CN115828603A - Construction method of recycled concrete mesoscopic aggregate model based on Fourier transform - Google Patents
Construction method of recycled concrete mesoscopic aggregate model based on Fourier transform Download PDFInfo
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Abstract
The invention discloses a construction method of a recycled concrete mesoscopic aggregate model based on Fourier transform, which comprises the following steps: 1, acquiring a digital image of a real section of concrete, processing the image and extracting boundary contour pixel coordinates of aggregate; 2, calculating and storing Fourier coefficients representing the shape profile of each aggregate, and establishing a two-dimensional aggregate information database based on the real aggregate; randomly selecting aggregates in a database, converting Fourier coefficients into aggregate contour coordinates, and constructing a common aggregate model; 4, building a recycled aggregate model by using an aggregate superposition method; and 5, randomly putting the common aggregate and the recycled aggregate. The construction method is simple and efficient, the aggregate model is derived from the real aggregate shape, an aggregate superposition method is provided to randomly generate the recycled aggregate model, and the constructed recycled concrete model is closer to the real recycled concrete section structure; the model can flexibly change the replacement rate of the recycled aggregate and the content of the attached old mortar, and realize the simulation of the mechanical property and the durability of the recycled concrete.
Description
Technical Field
The invention relates to the technical field of construction of a recycled concrete mesoscopic model, in particular to a Fourier transform-based two-dimensional five-phase mesoscopic modeling method for recycled concrete.
Background
The concrete material used for the infrastructure in China is huge in consumption, a large amount of gravels are consumed, meanwhile, waste concrete generated by dismantling old buildings is increased day by day, and at present, modes such as landfill and the like are mainly adopted, so that the environment is greatly influenced. The waste concrete can be prepared into recycled coarse aggregate after treatment, can be used for replacing natural aggregate to prepare recycled concrete, not only can solve the consumption of natural resources such as natural sand stones, but also can realize the recycling of the waste concrete, has remarkable social, economic and environmental benefits, and accords with the concept of green sustainable development.
In recent years, a lot of studies on various properties of recycled concrete have been carried out by many scholars, but most of the studies are based on macroscopic tests, and the differences of the elastic modulus and the strength property of each phase component are ignored, so that the obtained results can only meet the general engineering requirements. Compared with common concrete, the recycled concrete has a more complex internal structure, and from a microscopic structure, the research on the influence of each phase composition on the performance of the recycled concrete is necessary, so that a basis can be provided for further improving the performance of the recycled concrete. Along with the development of computer information technology, great convenience is provided for researching a microscopic structure of recycled concrete aggregate, a polygonal aggregate-based microscopic random aggregate model of recycled concrete is established by Julian and the like, and the heat-conducting property and the heat transfer mechanism of the recycled concrete are researched; the trypan and the like establish a circular and random polygonal two-dimensional recycled concrete mesoscopic structure and research the mechanical properties of the recycled concrete; CN112464523A provides a construction method of a recycled concrete mesoscopic model based on concentric oval recycled aggregate; CN113591195A proposes a construction method of a mesoscopic model of recycled concrete based on random polygonal aggregate. However, the two-dimensional recycled aggregate models used in the existing recycled concrete mesoscopic models, such as simplified particle shapes of circles, ellipses and the like, have certain limitations, and the shapes and the attachment positions of mortar in the models are greatly different from those of old mortar attached under the actual condition, so that the recycled concrete models have larger difference from the real mesoscopic structures, and the simple models cannot meet the simulation requirements of people along with the rapid development of computer technology.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides a construction method of a recycled concrete microscopic aggregate model based on Fourier transform, so that the recycled concrete model which is closer to the internal structure of real recycled concrete can be constructed, and the substitution rate of recycled aggregate and the content of attached old mortar can be flexibly changed, thereby realizing the simulation of the mechanical property and the durability of the recycled concrete, and further being beneficial to accelerating the research, the popularization and the efficient application of the recycled concrete.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a construction method of a recycled concrete mesoscopic aggregate model based on Fourier transform, which is characterized by comprising the following steps of:
step 1: establishing a planar rectangular coordinate system by taking a left lower corner point of a rectangular section of the concrete sample as a coordinate origin, taking the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a planar rectangular domain T with the width W and the height H, wherein the left lower corner point of the planar rectangular domain T is the coordinate origin;
step 2: acquiring a plurality of concrete real section digital images and CT scanning section images of aggregates, extracting boundary contour pixel coordinate sequences of the aggregates in each image in the plane rectangular coordinate system, calculating Fourier descriptors and phase angles of the boundary contour pixel coordinate sequences of the aggregates, numbering and storing the Fourier descriptors and the phase angles, and accordingly establishing a two-dimensional aggregate information database, and enabling the aggregate total number in the database to be N;
and step 3: determining basic parameters, including: section width W and height H of recycled concrete test piece, and aggregate volume ratio P k Size of sieve with holes [ D ] 1 ,D 2 …D i-1 ,D i ,D i+1 …D max ]The recycled aggregate substitution rate R; wherein D is max Represents the maximum particle size of the aggregate; d i Indicates the size of the ith screen; theoretical calculation of feeding area { S) for aggregate in each size fraction range i I =2,3, \8230;, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The feeding area is calculated theoretically for the aggregate;
and 4, step 4: initializing i = max;
and 5: followed byGenerating the ith number r i E (0, 1) if r i >R, the generation size range is (D) i-1 ,D i ) If r is a normal aggregate model of i Less than or equal to R, the size fraction generated by the aggregate superposition method is within (D) i-1 ,D i ) The recycled aggregate model of (1);
step 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the aggregate model of (2) satisfies both the boundary condition and the aggregate interference condition, and if so, the size fraction range is within (D) i-1 ,D i ) Is put into the plane rectangular field T, and the size fraction range is calculated to be (D) i-1 ,D i ) The area a of the s-th charged aggregate is S =1,2, \ 8230;, L; l represents the number of all the aggregates to be put, when the aggregate model is a recycled aggregate convex polygon model, the area F of an adhesive mortar polygon model in the kth recycled aggregate convex polygon model is calculated k ，k＝1,2,…,L 1 (ii) a Wherein L is 1 Representing the total number of the thrown recycled aggregates, otherwise, returning to the step 5; until a particle size range (D) is obtained i-1 ,D i ) L cumulative charging area for charging aggregate
Satisfying the formula (1);
A i ∈((1-σ)S i ,(1+σ)S i ) (1)
in formula (1), σ represents a parameter between (0, 1);
and 7: after i-1 is assigned to i, the step 5 is returned to for sequential execution until i<2 so as to obtain the cumulative charging area { A of the aggregates in each size fraction range i |i＝2,3,4…,max}；
And 8: calculating the aggregate input area ratio S A And the area ratio S of the attached old mortar M The method is used for constructing a recycled concrete mesoscopic aggregate model.
