Structural Reliability Methods Research Articles

Development of methods of structural reliability

The growth of structural reliability theory and applications, along with a recognition of its role in guiding the structural engineering profession in addressing some of the most important issues in design of the built environment, represents one of the key engineering achievements during the past five decades. Structural reliability provides a unifying framework for managing uncertainties affecting performance of structures and a quantitative link between the practice of structural engineering and its social consequences. Such links perhaps are most obvious in probability-based codified design and performance evaluation but there are numerous other applications, which are summarized in this special issue. As the field has matured, researchers in reliability have worked with structural engineers to elevate both the practice of structural engineering and the quality of research to levels that otherwise would not have been possible. The Joint Committee on Structural Safety has played a central role in this historic development and it will inspire future opportunities for the reliability community to build upon past successes to improve structural engineering and construction practices. This paper surveys the key theoretical developments and milestones that enable these opportunities.

Potential secondary seals within overburden: Observation from the CO2 storage sites Aurora and Smeaheia, northern North Sea

This study evaluates potential secondary seals within the overburden in two CO2 storage sites, Aurora and Smeaheia within the Horda Platform area, of the northern North Sea. Secondary sealing intervals provide for safe and reliable CO2 storage as they prevent injected fluids from migrating into the atmosphere in the case of primary seal failure. This study analyzes the possible fate of the CO2 plume in the case of primary seal failure for the Aurora and Smeaheia CO2 storage sites by evaluating the secondary caprock and sealing potential of polygonal fault systems within the overburden intervals using structural reliability methods. Our findings suggest that a ductile secondary caprock is present in the overburden intervals of the storage sites, which could act as a secondary seal in the case of primary seal failure. The trapped hydrocarbon leaked from the Troll field within this ductile unit indicating a good secondary sealing potential. The study also reveals the presence of polygonal fault systems in the entire study area, but their frequency and orientation vary between layers. However, polygonal fault systems are not structurally stable, posing a risk of fault-parallel flow within the overburden interval. Nonetheless, the ductile clay-rich secondary caprock provides a seal for the polygonal fault systems within the interval. Due to either erosion or non-deposition, the ductile rock interval is not present in the east of the study area. As such, the critical risk for the Alpha structure in the Smeaheia injection site is the Vette fault and the efficiency of the primary Draupne caprock. Moreover, the crucial factor in the western Aurora site is the connectivity between the depleted Troll reservoirs and the CO2-injected pressurized reservoirs underneath. Based on our qualitative assessment, it is concluded that the overburden interval in the Horda Platform has adequate secondary sealing potential to hold and accumulate CO2 in the case of primary seal failure. Still, further numerical simulations are recommended to quantify our findings for both the Aurora and Smeaheia sites.

Energy harvester reliability study by Gaidai reliability method

AbstractThis study validates a novel structural reliability method, particularly suitable for high‐dimensional green energy harvesting device dynamic systems, versus a well‐established bivariate statistical method, known to accurately predict two‐dimensional system extreme response contours. Classic reliability methods dealing with time series do not always have an advantage of dealing easily with dynamic system high dimensionality, along with complex cross‐correlations among different system components. Energy harvesters constitute an important part of modern offshore green energy engineering; hence, proper experimental study along with safety and reliability analysis are of practical design and engineering importance. To study the performance of galloping energy harvesters, a series of laboratory wind tunnel tests have been conducted, selecting different wind speeds. This study illustrates the usage of the advocated novel reliability method, by analyzing bivariate statistics of experimental galloping energy harvester's dynamics. The bivariate statistics was extracted from available experimental results, more specifically for the device's voltage‐force dataset. Advantage of the proposed methodology being that relatively short experimental data record may still yield meaningful design results, provided proper statistical methods have been applied. Safety and reliability are important engineering concerns for all kinds of green energy devices. In the case of measured device's structural response, an accurate prediction of system failure or damage probability is possible, as illustrated in this study. Distinctive advantage of advocated novel semi‐analytical reliability methodology being the fact that it can tackle dynamic systems with practically unlimited number of dimensions (or components), along with complex nonlinear cross‐correlations between different system key components.

