Reliability analysis of a torque estimation model

Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading

Reliability analysis of nonlinear structural systems using response surface method

In this paper tunnel probabilistic structural analysis (TuPSA) was performed using the first order reliability method (FORM). In TuPSA, a tunnel performance function is defined according to the boundary between the structural stability and instability. Then the performance function is transformed from original space into the standard normal variable space to obtain the design point, reliability index, and also the probability of tunnel failure. In this method, it is possible to consider the design factors as the dependent or independent random parameters with arbitrary probability distributions. A software code is developed to perform the tunnel probabilistic structural analysis (TuPSA) using the FORM. For validation and verification of TuPSA, a typical tunnel example with random joints orientations as well as mechanical properties has been studied. The results of TuPSA were compared with those obtained from Monte-Carlo simulation. The results show, in spite of deterministic analysis which indicates that the rock blocks are stable, that TuPSA resulted in key-blocks failure with certain probabilities. Comparison between probabilistic and deterministic analyses results indicates that probabilistic results, including the design point and probability of failure, are more rational than deterministic factor of safety.

In this work, a novel framework is proposed for the risk based design optimization of engineering systems by minimizing the demand on the system components’ accuracy (which directly relates to their cost). The fundamental development of this work is an analytical upper bound for calculating the probability of failure. This is in contrast with First Order Reliability Method (FORM), where a lower bound is used in calculating the probability of failure. FORM is one of the most popular methods for reliability analysis of engineering systems. In this paper, we show that FORM results in an optimistic measure of risk, hence potentially catastrophic in engineering design. A more accurate measure of failure is proposed by utilizing an analytical upper bound for the distribution of reliability index (the length of the most probable point vector to origin). This distribution is a function of the eigenvalues of the linearized limit state function in the normal space which results in a better understanding of failure phenomenon. The proposed formulation is computationally efficient and straightforward to solve, since it only involves finding eigenvalues in each iteration. This algorithm is applicable to any linearizable continuous limit state function with any type of distribution for the design variables. The method is applied to two examples and its accuracy is compared with the Monte Carlo simulation and FORM, demonstrating its effectiveness and value.

Methodologies to calculate failure probability and to estimate the reliability of fatigue loaded structures are developed. The applicability of the methodologies is evaluated with the help of the fatigue crack growth models suggested by Paris and Walker. The probability theories such as the FORM (first order reliability method), the SORM (second order reliability method) and the MCS (Monte Carlo simulation) are utilized. It is found that the failure probability decreases with the increase of the design fatigue life and the applied minimum stress, the decrease of the initial edge crack size, the applied maximum stress and the slope of Paris equation. Furthermore, according to the sensitivity analysis of random variables, the slope of Pairs equation affects the failure probability dominantly among other random variables in the Paris and the Walker models.

Formulations are presented for estimating probability of failure considering uncertainty of distribution parameters in time invariant and time variant reliability analyses. Based on the formulations the probability of failure can be calculated by recursively using the first order reliability method. Also, a more efficient approximate analysis procedure by using the point estimate method to estimate the probability of failure is given. In this analysis procedure, the point estimate method is used to discretize the uncertain distribution parameters in the time invariant reliability analysis, and to discretize the time-independent random variables and uncertain distribution parameters in the time variant reliability analysis. The probability of failure is then obtained by weighting the probability of failure conditioned at each of discrete points. The conditional probability of failure can be calculated by using first order reliability method, second order reliability method or any other convenient ...

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.

Risk analysis using stochastic reliability methods applied to two cases of deterministic water quality models

Based on the high dimensional model representation (HDMR) and Monte Carlo simulation (MCS), this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models. The HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. Once the limit state function is defined by using the HDMR, the failure probability can be obtained by using the MCS without increasing computational efforts. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the HDMR are both high in terms of series system and parallel system, the accuracy can be acceptable with respect to series system, and the accuracy can not be acceptable with respect to parallel system.

