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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 Jiao Tong University
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Abstract

一种基于振动响应差比函数的结构损伤识别方法，通过确定待测结构的振动响应测点后，根据实测数据计算待测结构的频响函数矩阵及全局传递率矩阵，通过与未损伤结构比较计算得到振动响应差比函数及全传递率矩阵，从而实现结构损伤检测与定位。本发明仅需少量的振动测量工作，实施过程简单，大大提高了的振动响应分析方法在复杂结构健康检测问题中的可适性和可操作性。

Figure 201910777483

A structural damage identification method based on the vibration response difference ratio function. After determining the vibration response measuring points of the structure to be tested, the frequency response function matrix and the global transmissibility matrix of the structure to be tested are calculated according to the measured data, and the frequency response function matrix and the global transmissibility matrix of the structure to be tested are calculated. The vibration response difference ratio function and the full transmissibility matrix are obtained by calculation, so as to realize the structural damage detection and localization. The invention only needs a small amount of vibration measurement work, the implementation process is simple, and the adaptability and operability of the vibration response analysis method in the complex structure health detection problem are greatly improved.

Figure 201910777483

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.
Drawings
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)

1.一种基于振动响应差比函数的结构损伤识别方法，其特征在于，通过确定待测结构的振动响应测点后，根据实测数据计算待测结构的频响函数矩阵及全局传递率矩阵，通过与未损伤结构比较计算得到振动响应差比函数及全传递率矩阵，从而实现结构损伤检测与定位；1. a structural damage identification method based on the vibration response difference ratio function, is characterized in that, after by determining the vibration response measuring point of the structure to be measured, calculate the frequency response function matrix and the global transmissibility matrix of the structure to be measured according to the measured data, The vibration response difference ratio function and the full transmissibility matrix are obtained by comparing with the undamaged structure, so as to realize the structural damage detection and location; 所述的待测结构的频响函数矩阵及全局传递率矩阵是指：根据潜在损伤点和参考点之间的所有频响函数，计算得到频响函数矩阵
Figure FDA0002938840490000011
其中：
Figure FDA0002938840490000012
为施加在未损伤结构S1处的力FS1与Sn处的振动响应
Figure FDA0002938840490000013
之间的频响函数，
Figure FDA0002938840490000014
全局传递率矩阵
Figure FDA0002938840490000015
The frequency response function matrix and the global transmissibility matrix of the structure to be tested refer to: calculating the frequency response function matrix according to all the frequency response functions between the potential damage point and the reference point
Figure FDA0002938840490000011
in:
Figure FDA0002938840490000012
is the vibration response at the force F S1 and Sn applied to the undamaged structure S1
Figure FDA0002938840490000013
The frequency response function between,
Figure FDA0002938840490000014
global transmissibility matrix
Figure FDA0002938840490000015
 所述的与未损伤结构比较计算得到振动响应差比函数是指：根据未损伤结构的频响函数矩阵计算得到两者频响函数差值，进而计算得到振动响应差比函数，具体为：未损伤结构的频响函数矩阵
Figure FDA0002938840490000016
其中：HSns1为施加在未损伤结构S1处的力FS1与Sn处的振动响应XSn之间的频响函数，HSnS1＝XSn/FS1；潜在损伤点为S1、S2...Sn，参考点为R；频响函数差值
Figure FDA0002938840490000017
振动响应差比函数
Figure FDA0002938840490000018
The vibration response difference ratio function obtained by comparing with the undamaged structure refers to: calculating the difference between the two frequency response functions according to the frequency response function matrix of the undamaged structure, and then calculating the vibration response difference ratio function, specifically: Frequency Response Function Matrix of Damaged Structures
Figure FDA0002938840490000016
Where: H Sns1 is the frequency response function between the force F S1 applied at the undamaged structure S1 and the vibration response X Sn at Sn, H SnS1 =X Sn /F S1 ; the potential damage points are S1, S2... Sn, the reference point is R; the difference of the frequency response function
Figure FDA0002938840490000017
Vibration Response Difference Ratio Function
Figure FDA0002938840490000018
 2.根据权利要求1所述的结构损伤识别方法，其特征是，所述的振动响应测点，包括潜在损伤点和参考点，具体通过结构的特点、受载情况、环境影响以及结构损伤点的历史记录信息，确定明显易损伤结构部位作为系统结构的潜在损伤点、确定明显不易损伤结构部位作为参考点；所述的实测数据通过加速度传感器测得。2 . The method for identifying structural damage according to claim 1 , wherein the vibration response measurement points include potential damage points and reference points, and are specifically determined by structural characteristics, load conditions, environmental influences, and structural damage points. 3 . The historical record information of the system is determined, and the obvious damage-prone structural part is determined as the potential damage point of the system structure, and the obviously difficult-to-damage structure part is determined as the reference point; the measured data is measured by the acceleration sensor. 3.根据权利要求1所述的结构损伤识别方法，其特征是，所述的结构损伤检测与定位是指：当
Figure FDA0002938840490000021
中的所有元素的绝对值都小于设定指标阈值矩阵相应元素，则认为待测结构未发生损伤，否则认为待测结构发生损伤；当检测到结构发生损伤，根据振动响应差比函数矩阵与未损伤结构的全局传递率矩阵差值
Figure FDA0002938840490000022
计算其展开以列向量表示
Figure FDA0002938840490000023
中的列向量的模，则具有最小模的列向量则代表损伤发生处，其对应的下标即为损伤发生点。3. The method for identifying structural damage according to claim 1, wherein the structural damage detection and location refers to: when
Figure FDA0002938840490000021
If the absolute value of all elements in the index is less than the corresponding element of the set index threshold matrix, it is considered that the structure to be tested is not damaged, otherwise it is considered that the structure to be tested is damaged; when the structure is detected to be damaged, according to the vibration response difference ratio function matrix Global Transmissibility Matrix Differences for Damaged Structures
Figure FDA0002938840490000022
Compute its expansion as a column vector
Figure FDA0002938840490000023
The modulus of the column vector in , the column vector with the smallest modulus represents the damage occurrence place, and its corresponding subscript is the damage occurrence point. 4.根据权利要求1所述的结构损伤识别方法，其特征是，所述的待测结构包括：六个质量单元，其中：第六质量单元分别与第三至第五质量单元通过弹性件相连，第四质量单元分别与第一和第三质量单元、通过弹性件相连，第五质量单元分别与第二和第三质量单元、通过弹性件相连，第三质量单元分别与第一和第二质量单元、通过弹性件相连，第一和第二质量单元、各自分别通过弹性件与地面相连；4 . The method for identifying structural damage according to claim 1 , wherein the structure to be tested comprises: six mass units, wherein: the sixth mass unit is respectively connected with the third to fifth mass units through elastic parts. 5 . , the fourth mass unit is respectively connected with the first and third mass units through elastic parts, the fifth mass unit is connected with the second and third mass units respectively through elastic parts, and the third mass unit is connected with the first and second mass units respectively The mass unit is connected through the elastic piece, and the first and second mass units are respectively connected with the ground through the elastic piece; 所述的确定待测结构的振动响应测点是指：以第二、第三和第四质量单元作为潜在损伤点、第五质量单元为参考点，组成振动响应测点。The determining the vibration response measuring point of the structure to be measured means: taking the second, third and fourth mass units as potential damage points and the fifth mass unit as a reference point to form a vibration response measuring point.
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