KR20000072450A - Damage detection in a structure using the wavelet transform of static deflection - Google Patents

Damage detection in a structure using the wavelet transform of static deflection Download PDF

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KR20000072450A
KR20000072450A KR1020000052306A KR20000052306A KR20000072450A KR 20000072450 A KR20000072450 A KR 20000072450A KR 1020000052306 A KR1020000052306 A KR 1020000052306A KR 20000052306 A KR20000052306 A KR 20000052306A KR 20000072450 A KR20000072450 A KR 20000072450A
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wavelet
defect
static deformation
wavelet transform
static
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KR1020000052306A
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Korean (ko)
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박광호
기창두
이윤석
김창구
김형오
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박광호
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00—Testing static or dynamic balance of machines or structures
    • G01M1/12—Static balancing; Determining position of centre of gravity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids

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  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)

Abstract

PURPOSE: A defect examination of a structure is provided to sense a defect occurring in a structure without a normal state data by applying a wavelet transform to the static deformation of the structure. CONSTITUTION: An element is divided into one hundred parts. After a 100Ib load is given to a fiftieth point, static deformation is measured. 5 percent of the defection is given to thirtieth and eightieth points and the measured static deformation is wavelet-transformed. A result of the static deformation is reflected in a high frequency element so that a defect is appeared. Then, a position of the detection is found by using the wavelet transform of the static deformation.

Description

정적 변형의 웨이블렛 변환을 이용한 구조물의 결함 진단{Damage detection in a structure using the wavelet transform of static deflection}Damage detection in a structure using the wavelet transform of static deflection}

본 발명에서 사용된 웨이블렛 변환(Wavelet Transform)은 수학의 조화해석 분야에서 태동되었다. 수학자들에 의해 웨이블렛 이론에 대한 연구가 진행되었고 신호처리나 전자공학 등의 분야에서는 웨이블렛이라는 것을 모른체 필터 뱅크(Filter Bank), 서브밴드 코딩(Subband Coding)이라 불리면서 독자적으로 연구가 진행되었다. 그러다가 80년대 후반에 필터뱅크와 웨이블렛 변환은 같은 이론으로 전개될 수 있고 결국은 같은 것이라는 것이 증명되면서 필터뱅크에서 디자인되던 필터들이 웨이블렛 영역으로 대치되게 되었고 필터 뱅크보다는 웨이블렛이라는 말이 더 일반적인 용어가 되었다. 그리고 그때부터 연구가 더욱 활성화되고 다양한 분야에 응용이 이루어 지고 있다.The wavelet transform used in the present invention was born in the field of harmonic analysis of mathematics. The mathematicians studied the wavelet theory, and in the fields of signal processing and electronics, the wavelet theory was called Filter Bank and Subband Coding. Then, in the late eighties, filterbank and wavelet transforms could be developed in the same theory, and eventually proved to be the same, so that the filters designed in the filterbank were replaced by the wavelet domain, and the term wavelet became more common than filter banks. And since then, research has become more active and applied in various fields.

최근 웨이블렛 변환을 이용한 구조 결함진단이 활발히 연구중이다. 이호철, 김윤영 등은 빔의 모드형상을 웨이블렛 변환하여 결함진단을 시도하였고 Chung-Jen Lu등은 변위와 모드 형상을 웨이블렛 변환하여 현의 결함진단을 시도하였다. 현재까지의 진동신호를 이용한 결함 진단은 주로 모달 파라미터를 사용하였다. 모달 파라미터중 공진 주파수가 결함에 가장 민감하지만 결함의 위치를 찾기 위해서는 정상인 구조물에 대한 정보를 가지고 있어야 한다는 단점이 있다. 모드 형상을 이용하는 경우에는 노달 포인트에 결함이 존재할 경우에는 결함진단이 불가능하다는 단점을 가지고 있고 모드 형상의 실측이 어려운 경우가 많다는 단점이 있다.Recently, structural defect diagnosis using wavelet transform has been actively studied. Lee Ho-cheol and Kim Yun-young attempted to diagnose the defect by wavelet transforming the mode shape of the beam and Chung-Jen Lu et al. Attempted to diagnose the defect of the string by wavelet converting the displacement and mode shape. To date, fault diagnosis using vibration signals mainly uses modal parameters. Among the modal parameters, the resonant frequency is most sensitive to defects, but it has a disadvantage of having information about a normal structure in order to locate the defects. In the case of using the mode shape, there is a disadvantage in that defect diagnosis is impossible when a defect is present at the nodal point, and there are many disadvantages in that it is difficult to measure the mode shape.

