Uncertainty Analysis for Time- and Space-Dependent Responses With Random Variables

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Xinpeng Wei ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Analysis ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Time And Space ◽  
Gaussian Stochastic Process ◽  
Reliability Method ◽  
Input Variables ◽  
Loop Procedure ◽  
Mean Variance

The performance of a product varies with respect to time and space if the associated limit-state function involves time and space. This study develops an uncertainty analysis method that quantifies the effect of random input variables on the performance (response) over time and space. The combination of the first order reliability method (FORM) and the second-order reliability method (SORM) is used to approximate the extreme value of the response with respect to space at discretized instants of time. Then the response becomes a Gaussian stochastic process that is fully defined by the mean, variance, and autocorrelation functions obtained from FORM and SORM, and a sequential single loop procedure is performed for spatial and random variables. The method is successfully applied to the reliability analysis of a crank-slider mechanism, which operates in a specified period of time and space.

Uncertainty Analysis for Time- and Space-Dependent Responses With Random Variables

2018 ◽  
Author(s):  
Xinpeng Wei ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Analysis ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Time And Space ◽  
Gaussian Stochastic Process ◽  
Reliability Method ◽  
Input Variables ◽  
Loop Procedure ◽  
Mean Variance

The performance of a product varies with respect to time and space if the associated limit-state function is a function of time and space. This study develops an uncertainty analysis method that quantifies the effect of random input variables on the performance (response) over time and space. The first order reliability method (FORM) is used to approximate the extreme value of the response with respect to space at discretized instants of time. Then the response becomes a Gaussian stochastic process that is fully defined by the mean, variance, and autocorrelation functions obtained from FORM, where a sequential single loop procedure is performed for spatial and random variables. The method is successfully applied to the reliability analysis of a crank-slider mechanism, which operates in a specified period of time and space.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Dimitrios I. Papadimitriou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Topology Optimization ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Probability Of Failure ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Sensitivity Derivatives ◽  
Reliability Method

A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer uses a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first- and second-order sensitivity derivatives of the limit state cumulant generating function (CGF), with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Third-order sensitivity derivatives, including the sensitivities of the saddlepoint, are calculated using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. Comparison with Monte Carlo simulation (MCS) shows that MVSOSA is more accurate than mean-value first-order saddlepoint approximation (MVFOSA) and more accurate than mean-value second-order second-moment (MVSOSM) method. Finally, the proposed RBTO-MVSOSA method for minimizing a compliance-based probability of failure is demonstrated using two two-dimensional beam structures under random loading. The density-based topology optimization based on the solid isotropic material with penalization (SIMP) method is utilized.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

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.

Effects of Various Types of Distribution on Probabilistic Method and FAD

2007 ◽  
Vol 353-358 ◽  
pp. 2561-2564
Author(s):  
Ouk Sub Lee ◽  
Dong Hyeok Kim
Keyword(s):  
Failure Probability ◽  
Probabilistic Method ◽  
Limit State ◽  
Random Variables ◽  
Reliability Estimation ◽  
Probabilistic Methods ◽  
State Function ◽  
Operating Pressure ◽  
Lognormal Distributions ◽  
Reliability Method

The reliability estimation of pipeline is performed in accordance with the probabilistic methods such as the FORM (first order reliability method) and the SORM (second order reliability method). A limit state function has been formulated with help of the FAD (failure assessment diagram). Various types of distribution of random variables are assumed to investigate its effect on the failure probability. It is noted that the failure probability increases with the increase of the dent depth, the operating pressure and the outside radius, and the decrease of the wall thickness. Furthermore it is found that the failure probability for the random variables having the Weibull distribution is larger than those of the normal and the lognormal distributions.

Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation

2017 ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Topology Optimization ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Probability Of Failure ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Sensitivity Derivatives ◽  
Reliability Method

A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer is based on a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first and second-order sensitivity derivatives of the limit state cumulant generating function with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Third-order sensitivity derivatives, including the sensitivities of the saddlepoint, are computed using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. The results are compared with the available mean value first-order saddlepoint approximation (MVFOSA) method and Monte Carlo simulation. Finally, the proposed RBTO-MVSOSA method for minimizing compliance-based probability of failure, is demonstrated using two 2D beam structures under random loading.

