KR101529690B1 - System for monitoring building shake using time domain decomposition - Google Patents

System for monitoring building shake using time domain decomposition Download PDF

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KR101529690B1
KR101529690B1 KR1020150052376A KR20150052376A KR101529690B1 KR 101529690 B1 KR101529690 B1 KR 101529690B1 KR 1020150052376 A KR1020150052376 A KR 1020150052376A KR 20150052376 A KR20150052376 A KR 20150052376A KR 101529690 B1 KR101529690 B1 KR 101529690B1
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module
vibration
building
signal processing
tdd
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Korean (ko)
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문대중
김병화
정진우
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주식회사 이제이텍
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H11/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties
    • G01H11/06—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties by electric means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector

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  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

An earthquake monitoring system using a time domain decomposition (TDD) technique is disclosed. The present invention comprises: a three-axis vibration sensor module for measuring the vibration of a building and outputting a vibration signal; a signal processing module for collecting the vibration signal outputted by the three-axis vibration sensor module and performing a signal processing; a TDD module for extracting a mode shape which is a spatial parameter in the time area without an FFT calculation of the vibration signal whose signal processing is conducted by the signal processing module, performing an FFT calculation on the vibration signal whose signal processing is performed by the signal processing module by using the extracted mode shape, and extracting a natural frequency which is a time parameter and a damping ratio; and a building damage determining module for using the natural frequency, damping ratio, and mode shape extracted by the TDD module and determining the position and degree of a damage of the building. According to the system for monitoring building vibration using a TDD technique, the system can extract directly a mode shape in a time area without a Fourier transform of a measured value of the vibration by a vibration sensor at a large building with a number of vibration sensors installed, and rapidly extract a high-resolution mode shape of a large structure in real time.

Description

[0001] SYSTEM FOR MONITORING BUILDING SHAKE USING TIME DOMAIN DECOMPOSITION [0002]

The present invention relates to a building vibration monitoring system, and more particularly, to a building vibration monitoring system using a time domain decomposition (TDD) technique.

Generally, high-rise buildings are constructed to have earthquake-proof characteristics, and there is a system for promptly coping with building vibration caused by earthquakes.

The dynamic characteristics of the vibration of the building are the characteristic values such as natural frequency, damping ratio and mode shape of the structure.

Here, the mode shape is determined by the shape (shape) and the frequency of vibration of the structure depending on the characteristics (mass and rigidity) of the structure when the structure vibrates due to an instantaneous load, The frequency is called the natural frequency. It is the dynamic characteristic of the structure which is most importantly used for dynamic analysis and dynamic design of seismic isolation, seismic isolation, and vibration control of buildings.

High-rise building is a large civil engineering structure. Numerous vibration sensors are installed everywhere in the building and there are many actual values to be extracted from each vibration sensor. Also, the characteristic values to be calculated from these measured values have considerable computational complexity and high degree of complexity.

The existing structural vibration analysis methods include PP method, ITD method, ERADC method, SSI method, and FDD method, which require a large amount of computation and high-level data processing technology, and these calculations and techniques are also difficult to automate.

It is not suitable for high-rise buildings that need to extract eigenvalues from a large number of vibration sensors in real time.

In recent years, a method of real-time extraction of a large-scale high-resolution mode shape has been developed. However, the method of extracting time variables from the digitally filtered terminal induction time history still follows the conventional method. There is still a problem that there is a limit.

Korean Registered Patent No. 1113660 (Feb. 29, 2012)

An object of the present invention is to provide a building vibration monitoring system using a TDD technique.

A building vibration monitoring system using the TDD technique according to the present invention comprises a three-axis vibration sensor module for measuring a vibration of a building and outputting a vibration signal; A signal processing module for collecting the vibration signal output by the three-axis vibration sensor module and performing signal processing; A signal analysis module for analyzing the waveform and spectrum of the vibration signal subjected to the signal processing by the signal processing module, performing statistical processing on the analyzed waveform and spectrum, and outputting the statistical processing; Extracting a mode shape, which is a spatial variable, in a time domain without performing an FFT operation on the vibration signal subjected to the signal processing by the signal processing module, and using the extracted mode shape, A time domain decomposition (TDD) module for performing a fast Fourier transform (FFT) operation on the vibration signal subjected to the signal processing by the frequency domain decomposition module and extracting a natural frequency and an attenuation ratio which are time variables; And a building damage determination module for determining a damage location and damage degree of the building using the natural frequency and the damping ratio and the mode shape extracted by the TDD module.

