CN108053479B - Multi-defect group nondestructive identification method based on extended finite element method - Google Patents

Multi-defect group nondestructive identification method based on extended finite element method Download PDF

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CN108053479B
CN108053479B CN201711179071.2A CN201711179071A CN108053479B CN 108053479 B CN108053479 B CN 108053479B CN 201711179071 A CN201711179071 A CN 201711179071A CN 108053479 B CN108053479 B CN 108053479B
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余天堂
马春平
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Abstract

The invention discloses a multi-defect group nondestructive identification method based on an extended finite element method, which consists of forward analysis and backward analysis. The computational grid of the extended finite element method is independent of the discontinuous surface in the structure, so that the computational grid does not need to be reconstructed when the defect geometry changes, and the extended finite element method is used for forward analysis to save time. The inverse analysis consists of three steps: (i) determining subdomains containing defect groups by sparse measuring points, and narrowing search domains; (ii) adding measuring points in the subdomain, and identifying the defect groups one by one to determine the approximate positions and sizes of the defects in the groups; (iii) with the second result as the initial solution, convergence to the true morphology of the defect is accelerated. The method can accurately identify the multi-defect group on the premise of unknown defect quantity, and can remarkably reduce the consumption of measuring points and the iteration times.

Description

Multi-defect group nondestructive identification method based on extended finite element method
Technical Field
The invention belongs to the field of engineering structure safety monitoring, and particularly relates to a multi-defect group nondestructive identification method based on an extended finite element method.
Background
The engineering structure contains defects which are large and small and are difficult to avoid, and the existence of the defects often causes great influence on the performance of the structure and is also a main reason for causing the failure of the structure. To assess the safety and reliability of a structure, it is of paramount importance to identify defects in the structure using non-destructive inspection means. In the past decades, technical means capable of identifying defects in a local range, such as a laser scanning method, a radiography method, an ultrasonic method, an infrared image method, an acoustic emission method, a holographic image method, and the like, have been introduced in the field of nondestructive testing, but some of the methods are limited by a strict operation environment, some of the methods cannot provide accurate defect information, and the methods are difficult to develop for large and medium-sized structures. Therefore, how to accurately and quickly identify defects in the whole structure range still remains a problem to be solved urgently.
With the improvement of computer technology and structure monitoring technology, forward analysis is performed by using numerical simulation, and reverse analysis is performed by an optimization algorithm to identify defects in a structure, which is a research hotspot in the field of structure nondestructive testing. However, the existing optimization scheme can only identify a plurality of defects which are far away from each other, and when a plurality of defects which are close to each other form a defect group locally, especially when a plurality of defect groups exist, the existing scheme is difficult to solve.
Disclosure of Invention
In order to solve the technical problems of the background art, the invention aims to provide a multi-defect group nondestructive identification method based on an extended finite element method, and the multi-defect group is accurately identified.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a multi-defect group nondestructive identification method based on an extended finite element method comprises the following steps:
(1) sparsely and uniformly arranging m on the surface of the structure to be measured0Measuring points, applying load and collecting measuring point response
Figure BDA0001478816580000021
Subscript i ═ 1,2, …, m0；
(2) Establishing an extended finite element numerical model of the structure to be measured, applying the same load as that in the step (1), and constructing the model into a response u at the position of the measuring point in the step (1) by taking the geometrical parameter theta of the defect as inputi s(θ) is the system of outputs;
