Interval Of Failure Probability Research Articles

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.

Hybrid reliability analysis with incomplete interval data based on adaptive Kriging

Hybrid reliability analysis with mixed random and interval uncertainties is a significant challenge in the reliability assessment of engineering structures. The situation will be more intractable when involving incomplete interval data. To obtain reliable estimates of the failure probability limits, an effective parameter estimation method, integrating the quantile variant of the Expectation-Maximization algorithm and Kullback-Leibler divergence, is proposed to transform uncertain variables with incomplete data into random variables with distribution uncertainty. Then, an adaptive Kriging-assisted hybrid reliability analysis method is developed to ensure computational accuracy and efficiency. In this method, a candidate pool incorporating the distribution uncertainty is constructed and its size is adaptively reduced by removing the samples that violate the projection uniformity on input dimensions with exact distributions. Meanwhile, an improved U learning function and an error-based convergence criterion are defined to drive and stop the adaptive process. Then the failure probability limits are estimated by combining the refined Kriging model and Monte Carlo simulation. Four application examples are employed to verify the superiority of the proposed method. Comparison results show that the proposed method can significantly improve computational efficiency while ensuring the accuracy and reliability of the estimated failure probability interval under incomplete interval observations.

Method study on failure probability and uncertainty analysis of stress corrosion cracking in fixed parts of PWR

To estimate the failure probability of stress corrosion cracking (SCC) in the fixed parts of pressurized water reactors (PWR), an approach based on the Paris model was developed and its uncertainty analysis was performed as well. In the study of SCC failure, the uncertainty of fracture toughness was translated into integral form to improve calculation efficiency. Moreover, uncertainty parameters such as crack size and Paris model coefficients were studied in the uncertainty analysis. On this basis, the thermowell of the pressurizer of PWR as an example was analyzed in this study. The Monte Carlo (MC) method and polynomial chaos expansion (PCE) approach were used to calculate the mean value, relative uncertainty, upper limit of tolerance interval of failure probability, and sensitivity coefficient of input parameter to compare the advantages and disadvantages of these methods. According to the results, compared with the other method, 300 sets of sampling with Latin Hypercube sampling (LHS) and Sobol sequences can converge the mean, and 300 sets of sampling with Halton sequence and Hammersley sequence can converge the relative uncertainty. When LHS with the 4th order Wilks' formula and Halton sequence with the 1st order Wilks' formula to compute the upper limit of tolerance interval, the accuracy and cost of the computation can be balanced. According to the results of the sensitivity analysis, crack aspect ratio is the most sensitive parameter. PCE surrogate model can accurately calculate the mean, relative uncertainty, the upper limit of tolerance interval and sensitivity coefficient, thereby reducing the computational cost.

A Partial Multiplicative Dimensional Reduction-Based Reliability Estimation Method for Probabilistic and Non-Probabilistic Hybrid Structural Systems

A new reliability estimation method based on partial multiplicative dimensional reduction is proposed for probabilistic and non-probabilistic hybrid structural systems. The proposed method is characterized by decorrelating interval input variables from random input variables using the partial multiplicative dimensional reduction method in conjunction with the weakest-link theory. In this method, the failure statistics of the original performance function are equivalent to a statical chain of two elements, in which one of the two elements represents the failures due to random input variables and the other represents the failures due to interval variables. Rather than yielding an estimated interval of failure probability, the proposed method produces a single value for failure probability, which is more meaningful for engineering. In addition, the accuracy, validity, and superiority of the proposed method are demonstrated, and the error-related properties of the proposed method are investigated.

Adaptive structural reliability analysis method based on confidence interval squeezing

Kriging-based adaptive structural reliability analysis methods can replace the structural performance function and perform reliability analysis accurately and efficiently by using appropriate learning functions. In this context, a novel adaptive structural reliability analysis strategy, namely, confidence interval squeezing (CIS) method, is presented in this paper. After obtaining the confidence interval of the failure probability on the basis of the given significance level α, CIS considers squeezing the confidence interval at the highest speed possible to improve the accuracy of estimating the failure probability. CIS strives to improve the estimation accuracy of failure probability rapidly rather than paying too much attention to the state of a single candidate sample, which is the primary difference between the CIS method and other learning functions. In addition, a new global convergence condition is proposed based on the confidence interval of failure probability. Considering the difficulty of direct application of CIS, three variants of the CIS method, namely, sCIS method for sequence additions, pCIS method for parallel additions based on a clustering algorithm, and improved pCIS (ipCIS) method, are proposed. Several examples are used to demonstrate that each CIS method can handle the complex limit state function and the engineering problem of implicit functions efficiently and accurately.

