Subtractive modeling using the reverse condensed transfer function method: influence of the numerical errors

2021 ◽  
Vol 263 (4) ◽  
pp. 2617-2628
Author(s):  
Florent Dumortier ◽  
Laurent Maxit ◽  
Valentin Meyer
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Numerical Models ◽  
Scattering Problem ◽  
Original System ◽  
Rigid Sphere ◽  
Test Case ◽  
Model Errors ◽  
Numerical Errors ◽  
Transfer Function Method

Decoupling procedures based on substructuring methods allow to predict the vibroacoustic behaviour of a given system by removing a part of an original system that can be easily modelled. The reverse Condensed Transfer Function (rCTF) method has been developed to decouple acoustical or mechanical subsystems that are coupled along lines or surfaces. From the so-called condensed transfer functions (CTFs) of the original system and of the removing part, the behaviour of the system of interest can be predicted. The theoretical framework as well as a numerical validation have been recently published. In the present paper, we focus on the influence of numerical errors on the results of the rCTF method, when the CTFs are calculated using numerical models for the original system and/or the removed part. The rCTF method is applied to a test case consisting in the scattering problem of a rigid sphere in an infinite water domain and impacted by an acoustic plane wave. Discrete green formulation and finite element method are used to estimate the CTFs. Numerical results will be presented in order to evaluate the sensitivity of the method to model errors and the potential promises and limitations of the method will be highlighted.

scholarly journals Using transfer functions to quantify El Niño Southern Oscillation dynamics in data and models

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140272 ◽  
Author(s):  
Douglas G. MacMartin ◽  
Eli Tziperman
Keyword(s):  
Transfer Function ◽  
El Niño ◽  
Transfer Functions ◽  
El Nino ◽  
Southern Oscillation ◽  
El Niño Southern Oscillation ◽  
El Nino Southern Oscillation ◽  
Control Analysis ◽  
Model Errors ◽  
Frequency Dependent

Transfer function tools commonly used in engineering control analysis can be used to better understand the dynamics of El Niño Southern Oscillation (ENSO), compare data with models and identify systematic model errors. The transfer function describes the frequency-dependent input–output relationship between any pair of causally related variables, and can be estimated from time series. This can be used first to assess whether the underlying relationship is or is not frequency dependent, and if so, to diagnose the underlying differential equations that relate the variables, and hence describe the dynamics of individual subsystem processes relevant to ENSO. Estimating process parameters allows the identification of compensating model errors that may lead to a seemingly realistic simulation in spite of incorrect model physics. This tool is applied here to the TAO array ocean data, the GFDL-CM2.1 and CCSM4 general circulation models, and to the Cane–Zebiak ENSO model. The delayed oscillator description is used to motivate a few relevant processes involved in the dynamics, although any other ENSO mechanism could be used instead. We identify several differences in the processes between the models and data that may be useful for model improvement. The transfer function methodology is also useful in understanding the dynamics and evaluating models of other climate processes.

scholarly journals Geomagnetic coast effect at two Croatian repeat stations

2017 ◽  
Vol 59 (6) ◽  
Author(s):  
Eugen Vujić ◽  
Mario Brkić
Keyword(s):  
Transfer Function ◽  
Function Method ◽  
Transfer Functions ◽  
First Order ◽  
Transfer Function Method ◽  
Coast Effect ◽  
Inductive Effects ◽  
Induction Arrows ◽  
Coastal Effect ◽  
Induced Currents

<p>Knowledge of inductive effects is important for the reliability of geomagnetic surveys as well as reduction of measurements, and hence for the accuracy of models and maps of the Earth’s magnetic field. Detection of anomalous induced fields, due to the geomagnetic coast effect, was carried out by the transfer function method to estimate the induction arrows indicating areas of anomalous induced currents. To determine the transfer function at the two coastal Croatian repeat stations used in this study, the so-called geomagnetic plane-wave events from July 2010 were used. Analysis of transfer functions for Krbavsko polje and Sinjsko polje first order repeat stations, using observatories Grocka and Tihany as references, revealed the existence of the Adriatic coastal effect on periods of 10-65 minutes.</p>

scholarly journals A condensed transfer function method as a tool for solving vibroacoustic problems

