A precast beam design optimization method and system based on a hybrid element heuristic algorithm

Abstract

The present application relates to the technical field of precast beam design optimization, and particularly relates to a precast beam design optimization method and system based on a hybrid element heuristic algorithm. The method comprises the following steps: processing original design parameter data through knowledge embedding to obtain geometric material comprehensive features; obtaining constraint compliance features by encoding and standardizing constraints, and obtaining construction schedule influence features by analyzing construction schedule data; based on a multi-criteria decision empowerment strategy, using the geometric material comprehensive features, the constraint compliance features and the construction schedule influence features, comprehensive priority features are obtained; using weighted knowledge fusion, manufacturability features and case analogy features are obtained to obtain manufacturing case heuristic features; combining performance approximation model features, the comprehensive priority features and the manufacturing case heuristic features, precast beam multi-objective design optimization is completed according to a hybrid element heuristic framework. The present application realizes the global optimization of the precast beam design scheme through phased feature extraction and multi-dimensional feature fusion.

Description

Technical Field

[0001] This invention relates to the field of precast beam design optimization technology, specifically to a precast beam design optimization method and system based on a hybrid element heuristic algorithm. Background Technology

[0002] As a core component of prefabricated bridge engineering, the design quality of precast beams directly determines the safety, economy, manufacturability, and construction efficiency of the bridge structure. Currently, precast beam design largely adopts the traditional approach of empirical design plus finite element simulation verification, supplemented by a single optimization algorithm for local parameter adjustments, which has the following technical shortcomings: Design disconnected from multiple elements: Traditional design focuses only on geometric parameters and mechanical properties, without systematically integrating core elements such as manufacturing processes, design specifications, historical cases, and the entire life cycle of the project into the optimization process. This can easily lead to problems such as optimal design but inability to manufacture, insufficient compliance, and project delays, resulting in repeated iterations of design solutions and low efficiency.

[0003] Constraints and features are difficult to quantify: Design specifications are mostly textual qualitative descriptions, and manufacturing process bottlenecks, schedule influencing factors, etc. are difficult to transform into quantitative features that can be identified by algorithms. They rely on manual verification and experience judgment, which are highly subjective and cannot be deeply coupled with optimization algorithms.

[0004] Poor adaptability of optimization algorithms: Most existing optimization algorithms are direct applications of general metaheuristic algorithms without combining the stress mechanism and production characteristics of precast beams to design a dedicated framework. They lack domain knowledge guidance and suffer from problems such as strong search blindness, slow convergence speed, and easy getting trapped in local optima. At the same time, finite element simulation is time-consuming and cannot be directly embedded into the optimization iteration process, further restricting optimization efficiency.

[0005] Insufficient ability to balance multiple objectives: The design of precast beams involves multiple objectives such as safety, cost, schedule, and manufacturing feasibility. Existing methods often use fixed weights to transform single objectives, which cannot achieve dynamic collaborative balance of multiple objectives and is difficult to adapt to the different needs of different engineering scenarios.

[0006] To address the aforementioned issues, there is an urgent need for an efficient optimization method that can integrate all elements and characteristics, quantify multi-dimensional constraints, and adapt to the engineering characteristics of precast beams, so as to achieve a balance between the global optimization of precast beam design schemes and their feasibility in engineering implementation. Summary of the Invention

[0007] To address the shortcomings of existing methods and the needs of practical applications, and in order to solve the aforementioned problems, this invention provides a precast beam design optimization method based on a hybrid meta-heuristic algorithm, comprising the following steps: By processing the original design parameter data through knowledge embedding, comprehensive geometric material characteristics are obtained; constraint compliance characteristics are obtained by encoding standard constraints, and construction schedule impact characteristics are obtained by analyzing construction progress data; based on a multi-criteria decision-making weighting strategy, comprehensive priority characteristics are obtained by utilizing the comprehensive geometric material characteristics, the constraint compliance characteristics, and the construction schedule impact characteristics; manufacturing case heuristic characteristics are obtained by using weighted knowledge fusion of manufacturability characteristics and case analogy characteristics; and by combining performance approximation model characteristics, the comprehensive priority characteristics, and the manufacturing case heuristic characteristics, multi-objective design optimization of precast beams is completed according to a hybrid element heuristic framework.

[0008] Optionally, the step of processing the original design parameter data through knowledge embedding to obtain comprehensive geometric material characteristics includes the following steps: accurately classifying the original parameters according to engineering functional attributes to obtain a structured parameter set after classification, which includes parameter category, value range, data source and integrity identifier; constructing precast beam engineering knowledge rules, embedding the precast beam engineering knowledge rules into the structured parameter set to obtain comprehensive geometric material characteristics.

[0009] Optionally, the coding specification constraint obtains constraint compliance characteristics by including the following steps: The structured parsing of the specification clauses yields a structured specification constraint set; based on the element types of the structured specification constraint set, constraint indicators are quantified and encoded, and constraint compliance features are extracted using the encoded constraint indicators.

[0010] Optionally, the analysis of construction progress data to obtain characteristics affecting the construction period includes the following steps: The entire life cycle time nodes of the precast beam are broken down to obtain a schedule node decomposition table; based on the schedule node decomposition table, time-influencing factors are quantified to obtain a schedule influencing factor quantification matrix; the total life cycle duration is calculated by combining the schedule node decomposition table and the schedule influencing factor quantification matrix, and schedule influence characteristics are generated.

[0011] Optionally, the multi-criteria decision-making weighting strategy, which utilizes the comprehensive characteristics of geometric materials, the constraint compliance characteristics, and the schedule impact characteristics to obtain comprehensive priority characteristics, includes the following steps: A multi-criteria evaluation system is constructed to obtain a set of multi-criteria evaluation indicators; a hybrid weighting model is established by combining subjective weighting using the analytic hierarchy process (AHP) and objective weighting using the entropy weighting method; based on the comprehensive characteristics of the geometric materials, the constraint compliance characteristics, and the project duration impact characteristics, the comprehensive priority characteristics are obtained using the multi-criteria evaluation indicator set and the hybrid weighting model.

[0012] Optionally, the step of using weighted knowledge fusion to obtain manufacturing case-inspired features by fusing manufacturability features and case analogy features includes the following steps: Based on the difficulty of precast beam production and the similarity of cases, feature weights are assigned to obtain a dynamic weight set; based on the location of manufacturability bottlenecks and the matching of advantageous solutions for similar cases, the dynamic weight set is used to obtain a manufacturing case feature set; heuristic rules are extracted from the manufacturing case feature set, and heuristic feature vectors for manufacturing cases are obtained through the heuristic rules.

[0013] Optionally, extracting the manufacturability features includes the following steps: Identify bottlenecks in the production process and obtain a set of bottleneck constraints; use the set of bottleneck constraints as the core basis to modify the process adaptability parameters and obtain a set of geometric and material features after process modification; extract the manufacturability features from the set of geometric and material features after process modification.

[0014] Optionally, extracting the case analogy features includes the following steps: A multi-dimensional similarity measurement model is constructed based on the current design requirements of precast beams to obtain a case similarity score matrix; a set of similar cases is selected based on the case similarity score matrix, and case analogy features are generated using the set of similar cases.

[0015] Optionally, the multi-objective design optimization of precast beams, based on the hybrid meta-heuristic framework, combines the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, and includes the following steps: A hybrid heuristic framework is constructed; a multi-objective optimization objective function is established by combining the performance approximation model characteristics, the comprehensive priority characteristics, and the manufacturing case heuristic characteristics; and the multi-objective design optimization of the precast beam is completed based on the hybrid heuristic framework and the multi-objective optimization objective function.

[0016] This invention relates to a multi-objective design optimization of precast beams based on a hybrid heuristic framework. It obtains comprehensive geometric and material characteristics by processing original parameters through knowledge embedding, encodes constraints, and analyzes construction progress to obtain constraint compliance and schedule impact characteristics. A comprehensive priority feature is generated through a hybrid weighting method combining the analytic hierarchy process (AHP) and entropy weighting. Weights are dynamically allocated based on production difficulty and case similarity, and heuristic rules are extracted by integrating manufacturability and case analogy features to form manufacturing case heuristic features. Finally, by linking performance approximation model features, a customized optimization framework and multi-objective function are constructed to achieve a globally optimal solution. This effectively solves problems such as the disconnect between multiple design elements, difficulty in constraint quantification, and poor algorithm adaptability in traditional design. It achieves multi-objective collaborative optimization, improves optimization efficiency and solution feasibility, significantly reduces production costs, and shortens the construction period, providing core technical support for cost reduction and efficiency improvement in prefabricated bridge engineering.

[0017] Secondly, to efficiently execute the precast beam design optimization method based on a hybrid element heuristic algorithm provided by this invention, this invention also provides a precast beam design optimization system based on a hybrid element heuristic algorithm, comprising: an input device, an output device, a processor, and a memory, wherein the input device, output device, processor, and memory are interconnected, and the memory stores program instructions used for the precast beam design optimization method based on the hybrid element heuristic algorithm. The precast beam design optimization system based on a hybrid element heuristic algorithm of this invention has a compact structure and stable performance, and can stably execute the precast beam design optimization method based on a hybrid element heuristic algorithm provided by this invention, further enhancing the overall applicability and practical application capability of this invention. Attached Figure Description

[0018] Figure 1 A flowchart illustrating a precast beam design optimization method based on a hybrid meta-heuristic algorithm, provided in this embodiment of the invention; Figure 2 This is a framework diagram of a precast beam design optimization system based on a hybrid meta-heuristic algorithm, provided for an embodiment of the present invention. Detailed Implementation

[0019] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0020] Throughout this specification, references to an embodiment, example, or illustration mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, phrases appearing in various places throughout the specification, such as "in one embodiment," "in an embodiment," "an example," or "an illustration," do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in any suitable combination and / or sub-combination in one or more embodiments or examples. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0021] Please see Figure 1 To address the aforementioned problems, this invention provides a precast beam design optimization method based on a hybrid meta-heuristic algorithm, such as... Figure 1 As shown, in one embodiment, the method includes the following steps: S1. The original design parameter data is processed through knowledge embedding to obtain the comprehensive characteristics of geometric materials.

[0022] In this embodiment, the process of processing the original design parameter data through knowledge embedding to obtain the comprehensive geometric material characteristics includes the following steps: S11. Accurately classify the original parameters according to the engineering function attributes to obtain a structured parameter set after classification, which includes parameter category, value range, data source and integrity identifier.

[0023] Original design parameter data, including precast beam geometric parameters (span, cross-sectional dimensions, web thickness, flange width, etc.), material parameters (concrete strength grade, steel reinforcement grade, prestressed tendon specifications, etc.), and design target parameters (bearing capacity, deflection limit, crack resistance grade, etc.).

[0024] Specifically, the original parameters are precisely classified according to their engineering functional attributes: geometric features, material features, and target features. Geometric features focus on the core structural parameters of precast beams, including span, cross-sectional shape and size, web thickness gradient, flange width and thickness, and reinforcement spacing. Material features cover the main and auxiliary material parameters, including concrete strength grade, aggregate type, steel grade and diameter, prestressed tendon specifications and tensioning method, and admixture type and dosage. Target features clarify the core design requirements, including bearing capacity grade, deflection control limit, crack resistance grade, and service life.

[0025] Data cleaning was performed based on classification: Abnormal data judgment rules were constructed using basic mechanical principles of precast beam design to eliminate invalid parameter combinations, such as those involving low-strength concrete matching high load-bearing capacity targets, or combinations where mismatched cross-sectional dimensions and spans resulted in severely insufficient bending resistance. For missing parameters, an empirical correlation table of span-cross-sectional dimensions-web thickness was established, and default values ​​were supplemented using standard design criteria for the project's region. For example, for a simply supported precast beam with a span of 16m, the default web thickness was supplemented to 160mm. Simultaneously, empirical supplementation attributes were labeled for the supplemented parameters to distinguish them from the original data. Finally, a structured parameter set, including parameter category, value range, data source, and integrity identifier, was obtained, providing a standardized data foundation for subsequent knowledge rule matching.