This paper aims to evaluate the reliability analysis for steel beam which represented by the probability of Failure and reliability index. Monte Carlo Simulation Method (MCSM) and First Order Reliability Method (FORM) will be used to achieve this issue. These methods need two samples for each behavior that want to study; the first sample for resistance (carrying capacity R), and second for load effect (Q) which are parameters for a limit state function. Monte Carlo method has been adopted to generate these samples dependent on the randomness and uncertainties in variables. The variables that consider are beam cross-section dimensions, material property, beam length, yield stress, and applied loads. Matlab software has been adopted to generate these pseudo-random variables dependent on its statistical characteristics such as coefficient of variance and probability density function that gathered from a review of literatures.

Metal-loss corrosion may result in pipeline’s failure and expensive downtime loss. Thus, to keep the pipeline’s normal operation, it is crucial to draw up scientific inspection and maintenance plans. This study is to optimize the inspection plan for corroded pipeline. Limit state functions are established for the corrosion leakage and burst respectively, and the pipeline’s failure probability is obtained with Monte Carlo simulation. The pipeline’s failure probability is further evaluated by the copula function and with considering the correlation of different failure modes. Moreover, a hybrid failure rate model is developed to update the pipeline’s failure probability, where the age reduction factor and failure rate increase factor are adopted, and imperfect maintenance is taken into account. On this basis, an optimization model is established with the objective to minimize the total maintenance cost, and genetic algorithm is applied to optimize the inspection plans. A case study is conducted, and the optimal results are analyzed according to acceptable maximum failure probability characteristics for the areas with different risk levels. The results show that periodic inspection and perfect maintenance are suitable for high-risk areas, and the proposed inspection plan is more suitable for corroded pipeline in low or medium-risk areas.

An investigation was performed to study the effect of uncertainty in applied loads, helix angles, and failure stresses on the probability of failure of composite cylinders. Also, the effect of the factor of safety on the probability of failure of the cylinder was studied. The probability of failure for a composite cylinder subject to axisymmetric loading was obtained using the First Order Reliability method (FORM). The failure of the cylinder was studied based on first ply failure. Ply failure was predicted using the non-smooth Hashin criterion. Hashin criterion is based on writing a different interaction equation for separate failure modes. Four failure modes are considered associated with matrix or fiber failure, in either tension or compression. The accuracy of FORM as applied to this problem was verified by comparing the FORM results to those obtained by Monte-Carlo Simulation method with importance sampling. i x µ = mean values of the design parameters i x

Tether system is a critical component for the TLPs, since its failure may lead to the collapse of the whole structure involving human lives, economic losses and damages to the environment. Due to this fact, reliability methods have been proposed to design TLP tethers and new codes are being developed to increase their safety level. The objective of this paper is to compare the probability of failure for TLP tethers considering the maximum tension limit state obtained with three methods, which are: a methodology based on Evolutionary Strategies and the Monte Carlo Importance Sampling, the First Order Reliability Method, and the Second Order Reliability Method. Von-Mises failure criterion is used as limit state function for the most loaded tether of a TLP submitted to different sea states. Efficiency of the ES algorithm to find design points and probabilities of failure obtained with the reliability methods are discussed.

ABSTRACTIn the present study, reliability analysis of near surface disposal facility is performed, by assessing the probability of sequential failure of the multi barrier system using the contaminant transport model. The concentration and dose rate of the radionuclide evolve with time hence there is a need for time dependent reliability analysis. Due to the low values of expected probabilities of failure, an enhanced Monte Carlo (EMC) method and Subset simulation is employed. The Result of the analysis show that, the EMC method is useful to evaluate the probability of failure associated with the barrier system which has low probability of failure.

The differences in the coefficient of thermal expansion (CTE) between the chip and the FR-4 board generate the shear strains and the bending moment in the solder joint. It seems to be a main cause of failure in the solder joint when the chip and the FR-4 board are heated repeatedly. Thus, the fatigue loading induced by thermal cycling is a major concern in the reliability of the solder joint. The magnitude of shear strain and the final failure are known to be influenced by varying boundary conditions such as the difference of CTE, the height of solder, the distance of the solder joint from the neutral point (DNP) and the temperature variation. In this paper, the effects of boundary conditions on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Monte Carlo Simulation (MCS). Furthermore, the stiffness of the solder joint is considered to investigate the influence at the failure probability.