4400 TEU cargo ship dynamic analysis by Gaidai reliability method

Modern cargo vessel transport constitutes an important part of global economy; hence it is of paramount importance to develop novel, more efficient reliability methods for cargo ships, especially if onboard recorded data is available. Classic reliability methods, dealing with timeseries, do not have the advantage of dealing efficiently with system high dimensionality and cross-correlation between different dimensions. This study validates novel structural reliability method suitable for multi-dimensional structural systems versus a well-established bivariate statistical method. An example of this reliability study was a chosen container ship subjected to large deck panel stresses during sailing. Risk of losing containers, due to extreme motions is the primary concern for ship cargo transport. Due to non-stationarity and complicated nonlinearities of both waves and ship motions, it is challenging to model such a phenomenon. In the case of extreme motions, the role of nonlinearities dramatically increases, activating effects of second and higher order. Moreover, laboratory tests may also be questioned. Therefore, data measured on actual ships during their voyages in harsh weather provides a unique insight into statistics of ship motions. This study aimed at benchmarking and validation of the state-of-the-art method, which enables extraction of the necessary information about the extreme system dynamics from onboard measured time histories. The method proposed in this study opens up broad possibilities of predicting simply, yet efficiently potential failure or structural damage risks for the nonlinear multi-dimensional cargo vessel dynamic systems as a whole. Note that advocated novel reliability method can be used for a wide range of complex engineering systems, thus not limited to cargo ship only.

A reliability-base method for thermal cracking prediction in asphalt concrete

This study focuses on understanding the impact of environmental factors that contribute to the deterioration and damage of Hot Mix Asphalt (HMA) pavements. One significant problem faced by HMA pavements is transverse (thermal) cracking, which refers to the formation of cracks perpendicular to the centerline of the pavement. Over the past few decades, researchers have put significant effort into analyzing and understanding how thermal cracking affects HMA pavements. Mechanistic-empirical models play a crucial role in this process, but they require a substantial amount of input data related to the pavement's structural and material properties. Obtaining this data can be done through various methods with different levels of quality, which affect the reliability of the pavement performance responses. The probabilistic base designs and specifications can consider the variation of input data and the impact of material and structural together with environmental parameters on pavement deterioration. In this project, transverse cracking, as one of the major asphalt concrete pavement cracking, particularly in the freezing areas, will be studied, and a reliability-based method will be introduced. To reach this goal, the long-term pavement performance (LTPP) database was used. A regression model from the key parameters of pavement material and structural properties and environmental and traffic indicators was generated. Then through the structural reliability method, the probability of overpassing of transverse cracking amount from the threshold for a pavement design was assessed.

A Research Paper on Study of Hydraulic Bridge

Abstract: Hydraulically assisted bridge a new concept in bridge design which incorporates an in integrated hydraulic system into the bridge in order to carry more weight. The system is most suitable for arch based bridge in which the main forces are directed in a horizontal sideways direction. Predication of the risk to build in infrastructure posed by climate and land use change have suggested that bridge. collapses may increase due to more frequent or intence flooding. Assessment of the united state often assume that bridges may Collapse when the 100year flood occurs but this Assumption has not been fally tested due to lack of comprensize collapse record 35 bridge. for which a stream gauge 35 bridges for which a stream gauge on or near the bridge recorded. The flow during total or partial collapse were identified and used to test this assumption. Flood frequency analyses, and used to test this assumption. Flood frequency analyses, and statistical analyses, other structural reliability methods. Where used to quantity the return periods of collapse. Indusing flows, identify trends linked to event and site characteristics and evaluate the potential importance of collapse return period variability in assessing the impact of climate and land use charge on hydraulic collapse risk.

How to close the gap between applied strategies for infrastructure maintenance planning and the current state of research?

