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Reliability-based design optimization (RBDO) is a valuable tool for optimizing while considering the impact of uncertainties. However, its application in engineering, specifically in pile foundation design, is complicated due to high computational costs and the potential for nonlinear iteration misconvergence. To address these challenges, we propose a modified optimization calculation method utilizing the mean first-order reliability method (MFORM). The revised function of the reliability index is introduced to ensure computational accuracy and linear regression is employed for its calculation. The results of the case study demonstrate that the modified optimization calculation method not only improves computational efficiency but also enhances computational accuracy. While the form of the performance function significantly influences initial and local optimizations, it has minimal impact on global optimization. Through local and global optimizations, the objective function values are reduced by 20.2% and 24.9%, respectively, for the first form of the performance function. For the second form of the performance function, reductions of 15.0% and 24.9%, respectively, are achieved through local and global optimizations. [ABSTRACT FROM AUTHOR]

A probability-based approach, combining deterministic and probabilistic methods, was developed for analyzing building and component failures, which are especially crucial for complex structures like nuclear power plants. This method links finite element and probabilistic software to assess structural integrity under static and dynamic loads. This study uses NEPTUNE software, which is validated, for a deterministic transient analysis and ProFES software for probabilistic models. In a case study, deterministic analyses with varied random variables were transferred to ProFES for probabilistic analyses of piping failure and wall damage. A Monte Carlo Simulation, First-Order Reliability Method, and combined methods were employed for probabilistic analyses under severe transient loading, focusing on a postulated accident at the Ignalina Nuclear Power Plant. The study considered uncertainties in material properties, component geometry, and loads. The results showed the Monte Carlo Simulation method to be conservative for high failure probabilities but less so for low probabilities. The Response Surface/Monte Carlo Simulation method explored the impact load–failure probability relationship. Given the uncertainties in material properties and loads in complex structures, a deterministic analysis alone is insufficient. Probabilistic analysis is imperative for extreme loading events and credible structural safety evaluations. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A reliability-based approach is presented to investigate the effects of structural and load uncertainties on the reliability estimation of ship hull girders. Structural uncertainties included randomness in material properties, geometric properties, initial geometric imperfections, and corrosion behavior. Load uncertainties included statistical uncertainties, model uncertainties, environmental uncertainties, and uncertainties related to nonlinearity. The hull girder ultimate strength was calculated using Smith’s method, and the probabilistic density function was evaluated by employing Monte Carlo simulations. In the load estimation, the still water bending moment and wave-induced bending moment were calculated using a simplified formula of the International Association of Classification Societies-Common Structural Rules code and then modified with load parameters. The reliability index was estimated using a first-order reliability method considering the operating time, the duration of the ship in the alternate hold loading condition, and the severity of the corrosion rate. As a result, sagging conditions dominated the collapse mode. The reliability indexes were obtained for the observed cases, and the viability of the ship was assessed accordingly.

This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading. The prediction of failure probability of composite laminates subjected to different loads involves many uncertainties associated with mechanical properties, loading, and boundary conditions. Failure in the composite material is truly hard to trace because there are individual faults in each ply, and we face a stochastic process due to the scatter in the mechanical properties. The continuum damage mechanics (CDM), as a powerful approach, is applied to model the damage of fiber, matrix, and fiber/matrix debonding. This method defines criteria for damage detection and determines safe zones. The material constitutive equations are executed using a subroutine in Abaqus. The first-order reliability method and second-order reliability method have been applied to examine the reliability of laminated composites. The results are compared with those of the Monte Carlo simulation. Different composite laminates under different stress levels are considered for the failure probability investigation. The limit state functions and random variables have been determined based on the CDM model. Finally, the effects of the number of cycles, applied stress, and stacking sequence of the laminate on the reliability and fatigue life in fiber-reinforced laminated composites are assessed. [ABSTRACT FROM AUTHOR]

Approximate analytical methods have been frequently used in geotechnical engineering to estimate the reliability of geotechnical structures due to their efficiency and simplicity. The main spirit of these methods is using the moments of the limit state function to estimate the reliability index. However, the moments are strongly dependent on the form of the limit state function, resulting in the fact that these methods are sensitive to the form of limit state functions. This study aims to systematically explore how various equivalent forms of limit state functions affect the performance of several commonly used approximate analytical methods, including the first-order second-moment method, the first-order reliability method, and the point estimation method. The applicable conditions of these methods are illustrated through five typical geotechnical examples. The results indicate that the estimated accuracy for the first-order second-moment method and the point estimation method is affected by the form of the limit state functions. Although the form of the limit state function does not affect the accuracy of the first-order reliability method, it affects computational efficiency. The limit state functions with an equivalent logarithmic form are almost always favorable for the investigated examples and are thus recommended in practice. [ABSTRACT FROM AUTHOR]

A probability-based approach, combining deterministic and probabilistic methods, was developed for analyzing building and component failures, which are especially crucial for complex structures like nuclear power plants. This method links finite element and probabilistic software to assess structural integrity under static and dynamic loads. This study uses NEPTUNE software, which is validated, for a deterministic transient analysis and ProFES software for probabilistic models. In a case study, deterministic analyses with varied random variables were transferred to ProFES for probabilistic analyses of piping failure and wall damage. A Monte Carlo Simulation, First-Order Reliability Method, and combined methods were employed for probabilistic analyses under severe transient loading, focusing on a postulated accident at the Ignalina Nuclear Power Plant. The study considered uncertainties in material properties, component geometry, and loads. The results showed the Monte Carlo Simulation method to be conservative for high failure probabilities but less so for low probabilities. The Response Surface/Monte Carlo Simulation method explored the impact load–failure probability relationship. Given the uncertainties in material properties and loads in complex structures, a deterministic analysis alone is insufficient. Probabilistic analysis is imperative for extreme loading events and credible structural safety evaluations.

