the intensity evolutions along tracks. Risk analyses for Hong Kong and along the southeast coastline of mainland China demonstrate that this model can simulate extreme TC events with high fidelity. And the Gaussian mixture model outperforms the Frank Copula in approximating the joint distributions of the annual maximum wind speeds and the corresponding wind directions. This model is driven by a set of environmental variables including relative vorticity, relative humidity, sea surface temperature, vertical wind shear, potential intensity, sub mixed layer depth stratification, mixture layer depth and so on. This enables the model to not only reproduce historical records, but also make predictions for future TC behaviors under climate change with combination of global climate models. Besides, the computational efficiency of the TC model is comparable to traditional purely statistical models. The proposed model can also be coupled with other natural hazard models to conduct multi-hazard analysis. [ABSTRACT FROM AUTHOR]

• An LRFD framework for embankments considering climate change effects is established. • Additional partial factors are introduced to account for the climate change effects. • Non-stationary maximum flood depth is developed using a peak-over-threshold method. • Embankment reliability is evaluated against overtopping and slope failure. • The proposed framework can serve as a reference for future code design. Riverine floods have become increasingly prevalent on a global scale, posing significant risks to infrastructure systems and communities. The escalating impacts of climate change associated with the increase in rainfall intensities and frequencies necessitate the improvement of the existing design methodologies to account for the non-stationary climate change effects to ensure that the reliability is above the target level and mitigate future flood disasters. This paper presents a novel LRFD approach for river embankments subjected to extreme rainfall under non-stationary climate change effects. This approach introduces an additional partial factor to account for the effects of climate change. Precipitation and temperature projections are collected from various climate models considering several cases of emission scenarios. An integrated hydrological and hydraulic modeling of the analyzed river is carried out to estimate the associated time-variant river discharge and water surface elevation. The non-stationary extreme value associated with the maximum flood level is leveraged using the peak-over-threshold approach. The embankment reliability and the corresponding most probable points are evaluated using limit states associated with overtopping and slope failures. Based on the estimated and target reliability indexes, the design point for each random variable is assessed considering the cases with and without climate change effects. Finally, the partial factors associated with climate change effects are determined. As an illustrative example, the proposed framework is applied to the Ashida River in Fukuyama city of Japan. [ABSTRACT FROM AUTHOR]

• Performance evaluation procedure for tall buildings using database assisted design approach is proposed. • Three performance levels of occupant comfort, operational, and continued occupancy with limited interruption are considered. • Wind directionality analysis using local climatological data. In recent years, performance-based design (PBD) has gained attention and is sought to be the benchmark approach in the field of wind engineering. While the concept of performance-based design is well-accepted in earthquake engineering, it is yet to be embraced for the design of buildings to resist severe wind loads. This paper introduces a framework for the performance-based wind design (PBWD) of tall steel buildings using a time domain analysis that keeps the process of wind effects and the structural design process integrated, transparent, and fully auditable. From the perspective of PBWD, the main objective is to achieve a desirable performance level for a given hazard level, i.e., mean recurrence interval of extreme wind. The wind effects are directly related to the mean annual return of wind through a well-accepted simulation approach. A 180 m tall standard CAARC building is used for the case study to illustrate the proposed methodology. The wind load time histories are determined using the pressure tap data on exterior faces of the building measured in the wind tunnel. With the calculated wind loads, nonlinear dynamic analysis is conducted with various wind directions and mean wind speeds based on database-assisted design (DAD) approach. The key performance measures such as demand-to-capacity indices, inter-story drift, damage deformation index, and floor accelerations are calculated as a function of wind directions and mean wind speed. The obtained responses are used in conjunction with a local wind climatological database to determine the extreme wind effects for any specific mean recurrence interval. The performance of the steel building is evaluated for three performance criteria, including occupant comfort, operational, and continuous occupancy. The conducted performance assessment reveals that building fails to satisfy the serviceability requirement of drifts. However, the building satisfies the requirements for the occupant comfort and operational performance levels for strength design, while it also satisfies the continuous occupancy, limited interruption in Risk category II. The result reveals that the proposed framework provides realistic assessment of performance of the building incorporating the wind directionality and return period of the wind speeds. [ABSTRACT FROM AUTHOR]

Assessing the seismic capacity of pier columns is a crucial element in the performance-based seismic design of bridges. Such assessment necessitates a probabilistic approach to accurately determine the marginal probability distributions of seismic capacities and to characterize the dependencies among these variables. In response to this need, this paper employs Multi-Output Gaussian Process Regression (MO-GPR), a probabilistic machine learning method, to jointly model the multiple seismic capacities of pier columns. We initially introduce a probabilistic seismic capacity model that utilizes MO-GPR for pier columns and validate its predictive accuracy in comparison to Bayesian linear regression and existing empirical methods. Subsequently, the methodology is augmented by the integration of hierarchical modeling within the MO-GPR framework, resulting in a Multi-Output Hierarchical Gaussian Process Regression (MO-HGPR) model that effectively estimates intraclass correlation coefficients for specific types of datasets. It is postulated that these correlation coefficients also reflect correlations associated with multiple components of the real structure. This study employs MO-HGPR and MO-GPR separately to investigate the potential correlations of seismic capacities among pier columns and distinct limit states. The results demonstrate that the MO-GPR model exhibits superior prediction accuracy and more effectively portrays uncertainty compared to existing empirical models. Moreover, the correlations of seismic capacities among piers and limit states are both robust and significantly impact the seismic fragility of bridges. This finding highlights the essential nature of considering capacities correlations in seismic fragility or risk assessment processes. • Probabilistic prediction of seismic capacity of piers via Gaussian process regression. • Proposed a Hierarchical Gaussian Process Regression model with random effects. • Characterizing the seismic capacities correlations among piers and limit states. • These correlations exert a significant impact on the seismic fragility of a bridge. [ABSTRACT FROM AUTHOR]

• Non-classical autocorrelation models for smoothness and hole effect. • Whittle-Matérn (WM) model for smoothness and cosine WM model for hole effect. • Approximate variance reduction for a vertical line in soil with strong hole effect. • Theoretical scale of fluctuation and variance reduction for an inclined line. • Approximate variance reduction for an inclined line in soil with weak hole effect. Variance reduction function for a spatially variable soil property is an important factor that affects the spatial average-based characteristic value, which in turn influences the design of a geotechnical structure in the context of Eurocode 7. This study derives the theoretical and approximate variance reduction functions (VRFs) for a potential inclined slip line in a spatially variable soil. Only stationary random fields are studied but more general spatial variability characteristics including smoothness and hole effect are considered. First, the closed-form one-dimensional (1D) VRFs are investigated, including the VRFs for classical one-parameter autocorrelation models, the non-classical two-parameter Whittle-Matérn (WM) model, and the most general three-parameter cosine Whittle-Matérn (CosWM) model proposed to date. It is found that closed-form solutions are not available or not practical to compute in general and the simple approximate VRF (equal to scale of fluctuation/averaging length) is not adequate for the non-classical autocorrelation models (WM and CosWM). Two approximate VRFs are developed in this study for the 1D WM and 1D CosWM models. For a spatial average over an inclined line, this paper derives the theoretical scales of fluctuation (SOFs) and VRFs for five commonly used 2D autocorrelation models. The theoretical solutions show that the equivalent SOFs proposed in the literature are only applicable under special conditions which are clarified in this paper. More general approximations for the VRF over an inclined line are proposed. The range of applicability for each approximation is stated. The proposed approximate VRFs are shown to be reasonably accurate when they are applied to the spatial average-based characteristic value and for the design of a vertical pile and an inclined soil nail. [ABSTRACT FROM AUTHOR]

