CN112580170A - Bayesian online diagnosis and prediction method for fatigue delamination damage of composite material - Google Patents

Bayesian online diagnosis and prediction method for fatigue delamination damage of composite material Download PDF

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CN112580170A
CN112580170A CN202011589760.2A CN202011589760A CN112580170A CN 112580170 A CN112580170 A CN 112580170A CN 202011589760 A CN202011589760 A CN 202011589760A CN 112580170 A CN112580170 A CN 112580170A
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陈健
袁慎芳
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Abstract

The invention discloses a Bayesian online diagnosis and prediction method for composite material fatigue layered damage, aiming at the fatigue layered damage of a composite material laminated plate, an augmentation state vector comprising a structural fatigue layered damage position variable and an area variable is defined; providing a fatigue layering damage area evolution equation based on an empirical index model and a damage position evolution equation based on a gamma process; under the Bayesian filtering theory framework, the position and the area of the structural fatigue layering damage are jointly diagnosed by combining the structural strain monitoring data based on the fiber bragg grating; and predicting the future evolution process of the layered damage area by combining the diagnosis result to obtain the remaining service life of the structure. The method can effectively realize online joint diagnosis of the layered damage position and area of the composite material and prediction of the remaining service life of the structure, and has important application prospect for ensuring the large application of the composite material structure and realizing the visual maintenance of the composite material structure.

Description

Bayesian online diagnosis and prediction method for fatigue delamination damage of composite material
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a Bayesian online diagnosis and prediction method for fatigue delamination damage of a composite material.
Background
Advanced composite materials, especially high-strength carbon fiber composite materials, are widely applied in the fields of aerospace and the like, and at present, a plurality of key problems exist in high-proportion application of the advanced composite materials in China. For example, the mechanical properties and failure modes of composite materials are much more complex than those of metal structures; and with the development of modern equipment, the load environmental conditions borne by the composite material structure are more and more severe. These issues place higher demands on the safety, reliability, and lifetime of composite structures; and further, the method provides a great challenge for safety assessment and maintenance guarantee of the composite material structure. The development of health monitoring and prediction technology of advanced composite material structures is urgently needed, and the health state of the structures is monitored and predicted in the service process, so that the large-scale application of the composite material structures is guaranteed, the structure design is guided, and the maintenance cost is reduced.
In recent years, a great deal of research has been conducted at home and abroad on the Structure Health Monitoring (SHM) technology of composite materials. The basic idea of SHM is to collect signals related to the structural state through sensors integrated on the structure, and to implement online structural health diagnosis through advanced algorithms. Most studies, however, are concerned with the current diagnosis of the health or damage state of composite structures. There is little research on how to predict the Remaining service Life (RUL) of the structure based on the SHM results, and it is precisely this that it is critical to ensure the mass application of composite structures, to implement context maintenance, and to reduce the cost of structure maintenance. Meanwhile, the existing research on the prediction of the service life of the composite material structure aims at the problem that the damage position is known, namely, the initial damage is prefabricated at the determined position of the structure, and then the evolution process of the damage and the residual service life of the structure are predicted. In practical engineering application, the position of the fatigue damage of the composite material structure caused by manufacturing defects or impact damage is strongly uncertain, and the diagnosis and prediction of the fatigue damage of the structure are greatly influenced.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide a bayesian online diagnosis and prediction method for fatigue delamination damage of composite materials, so as to solve the problems existing in online monitoring and prediction of composite material laminated plate structure in the prior art. The invention realizes the joint online diagnosis of the fatigue damage position and the damage area of the composite material structure by fusing the prior damage evolution model and the online structure health monitoring data through the Bayesian filtering theory, and further realizes the prediction of the residual service life of the structure.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a Bayesian online diagnosis and prediction method for fatigue delamination damage of a composite material, which comprises the following steps:
(1) aiming at the condition that only one fatigue delamination damage exists in the structure of the current composite material laminated plate, defining an augmentation state vector for describing the position and the area of the delamination damage;
(2) describing the evolution rate of the layered damage area under the action of the fatigue load through an empirical index model, and defining an evolution equation of the layered damage area and a model parameter evolution equation thereof; describing an evolution rule of the layered damage position through a gamma random process, and defining an evolution equation of the layered damage position;
(3) arranging a plurality of fiber bragg grating strain sensors on the surface of a current structure to obtain strain distribution of the surface of the structure; obtaining strain distribution data at different layered damage positions and areas in advance through a structure which is the same as the current structure and fiber bragg grating strain sensors at the same arrangement position, and training an observation model based on an artificial neural network through the strain distribution data;
(4) generating a layering damage with unknown position and area in the service process of the current structure; initializing the fatigue expansion time k of the layered damage to be 0; generating a particle set for representing probability distribution of the augmented state vector based on the augmented state vector defined in the step (1);
(5) predicting the evolution of the particle set for representing the probability distribution of the augmented state vector at the moment when k is k +1 in the structural service process based on the damage area evolution equation, the model parameter evolution equation and the damage position evolution equation defined in the step (2);
(6) if the structural strain distribution data is not collected through the fiber bragg grating strain sensors arranged on the surface of the structure at the moment k, repeating the step (5); if structural strain distribution data are collected through the fiber bragg grating strain sensors arranged on the surface of the structure at the moment k, the observation likelihood value of each particle is calculated; updating the weight of each particle according to a Bayes filtering theory, and simultaneously obtaining the posterior probability estimation of the structure damage position and the damage area; realizing the joint diagnosis of the structural layered damage position and the damage area at the moment k;
(7) calculating a damage area evolution prediction result at the k moment based on the posterior probability estimation obtained in the step (6), and realizing the online prediction of the residual service life of the structure at the k moment; resampling the particle set by adopting a system resampling algorithm; regularizing the model parameter component of each particle;
(8) and (5), repeating the steps (5), (6) and (7) to realize the combined online diagnosis of the layered damage position and the damage area of the structure at different k moments and the prediction of the residual service life of the structure until the structure is damaged at the k moment.