The construction method of the recycled concrete mesoscopic aggregate model based on Fourier transform is also characterized in that the step 2 comprises the following steps:
step 2.1: all images are convertedPerforming binarization processing on the gray level image to obtain a binary image, performing edge detection on the binary image to obtain a boundary contour pixel coordinate sequence E of each aggregate n ＝{(x mn ,y mn )|m＝1,2,3…M n N =1,2,3, \8230N, wherein E n A boundary contour pixel coordinate sequence representing the nth aggregate, (x) mn ,y mn ) M-th coordinate, M, representing the n-th aggregate boundary contour pixel coordinate sequence n Representing the number of coordinates of the boundary contour pixel coordinate sequence of the nth aggregate;
moving the center of the aggregate to the origin of coordinates to obtain a boundary contour coordinate sequence { E 'of the aggregate when the center of the aggregate is located at the origin of coordinates' n L N =1,2,3, \8230N }, wherein E' n Represents a boundary contour coordinate sequence of the nth aggregate with its center at the origin of coordinates, and E' n ＝{(x 0 mn ,y 0 mn )|m＝1,2,3…M n }，(x 0 mn ,y 0 mn ) An mth coordinate representing an nth aggregate boundary contour pixel coordinate sequence with a center located at the origin of coordinates; boundary contour coordinate sequence { E 'of each aggregate' n I N =1,2,3, \8230; N } is converted into a polar sequence { F } n L N =1,2,3 \ 8230n }, wherein F n A polar coordinate sequence of boundary contour pixels representing the nth aggregate, and F n ＝{(θ mn ,r mn )|m＝1,2,3,…M}；(θ mn ,r mn ) An mth polar coordinate representing an nth aggregate boundary contour pixel polar coordinate sequence;
step 2.2: selecting a resampling angle theta = { theta = [ [ theta ] ] j ＝j/2πN 1 |j＝1,2,3,…,N 1 F is interpolated by n Processing to obtain the polar diameter value R of the nth aggregate profile under the resampling angle theta n ＝{R jn |j＝1,2,3…N 1 }; thereby obtaining the polar diameter value { R ] of each aggregate profile under the resampling angle theta n L N =1,2,3, \8230; N }; wherein, theta j Denotes the jth resampling angle, R jn Represents the nth aggregate profile at a resampling angle theta j Value of lower pole diameter, N 1 Representing the number of sampling points;
step 2.3: calculating a real Fourier descriptor D of the nth aggregate profile n ＝{D tn |t＝1,2,3…N 1 And phase angle δ n ＝{δ tn |t＝1,2,3…N 1 Sequentially storing, establishing a two-dimensional aggregate information database for the file number of each aggregate, and recording the number N of the aggregates in the database; wherein D is tn The t-th real Fourier descriptor, δ, representing the nth aggregate profile tn The t-th phase angle representing the n-th aggregate profile.
The step of generating the common aggregate model in the step 5 comprises the following steps:
step 5.1a: randomly generating the aggregate sequence number s epsilon (1, N) and the aggregate contour rotation angle
Control parameter r of equivalent particle size of the s-th aggregate s ∈0.5(D i-1 ,D i )；
Step 5.2a: calculating a reconstruction polar diameter value { G ] of the s-th aggregate profile under the resampling point theta by using the formula (2) js |j＝1,2,3…N 1 In which G js Expressed at the resampling angle theta j Reconstructing the diameter value of the next s-th aggregate profile; the polar coordinate sequence J of the reconstructed s-th aggregate profile s ＝{(θ j ,G js )|j＝1,2,3…N 1 Converting into rectangular coordinate sequence and multiplying by angle
Obtaining a coordinate sequence Z of the s-th aggregate profile after rotating the matrix s ＝{(x js ,y js )|j＝1,2,3…N 1 }; wherein (x) js ,y js ) A jth coordinate representing an s-th aggregate contour coordinate sequence;
in the formula (6), D ts And delta ts T-th real Fourier descriptor andphase angle, N 2 A Fourier expansion order;
step 5.3a: calculating the equivalent particle diameter d of the s-th aggregate after reconstruction s If d is s ∈(D i-1 ,D i ) Then, the coordinate (x) of the center of the aggregate to be placed is randomly generated s ,y s ) And is combined with Z s The central coordinate of (a) is moved to the pre-placing center (x) of the aggregate s ,y s ) Obtaining a coordinate sequence Z' s From Z' s The surrounded graph is the s-th common aggregate model; otherwise, return to step 5.1a.
The process of generating the recycled aggregate model by using the aggregate superposition method in the step 5 comprises the following steps:
step 5.1b: repeating the steps 5.1a and 5.2a twice to obtain coordinate sequences Z of two different common aggregate models 1 And Z 2 Is a reaction of Z 1 And Z 2 Integrating into a group of points, calculating the boundary coordinate sequence X of the group of points 3 From X 3 The surrounded graph is marked as synthetic aggregate;
step 5.2b: calculating the equivalent grain diameter D of the synthetic aggregate, and if D belongs to (D) i-1 ,D i ) Generating the coordinate (X, y) of the pre-throwing center of the aggregate randomly, and dividing the X 3 And X 1 The center coordinate of (2) is moved to the aggregate pre-casting center (X, y) to obtain a coordinate sequence X' 3 And X' 1 From X' 1 The surrounded pattern is the aggregate phase of the recycled aggregate model and is X' 3 And X' 1 The difference set of the enclosed patterns is an attached mortar phase, and the aggregate phase and the attached mortar phase jointly form a recycled aggregate model; otherwise, return to step 5.1b.
The judging mode of whether the aggregate model meets the boundary condition in the step 6 is as follows:
minimum external rectangle T for judging aggregate model s The position relation with the plane rectangular field T if T s And within the T, the aggregate meets the boundary condition of the throwing area, otherwise, the aggregate model does not meet the boundary condition.
The judgment mode of whether the aggregate model AG meets the aggregate interference condition in the step 6 is to adopt a minimum circumscribed rectangle intersection method:
step 6.1: searching the minimum bounding rectangle T with AG in the minimum bounding rectangles of all the placed aggregate models 0 Intersecting rectangles C = { C f I f =1,2 \8230e }, and the corresponding aggregate set name is AGG, AGG = { A = { (A) } f L f =1,2 \ 8230e }, wherein c f Denotes the f-th and T 0 Intersecting minimum circumscribed rectangle of poured aggregate model, A f Represents the f-th minimum bounding rectangle and T 0 Intersecting charged aggregate model, e denotes the sum of T 0 The number of the intersected minimum external rectangles of the placed aggregate models; if the C is an empty set, the aggregate interference condition is met, otherwise, the step 6.2 is executed;
step 6.2: judging whether the maximum inscribed circle of the AG is intersected with the maximum inscribed circle of any aggregate in the AGG, if so, indicating that the aggregate interference condition is not met, otherwise, executing the step 6.3;
step 6.3: let f =1, perform step 6.4;
step 6.4: calculation of c f And T 0 Rectangle E of the overlapping area f Polar angle ψ = { ψ) of the four vertices of the aggregate model AG in a polar coordinate system with the center of the aggregate model AG as the origin of coordinates 1 ,ψ 2 ,ψ 3 ,ψ 4 Therein, ψ 1 ,ψ 2 ,ψ 3 ,ψ 4 Respectively represent E f The four vertexes of the angle model are polar angle values under a polar coordinate system taking the center of the aggregate AG as the origin of coordinates; and calculating a rectangle E under a rectangular coordinate system taking the center of the aggregate model AG as the origin of coordinates f Lower left corner coordinate vertex (X) lf ,Y lf ) And E f Central abscissa X of cf And E f Height L of 1 If X is cf > 0 and Y lf ×(Y lf +L 1 ) If < 0, let α = { α = p ＝2p·ψ m /N 5 |p＝0,1,2…N 5 /2}∪{α p ＝ψ n +(4π-2ψ n )·p/N 5 |p＝N 5 /2,N 5 /2+1,…N 5 Else, let α = { α = } p ＝ψ a +p·(ψ b -ψ a )/N 5 |p＝0,1,2…N 5 Therein, ψ m Is the maximum polar angle value phi smaller than pi n Is the minimum polar angle value larger than pi in psi a Is the minimum polar angle value, psi, in the set psi b Is the maximum polar angle value in psi, alpha represents the polar angle value set to be verified, alpha p Representing the p-th polar angle value to be verified, N 5 The number of division points;
step 6.5: calculating a polar coordinate value sequence of the contour points of the aggregate model AG under the polar angle value set alpha and converting the polar coordinate value sequence into a rectangular coordinate sequence Z 1 ＝{(x’ p ,y’ p )|p＝1,2,3…N 5 Wherein, x' p ,y’ p ) Representing the coordinates to be verified of the pth on the outline of the aggregate model AG; if Z is 1 All coordinate points are not in E f The f-th aggregate A inside f Does not interfere with the aggregate model AG, otherwise, calculates Z 1 All coordinate points in to the f aggregate A f Distance d of center = { d = { [ d ] p |p＝1,2,3…N 5 Z and 1 all coordinate points in the aggregate are defined as f-th aggregate A f A polar angle set τ = { τ = in a polar coordinate system with the center of (a) the origin of coordinates p |p＝1,2,3…N 5 }, calculating the f-th aggregate A f Set of polar values { I } of contour points under set of polar angles τ p |p＝1,2,3…N 5 In which d is p Representing the p-th coordinate point to be verified to the f-th aggregate A f Distance of the centers, τ p Represents Z 1 The p-th coordinate point in the specification is defined as the f-th aggregate A f Polar angle in a polar coordinate system with the center of origin of coordinates, I p Denotes the f-th aggregate A f At p polar angle τ p A polar diameter value of the lower contour point; if there is I p ＞d p Then, it means the f-th aggregate A f Interfering with aggregate model AG, otherwise, representing f aggregate A f The method does not interfere with an aggregate model AG;
step 6.6: and f +1 is assigned to f, the step 6.4 is returned to and sequentially executed until f is larger than e, if the aggregate model AG is not interfered with all aggregates in the AGG, the aggregate interference condition is met, and otherwise, the aggregate interference condition is not met.
