Hybrid Uncertain Analysis for Exterior Acoustic Field Prediction with Interval Random Parameters

2017 ◽  
Vol 15 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Ning Chen ◽  
Dejie Yu ◽  
Baizhan Xia ◽  
Michael Beer
Keyword(s):  
Acoustic Field ◽  
Stochastic Perturbation ◽  
Random Variables ◽  
Random Model ◽  
Sufficient Information ◽  
Uncertain Parameters ◽  
Field Problem ◽  
Interval Variables ◽  
Stochastic Perturbation Method ◽  
Response Vector

For exterior acoustic field problems that lack sufficient information to construct precise probability distributions, an interval random model is introduced to deal with the uncertain parameters. In the interval random model, the probability variables are employed to treat the uncertain parameters, whereas some distribution parameters of random variables are modeled as interval variables instead of precise values. Based on the interval random model, the interval random finite element equation for exterior acoustic fields is established and a hybrid uncertain analysis method is presented to solve the exterior acoustic field problem with interval random variables. In the presented method, by temporarily neglecting the uncertainties of interval variables, a first-order stochastic perturbation method is adopted to calculate the expectation and the variance of the response vector. According to the monotonicity of the expectation and variance of the response vector with respect to the interval variables, the lower and upper bounds of the expectation and variance of the response vector can be calculated by the vertex method. In addition, in order to ensure accuracy of the proposed method, the subinterval technique is introduced and investigated. The numerical example of a square flexible shell model is presented to demonstrate the effectiveness of the proposed method.

scholarly journals Statistical analyses of the energy demand and thermal comfort for multiple uncertain input parameters, performed using transformed variable and perturbation method

2021 ◽  
Vol 2069 (1) ◽  
pp. 012219
Author(s):  
Witold Grymin ◽  
Marcin Koniorczyk ◽  
Marcin Zygmunt ◽  
Dariusz Gawin
Keyword(s):  
Thermal Comfort ◽  
Perturbation Method ◽  
Energy Demand ◽  
Polynomial Regression ◽  
Stochastic Perturbation ◽  
Random Variables ◽  
Random Variable ◽  
Response Functions ◽  
Input Parameters ◽  
Stochastic Perturbation Method

Abstract In the calculations of buildings’ thermal comfort, the input parameters are usually considered as strictly determined values. Numerous of them may be characterized by certain probability density functions. In the energy related problems, the uncertainty analyses are usually performed using the Monte Carlo method. However, this method requires multiple calculations and, therefore, may be very time-consuming. In the proposed work, two approaches are applied for the probabilistic studies: the stochastic perturbation method and the transformed random variables method. The stochastic analysis is based on the response functions and their derivatives with respect to all random input parameters. The relation between the thermal comfort and the input (random) variables have been calculated using the Energy Plus software. Afterwards, the response functions were estimated using the polynomial regression. The expected value and central moments of the response functions were calculated by means of the perturbation method and the transformed random variable theorem. The latter method allowed to obtain, using the same response functions, the implicit form of probability distributions function of the output parameter.

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

scholarly journals Stochastic energy-demand analyses with random input parameters for the single-family house

2021 ◽  
Author(s):  
Marcin Koniorczyk ◽  
Witold Grymin ◽  
Marcin Zygmunt ◽  
Dalia Bednarska ◽  
Alicja Wieczorek ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Consumption ◽  
Monte Carlo Method ◽  
Energy Demand ◽  
Stochastic Perturbation ◽  
Random Variable ◽  
Single Family ◽  
The Monte Carlo Method ◽  
Stochastic Perturbation Method ◽  
Family House

AbstractIn the analyses of the uncertainty propagation of buildings’ energy-demand, the Monte Carlo method is commonly used. In this study we present two alternative approaches: the stochastic perturbation method and the transformed random variable method. The energy-demand analysis is performed for the representative single-family house in Poland. The investigation is focused on two independent variables, considered as uncertain, the expanded polystyrene thermal conductivity and external temperature; however the generalization on any countable number of parameters is possible. Afterwards, the propagation of the uncertainty in the calculations of the energy consumption has been investigated using two aforementioned approaches. The stochastic perturbation method is used to determine the expected value and central moments of the energy consumption, while the transformed random variable method allows to obtain the explicit form of energy consumption probability density function and further characteristic parameters like quantiles of energy consumption. The calculated data evinces a high accordance with the results obtained by means of the Monte Carlo method. The most important conclusions are related to the computational cost reduction, simplicity of the application and the appropriateness of the proposed approaches for the buildings’ energy-demand calculations.

