CN114923420B - Crack diagnosis method and system based on fiber Bragg grating and storage medium - Google Patents

Crack diagnosis method and system based on fiber Bragg grating and storage medium Download PDF

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CN114923420B
CN114923420B CN202210544130.6A CN202210544130A CN114923420B CN 114923420 B CN114923420 B CN 114923420B CN 202210544130 A CN202210544130 A CN 202210544130A CN 114923420 B CN114923420 B CN 114923420B
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阳劲松
王田天
谢劲松
张小振
田龙桢
李先钧
王钦民
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Central South University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G01B11/165—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by means of a grating deformed by the object
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Abstract

The invention relates to the technical field of train structure crack monitoring, in particular to a crack diagnosis method, a crack diagnosis system and a storage medium based on fiber Bragg gratings, wherein the method comprises the steps of determining material parameters of a manufacturing material of a structure to be analyzed; establishing a finite element simulation model, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor to different lengths; reconstructing the structural strain data into a reflectance spectrum; extracting a damage sensitive characteristic value and a reference signal in the reflection spectrum, wherein the damage sensitive characteristic value is used for indicating the length of the crack, and the reference signal is used for indicating that no crack is expanded; and taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model. The method can solve the problems that the traditional finite element method is complex in calculation for acquiring the strain output, complicated in steps and incomplete in quantitative diagnosis and monitoring of the cracks based on a single characteristic value.

Description

Crack diagnosis method and system based on fiber Bragg grating and storage medium
Technical Field
The invention relates to the technical field of train structure crack monitoring, in particular to a crack diagnosis method and system based on fiber Bragg gratings and a storage medium.
Background
A large number of structures with holes in rail vehicles, mechanical equipment and the like are easy to crack and damage under the action of cyclic load, and the crack propagation can cause structural function failure and serious safety accidents. The existing crack quantitative diagnosis method based on the fiber Bragg grating reflection spectrum generally utilizes a single characteristic value represented by reflection spectrum central wavelength and broadening to establish a crack quantitative diagnosis model. Since the reflection spectrum of the fiber bragg grating depends on the accuracy of a strain field to a great extent, the calculation for acquiring the strain output by the traditional finite element method is complex, the steps are complicated, and the quantitative diagnosis and monitoring of the cracks based on a single characteristic value are not comprehensive enough.
Disclosure of Invention
The invention provides a crack diagnosis method, a crack diagnosis system and a storage medium based on fiber Bragg gratings, and aims to solve the problems that the traditional finite element method is complex in calculation for obtaining strain output, complicated in steps and incomplete in quantitative crack diagnosis and monitoring based on a single characteristic value.
In order to achieve the purpose, the invention is realized by the following technical scheme:
in a first aspect, the present invention provides a crack diagnosis method based on fiber bragg grating, including:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method;
extracting damage sensitive characteristic values and reference signals in the reflection spectrum, wherein the damage sensitive characteristic values are used for representing the length of the crack, and the reference signals are used for representing no expansion crack;
and taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model.
In a second aspect, the present application provides a fiber bragg grating based crack diagnosis system, including M fiber bragg grating sensors disposed at a target structure of a train and a processing center, where M is a positive integer, the processing center is connected to the M sensors, and the processing center is configured to:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method;
extracting damage sensitive characteristic values and reference signals in the reflection spectrum, wherein the damage sensitive characteristic values are used for representing the length of the crack, and the reference signals are used for representing no expansion crack;
and taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model.
In a third aspect, the present application provides a fiber bragg grating based crack diagnosis system, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method according to the first aspect when executing the computer program.
In a fourth aspect, the present application provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the method steps of the first aspect.