Slope hybrid reliability analysis considering the uncertainty of probability-interval using three-parameter Weibull distribution

A reliability model is proposed to solve the problem of hybrid uncertainty with both random and interval variables in slope engineering. A hybrid uncertainty model based on the dimension reduction method and Taylor expansion is constructed to approximate the limit state function. Using the polynomial theorem and variable transformation method, the origin and center moments’ interval of the limit state function are calculated. Moment information is applied to the expansion of a three-parameter Weibull distribution, and the cumulative distribution function and probability density function of limit state function are determined. As a result, the failure probability interval of the slope is calculated. The interval uncertainty problem is transformed into an interval certainty problem using Taylor expansion without solving for the statistical moment of limit state function using multiple integrals and iteratively searching for the most probable failure points. The numerical results from two slopes show that the proposed method is effective and feasible.

Vulnerability analysis of aqueduct structure based on boundary method

The damage forms of aqueduct under earthquake are mainly reflected in column of bent and rubber bearing. Taking a typical aqueduct as an example, the uncertainty of structural materials of aqueduct is considered by Latin hypercube sampling method; the uncertainty of ground motion is considered by stratified sampling method; the aqueduct sample and seismic wave are randomly combined to carry out time history analysis to obtain structural response; the limit damage states of column of bent and rubber bearing are defined respectively; the vulnerability curves of components are established by classical vulnerability analysis method. The system vulnerability curve of aqueduct structure is obtained by boundary method. The results show that the rubber bearing of aqueduct is more vulnerable to damage than bent frame. The failure probability interval obtained by the second-order limit method is smaller than that obtained by the first-order limit method, and the second-order limit method is more reasonable to evaluate the seismic performance of aqueduct structure.

Random-interval hybrid reliability analysis for fan performance in the presence of epistemic uncertainty

With the aim of reducing fan performance failure, an effective method of fan reliability analysis based on a hybrid uncertainty model was investigated using a combination of orthogonal test design, an approximation model, and computational fluid dynamics (CFD) simulation and analysis technology. By introducing interval uncertainty, this method can effectively solve the problem of quantifying model uncertainty owing to the lack of experimental samples and can greatly expand the applicability of reliability analysis technology in fluid machinery research. Random and interval uncertainty parameters were introduced to describe the fan system and a mixed random-interval reliability analysis model of fan performance was established based on the traditional first-order reliability analysis method. Using CFD analysis of the renormalization group (RNG) model, the flow, pressure, shaft power, efficiency, and other fan performance parameters were calculated, and the performance function was obtained. Owing to the low efficiency of the CFD calculation, the effective iterative algorithm of response surface to solve hybrid reliability model was studied, and the failure probability interval of fan performance was calculated. The method was used to study the fan performance of a rail transit train, and the failure probability, reliability index, and performance parameter sensitivity and uncertainty were analyzed. The influence of parameter uncertainty on system reliability was determined, and the engineering measures necessary to improve the fan’s performance reliability were proposed.

A Most Probable Point-Based Univariate Method for Reliability Evaluation of Composite Laminates With Random and Interval Parameters

Due to complicated manufacturing processes and inherent dispersions of constituents, uncertainty is unavoidably existing in mechanical properties, including strength, of composite laminates which can be described as random or interval variables. Considering the multivariable and hybrid uncertainty, the hybrid reliability evaluation of composite laminates is quite an important problem. The objective of this paper is to construct a reliability evaluation method to evaluate hybrid reliability of composite laminates accurately and efficiently. The existence of interval variables produced a limit-state strip formed by minimum and maximum limit state function (LSF). Combining first-order reliability method (FORM) and univariate method, the paper developed a strategy to search the most probable point (MPP) of minimum and maximum LSF. In the process of MPP searching, the univariate function of interval variables is constructed by Legendre orthogonal polynomials and the least-square fitting method. Then, the minimum and maximum LSF are constructed at MPP in a similar way with interval variables which can ensure the accuracy of LSF approximation. Furthermore, Monte–Carlo simulation can be utilized to calculate interval of failure probability. Finally, the results of examples verified the accuracy and efficiency of the constructed model.

