Calculation Of Failure Probability Research Articles

Time-dependent reliability analysis of flood defenses under cumulative internal erosion

Internal erosion is a significant cause of failure in dams, levees and other hydraulic structures. This article studies the time-dependent reliability of such structures under Backward Erosion Piping (BEP), a form of internal erosion in the foundation. First, a physics-based time-dependent piping failure model is presented. Second, a time-variant reliability analysis method is presented which allows to quantify how the reliability evolves over the years due to cumulative pipe growth over multiple flood events. Finally, these models are used to study the importance of time-dependence for reliability estimates of flood defenses in The Netherlands. The findings show that, particularly in coastal areas, incorporating time-dependence significantly reduces the computed failure probability. Reductions vary widely, ranging from a factor of 5 to more than 10 6 , depending on flood duration and levee properties. Therefore, reliability estimates for levees can be improved by incorporating time-dependent pipe development in the BEP failure model, and thereby contribute to avoiding unnecessary reinforcements.

Investigating the Impact of Random Field Element Size on Soil Slope Reliability Analysis

The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/De) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/De on the distribution of safety factors (Fs) and failure probability (PF), with overestimation observed at smaller H/De ratios. When H/De exceeds 10 for Example 1 and 15 for Example 2, the Fs distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/De and remains basically unchanged when H/De exceeds 10 and 15, respectively. Consequently, a recommended H/De ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf.

A Curved Surface Integral Method for Reliability Analysis of Multiple Failure Modes System with Non-Overlapping Failure Domains

Abstract In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.

A method of combined metamodel and subset simulation for reliability analysis of rare events

Reliability analysis of large, complex structures with high reliability has always been a challenging task. The Subset Simulation (SUS) has proven highly effective for high-dimensional and small failure probability problems. However, the computational demands of time-consuming numerical simulations in the field of mechanical engineering remain substantial. Metamodeling techniques provide an effective means to reduce simulation computational costs. This paper introduces a novel approach, termed SUSAK, which combines the Subset Simulation with Kriging metamodels to address the challenge of small failure probability calculations. By using the original distribution of input variables representing the structural system, the SUSAK method establishes an adaptive metamodel and iteratively optimizes it with intermediate failure domain samples corresponding to the intermediate events. By replacing the performance function in subsequent calculations of the probability associated with intermediate events with metamodels, the enhanced method significantly reduces the computational burden compared to using the SUS method. This approach does not rely on solving for the design point, is not constrained by the shape of the failure domain, and retains the advantages of the SUS method in high-dimensional small failure probability calculations. As a result, it is well-suited for calculating small failure probabilities in nonlinear, discontinuous failure domains, multiple failure domains, and high-dimensional problems.

Research on the Quantitative Assessment Method of HVDC Transmission Line Failure Risk during Wildfire Disaster

It is increasingly important to effectively predict the failure of HVDC transmission lines caused by wildfire disasters. On the basis of comprehensively considering the distribution of fire points, the characteristics of wildfire propagation, and the failure factors of the transmission line, a method for calculating the probability of failure in HVDC transmission lines during wildfire disasters is proposed to quantify the risk of HVDC transmission line failures caused by wildfire disasters. Using the ArcGIS 10.7. platform, the study examined the quantity of fire points within the buffer zone of each HVDC transmission line from 2001 to 2022. The results indicate significant variations in the number of fire incidents in the buffer zones of various transmission lines. Notably, there has been a noticeable increase in the number of fire incidents along several HVDC transmission lines, including Xizhe, Baihetan-Jiangsu, Baihetan-Zhejiang, and Fufeng, in recent years. Based on the number of fire points in the buffer zone obtained through ArcGIS processing and the proposed failure probability calculation model, six HVDC hydropower transmission channels in the Sichuan Province were analyzed. At the same time, the proposed probability calculation model was simplified, and a corresponding linear evaluation index was introduced. The regression analysis results indicate that the proposed index can effectively assess the failure risk of HVDC transmission lines during wildfire disasters.