(3) assuming the defect form is a circular hole with an upper limit of n1Setting the initial range of the defect geometric parameters of each circular hole and setting a threshold value rtWhen the radius of the circular hole is larger than rtReserving the hole, otherwise, temporarily removing the hole;
(4) for the objective function
Figure BDA0001478816580000022
Optimizing to obtain a solution consisting of a plurality of candidate defects
Figure BDA0001478816580000023
(5) Identifying and removing solutions using a queue-removal method
Figure BDA0001478816580000024
An incorrect candidate defect;
(6) candidate to residual by hierarchical clustering analysisDefects are grouped to obtain q0A plurality of candidate defect groups;
(7) identifying and removing incorrect candidate defect groups using a queue-elimination method to obtain q1A plurality of candidate defect groups;
(8) for each candidate defect group, the centroid of all the defects is taken as the center, and the side length is set as d1All draw q1Each square subdomain is set as a new search domain of candidate defects, and the upper limit of the number of candidate defects in each square subdomain is set as n2When the new search domain exceeds the initial search domain, the new search domain is cut off according to the initial search domain; the initial search domain is the surface of a structure to be detected;
(9) uniformly arranging m into each square subdomainaddA total of m for each measurement point0+madd×q1Measuring points;
(10) repeating the steps (4) to (7) to obtain q2For each candidate defect group, using centroid of all defects as center and side length as d2All draw q2The square subdomains are set as new search domains of candidate defects, when the new search domains exceed the initial search domains, the new search domains are cut off according to the initial search domains, only 1 candidate defect is set in each square subdomain, and the candidate defect is located in the center of each square subdomain;
(11) changing defect form into elliptical hole, and rewriting the objective function into O2(θ)；
(12) For the objective function O2And (theta) optimizing to obtain an approximate solution of the real defects.
Further, in step (11), an objective function
Figure BDA0001478816580000031
Wherein c is a penalty factor,
Figure BDA0001478816580000032
Figure BDA0001478816580000033
and
Figure BDA0001478816580000034
j-th variable thetajN is the number of elliptical holes.
Further, in steps (5) and (7), the queue elimination method specifically comprises removing q candidate defects or candidate defect groups, respectively, to form q new solutions containing q-1 candidate defects or candidate defect groups
Figure BDA0001478816580000035
Calculating objective function values for each new solution
Figure BDA0001478816580000036
And calculate each new solution relative to
Figure BDA0001478816580000037
Normalized degree of degradation of
Figure BDA0001478816580000038
Setting a tolerance t ≧ 0, for each candidate defect or candidate defect group, if δjIf t is less than t, removing the defect to obtain q' candidate defects or candidate defect groups.
Further, in the step (4), a discrete artificial bee colony algorithm is adopted to perform on the objective function O1(theta) optimization.
Further, in step (12), the objective function O is calculated by a difference method2(theta) gradient, using BFGS algorithm to target function O2(theta) optimization.
Adopt the beneficial effect that above-mentioned technical scheme brought:
(1) the method uses the extended finite element method to carry out positive analysis of defect identification, does not need to re-partition grids in each optimization iteration, and greatly saves the calculation time compared with other methods;
(2) the invention provides a method for reversely analyzing defect identification, which comprises the following steps of firstly reducing an initial search domain to a subdomain where a defect group is located through sparse measuring point arrangement, then locally adding measuring points to the subdomain, determining the subdomain where each defect is located, and finally determining the specific form of the defect. Therefore, the optimization iteration times are reduced, the total usage amount of the measuring points is reduced, and the problem of multi-defect group identification is solved;
(3) the invention provides a 'queuing removal method' to actively identify and remove candidate defect identification with low representativeness to real defect groups and remove incorrect candidate defects or candidate defect groups, thereby not only reducing a large amount of iteration, but also improving the precision of the determined subdomain;
(4) the invention uses hierarchical clustering analysis to group the candidate defects, and realizes automatic identification of the approximate positions of the defect groups.
