CN110470738B - Structural damage identification method based on vibration response difference ratio function - Google Patents

Structural damage identification method based on vibration response difference ratio function Download PDF

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CN110470738B
CN110470738B CN201910777483.9A CN201910777483A CN110470738B CN 110470738 B CN110470738 B CN 110470738B CN 201910777483 A CN201910777483 A CN 201910777483A CN 110470738 B CN110470738 B CN 110470738B
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史熙
王增伟
刘超
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Shanghai Jiaotong University
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Abstract

A structural damage identification method based on a vibration response difference ratio function is characterized in that after a vibration response measuring point of a structure to be detected is determined, a frequency response function matrix and a global transfer rate matrix of the structure to be detected are calculated according to measured data, and a vibration response difference ratio function and a full transfer rate matrix are obtained through comparison calculation with an undamaged structure, so that structural damage detection and positioning are achieved. The invention only needs a small amount of vibration measurement work, has simple implementation process and greatly improves the adaptability and operability of the vibration response analysis method in the complex structure health detection problem.

Description

Structural damage identification method based on vibration response difference ratio function
Technical Field
The invention relates to a technology in the field of mechanical flaw detection, in particular to a structural damage identification method based on a vibration response difference ratio function.
Background
The method is characterized in that a large mechanical structure, a building structure and the like are inevitably affected by factors such as chemical corrosion, external load, material degradation and the like in the service process to generate structural damage and affect the structural strength of the large mechanical structure, the existing structural damage identification method mainly comprises an ultrasonic method, a vortex current method, an X-ray method, a vibration response method and the like, wherein the vibration response method is widely adopted due to low cost and easy realization of on-line continuous monitoring. The vibration response structure damage method is mainly divided into two types: a test data based identification method and a model based identification method. The disadvantage of the model-based identification method is that it is difficult to build an accurate model of the structure, and it is not possible to take the environment and the uncertainty of the physical parameters into account, and it is easy to generate wrong conclusions. The identification method based on the test data only uses the vibration response data obtained by the experimental test to identify the structural damage, and has many advantages, such as no need of modal parameter identification on the structure, no need of establishing a numerical value or an analytic model of the structure, and the method can effectively detect and quantify the structural damage, but has great limitation in the aspect of structural damage positioning.
Disclosure of Invention
The invention provides a structural damage identification method based on a vibration response difference ratio function, which aims at the defects in the prior art, can effectively extract and quantify the change of the vibration response relation caused by the structural damage according to the vibration response difference ratio, realizes the accurate detection and positioning of the structural damage, only needs a small amount of vibration measurement work, has simple implementation process and greatly improves the adaptability and operability of the vibration response analysis method in the complex structure health detection problem.
The invention is realized by the following technical scheme:
according to the invention, after the vibration response measuring point of the structure to be detected is determined, the frequency response function matrix and the global transfer rate matrix of the structure to be detected are calculated according to the measured data, and the vibration response difference ratio function and the full transfer rate matrix are obtained by comparing and calculating with the undamaged structure, so that the structure damage detection and positioning are realized.
The vibration response measuring point comprises a potential damage point and a reference point, and specifically, a part of an obviously vulnerable structure is determined as the potential damage point of the system structure and a part of an obviously non-vulnerable structure is determined as the reference point according to the characteristics of the structure, the loading condition, the environmental influence and the historical record information of the structure damage point.
The measured data is an acceleration signal and is measured by an acceleration sensor arranged at a potential damage point and a reference point.
The frequency response function matrix and the global transfer rate matrix of the structure to be detected refer to: calculating to obtain a frequency response function matrix according to all frequency response functions between the potential damage points and the reference points
Figure BDA0002175534410000021
Wherein:
Figure BDA0002175534410000022
for applying a force F at the undamaged structure S1S1Vibration response at Sn
Figure BDA0002175534410000023
The frequency response function of the two-way filter,
Figure BDA0002175534410000024
global transmissibility matrix
Figure BDA0002175534410000025
The step of comparing and calculating the undamaged structure to obtain a vibration response difference ratio function refers to the following steps: calculating according to the frequency response function matrix of the undamaged structure to obtain the difference value of the frequency response functions of the undamaged structure, and further calculating to obtain a vibration response difference ratio function, wherein the calculation specifically comprises the following steps: frequency response function matrix of undamaged structure
Figure BDA0002175534410000026
Wherein: hSnS1For applying a force F at the undamaged structure S1S1With vibration response X at SnSnFrequency response function between HSnS1＝XSn/FS1(ii) a Potential damage points are S1 and S2 … Sn, and a reference point is R; difference of frequency response function
Figure BDA0002175534410000027
