Stochastic Reliability Analysis Research Articles

QRP: quantum reliability polynomial for stochastic reliability analysis of reversible circuits

QRP: quantum reliability polynomial for stochastic reliability analysis of reversible circuits

Three-dimensional creep calculation model for reliability analysis of concrete-filled steel tubular (CFST) structure

For long-span concrete-filled steel tube (CFST) structure, it is essential to implement efficient and realistic prediction models for the long-term processes of core concrete creep. In order to systematically study the main influential factors in CFST structure creep effects, a probabilistic analysis can be performed. The objective of this paper is to analyse the long-term response of CFST structure by using time-dependent reliability method. To address the problem of creep calculation, a novel and comprehensive presentation was developed. By converting the integral-type creep law to a differential-type form with internal variables, based on the Kelvin chain model, an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains was established. We have compiled a three-dimensional (3-D) finite-element analysis programme that considers the creep Poisson effect of core concrete to analyse the long-term performance of the CFST structure. This is achieved by developing a commercial finite element code, such as Usermat in ANSYS. As calculation examples, several time-dependent analyses of a CFST stub column and long-span CFST arch bridge were performed. The calculated results of long-term behaviour agree well with experimental and measured data. Considering the randomness of various input parameters, such as physical dimensions and materials of the CFST structure, we have analysed the uncertainty using the Latin-hypercube-sampling (LHS) stochastic finite-element method. The results of creep sensitivity analysis revealed that coefficient of creep model uncertainty, steel and concrete elastic modulus were the three most influential parameters for CFST stub columns’ creep, and load, coefficient of creep model uncertainty, relative humidity, steel and concrete elastic modulus were the five for CFST arch bridges’ long-term deflection. In addition, the use of Monte Carlo (MC) and response surface (RS) methods for structural stochastic reliability analysis demonstrates the ability of these approaches to assess the reliability index of long-span CFST arch bridges. This provides a valuable reference for the design and performance evaluation of CFST structures.

Stochastic Substructural Response Reconstruction and Reliability Analysis of High-Dimensional Systems

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.

Static and Dynamic Reliability Analysis of Laterally Loaded Pile Using Probability Density Function Method

Pile foundation is one of the common foundation forms in marine geotechnical engineering, especially in wind power engineering. Its operation safety is seriously affected by many uncertainties, such as the randomness of ground motion in intensity and frequency. The stochastic reliability analysis method can better characterize these uncertainties in the evaluation of the safety performance of pile foundation. The probability density functions (PDFs) of stochastic systems are important prerequisites for reliability analysis. However, for geotechnical problems, the coupling between parametric and excitation randomness and the nonlinear mechanical properties of rock and soil make it very difficult to obtain the associated PDFs. Instead, the probability density evolution method (PDEM) is introduced and is used to investigate the static and dynamic reliability of laterally loaded piles as an example of a geotechnical problem. Compared with Monte Carlo stochastic simulations, PDEM-based computing is shown to be highly efficient when applied to the seismic design of pile in geotechnical engineering, and its calculation efficiency is 20 times of the former for the seismic dynamic reliability of pile foundation. This study provides a new reference for the efficient design and safety evaluation of offshore pile foundation engineering based on static and dynamic reliability of multiple random factors.

Machine learning aided stochastic reliability analysis of spatially variable slopes

This paper presents machine learning aided stochastic reliability analysis of spatially variable slopes, which significantly reduces the computational efforts and gives a complete statistical description of the factor of safety with promising accuracy compared with traditional methods. Within this framework, a small number of traditional random finite-element simulations are conducted. The samples of the random fields and the calculated factor of safety are, respectively, treated as training input and output data, and are fed into machine learning algorithms to find mathematical models to replace finite-element simulations. Two powerful machine learning algorithms used are the neural networks and the support-vector regression with their associated learningstrategies. Several slopes are examined including stratified slopes with 3 or 4 layers described by 4 or 6 random fields. It is found that with 200 to 300 finite-element simulations (finished in about 5 ~ 8 h), the machine-learning generated model can predict the factor of safety accurately, and a stochastic analysis of 105 samples takes several minutes. However, the same traditional analysis would require hundreds of days of computation.

