Prefabricated plate type foundation splitting design method based on optimal economic size of prefabricated part

Abstract

The invention provides an assembly type plate type foundation splitting design method based on the optimal economic size of a prefabricated part, and relates to the technical field of tower plate type foundations of power transmission lines, and the method comprises the following specific steps: under set constraint conditions, randomly generating various splicing combinations of a predetermined plate type foundation, a finite element analysis model is used for carrying out performance simulation testing and calculating cost, comprehensive performance indexes and comprehensive cost are generated through data processing, a cost-performance coupling coefficient is calculated, a double-optimal parameter combination is screened, a prediction model is constructed and trained, and an optimal combination of spliced combinations is obtained through iterative optimization in combination with a genetic algorithm. And the size is used as the optimal economic size of the splicing combination. According to the method, multi-dimensional collaborative optimization is achieved, traditional design limitation is broken through, performance and cost are accurately balanced through intelligent optimization, engineering practice is fully considered, design landing performance is enhanced, construction efficiency is effectively improved, cost is reduced, and foundation safety is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of power transmission line tower slab foundation technology, specifically to a modular design method for prefabricated slab foundations based on the optimal economic dimensions of prefabricated components. Background Technology

[0002] In the field of transmission line tower slab foundation technology, traditional design methods have significant limitations. Because transmission line towers must withstand complex external forces such as wind loads, conductor tension, and icing loads, and are exposed to various climatic environments for extended periods, traditional designs often separate foundation performance analysis from cost control, making it difficult to comprehensively balance the two in the early design stages. On the one hand, simply raising design standards to meet the tower foundation's load-bearing capacity, overturning resistance, and anti-slip stability requirements under extreme conditions can easily lead to excessive material usage and a significant increase in costs. On the other hand, excessive cost reduction may result in insufficient foundation settlement control and reduced structural safety redundancy, posing safety hazards under extreme weather conditions such as strong winds and ice storms.

[0003] Furthermore, with the widespread application of prefabricated construction technology in transmission line tower foundations, the dimensional design of the splicing assembly has become crucial. Inappropriate splicing assembly dimensions not only increase the complexity of production molds and raise the requirements for roads and vehicles during transportation, but also prolong the construction period and increase construction costs due to difficulties in on-site hoisting and low assembly precision. Simultaneously, improper component dimensions may affect the overall load-bearing performance of the foundation, weakening its supporting effect on the transmission line tower. Therefore, a scientific and rational design method is urgently needed to systematically and comprehensively consider the special performance requirements and cost control of transmission line tower slab foundations, determine the optimal economic dimensions of the splicing assembly, and achieve efficient modular design of prefabricated slab foundations.

[0004] The prior art, disclosed in CN119475541A, provides a prefabricated structure design method, apparatus, equipment, and storage medium, comprising the following steps: obtaining design parameters of the prefabricated structure of the project; selecting cross-sectional dimensions, reinforcement ratio, and cavity ratio from the design parameters as variable parameters; obtaining constraints on the mechanical performance and construction industry chain of the prefabricated structure, and obtaining the initial population size, maximum number of iterations, crossover rate, and mutation rate; writing the initial population size, the maximum number of iterations, the crossover rate, the mutation rate, and the constraints into configuration information; processing the variable parameters using a preset genetic algorithm according to the configuration information to obtain a design scheme that satisfies the mechanical performance of the prefabricated structure; obtaining the standard value of construction carbon emissions and the standard value of bending strength corresponding to each design scheme, and processing the standard value of construction carbon emissions and the standard value of bending strength corresponding to each design scheme through an objective function to obtain a comprehensive index corresponding to each design scheme; selecting the design scheme with the smallest comprehensive index as the optimal design scheme that satisfies the mechanical performance of the prefabricated structure, thereby quickly obtaining the optimal design scheme with high strength and low carbon emissions.

[0005] However, the following shortcomings still exist: it only focuses on mechanical properties and carbon emissions during construction, neglecting transportation and construction costs and their correlation, and the basic performance indicators are not fully considered, making it difficult to meet actual needs; it ignores practical constraints, failing to consider limitations in production molds, transportation equipment, and hoisting capabilities, leading to problems such as difficulty in demolding, overloading, and hoisting difficulties in component production, transportation, and construction, affecting construction efficiency and quality; and it lacks optimization depth, with unsystematic analysis of geometric parameter combinations when using genetic algorithms, lacking a scientific screening mechanism, easily getting trapped in local optima, and failing to achieve a balance between performance and cost and maximize overall benefits.

[0006] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to provide a modular design method for prefabricated slab foundations based on the optimal economic dimensions of prefabricated components, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A modular design method for prefabricated slab foundations based on the optimal economic dimensions of prefabricated components, comprising the following steps:

[0010] Under the set constraints, based on the splicing model, multiple splicing combinations of a predetermined slab foundation are randomly generated as individuals in the initial population. The individuals in the initial population are input into the finite element analysis model for performance simulation testing. The bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to different individuals are obtained, as well as the material cost, transportation cost and construction cost corresponding to different individuals.

[0011] The data of the bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to the same entity are processed to generate the comprehensive performance index of the entity. The data of the material cost, transportation cost and construction cost corresponding to the same entity are processed to generate the comprehensive cost of the entity.

[0012] By combining the ratio of transportation cost to construction cost for the same individual, the cost-performance coupling coefficient for that individual is calculated. All individuals are sorted in descending order based on the cost-performance coupling coefficient, and a threshold is pre-set to retain individuals with a cost-performance coupling coefficient greater than the threshold, so as to complete the construction of a set of individuals with both cost and performance advantages.

[0013] A performance and cost prediction model is constructed. Based on a set of individuals with both cost and performance advantages, the individuals of the initial population are input into the performance and cost prediction model to obtain the comprehensive performance index and comprehensive cost corresponding to different individuals.

[0014] The comprehensive cost and comprehensive performance index corresponding to the same individual are weighted and summed to generate the comprehensive evaluation index corresponding to that individual. Taking the maximization of the comprehensive evaluation index corresponding to that individual as the objective function, the individuals in the initial population are iteratively optimized through a genetic algorithm to obtain the optimal individual. The optimal combination of the corresponding splicing combination is extracted as the optimal economic size.

[0015] Furthermore, the geometric parameters of the prefabricated components include length, width, and height.