The design of an offshore wind turbine to resist fatigue damage during its whole service life requires to estimate an expectation over the pluri-annual joint statistics of wind and wave variables. Using a full factorial-based integration for the estimation of the cumulative fatigue damage represents a tremendous computational cost with aero-servo-hydro-elastic solvers which is generally not affordable by industrial designers. To overcome this limitation, strong approximations with lumping of environmental discretized joint probability (scatter diagram) are generally employed. We present in this paper a new method, called MAKSUR, involving the iterative enrichment of a design of experiments tailored to provide a good approximation of the long term mean damage. This method relies on a Kriging response surface with a learning criterion defined as the variance of the mean damage integral. It is compared to another previous similar approach called AK-DA, also dedicated to damage prediction, but is shown to converge more efficiently and with less numerical parameters to define by the user. The potential of the method for offshore wind turbine is demonstrated by a realistic 6D floating wind turbine case study with six wind and wave input variables. • Accurate offshore wind turbine damage assessment with reduced number of costly simulation. • Adaptive expectation estimation with Gaussian Process surrogate model. • Stepwise uncertainty reduction approach as a generalization of optimal Bayesian Quadrature. [ABSTRACT FROM AUTHOR]

• A probabilistic framework is used to calibrate burst strength models of pipelines based on the hierarchical Bayesian method. • The approach uses burst test data of intact and corroded pipelines of different steel grades. • The most appropriate burst strength models for corrosion-free and corroded pipelines are adopted. • Using the hierarchical Bayesian approach model uncertainty factors are derived to calibrate the burst strength models. • The differences in uncertainty resulting from the use of the proposed approach are compared to the conventional method. This paper proposes a probabilistic framework to calibrate burst strength models of intact and corroded pipelines based on the hierarchical Bayesian method. The approach uses burst test data of intact and corroded pipelines of different steel grades compiled from the literature and accounts for the variations among the data sources. First, the most appropriate burst strength models for corrosion-free and corroded pipelines are adopted. The burst pressure prediction models are categorised under low, medium and high-grade steel classes. Using the hierarchical Bayesian approach model uncertainty factors are derived to calibrate the burst strength models. The mean values and uncertainty of posterior probabilities of the model uncertainty factors are estimated for intact and corroded pipelines in three material categories. This study further investigates the uncertainty propagated by calibrated and non-calibrated models and draws important observations regarding the uncertainty associated with the calibration. The prediction uncertainties follow a non-linear increasing trend as corrosion defect increases. This study's importance is demonstrated with a case study that shows the differences in the uncertainty resulting from the use of the proposed approach compared to the conventional method. Additionally, for corroded pipes, model uncertainty factors are described as a function of defect depth with regression parameters estimated from hierarchical Bayesian-based regression analysis. Finally, a comparison between calibrated and non-calibrated models indicates that the calibrated models provide non-conservative predictions. [ABSTRACT FROM AUTHOR]

Estimation of second-order statistics allows characterizing the uncertainty associated with the response of stochastic finite element models. Two common approaches for estimating these statistics are Monte Carlo simulation and perturbation. The purpose of this paper is to present a framework to aggregate the results obtained by means of these two approaches under the umbrella of Control Variates with Splitting. This allows to produce estimates of the second-order statistics of the system's response with improved precision and accuracy. More specifically, Control Variates is implemented in such a way that the variance of the estimates of second-order statistics is minimized. In addition, the application of intervening variables for enhancing perturbation is considered as well, showing substantial advantages by increasing the accuracy of the estimates of second-order statistics. The application of the proposed framework is illustrated by means of an example involving the estimation of second-order statistics of a model involving confined seepage flow. • Estimation of second-order statistics of response of stochastic models. • Control Variates aggregates results from Monte Carlo simulation and perturbation. • Splitting technique is considered for practical implementation. • Proposed framework leads to precise and accurate estimates of sought statistics. [ABSTRACT FROM AUTHOR]

This paper proposes a multitask learning framework for probabilistic model updating by jointly using strain and acceleration measurements. This framework can enhance the structural damage assessment and response prediction of existing steel frame structures with quantified uncertainty. Multitask learning may be used to address multiple similar inference tasks simultaneously to achieve a more robust prediction performance by transferring useful knowledge from one task to another, even in situations of data scarcity. In the proposed model-updating procedure, a spatial frame is decomposed into multiple planar frames that are viewed as multiple tasks and jointly analyzed based on the hierarchical Bayesian model, leading to robust estimation results. The procedure uses a displacement–stress relationship in the modal space because it directly reflects the elemental stiffness and requires no prior knowledge concerning the mass, unlike most existing model-updating techniques. Validation of the proposed framework by using a full-scale vibration test on a one-story, one-bay by one-bay moment resisting steel frame, wherein structural damage to the column bases is simulated by loosening the anchor bolts, is presented. The experimental results suggest that the displacement–stress relationship has sufficient sensitivity toward localized damage, and the Bayesian multitask learning approach may result in the efficient use of measurements such that the uncertainty involved in model parameter estimation is reduced. The proposed framework facilitates more robust and informative model updating. • Bayesian multitask learning reduces model uncertainties arising from data scarcity. • Planar frames constituting the structure of interest are treated as multiple tasks. • A number of strain data were used for probabilistic model updating. • Strain-based model updating sensitively localizes structural damage to elements. • Full-scale tests on a steel frame with loosened anchor bolts validated the method. [ABSTRACT FROM AUTHOR]

• Stochastic model characterising the life-cycle performance of claddings against hailstorm. • Realistic predictions accounting for the variations of hailstone sizes in natural environment. • Response behaviour of panel under repeated hail impact was experimentally studied using a gas gun. • The model predicts average intervention rate which can be used for maintenance policies. This paper delves into cumulative damage on aluminium cladding panels attributed to hailstorms throughout the lifespan of the installations. 40 gas gun tests subjecting the cladding panel to repeated impact were undertaken for the purpose of studying cumulative damage behaviour. Insights from these tests were integrated into a hail size distribution model to characterise the probabilistic distribution of permanent indentation resulted from multiple hailstorm events. A life-cycle analysis framework was subsequently introduced, incorporating the natural variability of hailstone sizes and dynamic response of claddings to repeated ice impact. Intervention criterion can be established based on knowledge of the accumulation of permanent indentation into the cladding panels. Proactive actions are recommended should the indentations become visible to prevent worsening damage. Randomness of hailstorm occurrences was considered using hazard function which can be inferred from historical observations. Practical application of the proposed model is illustrated through case studies of two Australian states, coupled with comparative analyses highlighting key factors influencing cladding performance. The ability to account for stochasticity distinguishes the presented framework from existing deterministic approaches. [ABSTRACT FROM AUTHOR]