In this case, when the p-th triaxial vibration sensor module is provided with p pints in the simple support beam of the building, the time history of the response acceleration with respect to the time t is calculated according to the following equation,

Figure 112015036243020-pat00001
here,
Figure 112015036243020-pat00002
As an acceleration vector
Figure 112015036243020-pat00003
ego,
Figure 112015036243020-pat00004
Is an i-th mode shape vector
Figure 112015036243020-pat00005
ego,
Figure 112015036243020-pat00006
Is an i-th contribution factor, and p can be configured to indicate the position of the triaxial vibration sensor module.

The TDD module uses a digital band pass filter to generate a terminal induction signal having an i < th > mode according to the following equation: < EMI ID =

Figure 112015036243020-pat00007
And then,
Figure 112015036243020-pat00008
N acceleration time samples are collected by the following equation,
Figure 112015036243020-pat00009
And outputs an energy correlation of the ith terminal induced acceleration response signal by an output energy correlation matrix according to the following equation,
Figure 112015036243020-pat00010
here,
Figure 112015036243020-pat00011
Is a matrix having an i < th > terminal induced acceleration signal
Figure 112015036243020-pat00012
And
Figure 112015036243020-pat00013
Lt; RTI ID = 0.0 >
Figure 112015036243020-pat00014
Is substituted into the energy correlation matrix to calculate the following equation,
Figure 112015036243020-pat00015
here,
Figure 112015036243020-pat00016
The
Figure 112015036243020-pat00017
Contribution as
Figure 112015036243020-pat00018
And the noise existing in the energy correlation matrix is expressed as an orthogonal noise space with respect to the i-th mode shape as expressed by the following equation,
Figure 112015036243020-pat00019
Here, the px1 vector
Figure 112015036243020-pat00020
Represents the i < th > noise base,
Figure 112015036243020-pat00021
Represents the intensity of the i < th > noise mode, and the following equation
Figure 112015036243020-pat00022
As a i < th > mode shape vector,
Figure 112015036243020-pat00023
here,
Figure 112015036243020-pat00024
The
Figure 112015036243020-pat00025
Is a singular vector matrix,
Figure 112015036243020-pat00026
The
Figure 112015036243020-pat00027
As shown in FIG.

Also, the TDD module may use an i < th > mode shape vector extracted from the TDD module to calculate a cross correlation function representing an I < th >

Figure 112015036243020-pat00028
, And [Expression 1]
Figure 112015036243020-pat00029
the correlation matrix < RTI ID = 0.0 >
Figure 112015036243020-pat00030
, And [Mathematical Expression]
Figure 112015036243020-pat00031
The correlation matrix
Figure 112015036243020-pat00032
By performing singular value decomposition (SVD) on the singular value decomposition process according to the following equation to remove the orthogonal noise,
Figure 112015036243020-pat00033
Represents the i < th > mode in which the quadrature noise is removed and the correlation matrix
Figure 112015036243020-pat00034
The acceleration cross-correlation function vector having the largest singular value
Figure 112015036243020-pat00035
Is calculated, and [Expression 1]
Figure 112015036243020-pat00036
The calculated acceleration cross-correlation function vector
Figure 112015036243020-pat00037
Time for
Figure 112015036243020-pat00038
Free vibration function for
Figure 112015036243020-pat00039
Is calculated according to the following equation, and the calculated
Figure 112015036243020-pat00040
And a damping ratio,

[Mathematical Expression]

Figure 112015036243020-pat00041

here,

Figure 112015036243020-pat00042
The amplitude,
Figure 112015036243020-pat00043
Is the natural frequency,
Figure 112015036243020-pat00044
Damping ratio,
Figure 112015036243020-pat00045
Is the attenuation natural frequency,
Figure 112015036243020-pat00046
May be composed of a translation angle.

According to the building vibration monitoring system using the TDD technique, the vibration measurement value of the vibration sensor in a large building in which a large number of vibration sensors are installed is configured to directly extract a mode shape in the time domain without performing Fourier transformation , It is possible to quickly extract a high resolution mode shape of a large structure in real time.

Also, the inherent characteristic values such as the natural frequency and the damping ratio can also reduce the amount of computation by a large number of sensors by the TDD technique and perform the data processing of the high degree of ease more easily.

1 is a block diagram of a building vibration monitoring system using a TDD technique according to an embodiment of the present invention.
FIGS. 2 to 17 are graphs showing results of building vibration monitoring according to an embodiment of the present invention.
18 is a flowchart of a building vibration monitoring method using the TDD technique according to an embodiment of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail to the concrete inventive concept.