[0016] Furthermore, the individuals in the initial population are constructed through the following steps:

[0017] Let the initial population be labeled U, and the initial population U = {U1, U2, ..., U} i ,…,U μ}, U i Let U be the i-th individual in the initial population, where i is the index of the individual in the initial population and i∈[1,μ], and μ is the number of individuals in the initial population. i =(l i,j ,b i,j ,h i,j |j∈[1,λ i ]), where l i,j ,b i,j ,hi,j Let λ represent the length, width, and height of the j-th prefabricated component of the i-th individual, respectively, where j is the index of the prefabricated component, and λ is the index of the prefabricated component. i Let be the number of prefabricated components in the i-th individual.

[0018] Furthermore, the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index corresponding to the same individual are processed to generate a comprehensive performance index for that individual, based on the following formula:

[0019] P i =ω1×P 1,i +ω2×P 2,i +ω3×P 3,i +ω4×P 4,i

[0020] Among them, P i Let i be the comprehensive performance index corresponding to the i-th individual, where i is the index of the individual in the initial population;

[0021] In the formula, P 1,i Let P be the carrying capacity index corresponding to the i-th individual. 2,i Let P be the settlement performance index corresponding to the i-th individual. 3,i Let P be the overturning stability index corresponding to the i-th individual. 4,i This represents the anti-slip stability index corresponding to the i-th individual;

[0022] In the formula, ω1 is the weighting coefficient of the bearing capacity index, ω2 is the weighting coefficient of the settlement performance index, ω3 is the weighting coefficient of the overturning stability index, and ω4 is the weighting coefficient of the sliding stability index. Based on w1+w2+w3+w4=1, let 0 <w4<w3<w2<w1<1。

[0023] Furthermore, the material costs, transportation costs, and construction costs corresponding to the same entity are processed to generate the entity's comprehensive cost, based on the following formula:

[0024] C i =C α,i +C β,i +C δ,i

[0025] Among them, C i Let C be the comprehensive cost corresponding to the i-th individual. α,i Let C be the material cost corresponding to the i-th individual. β,i Let C be the transportation cost corresponding to the i-th individual. δ,i Let be the construction cost corresponding to the i-th individual.

[0026] Furthermore, by combining the ratio of transportation cost to construction cost for the same entity, the cost-performance coupling coefficient for that entity is calculated using the following formula:

[0027]

[0028] ΔP i =P i -P JZ

[0029] ΔC i =C i -C JZ

[0030]

[0031] Among them, C PC,i Let ΔP be the cost-performance coupling coefficient for the i-th individual. i Let ΔC be the change in the comprehensive performance index corresponding to the i-th individual. i Let P be the change in overall cost corresponding to i individuals. JZ C serves as the benchmark value for the overall performance index. JZ R is the benchmark value for comprehensive cost. i Let be the ratio of transportation cost to construction cost for the i-th individual.

[0032] Furthermore, the comprehensive cost and comprehensive performance index corresponding to the same individual are weighted and summed to generate the comprehensive evaluation index corresponding to that individual, based on the following formula:

[0033]

[0034] Among them, ZPzs i This represents the comprehensive evaluation index corresponding to the i-th individual.

[0035] In the formula, These are the weighting coefficients for the overall performance index. This is the weighting coefficient for the overall cost, and and The specific value is determined by the analytic hierarchy process (AHP).

[0036] Furthermore, the individuals in the initial population are iteratively optimized using a genetic algorithm to obtain the optimal individuals. The optimal combination of the corresponding splicing combinations is then extracted as the optimal economic size. The specific process is as follows:

[0037] The individuals in the initial population of the splicing combination are iteratively optimized. During the iterative optimization process, constraints are set on the geometric parameters of the splicing combination, namely, the maximum and minimum values ​​of length, width, and height are set respectively. Within the constraints of length, width, and height, the geometric parameters of the splicing combination are iteratively optimized. Specifically, the comprehensive evaluation index is sorted from largest to smallest, and individuals with the highest comprehensive evaluation index are selected as parents. Through crossover and mutation operations, the genes of the parent individuals are exchanged and mutated to generate new individuals. The comprehensive cost and comprehensive performance index of the newly generated individuals are obtained using a performance and cost prediction model, and their comprehensive evaluation index is calculated. The new individuals and their parents are used as a new population, and the selection, crossover, and mutation operations are repeated until a predetermined number of iterations are reached. The individual corresponding to the maximum comprehensive evaluation index is taken as the optimal combination of splicing combination geometric parameters, and the individual corresponding to the maximum comprehensive evaluation index is labeled as U. i1 =(l i1,j ,b i1,j ,h i1,j |j∈[1,λ i If the optimal economic dimension of the precast component is length l, then the optimal economic dimension of the precast component is length l. i1,j Width b i1,j and height h i1,j .

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] This invention is based on a splicing model, which randomly generates multiple splicing combinations of a predetermined plate foundation as individuals in the initial population. The individuals in the initial population are input into a finite element analysis model for performance simulation testing, and further processed to generate a comprehensive performance index and comprehensive cost. This changes the problem of the separation between performance and cost in traditional design, enabling designers to fully and intuitively understand the performance and cost of the foundation under different combinations of geometric parameters, thereby enabling targeted optimization in subsequent designs.

[0040] By introducing the ratio of transportation cost to construction cost to calculate the cost-performance coupling coefficient and setting a threshold for screening, a set of cost-performance dual-advantage splicing combinations is constructed. This process can quickly screen out the solution that takes into account both performance and cost advantages from a large number of parameter combinations. Compared with the existing technology that only optimizes around a single indicator, this method greatly improves the comprehensive benefits of the design solution, reduces the invalid attempts in subsequent design, and improves design efficiency.

[0041] By constructing a performance and cost prediction model and aiming to maximize the comprehensive evaluation index, combined with the iterative optimization of the initial population using a genetic algorithm, the design can predict the performance and cost of different splicing combinations based on historical data. The algorithm continuously searches for the optimal solution to obtain the optimal economic size of the splicing combination. Compared with the problem of the lack of in-depth analysis of geometric parameter combinations in existing technologies, this method can find the optimal geometric parameter combination more accurately, ensuring that the foundation achieves cost optimization while meeting performance requirements. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0043] Figure 2 This is a fitted curve of the load-bearing capacity index and the comprehensive performance index of the present invention;

[0044] Figure 3 This is a fitting curve of the settlement performance index and the comprehensive performance index of the present invention;

[0045] Figure 4 This is a fitting curve of the anti-overturning stability index and the comprehensive performance index of the present invention;

[0046] Figure 5 This is a fitting curve of the anti-slip stability index and the comprehensive performance index of the present invention;

