CN112529842B - Multi-excitation fusion plate structure damage identification method based on wavelet packet energy - Google Patents

Multi-excitation fusion plate structure damage identification method based on wavelet packet energy Download PDF

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CN112529842B
CN112529842B CN202011320945.3A CN202011320945A CN112529842B CN 112529842 B CN112529842 B CN 112529842B CN 202011320945 A CN202011320945 A CN 202011320945A CN 112529842 B CN112529842 B CN 112529842B
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余建星
马文韬
余杨
吴世博
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Tianjin University
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Abstract

The invention provides a multi-excitation fusion plate structure damage identification method based on wavelet packet energy, which is characterized in that a series of excitation forces with different frequency components are applied to a plate structure to be detected, and vibration response information of different positions of the plate structure under each excitation force is acquired by using a sensor; performing wavelet packet decomposition on the obtained acceleration response, constructing wavelet packet energy characteristic vectors, and then constructing variable quantities of the wavelet packet characteristic vectors before and after the damage at different positions of the plate structure to serve as initial damage identification indexes; and forming an index interval by the initial damage identification index, carrying out mean value processing on values at the end points of the interval, taking the value closest to the value 0 of the processed interval as a final damage identification index, and comparing the size of each final damage identification index to determine the damage position and the corresponding damage degree. The invention obviously reduces the index value of the normal position of the wavelet packet energy index, and can more effectively realize the damage positioning of the structure, particularly the multi-position local damage condition.

Description

Multi-excitation fusion plate structure damage identification method based on wavelet packet energy
Technical Field
The invention relates to the field of structural loss monitoring, in particular to a lossless multi-excitation fusion plate structural damage identification method based on wavelet packet energy.
Background
In recent decades, people have increasingly focused on health monitoring of structures. Compared with the traditional static nondestructive detection method (acoustic wave or ultrasonic wave, thermal imaging, ray method, pulse echo method, lamb wave method and the like), the structural health detection based on vibration has remarkable advantages. The vibration signal is used for identification, the approximate position of the structural damage does not need to be known in advance, and meanwhile, the method has the characteristics of low detection cost and no influence on normal use of the structure, so that the dynamic detection method becomes the mainstream of a large-scale structural damage identification method.
Damage to the structure can change the dynamic properties of the structure, such as vibrational response, modal parameters, etc., and direct or indirect identification of these changes can be used to detect the state of the structure. In recent years, modal parameters and derived indexes thereof, such as natural frequency, modal shape, frequency response function, modal strain energy, compliance matrix, residual force vector and the like, are widely used for damage identification. Artificial Neural Networks (ANN) also have unusual manifestations in the field of injury recognition, and recognition by combining with other injury recognition methods or directly using neural networks is a common method. However, training the neural network to achieve a better recognition effect requires a large amount of training data, which is not favorable for practical application.
Wavelet analysis is widely applied in the field of structural damage identification by virtue of good time-frequency localization characteristics of the wavelet analysis. Early scholars utilized wavelet analysis to detect local singularity of signal, realized on-line monitoring of structural health state, and can not only recognize the occurrence moment of damage but also locate the damage. Besides the time resolution of wavelet analysis, a plurality of scholars realize the damage positioning of one-dimensional structures and two-dimensional structures to structural space limiting signals (such as vibration modes) and qualitatively describe the damage degree of the structures. Due to the good damage sensitivity of the wavelet packet node energy index, the wavelet packet node energy index is a common identification index in structural damage identification. The method of identifying damage is common by using a sensitivity method or taking wavelet packet energy as artificial neural network input, and the method indicates that the wavelet packet node energy contains sensitive information of structural damage, however, both the sensitivity method and the artificial intelligent network need a large amount of calculation.