It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

Like reference numerals are used for like elements in describing each drawing.

The terms first, second, A, B, etc. may be used to describe various elements, but the elements should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

It is to be understood that when an element is referred to as being "connected" or "connected" to another element, it may be directly connected or connected to the other element, .

On the other hand, when an element is referred to as being "directly connected" or "directly connected" to another element, it should be understood that there are no other elements in between.

The terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise.

In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the contextual meaning of the related art and are to be interpreted as either ideal or overly formal in the sense of the present application Do not.

Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings.

1 is a block diagram of a building vibration monitoring system using a TDD technique according to an embodiment of the present invention.

Referring to FIG. 1, a building vibration monitoring system (hereinafter, referred to as 'building vibration monitoring system') 100 using a TDD technique according to an embodiment of the present invention includes a three-axis vibration sensor module 110, A signal analysis module 130, a TDD module 140, and a building damage determination module 150.

The building vibration monitoring system 100 of the present invention is configured to directly extract a mode shape in a time domain without performing Fourier transformation on a mode shape that is a spatial variable. Accordingly, it is possible to rapidly calculate the mode shape of the vibration signal measured by a large number of three-axis vibration sensor modules 110 installed in the very large building, thereby quickly extracting the mode shape in real time.

Hereinafter, the detailed configuration will be described.

The three-axis vibration sensor module 110 may be configured to measure a vibration of a building and output a vibration signal. The three-axis vibration sensor module 110 may be installed for each floor in a simple support beam of a building.

The three-axis vibration sensor module 110 may be configured to output a time history of the response acceleration with respect to time t, as shown in Equation (1), when p is provided in the simple support beam of the building.

Figure 112015036243020-pat00047

here,

Figure 112015036243020-pat00048
As an acceleration vector
Figure 112015036243020-pat00049
ego,
Figure 112015036243020-pat00050
Is an i-th mode shape vector
Figure 112015036243020-pat00051
ego,
Figure 112015036243020-pat00052
Is the i-th contribution factor, and p is the position 110 of the three-axis vibration sensor module.

The signal processing module 120 may be configured to collect the vibration signal output by the three-axis vibration sensor module 110 and perform signal processing.

The signal processing module 120 may perform signal processing such as data filtering and noise cancellation on the vibration signal.

The signal analysis module 130 uses the vibration signal to calculate the integral of the acceleration data, the sum of the acceleration vector and the maximum, minimum, average, kurtosis, distortion, square root mean square (RMS) May be configured to perform statistical processing.

The signal analysis module 130 analyzes the PGA (Peak Ground Acceleration), the MMA (Min, Max, Avg) data display, the cumulative absolute velocity (CAV) display, the time history damping, the power spectrum, and the response spectrum Velocity and displacement response spectral display), seismic intensity extraction, Arias intensity display, analysis of multiple data analysis, and statistical functions.

The TDD module 140 basically calculates and extracts a mode shape in a time domain with respect to a vibration signal subjected to signal processing by the signal processing module 120 and outputs the natural frequency and the attenuation ratio to the spatial domain And extracts an operation on the screen.

Previously, FFT (Fast Fourier Transform) was performed on the mode shape to increase the computational complexity and computational difficulty. Considering that the number of vibration sensors becomes very large as the building size increases, the computation amount becomes very large, and the calculation burden is very large. However, in the present invention, a mode shape can be monitored in real time by developing an algorithm capable of directly extracting a mode shape in a time domain without FFT operation. This will be explained in more detail.

First, in Equation 1,

Figure 112015036243020-pat00053
Symbol
Figure 112015036243020-pat00054
The measurement acceleration time response can be approximated as: < EMI ID = 2.0 >

Figure 112015036243020-pat00055

Here, n is the number of modes of the measurement acceleration signal.

The TDD module 140 designs a digital band-pass filter to extract a terminal induction signal having only the i-th mode, and calculates a terminal induction signal having an i-th mode

Figure 112015036243020-pat00056
As shown in FIG.

Figure 112015036243020-pat00057

And the TDD module 140 may be configured to collect N acceleration time samples according to Equation (4).

Figure 112015036243020-pat00058

Equation (4) can be simplified to Equation (5).

Figure 112015036243020-pat00059

here,

Figure 112015036243020-pat00060
procession
Figure 112015036243020-pat00061
represents the terminal induced acceleration signal having only the i-th mode. And vector
Figure 112015036243020-pat00062
Represents the contribution to the acceleration signal history in the i-th mode.