The electronic device of the invention comprises a memory and a processor, and is characterized in that the memory is used for storing programs for supporting the processor to execute the construction method, and the processor is configured to execute the programs stored in the memory.
The invention relates to a computer-readable storage medium, on which a computer program is stored, characterized in that the computer program executes the steps of the construction method when being executed by a processor.
Compared with the prior art, the invention has the beneficial effects that:
1. compared with the existing recycled concrete mesoscopic model, the method utilizes Fourier transform to reconstruct the complex shape outline of the real aggregate, and the complex shape outline is used as a common aggregate model, and the aggregate model is vivid and is derived from the real aggregate; a novel method is provided for generating a recycled aggregate model by an aggregate superposition method, wherein the attached mortar model has various shapes and random positions, and the constructed recycled concrete model is more consistent with a two-dimensional recycled concrete mesoscopic structure under a real condition, so that a simulation result is more accurate.
2. Compared with the existing recycled concrete mesoscopic model, the method provided by the invention has the advantages that whether the aggregates with irregular shapes interfere with each other is judged by the minimum circumscribed rectangle method, the method is strict, accurate and efficient, and the filling rate of the aggregates is improved.
3. Compared with the existing recycled concrete mesoscopic model, the method can control the replacement rate of the recycled aggregate and the adhesion content of the old mortar by changing the input parameters, can be used for simulating and researching the influence of the adhesion amount, the replacement rate and the like of the mortar of the recycled aggregate on various properties of the recycled concrete, and accelerates the popularization and application of the recycled concrete.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic drawing of the extracted aggregate profile of the process of the present invention;
FIG. 3 is a schematic diagram of a recycled aggregate model generated by an aggregate superposition method according to the present invention;
FIG. 4 is a boundary condition decision diagram of the present invention;
FIG. 5 is a schematic view of an irregular shaped aggregate intersection according to the present invention;
FIG. 6a is a schematic diagram of a minimum bounding rectangle intersection method of the present invention;
FIG. 6b is a schematic diagram illustrating the minimum circumscribed rectangle intersection method of the present invention;
FIG. 7a is a schematic diagram of a recycled concrete microscopically aggregate model of the present invention with a substitution rate of 30%;
FIG. 7b is a schematic diagram of a recycled concrete microscopically aggregate model of the present invention with a substitution rate of 70%;
FIG. 7c is a schematic diagram of a recycled concrete microscopically aggregate model of the present invention with a substitution rate of 100%.
Detailed Description
In this embodiment, as shown in fig. 1, in the method for constructing a fourier transform-based recycled concrete mesoscopic aggregate model, two-dimensional shape profile information of real aggregate is extracted according to fourier transform, two types of recycled aggregate models are randomly generated by different methods on the basis, the constructed common aggregate model and the constructed recycled aggregate model have strong randomness and better conform to the shape of the aggregate under the section of the real concrete, and the constructed mesoscopic structure model can simultaneously adjust parameters such as the recycled aggregate substitution rate and the mortar adhesion rate. Specifically, the method comprises the following steps:
step 1: establishing a planar rectangular coordinate system by taking a left lower corner point of a rectangular section of the concrete sample as a coordinate origin, taking the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a planar rectangular domain T with the width W and the height H, wherein the left lower corner point of the planar rectangular domain T is the coordinate origin;
step 2: cutting a concrete test piece, after polishing and grinding the section, taking a picture to obtain a plurality of digital images of the real section of the concrete, scanning a plurality of aggregates by an X-ray CT scanning technology to obtain CT scanning section images of a plurality of aggregates, extracting a boundary contour pixel coordinate sequence of each aggregate in each image in a plane rectangular coordinate system, calculating a Fourier descriptor and a phase angle of the boundary contour pixel coordinate sequence of each aggregate, numbering and storing the Fourier descriptor and the phase angle, thereby establishing a two-dimensional aggregate information database, and enabling the total number of the aggregates in the database to be N, and the method comprises the following steps:
step 2.1: converting the image into a gray image and binarizing, and obtaining a boundary contour pixel coordinate sequence E of each aggregate by an edge detection means of the digital image n ＝{(x mn ,y mn )|m＝1,2,3…M n N =1,2,3, \8230N, wherein E n A boundary contour pixel coordinate sequence representing the nth aggregate, (x) mn ,y mn ) M-th coordinate, M, representing the n-th aggregate boundary contour pixel coordinate sequence n Representing the number of coordinates of the boundary contour pixel coordinate sequence of the nth aggregate; obtaining a boundary pixel outline coordinate sequence { E 'of the aggregate when the center of the aggregate is positioned at the coordinate origin by using the formula (1)' n L N =1,2,3, \ 8230; N }, wherein E' n Represents a boundary contour coordinate sequence of the nth aggregate with its center at the origin of coordinates, and E' n ＝{(x 0 mn ,y 0 mn )|m＝1,2,3…M n }，(x 0 mn ,y 0 mn ) An mth coordinate representing an nth aggregate boundary contour pixel coordinate sequence with a center located at the origin of coordinates;
x in the formula (1) mn ,y mn Respectively represent the abscissa and ordinate, x, of the mth contour point of the nth aggregate 0mn ,y 0mn Respectively represent the abscissa and ordinate of the mth contour point when the center of the nth aggregate is positioned at the origin of coordinates.
The outline rectangular coordinate sequence E 'of each aggregate is obtained by the following formula (2)' n Conversion into polar coordinate series F n L N =1,2,3 \ 8230n }, wherein F n A polar coordinate sequence of boundary contour pixels representing the nth aggregate, and F n ＝{(θ mn ,r mn )|m＝1,2,3,…M}；(θ mn ,r mn ) An mth polar coordinate representing an nth aggregate boundary contour pixel polar coordinate sequence;
x in the formula (2) 0mn ,y 0mn Respectively represent the abscissa and ordinate theta of the mth contour point when the center of the nth aggregate is positioned at the origin of coordinates mn ,r mn Respectively represent the polar angle and the polar diameter of the mth contour point when the center of the nth aggregate is positioned at the origin of polar coordinates, and atan2 is an arctangent function taking the quadrant into consideration.