[0047] Figure 6 This is a fitted curve of the change in the overall performance index of the present invention and the cost-performance coupling coefficient;

[0048] Figure 7 This is a fitted curve of the change in the comprehensive cost index and the cost-performance coupling coefficient of the present invention;

[0049] Figure 8 This is a fitted curve of the ratio of transportation cost to construction cost and the cost-performance coupling coefficient of the present invention;

[0050] Figure 9 This is a fitted curve diagram of the comprehensive performance index and comprehensive evaluation index of the present invention;

[0051] Figure 10 This is a fitted curve diagram of the overall cost and overall evaluation index of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0053] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0054] Example 1:

[0055] Please see Figures 1 to 10 The present invention provides a technical solution:

[0056] A modular design method for prefabricated slab foundations based on the optimal economic dimensions of prefabricated components, comprising the following steps:

[0057] S1. Under the constraints of production process, transportation equipment, and on-site hoisting capacity, based on the splicing model, multiple splicing combinations of the predetermined slab foundation are randomly generated as individuals of the initial population. The splicing combination is the component combination of the prefabricated predetermined slab foundation. The individuals of the initial population are input into the finite element analysis model for performance simulation test, and the bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to different individuals are obtained. The material cost, transportation cost and construction cost corresponding to different individuals are also obtained.

[0058] Based on the above embodiments, the splicing model is an optimization model. This optimization model is guided by the goal of minimizing cost and maximizing structural performance. By adjusting the parameters of the splicing combination, it seeks the optimal splicing scheme under the constraints of production process, transportation equipment, and on-site hoisting capacity. This optimization model uses one of the following algorithms to realize multiple splicing combinations of the predetermined slab foundation: genetic algorithm, particle swarm algorithm, and simulated annealing algorithm.

[0059] Based on the above embodiments, and under the constraints of production process, transportation equipment, and on-site hoisting capacity, various splicing combinations of predetermined slab foundations are randomly generated based on the splicing model. The specific process is as follows:

[0060] Based on the assembly and production process, transportation equipment, and on-site hoisting capabilities, the precast slab foundation is disassembled, and the length, width, and height of each precast component must meet the following conditions:

[0061] Production process constraints: l≤L max b≤B max h≤H max ;

[0062] Transportation constraint: l≤L tr b≤b tr h≤h tr ;

[0063] Lifting constraint: ρ×V≤Gg max ;

[0064] Where l, b, and h are the length, width, and height of the precast component, respectively, and L max B max H max These are the maximum length, maximum width, and maximum height of the mold, respectively, L tr b tr h tr These represent the vehicle's length, width, and height limits, respectively; V is the volume of the prefabricated component; and Gg... max This refers to the maximum lifting capacity of the hoisting equipment.

[0065] Among them, the maximum length L of the mold max Maximum width B max Maximum height H max The specifications of the production equipment, production process requirements, and common market demands are usually determined by the manufacturer. These can be obtained directly from the technical parameters of the production equipment or by consulting the manufacturer.

[0066] Vehicle length limit L tr Width limit b tr Height limit h tr The volume V of the assembly is determined based on traffic regulations and the specifications of common transport vehicles. Generally, relevant standards and specifications for highway transport vehicles can be referenced, or the technical parameter manuals of commonly used vehicles of transport companies can be consulted directly. The volume V of the assembly can be calculated using the corresponding geometric volume formula based on the design dimensions of the prefabricated foundation and the dimensions of the disassembled prefabricated components.

[0067] Maximum lifting capacity of hoisting equipment (Gg) max Information can be obtained from the product manual and technical specifications of the hoisting equipment, or by consulting the equipment supplier and relevant technical personnel. Based on the above embodiments, the geometric parameters of the prefabricated components include length, width, and height.

[0068] Based on the above embodiments, the individual populations of the initial spliced ​​combination are input into the finite element analysis model for performance simulation tests to obtain the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index corresponding to different spliced ​​combinations. The method is as follows:

[0069] Finite element model establishment

[0070] Based on the actual material used, accurately input its elastic modulus, Poisson's ratio, density, strength and other properties into the finite element analysis software;

[0071] Based on the geometric parameters of the initial population individuals in the splicing combination, a three-dimensional geometric model is accurately established in the finite element software. For splicing combinations with complex shapes, appropriate simplification may be required, but it is necessary to ensure that the mechanical performance simulation of key parts is not affected.

[0072] Considering the interaction between the prefabricated slab foundation and the superstructure, foundation, etc., the boundary conditions should be set reasonably. For example, the contact between the bottom of the foundation and the foundation should be constrained by appropriate methods (such as fixed constraints, elastic constraints, etc.), and the connection between the foundation and the superstructure should be set according to the actual connection method (such as hinged connection, rigid connection, etc.).

[0073] The actual load conditions are simulated by applying vertical loads generated by the self-weight of the tower, the weight of the conductors and insulator strings, horizontal loads caused by strong winds and unbalanced conductor tension, eccentric loads caused by conductor tension and eccentrically arranged ground wires, additional vertical and horizontal loads caused by icing, and sudden loads caused by conductor breakage.

[0074] Through finite element analysis, the stress distribution of spliced ​​joints and their joints under different load combinations is calculated. Based on the strength criteria of the materials, the bearing capacity of the foundation is determined. The bearing capacity index can be determined based on the ratio of the actual bearing capacity to the design bearing capacity.

[0075] The settlement of the foundation under vertical load is analyzed. The settlement of different parts of the foundation is obtained by finite element calculation. Indicators such as settlement difference are calculated. The settlement performance index can be determined based on the ratio of settlement to allowable settlement.

[0076] Calculate the overturning moment and overturning resistance moment of the foundation under horizontal and eccentric loads. The overturning stability index can be expressed as the ratio of the overturning resistance moment to the overturning moment of the foundation. This index reflects the foundation's ability to resist overturning.

[0077] The analysis of the anti-sliding force and horizontal load of the foundation under horizontal load is as follows: the anti-sliding force is generally provided by the friction between the bottom surface of the foundation and the foundation soil, etc. The anti-sliding stability index can be expressed as the ratio of the anti-sliding force to the horizontal load. This index reflects the foundation's ability to resist sliding.

