Intelligent low-carbon structure design method based on double-layer inverse optimization and carbon emission path generation

Abstract

The intelligent low-carbon structure design method based on double-layer inverse optimization and carbon emission path generation comprises the following steps: 1, constructing a carbon emission accounting function to generate a carbon emission path; 2, generating a target carbon emission path through a path generator; 3, a double-layer inverse optimization model is established, the upper layer takes carbon emission path matching as a target, the lower layer restrains structural performance and construction feasibility, and a differentiable KKT or ADMM is adopted for iterative solution and outputting an optimal design variable vector; 4, sampling in a design space, calculating a path deviation and a path error threshold, judging a reachable area, obtaining a path reachable domain and reachable degree, and generating a reachable domain map; 5, updating the path generator parameters and the regular weight through the average reachability, and returning to the steps S2-S4 in a closed loop manner until a closed loop termination condition is met; and 6, outputting an optimal variable, a consistency index, a reachable domain map and a variable sensitivity sequence, and forming an emission reduction project suggestion. According to the invention, reverse design of path-level dynamic carbon control and target driving is realized, the self-adaption is strong, and the integration is easy.

Description

Technical Field

[0001] This invention belongs to the technical field of structural engineering and intelligent optimization design, specifically relating to an intelligent low-carbon structural design method based on bilayer inverse optimization and carbon emission path generation. Background Technology

[0002] With the continuous advancement of the "dual carbon" goals, the field of structural engineering widely adopts the Life Cycle Assessment (LCA) method to quantify carbon emissions during material production, construction, operation, maintenance, and demolition, and incorporates carbon emission indicators into the structural optimization design process. Existing low-carbon structural designs often aim to minimize total life-cycle carbon emissions or unit performance carbon emissions, balancing performance indicators such as strength, stiffness, and stability through multi-objective optimization or weighted summation methods. While these methods can reduce structural carbon emissions to some extent, their optimization objectives are usually static scalars, making it difficult to characterize the dynamic changes in carbon emissions as the design process unfolds, and also unable to deduce feasible design parameter sets from the target carbon emission trajectory.

[0003] Current research mainly includes the following categories:

[0004] (1) Multi-objective optimization method: Simultaneously optimize indicators such as carbon emissions, cost, and quality through metaheuristic algorithms, output static optimal solution set, but lacks time series description of carbon emission path;

[0005] (2) Carbon budget constraint method based on LCA: It incorporates carbon quotas or caps into the design process, emphasizes threshold control rather than path control, and cannot establish a mapping relationship between carbon emission trajectory and design variable evolution;

[0006] (3) Forward bilayer or hierarchical optimization method: Although a bilayer structure is adopted, it still mainly relies on forward calculation starting from the design variables, and no mechanism is established to solve the design parameters from the target carbon trajectory in reverse.

[0007] (4) Data-driven and proxy model approach: Machine learning is used to predict the relationship between “design variables and carbon emissions” to accelerate optimization, but it is still limited to forward response approximation and lacks target path inversion and closed-loop learning mechanism;

[0008] (5) Emission reduction optimization methods during construction and operation and maintenance phases: phased emission reduction is achieved through construction scheduling, transportation and energy dispatch, but the focus is on process management and the impact on structural design variables is limited.

[0009] In summary, while existing low-carbon design methods can reduce carbon emissions overall, they still have the following main problems:

[0010] Lack of carbon emission path modeling capabilities: It is impossible to describe carbon emissions as a trajectory function that changes over time or stages, and it cannot express complex features such as "high at first and then low", "segmented decay", and "dynamic constraint triggering".

[0011] The lack of a reverse mapping mechanism from the target trajectory to the design parameters makes it difficult to answer the key question of "given the target carbon trajectory, which combinations of design parameters are achievable", resulting in insufficient interpretability of the design space.

[0012] Lack of path reachability theory and quantitative indicators: There is no definition of "zero-carbon path reachability" or accessibility assessment method, making it impossible to determine whether the target trajectory is achievable or the gap between it and the achievable state;

[0013] Insufficient convergence efficiency and globality: Existing multi-objective search methods tend to converge prematurely in high-dimensional spaces and are not sensitive to path shape and stage strategy.

