Calculation Of Failure Probability Research Articles

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.

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.

Comprehensive condition assessment of circuit breakers in a power network for maintenance scheduling

AbstractEnhancing preventive maintenance (PM) by using condition monitoring of circuit breaker (CB) can reduce maintenance costs, if enough information about the condition of this expensive equipment are provided. Here, using recorded coil current data of CBs in a power system network and on the basis of their calculated failure probability function, an algorithm is developed for comprehensive CB condition assessment. For this purpose, first, CBs are prioritized according to their cumulative failure probability functions. Second, by introducing healthy/reference CBs and comparing them with the CB with the highest priority, the condition of the latter is assessed that whether it needs maintenance or not. At last, by creating two sets of reference CBs with healthy/reference features and/or mechanisms and comparing them with the features and/or mechanisms of the CB with the highest priority, the failure part of the considered CB that needs to be repaired will be identified. The proposed methodology is straightforward, completely rule‐based and relies just on recorded data and the results have enough clarity and reliability.

Common cause failures: definitions and typical errors

The Aim of the paper is to analyse the definitions of the term “common cause failures” given in various international and Russian standards and point out their shortcomings; to identify and analyse the typical errors in the use of this notion and consideration of such failures as part of system dependability calculation. The importance of the topic is due to the fact that such failures reduce the efficiency of redundancy and must be taken into account in the process of the design of systems with high dependability requirements. Methods. The paper provides a comparative analysis of the definition of common cause failures given in Russian and international standards; analyses the methods of taking into account the effect of such failures presented in various publications; uses methods of the probability theory. Results. Differences between standards were identified in terms of the definition of the term “common cause failure”, as well as shortcomings of such definitions. Typical errors were pointed out in some publications dedicated to the methods of taking such failures into consideration. The simplest and most common beta-factor model was considered in most detail, the limits of its application were pointed out. Conclusions. It is advisable to use a single definition of common cause failures in different standards. It is to be taken from the basic terminological dependability standard with an appropriate reference. In the term itself and its definition, the word “failures” is to be in plural. The definition of this term in GOST EN 1070-2003 and GOST 34332.3-2021 are wrong, as they in no way correspond to the content of the defined notion. The conventional beta-factor model intended for taking into account common cause failures in the process of failure probability calculation can only be used in case of such probabilities being low.

Prediction of corrosion failure probability of buried oil and gas pipeline based on an RBF neural network

Risk assessment is critical to ensure the safe operation of oil and gas pipeline systems. The core content of such risk assessment is to determine the failure probability of the pipelines quantitatively and accurately. Hence, this study combines the MATLAB neural network toolbox and adopts an Radial Basis Functions (RBF) neural network with a strong non-linear mapping relationship to build a corrosion failure probability prediction model for buried oil and gas gathering and transmission pipelines. Based on the hazard identification of pipeline corrosion failure, the model summarizes the causes of corrosion failure and determines the input and output vectors of the neural network based on the fault tree. According to the selected learning samples, through the design and training of network parameters, the RBF neural network that can predict the system failure probability is finally obtained. Taking the failure probability of 30 groups of high-pressure gathering and transmission pipelines of gas storage as an example, the capability of inputting the probability of the bottom event and outputting the probability of the top event is demonstrated through training data. Our results show that the calculated failure probability based on the fault tree analysis model is consistent with the predicted failure probability based on the RBF neural network model. Hence, the RBF neural network model is shown to be reliable in predicting the corrosion failure probability of buried pipelines.

Probabilistic estimation of thermal crack propagation in clays with Gaussian processes and random fields