Drawings
FIG. 1 is a schematic diagram of a defect group model used in an embodiment;
FIG. 2 is a schematic diagram of an expanded finite element mesh, loads, and boundary conditions of the model shown in FIG. 1;
FIG. 3 is an initial solution diagram of the model shown in FIG. 1;
FIG. 4 is a schematic diagram of the results of the initial solution shown in FIG. 3 after being optimized by the discrete artificial bee colony algorithm;
FIG. 5 is a diagram illustrating the results of FIG. 4 after "queue elimination" and hierarchical clustering analysis operations;
FIG. 6 is a schematic diagram of the subdomains shown in FIG. 5 after adding measurement points, which also includes the initial solutions in each subdomain;
FIG. 7 is a schematic diagram of the results of the initial solution of each subdomain shown in FIG. 6 after being subjected to discrete artificial bee colony algorithm, "queue elimination method" and hierarchical cluster analysis operations one by one;
FIG. 8 is a graph illustrating the final results of the results shown in FIG. 7 after BFGS optimization.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
To illustrate the process of the present invention, a square plate with a side length of 1 unit length is illustrated in FIG. 1. The flat plate contains 3 defect groups, each defect group contains 2 defects, and the defect forms comprise three forms of holes, crack clusters and holes and cracks. In the present invention, the cluster of cracks and the holes plus cracks are approximately elliptical holes.
Step 1, uniformly arranging 9 measuring points on the surface of a flat plate sparsely as shown in figure 1, applying load as shown in figure 2 and collecting measuring point response um(this step is implemented in numerical simulation in this example).
Step 2, establishing an extended finite element numerical model of the plate, applying the same load as that in the step 1 to a grid as shown in fig. 2, constructing the model by taking a defect geometric parameter theta as input and a response u at a measuring point position in the step 1sIs an output system.
Step 3, setting the defect form as circular holes with the upper limit of 20, and setting the defect parameter theta of each circular holeiIs the area of the flat plate, and a threshold value r is takent1/2 with a mesh size, when the radius of the circular hole is larger than rtThe hole is reserved, otherwise, the hole is temporarily removed.
Step 4, the initial solution is shown as a black dotted line circle in fig. 3, and a discrete artificial bee colony algorithm is used for aiming at the target function
Figure BDA0001478816580000051
Optimization was performed, and the result is shown by the black dashed circle in fig. 4, resulting in a solution consisting of 17 candidate defects
Figure BDA0001478816580000052
And step 5, identifying and removing incorrect candidate defect groups by using a queuing removal method, wherein the removed candidate defects are shown as 4 gray dotted circles in the figure 5.
And 6, grouping the remaining candidate defects by hierarchical clustering analysis to obtain 3 candidate defect groups, wherein the grouping result is shown as a black dotted line circle in a 3 dotted line square frame in fig. 5.
And 7, identifying and removing incorrect candidate defects by using a queuing removal method to obtain 3 candidate defect groups.
And 8, regarding each defect group, taking the centroid of all the defects in the defect group as the center, setting the side length as 0.3 unit length, dividing 3 square sub-fields (as shown by 3 dotted line boxes in fig. 5) in total, setting the square sub-fields as new search fields of candidate defects, setting the upper limit of the number of the candidate defects in each square sub-field as 5, and cutting the defect groups according to the initial search field when the new search fields exceed the initial search fields.
Step 9, uniformly arranging 5 measuring points in each square subdomain, as shown in fig. 6, wherein the total number of measuring points is 9+5 × 3-24.
And step 10, repeating the steps 4 to 7 for each square search domain in sequence to obtain 6 candidate defect groups in total, regarding the centroid of all the defects in each defect group as the center, setting the side length as 0.15 unit length, dividing 6 square sub-domains (as shown by 6 dotted line boxes in fig. 7) in total, setting the square sub-domains as new search domains of the candidate defects, when the new search domains exceed the initial search domains, cutting the new search domains according to the initial search domains, and setting only 1 candidate defect in each square sub-domain to be located at the center of the sub-domain.
Step 11, changing the defect form into an elliptical hole, and rewriting the objective function into
Figure BDA0001478816580000061
Wherein c is a penalty factor with the value of 1,
Figure BDA0001478816580000062
and
Figure BDA0001478816580000063
j-th variable thetajN is the number of elliptical holes.
