Failure Probability Analysis Research Articles

Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

Sensitivity analysis of system reliability using the complex-step derivative approximation

Sensitivity analysis of system failure probability is performed to evaluate the dependence of system reliability on design parameters or component events. Sensitivity analysis is integral for the implementation of efficient gradient-based optimization algorithms in system reliability-based design optimization, and for risk-informed decision-making. This paper presents a method for sensitivity analysis of system failure probability using complex-step differentiation. Many derivative approximations use a small step size to minimize subtractive cancellation errors. The complex-step approximation utilizes an imaginary number, such that the subtractive cancellation is not included in the formulation, resulting in calculations without the associated round-off error. The level of accuracy in sensitivity analysis using the finite difference method (FDM) can vary with change in the step size, which is generally selected arbitrarily, as the actual effect of the step size on the result itself is difficult to predict prior to actual calculation. The complex-step approximation, however, is not confined by the step size, as subtraction cancellation is not included. Compared to the FDM, the complex step approximation has only one limit, the numerical precision of evaluating the function. The proposed method integrates complex-step differentiation into a numerical integration scheme, for the assessment of system reliability and sensitivity. System failure probability and sensitivity are obtained by taking the real and imaginary part of the cumulative distribution function, which is numerically evaluated using the proposed method. The computational efficiency for system reliability problems involving high dimensionality is improved with the utilization of a dimension reduction technique. Numerical examples of sensitivity analysis for series, parallel, and general systems are presented to illustrate the performance of the proposed method.

System failure probability analysis of cohesive slope considering the spatial variability of undrained shear strength

System failure probability analysis of cohesive slope considering the spatial variability of undrained shear strength

Dynamic failure probability analysis of urban gas pipeline network

The gas pipeline network is an essential infrastructure for a smart city. It provides a much-needed energy source; however, it poses a significant risk to the community. Effective risk management assists in maintaining the operational safety of the network. The risk management of the network requires reliable dynamic failure probability analysis. This paper proposes a methodology of condition monitoring and dynamic failure probability analysis of urban gas pipeline network. The methodology begins with identifying key design and operational factors responsible for pipeline failure. Subsequently, a causation-based failure model is developed as the Bowtie model. The Bowtie model is transformed into a Bayesian network, which is analyzed using operational data. The key contributory factors of accident causation are monitored. The monitored data is used to analyze the updated failure probability of the network. The gas pipeline network's dynamic failure probability is combined with the potential consequences to assess the risk. The application of the approach is demonstrated in a section of the urban gas pipeline.

Vine Copula Data Fusion for Failure Probability Analysis of Steel Bridge Girder Section

Abstract For steel bridge girders, several control sections usually exist. If one or more sections fail, then the bridge girder might fail. Therefore, the failure probability analysis of each contr...

Investigation on the fracture and mechanical behaviors of simulated transversely isotropic rock made of two interbedded materials

Transversely isotropic rock composed of two interbedded layers has been rarely studied, although landslides frequently occur in bedded rock masses. With reference to the interbedded rock mass in the Miaowei Reservoir area of Yunnan Province, China, this study prepares transversely isotropic specimens made of two interbedded materials to investigate the fracture and mechanical behaviors of interbedded rock. The effect of the bedding plane dip angle and the application of the findings to an anti-dip interbedded rock slope are also studied. Specifically, two groups of isotropic specimens and five groups of transversely isotropic specimens are tested in a series of triaxial compressive tests; based on these tests, the crack types, failure modes and mechanical parameters are analyzed, and one damage model and its application to the failure probability analysis of an anti-dip interbedded rock slope are investigated. The experimental results show that twelve crack types, eight failure modes and five axial stress-strain curve types can be summarized and are significantly affected by the dip angle. The recognition of these crack types and failure modes can improve the qualitative instability analysis of bedded rock masses in the reservoir area, and five mechanical parameters, including peak stress, strain related to peak strength, residual strength, elastic modulus and Poisson's ratio, exhibit fluctuating variation trends versus the dip angle and confining stress due to the influence of the dip angle. Two groups of theoretical curves from the proposed damage model correspond with the pre-peak features of the test stress-strain curves. The proposed failure probability model considering rock damage shows good practicality when applied to an anti-dip interbedded rock slope; the slope displays discrete failure probabilities in various parts, e.g., the slope toe, slope shoulder and weaker layer show higher failure probabilities, and the relaxation behavior increases the failure probabilities and gradually eliminates the discreteness. Relevancy analysis shows that the strength of transversely isotropic rock is more sensitive to the elastic modulus, dip angle of bedding plane, confining stress and composition of the rock.

Discretisation and Product Distributions in Ring-LWE

Abstract A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts.

