System Failure Probability Research Articles

Grey Bayesian network model for electromagnetic pulse vulnerability assessment of engine system

Firstly, in view of the uncertainty of electromagnetic pulse vulnerability assessment of engine system caused by limited experimental data and incomplete information, a grey Bayesian network model is proposed by introducing interval grey numbers in grey system theory to characterize the uncertainty of sensitivity threshold and fault logic relationship of engine system components, so as to improve the processing ability of Bayesian network for uncertain information. Secondly, taking broadband high-power microwave as an example, the interval grey number failure probability of engine system and the posterior failure probability of sensor interval grey number are calculated. The former represents the survivability of the engine system as a whole under strong electromagnetic pulse, and the latter reflects the vulnerability order of each sensor under the condition of engine system failure. The evaluation conclusion can provide a reference for the design of vehicle electromagnetic protection.

Evaluation of the unavailability of the primary circuit of Triga SSR reactor, importance factors and risk criteria for its components

Abstract Probabilistic Safety Assessment is a tool for improving a nuclear installation and its safety in all its function phases. PSA provides a methodical way of identifying sequences resulting from a wide range of initiating events concerning an accident, and includes systematic and realistic determination of accident frequencies and their consequences. This paper analyzes the unavailability of the TRIGA SSR reactor primary circuit, obtaining the system unavailability value, identifying main contributors to system failure, and calculating risk importance factors. Two cases were considered: one without considering Common Cause Failure (CCF) in the developed fault tree, and the second considering CCF on pumps and heat exchangers lines. The aim was to assess their influence on the primary system’s unavailability. Two importance factors, Fussell–Vesely and Risk Achievement Worth, were employed to identify components with a strong impact on the risk (probability of system failure). These factors aid in enhancing maintenance activities and testing. The analysis utilized the EDFT code, part of the PSAMAN code package developed in SCN-Pitesti.

Adaptive support vector machine for time-variant failure probability function estimation

Time variant reliability analysis introduces additional complexity due to the inclusion of time. When the time-variant failure probability function (TFPF) of the structure is of interest, it inherently involves sequential evaluations of the failure probabilities of series systems varied with time in discretized space, posing a challenge to reliability analysis. An efficient approach for the evaluation of the TFPF, called ‘Time-dependent Adaptive Support Vector Machine combined with Monte Carlo Simulation’ (TASVM-MCS), is presented to reduce the corresponding computational cost. Based on the samples from Monte Carlo simulation (MCS), an iterative strategy is proposed to actively extract the most valuable sample points from the sample pool and iteratively update the support vector machine (SVM) model. In particular, an active learning function is proposed to take into account the diversity of samples and time simultaneously. In this way, the built SVM will be more suitable for the evaluation of TFPF other than a point-wise failure probability. The proposed TASVM-MCS method is relatively less sensitive to the dimensionality of the input variables, making it a powerful and promising approach for time-variant reliability computations. Four representative examples are given to demonstrate the significant effectiveness and efficiency of the proposed method.

Computationally efficient Complete-Sampling-based fault tree analyses for seismic probabilistic safety assessment of nuclear facilities

The seismic risk of nuclear power plants (NPPs) can be assessed through seismic probabilistic safety assessment (PSA) based on fault tree analyses (FT). The conventional FT-based approach has limitations for handling the correlated relation of basic events and utilizing the sampling-based FT analysis for addressing such issues demands considerable computational cost. In particular, accurate consideration of the partial dependences between the failure probabilities of NPP components in seismic hazard events can further increase the computational cost of risk quantification. Therefore, this paper presents an improved complete-sampling-based seismic PSA risk quantification method. The novelty of this method is that it increases the efficiency of the risk quantification by introducing sequential sampling and truncation to the conventional fault tree analysis. In addition, as sub-concepts, we eliminate unrequired sampling extraction steps via integrated multivariate response distribution-based sampling for components and continual evaluation of the convergence of system failure probabilities. On three considered examples, including an actual NPP, the proposed method requires 91%–96% fewer samples than the conventional method, without sacrificing accuracy. These results indicate the efficiency of the proposed method, which is expected to become a useful tool in the future.