Has the advantages that:
according to the crack diagnosis method based on the fiber Bragg grating, provided by the invention, the crack expansion process under the cyclic loading condition is simulated by using an expansion finite element method, the fiber Bragg grating reflection spectrum is reconstructed by using a transmission matrix method, the action mechanism of crack expansion change and the fiber Bragg grating reflection spectrum during crack expansion is further determined, a plurality of damage sensitive characteristic values of the reflection spectrum are extracted, and a crack length regression model of a plurality of damage sensitive characteristic values and the crack length is constructed by using a support vector regression method, so that the accuracy of the constructed model is higher, the diagnosis result of the model is close to the actual crack length, the problem that the calculation of the traditional finite element method in crack expansion simulation is complicated is solved, in addition, the method can carry out comprehensive monitoring based on the plurality of damage sensitive characteristic values, and realizes more comprehensive monitoring of the structure to be analyzed.
According to the crack diagnosis system based on the fiber Bragg grating, provided by the invention, the fiber Bragg grating sensor arranged at the key position of the structure can accurately sense the structural strain change caused by the crack, and a crack quantitative monitoring model can be established by extracting the characteristic value capable of representing the crack length in the reflection spectrum of the fiber Bragg grating, so that the real-time monitoring on the crack damage is realized.
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Fig. 1 is a flowchart of a crack diagnosis method based on fiber bragg grating according to a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of the dimensions of a simulation test piece according to the preferred embodiment of the present invention;
FIG. 3 is a schematic diagram of the reflection spectrum of the FBG3 sensor location in accordance with the preferred embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating the variation of damage characteristics in simulation according to the preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of the diagnostic results of the preferred embodiment of the present invention.
Detailed Description
The technical solutions of the present invention are described clearly and completely below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Unless otherwise defined, technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The use of "first," "second," and similar terms in the present application do not denote any order, quantity, or importance, but rather the terms are used to distinguish one element from another. Also, the use of the terms "a" or "an" and the like do not denote a limitation of quantity, but rather denote the presence of at least one. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships are changed accordingly.
It should be noted that, because the operating environment of the high-speed rail is complex, foreign objects often collide in each structure, and such an impact event easily causes structural damage and threatens driving safety, so it is necessary to monitor the impact event in each structure of the high-speed rail. Because the reflection spectrum of the fiber Bragg grating depends on the accuracy of a strain field to a great extent, the traditional finite element method has complex calculation and complex steps for acquiring strain output, and the quantitative diagnosis and monitoring of cracks based on a single characteristic value are not comprehensive enough. Based on the method, the application provides a crack diagnosis method based on the fiber Bragg grating.
Referring to fig. 1, an embodiment of the present application provides a crack diagnosis method based on a fiber bragg grating, including:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters of the damage sensitivity characteristic value, simulating the crack propagation condition based on the finite element simulation model of the damage sensitivity characteristic value, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the damage sensitive characteristic value structure strain data into a reflection spectrum by adopting a transmission matrix method;
extracting a damage sensitive characteristic value and a reference signal in a damage sensitive characteristic value reflectance spectrum, wherein the damage sensitive characteristic value of the damage sensitive characteristic value is used for indicating the length of the crack, and the reference signal of the damage sensitive characteristic value is used for indicating that no crack propagates;
and taking the damage sensitive characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model of the damage sensitive characteristic value.
In this embodiment, a Fiber Bragg Grating (FBG) sensor is used as the detection sensor. That is, an optical fiber sensor using a bragg grating as a sensing element can directly measure temperature and strain and can indirectly measure physical quantities related to temperature and strain. Thus, the sensitivity of the fiber bragg grating reflectance spectrum to the effects of strain fields is extremely high. Therefore, in the embodiment, accurate and reliable extension monitoring is carried out by analyzing the rule between the change of the reflection spectrum and the crack length, so that the failure rate of mechanical equipment can be reduced, and property loss can be reduced.
According to the crack diagnosis method based on the fiber Bragg grating, the crack expansion process under the cyclic loading condition is simulated by using the finite element expansion method, the fiber Bragg grating reflection spectrum is reconstructed by using the transmission matrix method, the action mechanism of the crack expansion change and the fiber Bragg grating reflection spectrum during crack expansion is further determined, a plurality of damage sensitive characteristic values of the reflection spectrum are extracted, and a crack length regression model of the plurality of damage sensitive characteristic values and the crack length is constructed by using the support vector regression method, so that the accuracy of the constructed model is higher, the diagnosis result of the model is close to the actual crack length, the problem that the traditional finite element method is complicated in calculation in crack expansion simulation is solved, in addition, the method can comprehensively monitor based on the plurality of damage sensitive characteristic values, and the structure to be analyzed is more comprehensively monitored.
The reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method comprises the following steps:
assuming that the length of the uniform grating is L, when calculating the fiber Bragg grating reflection spectrum (FBG reflection spectrum) under the action of non-uniform strain, uniformly dividing the non-uniform grating into N small sections, wherein N is a positive integer and simultaneously satisfies the requirement of
Figure BDA0003649164160000041
λ B For the center wavelength, the expression is:
λ B ＝2n eff Λ；
wherein Λ is the period of change of the refractive index of the grating, n eff Is the effective refractive index.
Regarding the average period of each segment in the N small segments as the equivalent period of the segment, and regarding the refractive index of each segment as the equivalent refractive index of the segment;
and substituting the parameters of each section into a coupling equation to carry out iterative calculation so as to obtain the reflection spectrum of the whole FBG, wherein the calculation process is as follows:
Λ i ＝Λ 0 (1+aε zz )；
in the formula, Λ 0 Initial grating period, ε zz Is the axial average strain of the ith segment, a is the grating strain coefficient, and the expression is as follows:
Figure BDA0003649164160000042
in the formula, n eff0 Is the average effective refractive index of FBG in free state, v is the modulation depth, p 11 And p 12 Respectively setting an optical transfer matrix of each grating segment to generate a 2 x 2T matrix T for effective optical stress tensor components based on modal coupling theory i The following:
Figure BDA0003649164160000043
in the formula, R i And S i Is the amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the i-th section, T i The expression satisfies the following relation:
Figure BDA0003649164160000044
wherein, delta z is the length of the grating segment,
Figure BDA0003649164160000045
and κ is the direct current self-coupling coefficient and the alternating current self-coupling coefficient of the i-th segment, respectively, and the expressions are:
Figure BDA0003649164160000051
Figure BDA0003649164160000052
in the formula, δ n eff The mean value of the refractive index variation over the grating period is defined as
Figure BDA0003649164160000053
Obtaining T matrix T = T of all grating segments by iterative computation N T N-1 T N-2 …T 2 T 1 Then, the following are obtained:
Figure BDA0003649164160000054
in the formula, R 0 、S 0 Is the amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the first section, R L 、S L The amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the tail section;
the reflectivity r of the FBG for each wavelength is calculated as follows:
Figure BDA0003649164160000055
where ρ is the reflection coefficient of FBG, T 21 And T 11 The intermediate calculation results for calculating the reflectivity r are shown as the 1 st number in the 2 nd row and the 1 st number in the 1 st row in the T matrix, respectively.
And obtaining the FBG reflection spectrum in the whole wavelength interval through iterative calculation, and calculating the corresponding FBG reflection spectrum under different crack lengths to obtain the reflection spectrum of the whole crack propagation process.
In the embodiment, simulation can be subdivided into two steps, firstly, crack propagation is simulated through abaqus software, and strain data at the position along the sensor is obtained; and then, converting the strain into a reflection spectrum by using a transmission matrix method, further analyzing the action mechanism of the strain on the reflection spectrum, extracting characteristics and the like. Therefore, reflection spectrum data under multiple groups of crack length samples can be obtained, and the method is low in cost, simple, efficient and feasible compared with the test.