[0078] Based on the above embodiments, the individuals of the initial population are constructed through the following steps:

[0079] Let the initial population be labeled U, and the initial population U = {U1, U2, ..., U} i,…,U μ}, U i Let U be the i-th individual in the initial population, where i is the index of the individual in the initial population and i∈[1,μ], and μ is the number of individuals in the initial population. i =(l i,j ,b i,j ,h i,j |j∈[1,λ i ]), where l i,j ,b i,j ,h i,j Let λ represent the length, width, and height of the j-th prefabricated component of the i-th individual, respectively, where j is the index of the prefabricated component, and λ is the index of the prefabricated component. i Let be the number of prefabricated components in the i-th individual.

[0080] Based on the above embodiments, the material costs, transportation costs, and construction costs corresponding to different individuals are obtained through the following specific process:

[0081] Formula for calculating material costs:

[0082] C α,i =C 1,i +C 2,i

[0083] C 1,i =V i ×P c

[0084] C 2,i =V i ×ρ×P s

[0085] Among them, C α,i Let C be the material cost corresponding to the i-th individual. 1,i Let C be the concrete cost corresponding to the i-th individual. 2,i V represents the cost of steel reinforcement for the i-th individual. i Let P be the volume corresponding to the i-th individual. c P represents the unit price of concrete. s ρ is the unit price of the steel reinforcement, and ρ is the density of the steel reinforcement.

[0086] Transportation costs are related to the volume of the base and the transportation distance. The formula for calculating transportation costs is as follows:

[0087] C β,i =V i ×P t ×S

[0088] Among them, C β,i Let P be the transportation cost corresponding to the i-th individual. t S represents the unit price for transportation, and S represents the transportation distance.

[0089] Formula for calculating construction costs:

[0090] C δ,i =V i ×P v

[0091] Among them, C δ,i Let P be the construction cost corresponding to the i-th individual. v This represents the average cost required for construction per unit volume.

[0092] The overall costs of concrete, steel reinforcement, transportation, and construction are calculated by first determining the cost of each precast component in its respective aspect, and then summing these costs together.

[0093] Among them, the unit price P of concrete c The unit price P of steel bars s Obtain information through market research, contacting local concrete suppliers, steel markets, or building material dealers to inquire about the current prices of different grades and types of concrete and steel bars;

[0094] Under normal circumstances, the density ρ of steel bars is approximately 7850 kg / m³. 3 ;

[0095] Transport unit price P t Consult with transportation companies to obtain the transportation price per unit volume of goods, based on factors such as the mode of transportation (e.g., road transport, rail transport), transportation distance, and type of goods.

[0096] The transportation distance S is determined based on the actual distance from the prefabricated component production site to the construction site. The accurate transportation distance can be obtained by measuring the distance between the two points using map software or by referring to the actual traffic route plan.

[0097] The average cost P required for construction per unit volume v Refer to industry standard quotas or relevant engineering cost index manuals to obtain approximate values.

[0098] Based on the above embodiments, the geometric parameters, bearing capacity index, settlement performance index, overturning stability index, sliding stability index, material cost, transportation cost, and construction cost of the spliced ​​assembly are standardized. The standardized data are then used for subsequent analysis and processing to ensure that all data are analyzed and processed under the same dimension, thus avoiding the problem of some data being overlooked due to different dimensions.

[0099] S2. Process the data of the bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to the same entity to generate the comprehensive performance index of the entity. Process the data of the material cost, transportation cost and construction cost corresponding to the same entity to generate the comprehensive cost of the entity.

[0100] Table 1 shows the changes in the overall performance index as a function of each performance index.

[0101]

[0102] Based on the above embodiments, according to the data in Table 1, it can be seen that the four individual performance indices—bearing capacity index, settlement performance index, overturning stability index, and sliding stability index—all show a significant positive correlation with the comprehensive performance index. As the bearing capacity index increases from 20 to 115, the settlement performance index from 15 to 54, the overturning stability index from 12 to 32, and the sliding stability index from 10 to 29, the comprehensive performance index also gradually increases from 13.3 to 66.6. That is, the larger the value of the individual performance index, the larger the value of the comprehensive performance index. For details, please refer to Table 1 below.

[0103] like Figure 2-5 As shown, each individual performance index (bearing capacity index, settlement performance index, overturning stability index, and sliding stability index) exhibits a clear linear positive correlation with the comprehensive performance index. That is, as the value of each individual performance index increases, the comprehensive performance index also increases linearly, as indicated by the black comprehensive performance index data points closely distributed near the red fitted curve. This suggests that the fitted curve effectively reflects the relationship between the two. An increase in an individual performance index leads to an approximately linear increase in the comprehensive performance index, indicating a linear relationship between the comprehensive performance index and the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index, respectively.

[0104] Based on the above embodiments, the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index corresponding to the same individual are processed to generate the comprehensive performance index of that individual, based on the following formula:

[0105] P i =ω1×P 1,i +ω2×P 2,i +ω3×P 3,i +ω4×P 4,i

[0106] Among them, P iLet P be the comprehensive performance index corresponding to the i-th individual. The comprehensive performance index is used to evaluate the comprehensive performance of the slab foundation by combining four indices: bearing capacity index, settlement performance index, overturning stability index, and sliding stability index. The larger the comprehensive performance index P is, the better the comprehensive performance of the slab foundation.

[0107] In the formula, P 1,i Let P be the carrying capacity index corresponding to the i-th individual. 2,i Let P be the settlement performance index corresponding to the i-th individual. 3,i Let P be the overturning stability index corresponding to the i-th individual. 4,i This represents the anti-slip stability index corresponding to the i-th individual;

[0108] Based on this, it should be noted that:

[0109] When the carrying capacity index P 1,i A larger value indicates that the slab foundation can safely and stably bear more external loads under vertical, horizontal, and eccentric loads, resulting in a lower probability of foundation structural failure and higher structural reliability and safety. Therefore, it significantly improves the overall performance of the slab foundation. The comprehensive performance index P... i When it is larger;

[0110] When the settlement performance index P of the slab foundation 2,i A larger value means less settlement under load, which better maintains the stability of the superstructure, reduces structural cracks and deformation caused by foundation settlement, ensures the normal use of the building, and effectively improves the overall performance of the slab foundation, resulting in a higher overall performance index P. i The larger;

[0111] When the overturning stability index P of the slab foundation 3,i A larger value indicates a stronger ability of the foundation to resist overturning due to horizontal loads, eccentric loads, etc. Under complex stress conditions, the foundation is less likely to overturn, ensuring the overall stability of the foundation and the superstructure. This results in a higher contribution to the overall performance, and consequently, a higher overall performance index P. i The larger;

[0112] When the anti-slip stability index P of the slab foundation 4,i A higher P value indicates that the friction between the foundation base and the subgrade soil can better resist horizontal thrust, significantly reducing the risk of foundation slippage and ensuring the foundation remains stable under horizontal loads. This effectively enhances the overall performance of the foundation, hence the higher comprehensive performance index P. i The larger.