Many scholars directly construct damage identification indexes based on wavelet packet node energy for damage identification, the calculation amount required by damage identification is reduced, and the method can identify the damage condition of the structure to a certain extent. In addition, sensitive indexes reflecting function changes such as slope and curvature are applied to the construction of the wavelet packet energy index, so that the sensitivity of damage identification can be improved, and the robustness of the index to noise is reduced while the sensitivity is improved. At present, the damage identification method based on wavelet packet energy is successfully applied to engineering structures such as wood structures, tunnel structures, jacket offshore platform components, railway axles, bridge columns and the like.
Although much research work is carried out on wavelet packet energy indexes, in the current stage, the damage identification method based on wavelet packet node energy is more directed at one-dimensional structures (such as beam structures, bridges, frames and the like), satisfactory damage positioning results are difficult to achieve on two-dimensional structures, misjudgment often occurs, and the method is particularly obvious when multi-damage working conditions are positioned.
Disclosure of Invention
The invention aims to provide a lossless multi-excitation fusion plate structure damage identification method based on wavelet packet energy.
Specifically, the invention provides a method for identifying damage to a multi-excitation fusion plate structure based on wavelet packet energy, which comprises the following steps:
step 100, applying a series of excitation forces with different frequency components to a plate structure to be detected, and acquiring vibration response information of different positions of the plate structure under each excitation force by using a sensor;
step 200, performing wavelet packet decomposition on the obtained vibration response, constructing wavelet packet energy characteristic vectors, and then constructing variable quantities of the wavelet packet characteristic vectors before and after damage at different positions of a plate structure to serve as initial damage identification indexes;
and 300, forming index intervals by the initial damage identification indexes under the action of a series of excitation forces, carrying out mean value processing on values at the end points of the intervals, taking the value closest to the value 0 of the processed interval as a final damage identification index, and determining the damage position and the corresponding damage degree by comparing the sizes of the final damage identification indexes.
The invention does not need the complete vibration mode of the structure, and can identify the local damage of the structure only by obtaining the acceleration response of the structure; the wavelet packet energy index is directly utilized for damage identification, and a large amount of training data and extra calculation amount are not needed; the index value at the normal position of the wavelet packet energy index is obviously reduced, and the damage positioning of the structure, particularly the multi-position local damage condition, can be more effectively realized.
Drawings
FIG. 1 is a flow chart of a method for lesion identification according to an embodiment of the present invention;
FIG. 2 is a time course plot of an applied load in one embodiment of the present invention;
FIG. 3 is a schematic diagram of a test of a plate structure in an embodiment, in which black dots are excitation positions and circled numbers are schematic diagrams of arrangement of test points;
FIG. 4 is a wavelet packet band energy ratio spectrum of the measured points of the normal structure portion in the example where (a) represents 23 measured points, (b) represents 40 measured points, (c) represents 54 measured points, and (d) represents 57 measured points;
FIG. 5 is a relationship curve of damage identification index DI along with frequency change of excitation force at some measuring points in the embodiment, where (a), (b), and (c) respectively indicate that measuring points 1, 3, and 30 are non-damaged measuring points, and (d) indicates that measuring point 40 is a damaged measuring point;
FIG. 6 is a damage identification result of single-location damage conditions 1-4 in the example, where (a) indicates condition 1, (b) indicates condition 2, (c) indicates condition 3, and (d) indicates condition 4;
FIG. 7 is a diagram illustrating damage identification results for multiple position damage conditions in one embodiment, where (a) indicates condition 5, (b) indicates condition 6, (c) indicates condition 7, (d) indicates condition 8, and (e) indicates condition 9;
FIG. 8 is a graph comparing the method of the present invention with the energy ratio mean square error indicator impairment recognition results, wherein (a) is the recognition result of the method of the present invention, and (b) is the existing energy ratio mean square error indicator impairment recognition result;
FIG. 9 is a flow chart of the improved wavelet packet based energy impairment recognition method of the present invention
Detailed Description
The detailed structure and implementation process of the present invention are described in detail by the following embodiments and the accompanying drawings.