Wherein the extracting of the damage sensitive characteristic value and the reference signal in the reflection spectrum comprises:
the change of the reflection spectrum along with crack propagation is represented by wavelength shift, the wavelength shift can be obtained by subtracting the wavelength of a reference spectrum from the central wavelength under the damage of cracks, and the central wavelength lambda of the reflection spectrum is extracted c Satisfies the following relation:
Figure BDA0003649164160000056
wherein λ represents a reflectance spectrum wavelength, and R (λ) represents a reflectance;
the variation of the broadening of different crack lengths during crack propagation is characterized by the full width of the reflection line at a reflectance value L, wherein the broadening b is expressed by the following relation:
b＝|λL1-λ Lend |；
in the formula, λ L1 Is the wavelength corresponding to the first limit of reflectivity L, and λ Lend The last wavelength for which the reflectivity is a limit value L;
the wave crest number is used for representing the change of the wave crest numbers of different crack lengths in the crack propagation process;
and representing the area change of the reflection spectrums with different crack lengths in the crack propagation process by using the area of the shape surrounded by the reflection spectrum line and the horizontal axis of the coordinate, wherein the area S expression of the normalized reflection spectrums meets the following relational expression:
Figure BDA0003649164160000061
in the formula, λ 1 Is the first wavelength, λ, of the wavelength range of the reflectance spectrum en d is the last wavelength of the wavelength range of the reflectance spectrum,
Figure BDA0003649164160000062
represents a reflection line;
representing the change of the overlapping area of different crack lengths in the crack propagation process by using the overlapping part of the crack-free reference reflection spectral line and each reflection spectrum in the crack propagation process, wherein the overlapping area S is normalized c The expression satisfies the following relation:
Figure BDA0003649164160000063
in the formula, λ s Is the first wavelength, λ, of the coincident range of the wavelengths of the reflection lines e Is the last wavelength of the coincidence range of the wavelengths of the reflection lines,
Figure BDA0003649164160000064
representing coincident reflection lines.
Representing the change of correlation coefficients of different crack lengths in the crack propagation process by using the crack-free reference reflection spectral line and the damage spectrum in the crack propagation process, wherein the correlation coefficient C m Satisfies the following relation:
Figure BDA0003649164160000065
in the formula, ρ 0 As a reference spectral reflectance vector, ρ m Is the damage spectral reflectance vector, N is the length of the reflectance vector,
Figure BDA0003649164160000066
k is the number of reflectivities in the reflectivity vector, k =1,2,.., N, for any wavelength shift relative to the damage spectrum R ；
Characterizing the significance degree of the chirp phenomenon of the reflection spectrum of different crack lengths in the crack propagation process by using a fractal dimension, wherein the fractal dimension FD is calculated by adopting a box counting method, and the expression of the FD satisfies the following relational expression:
Figure BDA0003649164160000071
wherein r is the length of the grid side dividing the image, and r =2 i I =0,1,2, 10, m is the number of grids, and finally a line graph of log (1/r) -log (m) is drawn, and the fractal dimension FD is calculated by taking two points in the log graph to calculate the slope.
It should be noted that the fractal dimension serves as a measure of the irregularity of complex geometric figures. In the embodiment, the box counting method is selected to calculate the fractal dimension of the reflection spectrum, which mainly reflects the significance degree of the chirp phenomenon of the reflection spectrum, wherein the box counting method is meaningful and intuitive, and the calculation is simple and efficient.
When the box counting method is adopted for calculation, firstly, the proportion of a horizontal axis and a vertical axis of a coordinate is set as 1, and a square reflection spectrum is drawn; then removing the coordinate axis and the frame of the image to obtain a pure reflection spectrum graph; dividing the whole square image by using a small grid with the side length of r, and calculating the number m of grids in which the ratio of the parts contained in the reflectance spectrum curve to the parts not contained in the grid is greater than a certain value; finally, a line graph of log (1/r) -log (m) is plotted. The fractal dimension is calculated by taking two points in a logarithmic graph to calculate the slope, and considering that the smaller the grid size is, the finer the grid division is, and the more accurate the fractal description of the reflection spectrum is, therefore, r =2 is selected in the embodiment 0 And r =2 1 The slope is calculated at two points, so that the fractal dimension of the reflection spectrum is calculated by adopting a box counting method, and the method is simple and direct and has high calculation efficiency.
