Structural parameter and topology optimization method and system based on Bayesian network learning

Abstract

The present invention provides a structural parameter optimization method based on Bayesian network learning, which is applied to the optimization and design of the opening parameters of the structure. The method establishes a Bayesian network for predicting the opening ratio, obtains a solid structure set A for the combination of different parent variable state values, obtains a hollow structure set B with different opening parameter values ​​based on the set A, uses the set B as a training sample to obtain the Bayesian network conditional probability, and obtains the expected opening effect Z corresponding to different opening parameters under different calculation parameter combinations through the conditional probability. m This allows the design process to directly optimize opening parameters based on the trained Bayesian network, eliminating numerous iterative calculations and significantly reducing time costs. Furthermore, based on this structural parameter optimization method, a topology optimization method and system are provided. These methods fully incorporate designer experience and Bayesian network learning results as prior probabilities, enabling rapid implementation of structural topology optimization design.

Description

Technical Field

[0001] The present invention is mainly applicable to the topology optimization design of load-bearing structures, and particularly relates to a structural parameter, topology optimization method and system based on Bayesian network learning. Background Art

[0002] Existing structural topology optimization methods require numerous finite element (FEM) iterations to achieve an optimal topological configuration, combined with manual pruning to complete the structural design. These FEM iterations are time-consuming and expensive. When applied to structures requiring dense FEM meshes or complex loads, such as rail transit equipment and bridges, excessive oscillations and iterations can occur, leading to a checkerboard pattern. Furthermore, existing topology optimization techniques rely on a fixed set of rules during the iteration process, with the optimization direction selected entirely by the computer. This neglects the designer's experience with various load-bearing structures, fails to fully leverage the valuable experience of the designer and existing design cases, and lacks the ability to independently learn from existing experience. Summary of the Invention

[0003] To solve the above problems, the present invention provides a structural parameter and topology optimization method and system based on Bayesian network learning, which can fully integrate the designer's experience and Bayesian network learning results as prior probabilities, quickly realize the topology optimization design of general building structures such as rail transit equipment and bridges, reduce the number of iterative optimization times of traditional topology optimization methods, and reduce the time cost of optimization calculations.

[0004] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0005] A structural parameter optimization method based on Bayesian network learning is applied to the optimization and design of opening parameters of a plane force-bearing structure, and is characterized in that the structural parameter optimization method based on Bayesian network learning comprises the following steps:

[0006] S1. Take the force mode x1, material type x2, opening shape x3, opening spacing x4, and opening number x5 as parent variables and the opening ratio y as child variable to establish a Bayesian network for predicting the opening ratio. The state value sequence of y is {y(1)∈[0,1 / n),y(2)∈[1 / n,2 / n),…,y(n)∈[(n-1) / n,1)};

[0007] S2. For different combinations of state values ​​in x1 and x2, under different calculation parameter combinations, conventional structural design methods are used to obtain solid structures that meet the load requirements under each parameter combination and form a set A;

[0008] S3, perform finite element unit division on each structure in set A, apply the calculation parameter combination corresponding to each solid structure in S2, set the unit of the outer contour of each solid structure as a non-optimized area and optimize the remaining area using the conventional topology optimization method, and obtain a set B of hollow structures with different state values ​​of the opening parameters {x3, x4, x5};

[0009] S4, using the set B as a training sample, and obtaining the conditional probability of the Bayesian network in step S1 through a parameter learning method;

[0010] S5. For the structure C to be designed, a solid structure C that satisfies the load is obtained by the structural mechanics method according to the calculation parameter combination of the structure C. A , determine C A x1=x1(m1 (1) ), x2=x2(m2 (1) ), calculate the solid structure C as follows A The probability P and expected opening effect Z corresponding to different combinations of x3, x4, and x5 state values m , press each Z m Sort the values ​​in descending order to form a vector

[0011]

[0012] S6. Select The opening parameters corresponding to the first R elements in the equation are applied to the solid structure C A and form a hollow structure set C B , change C B The opening size is adjusted until a set that satisfies the force is obtained. Select The structure with the largest opening ratio is the one with the optimal opening parameters.

[0013] The technical principle and effect of the above invention are as follows: Based on the principle of probability statistics, this method constructs a set of hollow structures B based on a large number of solid structures A, forms a structure database under a large number of different data combinations, directly constructs a Bayesian network based on the self-built database and completes parameter learning, and obtains the expected opening effect Z corresponding to different opening parameters under different calculation parameter combinations. m , so that for any actual structure C that needs to be designed, the expected opening effect can be predicted directly based on the conditional probability relationship of the Bayesian network learned, and according to Z m Vector of descending values Quickly preliminarily screen out the opening parameter combinations that may achieve a larger opening ratio, and based on the opening parameter combinations with a high probability of achieving better results, quickly select the structure with the best opening ratio through simple size optimization. Complete the optimization of opening parameters and design of load-bearing structures in a plane. This method uses conventional structural design methods (i.e., firstly, the solid cross-section size of the structure is formulated based on design experience, its internal forces are calculated and its stresses are verified based on conventional mechanical methods, and the cross-section size is changed until the minimum cross-section size that meets the stress limit is obtained) to construct a set A of solid structures that meet the load under various parameter combinations, and combines the hollow structure set B after topology optimization to achieve the prediction of the opening effect under different load modes, material types, and opening parameter combinations. In the process of constructing the two structural databases, the designer's experience and topology optimization results are fully integrated as prior probabilities. For new structures to be designed, their opening parameters can be directly optimized according to the trained Bayesian network, eliminating the large number of iterative calculation processes of traditional topology optimization methods, greatly reducing the time cost of optimization design, and can be applied to general building structures such as rail transit equipment and bridges.