As shown in fig. 1, in an embodiment of the present invention, a method for identifying a structural damage of a multi-excitation fusion plate based on wavelet packet energy is provided, which includes the following steps:
step 100, applying a series of excitation forces with different frequency components to a plate structure to be detected, and acquiring vibration response information of different positions of the plate structure under each excitation force by using a sensor;
the different frequencies are a series of half-wave sine excitations around the first-order natural frequency of the plate structure, and the excitation period is one period.
The expression is as follows: f = sin (2 pi ft) 0 ≤ t ≤ F/2
Where F represents the magnitude of the applied excitation force and F represents the frequency of the excitation.
The sensors are acceleration sensors which are evenly distributed in the length direction and the width direction of the plate structure, and the arrangement positions of the measuring points before and after damage are the same, so that the transverse acceleration response of each measuring point before and after the damage of the plate structure under each excitation force is obtained.
Step 200, performing wavelet packet decomposition on the obtained vibration response, constructing wavelet packet energy characteristic vectors, and then constructing variable quantities of the wavelet packet characteristic vectors before and after damage at different positions of a plate structure to serve as initial damage identification indexes;
and (3) carrying out wavelet packet decomposition on the acceleration response before and after the structure is damaged, and counting the frequency band energy of each node of the wavelet packet to construct a wavelet packet energy ratio spectrum. After j layers of wavelet packet decomposition, the signal x (t) can be written as:
Figure BDA0002792873830000051
wherein
Figure BDA0002792873830000052
Wavelet packet coefficient
Figure BDA0002792873830000053
Comprises the following steps:
Figure BDA0002792873830000054
ψ j,k,i (t) is a wavelet packet having a scale index j, a position index k, and a frequency index i. Because phi j,k,i (t) is also a set of orthonormal bases, so when m ≠ n:
ψ j,k,m ψ j,k,n ＝0
the total energy of the signal x (t) is:
Figure BDA0002792873830000055
the orthogonality of the wavelet packets can be found as:
Figure BDA0002792873830000056
wherein
Figure BDA0002792873830000057
Is the signal energy of the ith frequency band at the jth scale.
The wavelet basis function selects a Coif17 wavelet, and the wavelet packet transform decomposition layer number vision recognition effect is decomposed into 3 layers or 4 layers. After decomposition, the energy of each frequency band is arranged to form a wavelet packet energy spectrum:
Figure BDA0002792873830000058
and then, the wavelet packet energy spectrum ordering converts the Paley order into the Walsh order through Gray coding, so that the arrangement of the subband frequencies from low to high is realized:
Figure BDA0002792873830000061
wherein the content of the first and second substances,
Figure BDA0002792873830000062
refers to the frequency corresponding to the ith sub-band;
finally, the energy spectrum is normalized, and the normalized result is an energy ratio spectrum
Figure BDA0002792873830000063
Figure BDA0002792873830000064
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002792873830000065
the obtained wavelet packet energy ratio spectrum
Figure BDA0002792873830000066
Is a wavelet packet energy eigenvector.
And 300, forming index intervals by the initial damage identification indexes under the action of a series of excitation forces, carrying out mean value processing on values at the end points of the intervals, taking the value closest to the 0 value of the processed interval as a final damage identification index, and determining the damage position and the corresponding damage degree by comparing the sizes of the final damage identification indexes.
And taking the frequency band of the element with the largest energy ratio spectrum change of the wavelet packet before and after the damage of each measuring point of the plate structure as an identification frequency band, and taking the variation of the frequency band as a primary damage identification index. Assuming that n measuring points are arranged on the plate structure, the number of decomposed layers is i, and the preliminary damage index of the jth measuring point is defined as:
Figure BDA0002792873830000067
wherein s is a certain frequency band, and a certain measuring point t exists, so that the energy ratio variation of the frequency band satisfies the following conditions:
Figure BDA0002792873830000068
forming an index interval by using a series of initial damage identification indexes under the excitation action:
I＝{DI 1 ,DI 2 ,…,DI n }＝[DI 1 ,DI n ]in which DI 1 ≤DI 2 ≤…≤DI n 。
Then carrying out average processing on the numerical values at the interval end points:
Figure BDA0002792873830000069
the value closest to the 0 value in the processed interval is the final damage identification index d. The d index size of each measuring point is compared to clearly position the position where the damage occurs, and the structural damage degree can be qualitatively judged according to the index size at the damage position.