AbstractBridges and tunnels are the critical parts of the transport infrastructure. The efficient maintenance of their structural performance during service life requires strategies for scheduling inspections and possible structural and/or organization interventions over time. Infrastructure owners have developed such strategies that are characterized by a corrective (failure based) and predetermined preventive (e.g. time‐based or use‐based) maintenance approach. It is broadly recognized that the currently applied strategies do not provide the basis for the optimal allocation of resources into maintenance of bridges and tunnels of the traffic infrastructure. The complexity of defining efficient and proactive maintenance strategies of structures is also well recognized by the academia, and promising solutions for maintenance decision‐making based on structural reliability methods and Bayesian Decision Theory have been developed and broadly discussed in the last decades. The suggested methods have, in principle, the potential to become the basis for efficient decision making in bridge and tunnel maintenance. However, they are not yet well implemented in a practical context.In the current contribution we identify the gap between the technological developments in research and the corresponding applied knowledge in practice. Furthermore, we discuss how this gap might be closed. Special emphasis is directed to the corresponding role of standardization and education.

Intelligent Assessment Method of Structural Reliability Driven by Carrying Capacity Sustainable Target: Taking Bearing Capacity as Criterion

Large-scale building structures are subject to numerous uncertain loads during their service life, leading to a decrease in structural reliability. Real-time analysis and accurate prediction of structural reliability is a key step to improve the bearing capacity of buildings. This study proposes an intelligent assessment method for structural reliability driven by a sustainability target, which incorporated digital twin technology to establish an intelligent evaluation framework for structural reliability. Under the guidance of the evaluation framework, the establishment method of a structural high-fidelity twin model is formed. The mechanical properties and reliability analysis mechanism are established based on the high-fidelity twin model. The theoretical method was validated by experimental analysis of a rigid cable truss construction. The results showed the simulation accuracy of the high-fidelity twin model formed by the modeling method is up to 95%. With the guidance of the proposed evaluation method, the mechanical response of the structure under different load cases was accurately analyzed, and the coupling relationship between component failure and reliability indicators was obtained. The twinning model can be used to analyze the reliability of the structure in real time and help to set maintenance measures of structural safety. By analyzing the bearing capacity and reliability index of the structure, the safety of the structure under load is guaranteed. The sustainability of structural performance is achieved during the normal service period of the structure. The proposed reliability assessment method provides a new approach to improving the sustainability of building bearing capacity.

PDEM-based reliability assessment of RC frames against progressive collapse considering initial local failure

With the increased frequency of progressive collapse events, an accurate and efficient reliability-based method for preventing potential structural collapse has become a research focus. Several methods for structural reliability against progressive collapse have recently been proposed; however, they ignore the effect of initial local failure, which may have a significant influence on risk management in protecting structures against progressive collapse. Therefore, this study developed a computation framework for assessing the overall reliability of reinforced concrete (RC) frames against progressive collapse that considers the impact of the initial local failure. The proposed framework quantifies the overall reliability of the structure using the full probability method, which comprises three levels of determination of the initial local failure location, initial local failure assessment, and structural progressive collapse analysis. The efficient probability density evolution method (PDEM) was then employed to calculate the initial local failure probability and structural progressive collapse probability, which are required for achieving a trade-off between computational efficiency and accuracy. Thereafter, the developed framework was applied to a prototype RC frame, in which the structural resistance was captured using 3-D macro-based numerical modeling, which was initially validated by experimental data. Finally, the overall reliability of the RC frame was evaluated according to three different failure criteria, and based on reliability results, various structural strengthening strategies were discussed. Results show that the developed framework can effectively quantify the impact of initial local failure on the reliability of RC frames against progressive collapse. The overall reliability of the structure increases as the input energy decreases. When the input energy greater than or equal to 132 kJ, the overall reliability of the structure investigated is 0.933 for the ultimate damage criterion.