[0014] Preferably, in step S1, the parent variable x1 is the force type of the structure, and the state values ​​of the parent variable x1 include {x1(1) = bending and shear, x1(2) = small eccentric compression, x1(3) = large eccentric compression, x1(4) = small eccentric tension, x1(5) = large eccentric tension}, the parent variable x2 is the type of material used to manufacture the structure, and the state values ​​of the parent variable x2 include {x2(1) = steel, x2(2) = aluminum, x2(3) = polyethylene plastic, x2(4) = concrete, x2(5) = glass}, the parent variable x3 is the shape of the opening of the structure in the force plane, and the state values ​​of the parent variable x3 include {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = rounded quadrilateral shape, x3(4) = rounded pentagon, …, x3(t) = rounded t+1 polygon}, the parent variable x4 is the ratio of the average value of the distance between the centroid of each opening and the centroid of the most adjacent opening to the calculated length of the structure, and the possible state values ​​of the parent variable x4 include {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3), …, x4(w)∈[1 / (w+1),1 / w), x4(w+1)∈(0,1 / (w+1))}, the parent variable x5 is the total number of openings in the structure, and the possible state values ​​of the parent variable x5 include {x5(1) = 1 opening, x5(2) = 2 openings, x5(3) = 3 openings, …, x5(s) = s openings}.

[0015] Preferably, t=7, w=9, s=20, and n=10.

[0016] The technical principles and effects of the above invention are as follows: the above-mentioned desirable state values ​​cover the most common stress conditions and the most commonly used design parameters in practice. After a large number of trial calculations, better results can be achieved at t=7, w=9, s=20, and n=10. Continuing to increase the number of state values ​​is no longer meaningful, and the marginal benefits are obviously decreasing.

[0017] Preferably, the method for obtaining the solid structure by conventional structural design method in step S2 is: assuming a cylinder with a cross-sectional diameter of di or a cuboid with a cross-sectional width of b and a height of h, the direction perpendicular to the cross-sectional area is the calculation length direction, and applying the calculation parameter combination: {boundary conditions, load mode, load position, load magnitude, calculation length};

[0018] The boundary conditions include fixed hinge supports, movable hinge supports, and fixed end constraints;

[0019] The load modes include uniform load and concentrated load;

[0020] The load position includes the loading position along the calculated length direction and the eccentricity from the centroid of the cross section at the loading position;

[0021] The internal forces are calculated by conventional structural mechanics, and whether the solid structure meets the stress limit is verified by conventional material mechanics methods. If the solid structure meets the stress limit, di, b, or h is reduced and the solid structure is verified again to see whether it meets the stress limit. Until the solid structure no longer meets the stress limit, the cylinder or cuboid corresponding to the previous di, b, or h is taken as the solid structure described in step S2.

[0022] Preferably, the conventional topology optimization method in step S3 is a variable density topology optimization method; the method for determining the state value of the opening parameter x3 (opening shape) in step S3 is: according to the conventional topology optimization method, iterate the shapes of the holes of the hollow structure at convergence, and take the element with the closest number of straight edges from {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = rounded quadrilateral, x3(4) = rounded pentagon, ..., x3(t) = rounded t+1 polygon}, and use this element as the state value of x3.

[0023] Preferably, the method for determining the state value of the opening parameter x4 (opening spacing) in step S3 is: the holes of the hollow structure when the conventional topology optimization method is iterated to convergence are numbered as 1, 2, ..., V, is the vector formed by the distance between the centroid of the vth hole and the centroids of all other holes, For collection The mean value of all elements in , l0 is the calculated length of the solid structure before topology optimization corresponding to the hollow structure, and the judgment The state value of x4 is determined by the subordinate relationship between the value and the element value interval in {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3),…, x4(w)∈[1 / (w+1),1 / w), x4(w+1)∈[0,1 / (w+1))}.

[0024] Preferably, the parameter learning method of the Bayesian network in step S4 is a parameter learning method performed according to the following steps:

[0025] S41. Let |B| be the total number of structures in set B, |B y＝y(k) | represents the total number of structures in set B that satisfy y = y(k). The probability set {P(y = y(k) | k = 1, 2, 3, ..., n)} of the opening ratio y taking each state value is calculated according to the following relationship:

[0026]

[0027] S42. For any determined parent variable state value combination X(m) = {x1 = x1(m1), x2 = x2(m2), ..., x5 = x5(m5)}, where m1, m2, ..., m5 are the state value sequence numbers of the corresponding parent variables x1, x2, ..., x5, the probability set {P(x j =x j (m j )|y=y(k))|j=1,2,3,4,5}, where Indicates that in set B, both y=y(k) and x j =x j (m j ) total number of structures:

[0028]

[0029] S43. For X(m), the sum of the probabilities of the sub-variable y taking each state value is 1, and the following relationship is obtained:

[0030]

[0031] S44. For X(m), let P(x1=x1(m1), x2=x2(m2), ..., x5=x5(m5))=L, and obtain the following system of equations:

[0032]

[0033] S45. Add up both sides of the equations and solve all the above relationship equations to obtain the L value corresponding to X(m):

[0034]

[0035] S46. Substitute the solution of L back into the equation group of S44 to solve the conditional probability P(y|x1=x1(m1), x2=x2(m2),…,x5=x5(m5)) corresponding to the parent variable state value combination X(m). The above process is also used to calculate the remaining parent variable state value combinations, and finally obtain the conditional probability P(y|x1, x2,…,x5) of the child variable under all parent variable state value combinations, that is, the probability distribution of y (opening ratio) corresponding to different combinations of {x1 (force mode), x2 (material type), x3 (opening shape), x4 (opening spacing), x5 (number of openings)}.

[0036] The technical principle and effect of the above invention are as follows: the parameter learning method of the above steps S41 to S46 can significantly save computing power costs compared with the frequency statistics method commonly used in the prior art. The specific performance analysis is as follows: Taking the above t=7, w=9, s=20, n=10 as an example, the state numbers of the parent variables x1, x2, x3, x4, x5 and the child variable y are 5, 5, 8, 10, 20 and 10 respectively. When the frequency statistics method is used, the number of probability values ​​that need to be counted from the training samples is " The product of the number of states of all parent variables and child variables is 5*5*8*10*20*10=400,000, while the number of probability values ​​that need to be counted using the above parameter learning method is only "the product of the number of states between each pair of parent variables and child variables" + "the number of states of child variables" = (5*10+5*10+8*10+10*10+20*10)+10=490. It can be seen that the computing power requirement of the above parameter learning method is reduced by 99.88%, thereby greatly saving computing costs.