[0014] Lack of a closed-loop mechanism for generation, solution, and evaluation: Existing data-driven models are mostly offline unidirectional processes, which cannot realize dynamic interaction between path generation, inverse optimization and inversion, and result evaluation;

[0015] Insufficient system integration: Path setting, optimization solution and result evaluation are mostly implemented independently, lacking a unified architecture and standardized interfaces, which limits the engineering promotion of the method.

[0016] Therefore, existing low-carbon structural design methods cannot achieve dynamic modeling and control of carbon emission paths, and lack the theory and methods for solving design parameters from the target path and quantitatively evaluating path accessibility. There is an urgent need for a systematic low-carbon structural design technology solution with carbon emission paths as the core and inverse optimization and closed-loop adaptive learning capabilities, so as to achieve path-level control and accessibility determination of carbon emissions throughout the entire life cycle of the structure. Summary of the Invention

[0017] To address the problems existing in the prior art, this invention provides an intelligent low-carbon structural design method based on bilayer inverse optimization and carbon emission path generation. The purpose is to use the target carbon emission path to reverse-engineer structural design parameters that are both safe and low-carbon, thereby achieving dynamic, controllable, and explainable optimization of carbon emissions throughout the entire life cycle.

[0018] To achieve the above objectives, the specific solution of the present invention is as follows:

[0019] The intelligent low-carbon structure design method based on bi-layer inverse optimization and carbon emission path generation includes the following steps:

[0020] S1. Construct a design variable lifecycle coupling model: The parameter sets corresponding to material, geometric, and construction elements are defined as design variable vectors. Minimum and maximum value boundaries are set for each variable. The entire structural lifecycle is divided into no fewer than 7 stages. A stage carbon emission calculation function is established for each stage. The stage carbon emission calculation function takes the design variable vector as input and obtains the carbon emission amount for that stage. The carbon emission amounts of all stages are combined to derive the carbon emission path. Performance and construction constraint functions are set, with the structural response variables as input to the constraint functions.

[0021] S2, Generate target carbon emission path: Generate target carbon emission path that satisfies stage decay constraint and smoothness penalty term through path generator function;

[0022] S3, Establishing and solving a two-layer inverse optimization model: A two-layer inverse optimization model is established based on the target carbon emission path described in S2. The upper-layer optimization model uses the sum of path deviation metric, complexity regularization term, and path smoothing penalty term as the overall objective function. The lower-layer optimization model uses the design variable vector as the optimization variable and forms a subordinate objective function under performance and construction constraints. The optimal conditions of the lower-layer optimization model are embedded into the upper and lower-layer optimization models using the differentiable KKT method, or the ADMM method is used to iterate alternately between the variables of the upper-layer optimization model and the response variables of the lower-layer optimization model until the convergence condition is met, and the optimal design variable vector matching the target carbon emission path is output.

[0023] S4, Calculate the path reachability domain and generate a reachability domain map: Sample the design variable vector in the design space, calculate the path deviation between the actual carbon emission path of the sample and the target carbon emission path obtained in S2, determine the reachable area based on the path error threshold, obtain the path reachability domain and reachability, and generate a reachability domain map.

[0024] S5, Closed-loop adaptive optimization: Update the path generator parameters and regularization weights by average reachability until the closed-loop termination condition is met. Otherwise, return to S2 with the updated path generator parameters and regularization weights to regenerate the target carbon emission path and execute S3 to S4 sequentially to form a closed loop.

[0025] S6, Output Results and Engineering Evaluation: Output the optimal design variable vector obtained in S3 and its actual carbon emission path, calculate the consistency index between the actual carbon emission path and the target carbon emission path in S2; output the reachability map generated in S4, and calculate the sensitivity of each design variable based on the S4 sample, and sort them by sensitivity to form emission reduction engineering recommendations.

[0026] Furthermore, the carbon emission accounting function for stage S1 is as follows:

[0027] (4),

[0028] In the formula: This represents the carbon emissions in stage t. The function represents the carbon emission accounting function for a given stage; x represents the set of design variables. This represents the set of stage parameters, including the material unit carbon emission factor. Transportation distance Construction equipment power Equipment working time Energy emission coefficient ; Indicates carbon emissions from material production; Indicates carbon emissions during the transportation phase; Indicates carbon emissions during the construction process; Indicates carbon emissions from operation and maintenance; This indicates the recycling and offsetting of carbon emissions;

[0029] The combined carbon emissions from all stages yield carbon emission path c:

[0030] (5),

[0031] In the formula, T represents the total number of stages minus 1, usually taken as 7–11, corresponding to the stages of materials, transportation, construction, operation, and demolition;

[0032] The performance and construction constraint functions are as follows:

[0033] , (6),

[0034] In the formula: Indicates the first The term constraint function; x represents the set of design variables; Represents structural response variables, including stress. Displacement Buckling coefficient and frequency ; m represents the total number of constraints.

