A Human-Machine Collaborative Intelligent Modeling and Optimization Method for Mid-Span Steel Arch Bridges

Abstract

This invention discloses a human-computer collaborative intelligent modeling and optimization method for mid-span steel arch bridges, comprising the following steps: 1) determining the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the mid-span steel arch bridge, and drawing an initial condition diagram; 2) establishing an intelligent design model for the mid-span steel arch bridge structure based on human-computer collaboration, based on the initial condition diagram; 3) establishing an optimization model for the structural parameters of the mid-span steel arch bridge structure based on the intelligent design model; 4) solving the optimization model for the structural parameters of the mid-span steel arch bridge structure to obtain the optimization parameters for each structure. This invention requires only a small amount of human-computer interaction, utilizes layer analysis algorithms to extract initial condition diagram information, and combines prior knowledge to achieve rapid modeling of mid-span steel arch bridges, avoiding errors in manual modeling and improving modeling efficiency and quality.

Description

Technical Field

[0001] This invention relates to the field of intelligent design of bridge structures, specifically a human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges. Background Technology

[0002] In traditional bridge design, engineers must repeatedly adjust structural schemes and conduct trial calculations based on bridge construction conditions and requirements, combined with their own experience and knowledge, and bridge design rules, in order to obtain a better design. However, the traditional model inevitably leads to a large amount of modeling work. Every time an engineer adjusts the bridge structural layout, the overall structural layout, cross-sectional settings, and load arrangements in the model must be rebuilt, resulting in a long design cycle. Moreover, the structural optimization results often rely on the engineer's personal experience, making it difficult to balance safety, economy, and advanced technology. This contradiction is even more pronounced in the design of large bridges such as arch bridges. Therefore, there is an urgent need to propose intelligent design technologies based on parametric and intelligent methods.

[0003] Currently, domestic and international research has made some progress in parametric modeling, but it generally still suffers from problems such as applicability only to specific cross-sectional components and simple structural forms, incomplete models, and reliance on specific software. Preliminary explorations have been made in intelligent optimization of bridge structures, but these are generally still focused on specific bridge structural forms under simple loads, and their adaptability to optimizing similar bridges remains insufficient. Summary of the Invention

[0004] The purpose of this invention is to provide a human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges, comprising the following steps:

[0005] 1) Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the through-type steel arch bridge, and draw the initial condition diagram;

[0006] 2) Based on the initial condition diagram, establish an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration;

[0007] 3) Based on the intelligent design model of the mid-span steel arch bridge structure, establish an optimization model for the structural parameters of the mid-span steel arch bridge;

[0008] 4) Solve the structural parameter optimization model of the mid-span steel arch bridge to obtain the structural optimization parameters of each mid-span steel arch bridge.

[0009] Furthermore, the initial condition diagrams include an initial condition elevation view of the mid-span steel arch bridge, an initial condition plan view of the mid-span steel arch bridge, and an initial condition cross-sectional view of the steel-concrete composite bridge deck system.

[0010] The initial conditions diagram includes the elevation positioning of the arch axis centerline, the planar positioning of the arch ribs, the planar positioning of the supports, the bridge deck elevation, and the cross-sectional layout of the steel-concrete composite bridge deck system.

[0011] Furthermore, in step 2), the steps for establishing an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration include:

[0012] 2.1) Use layer analysis algorithms to read key component information from the initial condition diagram;

[0013] The key component information includes the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0014] 2.2) Based on spatial information reasoning, the components and connection units of the mid-span steel arch bridge are automatically generated using the key component information read;

[0015] 2.3) Automatically define constraints;

[0016] 2.4) Automatically arrange loads, including the self-weight of each component of the mid-span steel arch bridge, the self-weight of the asphalt pavement, the self-weight of the railings, and the load on the lanes;

[0017] 2.5) Output the intelligent design model of the mid-span steel arch bridge structure.

[0018] Furthermore, in step 2.1), the step of using the layer analysis algorithm to read the key component information in the initial condition diagram includes:

[0019] 2.1.1) Mark the inner edge lines of the supports and arch ribs on the initial condition plan of the bridge;

[0020] 2.1.2) Mark the center line of the arch axis and the top line of the bridge deck on the initial condition elevation view of the bridge;

[0021] 2.1.3) Mark the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system;

[0022] 2.1.4) Use layer analysis algorithms to read various curve information, determine the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0023] Furthermore, in step 2.2), the steps for generating the components and connection units of the through-span steel arch bridge include:

[0024] 2.2.1) Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers; determine the support information and arch axis coefficient.

[0025] 2.2.2) Based on spatial information reasoning, and combined with the information of key components, arch ribs, supports, crossbeams between arches, steel-concrete composite bridge deck system and hangers, the dimensions and start and end coordinates of each component are determined;

[0026] The components include arch ribs, inter-arch crossbeams, supports, steel longitudinal beams, steel transverse beams, bridge decks, and bearings;

[0027] 2.2.3) Based on the component unit size, formulate unit division criteria, determine the number of each component unit, and automatically number these component nodes in the order of arch rib, inter-arch crossbeam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing.

[0028] 2.2.4) Combining the node numbers of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing, number the connection units of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, bearing, hanger, and steel longitudinal beam-bridge deck, and record the start and end nodes of each connection unit.

[0029] 2.2.5) Define the fiber cross-section of each component element. The steps include:

[0030] 2.2.5.1) Based on the dimensions of the component unit in the thickness, width, and height directions, formulate the cross-sectional fiber division criteria;

[0031] 2.2.5.2) Define constitutive relations for various materials and establish a material library and a constitutive relation library;

[0032] 2.2.5.3) Automatically generate cross-sectional profiles based on the cross-sectional shape and geometric dimensions of each component unit, divide fiber cross-sections, and read material properties and constitutive relations based on material information;

[0033] 2.2.6) Define the category of each component unit to generate the components and connection units of the mid-span steel arch bridge.

[0034] Furthermore, in step 2.3), the steps for automatically defining constraints include:

[0035] 2.3.1) Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions;

[0036] 2.3.2) Based on prior knowledge, formulate the bridge deck support layout criteria and establish a support performance index database;

[0037] 2.3.3) Extract the nodes at the bottom of the supports at both ends of the arch beam and the bridge deck system, as well as the nodes at the corresponding positions of the steel longitudinal beams of the bridge deck system, and automatically generate the support elements at the top of the arch beam and both ends of the bridge deck system.

[0038] 2.3.4) Write the boundary conditions and support element information into the file to achieve automatic definition of the boundary conditions and support elements at the bottom of the supports at both ends of the arch and the bridge deck system.

[0039] Furthermore, in step 2.4), the steps for automatically arranging loads include:

[0040] 2.4.1) The self-weight of all components, asphalt pavement, and railings shall be applied in the form of uniform line loads;

[0041] Among them, the linear load intensity g L As shown below:

[0042] g L =A×ρ(1)

[0043] In the formula, A is the cross-sectional area; ρ is the material density;

[0044] 2.4.2) Lane loads are calculated based on the information read from the through-type steel arch bridge and are applied in the form of uniformly distributed loads and concentrated loads.

[0045] Furthermore, in step 3), the steps for establishing the structural parameter optimization model of the mid-span steel arch bridge include:

[0046] 3.1) Select the variables that need to be optimized for each type of component, and determine the range of values ​​for the decision variables;

[0047] The variables that need to be optimized include: the height and width-to-height ratio of the arch rib bottom section, the height ratio of the arch rib top section to the arch bottom section, the thickness of the arch rib flange and web, the thickness and concrete strength of the bridge deck, the height of the bridge deck steel beams, the width and thickness of the bridge deck steel beam flanges, and the thickness of the bridge deck steel beam web.