The invention does not need the complete vibration mode of the structure, and can identify the local damage of the structure only by obtaining the acceleration response of the structure; directly utilizes wavelet packet energy indexes to carry out damage identification without a large amount of training
Data training and additional computational effort; the index value at the normal position of the wavelet packet energy index is obviously reduced, and the damage positioning of the structure can be more effectively realized, particularly under the condition of multi-position local damage.
The foregoing process is illustrated by way of specific examples.
The selected object in the embodiment is a simply-supported flat plate with the length of 1m, the width of 0.8m and the thickness of 5mm, and a damage model with the reduced local rigidity of the structure is adopted. Young's modulus of 210GPA, poisson's ratio of 0.3, material density of 7850kg/m 3 The dimensionless damping ratio of the structure is ζ k And =0.01. To indicate the degree of damage, let DE = E d /E u . Wherein E u And E d The elastic modulus of the structure is shown without damage and with damage, respectively. The greater the degree of damage, the smaller the DE value. The damage is assumed to be a decrease in stiffness in the square area, with a side length of 0.04m. The damage position of the structure is represented by a square central coordinate, and the specific damage working condition is shown in table 1:
TABLE 1 Damage Condition
Figure BDA0002792873830000071
As shown in fig. 9, the specific implementation steps are as follows:
(1) The modal analysis is carried out on the model to obtain the first two orders of natural frequency f 1 =31.45Hz and f 2 =68.31Hz. Then applying a sine half-wave excitation force with the magnitude of 50N and the frequency of f on the surface of the structure, wherein the time course curve of the force is shown in figure 2, and the expression of the force is as follows:
F＝sin(2πft) 0≤t≤f/2
the value of f is a series of excitations around the first order natural frequency: the frequency range is 20HZ-46HZ, and the interval is 2HZ. And then, acquiring the lateral acceleration response of each measuring point before and after the damage of each excited lower plate structure through an acceleration sensor. In order to obtain a vibration response acceleration signal of the structure, 63 measuring points are uniformly distributed on the finite element model, and the sampling frequency of each measuring point is 2000HZ. The excitation positions and measuring point distribution are shown in FIG. 3:
(2) And carrying out wavelet packet decomposition on the acceleration response before and after the structural damage. After j layers of wavelet packet decomposition, the signal x (t) can be written as:
Figure BDA0002792873830000081
wherein
Figure BDA0002792873830000082
Wavelet packet coefficient
Figure BDA0002792873830000083
Comprises the following steps:
Figure BDA0002792873830000084
counting the energy of each node
Figure BDA0002792873830000085
Arranging the energy of each decomposed frequency band to form an energy spectrum of a wavelet packet:
Figure BDA0002792873830000086
then, sorting the energy spectrum of the wavelet packet, and converting a Walsh sequence into a Walsh sequence through Gray coding so as to realize the arrangement of the subband frequencies from low to high:
Figure BDA0002792873830000087
wherein the content of the first and second substances,
Figure BDA0002792873830000091
refers to the frequency corresponding to the ith sub-band.