Meanwhile, the TDD module 140 may be configured to output the energy correlation of the i-th terminal induced acceleration response signal by an output energy correlation matrix according to Equation (6).

Figure 112015036243020-pat00063

here,

Figure 112015036243020-pat00064
Is a matrix having an i < th > terminal induced acceleration signal
Figure 112015036243020-pat00065
.

The TDD module 140 may be configured to calculate Equation (7) by substituting Equation (5) into Equation (6).

Figure 112015036243020-pat00066

here,

Figure 112015036243020-pat00067
The
Figure 112015036243020-pat00068
Contribution as
Figure 112015036243020-pat00069
. ≪ / RTI > Equation (7) represents an ideal case in which there is no noise in the i-th acceleration response signal.

Meanwhile, the noise existing in the energy correlation matrix is an orthogonal noise space for the i-th mode shape, and can be expressed as Equation (8).

Figure 112015036243020-pat00070

Here, the px1 vector

Figure 112015036243020-pat00071
Represents the i < th > noise base,
Figure 112015036243020-pat00072
Represents the intensity of the ith noise mode.

Equation (8) can be simplified to Equation (9).

Figure 112015036243020-pat00073

here,

Figure 112015036243020-pat00074
The
Figure 112015036243020-pat00075
Is a singular vector matrix,
Figure 112015036243020-pat00076
The
Figure 112015036243020-pat00077
Which represents a singularity matrix. The dominant energy of the ith terminal induced acceleration response is the i-th mode shape
Figure 112015036243020-pat00078
, The order of magnitude of the singular value is
Figure 112015036243020-pat00079
.

Thus, the i-th mode shape vector is

Figure 112015036243020-pat00080
The first column vector in the singular matrix vector of < RTI ID = 0.0 > And the TDD module 140 outputs it as a mode shape.

The TDD module 140 may be configured to extract the natural frequency and the damping ratio in addition to the mode shape.

The TDD module 140 performs an FFT (Fast Fourier Transform) operation on the vibration signal subjected to the signal processing by the signal processing module 120 using the extracted mode shape to extract a natural frequency and an attenuation ratio .

In more detail, the TDD module 140 uses an i-th mode shape vector extracted from the TDD module 140 to calculate an acceleration cross-correlation function representing an i-th mode as shown in Equation (10)

Figure 112015036243020-pat00081
. ≪ / RTI >

Figure 112015036243020-pat00082

The acceleration cross-correlation function < RTI ID = 0.0 >

Figure 112015036243020-pat00083
Since the TDD module 140 includes time noise, the TDD module 140 calculates a correlation matrix
Figure 112015036243020-pat00084
.

Figure 112015036243020-pat00085

The TDD module 140 includes a correlation matrix

Figure 112015036243020-pat00086
And perform singular value decomposition (SVD) on the singular value decomposition process by Equation (12) to eliminate orthogonal noise.

Figure 112015036243020-pat00087

Here, it represents the i-th mode in which the orthogonal noise is removed, and the correlation matrix

Figure 112015036243020-pat00088
The acceleration cross-correlation function vector having the largest singular value
Figure 112015036243020-pat00089
Is a singular value matrix
Figure 112015036243020-pat00090
Is an singular value vector corresponding to the largest singular value among the three singular values, and can be calculated by the following equation (13).

Figure 112015036243020-pat00091

Here, the representative single degree of freedom (SDOF) acceleration cross-correlation function for each mode extracted by Equation (13) is the same as the free vibration function. The SI (system identification) technique is applied to each mode data extracted using the TDD technique to calculate the acceleration cross-correlation function vector

Figure 112015036243020-pat00092
Can be configured to extract the natural frequency and the damping ratio.

The SI method is a kind of inverse analysis that optimizes the simulation system variables such that the measurement value and the simulation value are the same.

The TDD module 140 may calculate the time

Figure 112015036243020-pat00093
Free vibration function
Figure 112015036243020-pat00094
Can be considered.

Figure 112015036243020-pat00095

here,

Figure 112015036243020-pat00096
The amplitude,
Figure 112015036243020-pat00097
Is the natural frequency,
Figure 112015036243020-pat00098
Damping ratio,
Figure 112015036243020-pat00099
Is the attenuation natural frequency,
Figure 112015036243020-pat00100
Is the translation angle, from which natural frequencies and damping ratios can be predicted.

The variables to be recognized are natural frequency, damping ratio, amplitude, and moving angle,

Figure 112015036243020-pat00101
The size can be expressed by the following equation (15).