[0048] 3.2) Establish the constrained mathematical model for the structural parameter optimization model of the mid-span steel arch bridge, including the constraint mathematical model under the ultimate limit state of bearing capacity, the constraint under the serviceability limit state, and the geometric constraint mathematical model;

[0049] 3.3) Establish an objective function with material cost as the optimization objective, namely:

[0050] (2)

[0051] In the formula, i is the component material number; i = 1, 2, 3, ..., n; n is the total number of component materials; A i L represents the cross-sectional area of ​​the component material. i P represents the length of the component material. i This refers to the unit price of the component materials.

[0052] 3.4) Establish a pseudo-objective function F based on the external penalty method, and use the pseudo-objective function F as the objective function of the structural parameter optimization model of the mid-span steel arch bridge;

[0053] The pseudo-objective function F is shown below:

[0054] (3)

[0055] In the formula, j represents the constraint number under the ultimate limit state and the constraint number under the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the constraint number under the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

[0056] Furthermore, the constraint mathematical model under the ultimate limit state of bearing capacity includes: constraint that the flexural bearing capacity of the section does not exceed the limit of the flexural bearing capacity of the section, and constraint that the shear bearing capacity of the section does not exceed the limit of the shear bearing capacity of the section;

[0057] The flexural bearing capacity of the section shall not exceed the limit constraint shown below:

[0058] (4)

[0059] In the formula, M is the flexural capacity of the section, M lim This refers to the limit value of the flexural bearing capacity of the cross section;

[0060] The shear capacity of the section is not subject to the limit constraint shown below:

[0061] (5)

[0062] In the formula, V is the shear capacity of the section, V lim This refers to the limit value of the shear capacity of the cross section;

[0063] The mathematical model for constraints under normal serviceability limit states includes: constraint that the component deflection does not exceed the deflection limit and constraint that the crack width does not exceed the crack width limit;

[0064] The component deflection must not exceed the deflection limit constraint as shown below:

[0065] (6)

[0066] In the formula, δ is the deflection of the component, δ lim The deflection limit of the component;

[0067] The requirement that the crack width does not exceed the crack width limit is as follows:

[0068] (7)

[0069] In the formula, w cr w is the crack width.crlim This is the limit for crack width;

[0070] The geometric constraint mathematical model includes: the flange width-to-thickness ratio of steel structure members does not exceed the limit constraint, and the web height-to-thickness ratio of steel structure members does not exceed the limit constraint.

[0071] The width-to-thickness ratio of the flange of the steel structure member shall not exceed the following limit constraint:

[0072] (8)

[0073] In the formula, B f t is the flange width parameter for steel structural members. f For the flange thickness of the steel structure component, rf lim This refers to the limit value for the width-to-thickness ratio of the flange of a steel structure component.

[0074] The following limits apply to the web height-to-thickness ratio of the steel structure member:

[0075] (9)

[0076] In the formula, h w t is the web height of the steel structure member. w rw is the web thickness of a steel structural member. lim This refers to the limit value for the height-to-thickness ratio of the web of a steel structure component.

[0077] Furthermore, the algorithms for solving the structural parameter optimization model of the through-type steel arch bridge include: genetic algorithm, particle swarm algorithm, and differential evolution algorithm;

[0078] The optimization algorithm employs an adaptive parameter adjustment strategy to optimize population quality when generating individuals, avoiding the generation of invalid individuals.

[0079] The adaptive adjustment strategy for adjusting the cross-sectional parameters of the arch rib includes the following steps:

[0080] a) Fix the flange width of the arch rib section and determine whether the width-to-thickness ratio of the flange of the steel structure member exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the flange of the steel structure member. If not, do not change the flange thickness.

[0081] b) Determine the web height of the arch rib section based on the arch rib section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0082] c) The adjustment sequence for the arch rib sections is from the arch crown section to the arch bottom section;

[0083] When the flange thickness of the section near the bottom of the arch is less than the flange thickness of the section near the top of the arch, the flange thickness is automatically updated to the flange thickness of the section near the top of the arch.

[0084] When the web thickness of the section near the bottom of the arch is less than the web thickness of the section near the top of the arch, the web thickness of the section is automatically updated to the web thickness of the section near the top of the arch.

[0085] When adjusting the cross-sectional parameters of the upper flange width of the bridge deck steel beams, the adaptive adjustment strategy includes the following steps:

[0086] I) Fix the flange width of the steel beam section and determine whether the width-to-thickness ratio of the steel structure member flange exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the steel structure member flange. If not, do not change the flange thickness.

[0087] II) Determine the web height of the steel beam section based on the steel beam section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0088] The technical advantages of this invention are undeniable. This invention proposes a human-computer collaborative intelligent modeling and optimization framework for mid-span steel arch bridges. This method requires only minimal human-computer interaction, utilizing layer analysis algorithms to extract initial condition diagram information and combining it with prior knowledge to achieve rapid modeling of mid-span steel arch bridges. This avoids errors from manual modeling and improves modeling efficiency and quality. Simultaneously, based on the established intelligent design model of the mid-span steel arch bridge structure, optimization algorithms are used to optimize structural parameters, effectively improving bridge design quality and efficiency. This method has strong flexibility and adaptability and can be extended to the design of different types of bridges. Attached Figure Description

[0089] Figure 1 This is a flowchart of the intelligent modeling and optimization method for an embodiment of the present invention;

[0090] Figure 2 This is a flowchart illustrating the intelligent modeling process for an embodiment of the present invention.

[0091] Figure 3 Example of drawing initial condition diagram for a mid-span steel arch bridge in an embodiment of the present invention;

[0092] Figure 4 This is an example of reading the initial condition diagram of a mid-span steel arch bridge, as an embodiment of the present invention.

[0093] Figure 5 This is an example of the intelligent modeling results of a mid-span steel arch bridge, as an embodiment of the present invention.

[0094] Figure 6 This is a schematic flowchart illustrating the intelligent optimization process of an embodiment of the present invention;

[0095] Figure 7 This is a schematic diagram of the intelligent optimization process in an embodiment of the present invention. Detailed Implementation

[0096] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0097] Example 1:

[0098] See Figures 1 to 7 A human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges includes the following steps:

[0099] 1) Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the through-type steel arch bridge, and draw the initial condition diagram;

[0100] 2) Based on the initial condition diagram, establish an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration;

[0101] 3) Based on the intelligent design model of the mid-span steel arch bridge structure, establish an optimization model for the structural parameters of the mid-span steel arch bridge;

[0102] 4) Solve the structural parameter optimization model of the mid-span steel arch bridge to obtain the structural optimization parameters of each mid-span steel arch bridge.

[0103] The initial condition diagrams include the initial condition elevation view of the mid-span steel arch bridge, the initial condition plan view of the mid-span steel arch bridge, and the initial condition cross-sectional view of the steel-concrete composite bridge deck system.

[0104] The initial conditions diagram includes the elevation positioning of the arch axis centerline, the planar positioning of the arch ribs, the planar positioning of the supports, the bridge deck elevation, and the cross-sectional layout of the steel-concrete composite bridge deck system.

[0105] Step 2) involves establishing an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration.

[0106] 2.1) Use the layer analysis algorithm to read the key component information in the initial condition drawing; the layer analysis algorithm can obtain relevant curve information by marking layers in CAD and then reading DXF files (e.g., reading in Python). For example, a straight line is the coordinate of its two endpoints.