[0026] S12. Construct precast beam engineering knowledge rules, embed the precast beam engineering knowledge rules into the structured parameter set, and obtain comprehensive geometric material characteristics.

[0027] A three-dimensional approach—literature review, engineering survey, and expert consultation—is used to organize the core engineering knowledge rules for precast beams, ensuring the scientific validity and practicality of the rules. The specific classification and construction process is as follows: Force correlation rule construction: Combining common stress forms of precast beams (simply supported, continuous, cantilever), we sorted out the parameter matching requirements under different stress scenarios. Through research on typical precast beam engineering cases in China, we extracted quantitative rules such as the web thickness should not be less than 180mm when the span is >20m, the web thickness should be increased by 20-30mm for every 5m increase in span, and the arrangement of prestressing tendons should avoid the area of ​​maximum shear force (within 1 / 4 of the span from the support). At the same time, we clarified the span range and structural type to which the rules apply.

[0028] Material matching rule construction: Based on the "Code for Design of Concrete Structures" and industry material application guidelines, the compatibility relationship between concrete of different strength grades and steel bars and prestressing tendons is sorted out, forming rules such as C50 concrete is compatible with HRB400 grade steel bars, C60 and above high-strength concrete is compatible with HRB500 grade steel bars, the tension control stress of prestressing tendons is positively correlated with concrete strength, and tensioning is not allowed when the concrete strength has not reached 80% of the design value. Material substitution schemes for different environments are added (such as corrosion-resistant steel bars being preferred for matching with marine concrete in marine environments).

[0029] Durability rules are established by classifying the service environment type (marine, inland, cold and frozen regions) and sorting out the protection parameter requirements for different environments. For example, the concrete protective layer thickness should not be less than 50mm in marine environments, the concrete freeze-thaw resistance grade should not be lower than F200 in cold and frozen regions, and an anti-corrosion coating should be added in chloride salt environments with a coating thickness of not less than 1.5mm.

[0030] All rules, after being reviewed and revised by senior engineers in the field of precast beam design, form an engineering knowledge rule base containing rule IDs, applicable scenarios, constraints, quantification thresholds, and priorities, facilitating quick matching and calling during subsequent parameter filtering and correction.

[0031] Furthermore, knowledge embedding is achieved through rule matching and parameter correction: First, the engineering knowledge rule base is matched parameter by parameter with the categorized structured parameter set. Each parameter combination is checked for compliance. If there is a violation of the core rules (such as a web thickness of only 150mm when the span is 25m), the parameter correction mechanism is automatically triggered. The adjustment is prioritized according to the rule quantification threshold (correcting the web thickness to 180mm). If there is a conflict with other parameters after the adjustment (such as the web thickness causing the component weight to exceed the standard), a conflict prompt is output and the correction trajectory is retained. For parameter combinations that meet the rules, they directly enter the feature fusion stage.

[0032] In the feature fusion stage, a feature mapping matrix is ​​constructed based on the mechanical transmission mechanism of precast beams, and the correlation logic between geometric parameters and material parameters is clarified: the moment of inertia of the section (geometric parameter) and the elastic modulus of concrete (material parameter) are associated with the bending stiffness feature through the bending stiffness calculation logic; the cross-sectional area of ​​the web (geometric parameter) and the reinforcement ratio of steel bars (material parameter) are associated with the shear bearing capacity feature; and the material usage (derived from geometric parameters) and the unit price of materials (associated with material parameters) are associated with the material cost feature.

[0033] During the feature mapping process, each associated feature is standardized (the feature value is mapped to the [0,1] interval) to eliminate the dimensional differences of parameters of different dimensions, and finally generate a geometric material comprehensive feature vector containing sub-features such as bending stiffness feature, shear bearing capacity feature, material cost feature, and durability adaptation feature.

[0034] S2. Obtain constraint compliance characteristics by standardizing coding constraints, and obtain the impact characteristics on the construction period by analyzing construction progress data.

[0035] In this embodiment, the acquisition of constraint compliance characteristics by the coding specification constraints includes the following steps: S211. Analyze the structured specification clauses to obtain the structured specification constraint set.

[0036] The first step is to screen and define the scope of the standards. First, select the clauses that are directly applicable to the entire process of precast beam design, production and construction from the collected standards. Remove the content in the general building structure standards that is not related to precast beams (such as the clauses related to masonry structures). Clarify the applicable scenarios of the clauses (such as beam fabrication, prestressed construction, hoisting and acceptance, etc.).

[0037] The second step is to classify and label the constraint types. Based on the legal effect and enforcement requirements of the standard provisions, the selected provisions are divided into two categories: mandatory constraints and advisory constraints. Mandatory constraints are marked with "must be implemented" and correspond to provisions that will render the design scheme invalid if violated (such as the prestressing tendon tension control stress shall not exceed the specified limit). Advisory constraints are marked with "priority reference" and correspond to provisions that optimize the design effect (such as the need to add reinforcing stirrups at the ends of precast beams).

[0038] The third step is multi-dimensional element extraction. Each clause is broken down into standardized elements. The core extraction dimensions include: constraint object (clearly defining the specific part or parameter acting on the precast beam, such as main reinforcement, protective layer, tensioning process, etc.), constraint type (dimensional limits, performance requirements, timing requirements, process requirements, etc.), constraint threshold (quantifiable numerical values ​​or qualitative standards), constraint level (mandatory / recommended), applicable conditions (such as specific span range, environmental type), and standard source (including standard name, number, and clause number). For example, the statement "The diameter of the main reinforcement of the precast beam should not be less than 12mm" can be completely extracted as: constraint object: precast beam main reinforcement; constraint type: lower limit of size; constraint threshold: 12mm; constraint level: mandatory; applicable conditions: general simply supported precast beam; standard source: Article 9.2.1 of the "Code for Design of Concrete Structures" GB50010-2010.

[0039] The fourth step is verification and integration. Precast beam design experts are organized to cross-verify the extracted elements, correct missing or incorrectly labeled items, and finally integrate them to form a structured set of standardized constraints containing unified element fields. Each constraint is accompanied by a unique identifier code to facilitate subsequent quantitative coding and related queries.

[0040] S212. Based on the element type quantification coding constraint index of the structured norm constraint set, extract constraint compliance features using the coded constraint index.

[0041] Based on the element types of the structured and standardized constraint set, a process of classification adaptation, quantization mapping, and rule verification is adopted to achieve accurate quantization encoding of constraint indicators, ensuring that the encoding results are adapted to the numerical calculation requirements of the optimization algorithm.

[0042] For constraints with clearly defined numerical thresholds (such as protective layer thickness, rebar spacing, concrete strength grade, prestressing tension control stress, etc.), first, standardize the threshold units (e.g., length unit is standardized to mm, strength unit is standardized to MPa), and then convert them into threshold constraint features according to the constraint type (upper limit / lower limit / interval): lower limit constraints are coded as [threshold, +∞) (e.g., protective layer thickness ≥ 50mm is coded as [50, +∞)), upper limit constraints are coded as (-∞, threshold] (e.g., rebar spacing ≤ 200mm is coded as (-∞, 200]), and interval constraints are coded as [lower limit threshold, upper limit threshold] (e.g., stirrup diameter 8-12mm is coded as [8, 12]). At the same time, the standard priority of the threshold is marked. If different standards have different threshold requirements for the same index, the latest published industry-specific standard shall prevail (e.g., when there is a conflict between the precast beam-specific standard and the general concrete standard, the precast beam-specific standard threshold shall be used first).

[0043] For constraints without explicit numerical values ​​but with clear judgment criteria (such as no cracks in appearance quality, good sealing of splice joints, and firm reinforcement binding), a mapping rule between qualitative standards and quantitative levels is first established. The quantitative code for each level is determined through expert scoring. Taking no cracks in appearance quality as an example, three levels are first defined: no cracks (excellent), minor cracks (acceptable), and obvious cracks (unacceptable), then coded as [0=no cracks, 1=minor cracks, 2=obvious cracks], and the judgment criteria for each level are clearly defined (e.g., minor crack width ≤ 0.1mm). For good sealing of splice joints, three levels are defined: intact seal, slight leakage, and severe leakage, coded as [0, 1, 2]. Practical standards for leakage detection are also developed (e.g., no leakage in a water storage test indicates an intact seal).

[0044] For constraints involving multiple parameters and multiple sequential processes (such as prestressing tensioning requiring the concrete strength to reach 75% of the design value, and hoisting requiring the prestressing tensioning to be completed and the anchoring to be reliable), the logical relationships between the associated parameters / processes are first sorted out, and then converted into sequential constraint features. Taking the constraint between prestressing tensioning and concrete strength as an example, the 75% concrete strength reaching the design value is first encoded as a sequential trigger threshold [75% design strength], and then prestressing tensioning is encoded as a sequential execution node, ultimately forming a sequential constraint pair of trigger threshold and execution node [75% design strength, prestressing tensioning]. For multi-process sequential constraints (such as steel cage fabrication → concrete pouring → curing → demolding), they are encoded as sequential chain features that include the process sequence and the time threshold between adjacent processes.

[0045] After all the quantization codes are completed, they are verified by comparing them with the elements of the structured constraint set to ensure that there are no omissions or mismatches in the codes, and to obtain a set of quantization constraint indicators that includes quantization thresholds / codes, constraint types, applicable conditions, and standard sources.

[0046] Furthermore, a constraint index-design parameter correlation matrix is ​​constructed. First, the correspondence between each index in the quantitative constraint index set and each parameter in the comprehensive characteristics of geometric materials is clarified, and a many-to-many mapping table is established (e.g., the main reinforcement diameter parameter corresponds to the two constraint indexes of the lower limit and upper limit of the main reinforcement diameter size, and the concrete strength parameter corresponds to the two constraint indexes of the concrete strength threshold before tensioning and the design strength grade). The matching priority of each pair of mapping relationships is clearly marked in the matrix (the matching priority of core parameters and mandatory constraints is the highest).

[0047] Then, the graded compliance score is calculated based on the correlation matrix, and the degree of matching between each design parameter combination and the corresponding constraint index is graded and scored: full compliance (parameter value falls within the constraint threshold or meets qualitative code level 0) gets 1 point; partial compliance (parameter value is close to the constraint threshold but does not exceed the allowable deviation range, or meets qualitative code level 1) gets 0.5 points (e.g., when the constraint threshold is [50,+∞), the parameter value is 48mm, and the specification allows a deviation of ±5mm, it is judged as partial compliance); non-compliance (parameter value exceeds the constraint threshold or meets qualitative code level 2) gets 0 points; for correlated time constraints, if the process execution order conforms to the time chain and the trigger threshold is met, 1 point is awarded, and if the order is reversed or the threshold is not met, 0 points are awarded.

[0048] Next, the constraint levels are weighted and integrated. First, the constraint level weights are determined using the analytic hierarchy process: the weight of mandatory constraints is set to 0.7, and the weight of suggested constraints is set to 0.3 (the weights can be dynamically adjusted according to the importance level of the project; for example, the weight of mandatory constraints for major bridge projects can be increased to 0.8). Then, the scores of each constraint index for each design parameter combination are multiplied by their corresponding weights to obtain the single-parameter compliance weighted score. Finally, the weighted scores of all parameters are integrated to generate a constraint compliance feature vector that includes the compliance scores of each parameter, the overall compliance score, and warnings of non-compliance indicators. The warnings of non-compliance indicators clearly indicate the source of the non-compliant constraint and the direction of rectification, which facilitates the subsequent correction of design parameters.

