Frequency Response Function Measurements of Multivariable Systems via Local Rational Modelling

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

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Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function

Water ◽

10.3390/w13020144 ◽

2021 ◽

Vol 13 (2) ◽

pp. 144

Author(s):

Yan Zhang ◽

Jijian Lian ◽

Songhui Li ◽

Yanbing Zhao ◽

Guoxin Zhang ◽

...

Keyword(s):

Frequency Response ◽

Frequency Distribution ◽

Response Function ◽

Frequency Response Function ◽

Ground Vibration ◽

Vibration Source ◽

Ground Vibrations ◽

High Energies ◽

Flood Discharge ◽

Opening Method

Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.

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Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

Journal of Mechanics ◽

10.1017/jmech.2020.49 ◽

2020 ◽

Vol 36 (6) ◽

pp. 867-879

Author(s):

X. H. Liao ◽

W. F. Wu ◽

H. D. Meng ◽

J. B. Zhao

Keyword(s):

Frequency Response ◽

Response Function ◽

Frequency Response Function ◽

Dynamic Properties ◽

Main Idea ◽

Prediction Method ◽

Response Prediction ◽

Synthesis Methods ◽

Dynamic Substructuring ◽

Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

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Alongshore Wind Forcing of Coastal Sea Level as a Function of Frequency

Journal of Physical Oceanography ◽

10.1175/jpo2972.1 ◽

2006 ◽

Vol 36 (11) ◽

pp. 2173-2184 ◽

Cited By ~ 7

Author(s):

Holly F. Ryan ◽

Marlene A. Noble

Keyword(s):

United States ◽

Frequency Response ◽

Sea Level ◽

Response Function ◽

Wind Field ◽

Frequency Response Function ◽

The United States ◽

The West ◽

Coastal Sea ◽

Alongshore Wind

Abstract The amplitude of the frequency response function between coastal alongshore wind stress and adjusted sea level anomalies along the west coast of the United States increases linearly as a function of the logarithm (log10) of the period for time scales up to at least 60, and possibly 100, days. The amplitude of the frequency response function increases even more rapidly at longer periods out to at least 5 yr. At the shortest periods, the amplitude of the frequency response function is small because sea level is forced only by the local component of the wind field. The regional wind field, which controls the wind-forced response in sea level for periods between 20 and 100 days, not only has much broader spatial scales than the local wind, but also propagates along the coast in the same direction as continental shelf waves. Hence, it has a stronger coupling to and an increased frequency response for sea level. At periods of a year or more, observed coastal sea level fluctuations are not only forced by the regional winds, but also by joint correlations among the larger-scale climatic patterns associated with El Niño. Therefore, the amplitude of the frequency response function is large, despite the fact that the energy in the coastal wind field is relatively small. These data show that the coastal sea level response to wind stress forcing along the west coast of the United States changes in a consistent and predictable pattern over a very broad range of frequencies with time scales from a few days to several years.

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