[0107] The key component information includes the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0108] 2.2) Based on spatial information reasoning, the components and connection units of the mid-span steel arch bridge are automatically generated using the key component information read;

[0109] 2.3) Automatically define constraints;

[0110] 2.4) Automatically arrange loads, including the self-weight of each component of the mid-span steel arch bridge, the self-weight of the asphalt pavement, the self-weight of the railings, and the load on the lanes;

[0111] 2.5) Output the intelligent design model of the mid-span steel arch bridge structure.

[0112] Step 2.1), the steps of reading key component information from the initial condition diagram using the layer analysis algorithm, include:

[0113] 2.1.1) Mark the inner edge lines of the supports and arch ribs on the initial condition plan of the bridge;

[0114] 2.1.2) Mark the center line of the arch axis and the top line of the bridge deck on the initial condition elevation view of the bridge;

[0115] 2.1.3) Mark the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system;

[0116] 2.1.4) Use layer analysis algorithms to read various curve information, determine the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0117] Step 2.2) involves generating the components and connection units of the through-span steel arch bridge, including:

[0118] 2.2.1) Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers; determine the support information and arch axis coefficient.

[0119] 2.2.2) Based on spatial information reasoning, and combined with the information of key components, arch ribs, supports, crossbeams between arches, steel-concrete composite bridge deck system and hangers, the dimensions and start and end coordinates of each component are determined;

[0120] The components include arch ribs, inter-arch crossbeams, supports, steel longitudinal beams, steel transverse beams, bridge decks, and bearings;

[0121] 2.2.3) Based on the component unit size, formulate unit division criteria, determine the number of each component unit, and automatically number these component nodes in the order of arch rib, inter-arch crossbeam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing.

[0122] The unit division criteria can be formulated as follows: the length of the component unit division is not greater than its cross-sectional height. For composite beams, since they are double-layer beam units, the steel beam units are divided with a length not exceeding the cross-sectional height of the steel beam. The length of the bridge deck unit is the same as the length of the steel beam unit.

[0123] 2.2.4) Combining the node numbers of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing, number the connection units of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, bearing, hanger, and steel longitudinal beam-bridge deck, and record the start and end nodes of each connection unit.

[0124] 2.2.5) Define the fiber cross-section of each component element. The steps include:

[0125] 2.2.5.1) Based on the dimensions of the component unit in the thickness, width, and height directions, formulate the cross-sectional fiber division criteria;

[0126] For example, steel structure unit plates are divided into 4 fibers in the thickness direction and the fiber length in the width or height direction is no more than 50mm. For concrete bridge deck units, the fiber length in the thickness and width directions is no more than 40mm and 100mm, respectively.

[0127] 2.2.5.2) Define constitutive relations for various materials and establish a material library and a constitutive relation library;

[0128] 2.2.5.3) Automatically generate cross-sectional profiles based on the cross-sectional shape and geometric dimensions of each component unit, divide fiber cross-sections, and read material properties and constitutive relations based on material information;

[0129] 2.2.6) Define the category of each component unit to generate the components and connection units of the mid-span steel arch bridge.

[0130] In step 2.3), the steps for automatically defining constraints include:

[0131] 2.3.1) Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions (set according to the specific situation, the boundary conditions are fixed, hinged, etc.).

[0132] 2.3.2) Based on prior knowledge, formulate bridge deck support layout criteria (combining the designer's experience to formulate rules) and establish a support performance index library;

[0133] 2.3.3) Extract the nodes at the bottom of the supports at both ends of the arch beam and the bridge deck system, as well as the nodes at the corresponding positions of the steel longitudinal beams of the bridge deck system, and automatically generate the support elements at the top of the arch beam and both ends of the bridge deck system.

[0134] 2.3.4) Write the boundary conditions and support element information into the file to achieve automatic definition of the boundary conditions and support elements at the bottom of the supports at both ends of the arch and the bridge deck system.

[0135] In step 2.4), the steps for automatically arranging loads include:

[0136] 2.4.1) The self-weight of all components, asphalt pavement, and railings shall be applied in the form of uniform line loads;

[0137] Among them, the linear load intensity g L As shown below:

[0138] g L =A×ρ(1)

[0139] In the formula, A is the cross-sectional area; ρ is the material density;

[0140] 2.4.2) Lane loads are calculated based on the information read from the through-type steel arch bridge and are applied in the form of uniformly distributed loads and concentrated loads.

[0141] Step 3) involves establishing a parameter optimization model for a through-span steel arch bridge, including the following steps:

[0142] 3.1) Select the variables that need to be optimized for each type of component, and determine the range of values ​​for the decision variables;

[0143] The variables that need to be optimized include: the height and width-to-height ratio of the arch rib bottom section, the height ratio of the arch rib top section to the arch bottom section, the thickness of the arch rib flange and web, the thickness and concrete strength of the bridge deck, the height of the bridge deck steel beams, the width and thickness of the bridge deck steel beam flanges, and the thickness of the bridge deck steel beam web.

[0144] 3.2) Establish the constrained mathematical model for the structural parameter optimization model of the mid-span steel arch bridge, including the constraint mathematical model under the ultimate limit state of bearing capacity, the constraint under the serviceability limit state, and the geometric constraint mathematical model;

[0145] 3.3) Establish an objective function with material cost as the optimization objective, namely:

[0146] (2)

[0147] In the formula, i is the component material number; i = 1, 2, 3, ..., n; n is the total number of component materials; A i L represents the cross-sectional area of ​​the component material. i P represents the length of the component material. i This refers to the unit price of the component materials.

[0148] 3.4) Establish a pseudo-objective function F based on the external penalty method, and use the pseudo-objective function F as the objective function of the structural parameter optimization model of the mid-span steel arch bridge;

[0149] The pseudo-objective function F is shown below:

[0150] (3)

[0151] In the formula, j represents the constraint number under the ultimate limit state and the constraint number under the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the constraint number under the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

[0152] The constraint mathematical model under the ultimate limit state of bearing capacity includes: constraint that the flexural bearing capacity of the section does not exceed the limit of the flexural bearing capacity of the section, and constraint that the shear bearing capacity of the section does not exceed the limit of the shear bearing capacity of the section;

[0153] The flexural bearing capacity of the section shall not exceed the limit constraint shown below:

[0154] (4)

[0155] In the formula, M is the flexural capacity of the section, M lim This refers to the limit value of the flexural bearing capacity of the cross section;

[0156] The shear capacity of the section is not subject to the limit constraint shown below:

[0157] (5)

[0158] In the formula, V is the shear capacity of the section, V lim This refers to the limit value of the shear capacity of the cross section;

[0159] The mathematical model for constraints under normal serviceability limit states includes: constraint that the component deflection does not exceed the deflection limit and constraint that the crack width does not exceed the crack width limit;

[0160] The component deflection must not exceed the deflection limit constraint as shown below:

[0161] (6)

[0162] In the formula, δ is the deflection of the component, δ lim The deflection limit of the component;

[0163] The requirement that the crack width does not exceed the crack width limit is as follows:

[0164] (7)

[0165] In the formula, w cr w is the crack width. crlim This is the limit for crack width;

[0166] The geometric constraint mathematical model includes: the flange width-to-thickness ratio of steel structure members does not exceed the limit constraint, and the web height-to-thickness ratio of steel structure members does not exceed the limit constraint.