The method for constructing the crack length regression model by taking the damage sensitivity characteristic value as an input and the crack length as an output comprises the following steps:
acquiring crack length sample data set { (x) i ,y i I =1,2, \ 8230;, n }, n being the number of samples of different crack lengths, x i ，y i Respectively an input quantity and an output quantity, where x i ＝{x i1 ，x i2 ，…，x ip To influence crack length y i Damage sensitive characteristic value of (2), y i Is the true crack length for the ith sample, p is the effect y i Wherein the estimation function of the crack length satisfies the following relation:
f(x)＝ωφ(x)+b；
in the formula, omega is weight, phi (x) is a high-dimensional nonlinear function, and b is offset;
solving ω and b requires minimizing the optimization model and introducing a relaxation factor ξ as follows:
Figure BDA0003649164160000072
y i -ωx i -b≤ε+ξ i ；ωx i -y i +b≤ε+ξ i * ；
wherein C is a penalty factor xi i 、ξ i * Introducing alpha for relaxation variables, epsilon for loss function and N for number of training samples i ,
Figure BDA0003649164160000081
The crack length regression model obtained by establishing a Lagrange function by the Lagrange operator to solve the dual problem meets the following relational expression:
Figure BDA0003649164160000082
in the formula, alpha i 、
Figure BDA0003649164160000083
Lagrangian for the ith sample, K (x) i ,x j ) Is a radial basis kernel function, x i ,x j Represents any two samples in the training samples, training samples for a given N crack lengths (x) i I =1,2,., N), one for each training sample consisting of seven features (wavelength shift, broadening, reflection spectral area, 1-coincidence areaWave crest number, 1-correlation coefficient, fractal dimension), for any two crack length samples { x ] in the training sample i ,x j I =1,2,. N; j =1, 2.., N } (with x) j Representing another crack length sample) into the radial basis kernel function computation K (x) i ,x j )。
Wherein the method further comprises: and optimizing the penalty factor C and the variance g of the radial basis kernel function by using a cross-validation method to optimize the crack length regression model. Finally, with R 2 And (4) making an evaluation standard, and then applying a crack length regression model to diagnose the crack length.
In conclusion, the quantitative relation model between the characteristics and the crack length is established by extracting the characteristic values. Specifically, when a support vector regression method is used for establishing a quantitative relation between multiple features and crack length, part of samples are selected from all sample data to serve as training samples, a multiple feature-crack length support vector regression model is trained, the training precision depends on selection of a penalty factor C and a variance g of a radial basis kernel function, C and g can be selected in a successive iteration mode by using a cross verification method, optimal model parameters are obtained, and meanwhile the fitting goodness R2 is used for evaluating the goodness of the training model. Finally, the remaining test sample can be used to diagnose the crack length. Thus, the diagnosis efficiency and the diagnosis accuracy can be improved.
The method steps of the present application are further explained below with a certain simulation example.
In this example, the strain at the crack propagation extraction sensor length location was simulated using the Abaqus finite element simulation software. The mechanical property parameters of the test piece material are shown in table 1, and the sensor parameters are shown in table 2.
TABLE 1 mechanical Property parameters of test piece materials
Figure BDA0003649164160000084
TABLE 2 sensor parameters
Figure BDA0003649164160000085
Figure BDA0003649164160000091
Referring to fig. 2, fig. 2 is a schematic diagram of the size and position of the test piece plate sensor, and in fig. 2, 1 denotes an FBG1;2 denotes FBG2;3 denotes an FBG3;4 denotes an FBG4;5 denotes an FBG5; and 6 denotes an FBG6. Fatigue crack propagation was triggered by introducing a 3mm pre-crack through a 10mm diameter hole in the center of the slab. And applying a constant-amplitude load to the test piece, wherein the maximum loading amplitude is 80MPa, the minimum amplitude is 8MPa, the loading frequency is 5Hz, the boundary of the top of the test piece is fixed, and the bottom of the test piece is applied with an even tensile load of 80 MPa.
In the simulation, the grid formed by linear triangular elements is discretized in the whole test piece plate range, the grid is refined in the right central part of the test piece with expected crack propagation, and the initial crack size is 3mm. The strain distribution along various crack sizes of the FBG1-6 sensors is calculated by using a high-order propagation finite element, and then the strain is reconstructed into a reflection spectrum by using a transmission matrix method.