Vibration response difference ratio function
Figure BDA0002175534410000028
The structural damage detection and positioning means that: when in use
Figure BDA0002175534410000029
If the absolute values of all elements in the index matrix are smaller than the corresponding elements of the set index threshold matrix, the structure to be detected is considered not to be damaged, otherwise, the structure to be detected is considered to be damaged; when the structure is detected to be damaged, the difference value of the vibration response difference ratio function matrix and the global transmissibility matrix of the undamaged structure is determined
Figure BDA00021755344100000210
Computing its expansion as a column vector representation
Figure BDA00021755344100000211
The modulus of the column vector in (b) represents the position where the damage occurs, and the subscript corresponding to the position where the damage occurs is the damage occurrence point.
Technical effects
Compared with the prior art, the invention has the advantages that the concept of the vibration response difference ratio function is utilized, the response of factors such as environment, external load and the like on the undamaged structure is eliminated, the change of the vibration response relation caused by the structural damage can be effectively extracted and quantized, and the accurate detection and positioning of the structural damage are realized. The method has strong engineering practicability, only needs a small amount of vibration measurement work, is low in cost, is simple in implementation process, and greatly improves the adaptability and operability of the vibration response analysis method in the complex structure health detection problem.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic view of a mass-spring discretization system;
FIG. 3 is a schematic diagram of the variation of the difference in transfer rate function with the same lesion point;
FIG. 4 is a diagram illustrating the variation of the vibration response difference ratio function along with a damage point.
Detailed Description
As shown in fig. 3, the simulation model of the present embodiment specifically includes: six mass units m 1-m 6, wherein: the sixth mass unit m6 is respectively connected with the third to fifth mass units m 3-m 5 through elastic pieces, the fourth mass unit m4 is respectively connected with the first and third mass units m1 and m3 through elastic pieces, the fifth mass unit m5 is respectively connected with the second and third mass units m2 and m3 through elastic pieces, the third mass unit m3 is respectively connected with the first and second mass units m1 and m2 through elastic pieces, and the first and second mass units m1 and m2 are respectively connected with the ground through elastic pieces.
As shown in fig. 1, the present embodiment includes the following steps:
step one, determining a structural vibration response measuring point: taking the mass-spring discretization system in fig. 2 as an example, assuming that mass elements m2, m3, and m4 are potential damage points and element m5 is selected as a reference point, these four mass elements are vibration response measurement points.
Step two, measuring frequency response function of undamaged structure and overall transfer rateMatrix calculation: measuring frequency response function between vibration response points on undamaged structure
Figure BDA0002175534410000031
Undamaged structure global transmissibility matrix
Figure BDA0002175534410000032
Step three, measuring a frequency response function of the structure to be measured and calculating a global transfer rate matrix: measuring frequency response function between vibration response points on structure to be measured
Figure BDA0002175534410000033
Global transmissibility matrix for structure under test
Figure BDA0002175534410000041
Frequency response function difference value of structure to be tested and undamaged structure
Figure BDA0002175534410000042
Step four, calculating a vibration response difference ratio function:
Figure BDA0002175534410000043
step five, calculating the difference value of the vibration response difference ratio function matrix and the global transmissibility matrix of the undamaged structure:
Figure BDA0002175534410000044
and (3) the global transmissibility matrix difference value of the structure to be detected and the undamaged structure is as follows:
Figure BDA0002175534410000051
in the embodiment, the severity of the same damage point is simulated by modifying the mass of the third mass unit m3 exemplarily, the transfer function difference value changes greatly with the change of the mass of the third mass unit m3, and when other mass units are damaged, the transfer function difference also changes greatly.
As shown in fig. 4, when the mass of the third mass unit m3 changes, the vibration response difference ratio function is kept as a constant frequency domain curve and is equal to the undamaged structure transfer rate function applying force at the position where the damage occurs, and the vibration response difference ratio function is different for different mass unit damages, so that the damage position can be effectively identified and located by comparing the difference between the vibration response difference ratio function and the undamaged structure transfer rate function.
Step six, setting the structural damage detection index threshold matrix to be 0.1% of the absolute value of the global transmissivity matrix of the undamaged structure, namely delta is 0.001| TGWhen Δ TG≤0.001|TGIf not, determining that the structure to be detected is not damaged, and otherwise, determining that the structure to be detected is damaged; further calculation of
Figure BDA0002175534410000052
And its vector expansion
Figure BDA0002175534410000053
The column vector with the smallest modulus represents the place where the damage occurs, and the corresponding subscript is the quality unit of the damage.
When the second mass element m2 is damaged, i.e. the damage is simulated by changing the mass of the second mass element m2, the result in the frequency domain [ 1200 ] Hz is calculated as:
Figure BDA0002175534410000054
through specific practical experiments, under the condition that the structure is damaged, the operation is carried out according to the above stepsThe method is operated by the following steps, and the obtained experimental data are as follows: delta TGAnd
Figure BDA0002175534410000055
compared with the prior art, the performance index of the method is improved as follows: whether damage occurs or not can be accurately identified, and the position where the damage occurs can be accurately identified.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (4)