[0113] Therefore, there is a positive correlation between the comprehensive performance index and the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index.

[0114] Furthermore, the effects of various bearing capacity indices, settlement performance indices, overturning stability indices, and sliding stability indices on the performance of slab foundations are independent yet cumulative. In other words, the change in each performance index affects the performance of the slab foundation independently of the other parameters, and their combined effect can be represented by simple addition.

[0115] In summary, the above weighted summation formula is used to express the functional relationship between the comprehensive performance index and the bearing capacity index, settlement performance index, overturning stability index, and sliding stability index.

[0116] In the formula, ω1 is the weighting coefficient of the bearing capacity index, ω2 is the weighting coefficient of the settlement performance index, ω3 is the weighting coefficient of the overturning stability index, and ω4 is the weighting coefficient of the sliding stability index.

[0117] Load-bearing capacity is the core function of slab foundations, directly related to whether the foundation can withstand the weight of the superstructure and various additional loads. If the load-bearing capacity is insufficient, the foundation may undergo excessive deformation or even failure, leading to the failure of the entire structure. It is the most critical factor in ensuring structural safety, and therefore it is given the highest weight ω1.

[0118] While settlement performance is also very important, it is slightly less important than bearing capacity. Excessive settlement can lead to problems such as cracks and tilting in the superstructure, affecting the building's functionality and aesthetics, and may even pose safety hazards. However, as long as the settlement is within a certain range, it can be mitigated or controlled through certain technical measures, so its weight ω2 is less than the weight ω1 of the bearing capacity index.

[0119] Overturning stability primarily addresses external forces that could cause the foundation to overturn, such as horizontal loads like wind and seismic forces, as well as eccentric loads. In most conventional buildings, these loads are not the primary, continuous loads, and excessive overturning moments are typically avoided in the design through reasonable structural layout and foundation selection. Therefore, its importance is relatively lower than that of bearing capacity and settlement performance, hence its weight ω3 is less than ω2.

[0120] Sliding stability mainly involves the ability of the foundation base to resist horizontal thrust due to friction between the foundation bottom and the subgrade soil. Under normal circumstances, the sliding stability of the foundation can be well guaranteed by properly designing the foundation bottom dimensions and subgrade treatment. Moreover, compared with bearing capacity, settlement performance, and overturning stability, the possibility of sliding failure is relatively low, and its impact on the overall performance of the foundation is relatively small. Therefore, its weight ω4 is the smallest.

[0121] Therefore, based on w1+w2+w3+w4=1, let 0 <w4<w3<w2<w1<1。

[0122] As one implementation method, the value range of w1 is 0.4-1, the value range of w2 is 0.3-0.4, the value range of w3 is 0.2-0.3, and the value range of w4 is 0-0.2. The specific values ​​are set by the technicians according to the actual situation, and are not limited here.

[0123] Based on the above embodiments, the material costs, transportation costs, and construction costs corresponding to the same entity are processed to generate the comprehensive cost of that entity, according to the following formula:

[0124] C i =C α,i +C β,i +C δ,i

[0125] Among them, C i Let C be the comprehensive cost corresponding to the i-th individual. α,i Let C be the material cost corresponding to the i-th individual. β,i Let C be the transportation cost corresponding to the i-th individual. δ,i Let be the construction cost corresponding to the i-th individual.

[0126] S3. Based on the ratio of transportation cost to construction cost corresponding to different splicing combinations, calculate the cost-performance coupling coefficient corresponding to different splicing combinations. Sort all splicing combinations in descending order according to the cost-performance coupling coefficient, and pre-set a threshold to retain splicing combinations with cost-performance coupling coefficient greater than the threshold, so as to complete the construction of a set of splicing combinations with both cost and performance advantages.

[0127] Table 2 shows the changes in the cost-performance coupling coefficient as a function of the comprehensive performance index, the comprehensive cost, and the ratio of transportation cost to construction cost.

[0128]

[0129] Based on the above embodiments, according to the data in Table 2, as the change in the comprehensive performance index increases from 10 to 80, the cost-performance coupling coefficient continuously increases from 0.0581 to 1.2. The two change in the same direction, so the change in the comprehensive performance index is positively correlated with the cost-performance coupling coefficient.

[0130] The change in overall cost decreased from 76 to 20, while the cost-performance coupling coefficient increased from 0.0581 to 1.2, showing an inverse relationship. Therefore, the change in overall cost is negatively correlated with the cost-performance coupling coefficient.

[0131] The ratio of transportation cost to construction cost decreased from 0.9 to 0.2, while the cost-performance coupling coefficient increased from 0.0581 to 1.2, showing an inverse relationship. Therefore, the ratio of transportation cost to construction cost is negatively correlated with the cost-performance coupling coefficient. For details, please refer to Table 2.

[0132] like Figure 6 As shown, the black data points represent the cost-performance coupling coefficient. As the change in the comprehensive performance index increases from left to right, the cost-performance coupling coefficient shows an upward trend. The red fitting curve is not a straight line, indicating that the two have a non-linear relationship. Moreover, as the change in the comprehensive performance index increases, the growth rate of the cost-performance coupling coefficient gradually accelerates, indicating that the influence of the change in the comprehensive performance index on the cost-performance coupling coefficient is constantly increasing.

[0133] like Figure 7 As shown, the black data points represent the cost-performance coupling coefficient. When the change in comprehensive cost decreases, the cost-performance coupling coefficient shows an upward trend. The red fitted curve is in the shape of a curve, indicating that the two have a non-linear relationship. When the change in comprehensive cost decreases, the growth rate of the cost-performance coupling coefficient is fast at first and then slows down, reflecting the complex non-linear relationship between the change in comprehensive cost and the cost-performance coupling coefficient.

[0134] like Figure 8 As shown, the black data points represent the cost-performance coupling coefficient. As the ratio of transportation cost to construction cost decreases, the cost-performance coupling coefficient (vertical axis) gradually increases. The red fitted curve is not a straight line, indicating that the relationship between the two is non-linear. As the ratio of transportation cost to construction cost decreases, the growth rate of the cost-performance coupling coefficient is first fast and then slows down, reflecting the non-linear functional relationship between the two.