[0167] The width-to-thickness ratio of the flange of the steel structure member shall not exceed the following limit constraint:

[0168] (8)

[0169] In the formula, B f t is the flange width parameter for steel structural members. f For the flange thickness of the steel structure component, rf lim This refers to the limit value for the width-to-thickness ratio of the flange of a steel structure component.

[0170] The following limits apply to the web height-to-thickness ratio of the steel structure member:

[0171] (9)

[0172] In the formula, h w t is the web height of the steel structure member. w rw is the web thickness of a steel structural member. lim This refers to the limit value for the height-to-thickness ratio of the web of a steel structure component.

[0173] The algorithms for solving the structural parameter optimization model of a through-type steel arch bridge include: genetic algorithm, particle swarm optimization algorithm, and differential evolution algorithm.

[0174] The optimization algorithm employs an adaptive parameter adjustment strategy to optimize population quality when generating individuals, avoiding the generation of invalid individuals.

[0175] The adaptive adjustment strategy for adjusting the cross-sectional parameters of the arch rib includes the following steps:

[0176] a) Fix the flange width of the arch rib section and determine whether the width-to-thickness ratio of the flange of the steel structure member exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the flange of the steel structure member. If not, do not change the flange thickness.

[0177] b) Determine the web height of the arch rib section based on the arch rib section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0178] c) The adjustment sequence for the arch rib sections is from the arch crown section to the arch bottom section;

[0179] When the flange thickness of the section near the bottom of the arch is less than the flange thickness of the section near the top of the arch, the flange thickness is automatically updated to the flange thickness of the section near the top of the arch.

[0180] When the web thickness of the section near the bottom of the arch is less than the web thickness of the section near the top of the arch, the web thickness of the section is automatically updated to the web thickness of the section near the top of the arch.

[0181] When adjusting the cross-sectional parameters of the upper flange width of the bridge deck steel beams, the adaptive adjustment strategy includes the following steps:

[0182] I) Fix the flange width of the steel beam section and determine whether the width-to-thickness ratio of the steel structure member flange exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the steel structure member flange. If not, do not change the flange thickness.

[0183] II) Determine the web height of the steel beam section based on the steel beam section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0184] Example 2:

[0185] A human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges includes the following steps:

[0186] 1) Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the through-type steel arch bridge, and draw the initial condition diagram;

[0187] 2) Based on the initial condition diagram, establish an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration;

[0188] 3) Based on the intelligent design model of the mid-span steel arch bridge structure, establish an optimization model for the structural parameters of the mid-span steel arch bridge;

[0189] 4) Solve the structural parameter optimization model of the mid-span steel arch bridge to obtain the structural optimization parameters of each mid-span steel arch bridge.

[0190] Example 3:

[0191] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as in Embodiment 2, further comprising the initial condition diagram including an initial condition elevation view of the mid-span steel arch bridge, an initial condition plan view of the mid-span steel arch bridge, and an initial condition cross-sectional view of the steel-concrete composite bridge deck system.

[0192] The initial conditions diagram includes the elevation positioning of the arch axis centerline, the planar positioning of the arch ribs, the planar positioning of the supports, the bridge deck elevation, and the cross-sectional layout of the steel-concrete composite bridge deck system.

[0193] Example 4:

[0194] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-3, further comprising the following steps in step 2) for establishing an intelligent design model of the mid-span steel arch bridge structure based on human-machine collaboration:

[0195] 2.1) Use layer analysis algorithms to read key component information from the initial condition diagram;

[0196] The key component information includes the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0197] 2.2) Based on spatial information reasoning, the components and connection units of the mid-span steel arch bridge are automatically generated using the key component information read;

[0198] 2.3) Automatically define constraints;

[0199] 2.4) Automatically arrange loads, including the self-weight of each component of the mid-span steel arch bridge, the self-weight of the asphalt pavement, the self-weight of the railings, and the load on the lanes;

[0200] 2.5) Output the intelligent design model of the mid-span steel arch bridge structure.

[0201] Example 5:

[0202] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-4, further comprising the following steps in step 2.1), which involves using a layer analysis algorithm to read the key component information in the initial condition diagram:

[0203] 2.1.1) Mark the inner edge lines of the supports and arch ribs on the initial condition plan of the bridge;

[0204] 2.1.2) Mark the center line of the arch axis and the top line of the bridge deck on the initial condition elevation view of the bridge;

[0205] 2.1.3) Mark the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system;

[0206] 2.1.4) Use layer analysis algorithms to read various curve information, determine the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0207] Example 6:

[0208] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-5, further comprising the following steps in step 2.2) for generating the components and connection units of the mid-span steel arch bridge:

[0209] 2.2.1) Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers; determine the support information and arch axis coefficient.

[0210] 2.2.2) Based on spatial information reasoning, and combined with the information of key components, arch ribs, supports, crossbeams between arches, steel-concrete composite bridge deck system and hangers, the dimensions and start and end coordinates of each component are determined;

[0211] The components include arch ribs, inter-arch crossbeams, supports, steel longitudinal beams, steel transverse beams, bridge decks, and bearings;

[0212] 2.2.3) Formulate unit division criteria, determine the number of each component unit, and automatically number these component nodes in the order of arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing.

[0213] 2.2.4) Combining the node numbers of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing, number the connection units of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, bearing, hanger, and steel longitudinal beam-bridge deck, and record the start and end nodes of each connection unit.

[0214] 2.2.5) Define the fiber cross-section of each component element. The steps include:

[0215] 2.2.5.1) Establish cross-sectional fiber division criteria;

[0216] 2.2.5.2) Define constitutive relations for various materials and establish a material library and a constitutive relation library;

[0217] 2.2.5.3) Automatically generate cross-sectional profiles based on the cross-sectional shape and geometric dimensions of each component unit, divide fiber cross-sections, and read material properties and constitutive relations based on material information;

[0218] 2.2.6) Define the category of each component unit to generate the components and connection units of the mid-span steel arch bridge.

[0219] Example 7:

[0220] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-6, further comprising the step of automatically defining constraints in step 2.3):

[0221] 2.3.1) Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions;

[0222] 2.3.2) Based on prior knowledge, formulate the bridge deck support layout criteria and establish a support performance index database;

[0223] 2.3.3) Extract the nodes at the bottom of the supports at both ends of the arch beam and the bridge deck system, as well as the nodes at the corresponding positions of the steel longitudinal beams of the bridge deck system, and automatically generate the support elements at the top of the arch beam and both ends of the bridge deck system.

[0224] 2.3.4) Write the boundary conditions and support element information into the file to achieve automatic definition of various constraints.

[0225] Example 8:

[0226] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-7, further comprising the following steps in step 2.4):

[0227] 2.4.1) The self-weight of all components, asphalt pavement, and railings shall be applied in the form of uniform line loads;

[0228] Among them, the linear load intensity g L As shown below:

[0229] g L =A×ρ(1)

[0230] In the formula, A is the cross-sectional area; ρ is the material density;

[0231] 2.4.2) The lane load is calculated based on the information of the through-type steel arch bridge and is applied in the manner of uniformly distributed load and concentrated load according to the requirements of the specification.

[0232] Example 9:

[0233] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-8, further comprising the following steps in step 3) for establishing an optimization model of the structural parameters of the mid-span steel arch bridge:

[0234] 3.1) Select the variables that need to be optimized for each type of component, and determine the range of values ​​for the decision variables;

[0235] The variables that need to be optimized include: the height and width-to-height ratio of the arch rib bottom section, the height ratio of the arch rib top section to the arch bottom section, the thickness of the arch rib flange and web, the thickness and concrete strength of the bridge deck, the height of the bridge deck steel beams, the width and thickness of the bridge deck steel beam flanges, and the thickness of the bridge deck steel beam web.