Referring to fig. 3, fig. 3 is a reflection spectrum of the FBG3 sensor position, wherein 46 sets of crack sample data are extracted, and as the crack propagates, the reflection spectrum generates a position shift chirp phenomenon. Referring to fig. 4, fig. 4 shows the change of the extracted damage features, and it can be determined from fig. 4 that the rule of the change of the features along with the crack length is more obvious, and the features are different, so that the single features are combined to obtain a more comprehensive monitoring result.
And (3) taking the characteristic value of the sample reflectance spectrum as the input of the neural network, taking the corresponding crack length as the output, establishing the relation between the multi-damage sensitive characteristic and the crack length, and realizing the monitoring of the crack length. For each FBG, 36 groups of random samples are selected from 46 groups of crack sample data as training samples, each group of samples contains 7 characteristic values as x i Input, x i The central wavelength, the broadening, the wave peak number, the reflection spectrum area, the coincidence area of the damage spectrum and the health spectrum, the fractal dimension and the correlation corresponding to each sensor7 inputs of coefficient, y i Inputting 1 output quantity corresponding to the crack length of the sample into an SVR neural network for training, and optimizing a penalty factor C and a kernel function g by using a cross-validation method. The remaining 10 groups were tested, and the crack length diagnostic values and errors for all sensor fusions are shown in table 3, which is schematically shown in fig. 5:
TABLE 3 diagnosis of crack length and error
Figure BDA0003649164160000092
Figure BDA0003649164160000101
As can be determined from table 3 and fig. 5, the results of the diagnosis crack length and the actual crack length are very similar, and it can be seen that the diagnosis result of the present application is relatively accurate.
The application also provides a crack diagnosis system based on fiber bragg grating, including setting up in M fiber bragg grating sensors and the processing center of the target structure department of train, M is the positive integer, the processing center with M sensor connection, the processing center is used for:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method;
extracting damage sensitive characteristic values and reference signals in the reflection spectrum, wherein the damage sensitive characteristic values are used for representing the length of the crack, and the reference signals are used for representing no expansion crack;
and taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model.
According to the crack diagnosis system based on the fiber Bragg grating, the fiber Bragg grating sensors arranged at the key positions of the structure can accurately sense the structural strain change caused by the crack, and a crack quantitative monitoring model can be established by extracting the characteristic value capable of representing the crack length in the reflection spectrum of the fiber Bragg grating, so that the real-time monitoring on the crack damage is realized.
The present application further provides a fiber bragg grating based crack diagnosis system, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method when executing the computer program. The crack diagnosis system based on the fiber bragg grating can realize each embodiment of the crack diagnosis method based on the fiber bragg grating, and can achieve the same beneficial effects, and the details are not repeated here.
Embodiments of the present application also provide a computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements the method steps as described above. The readable storage medium can implement the embodiments of the method described above, and can achieve the same beneficial effects, which are not described herein again.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations can be devised by those skilled in the art in light of the above teachings. Therefore, the technical solutions that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the prior art according to the concepts of the present invention should be within the scope of protection determined by the claims.