[0135] Based on the above embodiments, and combining the ratio of transportation cost to construction cost for the same entity, the cost-performance coupling coefficient for that entity is calculated using the following formula:

[0136]

[0137] ΔP i =P i -P JZ

[0138] ΔC i =C i -C JZ

[0139]

[0140] Among them, C PC,iLet be the cost-performance coupling coefficient of the i-th individual. The cost-performance coupling coefficient is used to comprehensively evaluate the merits of the splicing combination by combining three indicators: the change in the comprehensive performance index, the change in the comprehensive cost, and the ratio of transportation cost to construction cost. The larger the cost-performance coupling coefficient, the better the performance of the splicing combination.

[0141] Based on this, it should be noted that:

[0142] The greater the change in the overall performance index, the more significant the improvement in overall performance of the splicing combination compared to the benchmark solution. When the overall performance is significantly improved, it means that the performance improvement per unit cost is greater when the cost change is relatively stable. That is, the splicing combination can achieve greater performance improvement with relatively less cost investment, so its performance is better, thus making the cost-performance coupling coefficient larger.

[0143] The greater the change in overall cost, the more the cost of the splicing combination increases compared to the baseline solution. With a certain improvement in overall performance, the greater the increase in cost, the greater the cost required to obtain a unit performance improvement. This will lead to a decrease in the overall cost-effectiveness, and the performance of the splicing combination will be relatively worse, thus making the cost-performance coupling coefficient smaller.

[0144] The higher the ratio of transportation cost to construction cost, the higher the proportion of transportation cost in the total cost relative to construction cost. When transportation cost is too high, various restrictions during transportation may lead to increased construction difficulty, extended construction period, or the need for additional transportation measures to ensure the safe transportation of components. These will all have a negative impact on the overall splicing performance. Even if the comprehensive performance index is improved to a certain extent, the actual effective performance improvement is weakened due to the many adverse factors brought about by the high transportation cost, under the same comprehensive cost change. Therefore, the worse the splicing performance, the smaller the cost-performance coupling coefficient.

[0145] Therefore, there is a positive correlation between the cost-performance coupling coefficient and the change in the comprehensive performance index, and a negative correlation between the cost-performance coupling coefficient and the change in comprehensive cost, and between the ratio of transportation cost to construction cost.

[0146] Therefore, the above formula is used to express the functional relationship between the cost-performance coupling coefficient and the change in the comprehensive performance index, the change in comprehensive cost, and the ratio of transportation cost to construction cost.

[0147] In the formula, ΔP i Let ΔC be the change in the comprehensive performance index corresponding to the i-th individual. i Let P be the change in overall cost corresponding to i individuals. JZ C serves as the benchmark value for the overall performance index. JZR is the benchmark value for comprehensive cost. i Let be the ratio of transportation cost to construction cost for the i-th individual;

[0148] Among them, the benchmark values ​​of the comprehensive performance index and the comprehensive cost are calculated based on the design specifications of slab foundations, mechanical principles and related engineering theories, and are used as benchmark values.

[0149] The cost-performance coupling coefficient integrates three core indicators—the change in comprehensive performance index, the change in comprehensive cost, and the ratio of transportation cost to construction cost—into a single coefficient to comprehensively score splicing schemes, achieving balanced optimization of multiple objectives. By using the ratio of transportation and construction costs, it automatically identifies cost bottlenecks in the scheme (such as excessively high transportation costs) and guides targeted optimization. It can also quickly screen the optimal scheme.

[0150] S4. Construct a performance and cost prediction model. Based on the set of individuals with both cost and performance advantages, input the individuals of the initial population into the performance and cost prediction model to obtain the comprehensive performance index and comprehensive cost corresponding to different individuals.

[0151] Based on the above embodiments, the performance and cost prediction model is constructed using a deep learning network based on a multilayer perceptron. The deep neural network of the multilayer perceptron includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer. The first hidden layer, the second hidden layer, and the third hidden layer each have at least two neurons and all use ReLU (corrected linear unit) as the activation function.

[0152] In performance and cost prediction models, the input features of the deep learning network of the multilayer perceptron include individuals in the initial population.

[0153] The structure of a deep learning network with a multilayer perceptron is as follows:

[0154] Input layer: used to receive one set of features;

[0155] The first hidden layer has 128 neurons and uses ReLU as the activation function.

[0156] The second hidden layer has 64 neurons and also uses the ReLU activation function;

[0157] The third hidden layer has 32 neurons and uses the ReLU activation function;

[0158] Output layer: It has 7 neurons and is used to output the comprehensive performance index and comprehensive cost corresponding to different individuals.

[0159] The process of training the performance and cost prediction model is as follows:

[0160] The initial population of individuals is used as input, and the comprehensive performance index and comprehensive cost corresponding to different individuals are used as labels for training. The mean squared error is used as the loss function. When the mean squared error is in the range of [0, 0.01], the training of the performance and cost prediction model is completed.

[0161] S5. The comprehensive cost and comprehensive performance index corresponding to the same individual are weighted and summed to generate the comprehensive evaluation index corresponding to that individual. Taking the maximization of the comprehensive evaluation index corresponding to that individual as the objective function, under the constraint of the geometric parameters of the splicing combination, the individuals in the initial population are iteratively optimized through a genetic algorithm to obtain the optimal individual. Based on the optimal individual, the optimal combination of splicing combination is extracted and used as the optimal economic size of the prefabricated component.

[0162] Table 3 shows the changes in the comprehensive evaluation index as a function of the comprehensive cost and comprehensive performance index.

[0163] <![CDATA[Comprehensive Energy Index > Comprehensive cost Comprehensive evaluation index 20 115 0 25 110 1 30 105 2 35 100 3 40 95 4 45 90 5 50 85 6 55 80 7 60 75 8 65 70 9 70 65 10 75 60 11 80 55 12 85 50 13 90 45 14 95 40 15 100 35 16 105 30 17

[0164] Based on the above embodiments, as the overall performance index gradually increases from 20 to 105, the overall evaluation index correspondingly increases from 0 to 17, showing a positive correlation. Therefore, the overall performance index and the overall evaluation index are positively correlated. When the overall cost gradually decreases from 115 to 30, the overall evaluation index increases from 0 to 17, showing an inverse trend. Therefore, the overall performance index and the overall cost are negatively correlated. For details, please refer to Table 3.

[0165] like Figure 9 As shown, the black comprehensive evaluation index data points are closely distributed on the red fitted curve, presenting a straight line shape. This indicates that there is a linear relationship between the comprehensive evaluation index and the comprehensive performance index, and that the correlation is positive linear. That is, as the comprehensive performance index increases, the comprehensive evaluation index increases linearly by a fixed proportion, which is reflected in the graph as a straight upward trend.