Step 2.2: selecting a resampling angle theta = { theta = [ [ theta ] ] j ＝j/2πN 1 |j＝1,2,3…N 1 }(θ j E (0, 2 π)), and interpolating F n Processing to obtain the polar diameter value R of the nth aggregate profile under the resampling angle theta n ＝{R jn |j＝1,2,3…N 1 }; thereby obtaining the polar diameter value { R ] of each aggregate profile under the resampling angle theta n L N =1,2,3, \8230; N }; wherein, theta j Denotes the jth resampling angle, R jn Represents the nth aggregate profile at a resampling angle theta j Value of lower pole diameter, N 1 Number of sampling points N 1 Should satisfy the power of L of 2 to ensure that the FFT fast algorithm can be used, and N 1 Should not be less than 128 to ensure that detailed information of the particle profile can be retained;
step 2.3: calculating discrete Fourier coefficient { (A) of each aggregate profile by using equation (3) tn ,B tn )|t＝1,2,3…N 1 And mean polar diameter value r n (N =1,2,3, \ 8230n), and then a real number fourier descriptor D of the nth aggregate profile is calculated using equation (4) n ＝{D tn |t＝1,2,3…N 1 And phase angle δ n ＝{δ tn |t＝1,2,3…N 1 Storing the aggregate data into txt files or excel files in sequence so as to extract the files for scaling and reconstructing the aggregate outline and putting the files again (as shown in figure 2), establishing a two-dimensional aggregate information database for the file number of each aggregate, and recording the number N of the aggregates in the database, wherein N is not less than 100;
r in the formula (3) jn Showing the nth aggregate profile at the jth resampling angle theta j Value of lower pole diameter, A tn ,B tn Represents the nth aggregate profile R n (θ j ) Fourier coefficient of (r) n The average pole diameter values of the nth aggregate profile at all resampling angles theta are shown.
D in the formula (4) tn And delta tn Respectively represent the n-th aggregate profile R n (θ j ) Real fourier descriptors and phase angles.
And step 3: acquiring basic parameters, including: the section width W and the height H of the recycled concrete test piece, and the percentage P of the aggregate volume in the total volume of the recycled concrete k Size of sieve with holes [ D ] 1 ,D 2 …D i-1 ,D i ,D i+1 …D max ]The replacement rate R of the recycled aggregate belongs to (0, 1); wherein D is max Represents the maximum particle size of the aggregate; d i Indicates the size of the ith screen; determining the area ratio of the aggregates of each grade according to a Walraven formula (5)), and calculating the theoretical calculation input area { S) of the aggregates in each grade range according to a formula (6) i I =2,3, \8230;, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The feeding area is calculated theoretically for the aggregate;
S i ＝[P i (D＜D i )-P i-1 (D＜D i-1 )]×W×H (6)
in the formulae (5) and (6), P (D)<D 0 ) The particle diameter D of aggregate in the section is smaller than the sieve pore D 0 Probability within range, P k The volume of the aggregate accounts for the total volume of the recycled concrete, D max Is the maximum particle diameter of the aggregate, S i Indicates that the particle diameter is in the range of (D) i-1 ,D i ) Theoretical calculation of aggregateThrow area, P i (D<D i ) The particle diameter D of aggregate in the section is smaller than the sieve pore D i The probability in the range, W, is the section width of the test piece, and H is the section height of the test piece.
And 4, step 4: initializing i = max, and sequentially feeding aggregates according to the order of size fractions from large to small;
and 5: randomly generating a number r e (0, 1) if r>R, the generation size range is (D) i-1 ,D i ) The common aggregate model comprises the following steps:
step 5.1a: randomly generating an aggregate sequence number integer s epsilon (1, N) and an aggregate contour rotation angle
Control parameter r of equivalent particle size of aggregate s ∈0.5(D i-1 ,D i+1 )；
Step 5.2a: contour analytical formula R of aggregate s (θ j ) The formula (7) can be represented by Fourier series, the aggregate profile can be reconstructed by using the real Fourier descriptor and the phase angle of the s-th aggregate stored in the database, and the reconstruction polar diameter value { G ] of the s-th aggregate profile under the resampling point theta is calculated js |j＝1,2,3…N 1 In which G js Expressed at the resampling angle theta j Reconstructing the polar diameter value of the next s-th aggregate contour, and obtaining the polar coordinate sequence J of the reconstructed s-th aggregate contour s ＝{(θ j ,G js )|j＝1,2,3…N 1 Converting into a rectangular coordinate sequence and multiplying by an angle to obtain
The rotational matrix (6) ensures the randomness of the aggregate to obtain Z s ＝{(x js ,y js )|j＝1,2,3…N 1 Wherein (x) js ,y js ) A jth coordinate representing an s-th aggregate contour coordinate sequence;
d in formula (7) ts And delta ts Respectively show the s-th aggregate profile G s (θ j ) And the t-th real fourier descriptor and the phase angle, θ j Denotes the jth resampling angle, r s The parameter for controlling the equivalent particle size of the aggregate, G js Expressed at the jth resampling angle theta j Reconstruction polar diameter value, N, of the next s-th aggregate profile 2 For Fourier expansion order, according to Nyquist sampling theorem, N 2 ≤(N 1 /2)。
In the formula (8)
Is the rotation angle of the s-th aggregate, RT s Is a rotation matrix of the s-th aggregate.
Step 5.3a: calculating the equivalent particle diameter d of the s-th aggregate after reconstruction according to the formula (8) s (equivalent elliptical Feret minor axis);
s in formula (9) s Is the area of the s-th aggregate after reconstitution, a s Is the maximum Feret diameter after the s-th aggregate is reconstructed, d s The equivalent particle size of the s-th aggregate after reconstitution.