Study on seismic failure probability of high earth-rock dam considering dam body deformation and slope stability

The reliability analysis is one of the main methods for the quantitative analysis of the safety in the geotechnical engineering. This method can provide the failure probability with a clear physical meaning. Due to the complex structure of high earth-rock dams and the non-linear characteristics of the material properties, it is very difficult to perform the reliability analysis on such large nonlinear structures. Currently, there are few studies on the reliability analysis of high earth-rock dams that consider the earthquakes, the dam body deformation and the dam slope stability at the same time. In this paper, the dam cracks generated by the earthquakes are used as the criteria for the dam body seismic deformation evaluation, and the inclination method is adopted for the dam body seismic deformation analysis. The simplified Bishop method combined with the ratio of the safety margin method is used to analyze the dam slope stability. In order to consider the soil material properties, the thickness of the compressible soil layer and the uncertainty of the earthquakes, a seismic failure probability analysis method for evaluating the seismic danger of high earth-rock dams considering the dam body deformation and the dam slope stability is established based on the reliability theory. Taking a concrete face rockfill dam as an example, the method is used to analyze the seismic failure probability of the dam during the design reference period. It provides the reference for the seismic design and the risk analysis, and establishes the risk level of high earth-rock dams.

Failure probability analysis of overhead crane bridge girders within uncertain design parameters

In the design of steel crane girders, various sources of uncertainty such as material properties, loads, and geometric tolerances are inherent and inevitable. Using deterministic structural and/or load conditions may lead to low-reliability systems in real applications. In this paper, the probability of failure of overhead crane bridge girders with uncertain design parameters is investigated. First, the design problem of a crane double girder is introduced within a set of analytical stress and defection constraints. Then, the response surface method is used in conjunction with Monte Carlo methods to quantify the effect of the parameter uncertainties on the constraints of stress and deflection. For illustrative examples, various configurations of girders with original deterministic parameters proposed in the literature are selected and their deterministic optimization values are considered as the mean of random variables. The obtained results reveal that uncertainties such as coefficients of variation (COV) in structures and loads have strong effects on the probability of failure for all stated crane girder configurations. For only a wheel load COV of 0.05 and geometric dimension COV of 0.025, the means of geometric parameters have to be larger than 1.1 their deterministic-based values in order to reach a probability of failure at a level of 10-4.
 Keywords:
 failure probability; double-box girder; overhead crane; Monte Carlo method.

A novel active learning reliability method combining adaptive Kriging and spherical decomposition-MCS (AK-SDMCS) for small failure probabilities

Structural reliability analysis for small failure probabilities remains a challenging task, despite the significant progress made by the active learning reliability methods (ALRMs) represented by AK-MCS (ALRMs combining adaptive Kriging and Monte Carlo simulations). In order to address this issue, advanced ALRMs with improved computational efficiency than AK-MCS have been proposed, however at the expense of sacrificing the generality and simplicity of AK-MCS. Therefore, a novel ALRM combining adaptive Kriging and spherical decomposition-MCS (AK-SDMCS) was proposed to alleviate the computational cost and preserve the advantages of AK-MCS simultaneously. The key of AK-SDMCS lies in the spherical decomposition-MCS (SDMCS), which not only decomposes the computationally intensive active learning of AK-MCS into a series of easy-to-compute active learning in the divided subsets but also reduces the total number of candidate samples by focusing the sampling region on the most probable failure regions (MPFRs) and adaptively allocating samples in the divided subregions. As a result, AK-SDMCS significantly alleviates the computational cost of active learning of Kriging model. Since AK-SDMCS is built in the framework of AK-MCS, the advantages of AK-MCS can be preserved. Besides, the active learning strategy is modified to further increase the computational efficiency. Thus, AK-SDMCS provides an efficient, easy-to-implement and generalized option for reliability analysis of small failure probabilities. The application and efficiency of AK-SDMCS are demonstrated by three academic examples.

Reliability-based design optimization of steel frames using direct design

This paper presents an effective method for reliability-based design optimization (RBDO) of steel frames by combining direct design using nonlinear inelastic analysis, an improved importance sampling technique for structural failure probability analysis, and an improved differential evolution (DE) algorithm for optimization. The nonlinear inelastic analysis using the beam-column approach is used to capture the second-order effects and the inelastic behavior of structures. An improved importance sampling technique based on nonlinear inelastic analysis of the structure is employed that significantly reduces the number of structural analyses required for calculating the structural failure probability. An improved DE algorithm, which can effectively eliminate the redundant structural analyses for objective function evaluation, is utilized. A six-story space frame is studied to demonstrate the computational efficiency of the proposed method.