Reliability and availability analysis of high-altitude platform stations through semi-Markov modeling

In the development and deployment of both tethered and autonomous High Altitude Platform Station (HAPS), flight modules such as hexacopter and octocopter with 6 or 8 rotors are most often used. The primary focus of this article is to compute the reliability of tethered HAPS by analyzing the effectiveness of their redundant rotor systems. To measure the performance of such systems, it is convenient to consider mathematical models as k-out-of-n models. Although Markov models have extensively been reported to analyze the reliability of repairable k-out-of-n models, this work introduces an alternative and more thorough methodology. In this work, a semi-Markov model (SMM) is proposed to calculate the probability of rotors being operational after the failure of some rotors in order to analyze system reliability. We emphasize that an SMM model is more appropriate as it provides a more accurate assessment of the probability of system failure over time through non-exponential sojourn time. Further, the efficacy of the proposed SMM is studied through the evaluation of steady-state availability, mean time to failure and reliability. Overall, the findings of this study enhance our comprehension of the reliability of repairable systems and extend the existing knowledge base of HAPS reliability analysis.

Hybrid reliability analysis method for systems with random and non-parameterized p-boxes based on weight coefficients

This paper establishes a hybrid variable system failure probability optimization model based on sampling methods and weighting coefficients. By introducing auxiliary input variables, important sampling functions, and p-box, failure samples are mapped from the random variable space to the p-box variable space. The new weight coefficients are constructed, including important sampling weights and interval weights. Combining discretization methods and Monte Carlo simulation (MCS), the interval weights are transformed into variables, and constraints conforming to the p-box variable distribution are constructed. After calculating the weighting coefficients for all failure samples, the new failure probability optimization model is built. This model is independent of the performance functions and does not involve cyclic optimization, with computational complexity only related to the dimensions. Six cases are used for method comparison, validating that the new method exhibits higher efficiency and accuracy.

An active learning approach for reliability assessment of passive systems combining polynomial chaos expansion and adaptive sampling

Passive safety system is extensively employed in newly designed reactors to increase their inherent safety. However, the driving force is smaller, and the uncertainty of the thermal–hydraulic (T-H) process may potentially result in the inability of system to perform its intended function, which is often known as functional failure. Therefore, the passive systems reliability has received increasing attention. Unfortunately, the assessment of system failure probability utilizing Monte Carlo simulation (MCS) methods necessitates a significant quantity of repeated calculations employing the thermal–hydraulic code, which may be impractical in terms of computational cost. To enhance the assessment calculation efficiency, an adaptive surrogate model is proposed. The bootstrap method was employed to introduce an error estimate into the polynomial chaos expansion (PCE) model, which solves the obstacle of the PCE model in reliability evaluation applications due to the lack of error estimation. The method constructs an active learning approach through error estimation, strategically identifies and selects the best candidate samples, and iteratively updates the initial experimental design. The effectiveness of the method was verified through three benchmark cases, and it was employed for assessing the passive residual heat removal system (PRHRS) reliability within integral-type pressurized water reactor (IPWR200). The results demonstrated that the proposed method significantly diminishes the frequency of invocations to the T-H code and improves computational efficiency to a large extent. Furthermore, it can serve as a valuable guide for the design, operation, and reliability evaluation of the passive system.

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.

Modeling and reliability analysis of the micro-milling process considering stochastic tool wear with surrogate models

Micro-milling technology is widely employed in manufacturing micro-precision parts due to its flexible processing and high accuracy. Compared to the macro-milling process, micro-milling has a smaller machining size, which leads to tool wear, tool runout, and other factors being more sensitive to the impact of machining quality. This work proposes a reliability evaluation framework for machining systems based on the micro-milling mechanical model and its surrogate method. Establish a cutting force model under shear and plow conditions with periodic variations in instantaneous uncut thickness. Subsequently, the probability distribution of the cutting parameters is obtained based on Bayesian updates. An improved buffer failure probability method is proposed to quickly get the micro-milling system failure probability. Developing new ensemble and adaptive sampling methods and introducing stochastic configuration network (SCN), an adaptive stochastic configuration network ensemble (ASCNE) model is established to alleviate the time-consuming problem of repeated calculations of mechanical models in reliability analysis. Experimental results indicate that the mechanical model can achieve good predictive performance, and the constructed ASCNE model can achieve high-precision surrogate effects. Additionally, the reliability analysis results of the system can guide tool replacement during the machining process, ensuring safe and efficient execution of the micro-milling.

