scholarly journals Probabilistic Representation Approach for Multiple Types of Epistemic Uncertainties Based on Cubic Normal Transformation

2020 ◽  
Vol 10 (14) ◽  
pp. 4698
Author(s):  
Xiang Peng ◽  
Qilong Gao ◽  
Jiquan Li ◽  
Zhenyu Liu ◽  
Bing Yi ◽  
...  
Keyword(s):  
Computational Efficiency ◽  
Evidence Theory ◽  
Transformation Method ◽  
Distribution Functions ◽  
Statistical Moments ◽  
Probabilistic Representation ◽  
Representation Function ◽  
Interval Approach ◽  
Practical Engineering ◽  
Normal Transformation

Many non-probabilistic approaches have been widely regarded as mathematical tools for the representation of epistemic uncertainties. However, their heavy computational burden and low computational efficiency hinder their applications in practical engineering problems. In this article, a unified probabilistic representation approach for multiple types of epistemic uncertainties is proposed based on the cubic normal transformation method. The epistemic uncertainties can be represented using an interval approach, triangular fuzzy approach, or evidence theory. The uncertain intervals of four statistical moments, which contain mean, variance, skewness, and kurtosis, are calculated using the sampling analysis method. Subsequently, the probabilistic cubic normal distribution functions are conducted for sampling points of four statistical moments of epistemic uncertainties. Finally, a calculation procedure for the construction of probabilistic representation functions is proposed, and these epistemic uncertainties are represented with belief and plausibility continuous probabilistic measure functions. Two numerical examples and one engineering example demonstrate that the proposed approach can act as an accurate probabilistic representation function with high computational efficiency.

scholarly journals Hermite polynomial normal transformation for structural reliability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jinsheng Wang ◽  
Muhannad Aldosary ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Reliability Analysis ◽  
Hermite Polynomial ◽  
Structural Reliability ◽  
Hermite Polynomials ◽  
Random Variables ◽  
Transformation Method ◽  
Statistical Moments ◽  
Content Type ◽  
Structural Reliability Analysis ◽  
Normal Transformation

Purpose Normal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables. Design/methodology/approach The new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies. Findings Comprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems. Originality/value This study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy.

A Possibility Estimation Model and its Application

2013 ◽  
Vol 475-476 ◽  
pp. 423-427
Author(s):  
Lin Na Ji ◽  
Feng Bao Yang ◽  
Xiao Xia Wang
Keyword(s):  
Measurement Data ◽  
Engineering Application ◽  
Transformation Method ◽  
Estimation Model ◽  
Property Estimation ◽  
New Methods ◽  
Proposed Model ◽  
Practical Engineering ◽  
New Ideas ◽  
Possibility Distributions

Aiming at some uncertainty problems such as quality inspection of adhesive structure and risk assessment in the practical engineering application, a possibility estimation model is established. Firstly, according to the fuzziness, randomness and uncertainty of the measurement data, a transformation method of possibility distribution with non-single peak values and nonlinearity is proposed from probability density function. Secondly, for possibility distributions of measurement data of each sensor, a kind of possibility fusion rules is put forward, then the fusion distribution is estimated by the possibility mean. Finally the model is applied to the mechanical property estimation of adhesive structure, and the result forecasts the quality. The proposed model with strong applicability, not only provides convenience for the operations among possibility distributions, but also offers new ideas and new methods to deal with uncertain problems.

Evidence Theory Representations for Properties Associated with Weak Link/strong Link Systems, Part 2: Failure Time and Failure Temperature

2021 ◽  
Author(s):  
Jon C. Helton ◽  
Dusty M. Brooks ◽  
John L. Darby
Keyword(s):  
Failure Time ◽  
Weak Link ◽  
Evidence Theory ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Belief Functions ◽  
Strong Link ◽  
Cumulative Distribution Functions ◽  
Failure Temperature

Abstract The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility and probability for (i) time at which LOAS occurs for a 1 WL/2 SL system, (ii) time at which a 2 link system fails, (iii) temperature at which a 2 link system fails, and (iv) temperature at which LOAS occurs for a 1 WL/ 2 SL system. The presented results can be generalized to systems with more than 1 WL and 2 SLs.

The Transformation Method between Simple Matrix of Jordan and its Algebra Equivalence System

2012 ◽  
Vol 616-618 ◽  
pp. 2117-2126
Author(s):  
Zhong Xu Han ◽  
Ya Hong Chen
Keyword(s):  
Control System ◽  
Simple Calculation ◽  
Transformation Method ◽  
Standard Type ◽  
Matrix Block ◽  
Rapid Calculation ◽  
Practical Engineering ◽  
Simple Matrix ◽  
Engineering Projects ◽  
Application Scope

Algebra Equivalent Observer (AEO) is a derivate due to the nonsingularity of state in linear system, and also an observer usually applied in practical engineering projects. For the rapid calculation of what the parameters of AEO having effect on control system. Taking great inertia system as object to analyze relationship between a simple matrix J of Jordan standard type and its algebra equivalent system called as matrix block JBS of Jordan standard type in broad sense. A simple calculation method of the transform matrix P is given, in which P is used in JBS=PJP–1. Some simple methods of design and debug to control system can be got during expanding the application scope of the method in process of parameters setting of the observer.