[0166] like Figure 10 As shown, the black data points are distributed in a straight line along the red fitted curve, reflecting the linear relationship between the comprehensive evaluation index and the comprehensive cost. It is a negative linear correlation. As the comprehensive cost increases, the comprehensive evaluation index decreases linearly, which is shown as a straight downward trend in the figure.

[0167] Based on the above embodiments, the comprehensive cost and comprehensive performance index corresponding to the same individual are weighted and summed to generate the comprehensive evaluation index corresponding to that individual, according to the following formula:

[0168]

[0169] Among them, ZPzs iThe comprehensive evaluation index is the comprehensive evaluation index corresponding to the i-th individual. The comprehensive evaluation index is used to comprehensively evaluate the performance and economic benefits of the slab foundation by combining the two indicators of comprehensive cost and comprehensive performance index. The larger the comprehensive evaluation index, the better the performance and economic benefits of the slab foundation.

[0170] In the formula, These are the weighting coefficients for the overall performance index. This is the weighting coefficient for the overall cost, and and The specific value is determined by the Analytic Hierarchy Process (AHP), and the specific logic is as follows:

[0171] The comprehensive performance index and comprehensive cost are labeled, and the relative importance between each pair is determined using the nine-scale method. A judgment matrix is ​​constructed, where the index of the comprehensive performance index is labeled as 1 and the index of the comprehensive cost is labeled as 2. The constructed judgment matrix [q] uτ ] 2×2 for:

[0172]

[0173] Where u represents the index of the comprehensive performance index, v represents the index of the comprehensive cost, and u∈[1,2], τ∈[1,2], indicating the importance of the comprehensive performance index with index u to the comprehensive cost index relative to the comprehensive cost index with index τ, and q uτ The specific value was determined by relevant experts using a 1-9 scoring method. uv =9 indicates that the overall performance index of index u is extremely important to the overall evaluation index compared to the overall cost of index τ. uτ =1 indicates that the overall performance index of index u is extremely unimportant to the overall evaluation index compared to the overall cost of index τ;

[0174] Divide each element value in the judgment matrix by the sum of its columns to obtain a normalized judgment matrix. Calculate the mean of the element values ​​in each row of the normalized judgment matrix, and use the mean of the element values ​​in the first row as the scaling factor for the comprehensive performance index and the mean of the element values ​​in the second row as the scaling factor for the comprehensive cost. With the constraint that the sum of the scaled values ​​equals 1, scale the comprehensive performance index and comprehensive cost proportionally, and use the scaled values ​​as the weights of the corresponding comprehensive performance index and comprehensive cost.

[0175] Based on this, it should be noted that:

[0176] When the comprehensive performance index P iA higher ZPzs indicates superior performance in load-bearing capacity, settlement control, overturning stability, and sliding stability of the slab foundation. This means the foundation can better withstand the loads of the superstructure, reducing structural safety hazards and maintenance costs caused by excessive settlement, overturning, or sliding, while extending the building's lifespan and reducing total life-cycle costs. From an economic perspective, good performance can avoid secondary construction and reinforcement costs caused by insufficient foundation performance, as well as functional losses due to structural damage, thus improving the overall evaluation index ZPzs. i Increase;

[0177] When the comprehensive cost C i A smaller foundation size means less resources are needed in the design, material procurement, transportation, and construction of the slab foundation. While maintaining the overall performance index of the foundation, lower costs directly improve the project's economic benefits, demonstrating efficient resource utilization. For example, by optimizing material selection and rationally planning the construction process to reduce costs while maintaining high foundation performance, the performance value per unit cost is higher, thus increasing the overall evaluation index ZPzs. i Increase.

[0178] Therefore, there is a positive correlation between the comprehensive evaluation index and the comprehensive performance index, and a negative correlation between the comprehensive evaluation index and the comprehensive cost.

[0179] Furthermore, the comprehensive performance index and comprehensive cost are core indicators that comprehensively evaluate the performance and economic benefits of slab foundations from two different perspectives: performance and cost. In actual engineering, performance improvement and cost control are often mutually restrictive: higher load-bearing capacity and stronger stability usually require the use of higher-quality materials and more complex processes, leading to increased costs; while excessive cost reduction may sacrifice performance, affecting the safety and durability of the foundation.

[0180] Simply adding the two together cannot reflect this contradictory relationship; the weighted summation formula uses weighting coefficients... and It can effectively balance performance and cost. For example, for critical buildings with extremely high security requirements, it can increase... To highlight the importance of performance, it is permissible to appropriately increase costs in exchange for higher performance guarantees; for general projects that are cost-sensitive, costs can be increased. This will strengthen cost control and maximize economic benefits while meeting basic performance requirements.

[0181] Therefore, using a weighted summation formula to express the functional relationship between the comprehensive evaluation index, the comprehensive performance index, and the comprehensive cost can more scientifically and comprehensively reflect the balance between performance and economic benefits of slab foundations.

[0182] Based on the above embodiments, the individuals in the initial population are iteratively optimized using a genetic algorithm to obtain the optimal individuals. The optimal combination of the corresponding splicing combinations is then extracted as the optimal economic size. The specific process is as follows:

[0183] The individuals in the initial population of the spliced ​​combination are iteratively optimized. During the iterative optimization process, constraints are set on the geometric parameters of the spliced ​​combination, namely, the maximum and minimum values ​​of length, width, and height are set respectively. Within the constraints of length, width, and height, the geometric parameters of the spliced ​​combination are iteratively optimized. Specifically, the comprehensive evaluation index is sorted from largest to smallest, and individuals with the highest comprehensive evaluation index are selected as parents. The top-ranked individuals are those with a comprehensive evaluation index ZPzs. i The first 50% of individuals are crossovered and mutated, exchanging and combining genes from their parents to generate new individuals. A performance and cost prediction model is used to obtain the comprehensive cost and performance index of these new individuals, and their comprehensive evaluation index is calculated. These new individuals and their parents are then used as a new population, and the selection, crossover, and mutation operations are repeated until a predetermined number of iterations are reached. The individual corresponding to the highest comprehensive evaluation index is then selected as the optimal combination of splicing and combining geometric parameters, and labeled as U. i1 =(l i1,j ,b i1,j ,h i1,j |j∈[1,λ i If the optimal economic dimension of the precast component is length l, then the optimal economic dimension of the precast component is length l. i1,j Width b i1,j and height h i1,j .