[0236] 3.2) Establish the constrained mathematical model for the structural parameter optimization model of the mid-span steel arch bridge, including the constraint mathematical model under the ultimate limit state of bearing capacity, the constraint under the serviceability limit state, and the geometric constraint mathematical model;

[0237] 3.3) Establish an objective function with material cost as the optimization objective, namely:

[0238] (2)

[0239] In the formula, i is the component material number; i = 1, 2, 3, ..., n; n is the total number of component materials; A i L represents the cross-sectional area of ​​the component material. i P represents the length of the component material. i This refers to the unit price of the component materials.

[0240] 3.4) Establish a pseudo-objective function F based on the external penalty method, and use the pseudo-objective function F as the objective function of the structural parameter optimization model of the mid-span steel arch bridge;

[0241] The pseudo-objective function F is shown below:

[0242] (3)

[0243] In the formula, j represents the constraint number under the ultimate limit state and the constraint number under the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the constraint number under the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

[0244] Example 10:

[0245] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of embodiments 2-9, further comprising the following constraints in the ultimate limit state of bearing capacity: the bending bearing capacity of the section does not exceed the limit of the bending bearing capacity of the section, and the shear bearing capacity of the section does not exceed the limit of the shear bearing capacity of the section;

[0246] The flexural bearing capacity of the section shall not exceed the limit constraint shown below:

[0247] (4)

[0248] In the formula, M is the flexural capacity of the section, M lim This refers to the limit value of the flexural bearing capacity of the cross section;

[0249] The shear capacity of the section is not subject to the limit constraint shown below:

[0250] (5)

[0251] In the formula, V is the shear capacity of the section, V lim This refers to the limit value of the shear capacity of the cross section;

[0252] The mathematical model for constraints under normal serviceability limit states includes: constraint that the component deflection does not exceed the deflection limit and constraint that the crack width does not exceed the crack width limit;

[0253] The component deflection must not exceed the deflection limit constraint as shown below:

[0254] (6)

[0255] In the formula, δ is the deflection of the component, δ lim The deflection limit of the component;

[0256] The requirement that the crack width does not exceed the crack width limit is as follows:

[0257] (7)

[0258] In the formula, w cr w is the crack width. crlim This is the limit for crack width;

[0259] The geometric constraint mathematical model includes: the flange width-to-thickness ratio of steel structure members does not exceed the limit constraint, and the web height-to-thickness ratio of steel structure members does not exceed the limit constraint.

[0260] The width-to-thickness ratio of the flange of the steel structure member shall not exceed the following limit constraint:

[0261] (8)

[0262] In the formula, B f t is the flange width parameter for steel structural members. f For the flange thickness of the steel structure component, rf lim This refers to the limit value for the width-to-thickness ratio of the flange of a steel structure component.

[0263] The following limits apply to the web height-to-thickness ratio of the steel structure member:

[0264] (9)

[0265] In the formula, h w t is the web height of the steel structure member. w rw is the web thickness of a steel structural member. lim This refers to the limit value for the height-to-thickness ratio of the web of a steel structure component.

[0266] Example 11:

[0267] A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, with the same technical content as any one of Examples 2-10, further comprising the following algorithms for solving the structural parameter optimization model of the mid-span steel arch bridge: genetic algorithm, particle swarm algorithm, and differential evolution algorithm;

[0268] The optimization algorithm employs an adaptive parameter adjustment strategy to optimize population quality when generating individuals, avoiding the generation of invalid individuals.

[0269] The adaptive adjustment strategy for adjusting the cross-sectional parameters of the arch rib includes the following steps:

[0270] a) Fix the flange width of the arch rib section and determine whether the width-to-thickness ratio of the flange of the steel structure member exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the flange of the steel structure member. If not, do not change the flange thickness.

[0271] b) Determine the web height of the arch rib section based on the arch rib section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0272] c) The adjustment sequence for the arch rib sections is from the arch crown section to the arch bottom section;

[0273] When the flange thickness of the section near the bottom of the arch is less than the flange thickness of the section near the top of the arch, the flange thickness is automatically updated to the flange thickness of the section near the top of the arch.

[0274] When the web thickness of the section near the bottom of the arch is less than the web thickness of the section near the top of the arch, the web thickness of the section is automatically updated to the web thickness of the section near the top of the arch.

[0275] When adjusting the cross-sectional parameters of the upper flange width of the bridge deck steel beams, the adaptive adjustment strategy includes the following steps:

[0276] I) Fix the flange width of the steel beam section and determine whether the width-to-thickness ratio of the steel structure member flange exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the steel structure member flange. If not, do not change the flange thickness.

[0277] II) Determine the web height of the steel beam section based on the steel beam section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

[0278] Example 12:

[0279] A human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges includes the following steps:

[0280] 1) Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the mid-span steel arch bridge, and draw the initial condition diagram.

[0281] 2) Establish an intelligent design model for mid-span steel arch bridge structures based on human-machine collaboration.

[0282] 3) Based on the intelligent design model of the mid-span steel arch bridge structure, establish an optimization model for the structural parameters of the mid-span steel arch bridge.

[0283] 4) Solve the structural parameter optimization model of the mid-span steel arch bridge to obtain the structural optimization parameters of each mid-span steel arch bridge.

[0284] Step 1) The initial condition diagrams include the initial condition elevation view of the mid-span steel arch bridge, the initial condition plan view of the mid-span steel arch bridge, and the initial condition cross-section view of the steel-concrete composite bridge deck system.

[0285] Step 1) The initial condition diagram contains information such as the elevation positioning of the arch axis centerline, the planar positioning of the arch ribs, the planar positioning of the supports, the bridge deck elevation, and the cross-sectional layout of the steel-concrete composite bridge deck system.

[0286] Step 2) describes the steps for establishing an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration, including:

[0287] 2.1) Use layer analysis algorithms to read key component information from the initial condition map DXF vector graphics file.

[0288] 2.2) Based on spatial information reasoning, the components and connection units of the mid-span steel arch bridge are automatically generated using the read initial design information.

[0289] 2.3) Automatically define constraints.

[0290] 2.4) Automatically arrange loads, including the self-weight of various components, the self-weight of asphalt pavement, the self-weight of railings, and the load on the driveway.

[0291] 2.5) Output the intelligent design model of the mid-span steel arch bridge structure.

[0292] Step 2.1) includes the following sub-steps:

[0293] 2.1.1) Mark the inner side lines of the supports and arch ribs on the initial condition plan of the bridge.

[0294] 2.1.2) Mark the center line of the arch axis and the top line of the bridge deck on the initial condition elevation view of the bridge.

[0295] 2.1.3) Mark the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system.

[0296] 2.1.4) Use layer analysis algorithms to read various curve information, determine the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0297] Step 2.2) includes the following sub-steps:

[0298] 2.2.1) Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers, and determine the support information, arch axis coefficient, etc.

[0299] 2.2.2) Based on spatial information reasoning, the dimensions and start and end coordinates of each component are determined by combining the initial design information reading results in step 2.1.3) and the geometric information in step 2.2.1).

[0300] 2.2.3) Formulate unit division criteria, determine the number of each component unit, and automatically number the nodes in the order of arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing.

[0301] 2.2.4) Combining the node numbers of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing, number the units of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, bearing, hanger, and steel longitudinal beam-bridge deck connection unit, and record the start and end nodes of each unit.