[0037] Based on the structural parameter optimization method of Bayesian network learning, the present invention also provides a topology optimization method, which is applied to the topology optimization and design of bridge decks, and the topology optimization method includes the following steps:

[0038] S6. For the bridge deck, use steps S1 to S5 to obtain the solid structure C of the bridge deck. A and the expected opening effect vector Select The opening parameters corresponding to the first R elements in the equation are combined and defined as H (r) ={x3=x3(m3 (r) ), x4=x4(m4 (r) ), x5=x5(m5 (r) )|r=1,2,3,…,R},each combination H (r) Applicable to solid structure C A And form a hollow structure set CB ={C B (r) |r=1,2,3,…,R and C B The opening ratio of all elements in

[0039] S7, the solid structure C A The finite element unit is divided into I units to form a finite element model D (0) , number each unit as 1, 2, 3, ..., I, let f max is the allowable principal stress of the bridge deck material, is the stress screening coefficient and λ is the adjustment coefficient of the expected opening effect and 0<λ<1, let i=1, d=1, d max >1;

[0040] S8. For the i-th unit, calculate the elastic modulus reduction coefficient β according to the following formula i ;

[0041]

[0042] S9, let i = i + 1, if i ≤ I, go to step S8, otherwise go to step S10;

[0043] S10, {β i |i=1,2,3,…,I} is assigned to model D (0) For all units, the elastic modulus of each unit is calculated according to the corresponding β i Reduce to form model D (β) , for D (β) Perform linear elastic finite element calculation to obtain the principal stress set {σ i (β) |i=1,2,3,…,I};

[0044] S11、If max({σ i (β) |i=1,2,3,…,I}) <f max Then go to step S12, otherwise Then, go to step S8;

[0045] S12, find {σ i (β) |i=1,2,3,…,I} is less than The element numbers corresponding to the elements of the set u are formed, and the elastic modulus reduction coefficient β corresponding to each element in u is u =0, set β u Give model D (0) Forming Model D(d) , perform linear elastic finite element calculation and obtain the principal stress set of each unit {σ i (d) |i=1,2,3,…,I};

[0046] S13, let max({σ i (d) |i=1,2,3,…,I})=σ max , d=d+1, if σ max <f max Then go to step S14, otherwise go to step S15;

[0047] S14, if d <d max and make And go to step S12, otherwise go to step S16;

[0048] S15, order Go to step S12;

[0049] S16. Delete the unit formation model of set u That is, the optimal topological configuration of the bridge deck is obtained, and the design of the bridge deck is completed according to conventional structural design methods.

[0050] The technical principles and effects of the above invention are as follows: (1) the topology optimization method based on Bayesian network learning of the present invention is used to select a set of R hollow structures C with better expected opening effect. B , comprehensively considering the expected opening effect of each element And mapped to the elastic modulus reduction coefficient β of the finite element unit in each opening area i , β i Assign to solid structure C A Finite element model D (0) Post-formation model D (β) The smaller the elastic modulus, the better the unit is in model D. (β) Mean stress value σ i (β) The smaller it is, the sooner it is hollowed out in steps S11 to S16. That is, the influence of the expected opening effect of each element is comprehensively taken into account through the change of the elastic modulus, thereby fully integrating the designer's experience and the Bayesian network learning results as a priori probability, quickly realizing the topological optimization design of the bridge deck, reducing the number of iterative optimization times of the traditional topological optimization method, and reducing the time cost of the optimization design. (2) In S11, when the initial D (β) Does not meet the force requirements, that is, max({σ i (β) |i=1, 2, 3,…,I})≥f max When "It can increase the number of units with larger elastic modulus, that is, increase the number of units that share larger forces, and finally make D (β) The model is modified to meet the load requirements, effectively avoiding the situation where the optimization process is interrupted and the subsequent steps cannot be continued. (3) Through the above-mentioned topology optimization method, the solid structure area that contributes less to the overall load can be removed, and a bridge deck with greater specific stiffness (its bending stiffness corresponding to the unit weight of material is significantly greater than that of the solid structure) and its optimal opening parameters are obtained. Compared with the solid bridge deck of the existing technology, the material consumption is greatly reduced and the overall specific stiffness of the structure is significantly improved, thereby achieving a geometric mechanical effect similar to that of a "honeycomb structure" and technical and economic benefits.

[0051] Preferably, the described λ∈[0.80,0.95], d max ∈[10,100].

[0052] Preferably, after obtaining the optimal topological configuration of the bridge deck in step S16, the model The jagged edges of the openings are smoothed to straight lines or arcs and manually repaired as follows: holes with an area < δS are filled with solid, protrusions with a curvature radius < θT are trimmed, and grooves with a curvature radius < θT are filled, where S is the area of ​​the outer contour of the bridge deck cross section, T is the thickness of the bridge deck, and δ∈(0,0.01] and θ∈(0,0.05].

[0053] The beneficial effects of the present invention are summarized as follows:

[0054] 1. The structural parameter optimization method based on Bayesian network learning described in the present invention is adopted. Starting from the principles of probability statistics, based on the solid structure A constructed by the designer based on his own experience, and combined with the hollow structure set B after topology optimization, the opening effect prediction under different force modes, material types, and opening parameter combinations is realized. For the new structure to be designed, its opening parameters can be directly optimized according to the trained Bayesian network, eliminating a large number of iterative calculation processes in the traditional topology optimization method, greatly reducing the time cost of the optimization design, thereby quickly achieving structural performance improvement and efficiency improvement. It is applicable to general building structures such as rail transit equipment and bridges.

[0055] 2. The Bayesian network parameter learning method described in the present invention reduces computing power requirements by 99.88% compared to the frequency statistics method commonly used in the prior art, significantly saving computing costs.