A submerged floating tunnel (SFT) can be a promising solution for crossing a deep or wide waterway. This innovative concept however lacks research into its probabilistic design. In this research, the reliability of the tether-stabilized SFT is assessed. A first-order reliability method (FORM) and a Monte Carlo simulation (MCS) are performed for the limit state functions of the most important failure mechanisms. Stochastic variables are chosen so that a target reliability index of 3.8 for a reference period of 50 years is met. The calculated factors from the full probabilistic design are compared with the general recommended partial factors for strength and resistance from Eurocode EN1990. For the strength mechanisms, the calculated factors are smaller than the factors from Eurocode. However, for the equilibrium mechanism, the calculated factor for the unfavorable loading is larger than the factor from Eurocode and should be increased by 10% in order to design a safe enough SFT.

The reliability index approach (RIA) is one of the effective tools for solving the reliability‐based design optimization (RBDO) probabilistic model, which models the uncertainties with probability constraints. However, its wide application in engineering is limited due to low efficiency and convergence problems. The RIA‐based modified reliability index approach (MRIA) appears to be very robust and accurate than RIA but yields inefficient for the most probable point (MPP) search with highly nonlinear probabilistic constraints. In this study, an enhanced modified reliability index approach (EMRIA) is developed to improve the efficiency and robustness of searching for MPP and is utilized for RBDO. In the EMRIA, an innovative active set using rigorous inequality is applied to construct the region of exploring for MPP, where the unnecessary probabilistic constraint could be eliminated adaptively during the iterative process. Moreover, the double loop strategy (DLS) is integrated into the EMRIA to strengthen the efficiency and robustness of large‐scale RBDO problems. Two numerical examples demonstrated that the EMRIA is an efficient and robust method for MPP search in comparison with current first‐order reliability methods. Six RBDO problems quoted also indicate that DLS‐based EMRIA has good performance to solve complex RBDO problems. [ABSTRACT FROM AUTHOR]

This paper assesses the uncertainty of the partial safety factors for the design of corroded pipelines against burst failure due to the variability associated with the strength model selection. First, 10 calibrated burst pressure prediction models for corroded pipelines are adopted and duly categorised under low-, medium- and high-grade steel classes. The probabilistic characteristics of the pipe burst strength are studied using Monte Carlo simulation for the selected models. Model uncertainty factors are used to correct the burst pressure predictions by the design equations. Model strength factors are derived for models in each category that will provide coherent reliability. The first-order reliability method is employed to estimate the partial safety factors and their uncertainty as a function of operational time. Finally, the influence of the corrosion growth model on the evaluation of partial safety factors is assessed. The results obtained in this study can provide vital guidance regarding the design and maintenance of different steel-grade pipelines. [ABSTRACT FROM AUTHOR]

In this paper, the vibration serviceability of a two-bay composite floor under walking excitation was evaluated via both deterministic and stochastic methods. The floor framing was irregular with one bay being about 25 % longer than the other. Using the deterministic approach recommended by a widely recognized design guide, it was predicted that the vibration levels in both floor bays due to footfall were deemed acceptable in terms of human comfort in an office environment. The stochastic approach took account of random variations in the floor modal properties, the loading and the tolerance vibration limit. Statistical properties of the random variables were determined by reference to contemporary floor vibration guidelines as well as a modal analysis of the finite element model of the floor. Close-formed formulas for use with the first-order reliability method were developed to predict the failure probability of the floor. Reliability analysis using Monte Carlo simulation with a sufficiently large number of trials was also performed. Both of the analytical and numerical reliability analyses revealed an exceedance probability of around 36 % for the longer floor bay, which was in marked contrast to the deterministic method. For the shorter floor bay, a failure probability of practically zero was found by the random procedures. Furthermore, the excellent agreement between the results acquired from the first-order reliability method and the Monte Carlo simulation highlights the effectiveness of the former approach which requires much less computation effort.