The response of structures under rapidly varying loads can be affected by strain rate sensitivity generally expressed using Dynamic Increase Factor (D I F). Current models for estimating the D I F in Reinforced Concrete (RC) structures are generally deterministic and have restricted applicability due to their dependence on limited experimental data resulting in bias. This paper overcomes these limitations by proposing three probabilistic models that quantify compressive and tensile concrete and steel D I F , accounting for the relevant uncertainties. The proposed models are based on existing deterministic models with the addition of probabilistic correction terms. Bayesian updating is employed to estimate the unknown model parameters using observational data from a large collection of experimental observations. The models incorporate model uncertainties stemming from assumed model form and (potential) missing variables through a model error term. The proposed probabilistic models are used to evaluate the reliability of RC structures under dynamic loads. As an illustration, the proposed probabilistic models are used to estimate the reliability of an example RC column under combined dynamic axial force and moment, and a RC column or beam under dynamic bending moments resulting in cracking. In the two examples, we consider the ACI 318-19 requirements for Ultimate Limit State (ULS) and Serviceability Limit States (SLS). In comparison to deterministic D I F models, the proposed probabilistic models yield enhanced predictive accuracy, presenting a practical and robust approach to assess the structural reliability under impact and blast loads. • Probabilistic models improve D I F estimation in RC structures. • Models account for aleatory and epistemic uncertainties. • Bayesian updating refines model parameters using experimental data. • Two case studies showcase practical application in RC column reliability analysis under dynamic loads. • Proposed models offer robust performance assessment for structures under impact and blast loads. [ABSTRACT FROM AUTHOR]

• A novel probabilistic method for evaluating the sustainability performance of reinforced concrete (RC) structures made with conventional and green concretes and subjected to carbonation is presented. • The method is based on the combination of life cycle assessment (LCA) and life cycle cost analysis (LCCA) methodologies. • The method takes into account the impact of climate change, which is illustrated for three locations with different types of climate. • It is shown that green concretes demonstrate superior sustainability performance compared to conventional concrete, both in terms of CO 2 emissions and costs, and that climate change does not affect that. The paper presents a probabilistic method based on two methodologies – Life Cycle Cost Analysis (LCCA) and Life Cycle Assessment (LCA), for evaluating the sustainability of reinforced concrete (RC) structures in terms of their costs and CO 2 emissions. The method considers the whole life of a RC structure by taking into account CO 2 initially embodied in its construction materials, the absorption of CO 2 by concrete due to carbonation during the service life of the structure, potential damage to the structure due to carbonation-induced corrosion of reinforcing steel that may require repairs, and relevant costs. Since there are numerous uncertainties associated with the calculation of CO 2 emissions and costs, a probabilistic approach is beneficial. The emphasis is made on RC structures made of the so-called "green concretes", in which Portland cement is partially replaced with supplementary cementitious materials such as fly ash and ground granulated blast-furnace slag. The issue of a changing climate is also addressed. The method is illustrated by assessing the sustainability of a multi-story RC carpark made of different concrete types at three different locations (London, Paris and Marseille) for present and future climate conditions. This assessment's results show that using green concretes leads to a major reduction in CO 2 emissions and a small decrease in the life-cycle cost of the carpark RC elements. The relative sustainability performance of green concretes slightly improves compared to Portland cement concrete for future climate conditions. [ABSTRACT FROM AUTHOR]

• A reliability-based design optimization under multiple simulation models is proposed. • An active learning function is proposed by estimating how updates on simulation model affect reliability. • A concept of activity function is proposed, which estimates how active constraint functions are. • The proposed active learning function is modified to apply to problems where the cost of each simulation model is different. • Two numerical and one engineering examples are investigated to validate the proposed method. This paper proposes an effective active learning strategy for reliability-based design optimization (RBDO) problems in which the constraint functions are acquired from multiple simulation models. To achieve this goal, a new active learning function (ALF) is derived by estimating the increased reliability of active constraint functions after adding one point to the train points of constraint functions in each simulation model. The proposed ALF distinguishes possibly active constraint functions that seem active near the current optimum and considers how the constraint functions are active. In the proposed RBDO method, a Kriging model is iteratively updated by adding the best point to the train points of constraint functions included in the crucial simulation model until the optimum converges and the Kriging model is sufficiently accurate. The best point and the crucial simulation model are obtained by comparing the proposed ALF. The ALF is further modified to apply to problems where the cost of each simulation model is different. To verify the effectiveness of the proposed method, two numerical and one engineering examples are analyzed. The results show that the proposed method efficiently and accurately obtains the RBDO optimum involving multiple simulation models, regardless of simulation cost. [ABSTRACT FROM AUTHOR]

• Both the maximum and residual deformation are essential for seismic safety especially in the near-field. • These parameters, especially to bidirectional shaking, are very sensitive to several factors. • Besides the computational challenges and the several parametric uncertainties, responses are widely scattered. • Using principles of mechanics, an order in response is established in a dimensionless and orientationally homogeneous format. • Deterministic predictive models are constructed and extended in probabilistic framework by the Bayesian regression. Both maximum and residual deformations are essential for seismic safety during and following strong earthquakes, especially in the near field. These parameters are often calculated per unidirectional analysis, albeit bidirectional analysis may be carried out for important systems with the availability of growing computational power. However, a pressing challenge in earthquake engineering that continues to exist in the face of several uncertainties is to represent these response statistics – essentially with wide dispersion - in an expressive and effective format. The present paper aims to represent the maximum and residual deformation to unidirectional and bidirectional shaking in a rational format, even when uncertainties in ground motion and structural characteristics are prevalent. To this end, a bridge pier with uncertain material parameters is subjected to a wide range of stochastically simulated near-field motions with forward-directive signature, and the responses are computed to unidirectional and bidirectional shaking. In an attempt to develop predictive models, the responses are regressed first in terms of primary parameters characterizing structural material and ground motions. Next, by standard principles of mechanics, the response is recast in a dimensionless and orientationally consistent format in terms of derived parameters. This reduces the number of independent variables yet connotes a sound basis of mechanics. The predictive model in terms of derived dimensionless parameters is further extended in the Bayesian framework to improve the predictive model in a probabilistic sense. [ABSTRACT FROM AUTHOR]

The design of transmission lines is based on the Load and Resistance Factor Design approach, considering that their collapse limit state is governed by climatic actions (wind and ice). Even so, accident reports indicate the regular observation of moderate to severe damage of towers after strong ground motions, affecting the structure's capacity to withstand future load events. Therefore, integrating the concepts of Performance-Based and Multi-Hazard Design, successfully applied to buildings and still embryonic to transmission lines, seems to be promising. With such performance-based multi-hazard approaches, intermediate performances can be evaluated even when they are controlled by a non-dominant hazard. Hence, the present paper aims at performing an original multi-hazard assessment of a Chilean 230kV transmission line segment. For this purpose, direct geometric and material nonlinear time history analysis, using a finite element suitable for eccentrically loaded angle profiles (L-shaped cross-sections), is employed to construct the fragility curves. In addition, uncertainties in loads and material properties are accounted for to address the transmission line system failure probability. In the existing literature, fragility analysis has been performed through pushover approaches, whereas reliability has been assessed for a single structure rather than for the transmission line system, as recommended by line codes. Contrary to design practice, the results show that seismic loads control all limit states in TLs located from central to northern Chile. Numerical results presented in this paper are based on 5000 h of total computation time. • Seismic + wind multi-hazard assessment of full transmission line segment. • Performance-based approach considering multi-hazard curves. • Direct geometric and material nonlinear time history analysis performed. • Several locations in Chile considered; for some locations. • Collapse LS controlled by wind, but serviceability and damage LS controlled by seismic actions. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of ranking correlated random variables according to relative importance. The importance of a variable derives from its influence on the variability of the response from a model. Applications include any input–output model for which response derivatives are available from each response analysis. Structural analysis models, i.e., finite element models, represent the specific motivation for this paper. The response derivatives are collected in a vector and transformed into a standardized parameter space. Points along that vector are transformed back to the original parameter space and utilized for the purpose of model insights and parameter ranking. Comparisons are made with the first-order Sobol sensitivity index, which requires sampling instead of the proposed single-analysis approach. Results suggest that the proposed importance measure matches the first-order Sobol index in many situations. However, for pure multiplicative "interaction" models, the first-order Sobol index tends to be anchored at the zero-correlation case. In contrast, the proposed measures are sensitive to correlation and the effect of correlation can be significant. [ABSTRACT FROM AUTHOR]