A Novel Prediction Algorithm for Heavy Vehicles System Rollover Risk Based on Failure Probability Analysis and SVM Empirical Model

<div class="section abstract"><div class="htmlview paragraph">The study of heavy vehicles rollover prediction, especially in algorithm-based heavy vehicles active safety control for improving road handling, is a challenging task for the heavy vehicle industry. Due to the high fatality rate caused by vehicle rollover, how to precisely and effectively predict the rollover of heavy vehicles became a hot topic in both academia and industry. Because of the strong non-linear characteristics of Human-Vehicle-Road interaction and the uncertainty of modeling, the traditional deterministic method cannot predict the rollover hazard of heavy vehicles accurately. To deal with the above issues, this paper applies a probability method of uncertainty to the design of a dynamic rollover prediction algorithm for heavy vehicles and proposes a novel algorithm for predicting the rollover hazard based on the combined empirical model of reliability index and failure probability. Moreover, the paper establishes a classification model of heavy vehicles based on the support vector machine (SVM) and uses the Monte Carlo method to calculate the failure probability of rollover limit state of heavy vehicles. The fishhook, double lane change, and slalom maneuver tests of heavy vehicles are used to predict and validate the proposed algorithm in real-time. The simulation results show that the rollover prediction method based on failure probability is accurate and real-time, and can effectively improve the rollover prediction accuracy. Meanwhile, the proposed approach reduces the external interference of strong non-linear characteristics of Human-Vehicle-Road interaction and the uncertainty of the modeling to the system, thus significantly improving the prediction accuracy of active safety performance of heavy vehicles.</div></div>

Multidisciplinary reliability analysis of turbine blade with shape uncertainty by Kriging model and free-form deformation methods

This work presents an integrated approach for the multidisciplinary reliability analysis of turbine blades with shape uncertainty, including the metamodel, the free-form deformation, and the Monte Carlo simulation. The multidisciplinary analysis of turbine blade includes fluid, structure, and thermal analyses, which is time-consuming during integration with multidisciplinary reliability analysis. The metamodel is constructed by adaptive sampling to reduce computational cost. The shape uncertainty with small size changes in reliability analysis should be considered. The geometry-based multidisciplinary analysis may fail to capture the small size changes during the geometry and mesh regeneration process. The main contribution of this article is to introduce the free-form deformation in multidisciplinary reliability analysis to overcome the aforementioned problems. The mesh-based method supported by free-form deformation is proposed. Failure probability analysis of the multidisciplinary blade system is performed using the Monte Carlo simulation and the surrogate model. Through the numerical simulation, it is found that the failure probability increases as the blade shape uncertainty becomes larger. The methodology in this article provides a valuable and applicative way to calculate the risk of blade in multidisciplinary system.

Round robin analysis of vessel failure probabilities for PTS events in Korea

Round robin analyses for vessel failure probabilities due to PTS events are proposed for plant-specific analyses of all types of reactors developed in Korea. Four organizations, that are responsible for regulation, operation, research and design of the nuclear power plant in Korea, participated in the round robin analysis. The vessel failure probabilities from the probabilistic fracture mechanics analyses are calculated to assure the structural integrity of the reactor pressure vessel during transients that are expected to initiate PTS events. The failure probabilities due to various parameters are compared with each other. All results are obtained based on several assumptions about material properties, flaw distribution data, and transient data such as pressure, temperature, and heat transfer coefficient. The realistic input data can be used to obtain more realistic failure probabilities. The various results presented in this study will be helpful not only for benchmark calculations, result comparisons, and verification of PFM codes developed but also as a contribution to knowledge management for the future generation.

Estimating probability of fatigue failure of steel structures

The article deals with the analysis of failure probability of the effect of random factors in uencing fatigue crack propagation in a steel element under bending moment. The theoretical model of fatigue crack progression is based on linear fracture mechanics. When determining the required degree of failure probability, it is possible to specify the time of the first inspection of the construction, which will focus on the fatigue damage. Using a conditional probability, subsequent inspection times are specified. The failure probability is examined using a fairly new sensitivity analysis subordinated to a contrast. The importance ranking of the input random variables to the failure probability is investigated. Fatigue properties of steel are taken from recent experimental research. Numerical results are obtained using the Monte Carlo simulation.

Failure probability analysis of heliostat systems

Heliostats represent the most important maintenance cost in the solar power tower plant. The aim of this work is to provide a failure probability analysis for heliostat design in order to minimize this maintenance cost. Based on mechanics of material study and wind aerodynamic analysis, a performance function, with five random variables, has been developed wherein the random variables are: wind speed, inside and outside pedestal diameters, pedestal yield stress and mirror mass. Four main methods have been proposed: first order reliability method, second order reliability method, Monte Carlo (MC) method and subset simulation (SS) method. The variation of failure probability with the variation of pedestal wall thickness and wind speed, for different outside diameters and heliostat azimuth and elevation angles, has been simulated. The results show that SS is more efficient and accurate for small failure probabilities; however, MC is more accurate for high failure probabilities.