Prediction of thermal crack propagation in desiccated soils is imperfect due to the obscure field measurements, modeling approximations, and the underlying soil uncertainties. To address these issues, a probabilistic framework is developed to quantify the uncertainties and enhance the crack estimation reliability. Hence, the uncertainties associated with the soil properties, including the tensile strength, matric suction, Poisson’s ratio, elastic modulus and suction ratio are associated in a probabilistic model. Then, the probabilistic model is utilized with the improved Monte Carlo simulation to calculate the failure probability due to the exceedance of the crack propagation. Furthermore, failure probability optimization is exemplified by evaluating the spatial correlation between variables. The Bayesian optimization is employed to optimize the covariance kernels via the Gaussian process regression. Then, the covariance matrices are decomposed to generate random fields to further enhance the calculated failure probabilities. The results indicate that the cracking probability in near-surface layers is imminent. However, with the increase of the tensile strength and decrease in the matric suction, a sharp drop in crack propagation is highly expected. The findings also suggest that the importance of variable uncertainties is in the order of Matric suction> Elastic modulus and Suction ratio > Tensile strength> Poisson’s ratio. Also, the operation of the probabilistic model with different random field sampling outperforms the improved and directed Monte Carlo simulations because of the comprehension of the spatial correlation. However, the Gaussian fields are restricted to the second-order statistics, while lognormal fields show relatively lesser constraints. Hence, the random field sampling with a larger length scale as well the Karhunen–Loève expansion followed by the approximated eigenvalue decomposition offer viable options for the probabilistic estimation of the crack depth.

Risk-based maintenance time for oil and gas steel pipelines under corrosion including uncertainty on the corrosion rate and consequence-based target reliability

A risk-based procedure is proposed to recommend a sustainable maintenance strategy for oil and gas steel pipelines under internal pitting corrosion. The procedure considers the uncertainty and evolution on time of the corrosion depth, which depends on the initial depth and the corrosion rate, and includes the calculation of the time variant failure probability, or reliability, and its acceptable limit (target) which are calculated according to the importance of the pipeline failure consequences. Inspection results from pig runs, on an actual pipeline, are the basis to calculate the pipeline failure probability on segments of 20 km length. These calculations are performed via Monte Carlo simulation and the time variant reliability index is compared to the target reliability index per segment and per importance level. The optimal time is the time when the reliability index meets the target reliability for the considered level of failure consequences. The results allow for the priorization on the attention or pipeline segments, and funds allocation, for pipelines maintenance works according to the risk exposition conditions of the segments.

A Risk-Based Framework to Improve a Distribution System’s Resilience against Earthquakes

Earthquakes and other natural disasters have caused significant damages to power systems, indicating the necessity to enhance power system resilience. This paper proposes a risk-based resilience enhancement framework against earthquakes that considers their stochastic nature. The proposed framework supports the decision-making of distribution system operators (DSOs) for retrofitting substation components and underground cables to enhance distribution system resilience. The framework consists of four phases, namely earthquake modeling, vulnerability assessment, risk assessment, and resilience enhancement. An attenuation relationship is used to model the earthquake characteristics. Vulnerability assessment includes the failure probability calculation of substation components and a fault-tree method application to examine the seismic vulnerability of the substation. Conditional value at risk (CVaR) is used to assess the seismic risk, and includes the estimation of repair cost and customer interruption cost due to the damage caused by the earthquake, as well as the power generation cost of the distributed energy resources (DERs) used to meet the demand locally. A modified risk reduction worth (RRW) metric is adopted to determine the optimal retrofitting strategy to enhance resilience. The proposed framework was applied to a real distribution substation to examine the effectiveness of substation component retrofitting for resilience enhancement.

Supply reliability-driven joint optimization of maintenance and spare parts inventory in a gas pipeline system

This work proposes a method for the joint optimization of the maintenance and spare parts inventory to maximize the reliability of gas supply in a pipeline system. The method trades off maintenance costs and risk of gas shortages. System failure probability calculation and system maximum supply capacity analysis, joint optimization modeling and system maintenance planning, are performed. A gas compressor station is considered as object of the analysis and a discrete Markov model is used to describe the state transition process. A supply capacity model is proposed to analyze the maximum supply capacity of the pipeline system under different failure scenarios. The joint optimization of maintenance and spare parts inventory is performed using a genetic algorithm to optimize the inspection interval and spare ordering time, considering the stochastic behavior of lead time. The effectiveness of the method is validated on a case study of a pipeline system in China. The results demonstrate that the proposed method outperforms others in identifying optimal maintenance strategies. In addition, the sensitivity analysis of critical parameters is analyzed in detail, which can further ensure the robustness of the method.