On safe offshore energy exploration in the Gulf of Eilat

AbstractGulf of Eilat is rich with energy resources, however any industrial natural resource development requires additional safety, as local eco‐system has to be preserved. In contrast to bivariate reliability approaches, known to their accurate predictions of extreme response and load levels for two‐dimensional dynamic systems, this study suggests and validates novel structural reliability method, which is being appropriate method for high‐dimensional dynamic systems. Conventional reliability methods do not have an advantage of dealing easily with high‐dimensional nonlinear dynamic systems, especially with non‐linear cross‐correlations between different system components. Advocated approach does not have limitations on the system's number of degrees of freedom, and it can accurately assess dynamic system's failure risks. Main purpose of this study was to benchmark state‐of‐the‐art reliability methodology, while utilizing available dataset efficiently. Note that advocated approach is not limited to offshore engineering example, studied here, and it has wide range of potential engineering and design applications.

An improved active Kriging method for reliability analysis combining expected improvement and U learning functions

The reliability assessment of structures with multiple failure modes and small failure probability is challenging due to the time-consuming simulations required. Active learning Kriging methods for structural reliability with multiple failure modes have shown high computational efficiency and accuracy. However, selecting the appropriate sample and its failure mode to update the Kriging models remains a key problem. In this paper, we propose a new learning function and stopping criterion to further improve the efficiency of structural system reliability analysis. Firstly, we propose a new learning function that combines the expected improvement function and the U learning function. This function selects the most suitable samples, balancing the degree of expected improvement of samples to the limit state surface and the degree of misclassification probability of samples. Secondly, we propose a new stopping criterion that considers both the accurate construction of limit state surfaces and the probability of accurately predicting the signs of samples. This criterion avoids premature or late termination of the active learning process. Thirdly, the sequential MCS simulation method is employed in the active learning process to efficiently evaluate small failure probability problems. By analyzing four examples, we verify the accuracy and efficiency of the proposed structural reliability analysis method.

Adaptive Kriging-based Bayesian updating of model and reliability

Bayesian updating is a powerful tool to reassess and calibrate models and their reliability as new observations emerge, and the Bayesian updating with structural reliability method (BUS) is an efficient approach that reformulates it as a structural reliability problem. However, the efficiency and accuracy of BUS depend on a constant c determined by the maximum of likelihood function. To efficiently complete Bayesian updating with new observations related to implicit performance function, a method that combines adaptive Kriging with Bayesian updating is proposed. The proposed method involves three stages. Firstly, an innovatively advanced expected improvement (AEI) learning function is proposed to train the Kriging model of the likelihood function for estimating c, in which the convergence criterion and the strategy of selecting new training point guarantee the accuracy and efficiency of estimating c. Secondly, a new learning function based on expectation and variance of contribution uncertainty function (EVCUF) is proposed to adaptively train the Kriging model of the performance function constructed in BUS to extract posterior samples and complete Bayesian updating of model. By simultaneously taking the expectation and variance of the contribution of the candidate sample to improving accuracy of the Kriging model into consideration, the EVCUF learning function ensures the robust and efficient convergence of the Kriging model. Finally, based on the training points of the previous two stages, the traditional U learning function is employed to subsequentially update Kriging model of the performance function for classifying posterior samples and completing Bayesian updating of reliability. Additionally, a reduction strategy of the candidate sample pool is proposed to improve the efficiency of the proposed method. After demonstrating the basic principle and advantage of the proposed method, three examples are introduced to verify the efficiency and accuracy of the proposed method.

Gaidai-Xing reliability method validation for 10-MW floating wind turbines

In contrast to well-known bivariate statistical approach, which is known to properly forecast extreme response levels for two-dimensional systems, the research validates innovative structural reliability method, which is particularly appropriate for multi-dimensional structural responses. The disadvantage of dealing with large system dimensionality and cross-correlation across multiple dimensions is not a benefit of traditional dependability approaches that deal with time series. Since offshore constructions are built to handle extremely high wind and wave loads, understanding these severe stresses is essential, e.g. wind turbines should be built and operated with the least amount of inconvenience. In the first scenario, the blade root flapwise bending moment is examined, whereas in the second, the tower bottom fore-aft bending moment is examined. The FAST simulation program was utilized to generate the empirical bending moments for this investigation with the load instances activated at under-rated, rated, and above-rated speeds. The novel reliability approach, in contrast to conventional reliability methods, does not call for the study of a multi-dimensional reliability function in the case of numerical simulation. As demonstrated in this work, it is now possible to assess multi-degree-of-freedom nonlinear system failure probability, in the case when only limited system measurements are available.