Highlights • A method is proposed to assess social risk associated with transportation networks. • Robust traffic assignment based on expected residual minimization is used. • An efficient, robust algorithm is developed to conduct robust traffic assignment. • The method is demonstrated through two illustrative examples. Abstract Climate change and population growth can affect the supply and the demand sides of transportation networks, respectively. Rational assessment of societal risk of transportation networks should consider these effects, both of which are uncertain in nature. In this paper, a novel method is proposed to assess societal risk of transportation networks subjected to uncertainties due to climate change and future population growth. The method is posited on a robust traffic assignment model using the expected residual minimization approach. A novel algorithm, combining smoothing method, quasi-Newton technique, and Latin hypercube sampling, is developed for the efficient implementation of the proposed method. The proposed method can produce a deterministic traffic flow pattern that deviates as little as possible from the traffic flow patterns associated with all future scenarios. The obtained traffic flow pattern can then be used to estimate societal risk of transportation networks. A number of examples, including a real-world highway bridge network in Camden County, New Jersey, are provided in this paper to demonstrate the efficiency, effectiveness, and application of the proposed method. It is found from the examples that (a) the proposed method is more efficient and robust than existing algorithms for robust traffic assignment under uncertainties, and (b) climate change and population growth can significantly alter the traffic pattern in a transportation network and thus increase the societal risk posed upon traffic users. [ABSTRACT FROM AUTHOR]

Highlights • Reliability analysis of LVL beams from juvenile hardwood plantation logs is given. • Relationship between the reliability index and resistance factors is investigated. • Stochastic load processes and various duration of load parameters are considered. • "Dead + Sustained LL" load combination governs the choice of the capacity factor. • Calculated resistance factors are lower than the ones used in Australian standards. Abstract This paper presents the reliability analysis of Laminated Veneer Lumber (LVL) beams manufactured from veneers recovered from early to mid-rotation (juvenile) subtropical hardwood plantation logs, with plantations established either for sawn timber applications or pulpwood production. While these logs have a high number of natural defects (knots, gum veins, grain deviation, etc.), are considered of low quality and have little to no commercial value, they produce high strength Veneered Based Composite products, such as Plywood and LVL. Yet, the reliability of these products is unknown. In this paper, the relationship between the reliability index and the capacity factors, also referred to as "resistance factors", used in design equations of such LVL beams in both edge and flat bending is investigated taking into account the load duration effects (damage accumulation). The relationship is presented for six different beam sizes, four grades and three hardwood species (Gympie messmate (Eucalyptus cloeziana), spotted gum (Corymbia citriodora) and southern blue gum (Eucalyptus globulus)) using the strength distribution of the beams recently quantified by the authors. Parametric studies on five main design load combinations stipulated in the Australian standard and three rates of damage accumulation, based on the data available in the literature, are conducted. Results show that the reliability index is highly sensitive to the damage accumulation rate and that the "Dead + Sustained and Extraordinary live loads" and "Dead + Wind + Sustained live loads" load combinations govern the choice of the capacity factor. Recommendations are made on the appropriate capacity factors to be used for various service categories of structures. The proposed capacity factors are found to be 5%–12% lower than the ones currently used in Australia for the LVL beams manufactured from mature softwood logs, as opposed to juvenile hardwood logs as in the proposed products. [ABSTRACT FROM AUTHOR]

Highlights • The paper addresses the problem of spatial variability in the degradation process. • A spatio-temporal random field model is proposed to address this problem with the details of its construction and simulation. • Inference procedure is developed for such spatio-temporal model • Estimation of quantities of interest used in the reliability analysis and maintenance. • The model is applied to numerical examples in one and two dimensional case. • The results show that the uncertainties are reduced, the inference procedure is improved. Abstract The objective of this work is to propose a spatio-temporal random field for assessing the effect of spatial variability on the degradation process in structural reliability assessment. Our model extends the classical Gamma process which is usually developed for degradation temporal variability concerns to integrate spatial variability and heterogeneity issues. A log-normal distributed spatial random scale is then introduced in the Gamma process. Mathematical models for a structure degradation in space and time and estimation procedures are developed in this paper. Approximations and simulations are given to evaluate the failure time distribution and to characterize the residual lifetime after inspection. Simulation results are performed using pseudo-random data based on Monte-Carlo simulations to fit the model and the inference of their parameters. The two proposed estimation method – Method of Moments and Pseudo Maximum Likelihood – are numerically compared according to statistical measures. The accuracy of the methods are also discussed by numerical examples given the approximations of quantities of interests. [ABSTRACT FROM AUTHOR]

Highlights • A generic framework for structural design optimization is presented. • The framework is combined with a life safety acceptance criterion. • Optimal and acceptable reliabilities for structural design are derived. • The application for component and system level design is discussed. • A clear relation to structural robustness is established. Abstract A common approach to define criteria to reliability performance of structures in the development of semi-probabilistic design codes and for probabilistic design of individual structures is to make use of the tentative target reliabilities provided in the JCSS Probabilistic Model Code. An acceptable level of life safety is, however, not guaranteed when applying the target reliabilities provided by the JCSS, as these have been derived based on monetary optimization. In the present paper, the underlying generic framework for structural design optimization is reviewed and extended for the derivation of life safety related target reliabilities based on the marginal lifesaving costs principle. The resulting minimum acceptable reliabilities may be used in combination with the JCSS target reliabilities to achieve designs that are both cost-efficient and consistent with societal preferences for lifesaving investments. The framework presented in this paper forms the basis for the target reliabilities defined in ISO 2394:2015, where the target reliabilities proposed by the JCSS have been combined with minimum acceptable reliabilities to ensure societal acceptability in terms of life safety. An extended discussion of the general framework and its underlying assumptions includes considerations about the application of the target reliabilities at component or system level, accounting for structural robustness, as well as implications for the interpretation of the main variables entering the framework. [ABSTRACT FROM AUTHOR]

In probabilistic durability design of concrete structures in marine environment, the limit state is defined as the corrosion initiation of reinforced steel. However, the owner may more concern the cracking growth of concrete surface or the first repair time without maintenance, in that case, additional information on surface deterioration should be supplemented to eliminate owner’s concern. This paper employs the two-dimensional simulation method to predict the surface deterioration process for reinforced concrete structures exposed to aggressive chloride environment. The spatial variability of concrete cover ( c ), chloride diffusion coefficient ( D a 0 ) and other durability parameters are considered in the simulation, and the effect of batch-production of concrete is accounted for in the spatial variation modelling of c and D a 0 . Taking the Hong Kong-Zhuhai-Macau sea-link project as an example, the paper evaluates the durability performance of the immerged tube tunnel over the expected service life, and compares a range of durability design specifications with different target reliabilities and combinations of c and D a 0 , in terms of the probability & extent of surface damage. With three maintenance levels prescribed by surface damage grade at intervention, the paper compares the intervention time of different durability design specifications. The results provide a comparative tool to aid designers in selecting design specifications to achieve owner-concerned durability objective. [ABSTRACT FROM AUTHOR]

