scholarly journals Parametric Sensitivity Analysis for Importance Measure on Failure Probability and Its Efficient Kriging Solution

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yishang Zhang ◽  
Yongshou Liu ◽  
Xufeng Yang
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Computational Effort ◽  
Importance Measure ◽  
Sensitivity Index ◽  
Reliability Engineering ◽  
Parametric Sensitivity ◽  
Distribution Parameters ◽  
The Moment ◽  
Sensitivity Indicator

The moment-independent importance measure (IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging (ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

The trajectory importance measure of the shaping machine under stochastic excitation

2011 ◽  
Vol 226 (3) ◽  
pp. 808-815 ◽  
Author(s):  
L J Cui ◽  
Z Z Lu ◽  
C C Zhou
Keyword(s):  
Failure Probability ◽  
Computational Efficiency ◽  
Importance Measure ◽  
Stochastic Excitation ◽  
Input Uncertainty ◽  
Dynamic Reliability ◽  
Probability Density Evolution Method ◽  
Output Uncertainty ◽  
The Moment ◽  
Probability Density Evolution

Two trajectory importance measures, the trajectory importance measure based on variance and the moment-independent trajectory importance measure, are proposed to represent the time-variant effects of input uncertainty on the output uncertainty of the shaping machine under stochastic excitation in its work stroke, respectively. At the same time, the trajectory importance measure based on the failure probability is proposed to reflect the contribution of the input uncertainty on the dynamic reliability of the mechanism. These three trajectory importance measures provide different references to improve the performance and reliability of the mechanism from the time-variant perspective. As the probability density evolution method (PDEM) is employed to solve the proposed trajectory importance measures, it can improve the computational efficiency largely without losing precision. Results of the shaping mechanism illustrate the feasibility of the proposed trajectory importance measures and the veracity of the PDEM in solving the lathe mechanism.

scholarly journals Reliability Sensitivity Analysis Method for Mechanical Components

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan-Fang Zhang ◽  
Yan-Lin Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Reduction Method ◽  
Dimension Reduction Method ◽  
Edgeworth Series ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Distribution Parameters ◽  
Mechanical Components ◽  
Univariate Dimension Reduction Method

Based on the univariate dimension-reduction method (UDRM), Edgeworth series, and sensitivity analysis, a new method for reliability sensitivity analysis of mechanical components is proposed. The univariate dimension-reduction method is applied to calculate the response origin moments and their sensitivity with respect to distribution parameters (e.g., mean and standard deviation) of fundamental input random variables. Edgeworth series is used to estimate failure probability of mechanical components by using first few response central moments. The analytic formula of reliability sensitivity can be derived by calculating partial derivative of the failure probability P f with respect to distribution parameters of basic random variables. The nonnormal random parameters need not to be transformed into equivalent normal ones. Three numerical examples are employed to illustrate the accuracy and efficiency of the proposed method by comparing the failure probability and reliability sensitivity results obtained by the proposed method with those obtained by Monte Carlo simulation (MCS).

scholarly journals An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 649 ◽  
Author(s):  
Xufang Zhang ◽  
Jiankai Liu ◽  
Ying Yan ◽  
Mahesh Pandey
Keyword(s):  
Sensitivity Analysis ◽  
Maximum Entropy ◽  
Failure Probability ◽  
Dimensional Reduction ◽  
Structural Model ◽  
Simulation Method ◽  
Reliability Estimation ◽  
Sensitivity Index ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.