Further, the augmented state vector in the step (1) is defined as xkThe subscript k denotes the discrete time; x is the number ofk＝[zk,hk,θk]，zkDenotes the area of the structural layer damage at time k, hkCoordinate vector, θ, representing the lesion at time kkThe parameters of the model describing the evolution of the lesion for time k.
Further, the evolution rate of the layered damage area under the action of the fatigue load is described in the step (2) through an empirical index model, as shown below,
Figure BDA0002868574420000021
in the formula, zk-1The structural layered damage area at the time of k-1; z is a radical ofkThe damage area at the time k; n is the number of fatigue load cycles borne by the structure;
Figure BDA0002868574420000022
representing the evolution rate of the area of the stratified lesion, betakAnd ηkModel parameters at the time k are obtained;
the evolution equation of the damage area based on the empirical index model is defined as follows:
Figure BDA0002868574420000031
in the formula, Δ N is the load cycle number step, i.e. the number of load cycles that the structure undergoes from time k-1 to time k;
Figure BDA0002868574420000032
the increment of the damage area is characterized; omegakCharacterizing uncertainty of lesion evolution for random variables, which obey a Gaussian distribution
Figure BDA0002868574420000033
σωIs the standard deviation of the gaussian distribution;
the model parameter vector is defined as thetak＝[βk,ηk](ii) a The model parameter evolution equation is defined as:
θk＝θk-1
in the formula, thetak-1The parameters of the model describing the evolution of the lesion for time k-1.
Further, the damage position vector in the step (2) is defined as hk＝[h1,k,h2,k]，h1,kRepresenting the coordinate of the layered damage at the moment k in the X direction; h is2,kRepresenting the coordinate of the layered damage at the moment k in the Y direction; the evolution equation of the hierarchical lesion position based on the gamma process is defined as follows:
Figure BDA0002868574420000034
in the formula, h1,k-1Representing the coordinate of the layered damage at the k-1 moment in the X direction; h is2,k-1Representing the coordinate of the layered damage at the k-1 moment in the Y direction; epsilon1kAnd ε2kAre random variables, all obey Gaussian distribution
Figure BDA0002868574420000035
σεIs the standard deviation of the gaussian distribution.
Further, the observation model g (-) based on the artificial neural network obtained by training the strain distribution data in the step (3) is represented as follows:
y＝g([h,z])
in the formula, [ h, z ] is an input vector and represents an arbitrary layered damage position h and a damage area z; and y is an output vector and represents the strain distribution of the structure surface, and the elements of the output vector are strain values of various strain measurement points of the structure surface.
Further, initializing a particle set representing probability distribution of the augmented state vector in the step (4) specifically includes:
(41) setting the number N of particles used to characterize the probability distribution of augmented state vectorss；
(42) Defining the location h of the lesionk＝0Is uniformly distributed UhArea of damage zk＝0Is uniformly distributed UzModel parameter θk＝0＝[βk＝0,ηk＝0]Is uniformly distributed Uθ；
(43) Randomly sampling N from the prior probability distributions, respectivelysObtaining a sample
Figure BDA0002868574420000036
Figure BDA0002868574420000041
And
Figure BDA0002868574420000042
wherein,
Figure BDA0002868574420000043
the ith sample of lesion locations representing the initial time,
Figure BDA0002868574420000044
represents the ith sample of lesion area at the initial time,
Figure BDA0002868574420000045
an ith model parameter sample at the initial moment;
(44) combining the above samples to obtain particles, i.e. augmented state vector samples
Figure BDA0002868574420000046
Figure BDA0002868574420000047
Represents the ith particle at the initial time; initializing the weight of each particle at the same time to
Figure BDA0002868574420000048
Figure BDA0002868574420000049
Denotes the normalized weight of the ith particle, i ═ 1,2, …, Ns。
Further, predicting the evolution of the set of particles characterizing the probability distribution of the augmented state vector in step (5) is performed by:
Figure BDA00028685744200000410
in the formula,
Figure BDA00028685744200000411
the damage surface integral quantity of the ith particle at the k-1 moment is taken as the damage surface integral quantity of the ith particle;
Figure BDA00028685744200000412
the damage surface integral quantity of the ith particle at the k moment is taken as the damage surface integral quantity of the ith particle;
Figure BDA00028685744200000413
and
Figure BDA00028685744200000414
the model parameter component of the ith particle at the moment k-1;
Figure BDA00028685744200000415
and
Figure BDA00028685744200000416
the model parameter component of the ith particle at the moment k;
Figure BDA00028685744200000417
from a Gaussian distribution for time k
Figure BDA00028685744200000418
Sampling the obtained random number;
Figure BDA00028685744200000419
the damage coordinate X component of the ith particle at the k-1 moment is taken as the damage coordinate X component of the ith particle;
Figure BDA00028685744200000420
the damage coordinate X component of the ith particle at the k moment is taken as the damage coordinate X component of the ith particle;
Figure BDA00028685744200000421
the damage coordinate Y component of the ith particle at the k-1 moment is taken as the damage coordinate Y component of the ith particle;
Figure BDA00028685744200000422
the damage coordinate Y component of the ith particle at the k moment is taken as the damage coordinate Y component of the ith particle;
Figure BDA00028685744200000423
and
Figure BDA00028685744200000424
from a Gaussian distribution for time k
Figure BDA00028685744200000425
Sampling the obtained random number; the new set of particles obtained is represented by
Figure BDA00028685744200000426
Figure BDA00028685744200000427
Further, the observation likelihood value of each particle in the step (6) is defined as
Figure BDA00028685744200000428
ykThe structural surface strain monitoring data acquired at the moment k specifically comprises the following data: sequentially mixing the particles
Figure BDA00028685744200000429
Component (b) of
Figure BDA00028685744200000430
Inputting the strain vector into an observation model g (-) to obtain the corresponding strain vector output
Figure BDA00028685744200000431
Figure BDA00028685744200000432
Is the strain vector corresponding to the ith particle,
Figure BDA00028685744200000433
is composed of
Figure BDA00028685744200000434
J ═ 1,2, …, n, data characterizing the j-th strain monitoring point; n is the number of strain monitoring points; calculating an observation likelihood byThe value:
Figure BDA0002868574420000051
in the formula,
Figure BDA0002868574420000052
the observed likelihood value of the ith particle at the jth strain monitoring point at the time k is calculated as follows,
Figure BDA0002868574420000053
in the formula, σv,kThe standard deviation of the observed noise at the moment k; y isj,kFor strain observation vector ykThe jth element of (a), data characterizing the jth strain monitoring point on the actual structure.