[0049] In another embodiment, the analysis of construction progress data to obtain characteristics affecting the construction period includes the following steps: S221. Decompose the time nodes of the entire life cycle of the precast beam to obtain the schedule node breakdown table.

[0050] First, the statistical boundaries of the entire life cycle of precast beams are clearly defined, namely, from the receipt of design drawings at the factory and the start of mold preparation, to the completion and acceptance of the last precast beam on site. This covers the three core stages of factory production, off-site transportation, and on-site construction, excluding indirect related links such as early-stage survey and design and later-stage operation and maintenance. Secondly, the project is divided into three sub-phases based on the responsible party and process attributes, with clear core schedule management objectives for each phase: The production phase (responsible entity: prefabrication plant) aims to shorten the production cycle of a single piece and improve the efficiency of mass production while ensuring quality; the transportation phase (responsible entity: logistics unit) aims to shorten transportation time and reduce the risk of component damage while ensuring safety; the construction phase (responsible entity: construction unit) aims to shorten on-site assembly time and ensure construction quality while ensuring orderly connection.

[0051] Then, based on the process flow of each stage, the key time nodes are broken down step by step: the production stage is detailed as mold design and processing → mold installation and debugging → steel cage fabrication → prestressed tendon embedding → concrete pouring → concrete curing → prestressing tensioning → anchoring and sealing → demolding → component inspection; the transportation stage is detailed as component hoisting and loading → transportation route planning and departure → en route driving and stopping → on-site unloading and hoisting → temporary storage and acceptance of components; the construction stage is detailed as support installation and debugging → precise beam erection → splice joint treatment → wet joint pouring and curing → system conversion → final acceptance.

[0052] Finally, the logical relationships between nodes are sorted out and a decomposition table is generated: the prerequisite dependencies of each node are clarified (such as concrete curing must be started after concrete pouring is completed, and prestressing tensioning must be started after the concrete strength reaches 75% of the design value and curing is completed), and the standard time range of each node is marked (based on industry quotas and actual factory capacity, such as the standard time for making a standard 16m precast beam steel cage is 8-12 hours).

[0053] The final output is a schedule node breakdown table that includes node name, stage, preceding node, subsequent node, standard duration range, responsible party, and quality control requirements, providing a clear node benchmark for subsequent quantification of influencing factors.

[0054] S222. Based on the aforementioned schedule node decomposition table, quantify the time-influencing factors to obtain the schedule influencing factor quantification matrix.

[0055] First, key influencing factors were screened. Combining the design parameter characteristics of precast beams with the attributes of construction schedule milestones, Pearson correlation analysis was used to screen design parameters that have a significant impact on each time node. During the production stage, key parameters to be selected include cross-sectional dimensions, concrete strength grade, number and arrangement of prestressed tendons, and reinforcement ratio (e.g., if the concrete strength grade is increased from C40 to C60, the curing time needs to be extended from 7 days to 14 days). During the transportation stage, key parameters to be selected include component weight, component length, and cross-sectional shape (regular / irregular) (e.g., if the component weight increases from 30t to 50t, the hoisting and loading time increases from 1.5 hours to 2.5 hours, and more weight-restricted road sections need to be avoided during transportation, leading to increased travel time). During the construction stage, key parameters to be selected include the number of beams, the number of splices, and component connection methods (e.g., for every additional splice, the on-site splicing and curing time increases by 2-3 days).

[0056] Then, the correlation patterns were analyzed and a quantitative model was constructed: By collecting historical data from multiple projects (covering precast beam projects with different spans and cross-sectional forms), methods such as linear regression and nonlinear fitting were used to establish the correlation function between design parameters and time nodes: For linear correlations (such as a 1% increase in steel reinforcement ratio leading to an increase of 0.8 hours in steel cage fabrication time), a linear regression model was constructed. (Y represents node duration, X represents design parameter value, a represents influence coefficient, and b represents baseline duration); For nonlinear correlations (such as the quadratic increase in concrete pouring time due to increased cross-sectional size), a nonlinear fitting model is constructed. At the same time, a correction factor for engineering scenarios is introduced (e.g., the correction factor for concrete curing time during winter construction is 1.5-2.0, and the correction factor for transportation time during mountain transportation is 1.3-1.8).

[0057] Finally, a quantitative matrix of factors affecting the construction period is generated. A two-dimensional quantitative matrix is ​​constructed with design parameters as rows and key time nodes as columns. The corresponding correlation function expression, influence coefficient and applicable range are filled in the matrix cells. For example, the cell for section height (X, mm) - concrete pouring time (Y, hours) is filled with Y=0.002X+2.5, a=0.002, applicable range: X∈[800,2000]mm, winter correction coefficient 1.2. The matrix also marks the confidence level of each correlation (the confidence level is required to be ≥0.9 to ensure the reliability of the quantitative results).

[0058] S223. Calculate the total project duration throughout the entire lifecycle by combining the project duration node decomposition table and the project duration influencing factor quantification matrix, and generate project duration influencing characteristics.

[0059] Based on the aforementioned schedule node decomposition table and the aforementioned schedule influencing factor quantification matrix, the Critical Path Method (CPM) is used to calculate the total schedule of the current design scheme: First, the estimated duration of each critical node is calculated using the quantification matrix. Then, based on the logical relationship between the nodes, the critical path (the path with the longest total duration) from mold preparation to final acceptance is identified. The total duration of the critical path is the total lifecycle duration. At the same time, the total float of the non-critical path (the maximum duration that can be flexibly adjusted) is calculated to provide space for subsequent schedule optimization. For example, the critical path of a certain design scheme is mold processing → rebar cage fabrication → concrete pouring → curing → tensioning → transportation → erection → splicing and curing → acceptance, with a total duration of 45 days. The total float of equipment commissioning on the non-critical path is 3 days.

[0060] Next, the schedule sensitivity characteristics are extracted, and the schedule sensitivity coefficient of each design parameter is calculated using the elasticity coefficient method. This coefficient represents the percentage change in the total schedule caused by a 1% change in a parameter, satisfying the following condition: , Here, ΔT is the change in total project duration, T is the original total project duration, and ΔX is the change in parameters, where X is the original parameter value. Sensitivity levels are determined based on the magnitude of the sensitivity coefficient. ≥0.5 indicates a highly sensitive parameter (such as the number of prestressed tendons); 0.2≤ <0.5 indicates a moderately sensitive parameter (such as cross-sectional dimensions). <0.2 indicates a weakly sensitive parameter (such as the flange chamfer size); the sensitivity level and sensitivity coefficient are integrated into a schedule sensitivity feature.

[0061] Furthermore, the potential characteristics for schedule optimization were extracted, and the schedule optimization potential of each key node was evaluated in combination with actual conditions such as factory capacity, transportation resources, and construction equipment. The feasibility of optimization was analyzed from three dimensions: process improvement, resource allocation, and parameter adjustment. For example, in the production stage, the time for concrete curing can be shortened from 7 days to 3 days by adopting steam curing technology, with an optimization potential value of 57% ((7-3) / 7×100%). In the transportation stage, the time for mountain transportation can be shortened from 8 hours to 6 hours by optimizing the transportation route, with an optimization potential value of 25%. The optimization potential of each node was quantitatively scored (0-1 points, with 1 point being the maximum optimization potential) and integrated into the schedule optimization potential characteristics.

[0062] Finally, a schedule impact feature vector is generated: the total lifecycle duration, critical path duration, sensitivity coefficients and sensitivity levels of each design parameter, optimization potential values ​​and optimization schemes of each critical node are integrated into a standardized schedule impact feature vector.

[0063] S3. Based on the multi-criteria decision-making weighting strategy, the comprehensive priority characteristics are obtained by utilizing the comprehensive characteristics of the geometric materials, the constraint compliance characteristics, and the project schedule impact characteristics.

[0064] In this embodiment, the multi-criteria decision-making weighting strategy, which utilizes the comprehensive characteristics of geometric materials, the constraint compliance characteristics, and the schedule impact characteristics to obtain comprehensive priority characteristics, includes the following steps: S31. Construct a multi-criteria evaluation system and obtain a multi-criteria evaluation index set.

[0065] Combining the engineering objectives and industry standards of precast beam design, three core principles are precisely defined, with each dimension clearly defined in terms of its basis and scope: In terms of technical guidelines, the core basis is industry technical specifications such as the "Technical Standard for Precast Concrete Bridges". It focuses on the structural safety and functionality of precast beams, covering core indicators directly related to mechanical properties in the comprehensive characteristics of geometric materials (such as bending stiffness, shear bearing capacity, and durability adaptability). Among them, durability adaptability needs to be associated with the material protection parameters corresponding to the service environment (marine / inland / cold and frozen regions).

[0066] In terms of compliance criteria, the basis is the mandatory and recommended provisions of national and local precast beam design standards. It covers key indicators that directly reflect the compliance level of the design scheme in the constraint compliance characteristics, and focuses on the mandatory constraint score (which directly determines the effectiveness of the scheme) and the recommended constraint score (which affects the optimization effect of the scheme).

[0067] The schedule criteria are based on the overall project schedule requirements and the full life cycle schedule management objectives. They cover the core indicators that play a decisive role in the project schedule among the schedule impact characteristics. In addition to the overall schedule and schedule sensitivity, they supplement the critical path optimization potential indicators (which are directly related to the feasibility of schedule adjustments).

[0068] Then, correlation analysis and the coefficient of variation method were used to screen the indicators: First, the Pearson correlation coefficient of each candidate indicator under the same criterion was calculated. If the correlation coefficient of two indicators is ≥0.85, it is judged as highly redundant, and indicators with clearer physical meaning and easier data acquisition are retained (such as bending stiffness being highly correlated with the moment of inertia of the section, so the bending stiffness indicator is retained); then the coefficient of variation (CV) of each indicator is calculated, and low-difference indicators with a coefficient of variation <0.1 are eliminated (such indicators do not contribute to the scheme differentiation, such as the default value indicator of the foundation concrete strength grade in general scenarios); finally, the core indicator subsets of each criterion are formed: technical criterion subset (bending stiffness, shear bearing capacity, durability adaptability), compliance criterion subset (mandatory constraint score, suggested constraint score), and schedule criterion subset (total schedule, schedule sensitivity coefficient, critical path optimization potential).

[0069] Furthermore, experts in precast beam design, construction, and management can be organized to use the Delphi method to score the effectiveness of the selected indicator set (1-5 points, with 5 being the most effective), requiring an average score of ≥4.0 for the indicator set. At the same time, 2-3 typical precast beam engineering cases can be used to verify whether the indicator set can accurately distinguish the merits of different design schemes (e.g., the technical criteria score of a high-quality scheme is significantly higher than that of a low-quality scheme). If the verification fails, the indicators can be retrospectively supplemented or adjusted until the requirements are met, resulting in a multi-criteria evaluation indicator set that includes criterion dimensions, core indicators, indicator definitions, data sources, and effectiveness verification results.

[0070] S32. A hybrid weighting model is established by combining subjective weighting using the analytic hierarchy process (AHP) and objective weighting using the entropy weighting method.