Optimal Pipeline Maintenance Strategies in the United States: Stochastic Reliability Analysis of Gas Pipeline Network Failures

AbstractThe increasing number of corrosion-based incidents in pipeline systems within recent decades has encouraged decision makers to focus on predicting when pipelines will fail, and to improve m...

From full-scale testing of steel lattice towers to stochastic reliability analysis

analysis of the steel lattice telecommunication structure exposed to the wind pressure, whose average value is treated as the Gaussian random variable. The Least Squares Method is provided here for symbolic recovery of the polynomial responses of this structure in addition to the given uncertainty source and it serves to the twentieth order perturbation-based approximations for the first four probabilistic moments and coefficients. Static numerical analysis has been carried out by the use of the incremental BFGS (Broyden–Fletcher–Goldfarb–Shanno) procedure necessary for the so-called P-delta effect in steel structures, while the basic statistics of the ultimate limit state have been included into the formulas for the reliability indices of both first and second order. This study shows that the safety margin of such structures is definitely wider than it follows the basic Eurocodes statements, which means that designed durability period for these telecommunication structures is definitely longer.

Stochastic Reliability Analysis of Two Identical Cold Standby Units with Geometric Failure & Repair Rates

The present paper is based on the analysis of an two identical unit system wherein initially one unit is in operative state and other is in cold standby and total failure of the unit is via partial failure mode. Single repairman is always available with the system for any repair of failed unit (partially/ completely). Failure/repair time is considered to be a Geometric distribution. Measures of system effectiveness had also been calculated for the system.

Special Issue on Stochastic Dynamics and Reliability Analysis of Structural Systems Subject to Environmental Excitations

Special Issue on Stochastic Dynamics and Reliability Analysis of Structural Systems Subject to Environmental Excitations

Elastic critical moment for bisymmetric steel profiles and its sensitivity by the finite difference method

It is widely known that lateral-torsional buckling of a member under bending and warping restraints of its cross-sections in the steel structures are crucial for estimation of their safety and durability. Although engineering codes for steel and aluminum structures support the designer with the additional analytical expressions depending even on the boundary conditions and internal forces diagrams, one may apply alternatively the traditional Finite Element or Finite Difference Methods (FEM, FDM) to determine the so-called critical moment representing this phenomenon. The principal purpose of this work is to compare three different ways of determination of critical moment, also in the context of structural sensitivity analysis with respect to the structural element length. Sensitivity gradients are determined by the use of both analytical and the central finite difference scheme here and contrasted also for analytical, FEM as well as FDM approaches. Computational study is provided for the entire family of the steel I- and H - beams available for the practitioners in this area, and is a basis for further stochastic reliability analysis as well as durability prediction including possible corrosion progress.

Stochastic Fatigue Reliability Analysis for Torsion Shaft of Military Tracked Vehicles

There are coupled cases of high-cycle fatigue and low-cycle fatigue in torsion shaft of military tracked vehicles. To accurately analyze the stochastic fatigue reliability of torsion shaft, a new kind of decoupling method for high-cycle fatigue and low-cycle fatigue was firstly put forward. Probability fatigue accumulation damage theory and nominal stress method were combined to analyze high-cycle fatigue. Random response surface method was adopted to fit the life distribution function for low-cycle fatigue. To obtain the high-cycle and low-cycle stochastic fatigue reliability, probability fatigue accumulation damage theory and local stress and strain method were used. Then, composite damages of torsion shaft under high-cycle fatigue and low-cycle fatigue could be achieved based on probability fatigue accumulation damage thoery.