This paper presents an advanced Bayesian emulation-based approach (hereafter BEA) that allows a reduced number of analyses to be carried out to compute the probabilistic seismic response and fragility of buildings. The BEA, which is a version of kriging, uses a mean function as a first approximation of the expected Engineering Demand Parameter given Intensity Measure (EDP|IM) and then models the approximation errors as a Gaussian Process (GP). A main advantage of the BEA is its flexibility, as it does not impose a fixed mathematical form on the EDP|IM relationship (unlike other approaches such as the standard cloud method). In addition, BEA makes fewer assumptions than standard methods, and provides improved characterization of uncertainty. This paper first presents the BEA approach and then assesses its computational efficiency as compared to the standard cloud method. This is done through the creation of EDP|IM relationships and fragility functions using the outputs of nonlinear dynamic and nonlinear static analyses for two case-study buildings representing Pre- and Special-Code seismic vulnerability classes. The nonlinear dynamic and static analysis methods represent different levels of accuracy i.e., are of high and low fidelity, respectively. The BEA and standard cloud methods are compared in their ability to recreate three “pseudo-realities”, each represented by an artificially generated EDP|IM relationship derived from a large set of analysis runs. Several input configurations are tested, including, reduced sets of training inputs (analysis runs), training inputs of high and low fidelity, two sampling processes for these inputs (i.e., random and stratified sampling) and two different IM representations. The results demonstrate that BEA yields both an improved accuracy in terms of mean estimates, as well as smaller uncertainty bounds compared to the cloud method. The improved performance of the BEA is maintained for all “pseudo-realities” tested regardless of whether it is trained with high or low fidelity analysis data, with the improvement particularly pronounced in cases when the advanced IM I Np is used. It is demonstrated that good accuracy can be achieved with BEA even with reduced samples, yielding a saving in 25% in number of analyses required to generate the EDP|IM relationship. Finally, the use of BEA drastically improves both the accuracy and efficiency of the resultant seismic fragility functions. [ABSTRACT FROM AUTHOR]

In recent years, a rapid pace of climate change is becoming evident by a marked increase in the frequency and intensity of weather extremes, and this trend is expected to continue with an increase in global warming for decades to come. The paper presents the non-homogeneous Poisson process as a basis to model an environmental load process induced by non-stationary climate conditions. The distribution of maximum load generated by a non-stationary process is derived, which explicitly accounts for the loading frequency and intensity amplification over time. Using this distribution, structural reliability can be computed for any given time interval in future. The paper shows that traditional measures like the return period, extreme percentiles, and the annual probability of failure, would vary with time under the changing climate. Examples presented in the paper show that a modest amplification of the load magnitude has a drastic negative effect on reliability than that of the frequency of loading. Probabilistic models presented in this paper will be useful in revising currently used "stationary" design codes and ensuring a consistent level of safety in the non-stationary climate. • Non-homogeneous Poisson process for non-stationary reliability analysis. • Consideration of time-dependent frequency and intensity of applied loads. • An accurate, finite time solution for the non-stationary extreme load distribution. • The concept of the return period is not useful in the changing climate. • A modest load amplification has a major negative effect on reliability. [ABSTRACT FROM AUTHOR]

• The improvement of existing stochastic perturbation (SP) method. • Transform the SP method into non-intrusive format by divided-difference method. • Efficiently solving higher-order perturbation and multidimensional random problem. Most stochastic problems are based on the independent and symmetrically distributed random variables. Using this principle, in this study, we propose an efficient calculation scheme to obtain the statistical moments based on high-order stochastic perturbation (SP) expansion. This solves the long-existing problem of the SP method, namely, the low calculation efficiency of statistical moments using high-order perturbation expansion, and the complexity of the calculation format. The scheme involves adopting the divided-difference method to approximate the partial derivative items of the SP method. The proposed method, which is similar to the collocation point method, only requires the deterministic calculation result for each node in the divided-difference method. In addition, as the adoption of high-order perturbation expansion is limited in multidimensional random problems due to the curse of dimensionality, an adaptive partial derivative items selection method is proposed in this paper to efficiently and reasonably ignore the expansion items that have an insignificant influence on statistical moments. This considerably improves the calculation efficiency of the statistical moments. Finally, the adaptive divided-difference perturbation (ADDP) method proposed in this paper is compared with the quasi-Monte Carlo method and the adaptive sparse grid methods using three numerical examples. The results prove that the ADDP method not only has high efficiency but also leads to significant improvements in the accuracy of statistical moments. [ABSTRACT FROM AUTHOR]

Reconstructing the probability density function (PDF) of the limit state function (LSF) is regarded as a non-intrusive method for forward uncertainty propagation and reliability analysis. In this paper, a novel non-parametric density estimation method is proposed to derive the unknown distribution of the LSF for this purpose, where the efficiency and accuracy are ensured. The main innovation of the paper is to derive the PDF of the LSF via a novel concept, i.e., the harmonic transform, regardless of the complexity of the problem. First, the non-parametric method for PDF estimation based on complex fractional moments/Mellin transform is briefly revisited, where the limitations are also pointed out. Inspired from Mellin transform, the concept of harmonic transform is put forward, which overcomes the disadvantages of Mellin transform. Then, the unknown PDF is recovered via the inverse harmonic transform, where the analytical formula is derived accordingly. Numerical estimation method is also given for practical implementations, where some critical issues are also pointed out. Detailed step-by-step procedures of the proposed method are also outlined. The proposed method is a non-parametric one since it does not require a distribution model in advance. Some commonly-used distributions are first applied to validate the efficacy of the proposed method. Then, four numerical examples involving different types of problems are extensively investigated to validate the proposed method for forward uncertainty propagation and reliability analysis. The results demonstrate that the proposed method is effective for deriving the PDFs for both static and dynamic reliability analyses with nonlinear explicit or implicit LSFs. • A novel concept, named as harmonic transform, is proposed. • A non-parametric density estimation method is established. • The proposed method can recover the unknown distribution with irregular shape. • The proposed method outperforms Mellin transform and other reliability analysis methods. [ABSTRACT FROM AUTHOR]

For stochastic dynamical systems with multiple uncertain parameters, it is often of interest to detect which parameters are dominant, in which the global sensitivity analysis may be one of the common means. To measure the global sensitivity in both qualitative and quantitative terms, it is of significant importance to adopt a global sensitivity index with sufficient quantification information. The Fréchet-derivative-based global sensitivity index (Fre-GSI) proposed by Chen et al. (2020) is appropriate to this goal. The present paper aims to provide new aspects of the Fre-GSI, including: (1) The numerical solution of the Fre-GSI given by Chen et al. (2020) is investigated in both analytical and numerical aspects; (2) A novel global sensitivity evolution equation is derived from the generalized density evolution equation, thus the Fre-GSI can be estimated by directly solving the global sensitivity evolution equation, rather than repeatedly solving the generalized density evolution equation as suggested in Chen et al. (2020). Numerical examples are studied to illustrate the efficiency and accuracy of the proposed approach. Some problems to be further studied are also outlined. • Numerical solution of the Fréchet-derivative-based global sensitivity is studied. • A global sensitivity evolution equation is derived. • High efficient numerical algorithm for solving the evolution equation is proposed. • The accuracy and efficiency of the method is validated by engineering examples. [ABSTRACT FROM AUTHOR]