[0302] 2.2.5) Define the fiber cross-section of each component unit.

[0303] 2.2.6) Define the category of each component unit, and combine the information from steps 2.2.2)-2.2.5) to generate the components and connection units of the mid-span steel arch bridge.

[0304] Step 2.2.5) includes the following steps:

[0305] 2.2.5.1) Establish cross-sectional fiber division criteria.

[0306] 2.2.5.2) Define constitutive relations for various types of materials and establish a material library and a constitutive relation library.

[0307] 2.2.5.3) Automatically generate cross-sectional profiles based on the cross-sectional shape and geometric dimensions of each component unit, divide fiber cross-sections, and read material indices and constitutive relations based on material information.

[0308] Step 2.3) includes the following sub-steps:

[0309] 2.3.1) Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions.

[0310] 2.3.2) Based on prior knowledge, formulate the bridge deck support layout criteria and establish a support performance index database.

[0311] 2.3.3) Extract the nodes at the bottom of the supports at both ends of the arch beam and the bridge deck system, as well as the nodes at the corresponding positions of the steel longitudinal beams of the bridge deck system, and automatically generate the support elements at the top of the arch beam and both ends of the bridge deck system.

[0312] 2.3.4) Write the boundary conditions and support element information into the file to achieve automatic definition of various constraints.

[0313] Step 2.4) includes the following sub-steps:

[0314] 2.4.1) The self-weight of various components, asphalt pavement, and railings is applied as a uniform line load, with a line load intensity g. L The density of the component material is calculated using the following formula:

[0315] g L =A×ρ(1)

[0316] In the formula, A is the cross-sectional area; ρ is the material density.

[0317] 2.4.2) The lane load is calculated based on the information of the through-type steel arch bridge and is applied in the manner of uniformly distributed load and concentrated load according to the requirements of the specification.

[0318] Step 3) includes the following sub-steps:

[0319] 3.1) Select the variables that need to be optimized for each type of component and determine the range of values ​​for the decision variables.

[0320] 3.2) Establish a constraint mathematical model, including constraints under the ultimate limit state of bearing capacity, constraints under the serviceability limit state, and geometric constraints.

[0321] 3.3) Establish an objective function with material cost as the optimization objective, namely:

[0322] (2)

[0323] In the formula, i is the component material number; i = 1, 2, 3, ..., n; n is the total number of component materials; A i L represents the cross-sectional area of ​​the component material. i P represents the length of the component material. i This refers to the unit price of the component materials.

[0324] 3.4) Establish a pseudo-objective function F based on the external penalty method, as shown below:

[0325] (3)

[0326] In the formula, j represents the constraint number under the ultimate limit state and the constraint number under the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the constraint number under the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

[0327] The variables to be optimized in step 3.1) include: the height and width-to-height ratio of the arch rib bottom section, the height ratio of the arch rib top section to the arch bottom section, the thickness of the arch rib flange and web, the thickness and concrete strength of the bridge deck, the height of the bridge deck steel beams, the width and thickness of the bridge deck steel beam flanges, and the thickness of the bridge deck steel beam web.

[0328] The total number of optimization variables for the arch rib is determined by multiplying the number of optimization variables for a single section by the number of sections with different section sizes.

[0329] The constraint mathematical model under the ultimate limit state of bearing capacity involved in step 3.2) includes: constraint that the flexural bearing capacity of the section does not exceed the limit value of the flexural bearing capacity of the section, and constraint that the shear bearing capacity of the section does not exceed the limit value of the shear bearing capacity of the section.

[0330] The flexural bearing capacity of the section shall not exceed the limit constraint shown below:

[0331] (4)

[0332] In the formula, M is the flexural capacity of the section, M lim This is the limit value for the flexural bearing capacity of the cross section.

[0333] The shear capacity of the section is not subject to the limit constraint shown below:

[0334] (5)

[0335] In the formula, V is the shear capacity of the section, V lim This represents the limit value of the shear bearing capacity of the cross section.

[0336] The mathematical model of constraints under normal serviceability limit states involved in step 3.2) includes: constraint that the component deflection does not exceed the deflection limit and constraint that the crack width does not exceed the crack width limit.

[0337] The component deflection must not exceed the deflection limit constraint as shown below:

[0338] (6)

[0339] In the formula, δ is the deflection of the component, δ lim This is the limit value for component deflection.

[0340] The requirement that the crack width does not exceed the crack width limit is as follows:

[0341] (7)

[0342] In the formula, w cr w is the crack width. crlim This is the limit for crack width.

[0343] The geometric constraint mathematical model involved in step 3.2) includes: the flange width-to-thickness ratio of the steel structure member does not exceed the limit constraint, and the web height-to-thickness ratio of the steel structure member does not exceed the limit constraint.

[0344] The width-to-thickness ratio of the flange of the steel structure member shall not exceed the following limit constraint:

[0345] (8)

[0346] In the formula, B f t is the flange width parameter for steel structural members. f For the flange thickness of the steel structure component, rf lim This refers to the limit value for the width-to-thickness ratio of the flange of a steel structure component.

[0347] The following limits apply to the web height-to-thickness ratio of the steel structure member:

[0348] (9)

[0349] In the formula, h w t is the web height of the steel structure member. w rw is the web thickness of a steel structural member. lim This refers to the limit value for the height-to-thickness ratio of the web of a steel structure component.

[0350] The algorithms involved in step 4) for solving the structural parameter optimization model of the through-span steel arch bridge include: genetic algorithm, particle swarm algorithm, and differential evolution algorithm.

[0351] The optimization algorithm employs an adaptive parameter adjustment strategy to optimize population quality when generating individuals, thereby avoiding the generation of invalid individuals.

[0352] The adaptive adjustment strategy for the arch rib section parameters includes the following steps:

[0353] a) Fix the flange width of the arch rib section. Judge based on the fact that the flange width-to-thickness ratio of the steel structure member does not exceed the limit constraint. If the requirement is met, do not change the flange thickness. If the requirement is not met, automatically update it to the minimum flange thickness that meets the limit constraint of the flange width-to-thickness ratio of the steel structure member.

[0354] b) Determine the web height of the arch rib section based on the arch rib section height and flange thickness. Make a judgment based on the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If the requirement is met, do not change the web thickness. If the requirement is not met, automatically update it to the minimum web thickness that meets the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit.

[0355] c) The adjustment sequence for the arch rib sections is from the arch crown section to the arch base section. When the flange thickness of the section near the arch base is less than the flange thickness of the section near the arch crown, the flange thickness is automatically updated to the flange thickness of the section near the arch crown; when the web thickness of the section near the arch base is less than the web thickness of the section near the arch crown, the web thickness is automatically updated to the web thickness of the section near the arch crown.

[0356] The adaptive adjustment strategy for the width section parameters of the upper flange of the bridge deck steel beam includes the following steps:

[0357] a) Fix the flange width of the steel beam section. The judgment is based on the fact that the flange width-to-thickness ratio of the steel structure member does not exceed the limit constraint. If the requirement is met, the flange thickness is not changed. If the requirement is not met, it is automatically updated to the minimum flange thickness that meets the limit constraint of the flange width-to-thickness ratio of the steel structure member.

[0358] b) Determine the web height of the steel beam section based on the steel beam section height and flange thickness. Make a judgment based on the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If the requirement is met, do not change the web thickness. If the requirement is not met, automatically update it to the minimum web thickness that meets the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit.