Stochastic Dynamic Reliability Analysis of Seismic Response of Soft Ground Including Silt

Due to the uncertainties and randomness of earthquake loads, it is more logical that reliability method should be employed in dynamic geotechnical engineering analysis. A methodology of 2-D effective stress FEM analysis based on dynamic reliability of seismic response of soft ground including silt is proposed in this paper, Duncan-Chang and Hardin-Drnevich hyperbolic models are used for static and dynamic constitutive relations of soils, respectively. Furthermore, three stochastic dynamic reliability analysis approaches based on the cumulative damage, cyclic shear stress and pore water pressure ratio are respectively suggested. The proposed methodology was applied to the stochastic dynamic reliability analysis of ground seismic response of two typical soft soil profiles in Shanghai in terms of seismic wave input depths of 50m and 280m. Basically consistent conclusions can be drawn in the three aforementioned perspectives. In addition, the filtering effect of frequency components by deeper soil layers plays perhaps an important role in dynamic reliability analysis in view of the fact that remarkable differences of dynamic reliability analysis results exist between 50m and 280m seismic wave input depths.

Probability Function Estimation of Rock Random Variables Using Chebyshev Orthogonal Polynomial

The Chebyshev orthogonal polynomial with sample moments (the origin moments) were used to approximate the probability density function (PDF) or cumulative distribution function (CDF) of variable (CPA method). Three examples from observed datas of uniaxial compressive strength of a kind of hard rock were presented for illustrative purposes. The results show the PDF or CDF of rock variables can be accurately derived from CPA method with sample moments. The relative errors of estimation by CPA method is much smaller than that of TDF method (PDF fitted by some standard theoretical distributions). It is suggested that the presented method can be used in stochastic reliability analysis of rock engineering.

Bayesian 추계학적 신뢰도 기법을 이용한 소양강댐 퇴사용량 감소의 불확실성 분석

저수지 내 퇴적과정으로 의한 저수용량 감소에 대한 효율적 관리의 중요성에도 불구하고, 불확실성을 포함하는 확률론적 관점의 신뢰도 분석이론을 활용한 저수용량 감소에 관한 연구는 많지 않다. 본 연구에서는 신뢰도 분석모형의 하나인 추계학적 감마 과정(stochastic gamma process)을 이용하고 개발된 모형을 소양강댐에서 적용하여 향후 발생될 수 있는 저수용량의 감소를 불확실성 측면에서 분석하였다. 특히 불확실성을 분석하기 위하여 정보적 사전분포(informative prior distribution)를 이용한 Bayesian MCMC 기법을 사용하여 추계학적 감마 과정의 모수(parameter)를 추정하였다. 구축된 정보적 사전분포를 적용한 결과사전분포의 불확실성에 비해 사후분포의 불확실성이 상당히 감소되어져 정보적 사전분포의 효과를 확인할 수 있었으며, 소양강댐 퇴사용량의 기대수명은(expected life time)은 5%유의수준에서 119.3년부터 183.5년의 불확실성을 나타내는 것으로 분석되었다. 이와 같은 연구는 저수용량의 감소에 관한 불확실성 측면의 정보를 신뢰도 분석결과와 함께 제공할 수 있으므로, 향후 퇴적과정으로 인한 저수지의 유지관리계획을 수립함에 있어 댐관리자 등에게 효과적으로 활용될 수 있을 것으로 판단된다. Despite of the importance on the maintenance of a reservoir storage, relatively few studies have addressed the stochastic reliability analysis including uncertainty on the decrease of the reservoir storage by the sedimentation. Therefore, the stochastic gamma process under the reliability framework is developed and applied to estimate the reduction of the Soyang Dam reservoir storage in this paper. Especially, in the estimation of parameters of the stochastic gamma process, the Bayesian MCMC scheme using informative prior distribution is used to incorporate a wide variety of information related with the sedimentation. The results show that the selected informative prior distribution is reasonable because the uncertainty of the posterior distribution is reduced considerably compared to that of the prior distribution. Also, the range of the expected life time of the dead storage in Soyang Dam reservoir including uncertainty is estimated from 119.3 years to 183.5 years at 5% significance level. Finally, it is suggested that the improvement of the assessment strategy in this study can provide the valuable information to the decision makers who are in charge of the maintenance of a reservoir.