2015 ◽  
Vol 230 (6) ◽  
pp. 928-938 ◽  
Author(s):  
Valentin Meyer ◽  
Laurent Maxit ◽  
Jean-Louis Guyader ◽  
Thomas Leissing ◽  
Christian Audoly
Keyword(s):  
Transfer Function ◽  
Function Method ◽  
Transfer Functions ◽  
Mechanical Systems ◽  
Test Cases ◽  
Point Contacts ◽  
Transfer Function Method ◽  
Frequency Transfer ◽  
Complex Mechanical Systems

Substructuring approaches are nowadays widely used to predict numerically the vibroacoustic behavior of complex mechanical systems. Some of these methods are based on admittance or mobility frequency transfer functions at the coupling interfaces. They have already been used intensively to couple subsystems linked by point contacts and enable to solve problems at higher frequency while saving computation costs. In the case of subsystems coupled along lines, a Condensed Transfer Function method is developed in the present paper. The admittances on the coupling line are condensed in order to reduce the number of coupling forces evaluated. Three variants are presented, where the transfer functions are condensed using three different functions. After describing the principle of the CTF method, simple structures will be given as test cases for validation.

SEMI-ANALYTICAL SOLUTION OF TWO-DIMENSIONAL ELASTICITY PROBLEMS BY FINITE DIFFERENCE–DISTRIBUTED TRANSFER FUNCTION METHOD

2010 ◽  
Vol 10 (02) ◽  
pp. 315-334 ◽  
Author(s):  
YAUBIN YANG ◽  
BINGEN YANG
Keyword(s):  
Transfer Function ◽  
Finite Difference ◽  
Analytical Solution ◽  
Function Method ◽  
Transfer Functions ◽  
Two Dimensional ◽  
Dynamic Problems ◽  
Arbitrary Boundary ◽  
Transfer Function Method ◽  
Distributed Transfer Function

A semi-analytical solution method, called the Finite Difference–Distributed Transfer Function Method, is developed for static and dynamic problems of two-dimensional elastic bodies composed of multiple rectangular subregions. In the development, the original two-dimensional elasticity problem is first reduced into a one-dimensional boundary-value problem by finite difference; the exact solution of the reduced problem is then obtained by using the distributed transfer functions of the elastic continuum. The proposed technique, which combines the simplicity of finite difference and the closed form of analytical solutions, is capable of handling arbitrary boundary conditions, delivers highly accurate solutions for static and dynamic problems, and is computationally efficient. The proposed method is illustrated on a square region and an L-shaped region.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input

2012 ◽  
Vol 37 (4) ◽  
pp. 447-454
Author(s):  
James W. Beauchamp
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Cutoff Frequency ◽  
Sine Wave ◽  
Nonlinear Propagation ◽  
Linear Filter ◽  
Wave System ◽  
General Effect ◽  
Filter Characteristic ◽  
High Pass

Abstract Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone mouthpiece and anechoic output signals were made that provide a more accurate measurement of the trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972 verified the high-pass behavior, but they also showed a series of resonances whose minima correspond to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above cutoff are greater than would be expected from linear filter theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative strengths of the upper harmonics.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

scholarly journals Determination of the Optimal Neural Network Transfer Function for Response Surface Methodology and Robust Design

2021 ◽  
Vol 11 (15) ◽  
pp. 6768
Author(s):  
Tuan-Ho Le ◽  
Hyeonae Jang ◽  
Sangmun Shin
Keyword(s):  
Response Surface Methodology ◽  
Transfer Function ◽  
Response Surface ◽  
Robust Design ◽  
Transfer Functions ◽  
Desirability Function ◽  
Likelihood Estimation ◽  
Statistical Simulation ◽  
Screening Procedure ◽  
Function Estimation

Response surface methodology (RSM) has been widely recognized as an essential estimation tool in many robust design studies investigating the second-order polynomial functional relationship between the responses of interest and their associated input variables. However, there is scope for improvement in the flexibility of estimation models and the accuracy of their results. Although many NN-based estimations and optimization approaches have been reported in the literature, a closed functional form is not readily available. To address this limitation, a maximum-likelihood estimation approach for an NN-based response function estimation (NRFE) is used to obtain the functional forms of the process mean and standard deviation. While the estimation results of most existing NN-based approaches depend primarily on their transfer functions, this approach often requires a screening procedure for various transfer functions. In this study, the proposed NRFE identifies a new screening procedure to obtain the best transfer function in an NN structure using a desirability function family while determining its associated weight parameters. A statistical simulation was performed to evaluate the efficiency of the proposed NRFE method. In this particular simulation, the proposed NRFE method provided significantly better results than conventional RSM. Finally, a numerical example is used for validating the proposed method.

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