Further, the posterior probability estimation of the structure damage position and the damage area is obtained in the step (6), and the joint diagnosis of the structure layered damage position and the damage area at the time k is realized, as shown in the following formula:
Figure BDA0002868574420000054
Figure BDA0002868574420000055
in the formula,
Figure BDA0002868574420000056
estimating posterior probability of the layered damage area at the moment of the structure k, namely obtaining a diagnosis result of the damage area;
Figure BDA0002868574420000057
estimating posterior probability of the layered damage position at the moment k, namely obtaining a diagnosis result of the damage position;
Figure BDA0002868574420000058
the normalized weight of the ith particle is obtained through likelihood value calculation.
Further, the damage area evolution at the future time is predicted in the step (7), and the damage area evolution is realized by sequentially iterating the damage area integral quantity of the ith particle through a damage area evolution equation, as shown in the following formula:
Figure BDA0002868574420000059
wherein k + l represents a future time, l ═ 1,2,3, … n;
Figure BDA00028685744200000510
showing the delamination damage area of the ith particle at the time k + l-1,
Figure BDA00028685744200000511
is the delamination damage area of the ith particle at the time k + l,
Figure BDA00028685744200000512
is from a Gaussian distribution
Figure BDA00028685744200000513
Sampling the obtained random number; k + l is the future time, the strain distribution data is not obtained to update the particle weight, so the model parameter
Figure BDA00028685744200000514
And
Figure BDA00028685744200000515
the value at time k is maintained.
The invention has the beneficial effects that:
according to the method, the evolution rate of the fatigue hierarchical damage area is described through an empirical index model, the evolution rule of the hierarchical damage position is described through a gamma random process, online structure strain monitoring data are fused by adopting a Bayes filtering theory, the joint diagnosis of the damage area and the damage position and the prediction of the remaining service life of the structure can be realized, and the method can be effectively used for online diagnosis and prediction of the fatigue hierarchical damage of the composite material structure.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a composite material reinforcement structure of finite element simulation in the embodiment.
Fig. 3a is a schematic diagram of fatigue delamination damage at 0 load cycles.
FIG. 3b shows the signal level at 1.74X 105Fatigue delamination damage schematic at each load cycle.
FIG. 3c is a graph of 2.35X 105Fatigue delamination damage schematic at each load cycle.
FIG. 3d is a graph showing a graph of 2.71X 105Fatigue delamination damage schematic at each load cycle.
FIG. 3e shows the ratio of 2.75X 105Fatigue delamination damage schematic at each load cycle.
FIG. 3f shows the average particle size of 2.78X 105Fatigue delamination damage schematic at each load cycle.
Fig. 4 is a schematic diagram of a fiber grating strain sensor arrangement simulated in the embodiment.
FIG. 5 is a graph of simulated fiber grating strain monitoring data in an example.
FIG. 6 is a diagram showing the diagnosis result of the structural stratification lesion area in the example.
FIG. 7 is a diagram showing the diagnosis result of the lesion site of the structural hierarchy in the embodiment.
FIG. 8 is a diagram illustrating the prediction of the evolution of the future structure layer damage area in the embodiment.
Fig. 9 is a schematic diagram of a prediction result of the remaining service life of the structure in the embodiment.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the bayesian online diagnosis and prediction method for fatigue delamination damage of a composite material of the present invention is applied to a composite material laminated plate structure, and the specific implementation steps are as follows:
(1) for the composite material laminated plate structure, the impact of an external object borne in the service process can generate layered damage in the structure, and the position and the area of the layered damage are unknown; in the subsequent process of bearing alternating fatigue load, the delamination damage can be gradually expanded, and the structure is finally damaged; assuming that there is only one fatigue delamination damage in the structure, the augmented state vector describing the damage is defined as xkWherein the subscript k represents discrete time instants; this augmented state vector xkConsisting of three parts, xk＝[zk,hk,θk]Wherein z iskRepresents the fatigue delamination damage area, h, of the structure at time kkCoordinate vector, θ, representing fatigue delamination damage location of structure at time kkDescribing parameters of a model of damage evolution for time k;
(2) describing the evolution rate of the layered damage area under the action of the fatigue load through an empirical index model, wherein the evolution rate is shown as the following formula:
Figure BDA0002868574420000061
in the formula, zk-1The structural layered damage area at the time of k-1; z is a radical ofkThe damage area at the time k; n is the number of fatigue load cycles borne by the structure;
Figure BDA0002868574420000071
representing the evolution rate of the area of the stratified lesion, betakAnd ηkModel parameters at the time k are obtained;
the evolution equation of the damage area based on the empirical index model is defined as follows:
Figure BDA0002868574420000072
in the formula, Δ N is the load cycle number step, i.e. the number of load cycles that the structure undergoes from time k-1 to time k;
Figure BDA0002868574420000073
the increment of the damage area is characterized; omegakCharacterizing uncertainty of lesion evolution for random variables, which obey a Gaussian distribution
Figure BDA0002868574420000074
σωIs the standard deviation of the gaussian distribution.