Stochastic reliability analysis of armor units of rubble-mound breakwaters under the multiple loads

ABSTRACT Lee, C.-E., Kim, G. and Kim, S. U., 2013. Stochastic reliability analysis of armor units of rubble-mound breakwaters under the multiple loads. A stochastic reliability analysis model was developed for evaluating the time-dependent capacity variation of armor units of rubble-mound breakwaters subject to the multiple loads of arbitrary magnitudes which could occur randomly. The initial structural capacities and the damage rates of armor units of ruble-mound breakwaters was estimated as a function of the incident wave height with a given return period by using the modified Hudson's formula and Melby's formula. The structural capacity of armor units of rubble-mound breakwaters was also analyzed in detail through the lifetime reliability investigations according to the limit states such as the serviceability or ultimate limit state and the conditions of multiple loads. Finally, the repair intervals for the structural management was quantitatively evaluated by the present model that were developed by c...

Probability Density Evolution Method for Stochastic Earthquake Response and Reliability Analysis of Large-Scale Aqueduct Structures

The probability density evolution method (PDEM) has been used to research the stochastic earthquake response and reliability analysis of large-scale aqueducts structures, with the changeable water level in tub and under the condition of the interaction between water and boundary of the tub. The results show that，the probability distribution of stochastic seismic responses about aqueduct structure is rules distribution, the response and failure probability of large-scale aqueduct structures under the stochastic earthquake are increased as the rising of water level, however, with the water level unchangeably, the seismic response is distinctness smaller while the seismic reliability much higher after considering the water sloshing effect on the aqueduct structures. Within the calculation of seismic resistance about the large aqueduct structures, the impact should be considered including the changeable water level and water sloshing.

다중하중에 따른 경사제 피복재의 추계학적 신뢰성 해석

경사제에 불규칙하게 작용하는 임의 크기의 다중하중으로 인해 피복재의 안정성에 대한 성능이 시간에 따라 어떻게 달라지는지를 해석할 수 있는 추계학적 신뢰성 해석 모형이 개발되었다. Hudson의 공식과 Melby 공식을 이용하여 재현기간에 따른 파고의 함수로 경사제 피복재의 초기 저항력 크기와 피해율을 확률적으로 산정할 수 있는 새로운 방법이 제시되었다. 생애기간에 대한 신뢰성 분석을 실시하여 시간에 따른 다중하중의 작용과 사용한계나 극한한계 등 한계상태에 따른 구조물의 성능을 올바로 해석할 수 있었다. 마지막으로 보수보강 목표확률을 시간에 따른 누적파괴확률의 결과와 조합하여 구조물 유지관리에서 가장 중요한 변수인 보수보강 시점을 정량적으로 산정할 수 있는 방법이 제시되었다. A stochastic reliability analysis model has been developed for evaluating the time-dependent stability performance of armor units of rubble-mound breakwaters subjected to the multiple loads of arbitrary magnitudes which could be occurred randomly. The initial structural capacities and the damage rates of armor units of rubble-mound breakwaters could be estimated as a function of the incident wave height with a given return period by using the modified Hudson's formula and Melby's formula. The structural stability performances of armor units of rubble-mound breakwaters could be analyzed in detail through the lifetime reliability investigations according to the limit states such as the serviceability or ultimate limit state and the conditions of multiple loads. Finally, repair intervals for the structural management of armor units of rubble-mound breakwaters could quantitatively be evaluated by a new approach suggested in this paper that has been based on the target probability for repair and the accumulated probabilities of failure obtained from the present stochastic reliability analysis model.