Figure 112015036243020-pat00102

Here, at an arbitrary time t,

Figure 112015036243020-pat00103
Is a function of the cognitive variable vector and ignores the high order term after Taylor series expansion,
Figure 112015036243020-pat00104
Can be defined by the following equation (16).

Figure 112015036243020-pat00105

The cross-correlation variable can be expressed by the following equation (17).

Figure 112015036243020-pat00106

here,

Figure 112015036243020-pat00107
Is a recognition vector
Figure 112015036243020-pat00108
≪ / RTI >
Figure 112015036243020-pat00109
Represents the i-th natural frequency
Figure 112015036243020-pat00110
Is the damping ratio of the i-th mode
Figure 112015036243020-pat00111
.

Equation (17) can be normalized as Equation (18).

Figure 112015036243020-pat00112

When the number of samples of the cross-correlation function is q, equation (18) can be described by a simple linear sensitivity equation as shown in the following equation (19).

Figure 112015036243020-pat00113

Here, q X 1 vector

Figure 112015036243020-pat00114
Can be expressed by the following equation (20) as the rate of change of the natural frequency.

Figure 112015036243020-pat00115

p X 1 vector

Figure 112015036243020-pat00116
Represents the rate of change of recognition variables, and can be expressed by the following equation (21).

Figure 112015036243020-pat00117

P X q vector in the following equation (22)

Figure 112015036243020-pat00118
Is a sensitivity matrix representing the rate of change of the natural frequency for the recognition variables.

Figure 112015036243020-pat00119

The TDD module 140 can obtain a solution to the sensitivity equation of Equation (19) using an iterative method, the order of which is as follows.

1) Assume that the recognition variables in the j-th iteration step are as shown in the following equation (23).

Figure 112015036243020-pat00120

Here, superscript j of recognition variables means the number of repetition steps.

2) The cross-correlation is obtained by performing the simulation of Equation 14 on the recognition vector.

3) For the simulation model of 2) above, the sensitivity matrix of equation (22)

Figure 112015036243020-pat00121
. At this time, the sensitivity matrix is approximated by calculating the change of cross-correlation according to the unit change of each recognition variable.

4) Rate of change of cross-correlation vector

Figure 112015036243020-pat00122
Is expressed by the following equation (24).

Figure 112015036243020-pat00123

here,

Figure 112015036243020-pat00124
For the i < th >
Figure 112015036243020-pat00125
Is the measurement cross-correlation extracted from equation (13)
Figure 112015036243020-pat00126
Is obtained by using the recognition variable vectors at the j-th iteration step
Figure 112015036243020-pat00127
Is the simulation value of Equation (13) for the i-th mode.

5) Using the equation (19), the change rate

Figure 112015036243020-pat00128
Can be expressed by the following equation (25).

Figure 112015036243020-pat00129

here,

Figure 112015036243020-pat00130
The
Figure 112015036243020-pat00131
(Pseudo inverse matrix), and can be approximated by equation (26).

Figure 112015036243020-pat00132

6) The recognition vector vector can be updated as shown in the following Equation 27 in the (j + 1) -th iteration step.

Figure 112015036243020-pat00133

here,

Figure 112015036243020-pat00134
Is used as the recognition variable vector
Figure 112015036243020-pat00135
≪ / RTI >
Figure 112015036243020-pat00136
The change rate vector of the recognition variable
Figure 112015036243020-pat00137
.

7) With respect to the recognition variable vector updated by the equation (27), the recognition variable change rate of each of the equations (23) to (27)

Figure 112015036243020-pat00138
Lt; / RTI > converges to zero.

The building damage determination module 150 may be configured to determine damage locations and damage levels of the building using the natural frequency and damping ratio and the mode shape extracted by the TDD module 140.

FIGS. 2 to 17 are graphs showing results of building vibration monitoring according to an embodiment of the present invention.

FIG. 2 shows a building model for numerical verification by the TDD technique, and FIGS. 3 to 17 show numerical verification results by the TDD technique.

In FIG. 2, the mass m and the stiffness k of each layer are set to 4.689 kg and 5832.9 kgf / m, respectively, and natural frequencies and mode shapes of the building are set in Tables 1 and 2, respectively.

Figure 112015036243020-pat00139

Figure 112015036243020-pat00140

Fig. 3 shows the mode shapes of the numerical building by layers. And Fig. 4 shows the dynamic time response of the numerical building, and Fig. 5 shows the dynamic response spectrum of the numerical building. In the spectrum of acceleration time response of each layer, it is excited up to the total 6th mode, and the energy of the 1st mode is relatively large. It can be seen that the first mode exists at approximately 0.5 Hz to 1.5 Hz and the second mode exists at 2.2 Hz to 3.1 Hz.

