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

Abstract

An earthquake monitoring system using a TDD technique is disclosed. 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; And a controller for extracting a mode shape that is a spatial variable on a time domain without performing an FFT operation on the vibration signal on which the signal processing is performed by the signal processing module, A TDD module for performing an FFT operation on a signal to extract a natural frequency and an attenuation ratio, which are time variables; 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. According to the building vibration monitoring system using the TDD technique, the vibration measurement value of the vibration sensor can be directly extracted in the time domain without Fourier transformation in a large building in which a large number of vibration sensors are installed, Can be extracted quickly 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.

여기서,

는 가속도 벡터로서

이고,

는 i번째 모드 형상 벡터로서

이고,

는 i번째 기여도(contribution factor)이고, p는 상기 3축 진동 센서 모듈의 위치를 나타내도록 구성될 수 있다.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,

here,

As an acceleration vector

ego,

Is an i-th mode shape vector

ego,

Is an i-th contribution factor, and p can be configured to indicate the position of the triaxial vibration sensor module.

를 추출하고, [수학식]

하기 수학식에 의해 N개의 가속도 시간 샘플을 수집하고, [수학식]

하기 수학식에 따른 에너지 상관관계 행렬(output energy correlation matrix)에 의해 i번째 단자유도 가속도 응답신호의 에너지 상관관계를 출력하고, [수학식]

여기서,

는 i번째 단자유도 가속도 신호를 갖는 행렬

를 나타내고

로 간략화되며, 상기

를 상기 에너지 상관관계 행렬에 대입하여 하기 수학식을 산출하고, [수학식]

여기서,

는

로서 기여도

의 에너지 강도를 나타내고, 상기 에너지 상관관계 행렬에 존재하는 잡음을 i번째 모드 형상에 대한 직교 잡음 공간(orthogonal noise space)으로 다음 수학식과 같이 나타내고, [수학식]

여기서, px1 벡터

는 i번째 잡음 기저를 나타내고,

는 i번째 잡음 모드의 강도를 나타내며, 상기 수학식을 간략화한 하기 수학식에서

의 첫번째 열 벡터(column vector)를 i번째 모드 형상 벡터로서 추출하도록 구성되며, [수학식]

여기서,

는

로서 특이 행렬 벡터(singular vector matrix)이고,

는

로서 특이치 행렬을 나타내도록 구성될 수 있다.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 =

And then,

N acceleration time samples are collected by the following equation,

And outputs an energy correlation of the ith terminal induced acceleration response signal by an output energy correlation matrix according to the following equation,

here,

Is a matrix having an i < th > terminal induced acceleration signal

And

Lt; RTI ID = 0.0 >

Is substituted into the energy correlation matrix to calculate the following equation,

here,

The

Contribution as

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,

Here, the px1 vector

Represents the i < th > noise base,

Represents the intensity of the i < th > noise mode, and the following equation

As a i < th > mode shape vector,

here,

The

Is a singular vector matrix,

The

As shown in FIG.

을 산출하고, [수학식]

q의 시간 샘플에 대하여 하기 수학식과 같이 상관 관계 행렬

를 정의하고, [수학식]

상기 상관 관계 행렬

에 대하여 하기 수학식에 의해 특이치 분해 과정 SVD(singular value decomposition)을 수행하여 직교 잡음을 제거하고, [수학식]

상기 직교 잡음이 제거된 i번째 모드를 대표하며 상기 상관 관계 행렬

에서 가장 큰 특이치를 갖는 가속도 상호 상관 함수 벡터

를 산출하고, [수학식]

상기 산출된 가속도 상호 상관 함수 벡터

에 대해 시간

에 대한 자유 진동 함수

를 하기 수학식과 같이 산출하고, 산출된

로부터 고유 진동수, 감쇠비를 추출하도록 구성되며,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 >

, And [Expression 1]

the correlation matrix < RTI ID = 0.0 >

, And [Mathematical Expression]

The correlation matrix

By performing singular value decomposition (SVD) on the singular value decomposition process according to the following equation to remove the orthogonal noise,

Represents the i < th > mode in which the quadrature noise is removed and the correlation matrix

The acceleration cross-correlation function vector having the largest singular value

Is calculated, and [Expression 1]

The calculated acceleration cross-correlation function vector

Time for

Free vibration function for

Is calculated according to the following equation, and the calculated

And a damping ratio,

[Mathematical Expression]

는 진폭,

는 고유 진동수,

는 감쇠비,

는 감쇠 고유 진동수,

는 이동각(translation angle)으로 구성될 수 있다.
here,

The amplitude,

Is the natural frequency,

Damping ratio,

Is the attenuation natural frequency,

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.

는 가속도 벡터로서

이고,

는 i번째 모드 형상 벡터로서

이고,

는 i번째 기여도(contribution factor)이고, p는 3축 진동 센서 모듈의 위치(110)를 나타낸다.here,

As an acceleration vector

ego,

Is an i-th mode shape vector

ego,

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.