FPSO offloading operational safety study by a multi-dimensional reliability method

In contrast to the well-known bivariate statistical approach, which is known to properly anticipate extreme response levels for two-dimensional systems, the research validates a unique structural reliability method that is particularly appropriate for multi-dimensional structural responses. Traditional dependability techniques that deal with time series don't have an edge when it comes to handling high-dimensional systems and cross-correlation between several dimensions. A Floating Production Storage and Offloading Unit (FPSO) is a tanker that can produce, store and transport hydrocarbon products such as oil. The hawser during the offloading process is an important part used during operations, and a thorough prediction of its extreme tension is essential for operational safety. Failure of the offloading process may lead to great environmental harm and economic loss. This study assessed hydrodynamic forces acting on FPSO vessels in real-world environmental conditions based on the potential flow theory. A brief discussion of the experimental verification of numerical results is also included. The outlined method may be effectively employed during the vessel design phase for choosing the best vessel specifications to reduce potential FPSO hawser tension. The ability to foresee high hawser strains during the FPSO offloading operation is essential for reliability and safety.

An efficient surrogate model for reliability analysis of the marine structure piles

A hybrid random-forest-based subset simulation (RFSS) method for probabilistic assessment of scour around pile groups under waves is proposed. In the RFSS, a random forest is used to replace the true limit state function (LSF); it is updated based on design samples in the first and last levels of the subset simulation method. For modelling, 127 laboratory datasets collected from the literature were used. First, an existing equation for predicting the scour depth around piles was modified using a metaheuristic approach. The performance of the modified equation was compared with existing equations and models. The modified equation was found to be more accurate than the existing formulas and AI-based models. A probabilistic model based on the RFSS was then developed by considering the modified formula as the LSF of scour depth. Solving two numerical problems, one hydraulic engineering problem and one scour problem validated the robustness and accuracy of the structural reliability method. The results showed that the RFSS is a robust and efficient method for solving high-dimensional real-world problems. Furthermore, compared to the Monte Carlo simulation, the RFSS was able to estimate the reliability index with less computational cost and the same accuracy.

Novel Reliability Method Validation for Floating Wind Turbines

Wind turbines and associated parts are susceptible to cyclic stresses, including torque, bending, and longitudinal stress, and twisting moments. Therefore, research on the resilience of dynamic systems under such high loads is crucial for design and future risk‐free operations. The method described in this study is beneficial for multidimensional structural responses that have undergone sufficient numerical simulation or measurement. In contrast to established dependability methodologies, the unique technique does not need to restart the numerical simulation each time the system fails. Herein, it is demonstrated that it is also possible to accurately predict the probability of a system failure in the event of a measurable structural reaction. In contrast to well‐established bivariate statistical methods, which are known to predict extreme response levels for 2D systems accurately, this study validates a novel structural reliability method that is particularly suitable for multidimensional structural responses. In contrast to conventional methods, the novel reliability approach does not invoke a multidimensional reliability function in the Monte Carlo numerical simulation case. As demonstrated in this study, it is also possible to accurately anticipate the likelihood of a system failure in the case of a measurable structural reaction.