In order to extract the mode shape using the TDD technique, a digital band pass filter capable of filtering only the modes from the measured MDOF signal can be designed.

Here, the pass section of the digital filter is set to 0.5 Hz to 1.5 Hz in the case of the primary mode and 2.2 Hz to 3.1 Hz in the case of the secondary mode. There are various digital filters. In the present invention, a butterworth filter having a small in-band noise is set as a third-order filter.

Next, the cross-correlation time histories of the SDOF acceleration time histories based on the layer having the largest acceleration signal are calculated for each floor of each building. Fig. 4 shows an example of a single-layer acceleration SDOF cross-correlation time history filtered only in the primary mode, and Fig. 5 shows a single-layer acceleration SDOF cross-correlation filtered in the secondary mode only.

FIG. 6 shows a 1-layer cross-correlation time histories filtered only in the primary mode, and FIG. 7 shows a 1-layer cross-correlation time histories filtered in the secondary mode only.

The mode shape can be extracted by performing SVD of Equation (9) with respect to 10 SDOF cross-correlation time histories calculated for each mode. Figures 6 and 7 show extracted primary and secondary mode shapes.

FIG. 8 shows the primary mode shape of the numerical building extracted using the TDD technique, and FIG. 9 shows the secondary mode shape of the digital building extracted using the TDD technique. Table 3 below shows the comparison between the extracted mode shape and the exact mode shape of the numerical building.

Figure 112015036243020-pat00141

Fig. 10 shows the cross-correlation representing the first-order mode of the numerical building, Fig. 11 shows the cross-correlation representing the second mode of the numerical building, Fig. 12 shows the time history for the first- And Fig. 13 shows a time history for extracting the second-order natural frequency of the numerical building.

The mode shape extracted for each mode and the ten extracted SDOF cross-correlation time history data can be substituted into Equation 10 to calculate representative cross-correlation for each mode. FIGS. 10 and 11 show cross-correlation time histories representative of the primary and secondary modes, respectively.

The numerical model of the cross-correlation time histories shown in FIGS. 12 and 13 is shown in Equation 14, and four parameters of the numerical model shown in Equation 15 are estimated using the sensitivity-based SI technique. In order to increase the convergence speed of the iterative calculation, an initial natural frequency is set by a peak-picking method in the spectrum of FIG. 5, and other parameters are selected from FIGS. 12 and 13.

Fig. 14 shows the first mode convergence of the numerical building, Fig. 15 shows the second mode convergence of the numerical building, Fig. 16 shows the first mode final convergence curve of the numerical building, Represents the final convergence curve.

FIGS. 14 and 15 show the degree of convergence of the recognition vector solution in the first and second modes in the iterative calculation process, respectively. It can be seen that all recognition vectors converge. Table 4 shows the error of the estimated natural frequency and damping ratio.

Figure 112015036243020-pat00142

FIGS. 16 and 17 show the comparison between the target cross-correlation and the recognition cross-correlation by substituting the final recognition vector shown in Table 4 into the equation (14). It can be seen that all agree well.

18 is a flowchart of a building vibration monitoring method using the TDD technique according to an embodiment of the present invention.

Referring to FIG. 18, first, the three-axis vibration sensor module 110 measures vibration of a building and outputs a vibration signal (S101).

Here, when three pivot vibration sensor modules 110 are installed in a simple support beam of the building, the time history of the response acceleration with respect to the time t may be calculated as shown in Equation (28).

Figure 112015036243020-pat00143

here,

Figure 112015036243020-pat00144
As an acceleration vector
Figure 112015036243020-pat00145
ego,
Figure 112015036243020-pat00146
Is an i-th mode shape vector
Figure 112015036243020-pat00147
ego,
Figure 112015036243020-pat00148
Is an i-th contribution factor, and p represents the position of the three-axis vibration sensor module 110. [

Next, the signal processing module 120 collects the vibration signal output by the three-axis vibration sensor module 110 and performs signal processing (S102).

Next, the signal analysis module 130 analyzes the waveform and spectrum of the vibration signal subjected to the signal processing by the signal processing module 120, performs statistical processing on the analyzed waveform and spectrum, and outputs the waveform and spectrum (S103) .

Next, a time domain decomposition (TDD) module 140 generates a mode shape, which is a spatial variable, in a time domain without performing an FFT operation on the vibration signal subjected to the signal processing by the signal processing module 120, (S104).