If d is s ∈(D i-1 ,D i ) The size range of the aggregate model generated on the surface meets the requirement, and the pre-throwing central coordinate (x) of the aggregate is randomly generated s ,y s ) Is a reaction of Z s The central coordinate of (a) is moved to the pre-placing center (x) of the aggregate s ,y s ) Obtaining a coordinate sequence Z' s ＝{(x’ js ,y’ jsz )|j＝1,2,3…N 1 },Z’ s The enclosed pattern is used as a common aggregate model. Otherwise, returning to the step 5.1a;
if R is less than or equal to R, the aggregate superposition method is used for generating the product with the size fraction range of (D) i-1 ,D i ) As shown in fig. 3, the concrete steps of the recycled aggregate model are as follows:
step 5.1b: repeating the steps 5.1a and 5.1a twice to obtain rectangular coordinate sequences X of two different common aggregate models 1 And X 2 Is mixing X 1 And X 2 Integrating into a group of points, calculating the boundary coordinate sequence X of the group of points 3 ，X 3 The surrounded graph is marked as synthetic aggregate;
step 5.2b: calculating the equivalent particle diameter D of the synthetic aggregate according to the formula (9), if the D belongs to (D) i-1 ,D i ) Generating the coordinate (X, y) of the pre-casting center of the recycled aggregate model randomly, and calculating the X 3 And X 1 The center coordinates of (2) are moved to the aggregate pre-casting center (X, y) to obtain a coordinate sequence X' 3 And X' 1 ，X’ 1 The surrounded figure is used as an aggregate phase of a recycled aggregate model, X' 3 And X' 1 The difference set of the enclosed patterns is used as an attached mortar phase, and the two phases jointly form a recycled aggregate model. When there are 1 mortar remaining in the recycled aggregate model, it is designated as 1 type recycled aggregate, and when there are 2 adhering mortars, it is designated as 2 type recycled aggregate model (as shown in FIG. 3). Otherwise, returning to the step 5.1a;
step 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate model simultaneously satisfies the boundary condition and the aggregate interference condition or not, and if so, the size fraction range is within (D) i-1 ,D i ) Is put into the plane rectangular domain, and the size fraction range is calculated to be (D) i-1 ,D i ) The area a of the s-th charged aggregate is S =1,2, \ 8230;, L (when the aggregate model is a recycled aggregate convex polygonal model, the area F of the adhering mortar polygonal model in the kth recycled aggregate convex polygonal model is calculated k ，k＝1,2,…,L 1 ) (ii) a Otherwise, returning to the step 5; when the size fraction (D) i-1 ,D i ) Cumulative aggregate charging area A i Theoretical calculated area S less than the size fraction i Returning to the step 5 to continue throwing the aggregate in the size fraction section; a. The i Greater than S i When the aggregate is not put into the particle size section, the last aggregate is abandoned, and a smaller aggregate is generated in the particle size section again to continue to be put into the particle size section until the aggregate is obtainedTo a size fraction in the range of (D) i-1 ,D i ) L cumulative charging area for charging aggregate
Satisfying the formula (1);
A i ∈((1-σ)S i ,(1+σ)S i )(10)
in the formula (10), σ represents a parameter between (0, 1), S i Indicates that the particle size range is (D) i-1 ,D i ) The theoretical calculation of the aggregate of (A) the input area i Indicating that the size fraction is in the range of (D) i-1 ,D i ) The cumulative feeding area of the aggregate; in order to ensure the cumulative feeding area A of each grain size i As close as possible to the theoretical calculated area S of the fraction i And σ may take 0.2.
Firstly, the aggregate model carries out the judgment of boundary conditions: as shown in fig. 4, if the minimum bounding rectangle of the aggregate model is inside the drop rectangle, the aggregate inevitably satisfies the boundary condition, otherwise, the aggregate is determined not to satisfy the boundary condition. Minimum external rectangle T for judging aggregate model s (the minimum circumscribed rectangle side is parallel to the coordinate axis of the coordinate system generated in step 4) and the planar rectangle T, if T s And within the T, the aggregate meets the boundary condition of the throwing area, otherwise, the aggregate model does not meet the boundary condition. The aggregate model satisfying the boundary condition is further subjected to judgment of the aggregate interference condition, and the size fraction range is judged to be (D) i-1 ,D i ) Whether the aggregate model AG meets the aggregate interference condition:
step 6.1: in order to improve the efficiency of aggregate interference judgment, whether the minimum circumscribed rectangles of the irregular aggregates are intersected or not is utilized to roughly judge the position relationship of the aggregates, if the minimum circumscribed rectangles of the AG do not intersect with the minimum circumscribed rectangles of all the aggregates which are thrown in, the AG is inevitably not interfered with other aggregates and is directly thrown into the plane rectangular domain generated in the step 4, and otherwise, further judgment is needed. Searching for a circumscribed rectangle T of AG in circumscribed rectangles of all the placed aggregate models 0 Intersecting rectangles C = { C f L f =1,2 \8230e }, and the name of aggregate set corresponding to the same is recordedAGG，AGG＝{A f L f =1,2 \ 8230e }, wherein c f Denotes the f-th and T 0 Intersecting circumscribed rectangles of the poured aggregate model, A f Denotes the f-th circumscribed rectangle and T 0 Intersecting charged aggregate model, e denotes the sum of T 0 The number of the intersected external rectangles of the placed aggregate models; if the C is an empty set, the aggregate interference condition is met, otherwise, the step 6.2 is executed;
step 6.2: further judging by utilizing the maximum inscribed circle of the aggregate, judging whether the maximum inscribed circle of the AG and the maximum inscribed circle of any aggregate in the AGG have an intersection relation, if so, indicating that the aggregate interference condition is not met, otherwise, executing the step 6.3;
step 6.3: let f =1, perform step 6.4;
step 6.4: if the minimum bounding rectangles of the two irregular aggregates 1 and 2 intersect, and interference occurs between the aggregates, which inevitably occurs in the rectangles of the overlapping area, as shown in fig. 5, c is calculated f And T 0 Rectangle E of the overlapping area f Polar angle ψ = { ψ) of the four vertices of (2) in a polar coordinate system with the center of aggregate AG as the origin of coordinates 1 ,ψ 2 ,ψ 3 ,ψ 4 Therein, ψ 1 ,ψ 2 ,ψ 3 ,ψ 4 Respectively represent a rectangle E f The four vertexes of the angle model are polar angle values under a polar coordinate system taking the center of the aggregate AG as the origin of coordinates; and calculating a rectangle E under a rectangular coordinate system taking the center of the aggregate AG as the origin of coordinates f Lower left corner coordinate vertex (X) lf ,Y lf ) And E f Central abscissa X of cf And E f Height L of 1 (length of side parallel to y-axis) if X cf > 0 and Y lf ×(Y lf +L 1 ) If < 0, let α = { α = p ＝2p·ψ m /N 5 |p＝0,1,2…N 5 /2}∪{α p ＝ψ n +(4π-2ψ n )·p/N 5 |p＝N 5 /2,N 5 /2+1,…N 5 Else, α = { α = } p ＝ψ a +p·(ψ b -ψ a )/N 5 |p＝0,1,2…N 5 Therein, ψ m Is the maximum polar angle value phi smaller than pi n Is the minimum polar angle value larger than pi in psi a Is the minimum polar angle value, psi, in the set psi b Is the maximum polar angle value in psi, alpha represents the polar angle value set to be verified, alpha p Representing the p-th polar angle value to be verified, N 5 The number of division points; only the contour coordinates of the aggregate AG under the polar angle alpha need to be reconstructed, and whether the points are at the aggregate AG or not is judged f The AG and the AG can be obtained from the interior of f Whether or not interference occurs.