• Three advanced solution strategies for time-variant reliability-based robust design optimization are proposed. • An augmented step length adjustment method is developed for inverse reliability analysis. • Inappropriate discretization of time intervals for time-variant constraints is avoided. • The proposed solution strategies exhibit superior computational efficiency. Time-variant reliability-based robust design optimization (TRBRDO) has achieved certain progress recently for its ability to ensure both robustness of design and feasibility of time-variant probabilistic constraints. However, the existing TRBRDO methods have not specifically addressed the dynamic uncertainty of material degradation, and there is lack of a universal and efficient approach for this class of time-variant robust design problems. For this reason, this paper proposes three solution strategies, namely the reliability index based double-loop method, performance measure based double-loop method, and sequential single-loop method. In these approaches, the minimum reliability of each time-variant probabilistic constraint is considered by obtaining the extremum in a series system. With use of the first-order reliability analysis technique, two different single-loop multivariate optimization models are established to obtain the minimum reliabilities and minimum performance measures through sequential quadratic programming algorithm, respectively. Following this, two different double-loop models and a sequential single-loop model are developed. Furthermore, an augmented step length adjustment technique is proposed for inverse reliability analysis, which is integrated into the performance moment integration and percentile difference method to derive the robustness indicators for the design objective. Finally, three illustrative numerical examples and one engineering problem are provided to demonstrate the effectiveness of the proposed solution strategies for reliable and robust design optimization with high computational efficiency. [ABSTRACT FROM AUTHOR]

The reliability of a motion mechanism is affected by corrosion, wear, aging and other components’ performance degradations with the extension of service time. This paper tackles this problem by proposing a time-varying reliability analysis method for uncertain motion mechanisms. First, a model of motion mechanism error is constructed by assessing the difference between actual and expected motion. A time-varying reliability analysis method for a motion mechanism is proposed. The time-varying performance function is discretized into several static performance functions, which are further approximated with several normal variables. Then, the correlation coefficient matrix and probability density function of these normal variables are calculated, and the time-varying reliability of a motion mechanism is obtained via high-dimensional Gaussian integration. The study demonstrates that the proposed method successfully transforms the time-varying reliability problem into several time-invariant reliability problems for analysis, and handles the time-varying reliability problem of a nonlinear motion mechanism involving random variables and stochastic processes, and significantly increases the computational efficiency. Finally, the proposed method’s effectiveness is verified by two numerical examples and one practical engineering problem.

Seismic structural assessment of masonry arch bridges is essential due to their cultural, economic and strategic importance and vulnerability. A realistic and rigorous structural assessment is necessary in order to protect the bridges and use resources carefully. At this time, there are no standardised or widely accepted assessment procedures, and the performance criteria for masonry arch bridges are not available. This study presents an overarching reliability-based seismic assessment methodology based on analytical modelling, laboratory testing and probabilistic assessment. It investigates the performance criteria concept and proposes performance limit states. The methodology is applied to a historical masonry arch bridge in Turkey. To consider rigorously the uncertainties in material properties and seismic input, probabilistic nonlinear analyses are conducted using a detailed 3D finite element model. The results are combined with the proposed limit state definitions to generate the capacity and demand distributions. Both distributions are used in Monte Carlo simulation and First-Order Reliability Method (FORM) to estimate the probability of exceedance and reliability indexes for each limit state. The proposed probabilistic assessment methodology will be a useful approach to obtaining more reliable information about masonry arch bridges' expected seismic performance and for better-informed decision-making, especially when designing intervention actions and post-earthquake scenarios. [ABSTRACT FROM AUTHOR]

In probabilistic analysis, random variables with unknown distributions are often appeared when dealing with practical engineering problem. A Hermite normal transformation model has been proposed to conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions. Recently, linear moments (L-moments) are widely used due to the advantages of stability and insensitivity. In this paper, the complete expressions of the inverse transformation of L-moments Hermite (L-Hermite) model have been proposed. The criteria are proposed to derive the complete inverse transformation of performance function and the complete expressions of the inverse transformation of L-Hermite model are formulated. Moreover, a first-order reliability method for structural reliability analysis based on the proposed inverse transformation of L-Hermite model is then developed using the first four L-moments of random variables. Through the numerical examples, the proposed method is found to be efficient for normal transformations since the results of the proposed L-Hermite are in close agreement with the results of Rosenblatt transformation. Additionally, the reliability index obtained by the proposed method using the first four L-moments of random variables provides a close result to the reliability index obtained by first-order reliability method with known probability density functions in structural reliability assessment. [ABSTRACT FROM AUTHOR]

A submerged floating tunnel (SFT) can be a promising solution for crossing a deep or wide waterway. This innovative concept however lacks research into its probabilistic design. In this research, the reliability of the tether-stabilized SFT is assessed. A first-order reliability method (FORM) and a Monte Carlo simulation (MCS) are performed for the limit state functions of the most important failure mechanisms. Stochastic variables are chosen so that a target reliability index of 3.8 for a reference period of 50 years is met. The calculated factors from the full probabilistic design are compared with the general recommended partial factors for strength and resistance from Eurocode EN1990. For the strength mechanisms, the calculated factors are smaller than the factors from Eurocode. However, for the equilibrium mechanism, the calculated factor for the unfavorable loading is larger than the factor from Eurocode and should be increased by 10% in order to design a safe enough SFT. [ABSTRACT FROM AUTHOR]

A novel framework of reliability analysis was developed in this study to consider the uncertainty of geomaterials and geological conditions by combining the reduced-order model (ROM), reliability analysis, and numerical model. The reliability method was used to determine the reliability index using the simplicial homology global optimization (SHGO) based on the ROM. The developed method was verified and illustrated using three numerical examples and a simple slope. The limit state curve in all three numerical examples was in excellent agreement with the actual curve. The reliability index and failure probability were also in excellent agreement with those of the actual limit state function using the first-order reliability method (FORM) and Monte Carlo simulation, respectively, indicating that the ROM method can present the limit state function well. The results showed that the developed method is feasible and effective for reliability analysis of geotechnical and geological engineering problems with a complex, nonlinear, and implicit limit state function. Furthermore, the developed method is effective, efficient, and accurate for reliability analysis. It provides an excellent way to approximate the limit state function to avoid the time-consuming numerical model in a practical engineering system.

