An Efficient Iterative Algorithm for Accurately Calculating Impulse Response Functions in Modal Testing

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
J. M. Liu ◽  
W. D. Zhu ◽  
Q. H. Lu ◽  
G. X. Ren
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Iterative Algorithm ◽  
Impulse Response ◽  
Mimo Systems ◽  
Spectral Lines ◽  
Modal Testing ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Modal Parameter

Impulse response functions (IRFs) and frequency response functions (FRFs) are bases for modal parameter identification of single-input, single-output (SISO) and multiple-input, multiple-out (MIMO) systems, and the two functions can be transformed from each other using the fast Fourier transform and the inverse fast Fourier transform. An efficient iterative algorithm is developed in this work to directly and accurately calculate the IRFs of SISO and MIMO systems in the time domain using relatively short input and output data series. The iterative algorithm can avoid the time-consuming inversion of a large matrix in the conventional least-square method for calculating an IRF, greatly reducing the computation time. In addition, a fitting index and an error energy decreasing coefficient are introduced to evaluate the accuracy in calculating an IRF and to provide the termination criterion for the iterative algorithm. A new coherence function is also introduced to evaluate the accuracy of calculated IRFs and FRFs at different spectral lines. Two examples are given to illustrate the effectiveness and efficiency of the methodology.

Efficient and Accurate Calculation of Discrete Frequency Response Functions and Impulse Response Functions

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Frequency Response ◽  
Impulse Response ◽  
Coherence Function ◽  
Sampling Period ◽  
Spectral Lines ◽  
Infinite Length ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Discrete Frequency

Modal properties of a structure can be identified by experimental modal analysis (EMA). Discrete frequency response functions (FRFs) and impulse response functions (IRFs) between response and excitation series are bases for EMA. In the calculation of a discrete FRF, the discrete Fourier transform (DFT) is applied to both response and excitation series, and a transformed series in the DFT is virtually extended to have an infinite length and be periodic with a period equal to the length of the series; the resulting periodicity can be physically incorrect in some cases, which depends on an excitation technique used. An efficient and accurate methodology for calculating discrete FRFs and IRFs is proposed here, by which fewer spectral lines are needed and accuracies of resulting FRFs and IRFs can be maintained. The relationship between an IRF from the proposed methodology and that from the least-squares (LS) method is shown. A coherence function extended from a new type of coherence functions is used to evaluate qualities of FRFs and IRFs from the proposed methodology in the frequency domain. The extended coherence function can yield meaningful values even with response and excitation series of one sampling period. Based on the extended coherence function, a fitting index is used to evaluate overall qualities of the FRFs and IRFs. The proposed methodology was numerically and experimentally applied to a two degrees-of-freedom (2DOF) mass–spring–damper system and an aluminum plate to estimate their FRFs and IRFs, respectively. In the numerical example, FRFs and IRFs from the proposed methodology agree well with theoretical ones. In the experimental example, an FRF and its associated IRF from the proposed methodology with a random impact series agreed well with benchmark ones from a single impact test.

Efficient and Accurate Calculation of Discrete Frequency Response Functions and Impulse Response Functions

2015 ◽  
Author(s):  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Frequency Response ◽  
Impulse Response ◽  
Coherence Function ◽  
Sampling Period ◽  
Random Excitation ◽  
Spectral Lines ◽  
Data Series ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Discrete Frequency

Modal properties of a structure can be identified by experimental modal analysis (EMA). Discrete frequency response functions (FRFs) and impulse response functions (IRFs) between responses and excitation are bases for EMA. In calculation of a discrete FRF, discrete Fourier transform (DFT) is applied to both response and excitation data series, and a transformed data series in DFT is virtually extended to have an infinite length and be periodic with a period equal to the length of the series; the resulting periodicity can be physically incorrect in some cases, which depends on an excitation technique used. There are various excitation techniques in EMA, and periodic extension in DFT for EMA using periodic random and burst random excitation is physically correct. However, EMA using periodic random excitation needs a relatively long excitation time to have responses to be steady-state and periodic, and EMA using burst random excitation needs a long sampling period for responses to decay to zero, which can result in relatively long response and excitation data series and necessitate a large number of spectral lines for associated DFTs, especially for a high sampling frequency. An efficient and accurate methodology for calculating discrete FRFs and IRFs is proposed here, by which fewer spectral lines are needed and accuracies of resulting FRFs and IRFs can be maintained. The relationship between an IRF from the proposed methodology and that from the least-squares method is shown. A new coherence function that can evaluate qualities of FRFs and IRFs from the proposed methodology in the frequency domain is used, from which meaningful coherence function values can be obtained even with response and excitation series of one sampling period. Based on the new coherence function, a fitting index is used to evaluate overall qualities of the FRFs and IRFs. The proposed methodology was numerically and experimentally applied to a two-degree-of-freedom mass-spring-damper system and an aluminum plate to estimate their FRFs, respectively. In the numerical example, FRFs from the proposed methodology agree well with the theoretical one; in the experimental example, a FRF from the proposed methodology with a random impact series agreed well with the benchmark one from a single impact test.

Impulse-response functions and anthropogenic CO2

1995 ◽  
Vol 22 (4) ◽  
pp. 413-416 ◽  
Author(s):  
Francesco N. Tubiello ◽  
Michael Oppenheimer
Keyword(s):  
Impulse Response ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Anthropogenic Co2

IMPROVING EXTRACTION OF IMPULSE RESPONSE FUNCTIONS USING STATIONARY WAVELET SHRINKAGE IN TERAHERTZ REFLECTION IMAGING

2010 ◽  
Vol 09 (04) ◽  
pp. 387-394 ◽  
Author(s):  
YANG CHEN ◽  
YIWEN SUN ◽  
EMMA PICKWELL-MACPHERSON
Keyword(s):  
Experimental Data ◽  
Impulse Response ◽  
Response Function ◽  
Impulse Response Function ◽  
Terahertz Imaging ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Inverse Filtering ◽  
Wavelet Shrinkage ◽  
Gaussian Filtering

In terahertz imaging, deconvolution is often performed to extract the impulse response function of the sample of interest. The inverse filtering process amplifies the noise and in this paper we investigate how we can suppress the noise without over-smoothing and losing useful information. We propose a robust deconvolution process utilizing stationary wavelet shrinkage theory which shows significant improvement over other popular methods such as double Gaussian filtering. We demonstrate the success of our approach on experimental data of water and isopropanol.

A Comparison of Approaches to Select the Informativeness of Priors in BVARs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jan Prüser ◽  
Christoph Hanck
Keyword(s):  
Impulse Response ◽  
Prior Information ◽  
Hierarchical Modeling ◽  
Small Samples ◽  
Model Parameters ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Vector Autoregressions ◽  
The Rich ◽  
Bayesian Vars

Abstract Vector autoregressions (VARs) are richly parameterized time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, in small samples the rich parametrization of VAR models may come at the cost of overfitting the data, possibly leading to imprecise inference for key quantities of interest such as impulse response functions (IRFs). Bayesian VARs (BVARs) can use prior information to shrink the model parameters, potentially avoiding such overfitting. We provide a simulation study to compare, in terms of the frequentist properties of the estimates of the IRFs, useful strategies to select the informativeness of the prior. The study reveals that prior information may help to obtain more precise estimates of impulse response functions than classical OLS-estimated VARs and more accurate coverage rates of error bands in small samples. Strategies based on selecting the prior hyperparameters of the BVAR building on empirical or hierarchical modeling perform particularly well.

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