를 심볼

로 표시할 경우 계측 가속도 시간 응답은 하기 수학식 2와 같이 근사화될 수 있다.First, in Equation 1,

Symbol

The measurement acceleration time response can be approximated as: < EMI ID = 2.0 >

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

를 추출하도록 구성될 수 있다.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

As shown in FIG.

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

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

행렬

i번째 모드만 가지고 있는 단자유도 가속도 신호를 나타낸다. 그리고 벡터

는 i번째 모드의 가속도 신호 이력에 대한 기여도를 나타낸다.here,

procession

represents the terminal induced acceleration signal having only the i-th mode. And vector

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).

는 i번째 단자유도 가속도 신호를 갖는 행렬

를 나타낸다.here,

Is a matrix having an i < th > terminal induced acceleration signal

.

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

는

로서 기여도

의 에너지 강도를 나타낸다. 수학식 7은 i번째 가속도 응답 신호에 잡음이 없는 상태의 이상적인 경우를 나타낸다.here,

The

Contribution as

. ≪ / 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).

는 i번째 잡음 기저를 나타내고,

는 i번째 잡음 모드의 강도를 나타낸다.Here, the px1 vector

Represents the i < th > noise base,

Represents the intensity of the ith noise mode.

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

는

로서 특이 행렬 벡터(singular vector matrix)이고,

는

로서 특이치 행렬을 나타낸다. i번째 단자유도 가속도 응답의 지배적인 에너지는 i번째 모드 형상

이므로, 특이값의 크기 순서는

이 된다.here,

The

Is a singular vector matrix,

The

Which represents a singularity matrix. The dominant energy of the ith terminal induced acceleration response is the i-th mode shape

, The order of magnitude of the singular value is

.

의 특이행렬 벡터 중에서 첫번째 열 벡터(column vector)가 된다. TDD 모듈(140)은 이를 모드 형상으로서 출력하게 된다.Thus, the i-th mode shape vector is

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 .

을 산출하도록 구성될 수 있다.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)

. ≪ / RTI >

는 시간 잡음을 포함하고 있기 때문에, TDD 모듈(140)은 q의 시간 샘플에 대하여 하기 수학식 11과 같이 상관 관계 행렬

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

Since the TDD module 140 includes time noise, the TDD module 140 calculates a correlation matrix

.

에 대하여 하기 수학식 12에 의해 특이치 분해 과정 SVD(singular value decomposition)을 수행하여 직교 잡음을 제거하도록 구성될 수 있다.The TDD module 140 includes a correlation matrix

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

에서 가장 큰 특이치를 갖는 가속도 상호 상관 함수 벡터

는 특이치 행렬

중에서 가장 큰 특이치에 상응하는 특이치 벡터이며 다음 수학식 13과 같이 산출될 수 있다.Here, it represents the i-th mode in which the orthogonal noise is removed, and the correlation matrix

The acceleration cross-correlation function vector having the largest singular value

Is a singular value matrix

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).

에 대한 고유 진동수와 감쇠비를 추출하도록 구성될 수 있다.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

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.

에서 자유진동 함수

를 고려할 수 있다.The TDD module 140 may calculate the time

Free vibration function

Can be considered.

는 진폭,

는 고유 진동수,

는 감쇠비,

는 감쇠 고유 진동수,

는 이동각(translation angle)이며, 이로부터 고유 진동수와 감쇠비를 예측할 수 있다.here,

The amplitude,

Is the natural frequency,

Damping ratio,

Is the attenuation natural frequency,

Is the translation angle, from which natural frequencies and damping ratios can be predicted.

로서 그 크기는 다음 수학식 15와 같이 표현될 수 있다.The variables to be recognized are natural frequency, damping ratio, amplitude, and moving angle,

The size can be expressed by the following equation (15).

은 인식 변수 벡터의 함수이고 테일러(Taylor) 급수 전개 후 고차항을 무시하면 상호 상관의 변량

는 다음 수학식 16과 같이 정의될 수 있다.Here, at an arbitrary time t,

Is a function of the cognitive variable vector and ignores the high order term after Taylor series expansion,

Can be defined by the following equation (16).

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

은 인식 변수 벡터

의 n번째 항이며,

은 i번째 고유 진동수를 나타내고

는 i번째 모드의 감쇠비

를 나타낸다.here,

Is a recognition vector

≪ / RTI >

Represents the i-th natural frequency

Is the damping ratio of the i-th mode

.

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

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).

는 고유 진동수의 변화율로서 다음 수학식 20과 같이 표현될 수 있다.Here, q X 1 vector

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

는 인식 변수들의 변화율을 나타내며, 다음 수학식 21과 같이 표현될 수 있다.p X 1 vector

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

는 민감도 행렬(sensitivity matrix)로서 인식 변수들에 대한 고유 진동수의 변화율을 나타낸다.P X q vector in the following equation (22)

Is a sensitivity matrix representing the rate of change of the natural frequency for the recognition variables.

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).

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.

를 구한다. 이때, 민감도 행렬은 각 인식변수의 단위 변화에 따른 상호상관 변화를 계산하여 근사적으로 산정한다.3) For the simulation model of 2) above, the sensitivity matrix of equation (22)

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

는 다음 수학식 24와 같다.4) Rate of change of cross-correlation vector

Is expressed by the following equation (24).