• Using surrogate models for uncertainty propagation in bridge buffeting is efficient. • Sensitivity analysis is used to determine critical parameters on buffeting response. • Surrogate models are validated via comparison with direct Monte Carlo simulations. • Wind-induced fragility of a long-span bridge is analyzed under three wind climates. Buffeting of long-span bridges caused by the wind turbulence could result in problems of large deformation, fatigue, traffic safety and user comfort. The calculation of buffeting responses is greatly affected by multiple uncertainties, especially the randomness of flutter derivatives and structural damping. In buffeting analysis, these uncertainties are typically propagated using the brute-force Monte Carlo (MC) method, which requires enormous computational resources for a complicated structure involving multiple uncertainties. This study develops an efficient framework based on surrogate models to account for these uncertainties in buffeting responses and the assessment of structural fragility in a mixed climate. Two surrogate models, Kriging and polynomial chaos expansions (PCE), are applied in this framework. Comparison with the direct MC method shows that the Kriging model rather than the PCE model is the proper surrogate model, and the surrogate model contributes significantly to saving computing time from 17 h to 1 min for MC simulations. It is also observed that uncertainties propagated from structural parameters to responses will be more notable as the wind speed increase. Buffeting fragility curves of this bridge show that it's easier for responses in acceleration to achieve and exceed thresholds, indicating that performance related to user comfort might not be satisfied. By introducing the probability distributions of non-typhoon and typhoon winds at the site of the bridge, it is found that considering single climate may underestimate structural risk. The framework based on surrogate models in this paper can be further generalized to additional PBWE frameworks addressing different wind and structural engineering issues. [ABSTRACT FROM AUTHOR]

The appropriate assignment of gravity live loads is of fundamental importance in establishing a design base for safe and economical structures. This paper presents a critical review of the probabilistic modelling of live loads in buildings, providing a historical overview of the theoretical models found in the literature, as well as the load surveys that provided the empirical evidence for their development. As a general rule, these models divide the live load into sustained and extraordinary components, represented as a Poisson square wave and spike processes, respectively, with the differences lying in the underlying hypotheses and process parameters. A comparison of different models is presented, and it is shown that the model parameters currently in use in background documents on the reliability of the Eurocodes do not agree well with survey data, leading to an overestimation of extreme loads. While the Eurocodes lack clear specification regarding the exceedance probability for design loads, this study demonstrates, using a model with modified parameters, that the office design load corresponds to an approximate 27% exceedance probability over 50 years for a reference area of 20 m 2. The impact of employing this model on the reliability-based calibration of the Eurocode partial safety factors for loads is also examined, and it is found that the average reliability falls somewhat below the prescribed 50-year target reliability index of 3.8. [Display omitted] • An overview of the available survey data on live loads is presented. • JCSS and Eurocode live load models are discussed, and modified parameters are suggested. • Eurocode office design load has a 50-year exceedance probability of ∼ 27 % for A = 20 m 2 . • The impact on calibration of the Eurocode partial safety factors for loads is investigated. • The 50-year target reliability index of 3.8 is found to be incompatible with the suggested live load model. [ABSTRACT FROM AUTHOR]

• Bayesian Networks allow modeling spatial variability in aging steel bridges. • An algorithm has been developed to generate a Bayesian Network (BN) automatically. • The methodology provides excellent versatility for FEM-based probabilistic modeling. • Multiple random variables can be considered with a moderate computational cost. • The methodology has been implemented on a severely damaged riveted steel bridge. Finite Element (FE) modeling often requires unavoidable simplifications or assumptions due to a lack of experimental data, modeling complexity, or non-affordable computational cost. One such simplification is modeling corrosion phenomena or material properties, which are usually assumed to be uniform throughout the structure. However, e.g., corrosion has a local nature and severe consequences on the behavior of steel structures that should not be overlooked. To improve the current numerical modeling techniques in aging steel bridges, this paper proposes a Gaussian Copula-based Bayesian Network (GCBN) approach to model the spatial variability of structural element properties. Accordingly, a study of the automatic Bayesian network generation process is first conducted. Subsequently, the methodology is applied to a severely damaged riveted steel bridge built in 1897. The results show that the methodology has excellent flexibility for generating properties variability in FE models at a low computational cost, thus ensuring its practical feasibility and robustness for accurate numerical modeling. [ABSTRACT FROM AUTHOR]

To address the challenges of reliability analysis in high-dimensional probability spaces, this paper proposes a new metamodeling method that couples active subspace, heteroscedastic Gaussian process, and active learning. The active subspace is leveraged to identify low-dimensional salient features of a high-dimensional computational model. A surrogate computational model is built in the low-dimensional feature space by a heteroscedastic Gaussian process. Active learning adaptively guides the surrogate model training toward the critical region that significantly contributes to the failure probability. A critical trait of the proposed method is that the three main ingredients–active subspace, heteroscedastic Gaussian process, and active learning–are coupled to adaptively optimize the feature space mapping in conjunction with the surrogate modeling. This coupling empowers the proposed method to accurately solve nontrivial high-dimensional reliability problems via low-dimensional surrogate modeling. Finally, numerical examples of a high-dimensional nonlinear function and structural engineering applications are investigated to verify the performance of the proposed method. • Novel metamodeling method for high-dimensional reliability analysis. • Reduced features of a high-dimensional model are adaptively identified. • Heteroscedastic GP handles variabilities from reduced feature mapping. • Superior performance compared with existing reliability methods. [ABSTRACT FROM AUTHOR]

The condition of flood defence revetments is influenced by many different degradation processes such as animal burrowing, rutting and growth of weeds. Many of these processes are shock-based rather than progressive continuous. As shocks can cause a drop in performance, this means that the condition of a revetment can suddenly decrease, meaning that revetments can have significant initial damage at the beginning of a storm. Combined with the limited detection probability of common visual inspections of flood defences, this can have a significant influence on the reliability of flood defence systems, something typically not considered in reliability analysis. In this paper we study the reliability of a flood defence system subject to shock-based degradation. Various maintenance concepts are compared for a case study of a riverine flood defence of 20 kilometres length. This demonstrates that the current maintenance concept is insufficient to satisfy the reliability requirements for failure of the revetment. Overall, the joint influence of degradation and the existing maintenance concept leads to a 20 times higher failure probability estimate compared to a typical assessment without these aspects. Next, we demonstrate that both additional inspections, and targeted interventions to reduce the impact of for instance animal burrowing, can significantly reduce total cost and improve robustness of the considered flood defence system. • Influence of shock-based degradation on reliability of flood defences is considered. • Shock-based degradation is modelled using a Dynamic Bayesian Network. • Failure probability can be underestimated by a factor 20 if degradation is ignored. • Increasing frequency of inspections increases robustness and reduces total cost. • Targeted structural interventions are efficient in reducing the impact of degradation. [ABSTRACT FROM AUTHOR]