Large Scale Physical Model Study On Clay Erosion With Gras Cover On Primary Coastal Defence Structures

Sea dikes in the Netherlands consist of sandy or clay core with a clay layer with grass. The lower outer slope is often covered with a hard revetment, such as asphalt or a placed block revetment, to protect the dike material against wave impact. Since the strength of the clay layer with a grass subject to severe wave impact is unknown, the hard revetment needs to be constructed on a large part of the outer slope to ensure that the flood defence meets the safety requirements. Therefore, a research programme was started to determine the strength of the clay layer with grass on the upper slope of a dike. As a first step, large scale physical model tests have been performed. In the second step the CFD model OpenFOAM has been used to extend the physical model results by computing the peak pressure of the hydraulic load on the clay for the tested geometries and additional geometries with varying parameters that may influence the erosion rate. With all results, it was possible to derive formulas for failure probability calculations in the final step. The knowledge development on the erosion of a clay layer with grass on the outer slope by wave attack resulted into formulas that are currently used in the safety assessment of dikes contributing towards safer deltas and resilient designs of dikes.

Time-dependent probabilistic evaluation of rainstorm-induced shallow landslides considering influence of impermeable bedrock

ABSTRACT A time-dependent probabilistic evaluation method is proposed for assessing the stability of soil slopes during rainstorm events. The method considers multiple failure scenarios, including sliding along the wetting front and shallow soil–rock interface. The application of the method is demonstrated by a typical rainstorm-induced shallow landslide in Zhejiang Province, China. The results indicate that the landslides occurred when the failure probability exceeded a certain level, providing references for real-time landslide warnings. Moreover, the factors influencing the probabilistic results have been investigated. A two-dimensional limit state surface is used to explain the change of slope failure scenarios during the rainfall process, confirming the controlling role of the impermeable bedrock surface. The probabilistic evaluation results using the actual rainfall data can better reflect slope performance via comparing the computed failure probability using idealised rainfall patterns and actual rainfall data. Additionally, the parameter sensitivity analysis shows that the matric suction, the effective cohesion and the effective internal friction angle significantly influence the slope performance during the early stage of rainfall. However, during the later stage of rainfall, the saturated permeability coefficient becomes the most sensitive parameter. The applicability of the proposed method was further verified via three other typical rainstorm-induced shallow landslide cases.

Quantitative risk assessment of a spill fire caused by the continuously leaked fuel in a sealed ship engine room

There are a large number of high-temperature heat sources in a ship engine room. Once the oil leakage occurs, it is likely to be ignited and form a spreading and burning spill fire. In this paper, spill fire experiments are conducted in a model-scale ship engine room to investigate their characteristic parameters. The quantitative models of flame height and thermal radiant surface emission power applicable to such fires are verified by the experimental data. Based on that, the classical quantitative risk assessment method is adopted to assess the risk of spill fires using thermal radiation hazard as the main reference, and a detailed framework for quantitative risk assessment of spill fires in ship engine room is established, which includes hazard identification, probability of failure calculation, consequence assessment, and risk quantification. The possible causes of spill fire accidents are briefly analyzed based on the bow-tie model. In cases where thermal threats above the risk threshold for larger leakage rates (70 mL/min), the probability method outperforms the threshold method in terms of accuracy in risk quantification. Additionally, the variation of thermal radiation with combustion diameter is analyzed, and some recommendations for fire emergency rescue are presented.

Assessment of Fishing Vessel Vulnerability to Pure Loss of Stability Using a Self-Developed Program

A significant proportion of maritime incidents occurring in coastal waters are attributed to small fishing vessels. To analyze the root causes of such maritime accidents, it is imperative to conduct simulations to assess the potential pure loss of stability. This paper proposes a method of using a self-developed program to assess the vulnerability, which could be used in practice for seafarers to maintain shipping safety. To assess the vulnerability of three fishing vessels, the proposed method considers different wave conditions, where the parametric behaviors of the waves relative to the ship’s position (ξG/λ) and wave steepness (H/λ) are explored. Additionally, vulnerability is computed systematically under diverse loading conditions, resulting in visual representations such as 2D and 3D plots. We conduct comparative simulations between the proposed method and the ICS-Hydro STAB. The simulation results reveal that the proposed method has superior accuracy in executing failure probability calculations. The prediction error is consistently below 5%.

Time-Variant Reliability Analysis with an Adaptive Single-Loop Kriging Combined with Directional Sampling Method

The difficulty in calculating time-variant reliability lies in the large number of performance function calls. This paper proposes an efficient method for time-variant reliability analysis by incorporating the directional sampling method (DS). In this method, within the framework of single-loop active learning Kriging (SL–AK), the burden of fitting the Kriging surrogate model is alleviated by constructing a novel candidate sample pool. While reducing the computational burden, the accuracy of the Kriging surrogate model remains unaffected. Unlike the traditional SL–AK, the proposed method obtains the failure probability through an improved DS method. The improved DS utilizes a bisection method for root-finding, thereby circumventing the impact of interpolation coefficients on the computation results. This method of computing failure probability not only alleviates computational burden but also enhances the precision of the estimated failure probability. Furthermore, this paper introduces global sensitive analysis (GSA) into time-variant reliability analysis, thereby expanding the applicability of GSA. The accuracy and high efficiency of the proposed method are verified through three numerical examples and two engineering examples with implicit performance function.