Meanwhile, the model parameter vector is defined as thetak＝[βk,ηk]The evolution equation over time is defined as follows,
θk＝θk-1
(3) considering that once the structural fatigue layering damage occurs, the position of the structural fatigue layering damage does not change greatly in the subsequent structural service process, a damage coordinate vector h is definedk＝[h1,k,h2,k]And assuming that the evolution law is a gamma random process; h is1,kRepresenting the coordinate of the layered damage at the moment k in the X direction; h is2,kRepresenting the coordinate of the layered damage at the moment k in the Y direction; the evolution equation of the hierarchical lesion position based on the gamma process is defined as follows:
Figure BDA0002868574420000075
in the formula, h1,k-1Representing the coordinate of the layered damage at the k-1 moment in the X direction; h is2,k-1Representing the coordinate of the layered damage at the k-1 moment in the Y direction; epsilon1,kAnd ε2,kAre random variables, all obey a Gaussian distribution
Figure BDA0002868574420000076
σεIs the standard deviation of the gaussian distribution;
(4) arranging a plurality of fiber bragg grating strain sensors on the surface of the current structure, and strain the sensors through the fiber bragg gratingsAcquiring strain distribution data of the surface of the structure by using a demodulation device; recording the obtained strain distribution data as a vector y ═ y1,y2,...,yn]，ynAcquiring a strain value for the nth strain monitoring point, wherein n is the number of strain monitoring points arranged on the structure; before the structure is in service, strain distribution data under different layered damage positions and areas, namely different damage positions and damage areas [ h ], are obtained in advance through the fiber bragg grating strain sensors with the same structure and the same arrangement positions as the current structurem,zm]Corresponding strain monitoring data ymForm a training data set
Figure BDA0002868574420000077
The subscript M represents the mth data sample in the training data set, and the total number of the samples is M; the observation model g (-) based on the artificial neural network obtained by the sample training is represented as follows:
y＝g([h,z])
in the formula, [ h, z ] is an input vector and represents an arbitrary layered damage position h and a damage area z; y is the output vector.
(5) The steps (1), (2), (3) and (4) are completed before the structure is in service; in the service process of the structure, generating a layering damage with unknown position and area; initializing the fatigue expansion time k of the layered damage to be 0; setting the number N of particles used to characterize the probability distribution of augmented state vectorss(ii) a Meanwhile, the layered damage position and area of the structure are unknown, and the damage position h is definedk＝0Is uniformly distributed UhArea of damage zk＝0Is uniformly distributed UzModel parameter θk＝0＝[βk＝0,ηk＝0]Is uniformly distributed Uθ(ii) a Randomly sampling N from the prior probability distributions respectivelysObtaining a sample
Figure BDA0002868574420000081
Figure BDA0002868574420000082
And
Figure BDA0002868574420000083
Figure BDA0002868574420000084
the ith sample of lesion locations representing the initial time,
Figure BDA0002868574420000085
represents the ith sample of lesion area at the initial time,
Figure BDA0002868574420000086
an ith model parameter sample at the initial moment; combining these samples to obtain particles, i.e. augmented state vector samples
Figure BDA0002868574420000087
Figure BDA0002868574420000088
Represents the ith particle at the initial time; initializing the weight of each particle at the same time to
Figure BDA0002868574420000089
Wherein
Figure BDA00028685744200000810
Normalized weight value i of i-th particle is 1,2, …, Ns；
(6) At the moment when k is k +1 in the structural service process, predicting the evolution of the particle set representing the probability distribution of the augmented state vector based on the damage area evolution equation, the model parameter evolution equation and the damage position evolution equation defined in the step (2), as shown in the following formula:
Figure BDA00028685744200000811
in the formula,
Figure BDA00028685744200000812
the damage surface integral quantity of the ith particle at the k-1 moment is taken as the damage surface integral quantity of the ith particle;
Figure BDA00028685744200000813
the damage surface integral quantity of the ith particle at the k moment is taken as the damage surface integral quantity of the ith particle;
Figure BDA00028685744200000814
and
Figure BDA00028685744200000815
the model parameter component of the ith particle at the moment k-1;
Figure BDA00028685744200000816
and
Figure BDA00028685744200000817
the model parameter component of the ith particle at the moment k;
Figure BDA00028685744200000818
from a Gaussian distribution for time k
Figure BDA00028685744200000819
Sampling the obtained random number;
Figure BDA00028685744200000820
the damage coordinate X component of the ith particle at the k-1 moment is taken as the damage coordinate X component of the ith particle;
Figure BDA00028685744200000821
the damage coordinate X component of the ith particle at the k moment is taken as the damage coordinate X component of the ith particle;
Figure BDA00028685744200000822
the damage coordinate Y component of the ith particle at the k-1 moment is taken as the damage coordinate Y component of the ith particle;
Figure BDA00028685744200000823
damage coordinate of ith particle at k timeA Y component;
Figure BDA00028685744200000824
and
Figure BDA0002868574420000091
from a Gaussian distribution for time k
Figure BDA0002868574420000092
Sampling the obtained random number; the particle set obtained by sampling is represented as
Figure BDA0002868574420000093
Figure BDA0002868574420000094
(7) The fiber bragg grating strain demodulation equipment automatically carries out strain data acquisition operation according to a specific time interval, and if structural strain distribution data are not acquired through the fiber bragg grating strain sensors arranged on the surface of the structure at the moment k, the step (6) is repeated; if the strain distribution data y of the structure is collected by the fiber bragg grating strain sensor arranged on the surface of the structure at the moment kk＝[y1,k,y2,k,...,yn,k]Sequentially carrying out the subsequent steps (8) - (16); y isj,kRepresenting a strain value obtained by the jth strain monitoring point at the k moment;
(8) sequentially mixing the particles
Figure BDA0002868574420000095
Component (b) of
Figure BDA0002868574420000096
Inputting the strain vector into an artificial neural network observation model g (-) to obtain the corresponding strain vector output
Figure BDA0002868574420000097
Figure BDA0002868574420000098
For the ith granule at time kOutputting strain observation vectors corresponding to the son;
Figure BDA0002868574420000099
is composed of
Figure BDA00028685744200000910
The j element in the strain monitoring point represents a strain value obtained by the j strain monitoring point; calculating the observed likelihood value of each particle in turn