Finally, the energy spectrum is normalized, and the normalized result is the energy ratio spectrum
Figure BDA0002792873830000092
Figure BDA0002792873830000093
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002792873830000094
in wavelet packet decomposition, a Coif17 wavelet is selected as a wavelet basis function, acceleration response of each measuring point is decomposed to 3 or 4 layers through the Coif17 wavelet (working conditions 1 and 2 are decomposed to the 3 rd scale, and other working conditions are decomposed to the 4 th scale), and a wavelet packet coefficient of a formula (2) is obtained. The energy of each node is then counted according to equation (3) and a wavelet packet energy spectrum is formed as equation (4). And (4) performing ascending order arrangement on the obtained wavelet packet energy spectrum, and calculating by using a formula (6) to obtain a wavelet packet frequency band energy ratio spectrum. The wavelet packet band energy ratio spectrum of the normal structure part measuring point is shown in FIG. 4.
(3) And taking the frequency band of the element with the largest energy ratio spectrum change of the wavelet packet before and after the damage of each measuring point of the structure as an identification frequency band. Taking working condition 1 damage degree DE =0.9 as an example, the element value with the largest absolute value and the frequency band thereof in the wavelet packet damage feature vector spectrum of all the measuring points under each excitation are shown in table 2:
TABLE 2 elemental values for variation under different excitationsDistribution table of local frequency band (unit 10) -4 )
Figure BDA0002792873830000095
And then, the variation of the frequency band of each measuring point 1 is used as a preliminary damage identification index DI. Assuming that n measuring points are arranged on the plate structure, the number of decomposed layers is i, and defining the initial damage index of the jth measuring point as follows:
Figure BDA0002792873830000096
wherein s is a certain frequency band, and a certain measuring point t exists, so that the energy ratio variation of the frequency band satisfies the following conditions:
Figure BDA0002792873830000101
(4) Forming an index interval by using a series of initial damage identification indexes under the excitation action:
I＝{DI 1 ,DI 2 ,…,DI n }＝[DI 1 ,DI n ]in which DI 1 ≤DI 2 ≤…≤DI n 。
When the damage degree of the working condition 1 is DE =0.9, a relation curve of the damage identification index DI of the partial node along with the change of the excitation force frequency is obtained as shown in fig. 5, wherein the measuring points 1, 3 and 30 are undamaged measuring points, and 40 is a damaged measuring point. The damage identification index section of the damage position is deviated from the position of DI =0 more than the damage identification index section of the normal position in the applied excitation force frequency range. The damage index intervals of the 1, 3 and 30 measuring points at the normal position are respectively [ -0.93E-4,1.93E-4], [0.04E-4,2.37E-4] and [ -2.07E-4, -0.21E-4], and the damage index interval of the damage position is [4.53E-4,7.13E-4]. Relying only on the values at the end points as an indicator of impairment determination can significantly reduce the robustness of the indicator. The values at the end points of the interval need to be averaged:
Figure BDA0002792873830000102
in this example, m =3.
The value closest to the 0 value of the processed interval is the final damage identification index d. Through calculation, the d index results under each damage working condition are shown in fig. 6 and 7. The d index size of each measuring point is compared to clearly position the position where the damage occurs, and the structural damage degree can be qualitatively judged according to the index size at the damage position. As can be seen from fig. 6 and 7, no matter the damage is a single-position damage or a multi-position damage, the method can identify the position where the damage occurs more accurately, and qualitatively determine the damage degree according to the size of the index at the damage position. Fig. 8 is a difference between a conventional energy ratio mean square error index (DIS) and a recognition result of a multi-excitation fusion index d proposed by the present invention in a working condition 9, and the advantage of the present invention in multi-location damage recognition can be clearly seen from the figure.
TABLE 3 Single-site Damage Condition identification results
Figure BDA0002792873830000111
TABLE 4 Multi-position Damage Condition recognition results
Figure BDA0002792873830000112
Thus, it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been illustrated and described in detail herein, many other variations or modifications consistent with the principles of the invention may be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.