[0184] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0185] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by software, electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0186] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0187] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for modular design of prefabricated slab foundations based on the optimal economic dimensions of prefabricated components, characterized in that: The specific steps include: Under the set constraints, based on the splicing model, multiple splicing combinations of a predetermined slab foundation are randomly generated as individuals in the initial population. The individuals in the initial population are input into the finite element analysis model for performance simulation testing. The bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to different individuals are obtained, as well as the material cost, transportation cost and construction cost corresponding to different individuals. The data of the bearing capacity index, settlement performance index, overturning stability index and sliding stability index corresponding to the same entity are processed to generate the comprehensive performance index of the entity. The data of the material cost, transportation cost and construction cost corresponding to the same entity are processed to generate the comprehensive cost of the entity. By combining the ratio of transportation cost to construction cost for the same individual, the cost-performance coupling coefficient for that individual is calculated. All individuals are sorted in descending order based on the cost-performance coupling coefficient, and a threshold is pre-set to retain individuals with a cost-performance coupling coefficient greater than the threshold, so as to complete the construction of a set of individuals with both cost and performance advantages. A performance and cost prediction model is constructed. Based on a set of individuals with both cost and performance advantages, the individuals of the initial population are input into the performance and cost prediction model to obtain the comprehensive performance index and comprehensive cost corresponding to different individuals. The comprehensive cost and comprehensive performance index corresponding to the same individual are weighted and summed to generate the comprehensive evaluation index corresponding to that individual. Taking the maximization of the comprehensive evaluation index corresponding to that individual as the objective function, the individuals in the initial population are iteratively optimized through a genetic algorithm to obtain the optimal individual. The optimal combination of the corresponding splicing combination is extracted as the optimal economic size.

2. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 1, characterized in that: The geometric parameters of prefabricated components include length, width, and height.

3. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 2, characterized in that: The specific steps for constructing the initial population are as follows: Let the initial population be labeled U, and the initial population U = {U1, U2, ..., U} i ,…,U μ }, U i Let U be the i-th individual in the initial population, where i is the index of the individual in the initial population and i∈[1,μ], and μ is the number of individuals in the initial population. i =(l i,j ,b i,j ,h i,j |j∈[1,λ i ]), where l i,j ,b i,j ,h i,j Let λ represent the length, width, and height of the j-th prefabricated component of the i-th individual, respectively, where j is the index of the prefabricated component, and λ is the index of the prefabricated component. i Let be the number of prefabricated components in the i-th individual.

4. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 1, characterized in that: The bearing capacity index, settlement performance index, overturning stability index, and sliding stability index corresponding to the same individual are processed to generate the comprehensive performance index of that individual, based on the following formula: P i =ω1×P 1,i +ω2×P 2,i +ω3×P 3,i +ω4×P 4,i Among them, P i Let i be the comprehensive performance index corresponding to the i-th individual, where i is the index of the individual in the initial population; In the formula, P 1,i Let P be the carrying capacity index corresponding to the i-th individual. 2,i Let P be the settlement performance index corresponding to the i-th individual. 3,i Let P be the overturning stability index corresponding to the i-th individual. 4,i This represents the anti-slip stability index corresponding to the i-th individual; In the formula, ω1 is the weighting coefficient of the bearing capacity index, ω2 is the weighting coefficient of the settlement performance index, ω3 is the weighting coefficient of the overturning stability index, and ω4 is the weighting coefficient of the sliding stability index. Based on w1+w2+w3+w4=1, let 0 <w4<w3<w2<w1<1。 5. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 4, characterized in that: The material costs, transportation costs, and construction costs corresponding to the same entity are processed to generate the comprehensive cost of that entity, based on the following formula: C i =C α,i +C β,i +C δ,i Among them, C i Let C be the comprehensive cost corresponding to the i-th individual. α,i Let C be the material cost corresponding to the i-th individual. β,i Let C be the transportation cost corresponding to the i-th individual. δ,i Let be the construction cost corresponding to the i-th individual.

6. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 5, characterized in that: The cost-performance coupling coefficient for an individual is calculated by combining the ratio of transportation cost to construction cost, using the following formula: ΔP i =P i -P JZ ΔC i =C i -C JZ Among them, C PC,i Let ΔP be the cost-performance coupling coefficient for the i-th individual. i Let ΔC be the change in the comprehensive performance index corresponding to the i-th individual. i Let P be the change in overall cost corresponding to i individuals. JZ C serves as the benchmark value for the overall performance index. JZ R is the benchmark value for comprehensive cost. i Let be the ratio of transportation cost to construction cost for the i-th individual.

7. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 6, characterized in that: The comprehensive evaluation index for an individual is generated by weighted summing of its comprehensive cost and comprehensive performance index, based on the following formula: Among them, ZPzs i This is the comprehensive evaluation index corresponding to the i-th individual; In the formula, These are the weighting coefficients for the overall performance index. This is the weighting coefficient for the overall cost, and and The specific value is determined by the analytic hierarchy process (AHP).

8. The prefabricated slab foundation modular design method based on the optimal economic dimensions of prefabricated components according to claim 2, characterized in that: The initial population is iteratively optimized using a genetic algorithm to obtain the optimal individuals. The optimal combination of the corresponding splicing combinations is then extracted as the optimal economic size. The specific process is as follows: The individuals in the initial population of the splicing combination are iteratively optimized. During the iterative optimization process, constraints are set on the geometric parameters of the splicing combination, namely, the maximum and minimum values ​​of length, width, and height are set respectively. Within the constraints of length, width, and height, the geometric parameters of the splicing combination are iteratively optimized. Specifically, the comprehensive evaluation index is sorted from largest to smallest, and individuals with the highest comprehensive evaluation index are selected as parents. Through crossover and mutation operations, the genes of the parent individuals are exchanged and mutated to generate new individuals. The comprehensive cost and comprehensive performance index of the newly generated individuals are obtained using a performance and cost prediction model, and their comprehensive evaluation index is calculated. The new individuals and their parents are used as a new population, and the selection, crossover, and mutation operations are repeated until a predetermined number of iterations are reached. The individual corresponding to the maximum comprehensive evaluation index is taken as the optimal combination of splicing combination geometric parameters, and the individual corresponding to the maximum comprehensive evaluation index is labeled as U. i1 =(l i1,j ,b i1,j ,h i1,j |j∈[1,λ i If the optimal economic dimension of the precast component is length l, then the optimal economic dimension of the precast component is length l. i1,j Width b i1,j and height h i1,j .

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