[0035] Furthermore, the path generator function described in S2 is as follows:

[0036] (10)

[0037] In the formula: Indicates the target carbon emission path; This represents a path generator function; These represent the path generator parameters, i.e., spline coefficients or neural network weights; To represent the disturbance variable, usually , used to generate different schemes; This represents the set of path constraint parameters, including the stage upper limit. Net zero node Peak window and smoothing parameters;

[0038] Stage decay constraint:

[0039] (11),

[0040] In the formula: This represents the target carbon emissions of the target carbon emission path at stage t+1. This represents the stage decay coefficient, with a typical value of 0.7-0.95; This represents the target carbon emissions for the target carbon emission pathway at stage t. Indicates the allowable deviation for the stage, with typical values. ;

[0041] Smoothness penalty:

[0042] (12),

[0043] In the formula, This represents the smoothness penalty term for the target carbon emission path; This represents the target carbon emission amount for the target carbon emission path in stage t-1.

[0044] Furthermore, the formula for the upper-level optimization model described in S3 is as follows:

[0045] (13)

[0046] In the formula: Represent the overall objective function; c(x) represents the path deviation measurement function; c(x) represents the actual carbon emission path function determined by the design variable vector x. Indicates the target carbon emission path; Regularization terms indicating design complexity or cost; This represents the path smoothing penalty term; , >0: Weighting coefficient (taken as 1×10) -3 –1×10 -1 );

[0047] The formula for the path deviation metric is as follows:

[0048] (14)

[0049] In the formula: D represents the path deviation metric; This indicates the stage weight, i.e., 1.5–3.0 for the construction stage and 0.8–1.5 for the operation stage; Indicates the actual carbon emission value; Indicates the target carbon emission value;

[0050] The formula for the complexity regularization term is as follows:

[0051] (15)

[0052] In the formula: Regularization terms indicating complexity; Indicates the first Material density; Indicates the corresponding volume;

[0053] The formula for the lower-level optimization model is as follows:

[0054] (16)

[0055] (17)

[0056] exist Under the constraints, find the optimal response variable. ;

[0057] In the formula: This represents the subordinate objective function, namely, construction energy consumption / construction period; The function represents the performance constraint; x represents the set of design variables. Indicates a dependent response variable;

[0058] The convergence condition is formulated as follows:

[0059] , (18)

[0060] In the formula, J （k+1） J represents the total objective function value obtained in the (k+1)th iteration; (k) This represents the total objective function value obtained in the k-th iteration; Represents all constraint functions The maximum amount of constraint violation in the code is defined as the amount of constraint failure. When the amount of failure is less than or equal to zero, it means that all constraints have been satisfied. Indicates the index of the constraint function; Indicates the iteration count index.

[0061] Furthermore, the formula for calculating the path deviation mentioned in S4 is as follows:

[0062] , (19)

[0063] In the formula: D i Indicates path deviation; This represents the actual carbon emission path obtained from the design variables of the i-th sample group. With the target carbon emission pathway The path deviation metric between them; Indicates the actual carbon emission path of the sample; Indicates the target carbon emission path; Indicates the first Group sample design variables; This indicates the sample size, ranging from 200 to 2000.

[0064] The formula for the reachable region is as follows:

[0065] (20)

[0066] In the formula: This represents a set of designs that can achieve the target path; This represents the path error threshold, taken as 1×10. -2 –5×10 -3 ;

[0067] The formula for reachability is as follows:

[0068] (twenty one),

[0069] In the formula: This indicates reachability; a larger value indicates that the path is closer to the target path. Indicates the actual carbon emission pathway Target carbon emission pathway Path deviation measurement between; This represents the maximum bias in the sample set.