Step 6.5: the interference condition when the minimum circumscribed rectangles of the two irregular aggregates are intersected necessarily meets four conditions in fig. 6a, when the conditions (1) and (2) occur, although the minimum circumscribed rectangles of the aggregates 1 and 2 are intersected, all contour points of at least one aggregate are not in the interior of the rectangular EOB, the aggregates do not interfere in the two conditions, when the conditions (3) and (4) occur, namely part of contour points of the aggregates 1 and 2 are in the EOB, the aggregates may interfere or not, and further judgment is needed. Calculating a polar coordinate value sequence of the contour points of the aggregate model AG under the polar angle value set alpha and converting the polar coordinate value sequence into a rectangular coordinate sequence
Z 1 ＝{(x’ p ,y’ p )|p＝1,2,3…N 5 Wherein, x' p ,y’ p ) Representing the coordinates to be verified of the pth on the outline of the aggregate model AG; if Z is 1 All coordinate points are not in E f If the inside of the aggregate satisfies one of the conditions (1) and (2), the f-th aggregate A f The condition is (3) or (4), and further judgment is needed to calculate Z 1 All coordinate points in to the f aggregate A f Distance d = { d) of centers p |p＝1,2,3…N 5 Z and 1 all coordinate points in the aggregate are defined as f-th aggregate A f A polar angle set τ = { τ = in a polar coordinate system with the center of (a) the origin of coordinates p |p＝1,2,3…N 5 }, calculating the f-th aggregate A f Set of polar values { I } of contour points under set of polar angles τ p |p＝1,2,3…N 5 In which d is p Represents the p coordinate point to be verified to the f aggregate A f Distance of the centers, τ p Represents Z 1 The p-th coordinate point in the specification is defined as the f-th aggregate A f Polar angle in a polar coordinate system with the center of origin of coordinates, I p Denotes the f-th aggregate A f At p polar angle τ p A polar diameter value of the lower contour point; if I is present, as in FIG. 6b p ＞d p Description of Z 1 At the p-th point in aggregate A f The f-th aggregate A f Inevitably interfere with the aggregate AG, otherwise, it represents the f-th aggregate A f Does not interfere with the aggregate AG; the method can accurately, quickly and efficiently judge whether the two aggregates with irregular shapes interfere with each other;
step 6.6: assigning f +1 to f, returning to the step 6.4 for sequential execution until f is greater than e, and if the aggregate AG is not interfered with all aggregates in the AGG, satisfying the aggregate interference condition, otherwise not satisfying the aggregate interference condition;
and 7: assigning i-1 to i, returning to the step 4 for sequential execution, and sequentially putting the aggregate models of all the particle sizes according to the sequence of big first and small second until i<2 until the aggregate is calculated to obtain the cumulative feeding area { A of the aggregate in each size fraction range i |i＝2,3,…,max}；
And 8: the aggregate total charging area ratio S is calculated according to the formula (11) A And the area ratio S of the attached old mortar M The method is used for constructing a recycled concrete mesoscopic aggregate model.
S in formula (11) A And S M Respectively the aggregate total throwing area ratio and the attached old mortar area ratio, A i Is (D) i-1 ,D i ) The actual area of aggregate feeding in the grain size section, max is the number of the hole sieves, W and H are the width and the height of the section of the test piece respectively, and L 1 Number of particles to feed recycled aggregate, F k The area of the adhering mortar polygonal model in the kth recycled aggregate convex polygonal model.
In this embodiment, an electronic device includes a memory for storing a program that supports a processor to execute the above-described building method, and a processor configured to execute the program stored in the memory.
In this embodiment, a computer-readable storage medium stores a computer program, and the computer program is executed by a processor to execute the steps of the above-mentioned construction method.
Example (b): the method comprises the following steps of constructing a Fourier transform-based recycled concrete mesoscopic aggregate model:
step 1: preparing a concrete sample of 10cm multiplied by 10cm and cutting, and after polishing and grinding the obtained section, photographing to obtain a plurality of digital images of the real section of the concrete, or scanning a plurality of coarse aggregates by an X-ray CT scanning technology to obtain a plurality of CT scanning section images of the aggregates;
step 2: self-programming, processing the plurality of images obtained in the step 1 in batches, extracting boundary contour pixel coordinate sequences of all aggregates in each image, obtaining Fourier coefficients of all the aggregate coordinate sequences by utilizing Matlab built-in functions fft, then calculating Fourier descriptors and phase angles of all the aggregate coordinate sequences, storing the Fourier descriptors and the phase angles as txt files, storing the txt files of all the aggregates in the same folder for convenient calling, and establishing a two-dimensional aggregate information database with the aggregate quantity of 1997 by processing 500 images;
and step 3: determining basic parameters:
the section width W =100mm and the height H =100mm of the recycled concrete test piece, and the aggregate volume accounts for the total volume percentage P of the recycled concrete k =0.75, minimum particle diameter of aggregate D min =4.75mm, aggregate maximum particle size D max =25mm, the mesh size is 4.75mm,9.5mm,16mm,19mm,25mm, and the substitution rate of the recycled aggregate is respectively 30%,70%,100%, namely R =0.3,0.6,1; calculating the area ratio of the aggregates of each size fraction in the aggregate feeding area: according to the Walraven formula, calculating to obtain the aggregate with the particle size of 19-25 mm and the input area of 674mm 2 The aggregate with the grain size of 16-19 mm is put in the area of 494mm 2 The aggregate feeding area with the grain size of 9.5-16 mm is 1401mm 2 The particle size fraction was 4.75-9.5 mm of aggregate feeding area is 1434mm 2 The total charging area of the aggregate accounts for 40 percent.
And 4, step 4: establishing a plane rectangular coordinate system by taking a left lower corner point of a rectangular section of the test piece as a coordinate origin, the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, generating a plane rectangular domain with the width of W and the height of H, and initializing i =5;
and 5: the number R = rand (1) ranging from (0, 1) is randomly generated, and when R > R, the size fraction ranges from (D) 4 ,D 5 ) The general aggregate model of (1): randomly generating an aggregate number integer s = randi (1997, 1) and an aggregate contour rotation angle by using a Matlab built-in function randi
Control parameter r of equivalent particle size of aggregate s ＝0.5×[D i-1 +(D i -D i-1 )×rand(1)]And the coordinate x of the pre-placing center of the aggregate s ＝W×rand(1),y s = H × rand (1); calling data information of the s-th aggregate from the database, and converting the data information into a coordinate sequence Z 'with the particle size meeting the requirement' s Z 'is formed by using Matlab built-in function fill' s Filling to obtain a common aggregate model; if r>R, the generation size range is (D) i-1 ,D i ) The recycled aggregate model of (2): firstly, generating two different common aggregate models to obtain rectangular coordinate sequences X of the two different common aggregate models 1 And X 2 Is mixing X 1 And X 2 Combining the points into a group of points, and calculating a boundary coordinate sequence X of the group of points by using a Matlab built-in function boundry 3 Obtaining synthetic aggregate satisfying the particle size requirement, generating the pre-casting center coordinates X = W × rand (1), y = H × rand (1) of the recycled aggregate model, and mixing X 3 And X 1 The center coordinates of (2) are moved to the aggregate pre-casting center (X, y) to obtain a coordinate sequence X' 3 And X' 1 X 'is formed by using Matlab built-in function fill' 1 Filling to obtain an aggregate phase of a recycled aggregate model, filling X' 3 And X' 1 The difference set of the enclosed patterns is used as an attached mortar phase, and the attached mortar phase form a recycled aggregate model together.
Step 6: firstly, the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate model meets the boundary conditions:
and (4) determining whether the two rectangles are functions of the inclusion relationship by utilizing Matlab self-programming. And (5) judging whether the minimum circumscribed rectangle of each aggregate to be thrown is inside the large throwing area rectangle or not, if the conditions are met, carrying out next aggregate interference judgment, and if not, returning to the step 5. And further judging an aggregate interference condition by the aggregate model meeting the boundary condition: and (3) judging whether the two rectangles are functions of an intersection relation or not by utilizing Matlab self-programming, judging whether the minimum circumscribed rectangle of the newly generated aggregate has the intersection relation with the minimum circumscribed rectangle of any one thrown aggregate, if not, directly throwing, and if not, carrying out the next judgment: and (4) judging whether the two circles are functions of an intersection relationship by the self-programming function, judging whether the minimum circumscribed circle of the newly generated aggregate and the minimum circumscribed circle of the surrounding aggregates (the aggregates with the minimum circumscribed rectangle intersected with the minimum circumscribed rectangle of the newly generated aggregate) have the intersection relationship, if so, returning to the step 5, and otherwise, carrying out next judgment. And self-editing and judging whether the two irregularly-shaped aggregates are intersected according to a minimum circumscribed rectangle intersection judging method, if the newly generated aggregates meet the aggregate interference condition, smoothly throwing the aggregates, and otherwise, returning to the step 5.
