Putting Statistics Into the Statistical Energy Analysis of Automotive Vehicles

1993 ◽  
Author(s):  
Clark J. Radcliffe ◽  
Xian Li Huang
Keyword(s):  
Monte Carlo ◽  
Energy Analysis ◽  
Computational Effort ◽  
Design Tool ◽  
Physical Parameters ◽  
Statistical Energy Analysis ◽  
Mean Values ◽  
Interior Spaces ◽  
The Monte Carlo Method ◽  
Design Values

Abstract Sound and vibration transmission modeling methods are important to the design process for high quality automotive vehicles. Statistical Energy Analysis (SEA) is an emerging design tool for the automotive industry that was initially developed in the 1960’s to estimate root-mean-square sound and vibration levels in structures and interior spaces. Although developed to estimate statistical mean values, automotive design application of SEA needs the additional ability to predict statistical variances of the predicted mean values of sound and vibration. This analytical ability would allow analysis of vehicle sound and vibration response sensitivity to changes in vehicle design specifications and their statistical distributions. This paper will present an algorithm to extend the design application of the SEA method through prediction of the variances of RMS responses of vibro-acoustic automobile structures and interior spaces from variances in SEA automotive model physical parameters. The variance analysis is applied to both a simple, complete illustrative example and a more complex automotive vehicle example. Example variance results are verified through comparison with a Monte Carlo test of 2,000 SEA responses whose physical parameters were given Gaussian distributions with means at design values. Analytical predictions of the response statistics agree with the statistics generated by the Monte Carlo method but only require about 1/300 of the computational effort.

Putting Statistics into the Statistical Energy Analysis of Automotive Vehicles

1997 ◽  
Vol 119 (4) ◽  
pp. 629-634 ◽  
Author(s):  
C. J. Radcliffe ◽  
X. L. Huang
Keyword(s):  
Monte Carlo ◽  
Energy Analysis ◽  
Computational Effort ◽  
Design Tool ◽  
Physical Parameters ◽  
Statistical Energy Analysis ◽  
Mean Values ◽  
Interior Spaces ◽  
The Monte Carlo Method ◽  
Design Values

Sound and vibration transmission modeling methods are important to the design process for high quality automotive vehicles. Statistical Energy Analysis (SEA) is an emerging design tool for the automotive industry that was initially developed in the 1960’s to estimate root-mean-square sound and vibration levels in structures and interior spaces. Although developed to estimate statistical mean values, automotive design application of SEA needs the additional ability to predict statistical variances of the predicted mean values of sound and vibration. This analytical ability would allow analysis of vehicle sound and vibration response sensitivity to changes in vehicle design specifications and their statistical distributions. This paper will present an algorithm to extend the design application of the SEA method through prediction of the variances of RMS. responses of vibro-acoustic automobile structures and interior spaces from variances in SEA automotive model physical parameters. The variance analysis is applied to both a simple, complete illustrative example and a more complex automotive vehicle example. Example variance results are verified through comparison with a Monte Carlo test of 2,000 SEA responses whose physical parameters were given Gaussian distributions with means at design values. Analytical predictions of the response statistics agree with the statistics generated by the Monte Carlo method but only require about 1/300 of the computational effort.

Probability Distribution of Statistical Energy Analysis Model Responses Due to Parameter Randomness

1998 ◽  
Vol 120 (3) ◽  
pp. 641-647 ◽  
Author(s):  
X. L. Huang ◽  
C. J. Radcliffe
Keyword(s):  
Probability Distribution ◽  
Energy Analysis ◽  
Hypothesis Test ◽  
Noise Analysis ◽  
Response Probability ◽  
Statistical Hypothesis ◽  
Design Parameters ◽  
Physical Parameters ◽  
Frequency Noise ◽  
Statistical Energy Analysis

The Statistical Energy Analysis (SEA) methodology has been widely used in aerospace, ship and automotive industry for high frequency noise analysis and acoustic designs. SEA models are treated here as baseline representations of a population of models for systems such as automotive vehicles. SEA responses from the population of all possible models for a vehicle have a random distribution because of the unavoidable uncertainty in the physical parameters due to fabrication imperfection, manufacturing and assembly variations. The random characteristics of the SEA responses can be described by the response probability distribution. In this work, SEA energy response probability distributions due to parameter randomness in a small neighborhood of nominal design values in frequency bands are proven through the Central Limit Theorem to be Gaussian for infinite number of design parameters. Mean squared sound pressure and velocity are directly proportional to SEA energy responses, their distributions are also shown to be Gaussian. In engineering applications, the number of design parameters is always finite for any SEA models. A Monte Carlo test and Statistical Hypothesis test on a simple 3-element SEA model show that the theoretical, infinite order, Gaussian distributions are good approximations for response distributions of a finite parameter SEA model.