Figure BDA00028685744200000911
As follows:
Figure BDA00028685744200000912
in the formula,
Figure BDA00028685744200000913
the calculation method is that the observed likelihood value of the ith particle at the jth strain monitoring point at the k moment is as follows:
Figure BDA00028685744200000914
in the formula, σv,kIs the standard deviation of the observation uncertainty at time k; y isj,kFor strain observation vector ykThe jth element of (a), representing data of the jth strain monitoring point on the actual structure;
(9) the weight of each particle is calculated in turn as shown in the following formula:
Figure BDA00028685744200000915
Figure BDA00028685744200000916
in the formula,
Figure BDA00028685744200000917
the non-normalized weight of the ith particle at the moment k;
Figure BDA00028685744200000918
the normalized weight of the ith particle at the moment k is obtained;
Figure BDA00028685744200000919
the normalized weight of the ith particle at the moment of k-1;
(10) according to Bayesian filtering theory, the particle set obtained through the step (6) is
Figure BDA0002868574420000101
Substantially characterizing the transition from a prior to a probability density function
Figure BDA0002868574420000102
Sampling the obtained sample; these samples are compared with the observed value y of the strain at the current k timekUpdated particle weight
Figure BDA0002868574420000103
Jointly characterize the augmented state vector xkThe posterior probability density function of (a) is shown as follows:
Figure BDA0002868574420000104
in the formula, y1:kSet of representations y1,y2,...,yk}；y1Denotes yk＝1，y2Denotes yk＝2(ii) a δ (-) is a Dirac function, whose expression is as follows:
Figure BDA0002868574420000105
(11) calculating an area posterior probability estimate of the current stratified lesion as shown in the following formula:
Figure BDA0002868574420000106
in the formula,
Figure BDA0002868574420000107
the posterior probability estimation of the structural layered damage area at the moment k is the diagnosis result of the structural damage area at the moment k; calculating a posterior probability estimate of the location of the current stratified lesion as shown in the following equation:
Figure BDA0002868574420000108
Figure BDA0002868574420000109
in the formula,
Figure BDA00028685744200001010
for the posterior probability estimation of X-coordinate of the structural hierarchical lesion location at time k,
Figure BDA00028685744200001011
the posterior probability estimation of the Y coordinate of the structural layered damage position at the moment k is the diagnosis result of the structural damage position at the moment k;
since the diagnosis result of the damaged area is obtained at the same time
Figure BDA00028685744200001012
And the diagnosis result of the lesion site
Figure BDA00028685744200001013
Therefore, the method can realize the joint diagnosis of the hierarchical damage position and the damage area of the structure at the moment k;
(12) sequentially calculating the evolution process of the damage area of the ith particle at the future moment according to the estimation result of the posterior probability:
Figure BDA00028685744200001014
where k + l denotes the future time, l ═ 1,2,3, …;
Figure BDA00028685744200001015
showing the delamination damage area of the ith particle at the time k + l-1,
Figure BDA00028685744200001016
is the delamination damage area of the ith particle at the time k + l,
Figure BDA00028685744200001017
is from a Gaussian distribution
Figure BDA00028685744200001018
Sampling the obtained random number; since strain distribution data is not obtained to update the particle weights at the time when k + l is the future time, the model parameters
Figure BDA0002868574420000111
And
Figure BDA0002868574420000112
holding the value at time k;
sequentially calculating the remaining service life of the structure corresponding to each particle according to the damage area evolution prediction result, as shown in the following formula,
Figure BDA0002868574420000113
in the formula,
Figure BDA0002868574420000114
the time of structural failure corresponding to the ith particle is shown, and the hierarchical damage area of the particle is shown
Figure BDA0002868574420000115
Exceeding a predefined threshold value zthThe time of day;
Figure BDA0002868574420000116
the residual service life of the structure corresponding to the ith particle is represented by k, and the k is the current moment;
the posterior probability distribution of the remaining useful life of the target structure at time k is then expressed as follows:
Figure BDA0002868574420000117
in the formula, RULkThe remaining service life of the structure at time k;
(13) resampling the particles according to the normalized weight values of the particles, comprising the following steps:
(a) the cumulative number sequence W of all particle normalized weights is calculated as follows:
Figure BDA0002868574420000118
in the formula,
Figure BDA0002868574420000119
the normalized weight of the ith particle at the moment k is obtained;
(b) randomly sampling from the uniformly distributed U (0,1) to obtain a value U;
(c) calculating resampling weights q in sequence(r)＝u+(r-1)/Ns，r＝1,2,…,Ns；
(d) Sequentially searching the first more than q in the sequence W(r)The element (2) is numbered as(r)Obtaining an r-th resampled particle of
Figure BDA00028685744200001110
The weight of the particles is set as
Figure BDA00028685744200001111
(14) Resampled particles
Figure BDA00028685744200001112
The model parameter component in (1) is regularized to solve the problem of diversity deficiency of the model parameter component: the resampled particle set is recorded
Figure BDA00028685744200001113
Wherein the model parameter components are respectively
Figure BDA00028685744200001114
Wherein
Figure BDA00028685744200001115
And
Figure BDA00028685744200001116
is the model parameter component in the r-th particle after resampling; and sequentially carrying out regularization treatment on the model parameter samples, as shown in the following formula:
Figure BDA00028685744200001117
Figure BDA00028685744200001118
in the formula,
Figure BDA00028685744200001119
and
Figure BDA00028685744200001120
regularizing the model parameter component for the r-th particle; alpha is alpha(r)Is a random number sampled from a standard Epanechnikov kernel function; a iskAs a sample set
Figure BDA0002868574420000121
The variance of (a); bkAs a sample set
Figure BDA0002868574420000122
The variance of (a); h is the regularization window width;
(15) samples after resampling and regularization
Figure BDA0002868574420000123
Replacement of sets of particles
Figure BDA0002868574420000124
To obtain a new set of particles
Figure BDA0002868574420000125
By weight
Figure BDA0002868574420000126
Corresponding replacement weight
Figure BDA0002868574420000127
(16) And (5) repeating the steps (6) to (15) to realize the combined online diagnosis of the layered damage position and the damage area of the structure at different k moments and the prediction of the residual service life of the structure until the structure is damaged at the k moment.