[0359] Example 13:

[0360] See Figures 1 to 7 A human-machine collaborative intelligent modeling and optimization method for mid-span steel arch bridges includes the following steps:

[0361] 1) Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, steel-concrete composite bridge deck section, etc., based on the intended use, natural conditions and prior knowledge, and draw the initial condition diagram.

[0362] 2) Mark the plane positioning of the inner side line of the arch rib and the plane positioning of the support in the initial condition plan of the mid-span steel arch bridge.

[0363] 3) Mark the top of the supports, the center line of the arch axis, and the top line of the bridge deck in the initial condition elevation drawing of the bridge.

[0364] 4) Mark the web lines of the steel longitudinal beams in the initial condition section diagram of the steel-concrete composite bridge deck system.

[0365] 5) Use layer analysis algorithms to read key component information from the initial condition map DXF vector graphics file, determine the elevation coordinates of the arch crown and arch seat, the plane coordinates of the inner side lines of the supports and arch ribs, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system.

[0366] 6) Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers, and determine the support information, arch axis coefficient, etc.

[0367] 7) Combine the size information from step 6) and the key information reading results from step 5) to perform spatial information reasoning, and determine the size and start and end coordinates of each component.

[0368] 8) Establish unit division criteria, determine the number of each component unit, and automatically number the nodes in the order of arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing.

[0369] 9) Combining the node numbers of arch ribs, inter-arch beams, supports, steel longitudinal beams, steel crossbeams, bridge decks, and bearings, number the units of arch ribs, inter-arch beams, supports, steel longitudinal beams, steel crossbeams, bridge decks, bearings, hangers, and steel longitudinal beam-bridge deck connection units, and record the start and end nodes of each unit.

[0370] 10) Define the fiber cross-section of each component unit.

[0371] 11) Define the category of each component unit, and combine the information from steps 7)-10) to generate the components and connection units of the mid-span steel arch bridge.

[0372] 12) Write the node and element numbers and section information into the file to achieve automatic generation of each component.

[0373] 13) Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions.

[0374] 14) Based on prior knowledge, formulate the bridge deck support layout criteria and establish a support performance index database.

[0375] 15) Extract the nodes at the top of the cap beam and the bottom of the support at the abutment, as well as the nodes at the corresponding positions of the main steel beam, and automatically generate the support elements at the top of the cap beam and the abutment.

[0376] 16) Write boundary conditions and support element information into a file to achieve automatic definition of various constraints.

[0377] 17) The self-weight of various components, asphalt pavement, and railings is applied as a uniform line load, with a line load intensity of g. L The density of the component material is calculated using the following formula:

[0378] (1)

[0379] In the formula, A is the cross-sectional area and ρ is the material density.

[0380] 18) The lane load is calculated based on the information read from the mid-span steel arch bridge according to the specifications and is applied in the form of uniformly distributed load and concentrated load.

[0381] 19) Select the variables that need to be optimized for each type of component and determine the range of values ​​for the decision variables.

[0382] 20) Establish a constraint mathematical model, including constraints under the ultimate limit state of bearing capacity, constraints under the serviceability limit state, and geometric constraints.

[0383] 21) Establish the objective function for material cost optimization, namely:

[0384] (2)

[0385] In the formula, i is the component material number, i=1,2,3…,n, n is the total number of component materials, and A i L is the cross-sectional area of ​​the component material. i P is the length of the component material. i This refers to the unit price of the component materials.

[0386] 22) Establish a pseudo-objective function F based on the external penalty method, as shown below:

[0387] (3)

[0388] In the formula, j represents the constraint number under the ultimate limit state and the constraint number under the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the constraint number under the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

[0389] 23) Use optimization algorithms to solve for the variables that need to be optimized, and obtain the optimization parameters of each component.

Claims

1. A human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge, characterized in that, Includes the following steps: Step 1. Determine the structural system, span, rise-to-span ratio, arch axis shape, support form, and steel-concrete composite bridge deck section of the through-type steel arch bridge, and draw the initial condition diagram; Step 2. Based on the initial condition diagram, establish an intelligent design model for the mid-span steel arch bridge structure based on human-machine collaboration; Step 3. Based on the intelligent design model of the mid-span steel arch bridge structure, establish an optimization model for the structural parameters of the mid-span steel arch bridge; Step 4. Solve the structural parameter optimization model of the mid-span steel arch bridge to obtain the structural optimization parameters of each mid-span steel arch bridge; Step 2, the steps for establishing an intelligent design model for a mid-span steel arch bridge structure based on human-machine collaboration, include: Step 2.

1. Use layer analysis algorithms to read the key component information in the initial condition diagram; The key component information includes the elevation coordinates of the arch crown and arch seat of the arch axis centerline, the plane coordinates of the inner side lines of the support and arch rib, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional diagram of the steel-concrete composite bridge deck system. Step 2.

2. Based on spatial information reasoning, automatically generate the components and connection units of the mid-span steel arch bridge using the key component information read; Step 2.

3. Automatically define constraints; Step 2.

4. Automatically arrange loads, including the self-weight of each component of the mid-span steel arch bridge, the self-weight of the asphalt pavement, the self-weight of the railings, and the lane load; Step 2.

5. Output the intelligent design model of the mid-span steel arch bridge structure; Step 3, the steps for establishing the structural parameter optimization model of the mid-span steel arch bridge, include: Step 3.

1. Select the variables that need to be optimized for each type of component, and determine the range of values ​​for the decision variables; The variables that need to be optimized include: the height and width-to-height ratio of the arch rib bottom section, the height ratio of the arch rib top section to the arch bottom section, the thickness of the arch rib flange and web, the thickness and concrete strength of the bridge deck, the height of the bridge deck steel beams, the width and thickness of the bridge deck steel beam flanges, and the thickness of the bridge deck steel beam web. Step 3.

2. Establish the constrained mathematical model of the structural parameter optimization model of the mid-span steel arch bridge, including the constraint mathematical model of the ultimate limit state of bearing capacity, the constraint of the serviceability limit state, and the geometric constraint mathematical model; Step 3.

3. Establish an objective function with material cost as the optimization objective, namely: In the formula, i is the component material number; i = 1, 2, 3, ..., n; n is the total number of component materials; A i L represents the cross-sectional area of ​​the component material. i P represents the length of the component material. i This refers to the unit price of the component materials; Step 3.

4. Establish a pseudo-objective function F based on the external penalty method, and use the pseudo-objective function F as the objective function of the structural parameter optimization model of the mid-span steel arch bridge; The pseudo-objective function F is shown below: In the formula, j represents the constraint number under the ultimate limit state and the serviceability limit state; j = 1, 2, 3, ..., m; m represents the total number of constraints under the ultimate limit state and the serviceability limit state; C j This is the penalty function for the j-th constraint. It is set to 0 when the constraint is not violated, and to a predetermined penalty value when the constraint is violated.

2. The method for human-machine collaborative intelligent modeling and optimization of a mid-span steel arch bridge according to claim 1, characterized in that, The initial condition diagrams include the initial condition elevation view of the mid-span steel arch bridge, the initial condition plan view of the mid-span steel arch bridge, and the initial condition cross-sectional view of the steel-concrete composite bridge deck system. The initial condition diagram records the elevation positioning of the arch axis centerline, the planar positioning of the arch ribs, the planar positioning of the supports, the bridge deck elevation, and the cross-sectional layout of the steel-concrete composite bridge deck system.

3. The method for human-machine collaborative intelligent modeling and optimization of a mid-span steel arch bridge according to claim 1, characterized in that, Step 2.1, which involves using a layer analysis algorithm to read the key component information from the initial condition diagram, includes: Step 2.1.