[0071] First, subjective weighting is achieved through the Analytic Hierarchy Process (AHP): Step 1, a hierarchical model is established, clarifying the hierarchical relationships among the target layer (comprehensive priority evaluation of precast beam design schemes), the criteria layer (technical criteria, compliance criteria, and schedule criteria), and the indicator layer (core indicators of each criterion). Step 2, a judgment matrix is ​​constructed. Experts in the precast beam field are invited to assess the weighting based on engineering experience and project requirements (e.g., for major bridge projects, structural safety is prioritized, and the weight of technical criteria should be higher than other criteria; for municipal rapid transit projects, schedule is prioritized, and the weight of schedule criteria should be increased). A 1-9 scale (where 1 indicates both criteria are equally important, and 9 indicates one criterion is far more important than the other) is used to assess the weighting of the criteria. The relative importance of each element in the criteria and indicator layers is compared pairwise to form a judgment matrix. The third step is consistency verification and weight calculation. By calculating the maximum eigenvalue of the judgment matrix and the consistency index (CI), and combining it with the average random consistency index (RI), the consistency ratio (CR=CI / RI) is calculated. CR is required to be <0.1 to ensure the logical consistency of the judgment matrix. If CR≥0.1, feedback is given to experts to readjust the judgment matrix until the consistency requirement is met. Finally, the subjective weight of each criterion and indicator is calculated using the eigenvector method (e.g., subjective weight of 0.5 for the technical criteria of major bridge engineering, 0.3 for the compliance criteria, and 0.2 for the schedule criteria).

[0072] Next, objective weighting is applied using the entropy weight method: First, the indicator data is standardized. Since the units of the indicators are different (e.g., the technical standard indicator is in MPa, and the construction period standard indicator is in days), the min-max standardization method is used to map all indicator data to the [0,1] interval to eliminate the difference in units. Second, information entropy and entropy weight are calculated. Based on the standardized indicator data, the information entropy of each indicator is calculated (the smaller the entropy value, the greater the dispersion of the indicator data, and the greater its contribution to the evaluation result). The objective weight of each indicator is derived through the entropy value (objective weight = (1 - entropy value) / Σ(1 - entropy value)). For example, if the shear bearing capacity indicator data in the technical standard has a large dispersion (small entropy value), then its objective weight is higher than that of other indicators under the same standard.

[0073] Then, a hybrid weighting model is established by dynamically fusing subjective and objective weights: a linear weighting method is used to fuse subjective weights (W1) and objective weights (W2), with the fusion formula being W=α×W1+(1-α)×W2, where α is the fusion coefficient (ranging from 0.4 to 0.6), which is dynamically adjusted according to the engineering scenario: for scenarios with clear engineering needs and experienced experts (such as conventional span precast highway beams), α is set to 0.6 (emphasizing subjective needs); for scenarios with the application of new technologies and sufficient data accumulation (such as large span precast box girders), α is set to 0.4 (emphasizing objective data patterns); after fusion, the weight set is normalized (ensuring that the sum of the weights of each criterion is 1, and the sum of the weights of each indicator under the same criterion is 1), and finally a comprehensive weight set is generated that includes the comprehensive weight of the criterion layer, the comprehensive weight of the indicator layer, the basis for weight calculation, and the fusion coefficient.

[0074] S33. Based on the comprehensive characteristics of the geometric materials, the constraint compliance characteristics, and the construction period impact characteristics, the comprehensive priority characteristics are obtained by using the multi-criteria evaluation index set and the hybrid weighting model.

[0075] First, the feature data is preprocessed for consistency: the comprehensive features of geometric materials (technical criteria indicators), constraint compliance features (compliance criteria indicators), and schedule impact features (schedule criteria indicators) are classified and extracted according to the dimensions of the multi-criteria evaluation indicator set to ensure that the data of each indicator is complete and in a uniform format; a precise association mapping between each indicator and the corresponding feature data is established through parameter ID to avoid data mismatch (such as accurately associating the mandatory constraint score with the corresponding field in the constraint compliance feature).

[0076] Then, a weighted score is calculated in layers: a three-level weighted calculation logic of indicator score - criterion score - comprehensive score is adopted: First level, indicator score calculation, standardized scoring of each core indicator data of each design scheme (1-10 points, the better the indicator value, the higher the score, such as the shorter the total construction period, the higher the score, the greater the bending stiffness, the higher the score); Second level, criterion score calculation, the standardized score of each indicator under the same criterion is weighted and summed with the corresponding comprehensive weight of the indicator layer to obtain the technical criterion score (T), compliance criterion score (C), and construction period criterion score (S); Third level, comprehensive priority score calculation, the scores of the three criteria are weighted and summed with the corresponding comprehensive weight of the criterion layer, and the final comprehensive score formula is: Comprehensive score = W4×T+W5×C+W6×S (where W4, W5, and W6 are the comprehensive weights of the technical, compliance, and construction period criteria, respectively), the score range is 0-10 points, the higher the score, the more the scheme meets the comprehensive requirements of technical reliability, compliance compliance, and reasonable construction period.

[0077] Next, score calibration and anomaly correction are performed: the calculated comprehensive score is calibrated by combining the score range of historical high-quality cases of precast beams. If the comprehensive score of the current scheme exceeds the score range of historical high-quality cases (e.g., the score range of historical high-quality cases is 6.5-9.0 points, and the current scheme scores 9.2 points or 4.0 points), the indicator data, weight allocation and scoring criteria are checked back, and anomalies are corrected (e.g., if the weight allocation is biased, the fusion coefficient is readjusted; if the indicator data is incorrect, the original feature data is corrected). At the same time, the reasons for the score anomalies and the correction traces are marked to ensure the reliability of the score.

[0078] Finally, a comprehensive priority feature vector is generated. The calibrated comprehensive priority score is used as the core field. The auxiliary information such as the scores of each criterion item, the standardized scores of each core indicator, the weight ratio, and the score calibration instructions are integrated to generate a standardized comprehensive priority feature vector. The vector clearly marks the engineering meaning of each field (e.g., a technical criterion score of 8.5 points indicates that the scheme has excellent mechanical performance and meets the design safety requirements).

[0079] S4. Utilize weighted knowledge fusion of manufacturability features and case analogy features to obtain manufacturability case-inspired features.

[0080] In this embodiment, extracting the manufacturability features includes the following steps: S411. Identify bottlenecks in the production process and obtain the bottleneck constraint set.

[0081] Factory production data includes mold parameters (mold size, mold reuse rate, demolding process requirements), equipment parameters (lifting equipment load, vibrating equipment working range, prestressing tensioning equipment accuracy), process parameters (curing cycle, rebar tying efficiency, concrete pouring process), and cost parameters (mold wear, labor hours, material waste rate).

[0082] The collected factory production data is cleaned and classified, and abnormal fluctuation data (such as abnormal working hours caused by equipment failure or loss peaks caused by material quality problems) are removed. The data dimensions are sorted into equipment parameter category, process parameter category, and cost parameter category. Missing data items are supplemented (such as when the mold reuse rate is missing, it is supplemented by mold usage records and production batch statistics) to form a standardized production dataset.

[0083] Next, we will conduct multi-dimensional bottleneck identification, analyzing it from three core dimensions: equipment capacity, process flow, and cost losses. Equipment capability dimension: By statistically analyzing parameters such as the maximum size of the mold, the rated load of the hoisting equipment, and the effective working range of the vibrating equipment, we can identify hardware-limiting bottlenecks (such as a maximum mold length of 30m → limiting the span of a single precast beam to no more than 30m, and a hoisting equipment rated load of 50t → limiting the upper limit of the weight of a single piece). Process flow dimension: By analyzing the time distribution of processes such as rebar tying, concrete curing, and prestressing tensioning, we can identify bottlenecks in the process that lead to inefficiency (such as blind spots of the vibrating equipment causing insufficient compaction when the web thickness is less than 150mm, and insufficient curing period causing delays in achieving the required concrete strength). Cost loss dimension: By statistically analyzing the mold loss rate and material waste rate under different parameter combinations, cost-sensitive bottlenecks can be identified (such as the mold loss rate of irregular cross-section precast beams exceeding 20%, which is a high-cost bottleneck).

[0084] Then, bottleneck verification and priority classification are carried out: production technicians and equipment operators are organized to conduct cross-verification, and the authenticity of the identified bottlenecks is verified through small-batch trial production (such as trial production of precast beams with a web thickness of 140mm to verify whether the vibration blind zone leads to substandard compaction). Priorities are classified according to the impact on production feasibility (forced bottleneck) - impact on production efficiency (important bottleneck) - impact on production cost (general bottleneck).

[0085] Finally, the bottleneck constraints are quantified, transforming the verified bottlenecks into quantifiable constraints, clarifying the constraint thresholds, applicable scenarios, and consequences of violations, and forming a set of process bottleneck constraints that includes bottleneck ID, constraint type, quantification threshold, priority, and verification basis.

[0086] S412. Based on the process bottleneck constraint set, modify the process adaptability parameters to obtain the modified geometric material feature set.

[0087] Based on the core set of process bottleneck constraints and combined with the comprehensive characteristics of geometric materials (including mechanical performance parameters), a closed-loop correction process is constructed, consisting of bottleneck matching, solution formulation, collaborative verification, and iterative optimization. This ensures that the corrected parameters meet manufacturing requirements without deviating from the core design objectives, including: Bottleneck-parameter association matching: First, establish the association mapping between the process bottleneck constraint set and the comprehensive characteristics of geometric materials, and clarify the type of parameters that need to be modified for each bottleneck (such as the maximum mold length bottleneck corresponding to the span and beam length parameters; the hoisting load bottleneck corresponding to the beam weight, cross-sectional dimensions, and material density parameters; and the vibration blind zone bottleneck corresponding to the web thickness and cross-sectional shape parameters).

[0088] Targeted Correction Solution Development: Based on bottleneck priority and parameter type, differentiated correction strategies are developed: For mandatory bottlenecks (such as spans exceeding the mold length), a strategy of directly adjusting core parameters is adopted (e.g., splitting a 35m span into two 17.5m precast beams, or adjusting the beam segmentation method); for important bottlenecks (such as insufficient vibration due to excessively thin web thickness), a strategy of parameter fine-tuning + process adaptation is adopted (e.g., adjusting the web thickness from 140mm to 160mm, while optimizing the vibration point layout); for cost-sensitive bottlenecks (such as high mold wear due to irregular cross-sections), a strategy of structural optimization + material substitution is adopted (e.g., optimizing irregular flanges into standard rectangular flanges, or using modular mold adaptation).

[0089] Mechanical performance verification: The corrected geometric material parameters need to be verified simultaneously to ensure that they meet the mechanical performance requirements in the comprehensive characteristics of the geometric material (e.g., after adjusting the cross-sectional dimensions, it is necessary to verify whether the bending stiffness and shear bearing capacity still meet the standards). If the mechanical performance does not meet the standards, parameter callback and multi-scheme comparison should be initiated (e.g., the web thickness and steel reinforcement ratio should be adjusted at the same time to ensure that both mechanical performance and manufacturing requirements meet the standards).

[0090] The modified scheme is verified in multiple rounds until all bottleneck constraints are met and the mechanical properties meet the standards. The final output is a set of geometric and material features after process modification, which includes the modified geometric parameters, material parameters, modification basis, and mechanical property verification results.

[0091] S413. Extract the manufacturability features from the geometric material feature set after process correction.

[0092] Based on the geometric-material feature set after process modification, the core features of manufacturability are extracted through dimensional decomposition, index quantification, and standardized fusion, forming a manufacturability feature vector that takes into account manufacturing feasibility, economy, and efficiency. The specific implementation sub-steps are as follows: The first step is to break down the characteristic dimensions and define the indicators: clarify the specific evaluation indicators for the three core dimensions of process adaptability, production cost, and production efficiency, and ensure that the indicators are closely related to the actual production of precast beams. The process adaptability dimension defines three sub-indicators: bottleneck matching compliance rate (number of bottleneck constraints met / total number of bottleneck constraints), deviation of corrected parameters (percentage of deviation between corrected parameters and original design parameters), and process complexity level (based on the number and difficulty rating of production processes corresponding to the corrected parameters, from level 1 to 5, with higher levels indicating higher complexity).