In the embodiment, a reinforced composite material structure of finite element simulation is taken as an example to explain the specific implementation process of the method. FIG. 2 shows a composite stiffened structure of a finite element simulation, with dimensions 270X 320 mm. The structure is made of carbon fiber prepreg, the layering of the skin is [ -45,0,45, -45, -45,45,90,0] s, the thickness of each layer is 0.2mm, and the mechanical properties are shown in Table 1. In addition, the ply of the ribs was [90, -45,45,90,0, -45,45], 45mm in width and 23mm in height.
TABLE 1
Figure BDA0002868574420000128
And simulating structural fatigue delamination damage propagation by adopting a virtual crack closure technology of finite element software ABAQUS. The delamination damage is located between the structural ribs and the skin, as shown in fig. 2. The bottom end of the structure is fixedly supported, and the top end of the structure restrains other degrees of freedom except the translation in the Y direction. Then, a compressive fatigue load in the Y direction was applied to the tip of the structure, and the peak value and the bottom value of the fatigue load were 2mm and 0.2mm, respectively. The virtual crack closure technical parameters simulating fatigue delamination damage propagation are shown in table 2. It is assumed that the initial delamination damage due to external impact is as shown in fig. 3a, the damage being located between the structural ribs and the skin. After a certain load cycle, the fatigue delamination gradually expands, as shown in fig. 3b, fig. 3c, fig. 3d, fig. 3e, fig. 3 f.
TABLE 2
Figure BDA0002868574420000129
As shown in steps (1), (2) and (3), an augmented state vector and a state evolution equation of the structure are first defined. Since in this example the hierarchical lesion location is assumed to occur at the edge of a rib, the hierarchical lesion location vector need only contain the Y-direction coordinate variable, i.e., hk＝[h2,k]When the augmented state vector is defined as xk＝[zk,h2,k,θk]。
Furthermore, as shown in step (4), a plurality of fiber grating strain sensors are arranged on the upper surface of the rib structure in a simulated manner, as shown in fig. 4. Along the fiber, 22 strain monitoring points were arranged in an analog manner, with the spacing between each monitoring point being 12 mm. Typical strain monitoring data obtained for the surface of the structure by the analog sensor is shown in fig. 5, which is the relative change in strain with respect to the intact state. In addition, 35 additional examples were simulated by the finite element method, which had different positions of the initial delamination damage from the current structure, with the Y-coordinates of the initial delamination damage positions being 75mm, 80mm, …, 245mm, respectively. A training data set was composed based on the results of these 35 examples
Figure BDA0002868574420000131
Training to obtain an observation mapping model g (-) based on the artificial neural network, wherein h2,mThe Y-coordinate representing the centroid of the stratified lesion. In this example, a multilayer perceptron artificial neural network is adopted, the number of hidden layers is 2, and the number of hidden layer neurons is 10. Input is [ h ]2,z]The output is strain monitoring data
Figure BDA0002868574420000132
Wherein h is2Is the Y coordinate of the position of the injury in any layer, z is the area of the injury in any layer, Y*To output strain data.
As shown in step (5), the initial damage position and area of the target structure are unknown, and the initialization time k is 0. Setting a sufficient number of particles Ns5000 a; setting initial delamination damage position obeying uniform distribution h2,k＝0U (70,250); the initial stratified lesion area is equally amenable to uniform distribution zk＝0～U(0,400)；
Model parameter betak＝0Is obtained from the following formula:
log(βk＝0)＝-2.53×10-3(h2,k＝0)2+0.814(h2,k＝0)-81.6
model parameter ηk＝0Is obtained from the following formula:
ηk＝0＝-0.14·log(βk＝0)-0.32
and randomly sampling from the initial distributions to obtain initial particle sets, and initializing particle weights. In addition, a random variable ω representing uncertainty in fatigue stratified damage evolutionkIs set to sigmaω0.5; meanwhile, a random variable epsilon for representing evolution uncertainty of damage positionkIs set to sigmaε0.05, the fatigue cycle load step size Δ N is 200.