scholarly journals An Interval Process Method for Non-Random Uncertain Aeroelastic Analysis

Vibration ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 787-804
Author(s):  
Zahra Sotoudeh ◽  
Tyler Lyman ◽  
Leslie Montes Lucano ◽  
Natallia Urieva
Keyword(s):  
Monte Carlo Simulation ◽  
Sampling Method ◽  
Free Stream ◽  
Distribution Functions ◽  
Upper And Lower Bounds ◽  
Stream Velocity ◽  
Probability Distribution Functions ◽  
Aeroelastic Analysis ◽  
Practical Engineering ◽  
Process Method

In this paper, we use the Monte Carlo simulation to study aeroelastic behavior caused by non-random uncertain free-stream velocity. For sampling, we use the interval process method. Each family of samples is defined by a correlation function and upper and lower bounds. By using this sampling method, there is no need for constructing precise probability distribution functions; therefore, this method is suitable for practical engineering applications. We studied the aeroelastic behavior of an airfoil and a high aspect-ratio wing.

Uncertainty Propagation Analysis of T/R Modules

2019 ◽  
Vol 16 (07) ◽  
pp. 1850105 ◽  
Author(s):  
Z. H. Wang ◽  
C. Jiang ◽  
X. X. Ruan ◽  
Y. Q. Zhang ◽  
Z. L. Huang ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Phase Difference ◽  
Uncertainty Propagation ◽  
Distribution Functions ◽  
Statistical Moments ◽  
Electromagnetic Signal ◽  
Physical Parameters ◽  
Amplitude Difference ◽  
Uncertainty Propagation Analysis ◽  
Propagation Analysis

This paper develops an uncertainty propagation analysis method to analyze transmit/receive (T/R) modules with uncertain parameters, such as variability and tolerances in the physical parameters and geometry produced in the manufacturing processes. The method is a combination of the variance decomposition-based sensitivity analysis and the moment-based arbitrary polynomial chaos (MBaPC). First, the electromagnetic simulation model of a practical T/R module is created. Secondly, based on the model, the sensitivity analysis is carried out to determine the sensitive parameters to the amplitude difference and the phase difference between the input and output electromagnetic signal. Thirdly, their four order statistical moments are calculated using the MBaPC. At last, according to the maximum entropy principle, the statistical moments are used to fit the probability distribution functions of the amplitude difference and the phase difference of the T/R module. The results computed by MBaPC have been validated accurate and efficient compared with Monte Carlo simulation approach.

Non-Probabilistic Reliability Computation and Efficiency Assessment Based on Interval Model

2014 ◽  
Vol 685 ◽  
pp. 646-650
Author(s):  
Cheng Cheng Lv ◽  
Zong Zhan Gao ◽  
Feng Zhang ◽  
Tong Feng Gao
Keyword(s):  
Domain Structure ◽  
Computational Efficiency ◽  
Structural Reliability ◽  
Control Factor ◽  
Interval Model ◽  
Efficiency Assessment ◽  
Reliability Calculation ◽  
Reliability Method ◽  
Practical Engineering ◽  
Reliability Computation

A new interval non-probabilistic reliability method is proposed in this paper. The sampling control factor is introduced, which can regulate the distribution of the sampling domain structure. The efficiency of the reliability calculation is effectively improved. The numerical results prove that this method can effectively and feasibly improve the computational efficiency of structural reliability by changing the value in practical engineering calculations when is located at a suitable interval.

Numerical Simulation of Microflows by a DOM With Streaming and Collision Processes

2016 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Computational Efficiency ◽  
Kinetic Scheme ◽  
Current Method ◽  
Distribution Functions ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Present Scheme ◽  
Unified Gas Kinetic Scheme ◽  
Collision Processes ◽  
Cell Interface

Inspired from the idea of developing lattice Boltzmann method (LBM), a discrete ordinate method (DOM) with streaming and collision processes is presented for simulation of microflows in this work. The current method is quite different from the conventional discrete ordinate method (DOM), unified gas kinetic scheme (UGKS) and discrete unified gas kinetic scheme (DUGKS), in which the finite volume method (FVM) or the finite difference method (FDM) is usually utilized to discretize the discrete velocity Boltzmann equation (DVBE). Due to the application of FVM or FDM, the evaluation of the flux of distribution function at the cell interface becomes an essential step for these approaches. Besides that, for the UGKS and DUGKS, not only the flux of distribution functions but also the conservative variables at the cell interface are needed to be computed. These processes require a lot of computational efforts. In contrast, for the developed method, it only needs interpolations within the cell to perform the streaming process. Thus, the computational efficiency can be improved accordingly. To compare the accuracy and efficiency of present scheme with those of DSMC and/or UGKS, several numerical examples including the Couette flow, pressure driven Poiseuille flow and thermal transpiration flow are simulated. Numerical results showed that the solution accuracy of current scheme is comparable to that of DSMC and UGKS. However, as far as the computational efficiency is concerned, the present scheme is more efficient than UGKS.

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