[0056] 3. The topology optimization method based on Bayesian network learning of the present invention comprehensively takes into account the influence of the expected opening effect of different opening parameter combinations through the change of elastic modulus, thereby fully integrating the designer's experience and Bayesian network learning results as prior probability, and quickly realizing the topology optimization design of the bridge deck, reducing the number of iterative optimization times of the traditional topology optimization method and reducing the time cost of the optimization design.

[0057] 4. By adopting the bridge deck topology optimization method of the present invention, a bridge deck with high stiffness (i.e., the bending stiffness corresponding to the unit weight of material is significantly greater than that of a solid structure) and its optimal opening parameters can be obtained. Compared with the solid bridge deck of the prior art, the material usage is greatly reduced and the specific stiffness is improved, thereby achieving geometric mechanical effects and technical and economic benefits similar to a "honeycomb structure". BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of a Bayesian network for the structural parameter optimization method based on Bayesian network learning in the present invention;

[0059] Figure 2 Schematic diagram of some elements in a solid structure set A parallel to their cross-sectional directions in the structural parameter optimization method based on Bayesian network learning of the present invention;

[0060] Figure 3 A view of some elements in the hollow structure set B parallel to their cross-sectional directions in the structural parameter optimization method based on Bayesian network learning of the present invention;

[0061] Figure 4 The optimization design process of structure C in the structural parameter optimization method based on Bayesian network learning in Example 1 of the present invention (unit: cm);

[0062] Figure 5 The bridge deck solid structure C of the topology optimization method of embodiment 2 of the present invention A and finite element model D (0) Schematic diagram of;

[0063] Figure 6 The hollow structure set C of the topology optimization method of embodiment 2 of the present invention is B and elastic modulus reduction factor β i Schematic diagram of assignment;

[0064] Figure 7 Schematic diagram of the optimal topological configuration of the bridge deck according to the topology optimization method of Example 2 of the present invention. DETAILED DESCRIPTION

[0065] The present invention is further described in detail below in conjunction with test examples and specific implementation methods, but this should not be understood as the scope of the above-mentioned subject matter of the present invention being limited to the following embodiments. All technologies implemented based on the contents of the present invention belong to the scope of the present invention.

[0066] Example 1

[0067] like Figure 1-Figure 4 As shown, the present invention provides a structural parameter optimization method based on Bayesian network learning, which is applied to the optimization and design of opening parameters of a plane force-bearing structure. The structural parameter optimization method based on Bayesian network learning includes the following steps:

[0068] S1, with force mode x1, material type x2, opening shape x3, opening spacing x4, opening number x5 as parent variables, and opening ratio y as child variable, establish a Bayesian network for predicting opening ratio, and the state value sequence of y is {y(1)∈[0,1 / n),y(2)∈[1 / n,2 / n),…,y(n)∈[(n-1) / n,1};

[0069] S2. For different combinations of state values ​​in x1 and x2, under different calculation parameter combinations, conventional structural design methods are used to obtain solid structures that meet the load requirements under each parameter combination and form a set A;

[0070] S3, perform finite element unit division on each structure in set A, apply the calculation parameter combination corresponding to each solid structure in S2, set the unit of the outer contour of each solid structure as a non-optimized area and optimize the remaining area using the conventional topology optimization method, and obtain a set B of hollow structures with different state values ​​of the opening parameters {x3, x4, x5};

[0071] S4, using set B as a training sample, and obtaining the conditional probability of the Bayesian network in step S1 through parameter learning method;

[0072] S5. For the structure C to be designed, the solid structure C that meets the load is obtained by the structural mechanics method based on the calculation parameter combination of the structure C. A , determine C A x1=x1(m1 (1) ), x2=x2(m2 (1) ), calculate the solid structure C as follows A The probability P and expected opening effect Z corresponding to different combinations of x3, x4, and x5 state values m , press each Z m Sort the values ​​in descending order to form a vector

[0073]

[0074] S6. Select The opening parameters corresponding to the first R elements in the equation are applied to the solid structure C A and form a hollow structure set C B , change C B The opening size is adjusted until a set that satisfies the force is obtained. Select The structure with the largest opening ratio is the one with the optimal opening parameters.

[0075] In this embodiment, the structural parameter optimization method starts from the principle of probability statistics, constructs a hollow structure set B based on a large number of solid structures A, forms a structural database under a large number of different data combinations, directly constructs a Bayesian network based on the self-built database and completes parameter learning, and obtains the expected opening effect Z corresponding to different opening parameters under different calculation parameter combinations. m , so that for any actual structure C that needs to be designed, the expected opening effect can be predicted directly based on the conditional probability relationship of the Bayesian network learned, and according to Z m Vector of descending values Quickly preliminarily screen out the opening parameter combinations that may achieve a larger opening ratio, and based on the opening parameter combinations with a high probability of achieving better results, quickly select the structure with the best opening ratio through simple size optimization. The optimization of the opening parameters and the design of the load-bearing structure in the plane are completed. Among them, the conventional structural design method mentioned above is to first formulate the solid cross-sectional dimensions of the structure based on design experience, calculate the internal forces of the structure and verify its stress according to conventional mechanical methods, and change the cross-sectional dimensions of the structure until the minimum cross-sectional dimensions that meet the stress limit are obtained. In addition, the structural parameter optimization method uses the conventional structural design method to construct a solid structure set A that meets the load under various parameter combinations, and then combines it with the hollow structure set B after topology optimization to achieve the prediction of the opening effect under different load modes, material types, and opening parameter combinations. In the process of constructing the two structural databases, the designer's experience and topology optimization results are fully integrated as prior probabilities. For new structures to be designed, their opening parameters can be directly optimized according to the trained Bayesian network, eliminating the large number of iterative calculation processes of the traditional topology optimization method, greatly reducing the time cost of optimization design, and can be applied to general building structures such as rail transit equipment and bridges.

[0076] This structural parameter optimization method leverages the significant advantages of Bayesian networks in handling uncertainty and noisy data. By sharing parameters within the probabilistic model, it reduces model complexity and improves its generalization capabilities. This makes the model more efficient when processing large datasets and is highly robust to outliers and noise in the dataset. It automatically adjusts the model's complexity during training, reducing the risk of overfitting and further improving the designer's ability to predict the effects of the openings.