[0093] Production cost is broken down into four sub-indicators: mold cost (calculated by mold type and number of reuses, such as standard mold cost per use = total mold price / number of reuses, and special molds with additional customization costs), material cost (calculated by adjusted material usage × material unit price, including main materials, auxiliary materials and wastage), labor cost (calculated by production process hours × unit hour price, such as rebar tying hours, vibration hours, and maintenance hours), and equipment energy consumption cost (unit time energy consumption of large equipment such as hoisting and tensioning equipment × usage time).

[0094] In terms of production efficiency, three sub-indicators are defined: single component production cycle (total time from mold installation to component delivery, including parallel / serial time of each process), process parallelism rate (time of processes that can be carried out in parallel / total production cycle), and capacity matching degree (daily output corresponding to the current parameter / factory's average daily capacity limit). The second step is indicator quantification and weight allocation: Quantify and calculate each sub-indicator (e.g., bottleneck matching compliance rate = number of compliant bottlenecks / total number of bottlenecks × 100%, single component production cycle is calculated by accumulating through production process time sequence analysis); use the analytic hierarchy process (AHP) combined with factory production goals (e.g., cost priority, efficiency priority) to determine the weight of each dimension and sub-indicator (e.g., in the cost priority scenario, the production cost dimension has a weight of 0.4, process adaptability has a weight of 0.3, and production efficiency has a weight of 0.3; in the efficiency priority scenario, the production efficiency dimension has a weight of 0.4).

[0095] The third step is feature standardization and fusion: all quantified sub-indicators are standardized (mapped to the [0,1] interval to eliminate dimensional differences), and weighted summation is performed according to weights to obtain the comprehensive score of each core dimension; the comprehensive scores of process adaptability, production cost, and production efficiency are combined in sequence to generate a manufacturability feature vector containing the scores of each dimension, details of core sub-indicators, and weight basis.

[0096] The fourth step is to verify the effectiveness of the features: compare the feature vectors with the high-quality solutions (low cost, high efficiency, low failure rate) in the factory's historical production data to verify the discriminative power of the feature vectors (the manufacturability score of the high-quality solutions should be significantly higher than that of the low-quality solutions) and ensure that the features can accurately characterize the manufacturing adaptability of the precast beams.

[0097] In another embodiment, a multi-dimensional similarity measurement model is constructed using empirical data from historically successful precast beam design cases. This model mines case features similar to current design requirements, providing heuristic information for the optimization algorithm and shortening the optimization iteration cycle. The extraction of the case analogy features includes the following steps: S421. Construct a multi-dimensional similarity measurement model based on the current design requirements of precast beams to obtain a case similarity score matrix.

[0098] First, the collected historical successful case data is screened for validity, eliminating cases with missing core parameters (e.g., no span, no concrete strength grade), logically conflicting parameters (e.g., material parameters and mechanical performance data do not match), or significant differences in engineering scenarios (e.g., a mixture of municipal small-span beams and highway large-span beams). For abnormal data in the retained cases (e.g., performance test data exceeding the normal range), the 3σ criterion is used for judgment and correction is made in conjunction with the average of similar cases, while marking the correction traces. Then, a standardized unit system for the core parameters of precast beams is established, and the parameters of all cases are uniformly converted to standard units (e.g., span is uniformly standardized to meters, concrete strength to MPa, cross-sectional dimensions to millimeters, and weight to tons). For dimensionless parameters (e.g., reinforcement ratio, similarity ratio), three decimal places are uniformly retained to ensure accuracy. Next, feature alignment and missing value completion are performed: based on the geometric material comprehensive feature dimension constructed in the previous step. A mapping table was established between the original parameters of the cases and the standard feature dimensions to align the feature dimensions of different case data. For non-core features missing in some cases (such as admixture dosage and flange thickness gradient), interpolation of similar cases was used to complete them. That is, similar cases with the same span, structural type and design objectives were selected, and the missing feature values ​​were calculated by weighted interpolation (the weights were allocated according to the similarity between the case and the target case in the engineering scenario). Cases with missing core features were directly removed and not included in subsequent modeling. Finally, the processed case data was verified for consistency to ensure that the parameter dimensions, units and accuracy of all cases were completely consistent. The verified case data were integrated into a structured classification of geometric material features, compliance features, manufacturability features, performance features and application effect features to generate a standardized case feature library containing case ID, engineering scenario tags (such as span type and service environment), and standardized feature vectors.

[0099] Furthermore, guided by the current design requirements of precast beams, a multi-dimensional similarity measurement model is constructed, incorporating scenario matching, dynamic weighting, and multi-distance fusion. This model aims to achieve accurate matching between historical cases and current design requirements, avoiding similarity biases caused by single-dimensional matching. The steps include: First, extract and define the core dimensions of design requirements and scenarios: First, clarify the core design requirements of the current precast beams, including core technical parameters (such as target span, load-bearing capacity, and cross-sectional shape), engineering scenario constraints (such as service environment, construction conditions, and manufacturing plant capacity), optimization target priorities (such as cost priority, durability priority, and schedule priority), and mark the priority weights of the core requirement dimensions (such as the span dimension of large-span precast beams has a priority weight of 0.3, and the material parameter dimension of high durability requirements has a priority weight of 0.35).

[0100] Second, a dynamic weighted similarity calculation model is constructed: Based on the feature dimensions of the standardized case feature library, a dynamic weighted similarity calculation framework is built, and the weight allocation adopts a dual-driven mode of demand-oriented and engineering experience: For the technical parameter dimension, basic weights are allocated according to the priority of the core dimensions of the current design requirements; for the engineering scenario dimension (such as service environment, manufacturing conditions), the scenario matching weight is determined by expert scoring (e.g., if the current design is a marine environment, the scenario weight of the marine environment case in the case is increased to 0.2); for the optimization target dimension, the weights of the corresponding feature dimensions are adjusted according to the current optimization priority (e.g., cost priority) (e.g., the weight of cost-related features is increased to 0.25). Third, calculate the similarity of multi-distance fusion: For different types of feature dimensions, adopt appropriate distance calculation methods: For continuous features (such as span, cross-sectional dimensions, and strength grade), use Euclidean distance to calculate similarity; for discrete features (such as cross-sectional shape, steel grade, and construction technology), use Hamming distance to calculate similarity; for ordered categorical features (such as durability grade and process complexity), use ordered distance to calculate similarity. The distance calculation results for each dimension are then weighted and summed according to dynamic weights to obtain the comprehensive similarity score between the current design scheme and each historical case. (Score range 0-1, the closer the score is to 1, the higher the similarity). Fourth, similarity score matrix verification and correction: The comprehensive similarity scores of all cases are compiled into a case similarity score matrix of the current design and historical cases. The rationality of the scores is verified by calculating the consistency coefficient of the matrix (a consistency coefficient ≥ 0.8 is acceptable). If the consistency does not meet the standard, the weights of each dimension are readjusted and the calculation is repeated until the requirements are met.

[0101] S422. Based on the case similarity score matrix, filter similar case sets and use the similar case sets to generate case analogy features.

[0102] By generating analogy feature vectors through similar case screening, advantageous feature mining, comparative mapping, and priority ranking, the successful experiences of historical cases are transformed into heuristic information that can guide the optimization of current designs. The specific implementation steps are as follows: First, a precise selection of similar case sets is made: Based on the case similarity score matrix, the top 10% of cases with the highest comprehensive similarity scores are selected as the initial similar case set; then, the initial set is validated a second time to remove cases whose engineering scenarios (such as service environment, construction conditions) differ significantly from the current design requirements (e.g., cases in marine environments are removed if the current design is for a cold and frozen region). Finally, 3-8 core similar cases are determined to form the similar case set; at the same time, the core advantage tags of each similar case are marked (such as low cost, high durability, short construction period, and easy manufacturing). Then, the core advantages are extracted and quantified: For similar case sets, core advantages are extracted according to the optimization target dimension: If the case label is low cost, cost control-related features such as material ratio (e.g., the matching relationship between concrete strength grade and steel reinforcement amount) and mold reuse scheme are extracted; if the label is high durability, durability-related features such as protective layer thickness, anti-corrosion material selection, and concrete admixture dosage are extracted; if the label is easy to manufacture, manufacturability-related features such as cross-sectional shape, steel reinforcement density, and component weight are extracted; the extracted advantages are quantified and transformed into standardized feature values ​​consistent with the current design feature dimension.

[0103] Next, compare the advantageous features with the current design: construct a comparison mapping table of advantageous features of similar cases and features of the current design, and clarify the difference dimensions between the current design features and the advantageous features of similar cases (e.g., the current design has a concrete cover thickness of 45mm, while the similar high-durability case has a cover thickness of 50mm, the difference dimension is insufficient cover thickness); calculate the feature improvement potential value of each difference dimension (improvement potential value = (case advantageous feature value - current design feature value) / current design feature value × 100%, a positive value indicates that the corresponding performance can be improved after improvement).

[0104] Finally, the case analogy feature vector and priority ranking are generated: the extracted core advantage features, feature difference dimensions, and improvement potential values ​​are integrated into the basic elements of the case analogy features; the hierarchical analysis method is used in conjunction with the current design optimization goals to determine the reference priority of each advantage feature (e.g., if the current optimization goal is cost priority, then the advantage features related to low cost have the highest priority); the basic elements are combined according to priority to generate the case analogy feature vector, which contains five core fields: advantage feature type, quantitative feature value, difference dimension, improvement potential value, and reference priority. The reference priority is divided into three levels: high (level 1), medium (level 2), and low (level 3), providing clear experience reference directions for subsequent optimization.

[0105] Furthermore, the step of using weighted knowledge fusion to obtain manufacturing case-inspired features by fusing manufacturability features and case analogy features includes the following steps: S431. Assign feature weights based on the difficulty of precast beam production and the similarity of cases to obtain a dynamic weight set.

[0106] First, a quantitative assessment of production difficulty was conducted: a multi-dimensional assessment index system for production difficulty was constructed, covering four core dimensions: span size (small span < 20m, medium span 20-40m, large span > 40m), cross-sectional complexity (standard rectangular cross-section, irregular cross-section, composite cross-section), special process requirements (conventional tensioning, vacuum-assisted tensioning, special anti-corrosion process), and material specialties (ordinary concrete, high-strength concrete, marine concrete). The analytic hierarchy process (AHP) was used to assign weights to each dimension (span size weight 0.4, cross-sectional complexity 0.3, process requirements 0.2, material specialties 0.1). Each dimension was quantitatively scored using an expert scoring method (1-5 points, higher scores indicating greater difficulty). The final comprehensive production difficulty score D = Σ(dimensional weight × dimensional score). Difficulty levels were categorized based on the score: D ≥ 3.5 for high difficulty, 2.0 ≤ D < 3.5 for medium difficulty, and D < 2.0 for low difficulty.

[0107] Next, the similarity level is determined: ≥0.8 indicates high similarity, 0.6≤ <0.8 indicates moderate similarity. <0.6 indicates low similarity. The overall similarity score is calculated.

[0108] Then, a dynamic weight calculation model is constructed: a mapping relationship between production difficulty-similarity level and weight allocation is established, and a dynamic weight calculation model is constructed: Let the manufacturability feature weight be... The case analogy feature weights are ,satisfy When the production difficulty is high, The value ranges from 0.6 to 0.7. Values ​​range from 0.3 to 0.4 (e.g., for large-span irregularly shaped precast beams). =0.7、 =0.3); when the production difficulty is low and the similarity is high, The value ranges from 0.3 to 0.4. A value of 0.6-0.7 (e.g., for a typical small-span rectangular precast beam, a similar case score of 0.85) is considered. =0.3、 =0.7); when the production difficulty is medium or the similarity is medium, linear interpolation is used to calculate the weight, and the formula is: This ensures that the weights are dynamically adjusted based on difficulty and similarity.