And 7: assigning i-1 to i, and then returning to the step 4 to execute the sequence until i is less than 2, thereby obtaining the accumulated throwing area of each size range; when the accumulated feeding area of the aggregate of a certain size fraction is smaller than the theoretical calculation area of the size fraction, continuously feeding the aggregate of the size fraction; when the accumulated throwing area is larger than the theoretical calculation area, giving up the throwing of the last aggregate, generating a smaller aggregate again in the particle size section, continuing to throw the aggregate until the accumulated throwing area of the current particle size aggregate reaches 0.98-1.02 times of the theoretical calculation area of the particle size aggregate, and throwing the aggregate of the next particle size until all the particle size sections are thrown;
and 8: calculating the aggregate total throwing area ratio S A And the area ratio S of the attached old mortar M 。
FIG. 7a shows the regenerated concrete with a substitution rate of 30%Calculating to obtain S from a soil mesoscopic aggregate model diagram A 43.98% of S M 9.77%; FIG. 7b is a model diagram of a recycled concrete mesoscopic random aggregate with a substitution rate of 70%, and S is calculated A 43.02% of S M 16.63 percent; FIG. 7c is a model diagram of a recycled concrete mesoscopic random aggregate with a substitution rate of 100%, and S is calculated A 42.97% of S M The content was 25.70%.
Claims (8)
1. A construction method of a recycled concrete mesoscopic aggregate model based on Fourier transform is characterized by comprising the following steps:
step 1: establishing a planar rectangular coordinate system by taking a left lower corner point of a rectangular section of the concrete sample as a coordinate origin, taking the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a planar rectangular domain T with the width W and the height H, wherein the left lower corner point of the planar rectangular domain T is the coordinate origin;
step 2: acquiring a plurality of concrete real section digital images and CT scanning section images of aggregates, extracting boundary contour pixel coordinate sequences of the aggregates in each image in the plane rectangular coordinate system, calculating Fourier descriptors and phase angles of the boundary contour pixel coordinate sequences of the aggregates, numbering and storing the Fourier descriptors and the phase angles, and accordingly establishing a two-dimensional aggregate information database, and enabling the aggregate total number in the database to be N;
and step 3: determining basic parameters, including: section width W and height H of recycled concrete test piece, and aggregate volume ratio P k Size of sieve with holes [ D ] 1 ,D 2 …D i-1 ,D i ,D i+1 …D max ]The recycled aggregate substitution rate R; wherein D is max Represents the maximum particle size of the aggregate; d i Indicates the size of the ith screen; theoretical calculation of feeding area { S) for aggregate in each size fraction range i I =2,3, \8230;, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The theoretical calculation of the feeding area of the aggregate is carried out;
and 4, step 4: initializing i = max;
and 5: randomly generating the ith number r i E (0, 1) if r i >R, the generation size range is (D) i-1 ,D i ) If r is a normal aggregate model of i When the particle size is less than or equal to R, the aggregate superposition method is used for generating the particles with the size range of (D) i-1 ,D i ) The recycled aggregate model of (1);
step 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the aggregate model of (2) satisfies both the boundary condition and the aggregate interference condition, and if so, the size fraction range is within (D) i-1 ,D i ) Is put into the plane rectangular field T, and the size fraction range is calculated to be (D) i-1 ,D i ) The area a of the s-th charged aggregate is S =1,2, \ 8230;, L; l represents the number of all the aggregates to be put, when the aggregate model is a recycled aggregate convex polygon model, the area F of an adhesive mortar polygon model in the kth recycled aggregate convex polygon model is calculated k ，k＝1,2,…,L 1 (ii) a Wherein L is 1 Representing the total number of the thrown recycled aggregates, otherwise, returning to the step 5; until a particle size range (D) is obtained i-1 ,D i ) L cumulative charging area for charging aggregate
Satisfying the formula (1);
A i ∈((1-σ)S i ,(1+σ)S i ) (1)
in formula (1), σ represents a parameter between (0, 1);
and 7: after i-1 is assigned to i, the step 5 is returned to for sequential execution until i<2 so as to obtain the cumulative charging area { A of the aggregates in each size fraction range i |i＝2,3,4…,max}；
And 8: calculating the aggregate input area ratio S A And the area ratio S of the attached old mortar M The method is used for constructing a recycled concrete mesoscopic aggregate model.
2. The construction method of the fourier transform-based recycled concrete meso-aggregate model according to claim 1, wherein the step 2 comprises:
step 2.1: converting all images into gray level images, carrying out binarization processing to obtain binary images, carrying out edge detection on the binary images to obtain boundary contour pixel coordinate sequences E of all aggregates n ＝{(x mn ,y mn )|m＝1,2,3…M n N =1,2,3, \ 8230N, wherein E n A boundary contour pixel coordinate sequence representing the nth aggregate, (x) mn ,y mn ) M-th coordinate, M, representing the n-th aggregate boundary contour pixel coordinate sequence n Representing the number of coordinates of the boundary contour pixel coordinate sequence of the nth aggregate;
moving the center of the aggregate to the origin of coordinates to obtain a boundary contour coordinate sequence { E 'of the aggregate when the center of the aggregate is located at the origin of coordinates' n L N =1,2,3, \ 8230; N }, wherein E' n Represents a boundary contour coordinate sequence of the nth aggregate with its center at the origin of coordinates, and E' n ＝{(x 0 mn ,y 0 mn )|m＝1,2,3…M n }，(x 0 mn ,y 0 mn ) An mth coordinate representing an nth aggregate boundary contour pixel coordinate sequence with a center located at the origin of coordinates; boundary contour coordinate sequence { E 'of each aggregate' n I N =1,2,3, \8230; N } is converted into a polar sequence { F } n L N =1,2,3 \ 8230n }, wherein F n A polar coordinate sequence of boundary contour pixels representing the nth aggregate, and F n ＝{(θ mn ,r mn )|m＝1,2,3,…M}；(θ mn ,r mn ) An mth polar coordinate representing an nth aggregate boundary contour pixel polar coordinate sequence;
step 2.2: selecting a resampling angle theta = { theta = [ [ theta ] ] j ＝j/2πN 1 |j＝1,2,3,…,N 1 F is interpolated by n Processing to obtain the polar diameter value R of the nth aggregate profile under the resampling angle theta n ＝{R jn |j＝1,2,3…N 1 }; thereby obtaining the polar diameter value { R ] of each aggregate profile under the resampling angle theta n L N =1,2,3, \8230; N }; wherein, theta j Denotes the jth resampling angle, R jn Represents the nth aggregate profile at a resampling angle theta j Value of lower pole diameter, N 1 Representing the number of sampling points;
step 2.3: calculating a real Fourier descriptor D of the nth aggregate profile n ＝{D tn |t＝1,2,3…N 1 And phase angle δ n ＝{δ tn |t＝1,2,3…N 1 Sequentially storing, establishing a two-dimensional aggregate information database for the file number of each aggregate, and recording the number N of the aggregates in the database; wherein D is tn The t-th real Fourier descriptor, δ, representing the nth aggregate profile tn The t-th phase angle representing the n-th aggregate profile.