[0077] See also Figure 2 In step S1, the parent variable x1 is the force type of the structure, and the possible state values ​​of the parent variable x1 include {x1(1) = bending and shear, x1(2) = small eccentric compression, x1(3) = large eccentric compression, x1(4) = small eccentric tension, x1(5) = large eccentric tension}, the parent variable x2 is the type of material used in manufacturing the structure, and the possible state values ​​of the parent variable x2 include {x2(1) = steel, x2(2) = aluminum, x2(3) = polyethylene plastic, x2(4) = concrete, x2(5) = glass}, the parent variable x3 is the shape of the opening of the structure in the force plane, and the possible state values ​​of the parent variable x3 include {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = rounded quadrilateral, x3 (4) = rounded pentagon, …, x3(t) = rounded t+1 polygon}, the parent variable x4 is the ratio of the average value of the distance between the centroid of each opening and the centroid of the most adjacent opening to the calculated length of the structure, and the possible state values ​​of the parent variable x4 include {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3), …, x4(w)∈[1 / (w+1),1 / w), x4(w+1)∈[0,1 / (w+1))}, the parent variable x5 is the total number of openings in the structure, and the possible state values ​​of the parent variable x5 include {x5(1) = 1 opening, x5(2) = 2 openings, x5(3) = 3 openings, …, x5(s) = s openings}. In a preferred embodiment, t = 7, w = 9, s = 20, and n = 10. In this embodiment, the possible state values ​​cover the most common stress conditions and the most commonly used design parameters in practice. After a large number of trial calculations, it was found that good results can be achieved when t = 7, w = 9, s = 20, and n = 10. Further increasing the number of state values ​​is meaningless and the marginal benefits are obviously diminishing.

[0078] The method for obtaining the solid structure by conventional structural design method in step S2 is as follows: assuming a cylinder with a cross-sectional diameter of di or a rectangular parallelepiped with a cross-sectional width of b and a height of h, the direction perpendicular to the cross-sectional area is the calculation length direction, and applying the calculation parameter combination: {boundary conditions, load mode, load location, load magnitude, calculation length};

[0079] The boundary conditions include fixed hinge supports, movable hinge supports and fixed end constraints;

[0080] Loading modes include uniformly distributed loads and concentrated loads;

[0081] The load position includes the loading position along the calculation length direction and the eccentricity from the centroid of the cross section at the loading position;

[0082] The internal forces are calculated using conventional structural mechanics methods, and the solid structure is verified to see whether it meets the stress limit using conventional material mechanics methods. If the solid structure meets the stress limit, di, b, or h is reduced and the solid structure is verified again to see whether it meets the stress limit until the solid structure no longer meets the stress limit. In this case, the cylinder with the previous cross-sectional diameter of di or the rectangular parallelepiped with the cross-sectional width of b and the height of h is taken as the solid structure in step S2.

[0083] In this embodiment, when its solid structure is applied to different scenarios, its stress limit changes with the change of the scenario. For example, when it is applied to a bridge, the stress limit of its solid structure needs to be calculated according to the safety specifications of the bridge so that the maximum stress value of the solid structure does not exceed the stress limit.

[0084] In a preferred embodiment, the method for determining the state value of the opening parameter x3 (opening shape) in step S3 is: according to the conventional topology optimization method, iterate the shapes of the holes of the hollow structure until convergence, and select the element with the closest number of straight edges from {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = rounded quadrilateral, x3(4) = rounded pentagon, ..., x3(t) = rounded t+1 polygon}, and use this element as the state value of x3. In this embodiment, the conventional topology optimization method in step S3 is preferably a variable density topology optimization method.

[0085] The method for determining the state value of the opening parameter x4 (opening spacing) in step S3 is: the holes of the hollow structure when the conventional topology optimization method is iterated to convergence are numbered as 1, 2, ..., V, is the vector formed by the distance between the centroid of the vth hole and the centroids of all other holes, For collection The mean value of all elements in , l0 is the calculated length of the solid structure before topology optimization corresponding to the hollow structure, and the judgment The state value of x4 is determined by the subordinate relationship between the value and the element value interval in {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3),…, x4(w)∈[1 / (w+1),1 / w), x4(w+1)∈[0,1 / (w+1))}.

[0086] like Figure 3 As shown, the parameter learning method of the Bayesian network in step S4 is a parameter learning method performed according to the following steps: S41, let |B| be the total number of structures in set B, |B y＝y(k) | represents the total number of structures in set B that satisfy y = y(k). The probability set {P(y = y(k) | k = 1, 2, 3, ..., n)} of the opening ratio y taking each state value is calculated according to the following relationship:

[0087]

[0088] S42. For any determined parent variable state value combination X(m) = {x1 = x1(m1), x2 = x2(m2), ..., x5 = x5(m5)}, where m1, m2, ..., m5 are the state value sequence numbers of the corresponding parent variables x1, x2, ..., x5, the probability set {P(x j =x j (m j )|y=y(k))|j=1,2,3,4,5}, where Indicates that in set B, both y=y(k) and x j =x j (m j ) total number of structures:

[0089]

[0090] S43. For X(m), the sum of the probabilities of the subvariable y taking each state value is 1, and the following relationship is obtained:

[0091]

[0092] S44. For X(m), let P(x1=x1(m1), x2=x2(m2), …, x5=x5(m5))=L, and obtain the following system of equations:

[0093]

[0094] S45. Add up both sides of the above equations and solve all the above relations to obtain the L value corresponding to X(m):

[0095]

[0096] S46. Substitute the solution of L back into the equation group of S44 to solve the conditional probability P(y|x1=x1(m1), x2=x2(m2),…,x5=x5(m5)) corresponding to the parent variable state value combination X(m). The above process is also used to calculate the remaining parent variable state value combinations, and finally obtain the conditional probability P(y|x1, x2,…,x5) of the child variable under all parent variable state value combinations, that is, the probability distribution of y (opening ratio) corresponding to different combinations of {x1 (force mode), x2 (material type), x3 (opening shape), x4 (opening spacing), x5 (number of openings)}.