A robust method for reliability updating with equality information using sequential adaptive importance sampling

Reliability updating refers to a problem that integrates Bayesian updating technique with structural reliability analysis and cannot be directly solved by structural reliability methods (SRMs) when it involves equality information. The state-of-the-art approaches transform equality information into inequality information by introducing an auxiliary standard normal parameter. These methods, however, encounter the loss of computational efficiency due to the difficulty in finding the maximum of the likelihood function, the large coefficient of variation (COV) associated with the posterior failure probability and the inapplicability to dynamic updating problems where new information is constantly available. To overcome these limitations, this paper proposes an innovative method called RU-SAIS (reliability updating using sequential adaptive importance sampling), which combines elements of sequential importance sampling and K-means clustering to construct a series of important sampling densities (ISDs) using Gaussian mixture. The last ISD of the sequence is further adaptively modified through application of the cross entropy method. The performance of RU-SAIS is demonstrated by three examples. Results show that RU-SAIS achieves a more accurate and robust estimator of the posterior failure probability than the existing methods such as subset simulation.

Reliability Updating with a System Reliability Method Based on Adaptive Kriging

Reliability updating can improve the failure probability estimates of structural systems when new observations are obtained. At present, an efficient reliability updating method is one that transforms the equality observation information into the inequality type by introducing an auxiliary variable and then employs structural reliability methods to perform reliability updating. For this method, the computation of posterior failure probability Pr(F|Z), where Z is an observation event, requires two reliability analysis processes to estimate Pr(Z) and Pr(F∩Z), respectively. To improve the efficiency, this paper develops a reliability updating method with output observations, where the computation of Pr(Z) and Pr(F∩Z) is integrated into one system reliability problem, which is then solved by adaptive kriging with truncated candidate region (AKTCR). A composite adaptive learning process is developed to construct the kriging model, which can provide accurate estimates for both Pr(Z) and Pr(F∩Z). In this way, the proposed method can also deal with the problem of multiple failure modes and multiple observation events. In addition, a combined global and local sampling method is embedded into the proposed algorithm to reduce the size of candidate sample pool and improve the modeling efficiency. Finally, three examples can prove the efficiency and accuracy of the proposed reliability updating method.

Structural fatigue reliability analysis based on active learning Kriging model

The paper introduces the active learning Kriging (ALK) model into the structural fatigue reliability analysis. Firstly, the structural variable stress is obtained by experimental tests or finite element simulation (FES). On this basis, the cyclic stress corresponding to the fatigue life is analyzed based on the rain-flow counting method and the structural fatigue life is correspondingly computed using the Miner-Palmgren damage rule. Secondly, the uncertainties to affect the structural variable stress are considered and thus the prediction of structural fatigue lives can be obtained. Further, the structural fatigue reliability model is established, and its reliability is obtained by computing the probability that the predicted fatigue lives are greater than the allowable life. Finally, to balance the accuracy and efficiency for computing the structural fatigue reliability, a small number of boundary sample points for experiment or FES are produced and the corresponding fatigue lives are computed. Sequentially, the Kriging model is adopted to approximate the structural fatigue reliability model and it is adaptively updated by the active learning strategy. Several examples are also given to demonstrate the effectiveness of the proposed ALK-based structural fatigue reliability method.

Bayesian updating of model parameters using adaptive Gaussian process regression and particle filter

Bayesian model updating provides a powerful framework for updating and uncertainty quantification of models by making use of observations, following probability rules in the treatment of uncertainty. Particle filter (PF) and Bayesian Updating with Structural Reliability method (BUS) have been developed by researchers as promising computational tools for this purpose. However, reducing computational cost in the updating process, especially for complex models, remains one of the key challenges. Surrogate model approach achieves this by appropriately replacing, possibly adaptively, the evaluation of the original computationally costly models with approximate ones that are much less costly. This study proposes an efficient method to estimate the posterior probability density function (PDF) of model parameters by using a surrogate model constructed using adaptive Gaussian Process Regression and PF. Of critical importance is the development of ‘learning function’, which finds the location of large values of posterior PDF and avoids those that have been visited. The proposed methodology is illustrated using a single-variable example and compared with PF and BUS. Its application is illustrated through an example of structural dynamics and another one on settlement prediction by soil–water coupled FEM with Cam-clay model.