Here, the TDD module 140 uses a digital band pass filter to calculate a terminal induction signal having an i < th > mode according to the following equation (29)

Figure 112015036243020-pat00149
.

Figure 112015036243020-pat00150

Then, N acceleration time samples are collected by the following equation (30).

Figure 112015036243020-pat00151

And outputs an energy correlation of the ith terminal induced acceleration response signal by an output energy correlation matrix according to Equation (31).

Figure 112015036243020-pat00152

here,

Figure 112015036243020-pat00153
Is a matrix having an i < th > terminal induced acceleration signal
Figure 112015036243020-pat00154
And
Figure 112015036243020-pat00155
.

And

Figure 112015036243020-pat00156
Is substituted into the energy correlation matrix, and the following equation (32) is calculated.

Figure 112015036243020-pat00157

here,

Figure 112015036243020-pat00158
The
Figure 112015036243020-pat00159
Contribution as
Figure 112015036243020-pat00160
. ≪ / RTI >

Then, the noise existing in the energy correlation matrix is represented as an orthogonal noise space with respect to the i-th mode shape as shown in Equation (33).

Figure 112015036243020-pat00161

Here, the px1 vector

Figure 112015036243020-pat00162
Represents the i < th > noise base,
Figure 112015036243020-pat00163
Represents the intensity of the ith noise mode.

In Equation (34), which simplifies Equation (33)

Figure 112015036243020-pat00164
As a i-th mode shape vector.

Figure 112015036243020-pat00165

here,

Figure 112015036243020-pat00166
The
Figure 112015036243020-pat00167
Is a singular vector matrix,
Figure 112015036243020-pat00168
The
Figure 112015036243020-pat00169
Which represents a singularity matrix.

Next, the TDD module 140 performs an FFT (Fast Fourier Transform) operation on the vibration signal subjected to the signal processing by the signal processing module 120 using the extracted mode shape, The damping ratio is extracted (S105).

Here, an i < th > mode shape vector extracted from the TDD module 140 is used to calculate a cross correlation function representing an I < th >

Figure 112015036243020-pat00170
.

Figure 112015036243020-pat00171

Then, for the time sample of q, a correlation matrix

Figure 112015036243020-pat00172
.

Figure 112015036243020-pat00173

And the correlation matrix

Figure 112015036243020-pat00174
The singular value decomposition (SVD) is performed to remove the orthogonal noise by Equation (37).

Figure 112015036243020-pat00175

And represents the i-th mode in which orthogonal noise is removed, and a correlation matrix

Figure 112015036243020-pat00176
The acceleration cross-correlation function vector having the largest singular value
Figure 112015036243020-pat00177
.

Figure 112015036243020-pat00178

Here, the calculated acceleration cross-correlation function vector

Figure 112015036243020-pat00179
Time for
Figure 112015036243020-pat00180
Free vibration function for
Figure 112015036243020-pat00181
Is calculated according to the following equation (39), and the calculated
Figure 112015036243020-pat00182
And the damping ratio.

Figure 112015036243020-pat00183

here,

Figure 112015036243020-pat00184
The amplitude,
Figure 112015036243020-pat00185
Is the natural frequency,
Figure 112015036243020-pat00186
Damping ratio,
Figure 112015036243020-pat00187
Is the attenuation natural frequency,
Figure 112015036243020-pat00188
Is the translation angle.

Next, the building damage judgment module 150 judges the damage position and damage degree of the building using the natural frequency and the damping ratio and the mode shape extracted by the TDD module 140 (S106).

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention as defined in the following claims. There will be.

110: 3-axis vibration sensor module
120: Signal processing module
130: Signal Analysis Module
140: TDD module
150: Building Damage Judgment Module

Claims (4)

A 3-axis vibration sensor module for measuring the vibration of the building and outputting a vibration signal;
A signal processing module for collecting the vibration signal output by the three-axis vibration sensor module and performing signal processing;
A signal analysis module for analyzing the waveform and spectrum of the vibration signal subjected to the signal processing by the signal processing module, performing statistical processing on the analyzed waveform and spectrum, and outputting the statistical processing;
Extracting a mode shape, which is a spatial variable, in a time domain without performing an FFT operation on the vibration signal subjected to the signal processing by the signal processing module, and using the extracted mode shape, A time domain decomposition (TDD) module for performing a fast Fourier transform (FFT) operation on the vibration signal subjected to the signal processing by the frequency domain decomposition module and extracting a natural frequency and an attenuation ratio which are time variables; And
And a building damage determination module for determining a damage location and damage degree of the building using the natural frequency and the damping ratio and the mode shape extracted by the TDD module.
The three-axis vibration sensor module according to claim 1,
When p is provided in the simple support beam of the building, the time history of the response acceleration with respect to the time t is calculated according to the following equation,
[Mathematical Expression]
Figure 112015036243020-pat00189