• Probabilistic time-dependent models of durability parameters with both variance and bias considered. • Relationship between measurement plan of exposure trials and accuracy of calibrated chloride ingress model of concrete. • Design method of measurement plan targeting accuracy requirement of calibrated model. • Design method of measurement plan works for both linear fitting and Bayesian updating for model calibration. Surface chloride concentration (C S) and chloride diffusion coefficient (D Cl) are key parameters for durability assessment of concrete structures in marine environment; they are time-varying and highly dependent on the exposure condition. To reasonably model their behaviors at a specific location, durability measurement data are often needed to calibrate the apparent chloride ingress model based on Fick's second law. In view of the significant variability of measurements and the bias of chloride ingress model, it remains unaddressed how to formulate a measurement plan to make the calibrated model achieve the required accuracy. This paper first establishes the probabilistic time-dependent models of C S and D Cl with both sample variance and model bias considered, and then introduces the Bayesian method to update the two models using measurement data. By assuming realistic models of C S and D Cl and comparing them with updated ones, the effectiveness of Bayesian updating method is demonstrated, and the key factors affecting the updated model accuracy are discussed, including prior estimate of parameters, model bias and measuring times. On this basis, a determination method of measurement plan targeting the calibrated model accuracy is proposed, which works for both Bayesian updating and linear fitting for model calibration. And finally numerical examples are presented to show the validity of the proposed method. The sample size obtained by the proposed method is exact for linear fitting and slightly more than required for Bayesian updating. [ABSTRACT FROM AUTHOR]

It is well established that various sources of uncertainties play a critical role in the safety assessment of engineering structures. Some widely used frameworks, such as performance-based earthquake engineering (PBEE), explicitly consider the ground motion record-to-record randomness, while the material and modeling uncertainty remain to be primarily based on judgments or limited analysis. This paper presents the results of a comprehensive uncertainty quantification and sensitivity analysis of a reinforced concrete structural component. First, different modeling strategies are adopted to develop several parent models. Next, various sources of uncertainty are propagated through the parent models to generate thousands of children models. The children models are further combined with material uncertainty to produce grandchildren models, and nonlinear transient simulations are conducted using an innovative artificial acceleration at different seismic intensity levels. The results are post-processed using a range of probabilistic, statistical, and machine learning methods. The study finds that the modeling strategy and its associated variability can cause significant bias and dispersion in the drift response, while material uncertainty has a relatively minor effect. The study quantifies the importance of modeling uncertainty, which is often overlooked in engineering practice. • Proposing a framework for epistemic uncertainty quantification at the component level. • Exploring the separate and combined effects of modeling and material randomness. • Employing an innovative intensifying artificial acceleration for dynamic simulations. • Performing a detailed machine learning-based sensitivity analysis. [ABSTRACT FROM AUTHOR]

Partially or fully restrained steel moment connections are essential constituents of lateral force resisting moment frames. The constituents of the moment connection system – bolts, welds, plates and angles – are sized using their individual force demands by a limit state element-based load and resistance factor design procedure. The system reliability of the connection as a whole, which must be commensurate with reliabilities of adjoining frame components, has not been adequately investigated in the literature. This paper presents a methodology to determine the system reliability of commonly used steel moment connections that have been designed according to current element based procedures. A general expression is derived for a system factor that modifies element resistance factors to meet a specified system reliability target, as a function of the element's relative importance within the system, and associated uncertainties. Uncertainties in element capacities (including their mutual dependence) and system demands are considered. The approach can be used to rationalize element design equations to achieve system reliability targets for the connection system. A detailed numerical example and a set of parametric studies on a partially restrained moment connection with angle supports at top and bottom beam flanges are presented. The results suggest the existence of beneficial system effects in current AISC provisions for the design of partially restrained moment connections. • A novel system reliability design approach for steel connections is presented. • System to element reliability surfaces are constructed using nonlinear analysis. • An analytical expression for system design factor is derived. • A detailed example demonstrating potential application in design is provided. • Conservatism in current AISC design approaches results in system factor¿1.0. [ABSTRACT FROM AUTHOR]

• A mixed Bayesian Network-based reliability assessment framework is developed. • Time-variant environment and 2D chloride ingress are considered in the framework. • Finite element model is employed to improve reliability assessment. • Different Bayesian Networks are connected by pinch point nodes and soft evidence. • A real-world example is adopted for the reliability assessment of RC beams. Under environmental action, reinforced concrete (RC) structures might suffer from reinforcement corrosion caused by the surrounding environment, dramatically reducing structural reliability and threatening social development. However, most of the existing reliability assessment methods for RC structures only focused on the structural performance at the design stage given the original unchanged environment, ignoring the effects of realistic exposure conditions and inspection results on reliability evaluation. Thus, this paper develops a general reliability assessment framework based on a Mixed Bayesian network (MBN), incorporating three modules, i.e., durability assessment, load-bearing capacity analysis, and time-dependent reliability analysis. In MBN, separate sub-BNs are built based on different modules and connected by pinch point variables where probabilistic information is transmitted via soft evidence. Besides, this framework considers time-dependent environmental parameters and two-dimensional chloride transport and their effects on reliability. Meanwhile, adjustment coefficients are applied to improve the results of the analytical mechanical model with respect to different limit states through the finite element model (FEM). The proposed MBN framework is illustrated for a corroded RC beam under a marine atmospheric environment to investigate the effects of environmental modeling, chloride transport patterns, and concrete crack inspection on reliability assessment. The results indicate that under the assumed conditions in the case study, early inspection of large cracks may significantly overestimate the failure probability by about 500%. Besides, failure probability might be underestimated by about 95%, ignoring the time-variant environment and two-dimensional chloride transport. [ABSTRACT FROM AUTHOR]

• A novel method is proposed for GRS of system with multiple failure modes. • GRS of system is transformed into a multivariate Gaussian integral problem. • Bayesian inference is used to analytically approximate the intractable integral. • The proposed method can provide a closed-form system-level GRS analysis. Global reliability sensitivity analysis aims at quantifying the effects of each random source on failure probability or reliability over their whole distribution range and is highly concerned in reliability design and uncertainty control. And in practice, a structure or product usually has more than one component impacting their performance safety, which is essentially a system reliability problem. Therefore, this paper proposes a novel Bayesian-inference-based method for moment-based global sensitivity analysis of system reliability with multiple failure modes. First, the limit-state function of each component involved in the system is linearly approximated based on the reliability index. Then, the global reliability sensitivity is transformed into a problem of multivariable Gaussian probability within a given safe region where the dimension number is double of the failure modes. In this case, the Bayesian-inference-driven expectation propagation technique is introduced to solve this intractable problem in an analytical manner, based on which the closed-form solution to the global reliability sensitivity for system with multiple components is accordingly derived. Finally, a numerical case, a vehicle subjected to impact, a cantilever beam and a practical engineering application to a four-panel spaceborne deployable plane antenna are studied to demonstrate the effectiveness of the proposed method by comparison with Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient solution for solving hybrid reliability problems involving random and interval variables. To meet this aim, using the soft Monte Carlo (SMC) method, a solution is proposed that breaks the random variables space into local 1-D coordinates and then, considers 1-D coordinate as an additional dimension of interval variables. Accordingly, using an optimization in increased interval variables space, the upper and lower bounds of failure probability for each 1-D problem are estimated. In addition, the total failure probabilities are presented as the mathematical expectation of the obtained probability bounds for 1-D coordinates. Then, it is shown that this approach is fit for application of univariate dimension reduction method to reduce the function calls of analysis in the optimization phase. This approach is validated by solving benchmark reliability problems as well as the application of the proposed method for solving real world engineering problems investigated by solving hybrid reliability analysis of reinforced concrete columns. It is shown that the proposed approach efficiently approximates the failure probability bound of problems with moderate nonlinear limit state functions with high accuracy. • Developing a robust hybrid reliability framework without an optimization block. • Capturing both random and interval variables via coupling UDR and soft MCS methods. • Accurate/efficient estimation of upper and lower bounds with hybrid reliability tool. • Both mathematical and engineering problems are validated using hybrid technique. [ABSTRACT FROM AUTHOR]

