CN114387255A - Multi-fractal quantitative characterization method for concrete group cracks - Google Patents

Multi-fractal quantitative characterization method for concrete group cracks Download PDF

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CN114387255A
CN114387255A CN202210038046.7A CN202210038046A CN114387255A CN 114387255 A CN114387255 A CN 114387255A CN 202210038046 A CN202210038046 A CN 202210038046A CN 114387255 A CN114387255 A CN 114387255A
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concrete
fractal
crack
local pixel
local
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曹茂森
潘丽霞
苏玛拉·德拉戈斯拉夫
葛晶
德拉霍米尔·诺瓦克
谢春晖
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Jiangsu Hongyuan Technology & Engineering Co ltd
Hohai University HHU
JSTI Group Co Ltd
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Jiangsu Hongyuan Technology & Engineering Co ltd
Hohai University HHU
JSTI Group Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0004—Industrial image inspection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/13—Edge detection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30108—Industrial image inspection
    • G06T2207/30132—Masonry; Concrete

Abstract

The invention discloses a concrete group crack multi-fractal quantitative characterization method, which comprises the following steps: acquiring total pixels of a concrete crack binary image; under different box sizes, acquiring the local pixel proportion of local pixels in each box in the total pixels; introducing an index weight factor into the local pixel proportion, and normalizing the local pixel proportion; for each index weight factor, calculating a singularity index and a corresponding fractal dimension according to the local pixel proportion and the normalized local pixel proportion; and drawing a multi-fractal singular spectrum of the crack distribution of the concrete according to the singularity index and the fractal dimension. The method can fully represent the damage information of the concrete structure, better depict the complexity and nonlinearity of the concrete crack distribution, provide reference for performance evaluation, overrun early warning and service life prediction of the concrete structure, and effectively serve management and maintenance work of the concrete structure.

