scholarly journals Acceleration Response First Passage Failure Probability Analysis Method for Nonlinear Package

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Dapeng Zhu
Keyword(s):  
White Noise ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Acceleration Response ◽  
First Passage ◽  
Packaging System ◽  
Design Point ◽  
First Passage Failure

The acceleration response first passage failure problem of the nonlinear package base excited by Gaussian white noise is analyzed. The model correction factor method (MCFM) is implemented in conjunction with the first-order reliability method (FORM) to analyze the first passage failure probability of the nonlinear package. The white noise is discretized in standard normal space, and an iterative algorithm is proposed to find the design point of the packaging system. On the design point, the hypersurface representing the limit-state function of the nonlinear package is replaced approximately by a hyperplane representing the limit-state function of an equivalent linear system, and the FORM is employed to calculate the failure probability of the packaging system. The accuracy of this method is verified by crude Monte Carlo simulations. Numerical simulations are carried out to observe the effects of system parameters variations on failure probability which can be used for the improvement of packaging design.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

scholarly journals An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 209
Author(s):  
Bolin Liu ◽  
Liyang Xie
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Local Approximation ◽  
State Function ◽  
Limit State Function ◽  
Enrichment Technique ◽  
Reliability Method ◽  
Multiple Sample

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

A novel adaptive support vector machine method for reliability analysis

2021 ◽  
pp. 1748006X2110033
Author(s):  
Zhaoyin Shi ◽  
Zhenzhou Lu ◽  
Xiaobo Zhang ◽  
Luyi Li
Keyword(s):  
Support Vector Machine ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Adaptive Learning ◽  
Limit State ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Learning Function ◽  
Svm Model

For the structural reliability analysis, although many methods have been proposed, they still suffer from substantial computational cost or slow convergence rate for complex structures, the limit state function of which are highly non-linear, high dimensional, or implicit. A novel adaptive surrogate model method is proposed by combining support vector machine (SVM) and Monte Carlo simulation (MCS) to improve the computational efficiency of estimating structural failure probability in this paper. In the proposed method, a new adaptive learning method is established based on the kernel function of the SVM, and a new stop criterion is constructed by measuring the relative position between sample points and the margin of SVM. Then, MCS is employed to estimate failure probability based on the convergent SVM model instead of the actual limit state function. Due to the introduction of adaptive learning function, the effectiveness of the proposed method is significantly higher than those that employed random training set to construct the SVM model only once. Compared with the existing adaptive SVM combined with MCS, the proposed method avoids information loss caused by inconsistent distance scales and the normalization of the learning function, and the proposed convergence criterion is also more concise than that employed in the existing method. The examples in the paper show that the proposed method is more efficient and has broader applicability than other similar surrogate methods.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

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.

Development of Ultimate Strength Evaluation Method for Piping Subjected to Seismic Loads

2013 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Tatsuhiro Yamazaki
Keyword(s):  
Power Plants ◽  
Evaluation Method ◽  
Failure Modes ◽  
Limit State ◽  
Seismic Loading ◽  
Earthquake Resistance ◽  
State Function ◽  
Limit State Function ◽  
Input Acceleration ◽  
Resistance Tests

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

A New Reliability Evaluation Algorithm Using Response Surface Methodology Combined With Space Mapping Technique

2006 ◽  
Author(s):  
Lixin Zhang ◽  
Zhijun Jian ◽  
Zhaohui Xu
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Limit State ◽  
Space Mapping ◽  
Mapping Technique ◽  
State Function ◽  
Limit State Function ◽  
New Approach ◽  
Successive Response ◽  
Evaluation Algorithm

A new method is proposed to tackle the huge computation cost involved in Successive Response Surface Methodology applied to the reliability analysis, in which Space Mapping technique is combined with Response Surface Methodology. While the new approach is performed, the limit state function is only fitted at the first iteration; at other iterations Space Mapping technique is employed to map the original limit state function into the new ones. Experimental design, corresponding model evaluations and response surface fitting of the limit state function are not done repetitively as what we do while SRSM is used, which leads to the great cutting down of computational efforts.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

Fatigue Design Margin Evaluation for Carbon and Low-Alloy Steels by Reliability-Based Load and Resistance Factor Method

2011 ◽  
Author(s):  
Masahiro Takanashi ◽  
Makoto Higuchi ◽  
Junki Maeda ◽  
Shinsuke Sakai
Keyword(s):  
Applied Stress ◽  
Limit State ◽  
State Function ◽  
Low Alloy Steels ◽  
Limit State Function ◽  
Safety Factors ◽  
Fatigue Data ◽  
Alloy Steels ◽  
Partial Safety Factors ◽  
Two Parameters

This paper discusses the margins of the design fatigue curve in the ASME Boiler and Pressure Vessel Codes Section III from a reliability analysis point of view. It is reported that these margins were developed so as to cover uncertainties of fatigue data scatter, size effect, and surface condition[1], but the reasons for them remain unclear. In order to investigate the physical implications of the design margin, a probabilistic approach is taken for the collected fatigue data of carbon and low-alloy steels. In this approach, these three parameters are treated as random variables, and an applied stress is also taken into consideration as a random variable. For the analysis, to begin with, a limit state function for fatigue is proposed. Next, reliability index contours of the design fatigue curves for carbon and low-alloy steels are obtained based on the proposed limit state function. The contours indicate that the margins 2 on stress and 20 on life do not provide equal reliability. The margin 20 on life is more conservative and the margin became a minimum near intersections of the design curves with margins 2 on stress and 20 on life. For practical applications, the partial safety factors (PSF) for the target reliability are computed for all materials and several levels of coefficients of variation (COV) of the applied stress. A sensitivity analysis of the PSFs clarifies that only two parameters, the strength (or the life) and the applied stress, are predominant. Thus, the partial safety factors for these two parameters are proposed in a tabular form.

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