Probabilistic Analysis and Risk Assessment of Deep Water Composite Production Riser Against Fatigue Limit State

2015 ◽  
Author(s):  
Manander Singh ◽  
Suhail Ahmad
Keyword(s):  
Risk Assessment ◽  
Deep Water ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Reliability Assessment ◽  
Random Variables ◽  
State Function ◽  
Limit State Function ◽  
Wide Range ◽  
Reliability Method

Deep water composite risers are subjected to randomly fluctuating loads, induced by wind and waves in the presence of fluctuating axial tension which may be critical in deep sea conditions. Therefore, risers experience the extreme bending and randomly fluctuating stresses throughout their service life. Cumulative fatigue damage is a critical assessment of riser life in the presence of large dynamic stresses. Probabilistic analysis and risk assessment of composite risers for cumulative fatigue is a vital design requirement for its satisfactory service and survival for stipulated period. Without addressing the reliability assessment, composite risers may not be recommended for deep water oil and gas exploration and production. Hence, the reliability assessment is a critical issue that is to be addressed for the safety of the deep water composite riser. It is studied for the entire system for all possible sea states occurring in the exploration region. Unlike conventional risers, the wall structure of a composite riser is more complicated. Therefore, multiple failure mechanisms are used jointly to assess the safety of the composite riser. Fatigue reliability is a challenging task due to complex nature of dynamic response and associated uncertainties caused by the material and external loads. The present study is focused on reliability assessment using stochastic finite element analysis. Response time histories for random sea plus current have been obtained. Requisite numbers of sea states are considered for the simulation of a wide range of off-shore environment and estimation of accumulated damage. By using the S-N data, damage fractions are calculated then summed linearly using Miner-Palmgren rule. The total damage has been obtained by summing the accumulated damages over all the sea states under consideration. Non-linear limit state function is derived based upon the above given approach to calculate the fatigue life. Important uncertainties associated with random variables are considered while deriving the limit state function. Numerical methods, such as Monte Carlo simulation and Advanced First Order Reliability Method, are used for the calculation of the reliability. The sensitivities of various random variables on overall probability of failure have been studied and design points have been located on failure surface. Probabilities of failure for important parameters are investigated.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Probabilistic Optimum Design of Composite Laminates

1998 ◽  
Vol 32 (1) ◽  
pp. 68-82 ◽  
Author(s):  
S. Mahadevan ◽  
X. Liu
Keyword(s):  
Objective Function ◽  
Optimum Design ◽  
Composite Laminates ◽  
Plate Theory ◽  
Limit State ◽  
Strength Criterion ◽  
System Level ◽  
State Function ◽  
Practical Procedure ◽  
Reliability Method

This paper proposes a procedure for the optimum design of composite laminates under probabilistic considerations. The problem is formulated to consider the minimization of laminate weight as the objective function and the reliability requirements as the constraints. Both system-level and element-level reliabilities are considered. The first-order reliability method (FORM) is used to estimate the reliability of each ply group, and system reliability is computed based on series or parallel system assumptions. The Tsai-Wu strength criterion is adopted to derive the limit state function of individual ply groups in the laminate. The gradient and sensitivity information of the objective function and the constraints with respect to the design variables are obtained by using sensitivity analysis based on the composite plate theory. Thus the proposed procedure brings together modern concepts of reliability analysis, composite laminate behavior and nonlinear optimization to develop a rational and practical procedure for the optimum design of composite laminates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Assessment of Fatigue Safety Factors for Deep-Water Risers in Relation to VIV

2005 ◽  
Vol 127 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Bernt J. Leira ◽  
Trond Stokka Meling ◽  
Carl M. Larsen ◽  
Vidar Berntsen ◽  
Bernie Stahl ◽  
...  
Keyword(s):  
Fatigue Damage ◽  
Limit State ◽  
Random Variables ◽  
Response Surfaces ◽  
State Function ◽  
Safety Factors ◽  
Parameter Variations ◽  
Input Parameters ◽  
Steel Catenary Risers ◽  
Analytical Expressions

Safety factors required to control fatigue damage of deepwater metallic risers caused by vortex-induced vibration (VIV) are considered. Four different riser configurations are studied: Cases I and II: Vertical tensioned 12in. risers suspended from a spar buoy at water depths of 500 and 1500m. Cases III and IV: Steel catenary risers suspended from a spar buoy, both at 1000m. For Case III, the riser diameter is 12in., while for Case IV it is 33in. For each riser configuration, relevant design and analysis parameters which are subject to uncertainty are identified. For these quantities, random variables are established also representing model uncertainties. Subsequently, repeated analyses of fatigue damage are performed by varying the input parameters within representative intervals. The results are applied to fit analytical expressions (i.e., so-called response surfaces) utilized to describe the limit state function and to develop the probabilistic model for reliability analysis of the risers. By combining the random variables for the input parameters with the results from the parameter variations, a relationship between the fatigue safety factor and the failure probability is established for each riser configuration.

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