Claims (7)

1. A crack diagnosis method based on fiber Bragg grating is characterized by comprising the following steps:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method;
extracting damage sensitive characteristic values and reference signals in the reflection spectrum, wherein the damage sensitive characteristic values are used for representing the length of the crack, and the reference signals are used for representing no expansion crack;
taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing cracks based on the crack length regression model;
the reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method comprises the following steps:
setting the length of the uniform grating as L, and when calculating the fiber Bragg grating reflection spectrum under the action of non-uniform strain, uniformly dividing the non-uniform grating into N small sections, wherein N is a positive integer and simultaneously satisfies the requirements
Figure FDA0003914640450000011
λ B For the center wavelength, the expression satisfies the following relation:
λ B ＝2n eff Λ；
wherein Λ is the variation period of the refractive index of the grating, n eff Is the effective refractive index;
regarding the average period of each section in the N small sections as the equivalent period of the section, and regarding the refractive index of each section as the equivalent refractive index of the section;
substituting the parameters of each section into a coupling equation to carry out iterative calculation, wherein the process of calculating the fiber Bragg grating reflection spectrum is as follows:
Λ i ＝Λ 0 (1+aε zz )；
in the formula, Λ 0 Is the initial grating period, epsilon zz And (b) taking the axial average strain of the ith section, wherein a is a grating strain coefficient, and the expression is as follows:
Figure FDA0003914640450000012
in the formula, n eff0 Is the average effective refractive index of FBG in free state, v is the modulation depth, p 11 And p 12 Respectively setting an optical transfer matrix of each grating segment to generate a 2 x 2T matrix T for effective optical stress tensor components based on modal coupling theory i The following were used:
Figure FDA0003914640450000013
in the formula, R i And S i Is the amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the i-th section, T i The expression satisfies the following relationship:
Figure FDA0003914640450000021
wherein, delta z is the length of the grating segment, gamma is the intermediate calculation parameter,
Figure FDA0003914640450000022
and κ is the direct current self-coupling coefficient and the alternating current self-coupling coefficient of the i-th segment, respectively, and the expressions are:
Figure FDA0003914640450000023
Figure FDA0003914640450000024
wherein π is constant and δ n eff The mean value of the refractive index variation over the grating period is defined as
Figure FDA0003914640450000025
Obtained by iterative computationT matrix with grating segments T = T N T N-1 T N-2 …T 2 T 1 Then, the following are obtained:
Figure FDA0003914640450000026
in the formula, R 0 、S 0 Is the amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the first section, R L 、S L The amplitude of the forward transmission mode and the amplitude of the backward transmission mode of the tail section;
the reflectivity r of the FBG for each wavelength is calculated as follows:
Figure FDA0003914640450000027
where ρ is the reflection coefficient of the fiber Bragg grating, T 21 And T 11 The intermediate calculation result of the reflectivity r is calculated, and respectively represents the 1 st number of the 2 nd row and the 1 st number of the 1 st row in the T matrix;
and obtaining the fiber Bragg grating reflection spectrum in the whole wavelength interval through iterative calculation, and calculating the corresponding fiber Bragg grating reflection spectrum under different crack lengths to obtain the reflection spectrum of the whole crack propagation process.
2. The fiber bragg grating based crack diagnosis method according to claim 1, wherein the extracting damage sensitive characteristic values and reference signals in the reflection spectrum includes:
representing the change of the reflection spectrum along with crack propagation by wavelength deviation, wherein the wavelength deviation is obtained by subtracting the central wavelength of a reference signal from the central wavelength under crack damage, and extracting the central wavelength lambda of the reflection spectrum c Satisfies the following relation:
Figure FDA0003914640450000028
wherein λ represents a reflectance spectrum wavelength, and R (λ) represents a reflectance;
the variation of the broadening of different crack lengths during crack propagation is characterized by the full width of the reflection line at a reflectance value L, wherein the broadening b is expressed by the following relation:
b＝|λ L1 -λ Lend |；
in the formula of lambda L1 Is the wavelength corresponding to the first limit of reflectivity L, and λ Lend The wavelength corresponding to the last reflectivity limit value L;
the wave crest number is used for representing the change of the wave crest numbers of different crack lengths in the crack propagation process;
and representing the area change of the reflection spectrum of different crack lengths in the crack propagation process by using the area of the shape surrounded by the reflection spectrum line and the horizontal axis of the coordinate, wherein the area S expression of the normalized reflection spectrum meets the following relational expression:
Figure FDA0003914640450000031
in the formula of lambda 1 Is the first wavelength, λ, of the wavelength range of the reflectance spectrum end Is the last wavelength of the wavelength range of the reflectance spectrum,
Figure FDA0003914640450000036
represents a reflection line;
representing the change of the overlapping area of different crack lengths in the crack propagation process by the overlapping part of the crack-free reference reflection spectral line and each reflection spectrum in the crack propagation process, wherein the overlapping area S is normalized c The expression satisfies the following relation:
Figure FDA0003914640450000032
in the formula, λ s Is the first wavelength, λ, of the coincidence range of the wavelengths of the reflection lines e Is the last of the coincidence range of the wavelengths of the reflection linesOne of the wavelengths of the light beam is selected,
Figure FDA0003914640450000033
representing coincident reflection lines;
representing the change of correlation coefficients of different crack lengths in the crack propagation process by using the crack-free reference reflection spectral line and the damage spectrum in the crack propagation process, wherein the correlation coefficient C m Satisfies the following relation:
Figure FDA0003914640450000034
in the formula, ρ 0 As a reference spectral reflectance vector, ρ m As the spectral reflectance vector of the damage, N R To be the length of the reflectivity vector,
Figure FDA0003914640450000035
for any wavelength shift relative to the damage spectrum, k represents the number of reflectivities in the reflectivity vector (k =1,2 R ) (ii) a (brackets are removed)
Characterizing the significance degree of the reflection spectrum chirp phenomenon of different crack lengths in the crack propagation process by using a fractal dimension, wherein the fractal dimension FD is calculated by adopting a box counting method, and an expression formula meets the following relational expression:
Figure FDA0003914640450000041
wherein r is the length of the grid side dividing the image, wherein r =2 i I =0,1, 2.. 10,m is the number of grids.