here,
Figure 112015036243020-pat00190
As an acceleration vector
Figure 112015036243020-pat00191
ego,
Figure 112015036243020-pat00192
Is an i-th mode shape vector
Figure 112015036243020-pat00193
ego,
Figure 112015036243020-pat00194
Is the i-th contribution factor, and p is the position of the three-axis vibration sensor module.
3. The TDD module of claim 2,
A digital band pass filter is used to generate a terminal induction signal having an i < th > mode according to the following equation: < EMI ID =
Figure 112015036243020-pat00195
Respectively,
[Mathematical Expression]
Figure 112015036243020-pat00196

N acceleration time samples are collected by the following equation,
[Mathematical Expression]
Figure 112015036243020-pat00197

And outputs the energy correlation of the ith terminal induced acceleration response signal by an output energy correlation matrix according to the following equation,
[Mathematical Expression]
Figure 112015036243020-pat00198

here,
Figure 112015036243020-pat00199
Is a matrix having an i < th > terminal induced acceleration signal
Figure 112015036243020-pat00200
And
Figure 112015036243020-pat00201
≪ / RTI >
remind
Figure 112015036243020-pat00202
Into the energy correlation matrix to calculate the following equation,
[Mathematical Expression]
Figure 112015036243020-pat00203

here,
Figure 112015036243020-pat00204
The
Figure 112015036243020-pat00205
Contribution as
Figure 112015036243020-pat00206
, ≪ / RTI >
The noise existing in the energy correlation matrix is expressed as an orthogonal noise space with respect to the i-th mode shape as shown in the following equation,
[Mathematical Expression]
Figure 112015036243020-pat00207

Here, the px1 vector
Figure 112015036243020-pat00208
Represents the i < th > noise base,
Figure 112015036243020-pat00209
Represents the intensity of the i < th > noise mode,
In the following mathematical expression for simplifying the above equation
Figure 112015036243020-pat00210
As a i < th > mode shape vector,
[Mathematical Expression]
Figure 112015036243020-pat00211

here,
Figure 112015036243020-pat00212
The
Figure 112015036243020-pat00213
Is a singular vector matrix,
Figure 112015036243020-pat00214
The
Figure 112015036243020-pat00215
Wherein the building vibration monitoring system is characterized in that it represents a singularity matrix.
4. The TDD module of claim 3,
The i-th mode shape vector extracted from the TDD module is used as a cross correlation function representing an I-th mode,
Figure 112015036243020-pat00216
≪ / RTI >
[Mathematical Expression]
Figure 112015036243020-pat00217

the correlation matrix < RTI ID = 0.0 >
Figure 112015036243020-pat00218
Lt; / RTI >
[Mathematical Expression]
Figure 112015036243020-pat00219

The correlation matrix
Figure 112015036243020-pat00220
By performing singular value decomposition (SVD) on the singular value decomposition process according to the following equation to remove orthogonal noise,
[Mathematical Expression]
Figure 112015036243020-pat00221

Represents the i < th > mode in which the quadrature noise is removed and the correlation matrix
Figure 112015036243020-pat00222
The acceleration cross-correlation function vector having the largest singular value
Figure 112015036243020-pat00223
Lt; / RTI >
[Mathematical Expression]
Figure 112015036243020-pat00224

The calculated acceleration cross-correlation function vector
Figure 112015036243020-pat00225
Time for
Figure 112015036243020-pat00226
Free vibration function for
Figure 112015036243020-pat00227
Is calculated according to the following equation, and the calculated
Figure 112015036243020-pat00228
And a damping ratio,
[Mathematical Expression]
Figure 112015036243020-pat00229

here,
Figure 112015036243020-pat00230
The amplitude,
Figure 112015036243020-pat00231
Is the natural frequency,
Figure 112015036243020-pat00232
Damping ratio,
Figure 112015036243020-pat00233
Is the attenuation natural frequency,
Figure 112015036243020-pat00234
Is a translation angle. ≪ RTI ID = 0.0 > 11. < / RTI >
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007511741A (en) * 2003-09-22 2007-05-10 ヒョン−ユン，キム Structural health status monitoring method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007511741A (en) * 2003-09-22 2007-05-10 ヒョン−ユン，キム Structural health status monitoring method

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