1. A structural damage identification method based on a vibration response difference ratio function is characterized in that after a vibration response measuring point of a structure to be detected is determined, a frequency response function matrix and a global transfer rate matrix of the structure to be detected are calculated according to measured data, and a vibration response difference ratio function and a full transfer rate matrix are obtained through comparison calculation with an undamaged structure, so that structural damage detection and positioning are achieved;
the frequency response function matrix and the global transfer rate matrix of the structure to be detected refer to: calculating to obtain a frequency response function matrix according to all frequency response functions between the potential damage points and the reference points
Figure FDA0002938840490000011
Wherein:
Figure FDA0002938840490000012
for applying a force F at the undamaged structure S1S1Vibration response at Sn
Figure FDA0002938840490000013
The frequency response function of the two-way filter,
Figure FDA0002938840490000014
global deliveryRate matrix
Figure FDA0002938840490000015
The step of comparing and calculating the undamaged structure to obtain a vibration response difference ratio function refers to the following steps: calculating according to the frequency response function matrix of the undamaged structure to obtain the difference value of the frequency response functions of the undamaged structure, and further calculating to obtain a vibration response difference ratio function, wherein the calculation specifically comprises the following steps: frequency response function matrix of undamaged structure
Figure FDA0002938840490000016
Wherein: hSns1For applying a force F at the undamaged structure S1S1With vibration response X at SnSnFrequency response function between HSnS1＝XSn/FS1(ii) a The potential damage points are S1, S2.. Sn, and the reference point is R; difference of frequency response function
Figure FDA0002938840490000017
Vibration response difference ratio function
Figure FDA0002938840490000018
2. The structural damage identification method of claim 1, wherein the vibration response measuring points comprise potential damage points and reference points, and specifically, the structural parts which are obviously vulnerable are determined as the potential damage points of the system structure and the structural parts which are obviously not easily damaged are determined as the reference points according to the characteristics of the structure, the loading condition, the environmental influence and the historical record information of the structural damage points; and the measured data is measured by an acceleration sensor.
3. The method for identifying structural damage according to claim 1, wherein the structural damage detection and localization is: when in use
Figure FDA0002938840490000021
All ofIf the absolute values of the elements are smaller than the corresponding elements of the set index threshold matrix, the structure to be detected is considered not to be damaged, otherwise, the structure to be detected is considered to be damaged; when the structure is detected to be damaged, the difference value of the vibration response difference ratio function matrix and the global transmissibility matrix of the undamaged structure is determined
Figure FDA0002938840490000022
Computing its expansion as a column vector representation
Figure FDA0002938840490000023
The modulus of the column vector in (b) represents the position where the damage occurs, and the subscript corresponding to the position where the damage occurs is the damage occurrence point.
4. The method of identifying structural damage as claimed in claim 1, wherein said structure under test comprises: six mass units, wherein: the sixth mass unit is respectively connected with the third to fifth mass units through elastic pieces, the fourth mass unit is respectively connected with the first and third mass units through elastic pieces, the fifth mass unit is respectively connected with the second and third mass units through elastic pieces, the third mass unit is respectively connected with the first and second mass units through elastic pieces, and the first and second mass units are respectively connected with the ground through elastic pieces;
the step of determining the vibration response measuring point of the structure to be measured is as follows: and forming a vibration response measuring point by taking the second, third and fourth mass units as potential damage points and the fifth mass unit as a reference point.
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CN112710742A (en) * 2020-12-22 2021-04-27 中国航空工业集团公司沈阳飞机设计研究所 Nondestructive testing method for glass damage of aircraft canopy framework
CN113761470A (en) * 2021-09-01 2021-12-07 国家电投集团河南电力有限公司开封发电分公司 Holographic vibration mode testing method for structural component based on limited reference point
CN114923650B (en) * 2022-05-06 2024-05-10 暨南大学 Method for quickly identifying structural damage based on vibration mode difference ratio matrix and mode matching
CN116861544B (en) * 2023-09-04 2024-01-09 深圳大学 Building abnormal vibration source positioning method based on edge cloud cooperation and related equipment

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