[0097] In this embodiment, the specific performance analysis of the Bayesian network parameter learning is achieved by the parameter learning method of the above steps S41 to S46: Taking the above t = 7, w = 9, s = 20, and n = 10 as an example, the state numbers of the parent variables x1, x2, x3, x4, x5 and the child variable y are 5, 5, 8, 10, 20, and 10 respectively. When the frequency statistics method is used, the number of probability values ​​that need to be counted from the training samples is "the product of the state numbers of all parent variables and child variables" = 5*5*8*10*20*1 0=400,000, while the number of probability values ​​that need to be counted by the above parameter learning method is only "the product of the number of states between each pair of parent variables and child variables" + "the number of states of child variables" = (5*10+5*10+8*10+10*10+20*10)+10=490. It can be seen that the computing power requirement reduction rate of the above parameter learning method is as high as 99.88%. Compared with the frequency statistics method commonly used in the existing technology, it significantly reduces the complexity of statistical calculations, can significantly save computing power costs, and greatly reduces the amount of calculation.

[0098] Example 2

[0099] like Figure 5-Figure 7 As shown, the present invention also provides a topology optimization method, which is applied to the topology optimization and design of bridge decks. The topology optimization method is implemented based on the structural parameter optimization method of Bayesian network learning in Example 1, and the topology optimization method includes the following steps:

[0100] S6. For the bridge deck, the structural parameter optimization method of Bayesian network learning is implemented in steps S1 to S5 to obtain the solid structure C of the bridge deck. A and the expected opening effect vector Select The opening parameters corresponding to the first R elements in the equation are combined and defined as H (r) ={x3=x3(m3 (r) ), x4=x4(m4 (r) ), x5=x5(m5 (r) )|r=1,2,3,…,R},each combination H(r) Applicable to solid structure C A And form a hollow structure set C B , C B ={C B (r) |r=1,2,3,…,R and C B The opening ratio of all elements in

[0101] S7, solid structure C A The finite element unit is divided into I units to form a finite element model D (0) , number each unit as 1, 2, 3, ..., I, let f max is the allowable principal stress of the bridge deck material, is the stress screening coefficient and λ is the adjustment coefficient of the expected opening effect and 0<λ<1, let i=1, d=1, d max >1;

[0102] S8. For the i-th unit, calculate the elastic modulus reduction coefficient β according to the following formula i ;

[0103]

[0104] S9, let i = i + 1, if i ≤ I, go to step S8, otherwise go to step S10;

[0105] S10, {β i |i=1,2,3,…,I} is assigned to model D (0) For all units, the elastic modulus of each unit is calculated according to the corresponding β i Reduce to form model D (β) , for D (β) Perform linear elastic finite element calculation to obtain the principal stress set {σ i (β) |i=1,2,3,…,I};

[0106] S11、If max({σ i (β) |i=1,2,3,…,I}) <f max Then go to step S12, otherwise Then, go to step S8;

[0107] S12, find {σ i (β) |i=1,2,3,…,I} is less than The element numbers corresponding to the elements of the set u are formed, and the elastic modulus reduction coefficient β corresponding to each element in u isu =0, set β u Give model D (0) Forming Model D (d) , perform linear elastic finite element calculation and obtain the principal stress set of each unit {σ i (d) |i=1,2,3,…,I};

[0108] S13, let max({σ i (d) |i=1,2,3,…,I})=σ max , d=d+1, if σ max <f max Then go to step S14, otherwise go to step S15;

[0109] S14, if d <d max and make And go to step S12, otherwise go to step S16;

[0110] S15, order Go to step S12;

[0111] S16. Delete the unit formation model of set u That is, the optimal topological configuration of the bridge deck is obtained, and the design of the bridge deck is completed according to conventional structural design methods.

[0112] In this embodiment, the topology optimization method is based on the structural parameter optimization method of Bayesian network learning in Example 1, and is aimed at a set of R hollow structures C with better expected opening effects. B , comprehensively consider the expected opening effect of each element And mapped to the elastic modulus reduction coefficient β of the finite element unit in each opening area i , β i Assign to solid structure C A Finite element model D (0) Post-formation model D (β) , the smaller the elastic modulus of the unit is in the model D (β) Mean stress value σ i (β) The more likely it is to be smaller, and the sooner it is hollowed out in steps S11 to S16, that is, the influence of the expected opening effect of each element is comprehensively taken into account through the change of the elastic modulus, thereby fully integrating the designer's experience and the Bayesian network learning results as the prior probability, and quickly realizing the topological optimization design of the bridge deck. It reduces the complexity of the model through Bayesian network learning, improves the generalization ability of the model, reduces the number of iterative optimization times of the traditional topology optimization method, and reduces the time cost of the optimization design.

[0113] In addition, in step S11, when the initial D (β) Does not meet the force requirements, that is, max({σ i (β) |i=1, 2, 3,…,I})≥f max When the "Thereby increasing the number of units with larger elastic modulus, that is, increasing the number of units that share larger forces, thus ultimately making D (β) Correcting the model to one that can meet the stress requirements further ensures the continuous execution of the optimization process and effectively avoids the situation where the optimization process is interrupted and the subsequent steps cannot be continued.

[0114] Finally, through the above-mentioned topology optimization method, the solid structure area that contributes less to the overall force was removed, and a bridge deck with greater specific stiffness was obtained (the bending stiffness corresponding to its unit weight of material consumption is significantly greater than that of the solid structure) and its optimal opening parameters. Compared with the solid bridge deck of the existing technology, the material consumption is greatly reduced and the overall specific stiffness of the structure is significantly improved, thereby achieving geometric mechanical effects and technical and economic benefits similar to those of a "honeycomb structure".

[0115] In a preferred embodiment, λ∈[0.80,0.95], d max ∈[10,100].

