scholarly journals Bias Errors due to Leakage Effects When Estimating Frequency Response Functions

2012 ◽  
Vol 19 (6) ◽  
pp. 1257-1266 ◽  
Author(s):  
Andreas Josefsson ◽  
Kjell Ahlin ◽  
Göran Broman
Keyword(s):  
Frequency Response ◽  
Measurement Data ◽  
Approximate Expression ◽  
Bias Error ◽  
Systematic Bias ◽  
Response Functions ◽  
Random Errors ◽  
Frequency Response Functions ◽  
Rectangular Window ◽  
Wide Range

Frequency response functions are often utilized to characterize a system's dynamic response. For a wide range of engineering applications, it is desirable to determine frequency response functions for a system under stochastic excitation. In practice, the measurement data is contaminated by noise and some form of averaging is needed in order to obtain a consistent estimator. With Welch's method, the discrete Fourier transform is used and the data is segmented into smaller blocks so that averaging can be performed when estimating the spectrum. However, this segmentation introduces leakage effects. As a result, the estimated frequency response function suffers from both systematic (bias) and random errors due to leakage. In this paper the bias error in theH1andH2-estimate is studied and a new method is proposed to derive an approximate expression for the relative bias error at the resonance frequency with different window functions. The method is based on using a sum of real exponentials to describe the window's deterministic autocorrelation function. Simple expressions are derived for a rectangular window and a Hanning window. The theoretical expressions are verified with numerical simulations and a very good agreement is found between the results from the proposed bias expressions and the empirical results.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

Damage Detection of Shear Connectors Based on Power Spectral Density Transmissibility

2013 ◽  
Vol 569-570 ◽  
pp. 1241-1248 ◽  
Author(s):  
Jun Li ◽  
Hong Hao
Keyword(s):  
Spectral Density ◽  
Damage Detection ◽  
Frequency Response ◽  
Power Spectral Density ◽  
Experimental Studies ◽  
Measurement Data ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Shear Connectors ◽  
Power Spectral

Damage of shear connectors in slab-on-girder structures will result in shear slippage between slab and girder, which significantly reduces the load-carrying capacity of the bridge. This paper proposes a dynamic damage detection approach to identify the damage of shear connectors in slab-on-girder bridges with power spectral density transmissibility (PSDT). PSDT formulates the relationship between the auto-spectral density functions of two responses. Measured impact force and acceleration responses from hammer tests are analyzed to obtain the frequency response functions at the slab and girder sensor locations by experimental modal analysis. When measurement data from the undamaged structure are available, PSDT from the slab response to the girder response is derived with the obtained frequency response functions. PSDT matrices in the undamaged and damaged states are directly compared to identify the damage of shear connectors. When the measurement data from the undamaged structure are not available, PSDT matrices from measured response at a reference sensor response to those of the slab and girder in the damaged state can also be used to detect the damage of shear connectors. Experimental studies with a concrete slab supported by two steel girders are conducted to investigate the accuracy and efficiency of the proposed approach. Identification results demonstrated that damage of shear connectors can be identified accurately and efficiently with and without measurement data from the undamaged structure.

scholarly journals Identification of relevant acoustic transfer paths for WT drivetrains with an operational transfer path analysis

2021 ◽  
Author(s):  
W. Schünemann ◽  
R. Schelenz ◽  
G. Jacobs ◽  
W. Vocaet
Keyword(s):  
Path Analysis ◽  
Wind Turbine ◽  
Frequency Response ◽  
Mechanical System ◽  
Reference Point ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Transfer Path ◽  
Transfer Path Analysis ◽  
Turbine Model

AbstractThe aim of a transfer path analysis (TPA) is to view the transmission of vibrations in a mechanical system from the point of excitation over interface points to a reference point. For that matter, the Frequency Response Functions (FRF) of a system or the Transmissibility Matrix is determined and examined in conjunction with the interface forces at the transfer path. This paper will cover the application of an operational TPA for a wind turbine model. In doing so the path contribution of relevant transfer paths are made visible and can be optimized individually.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

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