[0109] Finally, the calculated dynamic weights are substituted into historical engineering cases for verification. If the features fused by the weights can accurately distinguish between high-quality and low-quality solutions (the overall score of high-quality solutions increases by ≥10%), then the weights are effective. If the verification fails, the coefficients in the weight calculation model are adjusted backtracking until the verification requirements are met. Finally, a dynamic weight set containing production difficulty score, similarity score, weight value, calculation basis, and verification results is obtained, providing a quantitative basis for subsequent feature fusion.

[0110] S432. Based on the manufacturability bottleneck location and the matching of advantageous solutions for similar cases, the manufacturing case feature set is obtained using the dynamic weight set.

[0111] First, accurately locate manufacturability bottlenecks: Based on manufacturability feature vectors, extract core bottleneck indicators with process adaptability scores <0.6, and classify and label them according to process feasibility bottlenecks (such as insufficient compaction and difficulty in demolding), cost control bottlenecks (such as excessive mold wear and serious material waste), and production efficiency bottlenecks (such as excessively long curing cycles and low process parallelism). Each bottleneck is clearly associated with design parameters (such as insufficient compaction being associated with web thickness and cross-sectional shape parameters), scope of influence (such as local process links and the entire production process), and severity (levels 1-3, with level 3 being the most severe).

[0112] Then, matching advantageous solutions from similar cases: Based on the case similarity score matrix, matching the corresponding advantageous solutions from the set of similar cases for each identified manufacturing bottleneck, prioritizing matching cases with the same type of bottleneck and high similarity (e.g., if the current bottleneck is the difficulty in hoisting a large-span beam, matching cases with a similarity score ≥ 0.8 and which have successfully solved the hoisting problem); extracting the core improvement measures for the bottleneck from the advantageous solutions and organizing them into a solution library of bottleneck type - improvement parameters - implementation effect (e.g., hoisting difficulty - optimizing the beam hoisting point layout + using special hoisting tools - hoisting efficiency increased by 30% and damage rate reduced to 0).

[0113] Next, based on the bottleneck type and improvement plan, the design parameters associated with manufacturability characteristics are modified: For process feasibility bottlenecks (such as difficulty in vibration due to excessively thin web thickness), the corresponding geometric parameters are adjusted with reference to the case improvement plan (the web thickness is modified from 140mm to 180mm), and auxiliary process parameters are added (such as adding vibration pre-reserved holes and optimizing vibration points); For cost control bottlenecks (such as high wear of irregular cross-section molds), the cross-sectional shape parameters are modified with reference to the case's structural simplification + modular mold solution (the irregular flange is optimized into a standard rectangular flange), and the cost change of the modified mold is calculated; For production efficiency bottlenecks (such as excessively long curing cycles), the material parameters (such as using early-strength concrete) or process parameters (such as using steam curing) are adjusted with reference to the case's material substitution + process improvement solution.

[0114] Then, multi-dimensional collaborative verification is carried out: the revised design parameters need to be verified in three ways: first, manufacturing feasibility verification (verifying whether the original bottleneck is solved after the revision, and the process adaptability score must be ≥0.8); second, mechanical performance verification (corresponding to the geometric-material comprehensive characteristics in step one, verifying whether the core performance such as bending stiffness and shear bearing capacity meet the standards after the revision); third, schedule adaptability verification (corresponding to the schedule impact characteristics in step six, verifying whether the revision will lead to an extension of the total schedule by more than 5%). If the verification fails, the scheme fine-tuning-second verification iteration is started until all verification requirements are met, and finally, a revised manufacturing case feature set is obtained, which includes the revised design parameters, the bottleneck solution effect, the verification results of each dimension, and the case reference basis.

[0115] S433. Extract heuristic rules from the manufacturing case feature set, and obtain the manufacturing case heuristic feature vector through the heuristic rules.

[0116] Through heuristic rule extraction, rule quantization and encoding, feature vector construction, and validity verification, standardized manufacturing case heuristic features are generated to ensure that they can accurately guide the search direction of the optimization algorithm. The specific implementation sub-steps are as follows: Core heuristic rule extraction: From the modified manufacturing case feature set, universally applicable heuristic rules are extracted according to three dimensions: process adaptability, cost optimization, and efficiency improvement. The extraction criteria are that the rules can clearly relate to design parameters and optimization goals, and can be verified as effective in ≥3 similar cases. For example, rules extracted for the process adaptability dimension include: web thickness ≥180mm can avoid vibration blind spots, improving process adaptability by ≥20%; when the spacing of precast beam lifting points is ≤1 / 4 of the span, the lifting stability is improved by 40%. Rules extracted for the cost optimization dimension include: using standard rectangular sections reduces the cost of molds by 30%-50% compared to irregular sections; C50 concrete reduces material costs by 15% compared to C60 concrete while meeting the mechanical requirements of medium-span beams. Rules extracted for the efficiency improvement dimension include: steam curing shortens the curing cycle by more than 60% compared to natural curing; modular rebar tying improves efficiency by 50% compared to on-site tying.

[0117] Then, the heuristic rules are quantified and encoded: the extracted heuristic rules are transformed into quantified expressions that the algorithm can recognize, using a condition-action-effect triplet encoding structure: the condition part clarifies the parameter range to which the rule applies (e.g., web thickness < 180mm), the action part clarifies the corresponding parameter adjustment direction (e.g., web thickness adjusted to 180-200mm), and the effect part clarifies the quantitative benefit after adjustment (e.g., process adaptability ≥ 0.8); for example, the rule that web thickness ≥ 180mm can improve process adaptability is encoded as: condition: web thickness < 180mm; action: web thickness ↑ to 180-200mm; effect: process adaptability ≥ 0.8; for numerical rules, specific quantification thresholds and adjustment steps are added (e.g., for every 0.5% reduction in steel reinforcement ratio, material cost decreases by 2%, step size 0.1%).

[0118] Next, a manufacturing case-inspired feature vector is constructed: the quantified heuristic rules are sorted by priority (process adaptability rules > cost optimization rules > efficiency improvement rules), and a structured feature vector is constructed. The core fields of the vector include rule ID, applicable parameter range, parameter adjustment direction, quantization threshold, optimization effect, and priority level. At the same time, each rule is associated with a corresponding design parameter ID to achieve accurate mapping with the comprehensive features of geometric materials and manufacturability features. For example, the feature vector entry is: Rule ID: G-001; Applicable parameter: web thickness; Adjustment direction: increase; Quantization threshold: ≥180mm; Optimization effect: process adaptability ≥0.8; Priority: level 1; Associated parameter ID: J-003.

[0119] Finally, the effectiveness of the heuristic features is verified: the constructed heuristic feature vectors are embedded into a simplified optimization algorithm for verification, and the optimization efficiency and solution quality of the algorithm before and after the introduction of heuristic features are compared: the algorithm's convergence speed should increase by ≥30% after the introduction, the process adaptability score of the output solution should be ≥0.8, and the cost should be reduced by ≥10%. If the verification fails, more universal heuristic rules are backtracked and selected, and the feature vectors are re-encoded and constructed until the verification requirements are met. Ultimately, standardized, quantifiable, and traceable manufacturing case heuristic feature vectors are obtained, providing accurate heuristic guidance information for subsequent hybrid heuristic algorithms.

[0120] S5. Combining the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, the multi-objective design optimization of the precast beam is completed based on the hybrid meta-heuristic framework.

[0121] To address the issues of time-consuming computation and inability to embed optimization algorithms in finite element analysis (FEA) of precast beams, a high-fidelity surrogate model is constructed to replace finite element simulation. Through sample data training and model structure optimization, rapid and accurate prediction of the mechanical properties of precast beams is achieved, providing performance constraint inputs for the optimization algorithm. The features of the combined performance approximation model are extracted, including the following steps: Based on the comprehensive characteristics of geometric materials, a complete sample construction system is established, encompassing parameter range definition, stratified sampling, marginal sample expansion, and sample validity verification. This ensures that the sample set covers both the core parameter range and accurately captures areas sensitive to mechanical properties. The specific implementation steps are as follows: Precise definition of parameter ranges: First, combine the design specifications for precast beams (such as the "Technical Standard for Precast Concrete Bridges") with the actual application scenarios of the project to clarify the reasonable value ranges of each geometric material parameter (such as the span range of 8-40m, the web thickness range of 140-300mm, and the concrete strength grade range of C40-C60), and eliminate parameter ranges that exceed the feasibility of the project; at the same time, mark the mechanical sensitivity level of each parameter (such as web thickness and prestressed tendon specifications are high-sensitivity parameters, and flange chamfer dimensions are low-sensitivity parameters).

[0122] Latin hypercube stratified sampling: The Latin hypercube sampling method (LHS) is used to extract sample points. This method divides each parameter interval into N equally probable sub-intervals, ensuring that only 1 sample point is extracted from each sub-interval, effectively avoiding sample clustering or omission problems that may occur in random sampling. The sampling number is determined according to the parameter dimension, following the rule of thumb of parameter dimension × 10-20 (e.g., when there are 8 core parameter dimensions, the basic sampling number is set to 120), ensuring uniform coverage of the parameter space by the samples.

[0123] Edge and sensitive parameter combination expansion: For edge parameter combinations that are sensitive to mechanical properties (such as maximum span + minimum web thickness, minimum span + maximum concrete strength, maximum prestressing tendon usage + minimum cross-sectional size, etc.), additional finite element simulation samples are conducted to supplement them. These combinations are prone to extreme situations such as stress exceeding limits and deflection exceeding standards, which are the key to the accurate prediction of the surrogate model. The number of expanded samples is no less than 20% of the basic sample size to ensure the model prediction accuracy under extreme working conditions.

[0124] Sample validity verification: The validity of the extracted and expanded sample set is verified by calculating the uniformity index of parameter spatial distribution of sample points (such as coefficient of variation CV≤0.2) and the degree of difference in mechanical properties (such as the difference in mid-span stress between different samples ≥30% of the design value), and eliminating redundant samples with uneven distribution or too small performance differences; the final output is a high-coverage finite element sample set that covers the core parameter range, includes extreme working conditions, and has a reasonable performance gradient. The sample set must be accompanied by complete attribute labels such as parameter values, simulation working conditions, and performance indicators.

[0125] Furthermore, considering the strong nonlinearity and zoned stress characteristics of the precast beam's mechanical properties, a process of model selection, structure customization, parameter optimization, and pre-training verification is adopted to optimize the surrogate model structure, ensuring that the model can accurately fit the mechanical performance laws while also possessing high computational speed. The specific implementation steps are as follows: Basic model selection and adaptability analysis: A BP neural network is adopted as the basic model. For the regression problem of precast beam performance prediction, a three-layer basic architecture of input layer-hidden layer-output layer is adopted to avoid the overfitting and training inefficiency problems caused by deep networks. Then, a customized structural design—the construction of a stress zoning feature mapping layer—is implemented. Based on the core stress mechanism of precast beam web shear resistance, flange bending resistance, and end force transmission, a dedicated stress zoning feature mapping layer is added to the hidden layer. The input geometric material comprehensive features are decomposed into three sub-modules according to stress function: web feature subset (web thickness, web reinforcement ratio, vertical arrangement of prestressing tendons), flange feature subset (flange width / thickness, flange reinforcement ratio), and end feature subset (number of end stiffeners, anchorage zone size). By introducing a local connection weight matrix, each sub-module is strongly correlated only with the corresponding mechanical performance indicators (web shear strength, flange bending strength, end compressive strength), while retaining weak connections between sub-modules to capture the overall stress coupling effect. The ReLU function is selected as the activation function for the mapping layer to solve the gradient vanishing problem and improve the feature mapping accuracy.