[0070] Furthermore, the formulas for updating the path generator parameters and the regularization weights as described in S5 are as follows:

[0071] (twenty two),

[0072] (twenty three),

[0073] In the formula: Indicates the first Next iteration generator parameters; Represents the learning rate (10) -4 -10 -2 ); Indicates the regularization weight; Indicates the step size; Indicates average reachability;

[0074] The formula for the closed-loop termination condition is as follows:

[0075] (twenty four),

[0076] In the formula, the threshold x is the current design variable vector; c(x) is its actual carbon emission path; c * The target carbon emission path; when this condition is met or the improvement amount is less than 10 for M=10 consecutive times. -3 When the closed loop terminates, the loop is closed.

[0077] Furthermore, the consistency metrics described in S6 are as follows:

[0078] (25),

[0079] In the formula: Indicates consistency index; Represents the optimal design variables; This represents the actual carbon emissions obtained from the optimal design variables at time t; This represents the target carbon emission value at time t; This represents the target carbon emission value at time t; This represents the actual carbon emission path function corresponding to the optimal design variables; Indexes representing time or lifecycle stages; This indicates taking the maximum value over the entire time interval;

[0080] The formula for the sensitivity of the design variable is as follows:

[0081]

[0082] In the formula, This represents the sensitivity of the j-th design variable to the consistency index; This represents the partial derivative of the consistency index with respect to the j-th optimal design variable; Represents the j-th optimal design variable; Indicates consistency index; Indicates the design variable index.

[0083] A computer program product comprising a storage medium and computer-readable instructions stored on the medium, which, when executed by a computer, implement the method described.

[0084] Advantages of the present invention

[0085] Compared with existing low-carbon structural design technologies, this invention achieves the following significant technical effects:

[0086] 1. Controllable carbon emissions in stages: The carbon emissions of the structure's life cycle are discretized into several stages of carbon emissions, and corresponding target carbon emission paths are generated, so that the carbon emissions of each stage can be preset and limited, thereby solving the shortcomings of existing technologies that can only control the total amount and cannot control the stage carbon peak and decay process.

[0087] 2. Inverse solution of design variables: A two-layer inverse optimization model is established with the target carbon emission path as input and design variables as output. The combination of design variables that satisfies the minimum path deviation and simultaneously meets the structural performance and construction constraints is obtained in one inverse process, avoiding the inefficiency and uncertainty caused by traditional forward trial calculation.

[0088] 3. Quantitative determination of target reachability: By sampling design variables and calculating the deviation between the actual carbon emission path and the target carbon emission path, the path reachability domain and reachability are formed. The feasibility of the target trajectory can be determined in the early stage of design, preventing the blind setting of targets.

[0089] 4. Closed-loop adaptive optimization: The path generator parameters and regularization weights are automatically updated using average reachability feedback, forming a closed-loop iteration of generation, solution, evaluation and feedback. When external carbon emission factors or process conditions change, it can continue to converge without remodeling.

[0090] 5. Hybrid variable collaborative optimization: Simultaneously handle continuous and discrete variables within the same optimization framework to achieve synchronous solution of material, geometric, and construction scheme parameters, ensuring that the optimization results directly meet the requirements of engineering procurement and construction.

[0091] 6. Parallel satisfaction of multiple constraints: During the optimization process, carbon emission path deviation and structural strength, stiffness, stability, fatigue, comfort and construction sequence constraints are considered simultaneously to achieve a parallel balance between carbon reduction and structural safety, avoiding post-correction.

[0092] 7. Results are interpretable and integrable: Outputs optimal design variables, actual carbon emission paths, consistency indicators, reachability maps, and variable sensitivity rankings. All parameters have clear physical meanings and can be directly embedded into existing BIM, finite element, or green certification platforms to achieve data sharing and multi-disciplinary collaboration.

[0093] In summary, this invention, through the synergistic effects of carbon emission path stage modeling, bi-layer inverse optimization, reachability domain determination, and closed-loop adaptive design, elevates low-carbon structural design from "post-hoc minimum total amount" to "pre-hoc path controllability, parameter reversibility, and target reachability determination." It achieves significant progress in carbon emission control accuracy, design efficiency, target reliability, and engineering applicability. It effectively solves the core problems of "uncontrollable carbon emission paths, irreversible design parameters, and inability to determine target reachability" in existing technologies, and is applicable to the full life-cycle low-carbon optimization design of engineering structures such as buildings, bridges, and aviation. Attached Figure Description

[0094] Figure 1 This is a flowchart of the structural design method based on life cycle carbon emission modeling and bi-layer inverse optimization of the present invention.