A novel univariate method for mixed reliability evaluation of composite laminate with random and interval parameters

Requiring probability density distribution functions of uncertain variables, it is difficult for conventional structural reliability analysis methods to calculate the reliability of composite laminates with both random and interval variables. To evaluate the safety of composite laminated structures under this circumstance, this paper is aimed at developing a precise and efficient univariate method for the reliability assessment of composite laminates taking use of Legendre orthogonal polynomials and Monte Carlo Simulation. In this paper, based on the Tsai-Wu failure criterion and first-ply failure assumption, the failure criterion of composite laminate is constructed firstly. Then the performance function of each lamina is approximately expressed as the sum of univariate contributions of all uncertain variables on the basis of the univariate method. Taking use of Legendre orthogonal polynomials, the univariate functions of random and interval variables are constructed by the least square fitting method and the univariate contribution bounds of interval variables are derived afterwards. Furthermore, the interval of failure probability can be calculated by substituting contribution bounds of interval variables and sample points of random variables into univariate function. At last, two examples and an engineering application are provided to demonstrate the efficiency and accuracy of the proposed method.

Failure Risk Interval Estimation of Traction Power Supply Equipment Considering the Impact of Multiple Factors

Quantifying the failure risk of traction power supply equipment (TPSE) is of significant importance to the safe and stable operation of the traction power supply system. This paper proposes a method for conducting failure risk interval estimation for the TPSE while accounting for the impact of multiple factors. This method consists of two parts, i.e., the estimation of failure probability interval, and the analysis and quantification of the failure consequences: 1) based on the historical statistical data of equipment failure, a credal network model of TPSE is constructed. By combining the imprecise Dirichlet model and the inference algorithm of credal network, the probability interval of equipment failure is estimated for a given operational condition and 2) the risk-based failure mode and effects analysis table is established for qualitatively analyzing the failure risk of TPSE. This, coupled with the consideration of equipment failure level, enables the quantification of failure consequences from the perspectives of both economic loss and time loss. Finally, the estimation of equipment’s failure risk interval is obtained by integrating the failure probability interval and the quantitative consequences. A case study is conducted utilizing the failure samples of contact mesh equipment derived from the practical power supply section, so as to verify the validity and usability of the proposed risk interval estimation method and the corresponding indices.

Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

SummaryReliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.

A Probabilistic and Interval Hybrid Reliability Analysis Method for Structures with Correlated Uncertain Parameters

This paper proposes a probability-interval mixed uncertainty model considering parametric correlations and a corresponding structural reliability analysis method. First of all, we introduce the sample correlation coefficients to express the correlations between different kinds of uncertain variables including probability and interval variables. Then dependent parameters are transformed into independent ones through a matrix transformation. A reliability analysis model is put forward, and an efficient method is built to obtain the reliability index or failure probability interval of the structure. Finally, four numerical examples are provided to verify the validity of the method.

신규 개발하는 소모성 발사체의 베이지안 신뢰도 추정

ABSTRACT Purpose: This paper explains how to obtain the Bayes estimates of the whole launch vehicle and of a vehicle stage, respectively, for a newly developed expendable launch vehicle. Methods: We determine the parameters of the beta prior distribution using the upper bound of the 60% Clopper-Pearson confidence interval of failure probability which is calculated from previous launch data con-sidering the experience of the developer. Results: Probability that a launch vehicle developed from an inexperienced developer succeeds in the first launch is obtained by about one third, which is much smaller than that estimated from the previous research. Conclusion: The proposed approach provides a more conservative estimate than the previous noninformative prior, which is more reasonable especially for the initial reliability of a new vehicle which is developed by an inexperienced developer.Key Words: Clopper-Pearson Confidence Interval, Beta Posterior Distribution, Stage-Based Reliability

Probabilistic interval reliability of structural systems

The probabilistic reliability approach is the most widely used method for reliability analysis. The recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model. It is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability. In this study, we introduce the interval approach into the conventional reliability theory. We present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables. This approach is a combination of the two techniques, namely the classical reliability theory and the interval analysis. In the end of this paper, we show the feasibility of the proposed approach through two examples of the truss systems.

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.