A multi-objective-optimization based importance sampling method and its application in seismic stability analysis of gravity dam

The stable reliability analysis of dams is a challenging topic in geotechnical engineering safety. Because there are more complex system failure modes and high-dimensional parameters in large solid structures, it is difficult to calculate failure probability efficiently and accurately using general reliability analysis methods. Most methods suffer from complex iterative processes and the curse of dimensionality. In this study, an improved importance sampling method based on multi-objective optimization is proposed and applied to reliability analysis for dam sliding. The optimization function is constructed from the limit state surface and the original probability density. The optimal sampling center is selected from the optimization results by considering the dominant performance function as well as the coefficient of variation of the weight function. Four numerical examples and a case study of the sliding stability of a gravity dam demonstrate the accuracy and efficiency of the proposed method. The results show that the proposed method is not sensitive to the specific multi-objective optimization algorithm used. Simulations using multiple sampling centers perform better overall than simulations using a single sampling center. In particular, the proposed method remains applicable to parallel systems with 20 high-dimensional parameters that are virtually immune to the curse of dimensionality.

Human reliability analysis of shared equipment in multi-unit site

ABSTRACT Currently, there is no mature method for calculating the probability of human failure that occurs in multi-unit. In this study, the single-unit HRA is expanded and improved, and we have compiled a method flow suitable for human reliability analysis in multi-unit. This method considers the communication of commands between different organizations and analyzes the equipment shared by multiple units. This research demonstrates the feasibility of the THERP+HCR method to calculate the human-caused failure probability of multiple units. In this paper, the human failure probability of the fifth emergency diesel engine is investigated during a station blackout at a multi-unit site. The calculated failure probability of personnel deploying a fifth diesel-engine between two units is 0.1061, which is higher than the failure probability of a single unit, and the consequences of failure of a dual-unit invocation would be more severe. Due to the uncertainty of some conditions and parameters, the variation of the failure probability after sensitivity analysis ranges from–0.0846–0.2083. Involvement of more organizations during the accident increases the risk of the plant site. Among the most influential factors on the probability of failure are the presence of inspection clauses in the operating procedures and the level of tension of personnel.

Probabilistic investigation of the pounding effect in steel moment resisting frames with equal and unequal heights

In this research, the influence of the pounding phenomenon of two adjacent steel moment resisting frames (SMRFs) with 2 and 5-story with an intermediate ductility is investigated by considering equal and unequal heights under seismic excitations. In this way, two scenarios are applied. The first and second scenarios are related to the pounding of two SMRFs with an equal height (both frames with 2-story) and an unequal height (2-story and 5-story frames), respectively. In the following, at first, sensitivity analysis is conducted by the Monte Carlo simulation (MCS) method. Then, the collapse performance of the studied SMRFs is evaluated by incremental dynamic analysis (IDA), and fragility curves under 14 far-fault records and also, the failure probability is predicted by the Kriging meta-model. The results of sensitivity analysis indicate that the yield strength of cross-sections and dead load were the greatest effect on failure probability computation. Also, in the statistical level of 50%, the collapse probability of SMRFs with an equal height is 17% compared to the SMRFs with an unequal height. Also, the results of the Kriging meta-model show that the failure probability is increased by 65% in an unequal height versus an equal height.

Issues of risk-oriented approach to electrical networks reliability management

The features of implementing a risk-oriented approach in Russian regulatory documents are examined. A brief overview of foreign experience is provided. The need for and a method of incorporating fault statistics in the calculation of failure probability based on asset health indexes are demonstrated. Additionally, the necessity of considering the duration of power supply interruptions in assessing the consequences of equipment failure is shown, along with a proposed method for doing so.

