System Failure Probability Research Articles

Reliability-Based Safety Evaluation of the BISTOON Historic Masonry Arch Bridge

This research examines the probabilistic safety assessment of the historic BISTOON arch bridge. Probabilistic analysis based on the Load-Resistance model was performed. The evaluation of implicit functions of load and resistance was performed by the finite element method, and the Monte-Carlo approach was used for experiment simulation. The sampling method used was Latin Hypercube. Four random variables were considered including modulus of elasticity of brick and infilled materials and the specific mass of brick and infilled materials. The normal distribution was used to express the statistical properties of the random variables. The coefficient of variation was defined as 10%. Linear behavior was assumed for the bridge materials. Three output parameters of maximum bridge displacement, maximum tensile stress, and minimum compressive stress were assigned as structural limit states. A sensitivity analysis for probabilistic analysis was performed using the Spearman ranking method. The results showed that the sensitivity of output parameters to infilled density changes is high. The results also indicated that the system probability of failure is equal to <i>p f system</i> =1.55 × 10<sup>−3</sup>. The bridge safety index value obtained is <i>β</i><i>t</i> = 2.96, which is lower than the recommended target safety index. The required safety parameters for the bridge have not been met and the bridge is at the risk of failure.

The Verification result of Permit to Work Assessment in Occupational Accident using Fault Tree Analysis

The objective of this paper is to elaborate and verified the results of the Permit To Work assessment that has been conducted using the Structural Equation Model (SEM) with Fault Tree Analysis (FTA) technique. The author used the Fault Tree Analysis to verify the result of five PTW elements i.e. Hazardous Activity, Worksite Inspection, Supporting Document, Work Description and Close Out. As it is known, the FTA is used to find the probability and cause of an accident or “Top Event”. FTA is a relatively well-known technique used to find the probability of system failure. After the analysis using FTA technique, it was found that all the results of SEM and FTA gives the similar rank to Occupational Accident which is indicated that the result is correct and acceptable for this study. This is Part II of two paper, focusing on PTW Assessment result validation using Fault Tree Analysis.

A comparative reliability study of corroded pipelines based on Monte Carlo Simulation and Latin Hypercube Sampling methods

Internal corrosion is categorized as one of the most destructive phenomena for pipeline services. This study compares the reliability analysis of pipelines against internal corrosion based on Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS) methods. Three different failure mechanisms (pitting perforation, local burst and rupture) have been considered for single corrosion defect and only local burst has been investigated for multiple corrosion defects. Furthermore, the effects of correlation between the defect depth and defect length for single defects as well as the correlation between the neighboring segments for multiple defects on the failure probability of the pipelines, have been comprehensively studied. The results show that LHS method could lead to quite acceptable accuracy with considerably less computational effort. Regarding multiple corrosion defects, the correlation between the defect depth or defect length of the neighboring segments can change the system failure probability without any monotonic trend.

EEK-SYS: System reliability analysis through estimation error-guided adaptive Kriging approximation of multiple limit state surfaces

In order to approximate the multiple limit state functions for different failure events, the active learning Kriging model proposed for component reliability analysis has been extended to system reliability analysis. Meanwhile, many efficient sampling strategies have been applied to reduce the high computational burden. However, these strategies meet a challenge in wasting some training points and terminating the training process inappropriately, since they do not directly relate to the estimation error of system failure probability. To address the challenge, this work proposes an estimation error-guided adaptive Kriging method. As Kriging prediction may be inaccurate before being well trained, the predicted system failure probability may deviate from the true result. To quantify this estimation error, the true number of failure points is approximated by adding the number of predicted failure points and the number of wrongly classified points. Since it is impossible to learn the exact number of wrongly classified points, its confidence interval is derived based on the probability of making wrong state classification. Subsequently, the refinement of Kriging is achieved by using the probability to identify new points and using the estimation error to determine the termination, which has been demonstrated by three different cases.