3. The construction method of the Fourier transform-based recycled concrete mesoscopic aggregate model as recited in claim 2, wherein the step of generating a common aggregate model in the step 5 comprises:
step 5.1a: randomly generating the aggregate sequence number s epsilon (1, N) and the aggregate contour rotation angle
Control parameter r of equivalent particle size of the s-th aggregate s ∈0.5(D i-1 ,D i )；
Step 5.2a: calculating a reconstruction polar diameter value { G ] of the s-th aggregate profile under the resampling point theta by using the formula (2) js |j＝1,2,3…N 1 In which G js Expressed at the resampling angle theta j Reconstructing the diameter value of the next s-th aggregate profile; the polar coordinate sequence J of the reconstructed s-th aggregate profile s ＝{(θ j ,G js )|j＝1,2,3…N 1 Converting into rectangular coordinate sequence and multiplying by angle
Obtaining a coordinate sequence Z of the s-th aggregate profile after rotating the matrix s ＝{(x js ,y js )|j＝1,2,3…N 1 }; wherein (x) js ,y js ) A jth coordinate representing an s-th aggregate contour coordinate sequence;
in the formula (6), D ts And delta ts The tth real Fourier descriptor and the phase angle, N, respectively representing the s-th aggregate profile 2 A Fourier expansion order;
step 5.3a: calculating the equivalent particle diameter d of the s-th aggregate after reconstruction s If d is s ∈(D i-1 ,D i ) Then, the coordinate (x) of the center of the aggregate to be placed is randomly generated s ,y s ) And is combined with Z s The central coordinate of (a) is moved to the pre-placing center (x) of the aggregate s ,y s ) Obtaining a coordinate sequence Z' s From Z' s The surrounded graph is the s-th common aggregate model; otherwise, return to step 5.1a.
4. The construction method of the recycled concrete mesoscopic aggregate model based on Fourier transform as recited in claim 3, wherein the step 5 of generating the recycled aggregate model by using an aggregate superposition method comprises the following steps:
step 5.1b: repeating the steps 5.1a and 5.2a twice to obtain coordinate sequences Z of two different common aggregate models 1 And Z 2 Is a reaction of Z 1 And Z 2 Integrating into a group of points, calculating the boundary coordinate sequence X of the group of points 3 From X 3 The surrounded graph is marked as synthetic aggregate;
step 5.2b: calculating the equivalent grain diameter D of the synthetic aggregate, and if D belongs to (D) i-1 ,D i ) Generating the coordinate (X, y) of the pre-throwing center of the aggregate randomly, and dividing the X 3 And X 1 The center coordinate of (2) is moved to the aggregate pre-casting center (X, y) to obtain a coordinate sequence X' 3 And X' 1 From X' 1 The surrounded pattern is the aggregate phase of the recycled aggregate model and is X' 3 And X' 1 The difference set of the enclosed patterns is an attached mortar phase, and the aggregate phase and the attached mortar phase jointly form a recycled aggregate model; otherwise, return to step 5.1b.
5. The construction method of the recycled concrete mesoscopic aggregate model based on Fourier transform as recited in claim 1, wherein the judging manner of whether the aggregate model meets the boundary condition in the step 6 is as follows:
minimum external rectangle T for judging aggregate model s The position relation with the plane rectangular field T if T s And within the T, the aggregate meets the boundary condition of the throwing area, otherwise, the aggregate model does not meet the boundary condition.
6. The construction method of the Fourier transform-based recycled concrete mesoscopic aggregate model according to claim 1, wherein the determination manner of whether the aggregate model AG meets the aggregate interference condition in the step 6 is a minimum circumscribed rectangle intersection method:
step 6.1: searching the minimum bounding rectangle T with AG in the minimum bounding rectangles of all the placed aggregate models 0 Intersecting rectangles C = { C f I f =1,2 \8230e }, and the corresponding aggregate set name is AGG, AGG = { A = { (A) } f L f =1,2 \ 8230e }, wherein c f Denotes the f-th and T 0 Intersecting minimum circumscribed rectangle of poured aggregate model, A f Represents the f-th minimum bounding rectangle and T 0 Intersecting charged aggregate model, e denotes the sum of T 0 The number of the intersected minimum external rectangles of the placed aggregate models; if the C is an empty set, the aggregate interference condition is met, otherwise, the step 6.2 is executed;
step 6.2: judging whether the maximum inscribed circle of the AG is intersected with the maximum inscribed circle of any aggregate in the AGG, if so, indicating that the aggregate interference condition is not met, otherwise, executing the step 6.3;
step 6.3: let f =1, perform step 6.4;
step 6.4: calculation of c f And T 0 Rectangle E of the overlapping area f Polar angle ψ = { ψ) of the four vertices of the aggregate model AG in a polar coordinate system with the center of the aggregate model AG as the origin of coordinates 1 ,ψ 2 ,ψ 3 ,ψ 4 Therein, ψ 1 ,ψ 2 ,ψ 3 ,ψ 4 Respectively represent E f The four vertexes of the angle model are polar angle values under a polar coordinate system taking the center of the aggregate AG as the origin of coordinates; and calculating a rectangle E under a rectangular coordinate system taking the center of the aggregate model AG as the origin of coordinates f Lower left corner coordinate vertex (X) lf ,Y lf ) And E f Central abscissa X of cf And E f Height L of 1 If X is cf > 0 and Y lf ×(Y lf +L 1 ) If < 0, let α = { α = p ＝2p·ψ m /N 5 |p＝0,1,2…N 5 /2}∪{α p ＝ψ n +(4π-2ψ n )·p/N 5 |p＝N 5 /2,N 5 /2+1,…N 5 Else, let α = { α = } p ＝ψ a +p·(ψ b -ψ a )/N 5 |p＝0,1,2…N 5 Therein, ψ m Is the maximum polar angle value phi smaller than pi n Is the minimum polar angle value larger than pi in psi a Is the minimum polar angle value, psi, in the set psi b Is the maximum polar angle value in psi, alpha represents the polar angle value set to be verified, alpha p Representing the p-th polar angle value to be verified, N 5 The number of division points;
step 6.5: calculating a polar coordinate value sequence of the contour points of the aggregate model AG under the polar angle value set alpha and converting the polar coordinate value sequence into a rectangular coordinate sequence Z 1 ＝{(x’ p ,y’ p )|p＝1,2,3…N 5 Wherein, x' p ,y’ p ) Representing the coordinates to be verified of the pth on the outline of the aggregate model AG; if Z is 1 All coordinate points in the coordinate system are not in E f The f-th aggregate A inside f Does not interfere with the aggregate model AG, otherwise, calculates Z 1 All coordinate points in to the f aggregate A f Distance d of center = { d = { [ d ] p |p＝1,2,3…N 5 Z and 1 all coordinate points in the aggregate are defined as f-th aggregate A f A polar angle set τ = { τ = in a polar coordinate system with the center of (a) the origin of coordinates p |p＝1,2,3…N 5 }, calculating the f-th aggregate A f Set of polar values { I } of contour points under set of polar angles τ p |p＝1,2,3…N 5 In which d is p Representing the p-th coordinate point to be verified to the f-th aggregate A f Distance of the centers, τ p Represents Z 1 The p-th coordinate point in the specification is defined as the f-th aggregate A f Polar angle in a polar coordinate system with the center of origin of coordinates, I p Denotes the f-th aggregate A f At p polar angle τ p A polar diameter value of the lower contour point; if present, I p ＞d p Then, it means the f-th aggregate A f Interfere with the aggregate model AG, otherwise, represent the f-th aggregate A f The method does not interfere with an aggregate model AG;
step 6.6: and f +1 is assigned to f, the step 6.4 is returned to and sequentially executed until f is larger than e, if the aggregate model AG is not interfered with all aggregates in the AGG, the aggregate interference condition is met, and otherwise, the aggregate interference condition is not met.
7. An electronic device comprising a memory and a processor, wherein the memory is configured to store a program that enables the processor to perform the construction method of any of claims 1-6, and the processor is configured to execute the program stored in the memory.
8. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the construction method according to any one of claims 1 to 6.
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