따라서, 본 발명은 위와 같은 종래기술의 문제를 극복하기 위해서 구조물의 정적변형에 웨이브렛 변환(wavelet transform)을 적용하여 정상상태 정보가 필요 없이 구조물에 발생하는 결함을 감지하는 것이 목적이다.Accordingly, an object of the present invention is to detect a defect occurring in a structure without requiring steady state information by applying a wavelet transform to the static deformation of the structure in order to overcome the problems of the prior art as described above.

도 1은 본 발명이 적용되는 구조물의 결함 진단 방법의 처리 흐름도1 is a processing flowchart of a method for diagnosing a defect of a structure to which the present invention is applied.

도 2은 본 발명의 성능을 나타내기 위해 사용된 구조물의 모형2 is a model of a structure used to demonstrate the performance of the present invention.

도 3는 본 발명의 성능을 나타내는 wavelet map이다.3 is a wavelet map showing the performance of the present invention.

도 4은 본 발명의 성능을 보여주기 위해 수치실험에 사용된 구조물 모델4 is a structure model used in the numerical experiment to show the performance of the present invention

도 5는 5%의 결함이 존재하는 경우의 wavelet map이다.5 is a wavelet map when 5% of defects are present.

도 6는 0.5%의 결함이 존재하는 경우의 wavelet map이다.6 is a wavelet map when 0.5% of defects are present.

푸리에 변환은 사인과 코사인을 기저함수로 신호를 분해하지만 웨이블렛은 허용조건을 만족하는 무수히 많은 웨이블렛을 이용하여 신호를 분해 할 수 있다. 본 발명에서 제안한 방법의 유용성을 보이기 위해 사용한 실험모델은 [도면 1]과 같다. 일정한 단면을 가진 양단이 고정된 보이다. 실험을 위해 요소를 100개로 분할 하였다. 50번째 포인트에 100lb의 하중을 가한후에 정적 변형을 측정하였다. 30번 포인트와 80번 포인트에 5%의 결함을 준후 각 지점에서 측정한 정적 변형을 웨이블렛 변환하였다. [도면 2]의 S는 측정한 정적 변형이다. 정적 변형 S만을 보아서는 전혀 특이점을 찾을수 없으므로 결함의 위치를 확인하기가 어렵다. 따라서 정적 변형을 웨이블렛 변환한 결과가 al과 dl이다. al은 low pass filtering한 결과이고 dl은 high pass filtering한 결과이다. 특이점은 고주파 성분에 반영되므로 dl에서 결함이 나타난다. [도면 2]를 보면 본 발명에서 제시한 정적 변형의 웨이블렛 변환을 이용하여 결함의 위치를 찾을 수 있음을 알 수 있다.The Fourier transform decomposes the signal using the sine and cosine as the basis function, but the wavelet can decompose the signal using a myriad of wavelets that satisfy the allowable conditions. The experimental model used to show the usefulness of the method proposed in the present invention is shown in [Fig. 1]. Both ends with a constant cross section are fixed. The element was divided into 100 for the experiment. The static strain was measured after applying 100 lb of load to the 50th point. After 5% defects were given at points 30 and 80, the static deformation measured at each point was wavelet transformed. S in FIG. 2 is a static deformation measured. By looking at the static strain S alone, it is difficult to locate the defect because no singularity can be found at all. Thus, the wavelet transform of the static deformation is al and dl. al is the result of low pass filtering and dl is the result of high pass filtering. Singularity is reflected in the high frequency components, so defects appear in dl. Referring to [Figure 2], it can be seen that the position of a defect can be found by using the wavelet transform of the static deformation proposed in the present invention.

본 발명의 강인성을 보이기 위해 수치실험을 실시하여 보았다. 수치 실험에 사용한 구조물은 [도면 3]과 같다. 32층의 구조물을 32자유도를 갖는 Shear Building으로 모델링 하였다. 구조물의 각층은 1자유도를 갖도록 하였고 강성값과 질량값은 [도면 3]에 나타내었다. 시스템의 강성행렬과 질량행렬은 Shear Building을 모델링하는 표준방법을 이용하였다. 정적 변형은 아래와 같은 식을 풀어서 구하였다.In order to show the robustness of the present invention, a numerical experiment was conducted. The structure used for the numerical experiment is shown in [Figure 3]. The 32-story structure was modeled as a Shear Building with 32 degrees of freedom. Each layer of the structure had one degree of freedom, and the stiffness and mass values are shown in [Figure 3]. The stiffness and mass matrices of the system used the standard method of modeling the Shear Building. Static deformation was obtained by solving the following equation.