Uncertainty Quantification in Fault Tree Analysis: Estimating Business Interruption due to Seismic Hazard

This paper presents an approach based on fault tree analysis and subset simulation for quantifying uncertainty in the risk assessment of complex industrial facilities. Downtime estimation of industrial facilities after an extreme event is critical for risk valuation, as business interruption contributes significantly to monetary losses. Industrial facilities are complex systems with many critical, interdependent components. Such facilities are thus amenable to modeling using fault trees. Fault tree analysis breaks down a facility’s layout into system components and links component failure probabilities through Boolean logic to estimate the larger system’s failure probability. In estimating system failure probability, the lack of knowledge about failure probabilities of individual components introduces uncertainty. Subset simulation offers an efficient approach for propagating these component-level uncertainties to the system level. However, when parameters are highly correlated, traditional algorithms used in subset simulation may suffer from low acceptance rates (ratio of new samples to total samples), resulting in repeated samples, thereby compromising efficiency. This paper demonstrates that the proposed treatment allows application of subset simulation to uncertainty quantification of large fault trees using a case study of a coal-fired power plant.

Evaluation of the dependability of an artificial DNA in a dynamic automotive environment

Abstract In the last decade, bio-inspired techniques like self-organization and emergence have been in the focus of several research projects to deal with the challenge to develop, to configure and to maintain highly distributed and embedded systems. They are promising approaches to handle real-world applications such as control tasks in cars which may suffer from processor or task failures and must adapt to a changing environment. In biology the structure and organization of a system is coded in its DNA, while dynamic control flows are regulated by the hormone system. We adapted these concepts to embedded systems using an artificial DNA (ADNA) and an artificial hormone system (AHS) and both were implemented in a middleware. Based on these concepts, highly reliable, robust and flexible systems can be created. These properties predestine the ADNA and AHS for the use in future automotive applications. We showed in recent publications several examples for the use of the ADNA/AHS approach dealing with automotive applications running on the processors of a distributed system. In this contribution, we compute the failure probabilities of a p: 1 redundant system where a group of p processors shares a redundant processor and compare it with the failure probability of the ADANA system. The results motivate us to go one step further and to extend the ADNA/AHS approach for applications running on the processors of different distributed systems which normally operate as isolated systems, but may temporarily merge if they get in communication range. We show this in an automotive example where a driving car uses the processors of others cars to run its tasks. We also evaluate performance measures like down-times, reaction times and so on. The evaluations show that this approach is very promising for automotive applications.

System reliability analysis of soil nail wall using random finite element method

Soil nail wall is a compound system which for safety margin determination, consideration of safety factors of its components and their correlations is required. In this paper, considering a real site using the random finite element method (RFEM), the reliability indices of global stability, lateral displacement stability, tensile strength, and pullout resistance stability as components of the soil nail wall system are obtained. In another section of the paper, using the sequential compounding method (SCM), the importance of the mentioned stability modes and their effects on system reliability and system probability of failure are represented. Results show that the most considerable interdependence is between the global and lateral displacement stabilities. Among the reliability indices of the components, the minimum one is attributed to the pullout resistance. Furthermore, the uppermost row of the nails has the most critical reliability index compared with the others. The locations of the slip surfaces and nail intersections varied from 0.05–0.90 of the nail length, which means that the uncertainty of the soil parameters has the most significant effect on the pullout resistance safety factor of the nails. The performance level of the soil nail wall decreases from below average to poor when the soil nail wall is considered to be a system with series components.

Transmuted Gumbel univariate exponential distribution

A functional composition of the distribution function of one prob ability distribution with the inverse distribution function of another is called the transmutation map. The present paper is purported to show how the transmuted distribution can be obtained by using the convex combination of failure probability of two-component systems. The transmuted Gumbel uni variate exponential distribution is presented by changing convex combination parameter. This new distribution is dened and studied. Some mathematical properties of this distribution including the generating function and ordinary moments are derived. The survival, hazard rate and mean residual life func tions are discussed. Finally, three applications to real data are presented.