Reliability is always considered as one of the most important factors in every system and it is commonly accepted to investigate reliability by employing reliability analysis problems. In this case, the need of existence of powerful reliability analysis methods has resulted in introducing different methods to solve first-order and higher-order reliability analysis problems. These methods have also been employed to ensure failure probability of a system is below an acceptable level. However, there are still disadvantages such as instability and inefficiency in some of these methods. The Hasofer - Lind and Rackwitz - Fiessler (HL-RF) method is still the most popular method to solve the first-order reliability analysis problems, but it will be shown in this paper that this method is not stable enough to solve highly non-linear problems. Also, it is found that the HL-RF method may show some inefficiency behaviour even when it converges to the optimum point. In this paper, a new reliability analysis method is introduced that solves first-order reliability analysis problems stably and efficiently. This method is based on the conjugate gradient direction that is used as a line search algorithm. The new reliability analysis method is called Conjugate Gradient Direction-Based (CGDB) method whose performance is compared with the performance of the existing HL-RF method by solving several numerical experiments at the end of this paper. [ABSTRACT FROM AUTHOR]

This paper is devoted to the reliability analysis of rotor-bearing systems, based on the combination of Kriging metamodels and the First-Order Reliability Method (FORM). The main motivation arises from the fact that high-fidelity structural models generally lead to high computation costs, which can be strongly alleviated using surrogate models. Since applications to rotating machines have not been sufficiently explored so far, the contribution of the present paper consists in the evaluation of the performance, both in terms of accuracy and computational effort, of a numerical strategy based on the combination of Kriging metamodels and FORM to this type of machines, accounting for their typical frequency domain responses and applicable limit-states. Such an evaluation is made by confronting four different strategies, combining: (i) full finite element models and Monte Carlo simulations; (ii) full finite element models and FORM; (iii) Kriging metamodels and Monte Carlo simulations; (iv) Kriging metamodels and FORM. Results show that the Kriging/FORM strategy provides substantial decrease of computation effort, while keeping satisfactory accuracy of reliability estimations. In addition, a procedure is proposed for improvement of the accuracy of Kriging/FORM reliability estimates, by enriching the Kriging design of experiments in the vicinity of the Most Probable Failure Point. [ABSTRACT FROM AUTHOR]

The finite step length (FSL) method is extensively used for structural reliability analysis due to its robustness and efficiency compared with traditional Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method. However, it may generate a large computational effort when it faces some complex nonlinear limit state functions. This study explains the basic reason of inefficiency of the FSL method and proposes an enhanced finite step length (EFSL) method to improve the ability for solving complex nonlinear problems, and then apply it to reliability-based design optimization (RBDO). The tactic is to present an iterative control criterion to compensate for the deficiency of the FSL method in the oscillation amplitude criterion, which solves the problem of large computational effort caused by unchanged step length during the iterative process. Then, a comprehensive step length adjustment formula is presented, which can adaptively adjust the step length to achieve fast convergence for limit state functions with different degrees of nonlinearity. Following that, the proposed method is combined with the double loop method (DLM) to improve the efficiency and robustness for solving complex RBDO problems. The robustness and efficiency of the proposed method compared to other commonly used first-order reliability analysis methods are demonstrated by five numerical examples. In addition, four design problems are used to validate the proposed EFSL-based DLM which is effective for solving complex nonlinear RBDO problems. [ABSTRACT FROM AUTHOR]

The inherent uncertainty in hydro-geotechnical parameters presents a significant challenge for accurately predicting rainfall-triggered shallow landslides in mountainous regions. In this study, a novel probabilistic framework was developed and implemented in the " Py.GIS-FSLAM-FORM " software, designed to address the complexities associated with parameter uncertainty, correlation, and distribution. By combining the Fast Shallow Landslide Assessment Model (FSLAM) with the First-Order Reliability Method (FORM), we have enhanced the traditional probabilistic approach to create more accurate landslide susceptibility maps. This study emphasizes the uncertainly of geotechnical parameters and the critical influence of hydrological conditions on landslide susceptibility, especially focusing on the interaction between antecedent recharge (q a) and event rainfall (P e). In our study area (Val d'Aran, Spain), the probabilistically based results revealed that areas of very high susceptibility are significantly affected by event rainfall, particularly on slopes of 30–40 degrees and aspects between 100 and 250 degrees. The variability in geotechnical parameters, especially the coefficient of variation (COV) in cohesion and friction angle, plays a crucial role in landslide susceptibility assessment, with increased COVs leading to greater landslide uncertainty. Additionally, cross-negative correlations and non-normal distributions of geotechnical parameters substantially influence the spatial distribution of landslides, notably when combining antecedent recharge with event rainfall. These results highlight the importance of incorporating parameter variability and hydrological conditions in susceptibility models to improve the precision of regional landslide forecasts. While the study was performed in Val d'Aran, its methodologies and conclusions are relevant to mountainous areas worldwide, offering insights for refining landslide prediction models and susceptibility assessments, contributing to global efforts in landslide disaster prevention. [ABSTRACT FROM AUTHOR]