Description

Multi-fractal quantitative characterization method for concrete group cracks
Technical Field
The invention relates to the field of health detection and safety early warning of concrete structures, in particular to a multi-fractal quantitative characterization method for concrete group cracks.
Background
In the long-term service process of a concrete structure, the concrete structure is inevitably damaged due to the coupling effect of factors such as material aging, environmental erosion, long-term action of load, fatigue and mutation and the like, so that catastrophic accidents are caused. Damage is first manifested as the appearance and propagation of structural cracks, the development of which determines to some extent the reliability, safety and durability of the structure and becomes a measure of the life cycle of the structure. Therefore, it is a natural idea to extract the damage factor of the concrete structure with the crack as the object of study. However, because concrete cracks exist in external substances and energy exchange, the concrete cracks are essentially an open, dissipative and chaotic nonlinear system, so that the conventional crack quantitative characterization method represented by a cross-sectional line intersection method cannot quantitatively evaluate irregular characteristics such as roughness, sharpness and geometric morphology of the cracks, and cannot accurately reflect the real damage state of a concrete structure.
Disclosure of Invention
In view of the above, it is necessary to provide a method for multi-fractal quantitative characterization of cracks in concrete groups.
The embodiment of the invention provides a concrete group crack multi-fractal quantitative characterization method, which comprises the following steps:
acquiring total pixels of a concrete crack binary image;
under different box sizes, obtaining the local pixel proportion of local pixels of the concrete crack binary image in each box in the total pixels;
introducing an index weight factor into the local pixel proportion, and normalizing the local pixel proportion;
for each index weight factor, calculating a singularity index and a corresponding fractal dimension according to the local pixel proportion and the normalized local pixel proportion;
and drawing a multi-fractal singular spectrum of the crack distribution of the concrete according to the singularity index and the fractal dimension.
Further, the acquiring of the total pixels of the concrete crack binary image specifically includes:
acquiring a concrete crack image;
removing pseudo crack information from the concrete crack image;
and carrying out binarization processing on the concrete crack image from which the pseudo crack information is removed by adopting Matlab software to obtain a pixel matrix of the concrete crack binarization image.
Further, the total pixel is represented as:
Figure BDA0003469196610000021
wherein, the concrete crack binary image is converted into a matrix with the element of 0 or 1, the unit containing the crack is represented as 0, and the number of the statistical element of 0 is the total pixel M (L); n (L) represents the number of boxes required for covering the concrete crack binary image, wherein L is the box size and mi(L) represents the number of elements 0 in the ith box.
Further, the local pixel scale is denoted as pi(L), the expression of which is as follows:
Figure BDA0003469196610000022
further, the normalized local pixel is recorded as μi(q, L), the expression of which is as follows:
Figure BDA0003469196610000023
wherein, mui(q, L) is in the range of [0,1 ]](ii) a The exponential weighting factor q is used for highlighting the difference of the local pixel proportion; when q is>When the pixel ratio is 0, the larger the local pixel ratio is, the dominant effect is; when q is<When the pixel ratio is 0, the smaller the local pixel ratio is, the dominant effect is; when q is 0, the local pixel scale size is not different.
Further, the singularity index and the corresponding fractal dimension are respectively denoted as a (q) and f (q), and the expressions are respectively as follows:
Figure BDA0003469196610000031
Figure BDA0003469196610000032
wherein, for each exponential weighting factor, logL is used as the abscissa,
Figure BDA0003469196610000033
fitting the point set by a least square method to obtain a slope of a straight line which is a (q) for the point set formed by the ordinate; in order to (log L,
Figure BDA0003469196610000034
) The slope of a straight line obtained by fitting the point set by a least square method is f (q) for the point set formed by coordinates.
Further, the drawing of the multi-fractal singular spectrum of the concrete crack distribution according to the singularity index and the fractal dimension specifically includes:
for each index weight factor, a convex curve which is drawn by taking the singularity index as a horizontal coordinate and the fractal dimension as a vertical coordinate is taken as a multi-fractal singular spectrum of the concrete crack distribution.
Compared with the prior art, the concrete group crack multi-fractal quantitative characterization method provided by the embodiment of the invention has the following beneficial effects:
the method is particularly suitable for representing the group crack damage of the complex concrete structure, fully utilizes crack distribution information, more accurately describes the complexity and nonlinearity of crack distribution, and more sensitively captures the difference of the crack distribution, thereby better reflecting the damage state of the concrete structure, ensuring the safe use of the structure, improving the disaster early warning capability of the concrete structure, and effectively serving the management and maintenance work of the concrete structure.
Drawings
FIG. 1 is a flow chart of a method for multi-fractal quantitative characterization of cracks in a concrete mass according to an embodiment;
FIG. 2 is a binary image of a crack distribution and a pixel matrix provided in one embodiment;
FIG. 3 is a graph of pixel fraction within each box for different box sizes as provided in one embodiment;
FIG. 4 is a fitting of a singular index at a weight factor q-1 provided in one embodiment;
fig. 5 is a fitting of fractal dimension under-1 with a weighting factor q ═ 1 provided in one embodiment;
FIG. 6 is a multi-fractal singular spectrum of a crack distribution provided in an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Example 1
And (3) performing multi-fractal characterization on crack distribution of the reinforced concrete shear wall under the action of static cyclic load:
the apparent crack distribution of a certain reinforced concrete shear wall under the action of static cyclic load is taken as a research object, an original image of the crack distribution is formed by marking on the wall body and drawing by adopting CAD according to a certain proportion in the loading process, and the crack distribution image is derived in a jpg format. The specific steps are implemented by referring to the flow shown in fig. 1, and specifically include the following steps:
the method comprises the following steps: the crack distribution image of the binary concrete can be regarded as a w × h matrix, each element in the matrix represents one pixel, for the binary image, the pixel point is black or white, and is respectively represented by 0 or 1 in the corresponding matrix, and fig. 2 shows a part of the binary image and a pixel matrix in a certain crack distribution image. And removing the pseudo crack information of the concrete crack image before binaryzation, and then carrying out binaryzation processing on the crack image by adopting Matlab to obtain a pixel matrix of the crack image.
Step two: and (3) counting the number of 0 elements in the binary image matrix according to a formula (1), namely, counting the total crack pixels of the binary image. Equation (1) is as follows:
Figure BDA0003469196610000041
wherein, the concrete crack binary image is converted into a matrix with the element of 0 or 1, the unit containing the crack is represented as 0, and the number of the statistical element of 0 is the total pixel M (L); n (L) represents the number of boxes required for covering the concrete crack binary image, wherein L is the box size and mi(L) represents the number of elements 0 in the ith box.
Step three: and extracting the proportion of crack pixels in each box to the total pixels under different box sizes. Regarding the selection of the box dimensions here, it is generally possible to follow 2nIs selected, and the maximum box size does not exceed w/2 or h/2. Fig. 3 shows the coverage of the box required and the pixel proportion within each box for both 8 pixel and 16 pixel box sizes, where the height of the columns indicates the pixel proportion for a single box. Wherein, the expression of the local pixel proportion is as follows:
Figure BDA0003469196610000051
step four: introducing a weight factor q for highlighting the difference of the local pixel proportion (when q is greater than 0, the local pixel proportion is larger and is dominant, when q is less than 0, the local pixel proportion is smaller and is dominant, and when q is 0, the size of the local pixel proportion is not distinguished), further developing normalization processing, and normalizing the pixel ratios of the single boxes under different weight factors according to a formula (3):
Figure BDA0003469196610000052
wherein, mui(q, L) is in the range of [0,1 ]]。
Step five: calculating the singularity index and the fractal dimension according to the calculation methods of formula (4) and formula (5) under different weight factors:
Figure BDA0003469196610000053
Figure BDA0003469196610000054
for each weight factor, let logL be the abscissa,
Figure BDA0003469196610000055
the slope of a straight line obtained by fitting a point set formed by the ordinate by a least square method is the singularity index under the weight factor. The same applies to the case of (logL,
Figure BDA0003469196610000056
) The linear slope is a corresponding fractal dimension through least square fitting. Fig. 4 shows the result of singular index fitting when the weighting factor q is-1, and fig. 5 shows the result of fitting the corresponding fractal dimension.
According to the above steps, the multi-fractal singular spectrum of the crack distribution obtained by calculation is shown in fig. 6.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (7)