• A probabilistic model for the spatial distribution of heavy vehicles on the bridge deck is proposed. • The methodology is developed for vehicle scenarios associated with the maximum effect of long-span bridges. • The proposed model is able to take into account the stationarity of vehicle distribution for different effect types. • A simulation example is given based on the site-specific WIM data, and the response results are compared with those calculated by load models from different national design codes. The traffic scenarios that may cause extreme load effects are of great importance to the safety assessment of bridge structures. The traditional simulation method of traffic flow cannot depict the distribution pattern of vehicles on the bridge deck when the maximum effect is induced. In this paper, a probabilistic Gaussian mixture model (GMM) for heavy vehicle scenarios on the bridge deck under free-flow condition is proposed for long-span bridges based on collected Weigh in Motion (WIM) data. The scenarios of extreme response under free-flow occur more frequently than congestion scenarios and are of similar value and relevance in the daily management and safety assessment of long-span bridges. A non-stationary Poisson process is utilized to simulate the uneven occurrence of heavy vehicles in different lanes, and it is assumed that they are located within the artificially defined cells on the bridge deck. Then, Nataf transformation is employed to consider the correlation of gross vehicle weights (GVWs) within close range in the same lane. The numerical study is carried out on a long-span cable-stayed bridge to investigate the effects of correlation in GVWs and stationarity of vehicle distribution location on the structural responses. The load responses calculated by the proposed model and Monte Carlo method for different effects are compared with the values derived from code model. The results show that with the increase of the correlation level of the neighboring GVWs, the simulated responses are more prone to get extreme values, which means an increasing probability of the most unfavorable spatial distribution of on-bridge vehicles. The same results are also found under the non-stationary simulation state for vehicle location. The non-stationary Poisson process provides an efficient, highly feasible method, which is also in the safe side, for simulating the vehicle spatial distribution for specific effects. [ABSTRACT FROM AUTHOR]

Bridge owners worldwide manage large numbers of assets with limited budgets through risk assessments, using asset-specific data. However, when managing a large stock of aging assets, maintaining robust and up-to-date data records can be challenging. This issue comes to the fore when trying to understand asset vulnerability to current and future weather events in the context of a changing climate. By using a sample of data on railway bridges in the UK, this paper explores uncertainty associated with raw data used in bridge scour risk assessments for bridge stocks and its interaction with climate change uncertainty. Results indicate that our ability to foresee climate change impacts is not only limited by the aleatory uncertainty of climate change projections; avoidable uncertainty in basic asset data can outweigh aleatory uncertainty by an order of magnitude. Some parameters, such as floodplain width and the width of abutments, were found to be both subject to high uncertainty and also very influential for the estimation of scour risk, leading to reduction in the confidence in scour risk assessments. This finding contrasts with the unchallenged assumption in the field that dimensions of bridge elements are not associated with uncertainty. The nature of scour implies that a potential increase in the frequency and severity of extreme weather events will increase scour risk. This paper shows that in order to be able to understand and account for this increase, scour management processes must effectively address data uncertainty. Active measures to control data quality would be an effective step towards understanding and managing bridge resilience in the context of current and future climatic conditions. [ABSTRACT FROM AUTHOR]

Part I of this two-part paper introduced a building portfolio recovery model (BPRM) to forecast the stochastic recovery process of building portfolios within a community following an extreme hazard event. The BPRM models restoration of individual building-level functionalities as a discrete state, continuous time Markov Chain, while it models portfolio-level recovery by aggregating the building-level restoration processes in both temporal and spatial dimensions. In this paper, we illustrate the implementation of the BPRM to project the building portfolio recovery of a mid-size community following a predefined scenario earthquake. The recovery analysis integrates the engineering process of building reconstructions with available community resources and social-economic characteristics of different population groups. The spatial variations in recovery speed in different residential zones within the community reflect the disparities in resourcefulness and recoverability of homeowners with different social and economic status. In addition, sensitivity studies are performed to investigate the capability of the BPRM to quantify the impact of candidate pre-disaster mitigation strategies on the building portfolio recovery time and trajectory, illustrating the potential use of the BPRM in supporting risk-informed community resilience planning. [ABSTRACT FROM AUTHOR]

• An augmented step size adjustment (ASSA) method is proposed to boost the iterative process of reliability analysis. • A fire-new strategy is established to identify the oscillation during iterative process and define the iterative step size. • The ASSA method is proven to achieve a well efficient and robust performance for RBDO problems. Heavy computational burden has been one of the largest barriers to the application of reliability-based design optimization (RBDO) in real-world structures. The key difficulty of RBDO lies in how to perform reliability analysis efficiently and robustly. In performance measure approach (PMA)-based RBDO, the reliability analysis process searches for the minimum performance target point (MPTP) with the target reliability index in standard normal space. Many methods have been proposed to improve the efficiency and robustness of the PMA. However, these methods may face the convergence problem for highly nonlinear constraint functions; or high computational cost for weakly nonlinear ones. More importantly, most existing methods are very sensitive to the selection of algorithm parameters. In this paper, an augmented step size adjustment (ASSA) method is proposed to boost the iterative process in terms of both efficiency and robustness. According to the relative positions of the direction vector and negative gradient direction and the angle between them at each iterative point, a fire-new strategy is established to identify the oscillation during the iterative process and define the iterative step size. Seven inverse reliability analysis problems and three RBDO benchmarks are used to validate the performance of the ASSA method. The results indicate that the ASSA method has wide applicability for nonlinear constraint functions and achieves efficient and robust performance. Furthermore, the results demonstrate that the ASSA method can be regarded as a reliable and effective method for addressing PMA-based RBDO problems. [ABSTRACT FROM AUTHOR]

• Random exploration of the management policies can be catastrophic under the risk of extreme events. • We propose model-free deep reinforcement learning approach with safe exploration. • Our results show promise in finding near-optimal management policies without random exploration. • We apply the method on modeling resilience of infrastructure systems to extreme events. Extreme events represent not only some of the most damaging events in our society and environment, but also the most difficult to predict. Model-based predictions of the disruptions induced by extreme events on urban infrastructure systems are often unreliable, as these events are unlikely by their very definition. Specifically, characterizing the effect of such disruptions to the urban infrastructure using a parameterized model is a difficult task. On the other hand, model-free approaches based on recent advancements in reinforcement learning can model the complex dynamics of urban society and infrastructure under the risk of extreme events explicitly without relying on any specific physics-based mechanism. However, these approaches usually require performing random exploration of the effects of management actions on the system (typically in the post-event situation) to allow for an acceptable approximation to the optimal management policy. When dealing with costly infrastructure systems and important communities, this random exploration can be unacceptable and risky. In this paper, we propose a method called Safe Q-learning, which is a model-free reinforcement learning approach with addition of a model-based safe exploration for near-optimal management of infrastructure system pre-event and their recovery post-event. Our method requires the decision-maker to model the structure of the state space of the problem, and a suitable equilibrium of the system (optimum functionality pre-event). This information is usually available for urban systems, as they spend long time in optimum equilibrium before the occurrence of such events. We show on several examples of infrastructure management how the proposed approach is able to achieve near-optimal performance without the risk due to random exploration. [ABSTRACT FROM AUTHOR]