This study develops a practical copula-based FORM in an original physical space for an efficient slope reliability analysis involving correlated non-normal variables. First, the copula theory for modeling the joint probability distribution of cohesion and friction angle of soils is briefly introduced. Second, the traditional expanding dispersion ellipse perspective of the FORM is reviewed. Then, a new expanding dispersion contour perspective of the copula-based FORM is formulated in detail. Finally, two illustrative slope examples are presented to illustrate and demonstrate the developed copula-based FORM and its expanding dispersion contour perspective. The results indicate that the developed copula-based FORM has good accuracy and efficiency in deriving the reliability index and design point for a typical slope reliability problem. It operates in an original physical space and thus is suitable for a complex slope reliability problem with an implicit performance function. The copulas for characterizing various dependence structures between the cohesion and friction angle of soils have a significant impact on slope reliability index, especially under a high reliability level and a strong degree of negative correlation. The proposed expanding dispersion contour perspective facilitates the understanding of the copula-based FORM, which can readily explain the slope reliability results produced by various copulas. The derived design points are obtained by simultaneously considering the marginal distributions, correlation as well as various non-Gaussian dependence structures of soil parameters. [ABSTRACT FROM AUTHOR]

Bi-planar sliding is one of main instabilities for bedding rock slope and is mainly dominated by the geometrical and strength properties of the weak structural plane. Traditional stability evaluation combines limit equilibrium method (LEM) with shear strength reduction (SSR) to derive the deterministic safety factor against slope stability. However, considering the uncertainties inherent in the geometrical and strength properties of the weak structural plane, as well as the variations of rock mass properties, the safety factor of rock bedding slopes against bi-planar sliding cannot be deterministically calculated. This study proposes a framework for probabilistic assessment on rock bedding slope stability against bi-planar sliding. Surrogate model for factor of safety against bi-planar sliding from LEM and SSR is developed based on back-propagation neural network (BPNN). The BPNN model, together with the design variables is implemented into the Excel Spreadsheet First-Order Reliability Method for the reliability assessment. [ABSTRACT FROM AUTHOR]

We present reliability-based optimization (RBO) of the Mechanically Stability Earth (MSE) walls, using constrained optimization, considering the external stability, under ultimate limit state conditions of sliding, eccentricity, and bearing capacity. The design is optimized for a target reliability index of 3 that corresponds to an approximate failure probability of 1 in 1000. Reliability index is calculated by the first-order reliability method (FORM). The MSE wall, founded on cohesionless soil, with horizontal backfill and uniform live traffic surcharge, is studied. The RBO results are reported for the height of MSE wall ranging from 1.5 m to 20 m. For target reliability index of 3, the optimized length to height ratio, L o p t / H , of the MSE wall is greater than 0.7 (the minimum length to height ratio requirement of AASHTO) for H ≤ 4.5 m, and then it decreases below the minimum required value of 0.7 for H > 4.5 m. The RBO approach presented in this study will help practitioners to achieve cost-effectiveness in design. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper assesses the uncertainty of the partial safety factors for the design of corroded pipelines against burst failure due to the variability associated with the strength model selection. First, 10 calibrated burst pressure prediction models for corroded pipelines are adopted and duly categorised under low-, medium- and high-grade steel classes. The probabilistic characteristics of the pipe burst strength are studied using Monte Carlo simulation for the selected models. Model uncertainty factors are used to correct the burst pressure predictions by the design equations. Model strength factors are derived for models in each category that will provide coherent reliability. The first-order reliability method is employed to estimate the partial safety factors and their uncertainty as a function of operational time. Finally, the influence of the corrosion growth model on the evaluation of partial safety factors is assessed. The results obtained in this study can provide vital guidance regarding the design and maintenance of different steel-grade pipelines.

Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application. [ABSTRACT FROM AUTHOR]

Floods, bridge scour, and flood-associated loads have caused over sixty percent of bridge failures in the U.S. Current practices for the vulnerability assessment of instream bridges under the effect of such flood largely rely on qualitative methods, such as visual inspection, without considering uncertainties associated with structural behaviors and flood loads. Recently, numerical methods have been investigated to quantitatively consider such uncertainty effects by adapting fragility analysis concept that has been well established in the earthquake engineering area. However, river hydraulics, geotechnical uncertainties of foundation, variable scour-depth effects, and their significance in structural fragility of bridges have rarely been systematically investigated. This study proposes a comprehensive fragility analysis framework that can effectively incorporate both flow hydraulics and geotechnical uncertainties, in addition to commonly considered components in flood-fragility analysis of bridges. The significance of flow hydraulics and geotechnical uncertainties has been demonstrated through a real-bridge case study. Conventional fragility curves with maximum scour depth may not represent actual vulnerability during floods, as the scour may not reach to the maximum in many cases. Therefore, fragility surface with two intensity measures, i.e. flow discharges and scour depths, is introduced for real-time vulnerability assessment during floods in this study. [ABSTRACT FROM AUTHOR]

• Accurate and robust approximate numerical differentiation methods for Kriging model. • Efficient conjugate analytical method for highly nonlinear structural reliability analysis problems. • Uniform sampling for global optimization and resampling strategy for local optimization. • Active Kriging-based CFORM for solving complex structural reliability analysis problems. Efficient structural reliability analysis method is crucial to solving reliability analysis of complex structural problems. High-computational cost and low-failure probability problems greatly limit the efficiency in structural reliability analysis problems, causing the safety and reliability of the structure to be questioned. In this work, a highly efficient structural reliability analysis method coupling active Kriging algorithm with conjugate first order reliability method (AK-CFORM) is proposed. Specifically, the resample strategy is considered to reduce the number of samples evaluated in each active learning process; the uniform sampling is used to better balance global and local optimal problems; the conjugate map is used to improve the robustness of analytical first order reliability method; and the approximate numerical differential formula is proposed to solve the problems of non-convergence when solving the gradient of the Kriging surrogate model. Finally, three numerical cases and four engineering cases are used to illustrate the effectiveness and robustness of the proposed method. The results show that the proposed AK-CFORM has greater advantages in the number of calling system response and surrogate model with robust and accurate performance. [ABSTRACT FROM AUTHOR]

Single-loop methods for reliability-based design optimization are characterized by high computational efficiency. However, the accuracy of these methods may be low for highly nonlinear probabilistic constraints. A new hybrid method called 'SLShV-CG' is proposed for improving accuracy in which the single-loop method is coupled with the shifting vector approach of the sequential optimization and reliability assessment method. This shifting vector approach is incorporated with the probabilistic constraints without approximating them for reliability analysis. The most probable points for the probabilistic constraints are found using the Karush–Kuhn–Tucker conditions and the conjugate gradient search direction is used for determining the approximate most probable point in every iteration. The proposed method is tested on four mathematical and four engineering reliability-based design optimization problems, and the accuracy of the solutions is verified using Monte Carlo simulations. The results demonstrate the better accuracy and computational efficiency of the proposed method over six reliability-based design optimization methods from the literature. [ABSTRACT FROM AUTHOR]

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single‐loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables. [ABSTRACT FROM AUTHOR]

The first-order reliability method (FORM) is a prevalent method in the structural reliability community. However, when solving the high-dimensional problem with a highly nonlinear limit state function, FORM usually encounters non-convergence or divergence. In this study, an improved FORM combining Harris Hawks Optimization (HHO-FORM) is presented for high-dimensional reliability analysis. HHO is a meta-heuristic algorithm mimicking the predatory behavior of Harris hawks, and efficient in finding the global optimum of high-dimensional problems. In HHO-FORM, the reliability index is firstly formulated as the solution of a constrained optimization problem according to the FORM theory. Then, the constraints are handled with the exterior penalty function method. In addition, the optimal reliability index is determined by the Harris Hawks Optimization that accelerates the convergence by the population-based mechanism and the strategy of Levy Flight. The HHO-FORM does not require the derivatives of the limit state functions that reduce the computational burden for high-dimensional problems. So the simplicity of HHO-FORM greatly improves the efficiency in solving high-dimensional reliability problems. The HHO-FORM is firstly tested on three challenging numerical high-dimensional problems and then applied to two high-dimensional engineering problems to verify its performance. Four gradient-based FORM algorithms and four heuristic-based FORM algorithms are also compared with the proposed method. The experimental results demonstrate that HHO-FORM provides good accuracy and efficiency for high-dimensional reliability problems. [ABSTRACT FROM AUTHOR]

The performances of first-order reliability method (FORM) are highly important owing to its accuracy and efficiency in the structural reliability analysis. In the gradient methods-based sensitivity analysis, the iterative formula of FORM is established using the gradient vector which it may not compute for some structural problems with discrete or non-continuous performance functions. In this study, the probabilistic Gaussian global-best harmony search (GGHS) optimization is implemented to search for the most probable point in the structural reliability analysis. The proposed GGHS approach for reliability analyses is performed based on two main adjusted processes using the random Gaussian generation. The accuracy and efficiency of the GGHS are compared with original harmony search (HS) algorithm and three modified versions of HS as improved HS, global-best HS, and improved global-best HS based on a mathematical and three structural problems. The obtained results illustrated that the PGGHS is more efficient than other modified versions of HS and provides the accurate results for discrete performance functions compared to original FORM-based gradient method. [ABSTRACT FROM AUTHOR]

