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The frequency distribution of a short interval period, the SIP distribution, obtained from the vibration of a structure that is excited by the force of non-stationary vibration is available for the robust estimation of the dynamic property of the structure. This paper shows experiments of the health monitoring of a model structure using the SIP distribution. Comparisons of SIP distributions with average DFT spectra are also shown.

One of the major problems after an earthquake, which causes certain changes in the dynamic property of a structure, is the investigation of structural damage. In principle, we can check the change using a shaker to obtain the frequency response of a structure. However, it is difficult and not practical to shake a big structure before and after an earthquake to detect the change. Regardless of size or weight, all structures such as buildings, towers, and bridges are vibrating due to the natural force of winds, ground motions, or both. Information of the dynamic property of a building, for example, is comprised of the forced vibration of a structure. Changes of dynamic property reflect structural changes. Then, the problem is how to extract information from the vibration of structures.

It was shown by one of the authors that the frequency distribution of a short-interval period, the SIP distribution, of the forced nonstationary vibration corresponds to the frequency response of a structure [

The discrete Fourier transform (DFT) is used in many disciplines to obtain the spectrum or frequency of a signal. The DFT produces reasonable results for a large class of signal processes. However, we do not use the DFT for detecting a short interval period because of its inherent limitation of frequency resolution [

The dominant frequency or period of a short-interval sequence

The SIP distribution is given by a number of dominant frequencies (or periods) of short sequences which are fractions of measured data. Thus, the normalized SIP distribution

If we assume that a structure is excited by the force of random noise and assign the frequency

Hence, we get an approximation

To confirm the theoretical result shown by (

The frequency responses of the model structures A and B, which are difficult to measure in real cases, are shown in Figure

Power frequency responses of model structures A (a) and B (b).

The force of stationary random vibration as well as nonstationary one was applied to excite a model structure, and the acceleration of the structure was measured at the fixed point of the frame. The measured data were provided for the DFT analysis and SIP distribution.

We assume that the average spectrum of nonstationary vibration is a clutter one which varies slowly with time, so that we represent a nonstationary vibration as a set of random noise sequences each having a different clutter average spectrum; see Figure

Examples of the clutter average spectrum of nonstationary vibration.

The measured data sequence was divided into 2,400 short-interval sequences for the nonharmonic Fourier analysis to get a SIP distribution, that is, the dominant frequency of each sequence is given by the analysis of 60 sampled data. To compare the SIP distribution with the average of DFT spectra, the measured data sequence was also divided into 240 sequences, so that the DFT frequency,

Figure

Power frequency response of the model structure A estimated by the average DFT spectrum (a), (b), and (c) and the SIP distribution (b), (d), and (f). (a) and (b) Stationary random vibration. (c)–(f) Nonstationary vibration. Relative frequency is given by

Similarly, Figure

Power frequency response of the model structure B estimated by the average DFT spectrum (a), (c), and (e) and the SIP disctribution (b), (d), and (e). (a) and (b) Stationary random vibration. (c)–(f) Nonstationary vibration. Relative frequency is given by

Figure

Illustration of the health-monitoring of a structure by the DFT spectrum and the SIP distribution for random noise excitation (a), (b) and nonstationary noise excitation (c), (d).

A number of buildings, bridges, and towers have been constructed in past decades. Consequently, there are many decrepit structures which need to be reconstructed. One may remember the accident in Minneapolis, USA where thirteen persons were killed by the sudden collapse of an old bridge over the Mississippi. The health monitoring of structures is an important mean for security against such an accident. The method described in this paper might be available. Further experiments using a real bridge, for example, will confirm the proposed method, though it will take decades.