As shown in steps (6) - (16), at the time when k is k +1 in the structure service process, the probability distribution of the characteristic augmented state vector is predicted based on the state evolution equation defined aboveEvolution of the set of particles. If a strain observation y is obtainedkAnd updating the particle weight according to the Bayes filter theory to obtain the posterior probability estimation of the structure damage position and the damage area as the combined diagnosis result of the damage position and the damage area, as shown in FIG. 6 and FIG. 7. It can be seen that the method of the invention can accurately estimate the area of fatigue delamination damage at the current moment. Meanwhile, along with the expansion of the damage, after enough online strain observation data are obtained, the position of the damage can be accurately positioned. Further, on the basis of the diagnosis result, the particles are projected to the future moment to obtain a prediction result of the evolution of the hierarchical damage area of each particle, as shown in fig. 8. Defining the threshold value of the area of the layered lesion as zth＝2000mm2The remaining useful life prediction result of the structure can be obtained as shown in fig. 9. After 15 ten thousand load cycles, the method of the invention obtains a more accurate prediction result of the residual service life of the structure.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (10)

1. A Bayesian online diagnosis and prediction method for fatigue delamination damage of composite materials is characterized by comprising the following steps:
(1) aiming at the condition that only one fatigue delamination damage exists in the structure of the current composite material laminated plate, defining an augmentation state vector for describing the position and the area of the delamination damage;
(2) describing the evolution rate of the layered damage area under the action of the fatigue load through an empirical index model, and defining an evolution equation of the layered damage area and a model parameter evolution equation thereof; describing an evolution rule of the layered damage position through a gamma random process, and defining an evolution equation of the layered damage position;
(3) arranging a plurality of fiber bragg grating strain sensors on the surface of a current structure to obtain strain distribution of the surface of the structure; obtaining strain distribution data at different layered damage positions and areas in advance through a structure which is the same as the current structure and fiber bragg grating strain sensors at the same arrangement position, and training an observation model based on an artificial neural network through the strain distribution data;
(4) generating a layering damage with unknown position and area in the service process of the current structure; initializing the fatigue expansion time k of the layered damage to be 0; generating a particle set for representing probability distribution of the augmented state vector based on the augmented state vector defined in the step (1);
(5) predicting the evolution of the particle set for representing the probability distribution of the augmented state vector at the moment when k is k +1 in the structural service process based on the damage area evolution equation, the model parameter evolution equation and the damage position evolution equation defined in the step (2);
(6) if the structural strain distribution data is not collected through the fiber bragg grating strain sensors arranged on the surface of the structure at the moment k, repeating the step (5); if structural strain distribution data are collected through the fiber bragg grating strain sensors arranged on the surface of the structure at the moment k, the observation likelihood value of each particle is calculated; updating the weight of each particle according to a Bayes filtering theory, and simultaneously obtaining the posterior probability estimation of the structure damage position and the damage area; realizing the joint diagnosis of the structural layered damage position and the damage area at the moment k;
(7) calculating a damage area evolution prediction result at the k moment based on the posterior probability estimation obtained in the step (6), and realizing the online prediction of the residual service life of the structure at the k moment; resampling the particle set by adopting a system resampling algorithm; regularizing the model parameter component of each particle;
(8) and (5), repeating the steps (5), (6) and (7) to realize the combined online diagnosis of the layered damage position and the damage area of the structure at different k moments and the prediction of the residual service life of the structure until the structure is damaged at the k moment.
2. The Bayesian online diagnosis and prediction method for composite fatigue stratified damage as recited in claim 1, wherein the Bayesian online diagnosis and prediction method is characterized in that the Bayesian online diagnosis and prediction method is used for the composite fatigue stratified damageThe augmented state vector in step (1) is defined as xkThe subscript k denotes the discrete time; x is the number ofk＝[zk,hk,θk]，zkDenotes the area of the structural layer damage at time k, hkCoordinate vector, θ, representing the lesion at time kkThe parameters of the model describing the evolution of the lesion for time k.
3. The Bayesian online diagnosis and prediction method for fatigue delamination damage of composite material according to claim 1, wherein the evolution rate of the delamination damage area under the fatigue load is described in the step (2) through an empirical index model as follows:
Figure FDA0002868574410000021
in the formula, zk-1The structural layered damage area at the time of k-1; z is a radical ofkThe damage area at the time k; n is the number of fatigue load cycles borne by the structure;
Figure FDA0002868574410000022
representing the evolution rate of the area of the stratified lesion, betakAnd ηkModel parameters at the time k are obtained;
the evolution equation of the damage area based on the empirical index model is defined as follows:
Figure FDA0002868574410000023
in the formula, Δ N is the load cycle number step, i.e. the number of load cycles that the structure undergoes from time k-1 to time k;
Figure FDA0002868574410000024
the increment of the damage area is characterized; omegakCharacterizing uncertainty of lesion evolution for random variables, which obey a Gaussian distribution
Figure FDA0002868574410000025
σωIs the standard deviation of the gaussian distribution;
the model parameter vector is defined as thetak＝[βk,ηk](ii) a The model parameter evolution equation is defined as:
θk＝θk-1
in the formula, thetak-1The parameters of the model describing the evolution of the lesion for time k-1.
4. The Bayesian online diagnosis and prediction method for composite fatigue delamination failure as recited in claim 1, wherein the failure location vector in the step (2) is defined as hk＝[h1,k,h2,k]，h1,kRepresenting the coordinate of the layered damage at the moment k in the X direction; h is2,kRepresenting the coordinate of the layered damage at the moment k in the Y direction; the evolution equation of the hierarchical lesion position based on the gamma process is defined as follows:
Figure FDA0002868574410000026
in the formula, h1,k-1Representing the coordinate of the layered damage at the k-1 moment in the X direction; h is2,k-1Representing the coordinate of the layered damage at the k-1 moment in the Y direction; epsilon1,kAnd ε2,kAre random variables, all obey Gaussian distribution
Figure FDA0002868574410000027
σεIs the standard deviation of the gaussian distribution.
5. The Bayesian online diagnosis and prediction method for composite fatigue delamination failure as recited in claim 1, wherein the observed model g (-) based on artificial neural network obtained by training strain distribution data in the step (3) is represented as follows:
y＝g([h,z])
in the formula, [ h, z ] is an input vector and represents an arbitrary layered damage position h and a damage area z; and y is an output vector and represents the strain distribution of the structure surface, and the elements of the output vector are strain values of various strain measurement points of the structure surface.