1. A multi-fractal quantitative characterization method for concrete group cracks is characterized by comprising the following steps:
acquiring total pixels of a concrete crack binary image;
under different box sizes, obtaining the local pixel proportion of local pixels of the concrete crack binary image in each box in the total pixels;
introducing an index weight factor into the local pixel proportion, and normalizing the local pixel proportion;
for each index weight factor, calculating a singularity index and a corresponding fractal dimension according to the local pixel proportion and the normalized local pixel proportion;
and drawing a multi-fractal singular spectrum of the crack distribution of the concrete according to the singularity index and the fractal dimension.
2. The concrete group crack multi-fractal quantitative characterization method according to claim 1, wherein the obtaining of the total pixels of the concrete crack binary image specifically comprises:
acquiring a concrete crack image;
removing pseudo crack information from the concrete crack image;
and carrying out binarization processing on the concrete crack image from which the pseudo crack information is removed by adopting Matlab software to obtain a pixel matrix of the concrete crack binarization image.
3. The multi-fractal quantitative characterization method for concrete group cracks according to claim 1, wherein the total pixels are represented as:
Figure FDA0003469196600000011
wherein, the concrete crack binary image is converted into a matrix with the element of 0 or 1, the unit containing the crack is represented as 0, and the number of the statistical element of 0 is the total pixel M (L); n (L) represents the number of boxes required for covering the concrete crack binary image, wherein L is the box size and mi(L) represents the number of elements 0 in the ith box.
4. The multi-fractal quantitative characterization method for concrete group cracks according to claim 3, wherein the local pixel proportion is recorded as pi(L), the expression of which is as follows:
Figure FDA0003469196600000021
5. the multi-fractal quantitative characterization method for concrete group cracks according to claim 3, wherein the normalized local pixels are recorded as μi(q, L), the expression of which is as follows:
Figure FDA0003469196600000022
wherein, mui(q, L) is in the range of [0,1 ]](ii) a The exponential weighting factor q is used for highlighting the difference of the local pixel proportion; when q is>When the pixel ratio is 0, the larger the local pixel ratio is, the dominant effect is; when q is<When the pixel ratio is 0, the smaller the local pixel ratio is, the dominant effect is; when q is 0, the local pixel scale size is not different.
6. The concrete group crack multi-fractal quantitative characterization method as claimed in claim 5, wherein the singularity index and the corresponding fractal dimension are respectively denoted as a (q) and f (q), and the expressions are respectively as follows:
Figure FDA0003469196600000023
Figure FDA0003469196600000024
wherein, for each exponential weighting factor, logL is used as the abscissa,
Figure FDA0003469196600000025
fitting the point set by a least square method to obtain a slope of a straight line which is a (q) for the point set formed by the ordinate; to be provided with
Figure FDA0003469196600000026
The slope of a straight line obtained by fitting the point set by a least square method is f (q) for the point set formed by coordinates.
7. The method for multi-fractal quantitative characterization of concrete group cracks according to claim 1, wherein the drawing of the multi-fractal singular spectrum of the concrete crack distribution according to the singularity index and the fractal dimension specifically comprises:
for each index weight factor, a convex curve which is drawn by taking the singularity index as a horizontal coordinate and the fractal dimension as a vertical coordinate is taken as a multi-fractal singular spectrum of the concrete crack distribution.
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Publication number Priority date Publication date Assignee Title
CN102277859A (en) * 2011-05-16 2011-12-14 河海大学 Method for optimizing grain composition of blasting rockfill material based on fractal theory
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CN110593829A (en) * 2019-08-14 2019-12-20 中国地质大学（武汉） Automatic judgment method and device for interwell communication mode of fracture-cavity type oil reservoir
CN110926328A (en) * 2018-09-20 2020-03-27 中国石油化工股份有限公司 Method and device for measuring characteristics of crack surface of rock crack
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Publication number Priority date Publication date Assignee Title
CN102277859A (en) * 2011-05-16 2011-12-14 河海大学 Method for optimizing grain composition of blasting rockfill material based on fractal theory
CN104808255A (en) * 2015-04-30 2015-07-29 武汉光谷北斗控股集团有限公司 Fractal theory-based mineralization anomaly information mining method
CN110926328A (en) * 2018-09-20 2020-03-27 中国石油化工股份有限公司 Method and device for measuring characteristics of crack surface of rock crack
CN110593829A (en) * 2019-08-14 2019-12-20 中国地质大学（武汉） Automatic judgment method and device for interwell communication mode of fracture-cavity type oil reservoir
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