Prognostics and Health Management of Unmanned Surface Vessels: Past, Present, and Future

Abstract With the increasing popularity and deployment of unmanned surface vessels (USVs) all over the world, prognostics and health management (PHM) has become an indispensable tool for health monitoring, fault diagnosis, health prognosis, and maintenance of marine equipment on USVs. USVs are designed to undertake critical and extended missions, often in extreme conditions, without human intervention. This makes the USVs susceptible to equipment malfunction, which increases the probability of system failure during mission execution. In fact, in the absence of any crew onboard, system failure during a mission can create a great inconvenience for the concerned stakeholders, which compels them to design highly reliable USVs that must have integrated intelligent PHM systems onboard. To improve mission reliability and health management of USVs, researchers have been investigating and proposing PHM-based tools or frameworks that are claimed to operate in real time. This paper presents a comprehensive review of the existing literature on recent developments in PHM-related studies in the context of USVs. It covers a broad perspective of PHM on USVs, including system simulation, sensor data, data assimilation, data fusion, advancements in diagnosis and prognosis studies, and health management. After reviewing the literature, this study summarizes the lessons learned, identifies current gaps, and proposes a new system-level framework for developing a hybrid (offline–online) optimization-based PHM system for USVs in order to overcome some of the existing challenges.

Thermal runaway safety analysis of eVTOL based on evidence theory and interval analysis

In order to ensure the safety of eVTOL, safety analysis of thermal runaway problem of lithium battery is needed. Due to insufficient failure data, a safety assessment method based on evidence theory and interval analysis is proposed. Firstly, a fault tree model for system is constructed. Secondly, for the imprecise failure rate of bottom events in fault tree analysis, the failure probability interval of bottom event is calculated by using the evidence theory, and combining with the importance analysis to address the problem of inaccurate failure rate of bottom events in fault tree analysis. The evidence theory is used to calculate the probability interval of failure of bottom events and combine it with interval theory to calculate the top events of the fault tree. Finally, the importance analysis is used to find out the basic events that have the greatest impact on the top events. The proposed method is used to analyze the safety of the eVTOL′s battery thermal runaway and calculate the importance of each bottom event, so as to provide a basis for reducing the system failure probability and improving the system safety level.

Statistical reliability analysis of marine systems with varied levels of redundancy

In designing autonomous vessels for long-duration independent operation, maintaining the performance of machinery systems without human intervention is a key challenge. Designers are faced with a range of potential system architecture choices but have little guidance on which will be optimal. Working only with high-reliability components can increase the probability of completing a voyage successfully, though the availability of such components may be limited. Alternatively, designers can select a redundant architecture to provide options for reconfiguration if a component fails during a voyage, such architectures typically have weight, space, and cost implications. This work presents a parametric exploration of the probability of system failures over time under different architectures. The reliability of individual components is expressed through exponential probability distributions and the weight of each component is approximated. Two systems are presented and the effectiveness of various architectures for both systems is compared. A simple design penalty function is also tracked to capture the different architectures’ weight and implication number of components. From this study optimal architectures for long-term autonomous missions are proposed.

System reliability analysis of Cable-stayed bridge using pair Copula and ICLHS with unequal weights under seismic loading

Considering the correlation between different components, quantifying the failure probability of a high-level hyper-static structure under non-stationary seismic loading is of great significance in guiding earthquake-resistant design and fortification of bridges. In this study, a high-pier and large-span railway cable-stayed bridge in the mountainous region were employed to evaluate the seismic performance. First, the basic theoretical methods of the non-stationary random seismic motion simulation, equivalent extreme value theory based on extreme value distribution (EVD), improved Latin hypercube sampling (ICLHS) with unequal weighted fractional moment estimation and Pair Copula technique are presented. Second, the finite element analysis model of the cable-stayed bridge was established based on the OpenSees platform, the seismic response samples of the bridge were calculated under three levels of seismic ground motion to determine the first passage failure probability of the main components of the bridge under the design failure modes. Finally, the Pair Copula function was introduced to estimate the seismic system reliability of the cable-stayed bridge. The optimal Copula type that can describe the correlation between the bridge components was selected through goodness-of-fit tests such as AIC, BIC, and the minimum distance method. The failure probability of the entire system was obtained by calculating the selected Copula function type under seismic loading.