[0116] After obtaining the optimal topological configuration of the bridge deck in step S16, the model The jagged edges of the openings were smoothed to straight lines or arcs and manually repaired as follows: holes with an area < δS were filled with solids, protrusions with a curvature radius < θT were trimmed, and grooves with a curvature radius < θT were filled, where S is the area of ​​the outer contour of the bridge deck section, T is the thickness of the bridge deck, δ∈(0,0.01], θ∈(0,0.05].

[0117] In this embodiment, after the topology optimization method is applied to the topology optimization and design of the bridge deck, the optimal topological configuration of the bridge deck is obtained. Since the model derived by topology optimization is mesh data, there are usually jagged edges in its edge area. Based on considerations in the actual application process, further optimization processing is required to make it smooth.

[0118] Example 3

[0119] The present invention also provides a computer system comprising a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the computer program to implement the steps of the above-described Bayesian network learning-based structural parameter and topology optimization methods. In this embodiment, the Bayesian network learning-based structural parameter optimization method of Example 1 and the Bayesian network learning-based structural parameter optimization method of Example 2 can both be implemented by the computer system of this embodiment. The processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. When executed by the processor, the computer program implements the Bayesian network learning-based structural parameter optimization method and the topology optimization method. Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the above-described method embodiments. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory.

[0120] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A structural parameter optimization method based on Bayesian network learning is applied to the optimization and design of opening parameters of in-plane force-bearing structures, characterized by: The structural parameter optimization method based on Bayesian network learning comprises the following steps: S1. Take the force mode x1, material type x2, opening shape x3, opening spacing x4, and opening number x5 as parent variables and the opening ratio y as child variable to establish a Bayesian network for predicting the opening ratio. The state value sequence of y is {y(1)∈[0,1 / n),y(2)∈[1 / n,2 / n),…,y(n)∈[(n-1) / n,1)}; S2. For different combinations of state values ​​in x1 and x2, under different calculation parameter combinations, conventional structural design methods are used to obtain solid structures that meet the load requirements under each parameter combination and form a set A; S3, perform finite element unit division on each structure in set A, apply the calculation parameter combination corresponding to each solid structure in S2, set the unit of the outer contour of each solid structure as a non-optimized area and optimize the remaining area using the conventional topology optimization method, and obtain a set B of hollow structures with different state values ​​of the opening parameters {x3, x4, x5}; S4, using the set B as a training sample, and obtaining the conditional probability of the Bayesian network in step S1 through a parameter learning method; S5. For the structure C to be designed, a solid structure C that satisfies the load is obtained by the structural mechanics method according to the calculation parameter combination of the structure C. A , determine C A x1=x1(m1 (1) ), x2=x2(m2 (1) ), calculate the solid structure C as follows A The probability P and expected opening effect Z corresponding to different combinations of x3, x4, and x5 state values m , press each Z m Sort the values ​​in descending order to form a vector S6. Select The opening parameters corresponding to the first R elements in the equation are applied to the solid structure C A and form a hollow structure set C B , change C B The opening size is adjusted until a set that satisfies the force is obtained. Select The structure with the largest opening ratio is the one with the optimal opening parameters.

2. The structural parameter optimization method based on Bayesian network learning according to claim 1, characterized in that: The force mode x1 in the parent variable in step S1 is the force type of the structure, and the possible state values ​​of the force mode x1 in the parent variable include {x1(1) = bending and shear, x1(2) = small eccentric compression, x1(3) = large eccentric compression, x1(4) = small eccentric tension, x1(5) = large eccentric tension}; the material type x2 in the parent variable is the material type used in manufacturing the structure, and the possible state values ​​of the material type x2 in the parent variable include {x2(1) = steel, x2(2) = aluminum, x2(3) = polyethylene plastic, x2(4) = concrete, x2(5) = glass}; the opening shape x3 in the parent variable is the opening shape of the structure in the force plane, and the possible state values ​​of the opening shape x3 in the parent variable include {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = Rounded quadrilateral, x3(4) = rounded pentagon, ..., x3(t) = rounded t+1 polygon}; the hole spacing x4 in the parent variable is the ratio of the average value of the distance between each hole centroid and the nearest hole centroid to the calculated length of the structure, and the possible state values ​​of the hole spacing x4 in the parent variable include {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3),…,x4(w)∈[1 / (w+1),1 / w),x4(w+1)∈(0,1 / (w+1))}; the number of openings x5 in the parent variable is the total number of openings of the structure, and the possible state values ​​of the number of openings x5 in the parent variable include {x5(1)=1 opening, x5(2)=2 openings, x5(3)=3 openings,…,x5(s)=s openings}.

3. The structural parameter optimization method based on Bayesian network learning according to claim 2, characterized in that: Said t=7, w=9, s=20, and n=10.

4. The structural parameter optimization method based on Bayesian network learning according to claim 1, characterized in that: The method for obtaining the solid structure by conventional structural design methods in step S2 is as follows: assuming a cylinder with a cross-sectional diameter of di or a cuboid with a cross-sectional width of b and a height of h, the direction perpendicular to the cross-sectional area is the calculation length direction, and applying the following calculation parameter combination: {boundary conditions, load mode, load location, load magnitude, calculation length}; The boundary conditions include fixed hinge supports, movable hinge supports and fixed end constraints; The load mode includes uniform load and concentrated load; The load position includes the loading position along the calculated length direction and the eccentricity from the centroid of the cross section at the loading position; The internal force is calculated by conventional structural mechanics methods, and whether the solid structure meets the stress limit is verified by conventional material mechanics methods. If the solid structure meets the stress limit, di, b, or h is reduced and the solid structure is verified again to see whether it meets the stress limit. Until the solid structure no longer meets the stress limit, the cylinder corresponding to the previous cross-sectional diameter di or the rectangular parallelepiped corresponding to the cross-sectional width b and height h is taken as the solid structure described in step S2.