Approximation-Aware Design of an Image-Based Control System

Image-based control (IBC) systems are common in many modern applications. In such systems, image-based sensing imposes massive compute workload, making them challenging to implement on embedded platforms. Approximate image processing is a way to handle this challenge. In essence, approximation reduces the workload at the cost of additional sensor noise. In this work, we propose an approximation-aware design approach for optimizing the energy, memory and performance of an IBC system, making it suitable for embedded implementation. First, we perform compute- and data-centric approximations and evaluate its impact on the energy efficiency, memory utilization and closed-loop quality-of-control (QoC) of the IBC system. We observe that the workload reductions due to approximations allow mapping these lighter approximated IBC tasks to embedded platforms with lower power consumption while still ensuring proper system functionality. Therefore, we explore the interplay between approximations and platform mappings to improve the energy-efficiency of IBC systems. Further, an IBC system operates under several environmental scenarios e.g., weather conditions. We evaluate the sensitivity of the IBC system to our approximation-aware design approach when operated under different scenarios and perform a failure probability (FP) analysis using Monte-Carlo simulations to analyze the robustness of the approximate system. Finally, we design an optimal approximation-aware controller that models the approximation error as sensor noise and show QoC improvements. We demonstrate the effectiveness of our approach using a concrete case-study of a lane keeping assist system (LKAS) using a heterogeneous NVIDIA AGX Xavier embedded platform in a hardware-in-the-loop (HiL) framework. We show energy and memory reduction of up to 92% and 88% respectively, for 44% QoC improvements with respect to the accurate implementation. We show that our approximation-aware design approach has an FP (per km) $\leq 9.6\times 10^{-6}$ %.

Failure Probability Analysis of Heliostat Systems

Heliostats represent the most important maintenance cost in the solar power tower plant. The aim of this work is to provide a failure probability analysis for heliostat design in order to minimize this maintenance cost. Based on mechanics of material study and wind aerodynamic analysis, a performance function, with five random variables, has been developed wherein the random variables are: wind speed, inside and outside pedestal diameters, pedestal yield stress and mirror mass. Four main methods have been proposed: first order reliability method, second order reliability method, Monte Carlo (MC) method and subset simulation (SS) method. The variation of failure probability with the variation of pedestal wall thickness and wind speed, for different outside diameters and heliostat azimuth and elevation angles, has been simulated. The results show that SS is more efficient and accurate for small failure probabilities; however, MC is more accurate for high failure probabilities.

Punch-Through Risk of Jack-Up Under the Dual Uncertainty of Structure and Foundation

Abstract The preload operation of Jack-up in complex multi-layered foundation requires an enhanced understanding of its behavior in punch-through accident and suitable safety analysis tools for the assessment of their reliability in a particular site. In order to evaluate punch-through risk, a risk-consistent method is proposed based on the model of foundation hazard and structural vulnerability. Besides, foundation bearing capacity is evaluated to quantify foundation hazard. Third, to improve the solution efficiency, higher-order moment method (HOMM)-Pushover method has been developed for assessing the structural vulnerability. In addition, case studies are presented to demonstrate the advantages of these techniques and important trends are highlighted by the results of parametric sensitivity studies. More specifically, failure probability analysis has been undertaken using improved method and the punch-through risk is evaluated quantitatively in different hazard levels. The results show that the dual uncertainty of both structure and foundation is crucial for assessment of foundation hazard and structural vulnerability. The randomness of foundation parameters is the dominant factor affecting the punch-through risk, and the risk increases with the increase of preload weight. The time-varying risk in the process of preload operation can be revealed using the risk analysis method mentioned in this paper.

Time interval of multiple crossings of the Wiener process and a fixed threshold in engineering

In analyzing the practical engineering problems involving stochastic processes, a key component is the estimation of time intervals between the crossings across a specified threshold. However, the former research works are mainly focusing on first-passage problem, the multiple-passage problem, more importantly, have not been investigated in details. In this paper, the multiple-passage problem associated with the Wiener process is studied. The work is focusing on the derivation of probability distribution for the time interval between two adjacent crossings of a Wiener process. First, it is demonstrated that the time intervals of any two adjacent crossings of the Wiener process are identically distributed. The probability density function of the second-passage time of a Wiener process across a threshold is derived. This is then implemented in the derivation of distribution of the time interval between the first-passage time and the second-passage time. Based on the derivation of the joint probability density function of the two-dimensional random vector consisting of the first-passage time and the second-passage time, the explicit analytical expression of the probability distribution function of the time interval between the first-passage time and the second-passage time are obtained finally. Since the probability distribution of each time interval is identical, the probability density function of each time interval is thus generalized. To demonstrate the proposed distribution model, the theoretical result is applied in the analysis of road surface unevenness beyond a limit and the failure probability analysis of electronic products under noice jamming, which shows that the developed approach has important applications in different fields of engineering.