Multivariate log-concave probability density class for structural reliability applications

2017 ◽  
Vol 69 ◽  
pp. 57-67 ◽  
Author(s):  
Farzad Faridafshin ◽  
Arvid Naess
Keyword(s):  
Probability Density ◽  
Structural Reliability ◽  
Density Class

A points estimation and series approximation method for uncertainty analysis

2009 ◽  
Vol 223 (9) ◽  
pp. 1997-2007 ◽  
Author(s):  
X F Zhang ◽  
Y E Zhao ◽  
Y M Zhang ◽  
X Z Huang ◽  
H Li
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Function Approximation ◽  
Structural Reliability ◽  
Estimation Method ◽  
Point Estimation ◽  
Performance Function ◽  
Density Function Approximation ◽  
Point Estimation Method

The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram—Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.

scholarly journals PROBABILITY DENSITY EVOLUTION FOR TIME-VARYING RELIABILITY ASSESSMENT OF WING STRUCTURES

Aviation ◽  
2018 ◽  
Vol 22 (2) ◽  
pp. 45-54 ◽  
Author(s):  
ajad Saraygord Afshari ◽  
Seid H. Pourtakdoust
Keyword(s):  
Probability Density ◽  
Structural Reliability ◽  
Structural Parameters ◽  
Reliability Assessment ◽  
Monitoring Methods ◽  
Density Evolution ◽  
Failure Prevention ◽  
Cantilevered Beam ◽  
Key Factor ◽  
Probability Density Evolution

Reliability evaluation is a key factor in serviceability and safety analysis of air vehicles. Structural health monitoring methods have grown to a degree of maturity in many industries. However, there is a challenging interest to tie in SHM with reliability assessment. In this respect, consideration of stochastic structural dynamics with SHM data and random loadings opens a new chapter in failure prevention. The current study focuses on the stochastic behavior of structures as a way to relate SHM data with reliability. In this respect, uncertain factors such as atmospheric turbulence, structural parameters, and sensor outputs are considered in the process of reliability assessment. Firstly, an experimental evaluation is conducted using a simple cantilevered beam. Subsequently, system identification is weaved in with a probability density evolution equation for calculating the reliability of a wing structural component. Numerical simulations demonstrate that structural reliability of a typical WSC can be effectively evaluated. The proposed scheme paves the way for new SHM research topics such as online life prediction and reliability based failure prevention.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals

2012 ◽  
Vol E95.B (7) ◽  
pp. 2257-2265
Author(s):  
Toru KITAYABU ◽  
Mao HAGIWARA ◽  
Hiroyasu ISHIKAWA ◽  
Hiroshi SHIRAI
Keyword(s):  
Probability Density ◽  
Delta Sigma Modulator ◽  
Delta Sigma ◽  
Input Signals

Functional and operational risk as a criterion for assessing the durability of an autonomous energy system

2019 ◽  
Vol 12 (1) ◽  
pp. 56-62 ◽  
Author(s):  
A. O. Nedosekin ◽  
A. V. Smirnov ◽  
D. P. Makarenko ◽  
Z. I. Abdoulaeva
Keyword(s):  
Service Life ◽  
Structural Reliability ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Operational Risk ◽  
Energy System ◽  
Technical System ◽  
Residual Service Life ◽  
Technological Parameters ◽  
Residual Service

The article presents new models and methods for estimating the residual service life of an autonomous energy system, using the functional operational risk criterion (FOR). The purpose of the article is to demonstrate a new method of durability evaluation using the fuzzy logic and soft computing framework. Durability in the article is understood as a complex property directly adjacent to the complex property of system resilience, as understood in the Western practice of assessing and ensuring the reliability of technical systems. Due to the lack of reliable homogeneous statistics on system equipment failures and recoveries, triangular fuzzy estimates of failure and recovery intensities are used as fuzzy functions of time based on incomplete data and expert estimates. The FOR in the model is the possibility for the system availability ratio to be below the standard level. An example of the evaluation of the FOR and the residual service life of a redundant cold supply system of a special facility is considered. The transition from the paradigm of structural reliability to the paradigm of functional reliability based on the continuous degradation of the technological parameters of an autonomous energy system is considered. In this case, the FOR can no longer be evaluated by the criterion of a sudden failure, nor is it possible to build a Markov’s chain on discrete states of the technical system. Assuming this, it is appropriate to predict the defi ning functional parameters of a technical system as fuzzy functions of a general form and to estimate the residual service life of the technical system as a fuzzy random variable. Then the FOR is estimated as the possibility for the residual life of the technical system to be below its warranty period, as determined by the supplier of the equipment.

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