3. The fiber bragg grating based crack diagnosis method according to claim 1, wherein the constructing a crack length regression model using the damage sensitivity characteristic value as an input and the crack length as an output comprises:
acquiring a crack length sample data set { (x) i ,y i |i＝1,2, \ 8230;, n }, n being the number of samples of different crack lengths, x i ，y i Respectively an input quantity and an output quantity, where x i ＝{x i1 ，x i2 ，…，x ip To influence crack length y i Damage sensitive eigenvalue of, y i Is the true value of the crack length of the ith sample, p is the influence y i Wherein the estimation function of the crack length satisfies the following relation:
f(x)＝ωφ(x)+b；
in the formula, omega is weight, phi (x) is a high-dimensional nonlinear function, and b is offset;
solving ω and b requires minimizing the optimization model and introducing the relaxation factor ξ as follows:
Figure FDA0003914640450000042
y i -ωx i -b≤ε+ξ i ；ωx i -y i +b≤ε+ξ i * ；
wherein C is a penalty factor xi i 、ξ i * For relaxation variables, e is the loss function, N is the number of training samples, introduce
Figure FDA0003914640450000043
The crack length regression model obtained by establishing a Lagrange function by the Lagrange operator to solve the dual problem meets the following relational expression:
Figure FDA0003914640450000044
in the formula, alpha i 、
Figure FDA0003914640450000045
Lagrangian, K (x), corresponding to the ith sample i ,x j ) Is a radial basis kernel function, x i ,x j Representing any two of the training samplesAnd (4) sampling.
4. The fiber bragg grating based crack diagnosis method as claimed in claim 3, further comprising: and optimizing the penalty factor C and the variance g of the radial basis kernel function by using a cross-validation method so as to optimize the crack length regression model.
5. A crack diagnosis system based on Fiber Bragg Gratings (FBGs) comprises M FBGs (FBGs) arranged at a target structure of a train and a processing center, wherein M is a positive integer, the processing center is connected with the M FBGs, and the processing center is used for:
determining material parameters of a manufacturing material of a structure to be analyzed;
establishing a finite element simulation model according to the material parameters, simulating the crack propagation condition based on the finite element simulation model, and acquiring structural strain data of the crack propagation detected by the fiber Bragg grating sensor under different lengths;
reconstructing the structural strain data into a reflection spectrum by adopting a transmission matrix method;
extracting damage sensitive characteristic values and reference signals in the reflection spectrum, wherein the damage sensitive characteristic values are used for representing the length of the crack, and the reference signals are used for representing no expansion crack;
and taking the damage sensitivity characteristic value as an input, taking the crack length as an output to construct a crack length regression model, and diagnosing the crack based on the crack length regression model.
6. A fiber bragg grating based crack diagnosis system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method as claimed in any one of the preceding claims 1 to 4 when executing the computer program.
7. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method steps of any one of claims 1 to 4.
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