Testing point spectral analysis based on FFT

Bridge vibration frequency resolving in the condition of motivation context

Based on the motivation context, bridge vibration signal is not all the pure sine form[5]. According to the Fourier analysis, vibrating signal could be decomposed into many harmonic components.
Each harmonic component may be expressed by its amplitude and phase.

Fig 4 Time series of 4 testing points during same time-interval

Fig 3 GPS device using in testing

form[5]. According to the Fourier analysis, vibrating signal could be decomposed into many harmonic components.
Each harmonic component may be expressed by its amplitude and phase.
Supposed there is a dynamic deformation observation system, recording deformation value is x1 at t1 time, and x2 at t2 …, . xn at the tn time, these observed data constitute group of discrete time series which can be writed as {xt} (t=1, 2 …n).If the frequency fs (s=1, 2 ......k) of every harmonics in this group of time series is known, then they can be simulated with Fourier expansive formula (4):

Actually, based on the time series, the
(a) first step

(b) second step

(c) third step

Fig.5 Power spectral density of bridge

bridge vibrates frequency of fs in various steps harmonics could be decides by spectral analysis which are supported by measured waveform or the data come

Tab.1 Comparison of vibration frequencies between GPS solution and other methods

Fig 6 bridge various vibration types using finite element method

from discrete processing. Formula (5) is the discrete form of Fourier transform.

In Eq (5), x(n) and X(k)
are the series of time order vibration and frequency response respectively at the testing point. k=0, 1, 2, …, n-1
In order to guarantee the operation speed, the fast discrete Fourier transform or FFT was introduced in computation, usually FFT algorithm has two method including the time extraction FFT and the frequency extraction FFT. The former makes the time domain signal into even-odd sequence, the latter makes the frequency range signal into even-odd sequence. All of them take advantage of two characteristic of one is the periodicity or another is symmetry or Where signal * means W is conjugate.
This paper chose the former method.
Because the GPS signal noise source in testing point is multipath primarily, and the multipath signal frequency is lower than the bridge natural frequency. In order to compare the finite element modality analysis result, with the Matlab signal processing toolbox, a 9 steps Butterworth bandpass filter has been designed. Firstly, the filter for the
structure vibration time interval curve has been carried out, then with the filtered signal the spectral analysis has been carried on by using the fast Fournier transformation (FFT), thus the structure frequency would be obtained. The result of the ANSYS finite element modality analysis and dynamic demonstration show that the bridge vibrates under the calm condition is primarily along the direction of vertical bridge floor, using fast Fournier transformation (FFT), the bridge self-oscillation along the vertical bridge floor direction has been obtained, because more number the vibration mode steps is, more difficult they can occur, the first three steps have been merely set in computation. Using Matlab signal processing, the first three steps power spectrogram.of the bridge are seen in fig 5

Where cross direction express the frequency (Hz) vertical direction express the PSD (dB).

Validity checking of GPS dynamic surveying technique

Deterministic model method based on finite element Because the testing bridge has complete structural design material, in order to understand the feasibility of using the GPS dynamic surveying technique to get the bridge multistage vibration frequency. A deterministic model has been established to resolve the bridge vibration frequency caused by load with the finite element method. The software of finite element computation is Ansys.
The first three step vibration mode graph of Beida bridge using the Ansys finite element resolving are shown in fig 6.

Accelerometer measurement method

In the same point and same time, Accelerometer with the type of 891, which was produced by State Bureau of Seismology Engineering mechanics Research institute, had been set to obtain bridge vibration frequency, and the data processing software adopted Donghua data collection and processing system.
Table 1 shows the comparing result of first three steps frequency in Beida bridge test among the Ansys finite element analysis method, the accelerometer method and GPS-RTK surveying method.
In table 1, the bias ratio refers to the deviation ratio between the GPS actual frequency compared to the frequency obtained from other two methods, and the computation follow equation (6).

It is shown from table 1 that the vibration mode deviation of bridge first three steps in same place is very small when comparing between the GPS surveying result and the accelerometer measurement as well as the result of using the Ansys finite element resolving. Every step data matchs well among them except the second step frequency value acquired by accelerometer is bigger. It is also known from the bridge testing that the accelerometer has been used in structure vibration test for its advantage of light weight, small volume and no affecting to testing system, but this method could make bigger measuring error than other’s and the deformation result is not direct-viewing too, when the structure oscillation is slow, it could not measure the structure of whole vibration amplitude.

Conclusion
The vibration mode measured by GPS sensor receiver and accelerometer coincide with the result of using the finite element method, it indicates that the overall rigidity of the testing bridge structure conforms to the actual requirement From the view of testing analysis flow, the GPS-RTK method has the characteristic of simple operation, nimble and convenient; with the GPS receiver, it is easy to monitor the bridge of three dimensional dynamic deformation in real-time as well as first step bridge vibration mode frequency or higher step one which can provide the datum data directly for the bridge use,
maintenance and condition evaluation.

Reference:
[1] J.J.Guo, L.J.Dai, Y.C.Lu, Study of the Humen bridge GPS(RTK) realtime displacement monitors Bulletin of Surveying and Mapping, 2000.12:4-5.
[2] Leroy E. monitor on longest hanging bridge in the world with GPS real-time, Bulletin of Surveying and Mapping, 1996, 6:46-48.
[3]G.X.Zhu, X.D.Chen, Y.J.Wang. Application in Humen bridge operation safe monitor using GPS-RTK Technology, ROAD, 2002, 7:55-58.
[4] H.N.Li, T.H.Yi, X.D.Yi.Real-time monitor and data-analysisof long-span bridge base on total station and GPS technology, Disaster prevention disaster reduction project journal, 2005, 25(1):8-13.
[5] H.N.Li, T.H.Yi, G.X.Wang. GPS used in structure health monitor research and application progress. Natural disaster journal, 2004, 13(6): 122-130.
[6] H.N.Li, T.H.Yi, X.D.Yi. On GPS Observation Errors with ANC Principles and Wavelet Denoise Method [J]. Wuhan University journal (information science version), 2006, 11, 995-998.
[7] H.Li, W.S.Zhou, J.P.Ou. Study of Large-scale bridge structure intelligence health monitor system integration. Civil engineering journal, 2006, 39(2), 46-52. March