[0126] Then, the model parameters were refined and optimized: K-fold cross-validation (K=5) was used to adjust the core model parameters: the number of hidden layer nodes was initially set to be 1.5-2 times the number of input layer nodes (e.g., when the input layer has 12 features, the number of nodes ranges from 18 to 24), and the optimal value was selected through iterative filtering using the validation set accuracy; the learning rate adopted a dynamic adjustment strategy, with the initial learning rate set to 0.01. When the validation set loss function did not decrease for 5 consecutive rounds, the learning rate was reduced to 0.5 times the original value to avoid getting trapped in local optima; the number of training iterations was set to 1000 rounds, and an early stopping mechanism was set (training was terminated if the validation set loss function did not improve for 10 rounds).

[0127] Next, 70% of the high-coverage finite element sample set was used as the training set for pre-training, and mean squared error (MSE) was used as the loss function to optimize the network weights. After training, the fitting effect of the pre-trained model was verified by the remaining 30% of the samples. If there were local performance prediction deviations (such as the deflection prediction error of large-span beams exceeding 8%), the mapping layer weights of the corresponding stress zones were adjusted in a targeted manner until the model's initial fitting accuracy met the prediction error <10%, thus obtaining a high-fidelity precast beam performance proxy model with customized structure and optimal parameters.

[0128] Then, through multi-dimensional verification, accuracy assessment, and feature extraction and quantization, the effectiveness of the surrogate model is verified and approximate performance features are generated to ensure that the extracted features can accurately support subsequent optimization algorithms. The specific implementation sub-steps are as follows: Validation dataset partitioning and validation metric system construction: 30% of the samples were randomly selected from the high-coverage finite element sample set as an independent validation set (not involved in any training process), and the remaining 70% served as the training set; a multi-dimensional validation metric system was constructed, supplementing the core prediction error (relative error RE) with mean absolute error (MAE) and coefficient of determination (R²). 2 The model's prediction accuracy is comprehensively evaluated using metrics such as root mean square error (RMSE) under different parameter ranges and performance indicators. The prediction error is required to be ≤5%, and R0 is also required to be within the specified range. 2 A value ≥ 0.95 is required to ensure high fidelity of the model.

[0129] Scenario-based accuracy verification: The validation set is grouped according to the core design scenarios of precast beams (such as small-span conventional beams, large-span prestressed beams, and marine environment durability beams) and scenario-based accuracy verification is carried out. The focus is on verifying the prediction accuracy of extreme working condition samples (marginal parameter combinations). If the prediction error of a certain scenario exceeds the threshold (>5%), the weight of the stress partition mapping layer of the model is adjusted back, and samples of that scenario are added for secondary training until the accuracy of the whole scenario reaches the standard. At the same time, the prediction error distribution of each scenario is recorded to form a model accuracy heatmap and clarify the applicable boundaries of the model.

[0130] Performance approximation model feature extraction and quantification: After the model verification meets the standards, the output parameters of the proxy model are transformed into standardized performance approximation model features: core features include the predicted values ​​of mechanical properties of key parts (maximum tensile / compressive stress at mid-span, maximum shear stress of web, deflection value at mid-span, crack resistance safety factor, ultimate bearing capacity). Each feature is normalized according to the ratio of actual predicted value / standard limit (mapped to the [0,1] interval) to facilitate the target quantification of subsequent optimization algorithms; supplementary features include performance redundancy features (such as crack resistance safety factor -1.0, which characterizes performance reserve capacity).

[0131] Uncertainty feature extraction: Based on the error distribution data from the validation phase, the model's uncertainty features are extracted. Monte Carlo simulation (predicting 100 times under random perturbations for the same input parameter combination) is used to calculate the standard deviation and coefficient of variation of the prediction results as uncertainty quantification indicators. Simultaneously, high-uncertainty parameter combinations (e.g., those with a coefficient of variation > 0.05) are labeled to provide risk warning information for subsequent optimization algorithms. These parameter combinations require key verification during optimization, and finite element simulation verification should be supplemented if necessary. The final output is a feature vector of the approximate performance model containing core mechanical performance characteristics, performance redundancy characteristics, and uncertainty features.

[0132] Based on this, the multi-objective design optimization of precast beams is completed according to the hybrid meta-heuristic framework by combining the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, including the following steps: S51. Construct a hybrid metaheuristic framework.

[0133] Specifically, a hybrid heuristic algorithm framework is constructed using a combination of genetic algorithm (GA) for global exploration, particle swarm optimization (PSO) for local development, and heuristic guidance for enhancement. This framework balances the breadth of global search with the accuracy of local optimization, while incorporating knowledge from the precast beam engineering domain to improve the targeting of optimization. Specific implementation details are as follows: 1. Genetic Algorithm Stage – Global Optimal Solution Space Exploration: The first step, design parameter encoding and initial population generation, uses a real number encoding method combined with parameter boundary constraints to map the core design parameters of the precast beam (span, cross-sectional dimensions, concrete strength grade, steel reinforcement ratio, prestressed tendon specifications, etc.) into chromosome gene sequences. Each gene corresponds to a design parameter, and the gene value range strictly matches the reasonable parameter range defined in the first step (e.g., the span gene value range is 8-40m, and the web thickness gene value range is 140-300mm). The initial population is generated based on the Latin hypercube sampling method, and the population size is determined according to the parameter dimension (when the parameter dimension is 8-12, the population size is set to 100-150) to ensure that the initial population uniformly covers the parameter space.

[0134] The second step is to construct and optimize the fitness function: using the comprehensive priority feature score generated in step seven as the core fitness index, a fitness function is constructed. ,in The overall priority score is calculated (0-10 points are standardized to 0-1). The deviation coefficient of parameters from the normal range of engineering (the larger the deviation) The closer to 1), The fitness function can be dynamically adjusted according to engineering needs. The larger the function value, the more significant the comprehensive advantages of the solution. At the same time, the constraint compliance characteristics (mandatory constraint score ≥ 0.9) and performance approximation model characteristics (stress ≤ standard limit, deflection ≤ standard limit) are used as penalty terms of the fitness function. If the solution violates the mandatory constraints, the fitness function value is directly set to 0 to ensure that the optimization direction conforms to compliance and safety requirements.

[0135] The third step involves genetic operation design and parameter configuration: The selection operator employs a tournament selection + elite retention strategy, with the tournament size set to 3. Simultaneously, the top 5% of individuals with the highest fitness values ​​in each generation are retained to directly enter the next generation, preventing the loss of high-quality genes. The crossover operator uses simulated binary crossover (SBX), with the crossover probability Pc dynamically adjusted based on the population convergence (initially Pc=0.8, decreasing to 0.5 when the population converges). The crossover distribution index is set to 20 to ensure that genes remain within a reasonable parameter range after crossover. The mutation operator uses polynomial mutation, with the mutation probability Pm set to 0.01-0.03 (the higher the parameter dimension, the larger the value of Pm), and the mutation distribution index set to 10, breaking local population convergence through low-probability mutations.

[0136] The fourth step is to set the global search termination condition: when the number of iterations of the genetic algorithm reaches 50 generations, or when the fluctuation of the optimal fitness value of the population is less than 0.001 for 10 consecutive generations, the global search is terminated, and the set of the global optimal solutions (the top 20% of high-quality individuals) is output as the initial particle set of the particle swarm algorithm.

[0137] 2. Particle Swarm Optimization Stage – Precise Discovery of Local Optimum Solutions: The first step is initial particle initialization and parameter mapping: the set of global optimal solutions output by the genetic algorithm is directly used as the initial particles of the particle swarm. Each particle corresponds to a precast beam design scheme, the particle position vector corresponds to the design parameter combination, and the initial value of the particle velocity vector is set to 10% of the parameter range (e.g., when the span parameter range is 8-40m, the initial velocity range is set to ±3.2m).

[0138] The second step is to customize the velocity and position update formula: based on the strong coupling characteristics of the precast beam design parameters, a customized velocity update formula is developed. , where ω is the inertia weight (using a linear decreasing strategy, decreasing from 0.9 to 0.4 to balance global and local search). For acceleration coefficient ( Focus on local optimum mining (Focusing on global optimal guidance) A random number between 0 and 1. This represents the historical best position of the i-th particle. The global optimal position for the entire particle swarm; position update formula. At the same time, parameter boundary constraints are added. If the updated parameters exceed the reasonable range, the parameters will be automatically truncated to the range boundary and the velocity direction will be reset.

[0139] The third step is to strengthen local optimization constraints: using the performance approximation model features as core local constraints, the performance indicators such as mid-span stress, web shear stress, and deflection for each particle are calculated in real time. If the performance indicators exceed the specification limits, a position correction term is added. Adjust the particle positions to ensure that the solution always meets the mechanical performance requirements during the local optimization process.

[0140] 3. A case-based inspirational feature-guided mechanism is implemented, constructing a three-tiered guidance logic: bottleneck identification, direction guidance, and parameter fine-tuning. The first step is bottleneck region identification: real-time monitoring of particle design parameter combinations during the algorithm search process. If the process adaptability score in the manufacturability feature corresponding to the parameter combination is <0.7 (i.e., entering the process bottleneck region), a heuristic guidance mechanism is triggered.

[0141] The second step is to guide the direction of calibration: extract the optimal improvement rules for the corresponding bottleneck type from the feature vector inspired by manufacturing cases (e.g., when the web thickness is <180mm, extract the rule to adjust the web thickness to 180-200mm) and determine the direction of parameter adjustment and the target range.

[0142] The third step is the embedding of guiding factors: guidance is achieved by adjusting the particle velocity weights. For the parameter dimensions that need to be adjusted, the acceleration coefficient is... Upgrade to 2.5, and set the speed correction option: , The guiding intensity coefficient is set to 0.3-0.5 to guide particles to move quickly towards the parameter range that meets the process requirements. If a superior parameter combination with high similarity is found, this combination is directly used as the temporary gbest to guide the particle swarm convergence, which greatly improves the efficiency of local optimization.

[0143] S52. Combining the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, a multi-objective optimization objective function is established.

[0144] Based on the preceding multi-dimensional features, a multi-objective optimization function system with objective quantification, constraint strengthening, and weight dynamics is constructed. The core objectives and boundary conditions for precast beam design optimization are clarified, and multi-objective synergistic balance is achieved through Pareto optimal solutions. Specific construction details are as follows: ① Quantification and Functional Expression of Core Optimization Objectives: Combining the core requirements of prioritizing safety while considering economy and efficiency in precast beam engineering, three major optimization objectives are identified and quantified into mathematical functions: Objective 1: Maximize the overall priority score, satisfying: ,in The three criteria are: technology, compliance, and schedule. The scores are T, C, and S, which are the standardization scores of the three criteria. This objective comprehensively reflects the technical reliability, compliance, and schedule rationality of the solution and is the core guiding objective for optimization.

[0145] Objective 2: Optimal mechanical properties (minimum stress and deflection), satisfying: ,in , These represent the maximum tensile stress at mid-span and the maximum shear stress in the web, respectively. For mid-span deflection, For performance weighting, all performance indicators are normalized to the ratio of predicted value to specification limit. A smaller function value indicates better mechanical performance, and the following conditions must be met. (That is, all performance indicators do not exceed the specified limits).

[0146] Objective 3: Minimize production costs, satisfying: ,in , , These are the standardized costs of molds, materials, labor, and equipment energy consumption (mapped to the 0-1 range). As a weighted component of cost, this objective is directly related to the economics of precast beams, preventing optimization schemes from excessively pursuing performance and leading to uncontrolled costs.