Comparison of two metamodeling approaches for sensitivity analysis of a geological disposal model

2020 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Higher Order ◽  
Second Order ◽  
High Dimensional Model Representation ◽  
Sensitivity Index ◽  
Reliability Engineering ◽  
System Safety ◽  
First Order ◽  
Sensitivity Indices ◽  
Parameter Interactions

<p>Probabilistic methods of higher order sensitivity analysis provide a possibility for identifying parameter interactions by means of sensitivity indices. Better understanding of parameter interactions may help to better quantify uncertainties of repository models, which can behave in a highly nonlinear, non-monotonic or even discontinuous manner. Sensitivity indices can efficiently be estimated by the Random-Sampling High Dimensional Model Representation (RS-HDMR) metamodeling approach. This approach is based on truncating the ANOVA-HDMR expansions up to the second order, while the truncated terms are then approximated by orthonormal polynomials. By design, the sensitivity index of total order (SIT) in this method is approximated as the sum of the indices of first order (SI1’s) plus all corresponding indices of second order (SI2’s) for a considered parameter. RS-HDMR belongs to a wider class of methods known as polynomial chaos expansion (PCE). PCE methods are based on Wiener’s homogeneous chaos theory published in 1938. It is a widely used approach in metamodeling. Usually only a few terms are relevant in the PCE structure. The Bayesian Sparse PCE method (BSPCE) makes use of sparse PCE. Using BSPCE, SI1 and SIT can be estimated. In this work we used the SobolGSA software [1] which contains both the RS-HDMR and BSPCE methods.</p><p>We have analysed the sensitivities of a model for a generic LILW repository in a salt mine using both the RS-HDMR and the BSPCE approach. The model includes a barrier in the near field which is chemically dissolved (corroded) over time by magnesium-containing brine, resulting in a sudden significant change of the model behaviour and usually a rise of the radiation exposure. We investigated the model with two sets of input parameters: one with 6 parameters and one with 5 additional ones (LILW6 and LILW11 models, respectively). For the time-dependent analysis, 31 time points were used.</p><p>The SI1 indices calculated with both approaches agree well with those obtained from the well-established and reliable first-order algorithm EASI [2] in most investigations. The SIT indices obtained from the BSPCE method seem to increase with the number of simulations used to build the metamodel. The SIT time curves obtained from the RS-HDMR approach with optimal choice of the polynomial coefficients agree well with the ones from the BSPCE approach only for relatively low numbers of simulations. As, in contrast to RS-HDMR, the BSPCE approach takes account of all orders of interaction, this may be a hint for the existence of third- or higher-order effects.</p><p><strong>Acknowledgements</strong></p><p>The work was financed by the German Federal Ministry for Economic Affairs and Energy (BMWi). We would also like to thank Dirk-A. Becker for his constructive feedback.</p><p><strong>References</strong></p><p>[1]         S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus, Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004, (2018).</p><p>[2]          E. Plischke, An effective algorithm for computing global sensitivity indices (EASI). Reliability Engineering and System Safety, 95: 354–360, (2010).</p>

Parametric Reliability Sensitivity Analysis Using Failure Probability Ratio Function

2016 ◽  
Vol 13 (04) ◽  
pp. 1641005 ◽  
Author(s):  
Pengfei Wei ◽  
Zhenzhoug Lu
Keyword(s):  
Sensitivity Analysis ◽  
Importance Sampling ◽  
Failure Probability ◽  
Probability Ratio ◽  
Sensitivity Indices ◽  
Analysis Technique ◽  
Parametric Reliability ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Distribution Parameters

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters of model inputs are changed. Then, based on the failure probability ratio function, a global sensitivity analysis technique, called R-index, is proposed for measuring the average contribution of the distribution parameters to the failure probability while they vary in intervals. The proposed failure probability ratio function and R-index can be especially useful for failure probability reduction, reliability-based optimization and reduction of the epistemic uncertainty of parameters. The Monte Carlo simulation (MCS), Importance Sampling (IS) and Truncated Importance Sampling (TIS) procedures, which need only a set of samples for implementing them, are introduced for efficiently computing the proposed sensitivity indices. A numerical example is introduced for illustrating the engineering significance of the proposed sensitivity indices and verifying the efficiency and accuracy of the MCS, IS and TIS procedures. At last, the proposed sensitivity techniques are applied to a planar 10-bar structure for achieving a targeted 80% reduction of the failure probability.

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