scholarly journals Monte Carlo simulation of climate-weather change process at maritime ferry operating area

2017 ◽  
Vol 1 (21) ◽  
pp. 5-17
Author(s):  
Ewa Kuligowska
Keyword(s):  
Monte Carlo ◽  
Change Process ◽  
Fixed Time ◽  
Limit Values ◽  
Mean Values ◽  
Sojourn Times ◽  
Process Characteristics ◽  
The Monte Carlo Method ◽  
The Mean ◽  
Weather Change

The paper presents a computer simulation technique applied to generating the climate-weather change process at Baltic Sea restricted waters and its characteristics evaluation. The Monte Carlo method is used under the assumption of semi-Markov model of this process. A procedure and an algorithm of climate-weather change process’ realizations generating and its characteristics evaluation are proposed to be applied in C# program preparation. Using this program, the climate-weather change process’ characteristics are predicted for the maritime ferry operating area. Namely, the mean values and standard deviations of the unconditional sojourn times, the limit values of transient probabilities and the mean values of total sojourn times for the fixed time at the climate-weather states are determined.

Analysis of the Core Physical Characteristics of China Experimental Fast Reactor With MCNP

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Xiong Wenbin ◽  
Xie Qin ◽  
Li Huwei ◽  
Yang Sengai ◽  
Mao Huan ◽  
...  
Keyword(s):  
Monte Carlo ◽  
International Atomic Energy Agency ◽  
Fast Reactor ◽  
Physical Parameters ◽  
Energy Agency ◽  
Safety Review ◽  
The Core ◽  
Calculation Results ◽  
Design Values ◽  
China Experimental Fast Reactor

The whole core model of China experimental fast reactor (CEFR) is established according to the parameters of China experimental fast reactor, which are given by technical publication from the International Atomic Energy Agency (IAEA-TECDOC-1531), and the physical parameters of CEFR are simulated with the Monte Carlo N-particle code (MCNP4a). The calculation results are compared with the data contained in the safety analysis report of CEFR. The calculation results are consistent with the design values, which successfully demonstrate the acceptable fidelity of the MCNP model. The MCNP model will be further refined and applied for nuclear safety review of the CEFR in the future.

scholarly journals CALCULATION OF THE MOLIÈRE RADIUS FOR VARIOUS CONFIGURATIONS OF AN ELECTROMAGNETIC SAMPLING CALORIMETER ECaL SPD NICA

2021 ◽  
pp. 86-90
Author(s):  
V.E. Kovtun ◽  
T.V. Malykhina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Energy Range ◽  
Physical Parameters ◽  
The Monte Carlo Method ◽  
Current Task ◽  
Electromagnetic Calorimetry ◽  
Further Development

One of the main tasks of the electromagnetic calorimetry of the SPD setup is effective π0-γ separation in the energy range from 50 MeV to 10 GeV. Therefore, the current task is to optimize the design of the module cells in order to improve the physical parameters of the ECaL calorimeter. The Molière radius is determined in this work by the Monte Carlo method using Geant4 toolkit for various cell configurations of the calorimeter module. The results obtained in this work will be taken into account in the further development of the detecting systems of the ECaL SPD NICA.

scholarly journals Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations

2015 ◽  
Vol 11 (22) ◽  
pp. 49-72 ◽  
Author(s):  
Gilberto González Parra ◽  
Abraham J Arenas ◽  
Miladys Cogollo
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Hybrid Method ◽  
Source Term ◽  
Closed Form Solution ◽  
Random Variables ◽  
Form Solution ◽  
Mean Values ◽  
The Monte Carlo Method ◽  
Condi Tions

A numerical method to solve a general random linear parabolic equationwhere the diffusion coefficient, source term, boundary and initial condi-tions include uncertainty, is developed. Diffusion equations arise in manyfields of science and engineering, and, in many cases, there are uncertaintiesdue to data that cannot be known, or due to errors in measurements andintrinsic variability. In order to model these uncertainties the correspon-ding parameters, diffusion coefficient, source term, boundary and initialconditions, are assumed to be random variables with certainprobabilitydistributions functions. The proposed method includes finite differenceschemes on the space variable and the differential transformation methodfor the time. In addition, the Monte Carlo method is used to deal withthe random variables. The accuracy of the hybrid method is investigatednumerically using the closed form solution of the deterministic associated equation. Based on the numerical results, confidence intervals and ex-pected mean values for the solution are obtained. Furthermore, with theproposed hybrid method numerical-analytical solutions are obtained.

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