[0095] Figure 2 for Figure 1 The closed-loop adaptive optimization logic block diagram for step 5. Detailed Implementation

[0096] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0097] like Figure 1 As shown in the figure, the intelligent low-carbon structure design method based on two-layer inverse optimization and carbon emission path generation provided in this specific embodiment includes the following steps:

[0098] S1. Construct a design variable lifecycle coupling model: The parameter sets corresponding to material, geometric, and construction elements are defined as design variable vectors. Minimum and maximum value boundaries are set for each variable. The entire structural lifecycle is divided into at least seven stages. A stage carbon emission calculation function is established for each stage. This stage carbon emission calculation function takes the design variable vector as input and obtains the carbon emission amount for that stage. The carbon emission amounts from all stages are combined to derive the carbon emission path. Performance and construction constraint functions are set, with the structural response variables as input to these constraint functions. Specific steps are as follows:

[0099] (1) Design variable vector construction

[0100] During the structural design phase, the design variable vector is first defined by the parameter set corresponding to material, geometric, and construction elements, as shown in the following formula:

[0101] (1),

[0102] In the formula: Represents the set of design variables; Indicates the first Each design parameter can be a continuous variable, such as the cross-sectional area of ​​a component. Or discrete variables, such as material grade or construction plan number; This indicates the total number of design variables.

[0103] Feasible range for each variable:

[0104] (2),

[0105] In the formula, , These represent the minimum and maximum values ​​of the variables. These variables determine the structural performance and carbon emission levels, and are the basic inputs for subsequent optimization solutions.

[0106] (2) Life cycle stage discrete

[0107] To characterize the entire process of a structure from material production to recycling, the lifecycle is discretized into... Stages:

[0108] (3),

[0109] In the formula: Represents the stage index, rounded to an integer; This indicates the total number of stages minus 1, typically ranging from 7 to 11, corresponding to stages such as materials, transportation, construction, operation, and demolition.

[0110] This discretization method allows carbon emissions to be modeled as they change over time, laying the foundation for the generation of subsequent "carbon emission paths".

[0111] (4) The carbon emission accounting function for the aforementioned stage is as follows:

[0112] (4),

[0113] In the formula: This represents the carbon emissions in stage t. The function represents the carbon emission accounting function for a given stage; x represents the set of design variables. This represents the set of stage parameters, including the material unit carbon emission factor. Transportation distance Construction equipment power Equipment working time Energy emission coefficient ; Indicates carbon emissions from material production; Indicates carbon emissions during the transportation phase; Indicates carbon emissions during the construction process; Indicates carbon emissions from operation and maintenance; This indicates the recycling and offsetting of carbon emissions;

[0114] The carbon emission accounting function at this stage maps structural parameters to staged carbon emissions, providing a data foundation for path generation.

[0115] The combined carbon emissions from all stages yield carbon emission path c:

[0116] (5),

[0117] In the formula, T represents the total number of stages minus 1, usually taken as 7–11, corresponding to the stages of materials, transportation, construction, operation, and demolition;

[0118] (5) Performance and construction constraints

[0119] To ensure mechanical safety and construction feasibility, the constraint functions for performance and construction are as follows:

[0120] , (6),

[0121] In the formula: Indicates the first The term constraint function; x represents the set of design variables; Represents structural response variables, including stress. Displacement Buckling coefficient and frequency ; m represents the total number of constraints.

[0122] Typical constraint example:

[0123] Strength constraints: (7),

[0124] Stiffness constraints: (8),

[0125] Stability constraints: (9),

[0126] This step establishes a structural model that can both calculate carbon emissions and verify performance, providing physical support for the next step of generating the target path.

[0127] S2, Generate target carbon emission path: In order to achieve a controllable emission reduction trajectory, a target carbon emission path that satisfies the stage decay constraint and smoothness penalty term is generated through the path generator function.

[0128] The path generator function is as follows:

[0129] (10)

[0130] In the formula: Indicates the target carbon emission path; This represents a path generator function; These represent the path generator parameters, i.e., spline coefficients or neural network weights; To represent the disturbance variable, usually , used to generate different schemes; This represents the set of path constraint parameters, including the stage upper limit. Net zero node Peak window and smoothing parameters;

[0131] Stage decay constraint:

[0132] (11),

[0133] In the formula: This represents the target carbon emissions of the target carbon emission path at stage t+1. This represents the stage decay coefficient (typical value 0.7-0.95). This represents the target carbon emissions for the target carbon emission pathway at stage t. Indicates the allowable deviation for the stage (typical value) );

[0134] The smoothness penalty term is used to control the continuity of the carbon trajectory change, and the formula is as follows:

[0135] (12),

[0136] In the formula, This represents the smoothness penalty term for the target carbon emission path; This represents the target carbon emission amount for the target carbon emission path in stage t-1.