[0147] ② Definition and Quantification of Multi-Objective Constraints: To ensure the engineering feasibility of the optimization scheme, four types of core constraints are added and their thresholds are quantified: First, geometric parameter constraints, based on the manufacturing and construction capabilities of precast beams, constrain the span ≤ 40m (single-segment precast), web thickness ≥ 140mm, flange width ≤ 2.5m, etc., expressed as x∈[xmin,xmax] (x is the geometric parameter, xmin and xmax are the boundaries of the reasonable interval); Second, material matching constraints, based on the engineering knowledge rule base, constrain the compatibility relationship between concrete strength grade and steel reinforcement grade (e.g., C50 concrete). The concrete is only compatible with HRB400 / HRB500 steel bars), and the expression is (x material 1, x material 2) ∈ Ω (Ω is the set of compliant material combinations); the third is the standard compliance constraint, based on the constraint compliance characteristics, the constraint mandatory constraint score ≥ 0.9, the overall compliance total score ≥ 0.85, and the expression is C strong ≥ 0.9, C total ≥ 0.85; the fourth is the manufacturing process constraint, based on the manufacturability characteristics, the constraint process adaptability score ≥ 0.8, the single component production cycle ≤ 1.2 times the industry quota, and the expression is M adaptability ≥ 0.8, T production ≤ 1.2 × T quota.

[0148] ③ Multi-objective balancing and Pareto optimal solution generation: The core idea of ​​the Non-dominated Sorting Genetic Algorithm (NSGA-II) is adopted to achieve multi-objective balancing. The design schemes in the population are classified through three-level non-dominated sorting: the first-level non-dominated solution (no other scheme is better than this scheme in all objectives) is the Pareto optimal solution candidate; in order to avoid Pareto optimal solution set, a crowding degree calculation mechanism is introduced to sort the solutions of the same level according to the parameter space distribution density, retain the uniformly distributed solutions, and ensure that the optimal solution set covers schemes with different objective priorities (such as schemes focusing on cost, schemes focusing on performance, and schemes focusing on schedule); the final Pareto optimal solution set must meet the following requirements: the number of solutions ≥ 30, and the objective difference between any two solutions ≥ 5%, to ensure that sufficient scheme selection space is provided for engineering decision-making.

[0149] S53. Based on the hybrid meta-heuristic framework and the multi-objective optimization objective function, complete the multi-objective design optimization of the precast beam.

[0150] Specifically, firstly, multi-dimensional iteration termination conditions are set to ensure algorithm convergence and stable optimization results: Condition 1: The number of iterations reaches the preset maximum value (the total number of iterations for the hybrid algorithm is set to 1000, including 50 generations of genetic algorithm and 950 generations of particle swarm algorithm). Condition 2: No new solutions are added to the Pareto optimal solution set after 50 consecutive iterations (i.e., the optimal solution set tends to be stable). Condition 3: The fluctuation range of the core optimization objective (comprehensive priority score) is ≤0.001, and the mechanical performance function value... (i.e., sufficient performance reserves); The iteration can be terminated when any two conditions are met. During the iteration process, key indicators are monitored in real time, and three types of monitoring charts are generated: fitness function value change curve, Pareto front formation trajectory, and core parameter convergence trend chart, which intuitively present the optimization process. If premature convergence of the population occurs (no new solution for 20 consecutive generations), the genetic algorithm mutation probability enhancement mechanism (Pm is temporarily increased to 0.05) or the particle swarm algorithm inertial weight reset (ω is restored to 0.9) is automatically triggered to break the local convergence.

[0151] Secondly, Pareto optimal solution set clustering and filtering: The generated Pareto optimal solution set is subjected to hierarchical clustering and targeted filtering to improve the efficiency of solution decision-making. The first step is to divide the optimal solution set into 3-5 clusters based on the K-means clustering algorithm. The clustering is based on the score difference of the three optimization objectives. Each cluster corresponds to a target priority scheme (e.g., cluster 1: performance priority, cluster 2: cost priority, cluster 3: balanced).

[0152] The second step is to calculate the comprehensive evaluation index of the scheme within each cluster. ), and select 3-5 schemes with the best comprehensive evaluation index within each cluster as candidate schemes.

[0153] The third step is to eliminate candidates with engineering conflicts (such as the cost-optimal solution but the process adaptability is not up to standard, or the performance-optimal solution but the construction period is overdue), and finally retain 5-8 core candidate solutions that are conflict-free and cover different target priorities.

[0154] Next, engineering verification of candidate solutions and determination of the optimal solution: Multi-dimensional engineering verification was conducted on core candidate solutions to ensure their feasibility: First, detailed mechanical performance verification was performed by calling a high-fidelity proxy model to predict the performance of candidate solutions under all working conditions. At the same time, two key solutions were selected for finite element simulation verification. The relative error between the simulation value and the predicted value of the proxy model was required to be ≤5%, and all mechanical performance indicators were required to meet the specifications. Second, manufacturing feasibility verification was performed by checking whether the parameter combination of the candidate solution matched the factory's production capacity (such as mold size, hoisting equipment load, and vibrating equipment working range) in combination with manufacturability characteristics. Production technicians were organized to conduct a feasibility review of the production process of the solution, and potential production risks and solutions were marked. Third, the linkage verification between schedule and cost was performed by calculating the full life cycle schedule of the candidate solution based on the schedule impact characteristics, verifying whether it met the total project schedule requirements, and conducting cost sensitivity analysis (such as the impact of material price fluctuations of ±5% on total cost) to evaluate the economic stability of the solution. Based on the engineering verification results and in combination with the actual needs of the project (such as prioritizing performance-oriented solutions for major bridge projects and prioritizing time-cost balanced solutions for municipal expressway projects), one optimal design scheme and two alternative schemes are selected from the candidate schemes (to cope with changes in engineering requirements).

[0155] Finally, the complete technical document of the optimal design scheme is output, and its core contents include: First, a detailed parameter list, covering geometric parameters (span, cross-sectional dimensions, reinforcement layout, etc.), material parameters (concrete strength grade, steel grade, prestressed tendon specifications, etc.), and process parameters (curing method, tensioning sequence, hoisting scheme, etc.), with all parameters labeled with the basis for their values ​​and their engineering significance; Second, a summary table of multi-objective optimization results, clarifying the specific indicators of the scheme in terms of comprehensive priority score, mechanical performance, production cost, and full life cycle construction period, and comparing it with the industry average to illustrate its advantages (such as a 12% reduction in production cost and an 8% reduction in construction period compared to the industry average); Third, a parameter traceability report, which links the characteristic data of each previous step (such as geometric material characteristics, compliance characteristics, and manufacturability characteristics) through parameter IDs, clearly presenting the evolution process and constraint basis of parameter optimization; Fourth, engineering implementation suggestions, providing targeted suggestions for key aspects of the production and construction of the scheme (such as modular design suggestions for irregular cross-section molds and safety control suggestions for hoisting large-span beams), providing technical support for subsequent engineering implementation.

[0156] Please see Figure 2 In an embodiment, to efficiently execute the precast beam design optimization method based on a hybrid element heuristic algorithm provided by this invention, this invention also provides a precast beam design optimization system based on a hybrid element heuristic algorithm, comprising: an input device 1, an output device 2, a processor 3, and a memory 4. The input device 1, output device 2, processor 3, and memory 4 are interconnected. The memory 4 stores program instructions used to execute the steps of the precast beam design optimization method based on a hybrid element heuristic algorithm. The precast beam design optimization system based on a hybrid element heuristic algorithm of this invention has a compact structure and stable performance, and can stably execute the precast beam design optimization method based on a hybrid element heuristic algorithm of this invention, further improving the overall applicability and practical application capability of this invention.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the present invention.

Claims

1. A precast beam design optimization method based on a hybrid meta-heuristic algorithm, characterized in that, Includes the following steps: By processing the original design parameter data through knowledge embedding, the comprehensive characteristics of geometric materials are obtained; Coding and standardizing constraints yields constraint compliance characteristics, while analyzing construction progress data reveals the impact characteristics on the construction period. Based on a multi-criteria decision-making weighting strategy, a comprehensive priority feature is obtained by utilizing the comprehensive characteristics of the geometric materials, the constraint compliance features, and the project duration impact features. By leveraging weighted knowledge fusion of manufacturability features and case analogy features, manufacturing case-inspired features are obtained; Combining the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, the multi-objective design optimization of precast beams is completed based on the hybrid element heuristic framework.

2. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The process of processing the original design parameter data through knowledge embedding to obtain the comprehensive characteristics of geometric materials includes the following steps: The original parameters are accurately classified according to the functional attributes of the project to obtain a structured parameter set after classification, which includes parameter category, value range, data source and integrity identifier; Construct precast beam engineering knowledge rules, embed these rules into the structured parameter set, and obtain comprehensive geometric material characteristics.

3. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The coding specification constraints obtain constraint compliance characteristics, including the following steps: The specification clauses are parsed in a structured manner to obtain a set of structured specification constraints; Based on the element type quantification coding constraint index of the structured norm constraint set, constraint compliance features are extracted using the coded constraint index.

4. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The analysis of construction progress data to obtain characteristics affecting the construction period includes the following steps: Break down the time nodes of the entire life cycle of precast beams to obtain a schedule node breakdown table; Based on the aforementioned schedule node decomposition table, the time-influencing factors are quantified to obtain the schedule influencing factor quantification matrix. The total project duration throughout the entire lifecycle is calculated by combining the project duration node decomposition table and the project duration influencing factor quantification matrix, and project duration impact characteristics are generated.

5. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The multi-criteria decision-making weighting strategy, which utilizes the comprehensive characteristics of geometric materials, the constraint compliance characteristics, and the schedule impact characteristics to obtain comprehensive priority characteristics, includes the following steps: Construct a multi-criteria evaluation system and obtain a multi-criteria evaluation index set; A hybrid weighting model is established by combining subjective weighting using the analytic hierarchy process (AHP) and objective weighting using the entropy weighting method. Based on the comprehensive characteristics of the geometric materials, the constraint compliance characteristics, and the project duration impact characteristics, the comprehensive priority characteristics are obtained by using the multi-criteria evaluation index set and the hybrid weighting model.

6. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The method of using weighted knowledge fusion to obtain manufacturing case-inspired features by fusing manufacturability features and case analogy features includes the following steps: A dynamic weight set is obtained by assigning feature weights based on the difficulty of precast beam production and the similarity of cases. Based on the identification of manufacturability bottlenecks and the matching of advantageous solutions for similar cases, the dynamic weight set is used to obtain a manufacturing case feature set. Heuristic rules are extracted from the feature set of manufacturing cases, and heuristic feature vectors of manufacturing cases are obtained through the heuristic rules.

7. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 6, characterized in that, Extracting the manufacturability features includes the following steps: Identify bottlenecks in the production process and obtain the bottleneck constraint set. Based on the aforementioned process bottleneck constraint set, the process adaptability parameters are modified to obtain the geometric material feature set after process modification. The manufacturability features are extracted using the geometric material feature set after process modification.

8. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 6, characterized in that, Extracting the analogy features of the cases includes the following steps: A multi-dimensional similarity measurement model was constructed based on the current design requirements of precast beams to obtain a case similarity score matrix; Based on the case similarity score matrix, a set of similar cases is selected, and case analogy features are generated using the set of similar cases.

9. The precast beam design optimization method based on a hybrid meta-heuristic algorithm according to claim 1, characterized in that, The multi-objective design optimization of precast beams is completed based on the hybrid meta-heuristic framework, which combines the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, including the following steps: Build a hybrid metaheuristic framework; By combining the performance approximation model features, the comprehensive priority features, and the manufacturing case heuristic features, a multi-objective optimization objective function is established. Based on the hybrid meta-heuristic framework and the multi-objective optimization objective function, the multi-objective design optimization of precast beams is completed.

10. A precast beam design optimization system based on a hybrid meta-heuristic algorithm, characterized in that, The precast beam design optimization system based on the hybrid element heuristic algorithm includes: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory stores program instructions, which are used to execute the precast beam design optimization method based on the hybrid element heuristic algorithm according to any one of claims 1-9.

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