Parameterized fragility models for multi-bridge classes subjected to hurricane loads

Past hurricanes in the United States have highlighted the structural vulnerability of bridges exposed to storm surge and wave loads, triggering the development of fragility models. These models are essential for estimating the likelihood of structural failures in bridges during extreme events to support risk mitigation and resilience enhancement. However, the literature still lacks fragility models that can accommodate the effects of spatial variability of surge and wave loads and bridge characteristics like superstructure type and span slope. In addition, the presence of different types of superstructure within the same bridge necessitates the development of fragility models which can handle such variations. In this light, first, this study develops fragility models for individual spans of different bridge classes (concrete girder, steel girder, slab, box girder) considering spatial variability of wave loads and variations in structural characteristics. Herein, nonlinear dynamic analyses are employed for calculating the structural response and stepwise logistic regression is used for deriving the predictive fragility models. Then, a bridge system fragility assessment framework is proposed for system reliability assessment of the entire bridge, which accounts for different types of superstructures within the bridge and partially correlated span failures. In order to demonstrate the application of the fragility models and the system fragility assessment framework for regional level risk mitigation, the performance of bridges in the Houston-Galveston region is evaluated for two storm scenarios. The results show that the system failure probability obtained using no correlated span failure assumption is close to the actual failure probability obtained using the proposed approach highlighting the effects of correlations (or the lack of) on the system fragility.

Zonotopic fault detection observer design for discrete‐time systems with adaptively adjusted event‐triggered mechanism

This study addresses the event-triggered fault detection for a class of discrete-time systems with unknown but bounded external disturbance and measurement noise. In order to save limited network bandwidth, an adaptively adjusted event-triggered scheme is designed by considering the probability of system failure and the fault detection progress. Based on the event-triggered system output, an H _ / L ∞ fault detection observer is well designed in finite frequency ranges, such that the generated residual is sensitive to injected faults and robust against disturbance and noise. Moreover, a novel zonotope-based residual evaluation strategy is constructed to reduce conservatism by considering the impacts of external disturbance, measurement noise and measured error caused by event-triggered scheme. Finally, simulation results are provided to demonstrate the effective performance of the proposed event-triggered fault detection strategy.

Conditional Probability Voting Algorithm Based on Heterogeneity of Mimic Defense System

In recent years network attacks have been increasing rapidly, and it is difficult to defend against these attacks, especially attacks at unknown vulnerabilities or backdoors. As a novel method, Mimic defense architecture has been proposed to solve these cyberspace security problems by using heterogeneous redundant variants to perform the same task. How to choose appropriate variants and voting algorithm according to heterogeneities of these variants become the key issue of designing mimic defense architecture. Most of current researches are based on the 2-level similarity of variants, but the results are not accurate enough. This article presents an attack model based on mimic defense architecture, abstracts binary division vector and relevant indexes to describe the heterogeneity of these variants, and innovatively proposes conditional probability voting algorithm, which is different from classic majority voting algorithm. This article also analyzes the system failure probability and scalability of these voting algorithms, experiment results show that conditional probability voting algorithm is the best, both in system failure probability and scalability.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

System reliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods. A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method. The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient, and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function. Thus the calculation of system failure probability can be represented as a summation of conditional probability terms, which is convenient to be computed by iterative solving sequentially. Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode. Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis, and it can avoid multi-dimension integral calculation and reduce complexity and difficulty. Compared with the product of conditional marginal method, a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Concatenated Graph Coding on Bandwidth Part for Secure Pilot Authentication in Grant-Free URLLC