[0137] This step establishes the target carbon emission path, which is equivalent to setting a dynamic emission reduction target curve for the structural design, such as the carbon peak during construction, the decrease during operation, and the final net zero point.

[0138] S3, Establishing and Solving a Two-Layer Inverse Optimization Model: A two-layer inverse optimization model is established based on the target carbon emission path described in S2. The upper-layer optimization model uses the sum of path deviation metric, complexity regularization term, and path smoothing penalty term as the overall objective function. The lower-layer optimization model uses the design variable vector as the optimization variables and forms a subordinate objective function under performance and construction constraints. The optimal conditions of the lower-layer optimization model are embedded into the upper and lower-layer optimization models using the differentiable KKT method, or the ADMM method is used to iterate alternately between the variables of the upper-layer optimization model and the response variables of the lower-layer optimization model until the convergence condition is met. The optimal design variable vector matching the target carbon emission path is output. Details are as follows:

[0139] Under the constraint of ensuring structural performance, from the target carbon emission path Inverse solution of design variables The entire solution framework has a two-layer structure: the upper-layer optimization model is responsible for path matching, and the lower-layer optimization model is responsible for performance feasibility.

[0140] (1) The formula for the upper-level optimization model is as follows:

[0141] (13)

[0142] In the formula: Represent the overall objective function; c(x) represents the path deviation measurement function; c(x) represents the actual carbon emission path function determined by the design variable vector x. Indicates the target carbon emission path; Regularization terms indicating design complexity or cost; This represents the path smoothing penalty term; , >0: Weighting coefficient (taken as 1×10) -3–1×10 -1 );

[0143] (2) The formula for the path deviation metric is as follows:

[0144] (14)

[0145] In the formula: D represents the path deviation metric; This indicates the stage weight, i.e., 1.5–3.0 for the construction stage and 0.8–1.5 for the operation stage; Indicates the actual carbon emission value; Indicates the target carbon emission value;

[0146] The formula for the complexity regularization term is as follows:

[0147] (15)

[0148] In the formula: Regularization terms indicating complexity; Indicates the first Material density; Indicates the corresponding volume;

[0149] (3) The formula for the lower-level optimization model is as follows:

[0150] (16)

[0151] (17)

[0152] exist Under the constraints, find the optimal response variable. .

[0153] In the formula: This represents the subordinate objective function, namely, construction energy consumption / construction period; The function represents the performance constraint; x represents the set of design variables. Indicates a dependent response variable;

[0154] (4) Solution method and convergence conditions

[0155] The solution can be obtained using the differentiable KKT method or the ADMM method:

[0156] Differentiable KKT method: Transforms the lower-level optimal conditions into upper-level penalty terms, making the entire problem solvable by gradient;

[0157] Differentiable KKT methods embed lower-level KKT conditions into upper-level conditions;

[0158] ADMM method: In , Alternating updates, introducing Lagrange multipliers .

[0159] The convergence condition is formulated as follows:

[0160] , (18)

[0161] In the formula, J （k+1） J represents the total objective function value obtained in the (k+1)th iteration; (k) This represents the total objective function value obtained in the k-th iteration; Represents all constraint functions The maximum amount of constraint violation in the code is defined as the amount of constraint failure. When the amount of failure is less than or equal to zero, it means that all constraints have been satisfied. Indicates the index of the constraint function; Indicates the iteration count index.

[0162] Take after satisfaction This is a feasible solution.

[0163] In engineering, this step yields the optimal set of parameters that satisfies both structural safety and emission reduction pathways, and can be considered the "reverse design" stage.

[0164] S4, Calculate the path reachability domain and generate a reachability domain map: In order to determine the feasibility of the target trajectory, the design variable vector is sampled in the design space, the path deviation between the actual carbon emission path of the sample and the target carbon emission path obtained in S2 is calculated, the reachable area is determined by the path error threshold, the path reachability domain and reachability are obtained, and a reachability domain map is generated.