6. The Bayesian online diagnosis and prediction method for composite fatigue delamination failure as recited in claim 1, wherein the initializing a particle set characterizing probability distribution of augmented state vectors in the step (4) specifically comprises:
(41) setting the number N of particles used to characterize the probability distribution of augmented state vectorss；
(42) Defining the location h of the lesionk＝0Is uniformly distributed UhArea of damage zk＝0Is uniformly distributed UzModel parameter θk＝0＝[βk＝0,ηk＝0]Is uniformly distributed Uθ；
(43) Randomly sampling N from the prior probability distributions, respectivelysObtaining a sample
Figure FDA0002868574410000031
Figure FDA0002868574410000032
And
Figure FDA0002868574410000033
wherein,
Figure FDA0002868574410000034
the ith sample of lesion locations representing the initial time,
Figure FDA0002868574410000035
represents the ith sample of lesion area at the initial time,
Figure FDA0002868574410000036
an ith model parameter sample at the initial moment;
(44) combining the above samples to obtain particles, i.e. augmented state vector samples
Figure FDA0002868574410000037
Figure FDA0002868574410000038
Represents the ith particle at the initial time; initializing the weight of each particle at the same time to
Figure FDA0002868574410000039
Figure FDA00028685744100000310
Denotes the normalized weight of the ith particle, i ═ 1,2, …, Ns。
7. The Bayesian online diagnosis and prediction method for composite fatigue delamination failure as recited in claim 5, wherein the step (5) of predicting the evolution of the particle set characterizing the probability distribution of the augmented state vector is implemented by the following formula:
Figure FDA00028685744100000311
in the formula,
Figure FDA00028685744100000312
the damage surface integral quantity of the ith particle at the k-1 moment is taken as the damage surface integral quantity of the ith particle;
Figure FDA00028685744100000313
the damage surface integral quantity of the ith particle at the k moment is taken as the damage surface integral quantity of the ith particle;
Figure FDA00028685744100000314
and
Figure FDA00028685744100000315
the model parameter component of the ith particle at the moment k-1;
Figure FDA00028685744100000316
and
Figure FDA00028685744100000317
the model parameter component of the ith particle at the moment k;
Figure FDA00028685744100000318
from a Gaussian distribution for time k
Figure FDA00028685744100000319
Sampling the obtained random number;
Figure FDA00028685744100000320
the damage coordinate X component of the ith particle at the k-1 moment is taken as the damage coordinate X component of the ith particle;
Figure FDA00028685744100000321
the damage coordinate X component of the ith particle at the k moment is taken as the damage coordinate X component of the ith particle;
Figure FDA00028685744100000322
the damage coordinate Y component of the ith particle at the k-1 moment is taken as the damage coordinate Y component of the ith particle;
Figure FDA00028685744100000323
the damage coordinate Y component of the ith particle at the k moment is taken as the damage coordinate Y component of the ith particle;
Figure FDA00028685744100000324
and
Figure FDA00028685744100000325
from Gauss for time kCloth
Figure FDA00028685744100000326
Sampling the obtained random number; the new set of particles obtained is represented by
Figure FDA00028685744100000327
Figure FDA00028685744100000328
8. The Bayesian online diagnosis and prediction method for composite fatigue stratified damage as recited in claim 5, wherein the observed likelihood of each particle in the step (6) is defined as
Figure FDA0002868574410000041
ykThe structural surface strain monitoring data acquired at the moment k specifically comprises the following data: sequentially mixing the particles
Figure FDA0002868574410000042
Component (b) of
Figure FDA0002868574410000043
Inputting the strain vector into an observation model g (-) to obtain the corresponding strain vector output
Figure FDA0002868574410000044
Figure FDA0002868574410000045
Is the strain vector corresponding to the ith particle,
Figure FDA0002868574410000046
is composed of
Figure FDA0002868574410000047
To (1)j elements, j being 1,2, …, n, data characterizing the jth strain monitoring point; n is the number of strain monitoring points; the observation likelihood is calculated by:
Figure FDA0002868574410000048
in the formula,
Figure FDA0002868574410000049
the observed likelihood value of the ith particle at the jth strain monitoring point at the time k is calculated as follows,
Figure FDA00028685744100000410
in the formula, σv,kThe standard deviation of the observed noise at the moment k; y isj,kFor strain observation vector ykThe jth element of (a), data characterizing the jth strain monitoring point on the actual structure.
9. The Bayesian online diagnosis and prediction method for fatigue delamination damage of composite material according to claim 5, wherein the posterior probability estimation of the structure damage position and damage area is obtained in the step (6), so as to realize the joint diagnosis of the structure delamination damage position and damage area at the time k, as shown in the following formula:
Figure FDA00028685744100000411
Figure FDA00028685744100000412
in the formula,
Figure FDA00028685744100000413
estimating posterior probability of the layered damage area at the moment of the structure k, namely obtaining a diagnosis result of the damage area;
Figure FDA00028685744100000414
estimating posterior probability of the layered damage position at the moment k, namely obtaining a diagnosis result of the damage position;
Figure FDA00028685744100000415
the normalized weight of the ith particle is obtained through likelihood value calculation.
10. The Bayesian online diagnosis and prediction method for fatigue delamination damage of composite materials according to claim 5, wherein the prediction of the damage area evolution at the future time in step (7) is implemented by sequentially iterating the damage area integral of the ith particle through a damage area evolution equation, as shown in the following formula:
Figure FDA00028685744100000416
wherein k + l represents a future time, l ═ 1,2,3, … n;
Figure FDA00028685744100000417
showing the delamination damage area of the ith particle at the time k + l-1,
Figure FDA0002868574410000051
is the delamination damage area of the ith particle at the time k + l,
Figure FDA0002868574410000052
is from a Gaussian distribution
Figure FDA0002868574410000053
Sampling the obtained random number; k + l is the future time, the strain distribution data is not obtained to update the particle weightParameters of the model
Figure FDA0002868574410000054
And
Figure FDA0002868574410000055
the value at time k is maintained.
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