5. The structural parameter optimization method based on Bayesian network learning according to claim 1, characterized in that: The method for determining the state value of the opening shape x3 in step S3 is: according to the conventional topology optimization method, iterate the shapes of the holes of the hollow structure until convergence, and select the element with the closest number of straight edges from {x3(1) = circle or ellipse, x3(2) = rounded triangle, x3(3) = rounded quadrilateral, x3(4) = rounded pentagon, ..., x3(t) = rounded t+1 polygon}, and use the element as the state value of x3; The method for determining the state value of the hole spacing x4 in step S3 is: the holes of the hollow structure when the conventional topology optimization method is iterated to convergence are numbered as 1, 2, ..., V, is the vector formed by the distance between the centroid of the vth hole and the centroids of all other holes, For collection The mean value of all elements in , l0 is the calculated length of the solid structure before topology optimization corresponding to the hollow structure, and the judgment The state value of x4 is determined by the subordinate relationship between the value and the element value interval in {x4(1)∈[1 / 2,1 / 1), x4(2)∈[1 / 3,1 / 2), x4(3)∈[1 / 4,1 / 3),…, x4(w)∈[1 / (w+1),1 / w), x4(w+1)∈(0,1 / (w+1))}.

6. The structural parameter optimization method based on Bayesian network learning according to claim 1, characterized in that: The parameter learning method of the Bayesian network in step S4 is a parameter learning method performed according to the following steps: S41. Let |B| be the total number of structures in set B, |B y＝y(k) | represents the total number of structures in set B that satisfy y = y(k). The probability set {P(y = y(k) | k = 1, 2, 3, ..., n)} of the opening ratio y taking each state value is calculated according to the following relationship: S42. For any determined parent variable state value combination X(m) = {x1 = x1(m1), x2 = x2(m2), ..., x5 = x5(m5)}, where m1, m2, ..., m5 are the state value sequence numbers of the corresponding parent variables x1, x2, ..., x5, the probability set {P(x j =x j (m j )|y=y(k))|j=1,2,3,4,5}, where Indicates that in set B, both y=y(k) and x j =x j (m j ) total number of structures: S43. For X(m), the sum of the probabilities of the sub-variable y taking each state value is 1, and the following relationship is obtained: S44. For X(m), let P(x1=x1(m1), x2=x2(m2), ..., x5=x5(m5))=L, and obtain the following system of equations: S45. Add up both sides of the equations and solve all the above relationship equations to obtain the L value corresponding to X(m): S46. Substitute the solution of L back into the equation group of S44 to solve the conditional probability P(y|x1=x1(m1), x2=x2(m2),…,x5=x5(m5)) corresponding to the parent variable state value combination X(m). The remaining parent variable state value combinations are also calculated according to the above process, and finally the conditional probability P(y|x1, x2,…,x5) of the child variable under all parent variable state value combinations is obtained, that is, the probability distribution of the corresponding opening ratio y under different {force mode x1, material type x2, opening shape x3, opening spacing x4, number of openings x5} combinations.

7. A topology optimization method, which is applied to the topology optimization and design of bridge decks, characterized in that: The topology optimization method is implemented based on the structural parameter optimization method of Bayesian network learning according to any one of claims 1 to 6, and the topology optimization method includes the following steps: S6. For the bridge deck, the steps S1 to S5 of the structural parameter optimization method of the Bayesian network learning are implemented to obtain the solid structure C of the bridge deck. A and the expected opening effect vector Select The opening parameters corresponding to the first R elements in the equation are combined and defined as H (r) ={x3=x3(m3 (r) ), x4=x4(m4 (r) ), x5=x5(m5 (r) )|r=1,2,3,…,R},each combination H (r) Applicable to solid structure C A And form a hollow structure set C B , C B ={C B (r) |r=1,2,3,…,R and C B The opening ratio of all elements in S7, the solid structure C A The finite element unit is divided into I units to form a finite element model D (0) , number each unit as 1, 2, 3, ..., I, let f max is the allowable principal stress of the bridge deck material, is the stress screening coefficient and λ is the adjustment coefficient of the expected opening effect and 0<λ<1, let i=1, d=1, d max >1; S8. For the i-th unit, calculate the elastic modulus reduction coefficient β according to the following formula i ; S9, let i = i + 1, if i ≤ I, go to step S8, otherwise go to step S10; S10, {β i |i=1,2,3,…,I} is assigned to model D (0) For all units, the elastic modulus of each unit is calculated according to the corresponding β i Reduce to form model D (β) , for D (β) Perform linear elastic finite element calculation to obtain the principal stress set {σ i (β) |i=1,2,3,…,I}; S11、If max({σ i (β) |i=1,2,3,…,I}) <f max Then go to step S12, otherwise Then, go to step S8; S12, find {σ i (β) |i=1,2,3,…,I} is less than The element numbers corresponding to the elements of the set u are formed, and the elastic modulus reduction coefficient β corresponding to each element in u is u =0, set β u Give model D (0) Forming Model D (d) , perform linear elastic finite element calculation and obtain the principal stress set of each unit {σ i (d) |i=1,2,3,…,I}; S13, let max({σ i (d) |i=1,2,3,…,I})=σ max , d=d+1, if σ max <f max Then go to step S14, otherwise go to step S15; S14, if d <d max and make And go to step S12, otherwise go to step S16; S15, order Go to step S12; S16. Delete the unit formation model of set u That is, the optimal topological configuration of the bridge deck is obtained, and the design of the bridge deck is completed according to conventional structural design methods.

8. The topology optimization method according to claim 7, characterized in that: described described λ∈[0.80,0.95], d max ∈[10,100].

9. The topology optimization method according to claim 7, characterized in that: After obtaining the optimal topological configuration of the bridge deck in step S16, the model The jagged edges of the openings are smoothed to straight lines or arcs and manually repaired as follows: holes with an area < δS are filled with solid, protrusions with a curvature radius < θT are trimmed, and grooves with a curvature radius < θT are filled, where S is the area of ​​the outer contour of the bridge deck cross section, T is the thickness of the bridge deck, and δ∈(0,0.01] and θ∈(0,0.05].

10. A computer system comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: The processor executes the computer program to implement the steps of the structural parameter and topology optimization method based on Bayesian network learning according to any one of claims 1 to 8.

Images