Reliability analysis of the impact of thickness measurement accuracy on the longitudinal strength assessment of CAP

The reliability analysis of the longitudinal bending strength of ships is conducted using the total probability method, taking into account and analyzing the accuracy error in thickness measurement of transverse section members on existing servicing ships. A mathematical model for calculating failure probability CAP ratings is established. By calculating the CAP rating of an aged LPG carrier, it is observed that when the deterministic method reaches the target rating, the failure probability in rating calculation by the reliability analysis method is high. This indicates a significant influence of thickness measurement accuracy on CAP rating accuracy.

Predicting steel column stability with uncertain initial defects using bayesian deep learning

The stability of steel columns is difficult to predict accurately due to uncertain initial defects such as geometric imperfections and residual stress. To address this issue, we propose a probabilistic model that uses variational autoencoder (VAE) and transfer learning to estimate the loading capacities of steel columns. Our model can predict the confidence intervals of buckling loads without knowing the exact distribution of initial defects, providing more comprehensive information for engineering applications than traditional deterministic strength index. We establish a dataset of 1500 load-displacement curves of steel columns using four data augmentation approaches, and analyze the data distribution to validate the model's assumptions. Various criterions, including the mean squared error (MSE), the prediction interval coverage probability (PICP), and the prediction interval normalized average width (PINAW), are adopted to comprehensively measure the performance of confidence interval prediction. The numerical experiment validates that the trained model accurately predicts the confidence intervals for load-displacement responses, which perfectly cover the true curves with reasonable PINAW. Finally, we conduct a case study with a practical experiment to illustrate the model's potential application in failure probability calculation and reliability design. Our proposed model provides a promising probabilistic solution for quantifying the impact of uncertain parameters on structural analysis and significantly simplifies probability-based reliability design and optimal design processes.

Reliability analysis of parted rope injuries during ship mooring operation under neutrosophic environments

At the national and international levels, many efforts have been made over recent decades to ensure the safety of ships at sea. In marine environments, crews face serious concerns during parted rope injuries during ship mooring operation. This problem can be tackled with the help of failure probability analysis which plays a vital role in detecting and eliminating the aforesaid threats in maritime transportation. Therefore, determining the fundamental causes of parted rope injuries during ship mooring operation is essential for maritime safety researchers. When the failure probability values of basic events are exact, conventional fault tree analysis has previously been successfully applied to determine the cause of failure of the top events. However, sometimes the failure information provided by different analysts for mooring operation may be uncertain and inconsistent. To properly address this important issue, the proposed research reflects a novel approach by extending crisp sets, fuzzy sets, and intuitionistic fuzzy sets into neutrosophic sets. The aforesaid approach is used to compute failure probabilities and reliability intervals for truth-membership, indeterminacy-membership and falsity-membership functions, along with a measure of how much each basic failure event contributes to the failure of the top event. The results obtained by incorporating the proposed approach are compared with those obtained using earlier approaches.

Verified propagation of imprecise probabilities in non-linear ODEs

We combine reachability analysis and probability bounds analysis, which allow for imprecisely known random variables (multivariate intervals or p-boxes) to be specified as the initial states of a dynamical system. In combination, the methods allow for the temporal evolution of p-boxes to be rigorously computed, and they give interval probabilities for formal verification problems, also called failure probability calculations in reliability analysis. The methodology places no constraints on the input probability distribution or p-box and can handle dependencies generally in the form of copulas. We also provide a consonant approximation method for multivariate p-boxes, which allows for the prediction sets of dynamical systems to be efficiently computed. The presented methodology is rigorous and automatically verified, as both the dynamics and uncertainties are represented and solved with guaranteed enclosures.

System reliability analysis of mooring system for floating offshore wind turbine based on environmental contour approach

The system reliability of the mooring system for floating offshore wind turbines (FOWT) is analyzed in this paper. Various failure modes such as mooring line breaking, fatigue and floater offset are included and solved as a series system. This work employed a new mooring breaking assessment algorithm, wherein the effect of fatigue damage on breaking strength is simulated by introducing functional dependences into the coupled dynamic analysis. In this research, the extreme design loads are estimated using the environmental contour (EC) approach and a logarithmic function is proposed to describe the relationship between the extreme response and the target return period to simplify the full long-term analysis. The time-domain coupling analysis of the FOWT is performed considering all one-year sea states, the long-term fatigue damage was approximated based on linear criterion. The fatigue damage can contribute significantly to the breaking strength of mooring lines. The results indicate that ignoring the dependence between the residual strength and cumulative fatigue damage would cause under-estimated results. The calculated failure probability of the floating system is larger than that of any single failure mode, while it is mainly dominated by the main single failure mode with the largest failure probability.