Grant-free multiple access is a critical mechanism introduced in 5G new radio (NR) to support ultra-reliable low-latency communication (URLLC) services. Pilot authentication (PA) is a key security mechanism to guarantee reliable performance of grant-free URLLC. However, PA can be easily paralyzed by pilot-aware attack since pilot signals are usually publicly known, and unprotected. To solve this, we develop the concatenated graph coding (CGC) theory by which time-frequency resources on bandwidth part (BWP) can be encoded flexibly to protect PA securely. Particularly, we use bipartite graph, and multigraph theory to model PA on BWP as transmission, and retrieval of pilot (TRP). Each transmitter in the uplink needs transmit a unique random pilot sequence as subcarrier activation pattern (SAP) on BWP. After observing SAPs from multiple transmitters, the receiver decodes a pilot sequence of interest, and tests its authenticity. The retrievability of authentic pilots is defined, and formulated analytically. We also derive the analytical closed-form expression of system failure probability, and accessibility in the regime of large-scale antenna arrays, and short data packets. Interestingly, we find that four trade-offs exist: retrievability-latency, retrievability-accessibility, reliability-latency, and reliability-accessibility. Simulation results show the security advantage of our proposed theory in grant-free URLLC system.

System Reliability Based Design Optimization of Truss Structures with Interval Variables

New products ranging from simple components to complex structures should be designed to be optimal and reliable. In this paper, for the first time, a hybrid uncertain model is applied to system reliability based design optimization (RBDO) of trusses. All uncertain variables are described by random distributions but those lack information are defined by variation intervals. For system RBDO of trusses, the first order reliability method, as well as an equivalent model and the branch and bound method, are utilized to determine the system failure probability; and Improved (μ + λ) constrained differential evolution (ICDE) is employed for the optimization process. Reliability assessment of some engineering examples is proposed to verify our results. Moreover, the effect interval variables on the optimum weight of the truss structures are investigated. The results indicate that the optimal weight depends not only on the uncertainty level but also on the equivalent standard deviation; and a falling-rising behavior is observed.

Spatially dependent flood probabilities to support the design of civil infrastructure systems

Abstract. Conventional flood risk methods typically focus on estimation at a single location, which can be inadequate for civil infrastructure systems such as road or railway infrastructure. This is because rainfall extremes are spatially dependent; to understand overall system risk, it is necessary to assess the interconnected elements of the system jointly. For example, when designing evacuation routes it is necessary to understand the risk of one part of the system failing given that another region is flooded or exceeds the level at which evacuation becomes necessary. Similarly, failure of any single part of a road section (e.g., a flooded river crossing) may lead to the wider system's failure (i.e., the entire road becomes inoperable). This study demonstrates a spatially dependent intensity–duration–frequency (IDF) framework that can be used to estimate flood risk across multiple catchments, accounting for dependence both in space and across different critical storm durations. The framework is demonstrated via a case study of a highway upgrade comprising five river crossings. The results show substantial differences in conditional and unconditional design flow estimates, highlighting the importance of taking an integrated approach. There is also a reduction in the estimated failure probability of the overall system compared with the case where each river crossing is treated independently. The results demonstrate the potential uses of spatially dependent intensity–duration–frequency methods and suggest the need for more conservative design estimates to take into account conditional risks.

Structural reliability analysis based on ensemble learning of surrogate models

Assessing the failure probability of complex structure is a difficult task in presence of various uncertainties. In this paper, a new adaptive approach is developed for reliability analysis by ensemble learning of multiple competitive surrogate models, including Kriging, polynomial chaos expansion and support vector regression. Ensemble of surrogates provides a more robust approximation of true performance function through a weighted average strategy, and it helps to identify regions with possible high prediction error. Starting from an initial experimental design, the ensemble model is iteratively updated by adding new sample points to regions with large prediction error as well as near the limit state through an active learning algorithm. The proposed method is validated with several benchmark examples, and the results show that the ensemble of multiple surrogate models is very efficient for estimating failure probability (>10−4) of complex system with less computational costs than the traditional single surrogate model.