Step 12, calculating the gradient of the objective function by a difference method, and using a BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm to carry out the calculation on the objective function O2(θ) optimization was performed to obtain an approximate solution of the real defect as shown by the 6 dashed ellipses in FIG. 8.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (3)

1. A multi-defect group nondestructive identification method based on an extended finite element method is characterized by comprising the following steps:
(1) sparsely and uniformly arranging m on the surface of the structure to be measured0Measuring points, applying load and collecting measuring point response
Figure FDA0002356786660000011
Subscript i ═ 1,2, …, m0；
(2) Establishing an extended finite element numerical model of the structure to be measured, applying the same load as that in the step (1), and constructing the model into a response at the position of the measuring point in the step (1) by taking the geometrical parameter theta of the defect as an input
Figure FDA0002356786660000012
A system that is an output;
(3) assuming the defect form is a circular hole with an upper limit of n1Setting the initial range of the defect geometric parameters of each circular hole and setting a threshold value rtWhen the radius of the circular hole is larger than rtReserving the hole, otherwise, temporarily removing the hole;
(4) for the objective function
Figure FDA0002356786660000013
Optimizing to obtain a solution consisting of a plurality of candidate defects
Figure FDA0002356786660000014
(5) Identifying and removing solutions using a queue-removal method
Figure FDA0002356786660000015
An incorrect candidate defect;
(6) grouping the remaining candidate defects by hierarchical clustering analysis to obtain q0A plurality of candidate defect groups;
(7) identifying and removing incorrect candidate defect groups using a queue-elimination method to obtain q1A plurality of candidate defect groups;
in steps (5) and (7), the queue elimination method specifically comprises removing q candidate defects or candidate defect groups respectively to form q new solutions containing q-1 candidate defects or candidate defect groups
Figure FDA0002356786660000016
Calculating objective function values for each new solution
Figure FDA0002356786660000017
And calculate each new solution relative to
Figure FDA0002356786660000018
Normalized degree of degradation of
Figure FDA0002356786660000019
Setting a tolerance t ≧ 0, for each candidate defect or candidate defect group, if δjIf t is less than t, removing the defect to obtain q' candidate defects or candidate defect groups;
(8) for each candidate defect group, the centroid of all the defects is taken as the center, and the side length is set as d1All draw q1Each square subdomain is set as a new search domain of candidate defects, and the upper limit of the number of candidate defects in each square subdomain is set as n2When the new search domain exceeds the initial search domain, the new search domain is cut off according to the initial search domain; the initial search domain is the surface of a structure to be detected;
(9) uniformly arranging m into each square subdomainaddA total of m for each measurement point0+madd×q1Measuring points;
(10) repeating the steps (4) to (7) to obtain q2For each candidate defect group, using centroid of all defects as center and side length as d2All draw q2The square subdomains are set as new search domains of candidate defects, when the new search domains exceed the initial search domains, the new search domains are cut off according to the initial search domains, only 1 candidate defect is set in each square subdomain, and the candidate defect is located in the center of each square subdomain;
(11) changing defect form into elliptical hole, and rewriting the objective function into O2(θ)：
Figure FDA0002356786660000021
Wherein c is a penalty factor,
Figure FDA0002356786660000022
Figure FDA0002356786660000023
and
Figure FDA0002356786660000024
j-th variable thetajN is the number of the elliptical holes;
(12) for the objective function O2And (theta) optimizing to obtain an approximate solution of the real defects.
2. The extended finite element method-based multi-defect group nondestructive identification method of claim 1, wherein in the step (4), a discrete artificial bee colony algorithm is adopted to perform the objective function O1(theta) optimization.
3. The extended finite element method-based multi-defect group lossless recognition method of claim 1, wherein in the step (12), the objective function O is calculated by a difference method2(theta) gradient, using BFGS algorithm to target function O2(theta) optimization.
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