A new structural reliability analysis framework is developed to extend the performance of first-order reliability method, which is low robustness and poor accuracy when dealing with highly nonlinear functions. Initially, an improved conjugate sensitivity factor method is proposed to find the most probable point. The method enhances its robustness of convergence by introducing a conjugate gradient direction based sensitivity factor technique and improves its computational efficiency by putting forward a hybrid conjugate gradient factor and an adaptive step length strategy. Subsequently, the dimension reduction-based saddlepoint approximation method is developed, which uses the dimension reduction approach to construct the limit state function as the additive univariate quadratic functions and applies saddlepoint approximation to obtain the result with higher precision. A comparison analysis from five mathematical and structural examples illustrates that the proposed method is better than most existing methods in terms of robustness, efficiency and accuracy for estimating the failure probability of structures. [ABSTRACT FROM AUTHOR]

The first‐order reliability method (FORM) is well recognized as an efficient approach for reliability analysis. Rooted in considering the reliability problem as a constrained optimization of a function, the traditional FORM makes use of gradient‐based optimization techniques to solve it. However, the gradient‐based optimization techniques may result in local convergence or even divergence for the highly nonlinear or high‐dimensional performance function. In this paper, a hybrid method combining the Salp Swarm Algorithm (SSA) and FORM is presented. In the proposed method, a Lagrangian objective function is constructed by the exterior penalty function method to facilitate meta‐heuristic optimization strategies. Then, SSA with strong global optimization ability for highly nonlinear and high‐dimensional problems is utilized to solve the Lagrangian objective function. In this regard, the proposed SSA‐FORM is able to overcome the limitations of FORM including local convergence and divergence. Finally, the accuracy and efficiency of the proposed SSA‐FORM are compared with two gradient‐based FORMs and several heuristic‐based FORMs through eight numerical examples. The results show that the proposed SSA‐FORM can be generally applied for reliability analysis involving low‐dimensional, high‐dimensional, and implicit performance functions. [ABSTRACT FROM AUTHOR]

In this paper, a method for predicting the extreme value distribution of the vertical bending moment (VBM) in a ship under a given short-term sea state is presented. To predict the extreme value distribution of the VBM, the first-order reliability method (FORM), by which the most probable wave episodes (MPWEs) leading to given VBMs are identified, is introduced. The coupled computational fluid dynamics (CFD) and finite-element analysis (FEA) are used to provide the high-fidelity numerical solutions for the wave-induced and whipping components of the VBM. Then, a Reduced-Order Model (ROM) which can yield the predictions equivalent to the coupled CFD–FEA results in a relatively short time is developed. The ROM is incorporated into FORM to identify the MPWEs, in lieu of the coupled CFD–FEA. The accuracy of the ROM is verified by comparing with the coupled CFD–FEA results under identified MPWEs, in terms of both the wave-induced and whipping VBM. Then, a series of tank tests using a scaled container ship is conducted. In the first series of the tests, the VBM measurements under the MPWEs identified from the FORM-based approach using the ROM are made, to validate the accuracy of the ROM. The extreme value distribution of the combined wave-induced and whipping VBM is also measured by performing the second series of the tests, in random waves. The validity of the FORM-based extreme value prediction using the ROM is investigated by comparing with the second series of the tests. [ABSTRACT FROM AUTHOR]

The best estimate shear strength predictions of the operational EN 1992‐1‐1 (EC2) variable strut inclination method (VSIM) have been shown to underestimate shear capacity at low stirrup quantities. Conversely, the model overestimates shear capacity at high stirrup quantities (Cladera and Mari, 2007; Olalusi and Viljoen, 2019). Sufficient safety performance of the design formulation should be confirmed at high levels of stirrup reinforcement, and over conservatism at low stirrup reinforcement is not ideal. This contribution assesses the consistency and uniformity of the reliability index of EC2 shear design formulation over the range of practical design situations. Prediction model uncertainty is an important parameter in the assessment (Olalusi and Viljoen, 2019). The principal reliability assessment was performed using as general probabilistic model (GPM), the probabilistic representation of the modified compression field theory (MCFT) as implemented in analysis program Response 2000 (R2k), which was shown to provide the most accurate estimates of shear capacity (Bentz, 2000). This was validated by means of a similar reliability analysis using the compression chord capacity model (CCC) as GPM. The outcome of EC2 reliability analysis indicated uneconomically high reliability at low levels of shear reinforcement, high concrete strength and large beam depth, and actively reducing reliability with increased levels of shear reinforcement, reduced concrete strength and reduced beam depth for both rectangular and I‐shaped beam cross‐sections. Reliability indices of all the test sections investigated meet the target reliability requirements for Reliability Class 2 structures prescribed by basis of design standards SANS 10160 and EN 1990, for the design range considered. [ABSTRACT FROM AUTHOR]