[0165] The formula for calculating the path deviation is as follows:

[0166] , (19)

[0167] In the formula: D i Indicates path deviation; This represents the actual carbon emission path obtained from the design variables of the i-th sample group. With the target carbon emission pathway The path deviation metric between them; Indicates the actual carbon emission path of the sample; Indicates the target carbon emission path; Indicates the first Group sample design variables; This indicates the sample size, ranging from 200 to 2000.

[0168] The formula for the reachable region is as follows:

[0169] (20)

[0170] In the formula: This represents a set of designs that can achieve the target path; This represents the path error threshold, taken as 1×10. -2 –5×10 -3 ;

[0171] The formula for reachability is as follows:

[0172] (twenty one),

[0173] In the formula: This indicates reachability; a larger value indicates that the path is closer to the target path. Indicates the actual carbon emission pathway Target carbon emission pathway Path deviation measurement between; This represents the maximum bias in the sample set.

[0174] The reachability domain reflects whether the target trajectory can be achieved, and the map shows the area of ​​influence of different parameters on the reachability of the target.

[0175] S5, Closed-Loop Adaptive Optimization: Update the path generator parameters and regularization weights using average reachability until the closed-loop termination condition is met. If the termination condition is not met, return to S2 with the updated path generator parameters and regularization weights to regenerate the target carbon emission path and sequentially execute S3 to S4, forming an adaptive closed-loop optimization process; Figure 2 As shown.

[0176] The formulas for the updated path generator parameters and regularization weights are as follows:

[0177] (twenty two),

[0178] (twenty three),

[0179] In the formula: Indicates the first Next iteration generator parameters; Represents the learning rate (10) -4 -10 -2 ); Indicates the regularization weight; Indicates the step size; Indicates average reachability;

[0180] The formula for the closed-loop termination condition is as follows:

[0181] (twenty four),

[0182] In the formula, the threshold x is the current design variable vector; c(x) is its actual carbon emission path; c * The target carbon emission path; when this condition is met or the improvement amount is less than 10 for M=10 consecutive times. -3 When the closed loop terminates, the loop is closed.

[0183] If the target carbon emission path is not achieved, return to S2 with the updated path generator parameters and regularization weights to regenerate the target carbon emission path and execute S3 to S4 sequentially to form an adaptive closed loop.

[0184] This mechanism can automatically adjust the path difficulty and weight, giving the algorithm self-learning ability and higher robustness.

[0185] S6, Output Results and Engineering Evaluation: Output the optimal design variable vector obtained in S3 and its actual carbon emission path, calculate the consistency index between the actual carbon emission path and the target carbon emission path in S2; output the reachability map generated in S4, and calculate the sensitivity of each design variable based on the S4 samples, forming emission reduction engineering recommendations by sorting by sensitivity. Details are as follows:

[0186] (1) Output indicators

[0187] Optimal design variables ;

[0188] Actual path With the target path contrast;

[0189] The consistency metrics are as follows:

[0190] (25),

[0191] In the formula: Indicates consistency index; Represents the optimal design variables; This represents the actual carbon emissions obtained from the optimal design variables at time t; This represents the target carbon emission value at time t; This represents the target carbon emission value at time t; This represents the actual carbon emission path function corresponding to the optimal design variables; Indexes representing time or lifecycle stages; This indicates taking the maximum value over the entire time interval;

[0192] (2) Reachable Domain Map and Sensitivity: Generating Reachable Domain The map identifies the main reachable channels and narrow neck regions; and the sensitivity of each variable is calculated. Sort and identify the parameters that have the greatest impact on carbon emissions.

[0193] The formula for the sensitivity of the design variable is as follows:

[0194]

[0195] In the formula, This represents the sensitivity of the j-th design variable to the consistency index; This represents the partial derivative of the consistency index with respect to the j-th optimal design variable; Represents the j-th optimal design variable; Indicates consistency index; Indicates the design variable index.

[0196] (3) Based on the above results, output specific emission reduction measures in order of sensitivity:

[0197] Construction period: Reduce equipment power Adjusting the duration of work Use low-carbon energy (reduce) )

[0198] Material stage: Increase the recycling rate ;

[0199] Transportation period: Restricted transportation distance ;

[0200] Operational phase: Rearrange the maintenance plan to smooth the carbon peak.

[0201] These outputs not only provide the "best design," but also offer operational suggestions for achieving the path objectives.