Deterministic Optimization and Reliability Analysis of a Cam Mechanism with Translating Flat-Face Follower

The objective of this work is to perform a synthesis of a cam mechanism of the first species, with translating flat-face follower, based on deterministic and probabilistic approaches. The study consists of two parts: the first consists of optimization of the mechanism to obtain an optimal size and ensure a more efficient operation, taking into account the three major parameters that generally influence the design of this type mechanism, namely the base radius of the cam, the length of the plate and the eccentricity of the rod. In addition, the constraints related to the performance and resistance indicators as well as the geometric conditions are taken into account. The second part of this work is devoted to the reliability analysis whose probability of system failure is estimated by the approximate methods: FORM / SORM and Monte Carlo simulation, using the software Phimeca Software. Sensitivity measurements have demonstrated their effectiveness on system reliability by making it more robust.

Adaptive Monte Carlo simulation method for system reliability analysis of slope stability based on limit equilibrium methods

A slope fails if it slides along any slip surface. Proper assessment of slope failure risk in geological and geotechnical engineering needs to account, rationally, for a large, or even unlimited, number of circular and/or non-circular potential slip surfaces, which can be modeled as components of a series system. Nevertheless, the computational efforts for incorporating a large number of potential slip surfaces into slope system reliability analysis might be prohibitively expensive, particularly if non-circular slip surfaces are considered. This paper develops an efficient direct Monte Carlo simulation (MCS) method, called adaptive MCS, for slope system reliability analysis based on limit equilibrium methods (LEM), in which a novel sample manipulation strategy is proposed in lieu of brute-force exploration of failure samples amongst direct MCS samples. Equations are derived for the proposed approach and are illustrated using two slope examples considering circular and non-circular potential slip surfaces, respectively. Results show that the proposed approach provides proper estimates of slope system failure probability considering a large number of circular and/or non-circular potential slip surfaces. It significantly improves the computational efficiency of LEM-based slope system reliability analysis compared with brute-force exploration of failure samples.

Multi-mode reliability analysis of mooring system of deep-water floating structures

This paper proposes a comprehensive method for reliability analysis of a deep-water mooring system. The novelty of the newly developed method is that it considers the failure modes of floater offset excess (the function of the intact mooring system), mooring line breakage (safety), and fatigue (persistence) as part of the mooring system's reliability assessment. In addition, the quantitative relation between mooring line breaking strength and cumulative fatigue damage is considered. In this research, the annual maximum floater offset and mooring line tension are calculated based on the wave condition with a 1-year return period. Long-term mooring line tension ranges are obtained from coupled analysis in the time domain for all the sea states in the wave scatter diagram and the fatigue damage is assessed using the Palmgren–Miner rule and T-N curve. Then, the mooring system's reliability is investigated by running Monte Carlo simulations. The results demonstrate that the failure probability considering the three failure modes is much greater than that of any single mode and neglecting the correlation between different failure modes leads to significant underestimation of the mooring system failure probability. Moreover, the sensitivity analysis indicates that the underestimation proportion is obviously affected by the fatigue exponent (m).

METHODS MODELING SYSTEMS FOR THE IMPROVEMENT OF THEIR RELIABILITY


 
 
 
 The method of Markov’s processes for the analysis of systems with constant bounce and recovery intensities considered. The article presents calculations of the failure probability of the system for describing the various cases of redundancy of its components using Markov’s models. Expressions obtained for calculating the approximate value of the failure probability of the system and analyzed of failures to improve the reliability of the system. The Markov’s graph of transitions in the reservation of the system, which reflects its behavior, described. Analysis of the results of numerical solution of systems shows that when loaded with redundancy, the probability of failure is higher than with partially loaded, and with partially loaded - higher than with unloaded backup. A tree of errors for the system of cooling and clearing of flue gas at the reservation made by replacing "2 of 3", which has seven minimum bounce cross sections. Calculated the probability of system failure. The obtained calculations allow to analyze failures of technical systems in order to increase the reliability of their functioning.