• A new solution framework for time-dependent RBDO (TRBDO) is proposed. • Three different time-independent equivalent models are developed in this framework. • This solution framework avoids time-consuming time-dependent reliability analysis. • The proposed decoupled model is superior in efficiency to existing TRBDO methods. • Numerical examples and engineering problems validate this solution framework. Time-dependent reliability-based design optimization (TRBDO) has attracted intensive research attentions in recent years by virtue of its unique ability to allow consideration of dynamic uncertainties caused by stochastic processes and material property degradation. However, existing TRBDO methods are generally too intricate to be practically applicable for practical engineering application. On top of that, extremely high computational cost for complex TRBDO problems further hinders its practicability. To facilitate smooth implementation via enhancing computational efficiency in solving TRBDO problems, this study proposes an innovative and efficient solution framework. The strategy is that time-dependent performance function in each probabilistic constraint is discretized into a series of instantaneous performance functions to transform the original TRBDO problem into a RBDO problem. The reliability of each probabilistic constraint in the transformed RBDO problem is then considered under extreme value condition. With engagement of the first-order reliability method, the RBDO problem is transformed into two different triple-loop timeindependent RBDO problem. However, the issue of expensive computational cost still persists due to the triple-loop structure and identification of temporal variables under extreme value condition. To this gap, a decoupled strategy is adopted to resolve the triple-loop structure into a series of cycles of double-loop reliability analyses and deterministic optimization. Two numerical examples and three engineering applications are employed to demonstrate the supreme computational performance of the currently proposed solution framework. Results show that the proposed framework is capable of achieving a reliable optimal design at a fast convergence speed. [ABSTRACT FROM AUTHOR]

Two slopes are analysed probabilistically, emphasising the insights and sensitivity information obtainable from the design point of the first-order reliability method (FORM). The first case was an underwater slope in San Francisco Bay Mud that failed during excavation. The second case was a rock slope in Hong Kong which had been identified as being potentially unstable. Insights from FORM-based reliability analysis and reliability-based design (RBD) are presented, and RBD's ability to overcome some of the limitations of partial factor design approaches are discussed. [ABSTRACT FROM AUTHOR]

Uncertainty quantification (UQ) is becoming an essential attribute for development of computational tools in gas turbine combustion systems. Prediction of emissions with a variety of gaseous fuels and uncertain conditions requires probabilistic modeling tools, especially at part load conditions. The aim of this paper was to develop a computationally efficient tool to integrate uncertainty, sensitivity, and reliability analyses of CO and NOx emissions for a practical swirl-stabilized premixed burner. Sampling-based method (SBM), nonintrusive polynomial chaos expansion (NIPCE) based on point collocation method (PCM), Sobol sensitivity indices, and first-order reliability method (FORM) approaches are integrated with a chemical reactor network (CRN) model to develop a UQ-enabled emissions prediction tool. The CRN model consisting of a series of perfectly stirred reactors (PSRs) to model CO and NOx is constructed in Cantera. Surrogate models are developed using NIPCE-PCM approach and compared with the results of CRN model. The surrogate models are then used to perform global sensitivity and reliability analyses. The results show that the surrogate models substantially reduce the required computational costs by 2 to 3 orders of magnitude in comparison with the SBM to calculate sensitivity indices, importance factors and perform reliability analysis. Moreover, the results obtained by the NIPCE-PCM approach are more accurate in comparison with the SBM. Therefore, the developed UQ-enabled emissions prediction tool based on CRN and NIPCE-PCM approaches can be used for practical combustion systems as a reliable and computationally efficient framework to conduct probabilistic modeling of emissions. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) methods are widely used for classification and regression analysis. In many engineering applications, only one class of data is available, and then one-class SVM methods are employed. In reliability applications, the one-class data may be failure data since the data are recorded during reliability experiments when only failures occur. Different from the problems handled by existing one-class SVM methods, there is a bias constraint in the SVM model in this work and the constraint comes from the probability of failure estimated from the failure data. In this study, a new one-class SVM regression method is proposed to accommodate the bias constraint. The one class of failure data is maximally separated from a hypersphere whose radius is determined by the known probability of failure. The proposed SVM method generates regression models that directly link the states of failure modes with design variables, and this makes it possible to obtain the joint probability density of all the component states of an engineering system, resulting in a more accurate prediction of system reliability during the design stage. Three examples are given to demonstrate the effectiveness of the new one-class SVM method. [ABSTRACT FROM AUTHOR]

Featured Application: The effect of imperfections of node locations on the reliability of single-layer steel domes is a very important issue in the design of steel structures. This paper shows that, with reliability analysis methods, it is possible to analyze the failure probability level while moving along the load displacement path towards the limit point. In this paper, the impact of changes in the standard deviation of random variables describing coordinates of nodes on the reliability index β of the single-layer steel dome was analyzed. The changes in the standard deviation of variables describe imperfections of node locations. Reliability analysis is also employed to find sensitivity of the reliability index to mean values or standard deviation of random variables by calculating the elasticity index. This method can be used to design single-layer steel domes. This study is an attempt to assess the effect of node location imperfections on the reliability dome. The analysis concerns a single-layer steel lattice dome that is very sensitive to node snap-through. The load-displacement path of the structure was determined using the program, Finite Element Method-Krata. To determine the failure probability, reliability index, and elasticity index, the first-order reliability method approximation method was employed. The reliability analysis was conducted with Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw. In this paper, it is shown how large differences in the assessment of the safety of a structure can appear when we incorrectly estimate the standard deviation of the random variable responsible for the imperfections of node locations. [ABSTRACT FROM AUTHOR]