A novel joint diagonalization approach for linear stochastic systems and reliability analysis

PurposeThe purpose of this paper is to present a novel gradient‐based iterative algorithm for the joint diagonalization of a set of real symmetric matrices. The approximate joint diagonalization of a set of matrices is an important tool for solving stochastic linear equations. As an application, reliability analysis of structures by using the stochastic finite element analysis based on the joint diagonalization approach is also introduced in this paper, and it provides useful references to practical engineers.Design/methodology/approachBy starting with a least squares (LS) criterion, the authors obtain a classical nonlinear cost‐function and transfer the joint diagonalization problem into a least squares like minimization problem. A gradient method for minimizing such a cost function is derived and tested against other techniques in engineering applications.FindingsA novel approach is presented for joint diagonalization for a set of real symmetric matrices. The new algorithm works on the numerical gradient base, and solves the problem with iterations. Demonstrated by examples, the new algorithm shows the merits of simplicity, effectiveness, and computational efficiency.Originality/valueA novel algorithm for joint diagonalization of real symmetric matrices is presented in this paper. The new algorithm is based on the least squares criterion, and it iteratively searches for the optimal transformation matrix based on the gradient of the cost function, which can be computed in a closed form. Numerical examples show that the new algorithm is efficient and robust. The new algorithm is applied in conjunction with stochastic finite element methods, and very promising results are observed which match very well with the Monte Carlo method, but with higher computational efficiency. The new method is also tested in the context of structural reliability analysis. The reliability index obtained with the joint diagonalization approach is compared with the conventional Hasofer Lind algorithm, and again good agreement is achieved.

Stochastic failure analysis of the gusset plates in the Mississippi River Bridge

The I-35W Mississippi River Bridge over Minneapolis, Minnesota, collapsed suddenly on August 1, 2007. Previous studies showed that the demand-to-capacity ratio for one of the gusset plates had become extremely high after about 40 years of service of the bridge and therefore, the failure of the gusset plate caused the failure of the whole bridge. A forensic assessment using stochastic reliability analysis is carried out in this research to check whether the collapse of the bridge could have been predicted at the design stage. For this purpose, the probabilities of failure for different types of stresses in the gusset plate are estimated. To consider the uncertainties involved in dead load and live load increments with time, the gamma process concept is employed to model stress increments. It is shown that the probability of failure in the year 2007 was higher than the recommended value. Therefore, it can be concluded that if the results of this study had been available at the design stage, the lack of reliability in 2007 could have been predicted and the collapse of the bridge and its disastrous consequences could have been prevented. It is also concluded that stochastic reliability analysis can be used as a rational tool for failure analysis and reliability assessment of bridges to prevent the risk of collapse.

A study on safety assessment of cable-stayed bridges based on stochastic finite element analysis and reliability analysis

It is more reasonable to evaluate the effect of uncertainty included in actual structures using the reliability assessment method. However, using the reliability assessment method to evaluate complicated structures, such as cable-stayed bridges whose limit state function is given as a nonlinear function, was very difficult. Therefore, in this study the structural response characteristics are investigated quantitatively using Stochastic Finite Element Analysis (SFEA) according to the external uncertainty of random variables included in cable-stayed bridges, and Reliability Analysis (RA) considering external uncertainty is performed more efficiently using the result of SFEA. For this approach, after performing the initial shape analysis of the cable-stayed bridge, improved Stochastic Finite Element Method Program (SFEMP) is developed for executing nonlinear SFEA by considering correlation of random variables. The feasibility of the developed program was investigated by comparing the analysis results of beam-cable structures with those of the verified program using Direct Monte Carlo Simulation (DMCS). The effect of each random variable on the structural response was examined by performing sensitivity analysis. The safety index and failure probability according to the correlation was investigated by applying RA that considered the correlation of the major random variables. The critical percentile distribution of the RA result is re-evaluated quantitatively considering the effect of the internal uncertainty.