Self-tuning Kalman filter for compensation of transmission delay and loss in line-of-sight guidance

2018 ◽  
Vol 233 (11) ◽  
pp. 4191-4201
Author(s):  
Akram Nikfetrat ◽  
Reza Mahboobi Esfanjani
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Random Variables ◽  
Measurement Model ◽  
Line Of Sight ◽  
Uncertain Parameters ◽  
Suggested Approach ◽  
Self Tuning ◽  
Simulation Results ◽  
Sequence Simulation

A self-tuning Kalman filter is introduced to reduce the destructive effects of the delayed and lost measurements in the guidance systems employing command to line-of-sight strategy. A sequence of Bernoulli distributed random variables with uncertain probabilities are used to model the delayed and lost observations. Besides the state estimation, the uncertain parameters of the measurement model are identified online using the covariance of innovation sequence. Simulation results are given to demonstrate the merits of the suggested approach.

scholarly journals Energy Fluctuations in the Homogenized Hyper-Elastic Particulate Composites with Stochastic Interface Defects

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2011
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński ◽  
Artur Wirowski
Keyword(s):  
Perturbation Method ◽  
Volume Fraction ◽  
Stochastic Perturbation ◽  
Fem Analysis ◽  
Spherical Shape ◽  
Deformation Energy ◽  
Particulate Composites ◽  
Interface Defects ◽  
Hyper Elastic ◽  
Stochastic Perturbation Method

The principle aim of this study is to analyze deformation energy of hyper-elastic particulate composites, which is the basis for their further probabilistic homogenization. These composites have some uncertain interface defects, which are modelled as small semi-spheres with random radius and with bases positioned on the particle-matrix interface. These defects are smeared into thin layer of the interphase surrounding the reinforcing particle introduced as the third component of this composite. Matrix properties are determined from the experimental tests of Laripur LPR 5020 High Density Polyurethane (HDPU). It is strengthened with the Carbon Black particles of spherical shape. The Arruda–Boyce potential has been selected for numerical experiments as fitting the best stress-strain curves for the matrix behavior. A homogenization procedure is numerically implemented using the cubic Representative Volume Element (RVE). Spherical particle is located centrally, and computations of deformation energy probabilistic characteristics are carried out using the Iterative Stochastic Finite Element Method (ISFEM). This ISFEM is implemented in the algebra system MAPLE 2019 as dual approach based upon the stochastic perturbation method and, independently, upon a classical Monte-Carlo simulation, and uniform uniaxial deformations of this RVE are determined in the system ABAQUS and its 20-noded solid hexahedral finite elements. Computational experiments include initial deterministic numerical error analysis and the basic probabilistic characteristics, i.e., expectations, deviations, skewness and kurtosis of the deformation energy. They are performed for various expected values of the defects volume fraction. We analyze numerically (1) if randomness of homogenized deformation energy can correspond to the normal distribution, (2) how variability of the interface defects volume fraction affects the deterministic and stochastic characteristics of composite deformation energy and (3) whether the stochastic perturbation method is efficient in deformation energy computations (and in FEM analysis) of hyper-elastic media.

Response Probability Analysis of Random Acoustic Field Based on Perturbation Stochastic Method and Change-of-Variable Technique

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Acoustic Field ◽  
Random Variables ◽  
Stochastic Finite Element Method ◽  
Variable Technique ◽  
Change Of Variable

To calculate the probability density function of the response of a random acoustic field, a change-of-variable perturbation stochastic finite element method (CVPSFEM), which integrates the perturbation stochastic finite element method (PSFEM) and the change-of-variable technique in a unified form, is proposed. In the proposed method, the response of a random acoustic field is approximated as a linear function of the random variables based on a first order stochastic perturbation analysis. According to the linear relationship between the response and the random variables, the formal expression of the probability density function of the response of a random acoustic field is obtained by the change-of-variable technique. The numerical examples on a two-dimensional (2D) acoustic tube and a three-dimensional (3D) acoustic cavity of an automobile cabin verify the accuracy and efficiency of the proposed method. Hence, the proposed method can be considered as an effective method to quantify the effects of the parametric randomness of a random acoustic field on the sound pressure response.

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