Claims (1)

1. A multi-excitation fusion plate structure damage identification method based on wavelet packet energy is characterized by comprising the following steps:
step 100, applying a series of excitation forces with different frequency components to a plate structure to be detected, and acquiring vibration response information of different positions of the plate structure under each excitation force by using a sensor;
different frequencies are a series of sine half-wave excitations near the first-order natural frequency of the plate structure, and the excitation period is one period; the expression is as follows: f = sin (2 pi ft) 0 ≤ t ≤ F/2
Wherein F represents the magnitude of the applied excitation force and F represents the excited frequency;
the sensors are acceleration sensors which are evenly distributed in the length direction and the width direction of the plate structure, and the arrangement positions of the measuring points before and after damage are the same, so that the transverse acceleration response of each measuring point before and after damage of the plate structure under each excitation force is obtained;
step 200, performing wavelet packet decomposition on the obtained vibration response, constructing wavelet packet energy characteristic vectors, and then constructing variable quantities of the wavelet packet characteristic vectors before and after damage at different positions of a plate structure to serve as initial damage identification indexes;
carrying out wavelet packet decomposition on acceleration response before and after structural damage, and counting the frequency band energy of each node of a wavelet packet to construct a wavelet packet energy ratio spectrum;
after j layers of wavelet packet decomposition, the signal x (t) can be written as:
Figure FDA0003956217210000011
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003956217210000012
wavelet packet coefficient
Figure FDA0003956217210000013
Comprises the following steps:
Figure FDA0003956217210000014
ψ j,k,i (t) is a wavelet packet with a scale index j, a position index k and a frequency index i, since j,k,i (t) is also a set of orthonormal bases, so when m ≠ n:
ψ j,k,m ψ j,k,n ＝0
the total energy of the signal x (t) is:
Figure FDA0003956217210000021
the orthogonality from the wavelet packets yields:
Figure FDA0003956217210000022
wherein
Figure FDA0003956217210000023
Is the signal energy of the ith frequency band at the jth scale;
selecting Coif17 wavelet from wavelet basis function, decomposing the wavelet packet transform decomposition layer number vision recognition effect into 3 or 4 layers, and arranging the energy of each frequency band after decomposition to form a wavelet packet energy spectrum:
Figure FDA0003956217210000024
then, sorting the energy spectrum of the wavelet packet, and converting a Walsh sequence into a Walsh sequence through Gray coding so as to realize the arrangement of the subband frequencies from low to high:
Figure FDA0003956217210000025
wherein the content of the first and second substances,
Figure FDA0003956217210000026
refers to the frequency corresponding to the ith sub-band;
finally, the energy spectrum is normalized, and the normalized result is the energy ratio spectrum
Figure FDA0003956217210000027
Figure FDA0003956217210000028
Wherein the content of the first and second substances,
Figure FDA0003956217210000029
the obtained wavelet packet energy ratio spectrum
Figure FDA00039562172100000210
Is a wavelet packet energy eigenvector;
taking the frequency band of the element with the largest energy ratio spectrum change of the wavelet packet before and after damage of each measuring point of the plate structure as an identification frequency band, and taking the variation of the frequency band as a primary damage identification index;
assuming that n measuring points are arranged on the plate structure, the number of decomposed layers is i, and the preliminary damage index of the jth measuring point is defined as:
Figure FDA0003956217210000031
wherein s is a certain frequency band, and a certain measuring point t exists, so that the energy ratio variation of the frequency band satisfies the following conditions:
Figure FDA0003956217210000032
forming an index interval by using a series of initial damage identification indexes under the excitation action:
I＝{DI 1 ,DI 2 ,…,DI n }＝[DI 1 ,DI n ]in which DI 1 ≤DI 2 ≤…≤DI n ；
Then carrying out average processing on the numerical values at the interval end points:
Figure FDA0003956217210000033
and 300, forming index intervals by the initial damage identification indexes under the action of a series of excitation forces, carrying out mean value processing on values at the end points of the intervals, taking the value closest to the value 0 of the processed interval as a final damage identification index, and determining the damage position and the corresponding damage degree by comparing the sizes of the final damage identification indexes.
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