A novel decoupled approach combining invertible cross-entropy method with Gaussian process modeling for reliability-based design and topology optimization

Design optimization considering the presence of uncertainties in parameters poses an extremely challenging problem. The source of difficulties comes with reliability-based formulations, where addressing the probabilistic problem exhausts the large computing efforts for failure estimations of the structure violating limit-state functions (LSFs). This paper proposes a novel decoupled approach for effectively solving reliability-based design optimization (RBDO) problems, namely an invertible cross-entropy (iCE) method advantageously combined with a Gaussian process regression (GPR) model, termed as iCE-GPR. The GPR model is applied to approximate the spectrum of LSFs under random parameters. Furthermore, to enhance the accurate prediction of the system failure probability, an active learning process is applied to systematically refine the GPR model by adding new learning points in the region with the largest uncertainty and high-reliability sensitivity through the maximization of an expected feasibility function (EFF). Based on the updated GPR model, the failure probability is estimated by a cost-effective cross-entropy (CE) method without any calls to the actual performance function. To perform the decoupling optimization process with the reliability analysis, the novel iCE, based on the CE method, is developed to update the most probable point (MPP) assigned for the next deterministic optimization process in determining the new optimal design. The method iteratively performs the deterministic optimization process based on the MPP underpinning LSFs sequentially updated by the active learning process. The proposed iCE-GPR method fast-converges the optimal design and significantly alleviates computational burdens associated with reliability analyses. The proposed method is also applied to solve a reliability-based topology optimization (RBTO) problem. Four numerical examples for both the RBDO and RBTO problems are provided to illustrate efficiency and robustness of the proposed iCE-GPR method.

Probabilistic assessment of existing shield tunnel longitudinal responses to tunnelling

AbstractThis paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second, the longitudinal beam‐spring model (LBSM), which can explicitly consider the circumferential joints, is applied to reflect the performances of the existing shield tunnel. Two well‐documented case histories are selected to validate the effectiveness of the deterministic analysis model. The predictions are also compared with previous analytical methods. Afterward, to improve the computational efficiency, a surrogate model is then established to replace deterministic model and perform the global sensitivity analysis (GSA). A probabilistic analysis is further performed to explore the tunnelling‐induced deformation characteristics of the shield tunnel by means of Monte Carlo simulation (MCS) method. Parametric analyses are further performed to explore the influences of key variables on the failure probabilities of the existing shield tunnel. The results show the proposed deterministic model gives a satisfactory prediction in tunnelling‐induced responses of the existing shield tunnel. The LBSM can reflect the segmental ring and joint deformations more realistically. The uncertainties in the ground elastic modulus, joint rotation stiffness and the joint shearing stiffness dominate the tunnel settlement, joint opening and dislocation, respectively. The failure probability of tunnel settlement is more sensitive to volume loss than that of the joint opening and dislocation. The whole system failure probability is identical to that of the tunnel settlement failure mode. By increasing the coefficient of variation (COV) of random variables, probability density function (PDF) curves for neutral and pessimistic conditions become lower and wider, and the maximum joint opening and dislocation positions corresponding to the peaks of PDF apparently deviate from that of the determinate results. Increasing the two tunnel clearances, the allowable volume loss for opening and dislocation increase linearly, but it has insignificant influence on the tunnel failure mode. However, enlarge the new tunnel diameter leads to rapid decrease in the allowable volume loss for all failure modes.

Quantifying the impact of risk mitigation measures using SPAR-H and RCM Approaches: Case study based on VVER-1000 systems

Probabilistic Safety Assessment (PSA) provides a systematic and quantitative approach to assess the risk associated with different components and systems within a nuclear power plant. By quantifying the impact of risk mitigation measures, decision-makers can prioritize and implement solutions that have the most significant impact on reducing risk. Fault Tree Analysis (FTA) is employed as a systematic method within PSA, encompassing all modes of failure across equipment and associated support systems, including unavailability due to maintenance (UDM), human errors (HEs), and common cause failures (CCFs). In the present research, the Extra Borating System (EBS) and the Chilled Water Operating Circuit System (CWOCS) of essential loads are modeled in the SAPHIRE code using VVER-1000 design data. Through importance analysis employing the Fussell-Vesley criterion, the most significant basic events for these two systems are identified. Subsequently, the outcomes of the importance analysis are examined using diversity, SPAR-H, and Reliability Centered Maintenance (RCM) techniques. Recommendations such as the enhancement of diversity, increasing staff training, promoting Human Machine Interface (HMI), reduction of maintenance time, and improvement of power supply reliability are proposed for the most crucial basic events. The ensuing impact of these measures on the reliability of the EBS and CWOCS is subsequently assessed. Through a comparison between the new failure probability and the previous, it is determined that improvements in CCFs contribute a 30% effect; HEs have a 14% effect and UDMs have a 5% effect, with a cumulative impact of 35% on the failure probability of the EBS system. Similarly, for the CWOCS system, enhancements in CCFs contribute 20%, UDMs 17%, and improved power supply reliability 19%, with a cumulative impact of 29%.