1. Mark the inner edge lines of the supports and arch ribs on the initial condition plan of the bridge; Step 2.1.

2. Mark the arch axis centerline and the top line of the bridge deck on the initial condition elevation view of the bridge; Step 2.1.

3. Mark the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system; Step 2.1.

4. Use layer analysis algorithms to read various curve information, determine the elevation coordinates of the arch crown and arch seat, the plane coordinates of the inner side lines of the supports and arch ribs, the top elevation information of the bridge deck, and the coordinate information of the web of the steel longitudinal beam in the cross-sectional view of the steel-concrete composite bridge deck system.

4. The human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge according to claim 3, characterized in that, Step 2.2, the steps for generating the components and connection units of the through-span steel arch bridge, include: Step 2.2.

1. Determine the cross-sectional form, preliminary geometric dimensions and material information of the arch ribs, supports, inter-arch crossbeams, steel-concrete composite bridge deck system and hangers; determine the support information and arch axis coefficient. Step 2.2.

2. Based on spatial information reasoning, and combined with the information of key components, arch ribs, supports, crossbeams between arches, steel-concrete composite bridge deck system and hangers, determine the size and start and end coordinates of each component; The components include arch ribs, inter-arch crossbeams, supports, steel longitudinal beams, steel transverse beams, bridge decks, and bearings; Step 2.2.

3. Based on the component unit dimensions, formulate unit division criteria, determine the number of each component unit, and automatically number these component nodes in the order of arch rib, inter-arch beam, support, steel longitudinal beam, steel transverse beam, bridge deck, and bearing. Step 2.2.

4. Combining the node numbers of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, and bearing, number the connection units of the arch rib, arch beam, support, steel longitudinal beam, steel crossbeam, bridge deck, bearing, hanger, and steel longitudinal beam-bridge deck, and record the start and end nodes of each connection unit. Step 2.2.

5. Define the fiber cross-section of each component element. The steps include: Step 2.2.5.

1. Based on the dimensions of the component unit in the thickness, width, and height directions, formulate the cross-sectional fiber division criteria; Step 2.2.5.

2. Define constitutive relations for various materials and establish a material library and a constitutive relation library; Step 2.2.5.

3. Automatically generate the cross-sectional profile based on the cross-sectional shape and geometric dimensions of each component unit, divide the fiber cross-section, and read the material properties and constitutive relations based on the material information; Step 2.2.

6. Define the category of each component unit to generate the components and connection units of the mid-span steel arch bridge.

5. The human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge according to claim 1, characterized in that, In step 2.3, the steps for automatically defining constraints include: Step 2.3.

1. Extract the nodes at the bottom of the supports at both ends of the arch abutment and the bridge deck system, and define the boundary conditions; Step 2.3.

2. Based on prior knowledge, formulate the bridge deck support layout criteria and establish a support performance index library; Step 2.3.

3. Extract the nodes at the bottom of the supports at both ends of the arch beam and the bridge deck system, as well as the nodes at the corresponding positions of the steel longitudinal beams of the bridge deck system, and automatically generate the support elements at the top of the arch beam and both ends of the bridge deck system. Step 2.3.

4. Write the boundary conditions and support element information into the file to automatically define the boundary conditions and support elements at the bottom of the supports at both ends of the arch abutment and bridge deck system.

6. The human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge according to claim 1, characterized in that, Step 2.4, the steps for automatically placing loads include: Step 2.4.

1. The self-weight of various components, asphalt pavement, and railings is applied in the form of uniform line load; Among them, the linear load intensity g L As shown below: g L =A×ρ In the formula, A is the cross-sectional area; ρ is the material density; Step 2.4.

2. Lane loads are calculated based on the information read from the through-type steel arch bridge and applied as uniformly distributed loads and concentrated loads.

7. The human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge according to claim 1, characterized in that, The constraint mathematical model under the ultimate limit state of bearing capacity includes: constraint that the flexural bearing capacity of the section does not exceed the limit of the flexural bearing capacity of the section, and constraint that the shear bearing capacity of the section does not exceed the limit of the shear bearing capacity of the section; The flexural bearing capacity of the section shall not exceed the limit constraint shown below: In the formula, M is the flexural capacity of the section, M lim This refers to the limit value of the flexural bearing capacity of the cross section; The shear capacity of the section is not subject to the limit constraint shown below: In the formula, V is the shear capacity of the section, V lim This refers to the limit value of the shear capacity of the cross section; The mathematical model for constraints under normal serviceability limit states includes: constraint that the component deflection does not exceed the deflection limit and constraint that the crack width does not exceed the crack width limit; The component deflection must not exceed the deflection limit constraint as shown below: In the formula, δ is the deflection of the component, δ lim The deflection limit of the component; The requirement that the crack width does not exceed the crack width limit is as follows: In the formula, w cr w is the crack width. crlim This is the limit for crack width; The geometric constraint mathematical model includes: the flange width-to-thickness ratio of steel structure members does not exceed the limit constraint, and the web height-to-thickness ratio of steel structure members does not exceed the limit constraint; The width-to-thickness ratio of the flange of the steel structure member shall not exceed the following limit constraint: In the formula, B f t is the flange width parameter for steel structural members. f For the flange thickness of the steel structure component, rf lim The width-to-thickness ratio limit for the flange of a steel structure component; The following limits apply to the web height-to-thickness ratio of the steel structure member: In the formula, h w t is the web height of the steel structure member. w rw is the web thickness of a steel structural member. lim This refers to the limit value for the height-to-thickness ratio of the web of a steel structure component.

8. The human-machine collaborative intelligent modeling and optimization method for a mid-span steel arch bridge according to claim 1, characterized in that, The algorithms for solving the structural parameter optimization model of a through-type steel arch bridge include: genetic algorithm, particle swarm optimization algorithm, and differential evolution algorithm. The optimization algorithm employs an adaptive parameter adjustment strategy to optimize population quality and avoid generating invalid individuals when generating individuals; The adaptive adjustment strategy for adjusting the cross-sectional parameters of the arch rib includes the following steps: Step a. Fix the flange width of the arch rib section and determine whether the width-to-thickness ratio of the steel structure member flange exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the steel structure member flange. If not, do not change the flange thickness. Step b. Determine the web height of the arch rib section based on the arch rib section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness. Step c. The adjustment sequence for the arch rib sections is from the arch crown section to the arch base section; When the flange thickness of the section near the bottom of the arch is less than the flange thickness of the section near the top of the arch, the flange thickness is automatically updated to the flange thickness of the section near the top of the arch. When the web thickness of the section near the bottom of the arch is less than the web thickness of the section near the top of the arch, the web thickness of the section is automatically updated to the web thickness of the section near the top of the arch. When adjusting the cross-sectional parameters of the upper flange width of the bridge deck steel beams, the adaptive adjustment strategy includes the following steps: Step I. Fix the flange width of the steel beam section and determine whether the width-to-thickness ratio of the steel structure member flange exceeds the limit. If it does, automatically update it to the minimum flange thickness that meets the limit constraint of the width-to-thickness ratio of the steel structure member flange. If not, do not change the flange thickness. Step II. Determine the web height of the steel beam section based on the steel beam section height and flange thickness, and determine whether the web height-to-thickness ratio of the steel structure member exceeds the limit. If so, automatically update it to the minimum web thickness that satisfies the constraint that the web height-to-thickness ratio of the steel structure member does not exceed the limit. If not, do not change the web thickness.

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