는 i번째 모드에 대한

에서 수학식 13으로부터 추출된 계측 상호 상관이고,

는 j번째 반복 단계에서 인식 변수 벡터들을 이용하여 구한

에서 i번째 모드에 대한 수학식 13의 시뮬레이션 값이다.here,

For the i < th >

Is the measurement cross-correlation extracted from equation (13)

Is obtained by using the recognition variable vectors at the j-th iteration step

Is the simulation value of Equation (13) for the i-th mode.

는 다음 수학식 25와 같이 표현될 수 있다.5) Using the equation (19), the change rate

Can be expressed by the following equation (25).

는

의 의사역행렬(pseudo inverse matrix)이고, 수학식 26에 의해 근사화될 수 있다.here,

The

(Pseudo inverse matrix), and can be approximated by equation (26).

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

는 j번째 반복 단계에서 인식 변수 벡터

의 n번째 항이며,

은 인식 변수의 변화율 벡터

의 n번째 항이다.here,

Is used as the recognition variable vector

≪ / RTI >

The change rate vector of the recognition variable

.

이 0으로 수렴할 때까지 반복한다.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)

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.

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.

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.

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).

는 가속도 벡터로서

이고,

는 i번째 모드 형상 벡터로서

이고,

는 i번째 기여도(contribution factor)이고, p는 3축 진동 센서 모듈(110)의 위치를 나타낸다.here,

As an acceleration vector

ego,

Is an i-th mode shape vector

ego,

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).

를 추출한다.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)

.

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

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

는 i번째 단자유도 가속도 신호를 갖는 행렬

를 나타내고

로 간략화된다.here,

Is a matrix having an i < th > terminal induced acceleration signal

And

.

를 에너지 상관관계 행렬에 대입하여 하기 수학식 32를 산출한다.And

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

는

로서 기여도

의 에너지 강도를 나타낸다.here,

The

Contribution as

. ≪ / 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).

는 i번째 잡음 기저를 나타내고,

는 i번째 잡음 모드의 강도를 나타낸다.Here, the px1 vector

Represents the i < th > noise base,

Represents the intensity of the ith noise mode.

의 첫번째 열 벡터(column vector)를 i번째 모드 형상 벡터로서 추출한다.In Equation (34), which simplifies Equation (33)

As a i-th mode shape vector.

는

로서 특이 행렬 벡터(singular vector matrix)이고,

는

로서 특이치 행렬을 나타낸다.here,

The

Is a singular vector matrix,

The

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).

을 산출한다.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 >

.

를 정의한다.Then, for the time sample of q, a correlation matrix

.

에 대하여 수학식 37에 의해 특이치 분해 과정 SVD(singular value decomposition)을 수행하여 직교 잡음을 제거한다.And the correlation matrix

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

에서 가장 큰 특이치를 갖는 가속도 상호 상관 함수 벡터

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

The acceleration cross-correlation function vector having the largest singular value

.

에 대해 시간

에 대한 자유 진동 함수

를 하기 수학식 39와 같이 산출하고, 산출된

로부터 고유 진동수, 감쇠비를 추출한다.Here, the calculated acceleration cross-correlation function vector

Time for

Free vibration function for

Is calculated according to the following equation (39), and the calculated

And the damping ratio.

는 진폭,

는 고유 진동수,

는 감쇠비,

는 감쇠 고유 진동수,

는 이동각(translation angle)이다.here,

The amplitude,

Is the natural frequency,

Damping ratio,

Is the attenuation natural frequency,

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]

here,

As an acceleration vector

ego,

Is an i-th mode shape vector

ego,

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 =

Respectively,
[Mathematical Expression]

N acceleration time samples are collected by the following equation,
[Mathematical Expression]

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]

here,

Is a matrix having an i < th > terminal induced acceleration signal

And

≪ / RTI >
remind

Into the energy correlation matrix to calculate the following equation,
[Mathematical Expression]

here,

The

Contribution as

, ≪ / 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]

Here, the px1 vector

Represents the i < th > noise base,

Represents the intensity of the i < th > noise mode,
In the following mathematical expression for simplifying the above equation

As a i < th > mode shape vector,
[Mathematical Expression]

here,

The

Is a singular vector matrix,

The

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,

≪ / RTI >
[Mathematical Expression]

the correlation matrix < RTI ID = 0.0 >

Lt; / RTI >
[Mathematical Expression]

The correlation matrix

By performing singular value decomposition (SVD) on the singular value decomposition process according to the following equation to remove orthogonal noise,
[Mathematical Expression]

Represents the i < th > mode in which the quadrature noise is removed and the correlation matrix

The acceleration cross-correlation function vector having the largest singular value

Lt; / RTI >
[Mathematical Expression]

The calculated acceleration cross-correlation function vector

Time for

Free vibration function for

Is calculated according to the following equation, and the calculated

And a damping ratio,
[Mathematical Expression]

here,

The amplitude,

Is the natural frequency,

Damping ratio,

Is the attenuation natural frequency,

Is a translation angle. ≪ RTI ID = 0.0 > 11. < / RTI >

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