본 발명에서는 2가지 경우에 대해서 수치 실험을 실시하였다. 32층에 힘을 가하고 10층과 20층에 5%와 0.5% 강성 변화를 준 후 구조물 결함진단을 수해해 보았다. 위의 실험은 웨이블렛 변환을 이용한 구조결함 진단법이 결함크기와 결함위치를 판별할 수 있는지를 조사하기 위하여 인위적으로 생성하였다. [도면 4, 5]는 정적 변형을 웨이블렛 변환한 결과이다. [도면 4]는 5%의 결함이 존재하는 경우이고 [도면 5]는 0.5%의 결함이 존재하는 경우이다. Mexican Hat 웨이블렛을 모웨이블렛으로 하여 연속웨이블렛 변환을 수행하였다. 수치실험 결과 결함이 생겼다는 겻을 확인할 수 있고 5%와 0.5%의 결함 크기에 대한 정보도 들어 있음을 알 수 있다.In the present invention, numerical experiments were conducted for two cases. After applying force to the 32nd floor and changing the 5% and 0.5% stiffness to the 10th and 20th floors, the structural defect diagnosis was performed. The above experiment was artificially generated to investigate whether the structural defect diagnosis method using wavelet transform can discriminate the defect size and location. 4 and 5 show the wavelet transform of the static deformation. FIG. 4 shows a case where 5% of defects exist and FIG. 5 shows a case where 0.5% of defects exist. Continuous wavelet transformation was performed using a Mexican Hat wavelet as the mowavelet. Numerical experiments show that there is a defect, and it also contains information about 5% and 0.5% defect size.

이상에서 상술한 바와 같이 본 발명은 정적 변형의 특이점이 웨이블렛 계수중 Low Scal 성분 또는 Detail요소에 영향을 준다는 것에 착안하여 구조물의 결함 진단을 수행하였다. 본 발명에서 사용한 방법은 정상적인 구조물에 대한 정보(FEM모델/실험결과)가 필요없이 결함의 위치를 찾을 수 있는 효과가 있는 것이다.As described above, the present invention focused on the fact that the singularity of the static deformation affects the Low Scal component or the Detail element among the wavelet coefficients. The method used in the present invention has the effect of finding the location of the defect without the need for information on the normal structure (FEM model / test results).

Claims (5)

구조물의 결함을 찾는 방법에 있어서, 정적 변형을 측정하고 측정된 정적 변형을 웨이블렛 변환하여 구조물에 대한 사전 정보(FEM모델/실험결과)가 필요없이 구조물의 결함을 진단하는 방법In the method of finding the defect of the structure, the method of diagnosing the defect of the structure without measuring the static deformation and wavelet transforming the measured static deformation without the need for advance information (FEM model / experimental results) of the structure. 제 1항에 있어서 구조물의 결함 진단을 위해 웨이블렛 변환을 적용하는 단계에서 기존의 모달 파라미터가 아닌 정적 변형을 이용하는 점The method of claim 1, wherein the static deformation is used instead of the existing modal parameter in applying the wavelet transform to diagnose the defect of the structure. 웨이블렛이 가지는 중요한 특징중의 하나인 소멸 모멘트 즉 특이점 분석 기능을 이용하는점One of the important features of wavelets is the extinction moment, that is, the feature that uses singularity analysis 제 3항의 웨이블렛의 특이점 분석 기능을 이용하는 단계에서 연속 웨이블렛 변환과 이산웨이블렛 변환 둘다 사용한다는 점The use of both wavelet and discrete wavelet transforms in the step of using the singularity analysis function of the wavelet of claim 3 제 3항 있어서 구조물의 결함은 정적 변형에 특이점으로 반영되고 연속 웨이블렛의 low scale또는 이산 웨이블렛 변환의 detail성분에서 결함이 감지된다는 점The defect of the structure is reflected as a singularity in the static deformation and the defect is detected in the detail component of the low scale or discrete wavelet transform of the continuous wavelet.
KR1020000052306A 2000-09-05 2000-09-05 Damage detection in a structure using the wavelet transform of static deflection KR20000072450A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100394134B1 (en) * 2001-02-20 2003-08-09 학교법인 성균관대학 Method for detecting high impedance fault using wavelet transformation and for measuring fault distance using thereof
CN109959493A (en) * 2019-04-29 2019-07-02 中国矿业大学 A kind of cable-stayed bridge cable damage real-time quantitative appraisal procedure based on natural bow modeling

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100394134B1 (en) * 2001-02-20 2003-08-09 학교법인 성균관대학 Method for detecting high impedance fault using wavelet transformation and for measuring fault distance using thereof
CN109959493A (en) * 2019-04-29 2019-07-02 中国矿业大学 A kind of cable-stayed bridge cable damage real-time quantitative appraisal procedure based on natural bow modeling
CN109959493B (en) * 2019-04-29 2020-07-24 中国矿业大学 Cable-stayed bridge cable damage real-time quantitative evaluation method based on static deflection modeling

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