A novel approach towards parametric assessment of reliability and resilience of high voltage mica‐based insulation systems by statistical analysis of experimental failure data

AbstractInsulation systems in high‐voltage electric machines play a pivotal role in the reliable operation and longevity of the equipment. Mica‐based insulation materials have proven to possess and maintain excellent dielectric properties in the long run and prevent premature insulation degradation. Numerous qualifications tests, such as voltage endurance, are outlined in IEC and IEEE standards. The authors, however, take a different parametric approach, opting for reliability assessment of insulation systems using derived three‐parameter Weibull models. Therefore, instead of simple pass–fail criteria, empirical data is employed to determine failure rate probabilities quantitatively and objectively. Experimental data, including breakdown, dissipation factor, and partial discharge measurements, are used to construct the Weibull distribution model to predict fault and failure rates and calculate hazard functions. The rigorous examinations interpreted through the analytical model help assess insulation system resilience and particularly the impact of electrical field stress and mica content. Variation of electrical stress from 66.75 to 71.20 V/mil demonstrated how the mean time to failure of the system changed from 146.4 to 85.1 at 3 Un, hence identifying opportunities for design improvement and uncovering performance boundaries. Ultimately, the developed framework enhances comprehension of insulation system failure probabilities, guiding design decisions and ensuring a secure and reliable operation of electrical machines across applications.

Meta model-based and cross entropy-based importance sampling algorithms for efficiently solving system failure probability function

The multi-mode system failure probability function (SFPF) can quantify how the distribution parameters of the random input vector affect the system safety and decouple the system reliability-based design optimization model. However, for a problem with a time-consuming implicit performance function and rare failure domain, efficiently solving the SFPF remains significantly challenging. Therefore, in this study, two efficient algorithms are proposed, namely, the meta model-based importance sampling and cross entropy-based importance sampling. The contributions of this study are twofold. The first is constructing a single-loop optimal importance sampling density (SL-OISD) method to decouple the double-loop framework for analyzing the SFPF. The second is establishing two methods to efficiently approximate the SL-OISD and complete the SFPF estimation. The first method is based on the meta model of the system performance function, which is abbreviated as SL-Meta-IS. The second method is based on minimizing the cross entropy between the Gaussian mixture density model and SL-OISD, which is abbreviated as SL-CE-IS. To reduce the number of evaluating the system performance function when approximating the SL-OISD, sampling the SL-OISD, and identifying the state of the samples for completing the SFPF estimation, an adaptive Kriging model of the system performance function is introduced into SL-Meta-IS and SL-CE-IS. Owing to decoupling the double-loop framework into a single-loop framework, replacing the time-consuming system performance function with the economic Kriging model, and employing importance sampling variance reduction techniques to address issues related to the rare failure domain, the proposed SL-Meta-IS and SL-CE-IS methods greatly enhance the efficiency of SFPF estimations. The numerical and practical examples demonstrate that the two proposed methods are superior to the existing algorithms; moreover, the efficiency of SL-CE-IS is higher than that of SL-Meta-IS.

Hybrid response surface method for system reliability analysis of pile-reinforced slopes

To consider the complex soil-structure interaction in a pile-slope system, it is necessary to analyze the performance of pile-slope systems based on a three-dimensional (3D) numerical model. Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability. In this paper, an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes, where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure, respectively. The versatility of the suggested method is illustrated in detail with an example. For the example examined in this paper, it is found that the pile failure can significantly contribute to system failure, and the reinforcement ratio can effectively reduce the probability of pile failure. There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio. The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope. There exists an optimal location and an optimal length for the stabilizing piles.

Alarm rationalization and dynamic risk analyses for rare abnormal events

In this paper, improved alarm rationalization strategies are introduced to evaluate the quality of the multivariate alarm systems developed in previous work – with the alarm thresholds and response actions modified appropriately, based on key statistical metrics. For an exothermic CSTR, our strategies resulted in a significant reduction in the number of nuisance alarms, focusing on only quality alarms, which, if ignored, are more likely to result in an abnormal shift in operation to the undesirable regions. Next, their real-time performance is evaluated using dynamic risk analysis (DRAn), in which, the associated risk is analyzed by estimating the failure probabilities of the multivariate alarm systems using Bayesian statistics, based on multiple dynamic simulations for the process, inclusive of control, alarms and response actions. As expected, the failure probability distribution developed for the exothermic CSTR has a much lower variance as compared to one developed using a flat prior distribution.