[0202] A computer program product comprising a storage medium and computer-readable instructions stored on the medium, which, when executed by a computer, implement the method described.

Claims

1. A smart low-carbon structure design method based on bi-layer inverse optimization and carbon emission path generation, characterized in that, Includes the following steps: S1, Construct a life cycle coupling model for design variables: The parameter set corresponding to material, geometry and construction elements is taken as a design variable vector, and a minimum and maximum value boundary is set for each variable. The entire life cycle of the structure is divided into no less than 7 stages. A stage carbon emission accounting function is established for each stage. The stage carbon emission accounting function takes the design variable vector as input and obtains the carbon emission of that stage. The carbon emission of all stages is combined to obtain the carbon emission path. Set performance and construction constraint functions, and use structural response variables as inputs to the constraint functions; S2, Generate target carbon emission path: Generate target carbon emission path that satisfies stage decay constraint and smoothness penalty term through path generator function; S3, Establishing and solving a two-layer inverse optimization model: A two-layer inverse optimization model is established based on the target carbon emission path described in S2. The upper-layer optimization model uses the sum of path deviation metric, complexity regularization term, and path smoothing penalty term as the overall objective function. The lower-layer optimization model uses the design variable vector as the optimization variable and forms a subordinate objective function under performance and construction constraints. The optimal conditions of the lower-layer optimization model are embedded into the upper and lower-layer optimization models using the differentiable KKT method, or the ADMM method is used to iterate alternately between the variables of the upper-layer optimization model and the response variables of the lower-layer optimization model until the convergence condition is met, and the optimal design variable vector matching the target carbon emission path is output. S4, Calculate the path reachability domain and generate a reachability domain map: Sample the design variable vector in the design space, calculate the path deviation between the actual carbon emission path of the sample and the target carbon emission path obtained in S2, determine the reachable area based on the path error threshold, obtain the path reachability domain and reachability, and generate a reachability domain map. S5, Closed-loop adaptive optimization: Update the path generator parameters and regularization weights by average reachability until the closed-loop termination condition is met. Otherwise, return to S2 with the updated path generator parameters and regularization weights to regenerate the target carbon emission path and execute S3 to S4 sequentially to form a closed loop. S6, Output Results and Engineering Evaluation: Output the optimal design variable vector obtained in S3 and its actual carbon emission path, calculate the consistency index between the actual carbon emission path and the target carbon emission path in S2; output the reachability map generated in S4, and calculate the sensitivity of each design variable based on the S4 sample, and sort them by sensitivity to form emission reduction engineering recommendations.

2. The method according to claim 1, characterized in that, The carbon emission accounting function for stage S1 is as follows: （4）， In the formula: This represents the carbon emissions in stage t. The function represents the carbon emission accounting function for a given stage; x represents the set of design variables. This represents the set of stage parameters, including the material unit carbon emission factor. Transportation distance Construction equipment power Equipment working time Energy emission coefficient ; Indicates carbon emissions from material production; Indicates carbon emissions during the transportation phase; Indicates carbon emissions during the construction process; Indicates carbon emissions from operation and maintenance; This indicates the recycling and offsetting of carbon emissions; The combined carbon emissions from all stages yield carbon emission path c: （5）， In the formula, T represents the total number of stages minus 1, usually taken as 7–11, corresponding to the stages of materials, transportation, construction, operation, and demolition; The performance and construction constraint functions are as follows: ， （6）， In the formula: Indicates the first The term constraint function; x represents the set of design variables; Represents structural response variables, including stress. Displacement Buckling coefficient and frequency ; m represents the total number of constraints.

3. The method according to claim 1, characterized in that, The path generator function described in S2 is as follows: （10）， In the formula: Indicates the target carbon emission path; This represents a path generator function; These represent the path generator parameters, i.e., spline coefficients or neural network weights; To represent the disturbance variable, usually , used to generate different schemes; This represents the set of path constraint parameters, including the stage upper limit. Net zero node Peak window and smoothing parameters; Stage decay constraint: （11）， In the formula: This represents the target carbon emissions of the target carbon emission path at stage t+1. This represents the stage decay coefficient, with a typical value of 0.7-0.95; This represents the target carbon emissions for the target carbon emission pathway at stage t. Indicates the allowable deviation for the stage, with typical values. ; Smoothness penalty: （12）， In the formula, This represents the smoothness penalty term for the target carbon emission path; This represents the target carbon emission amount for the target carbon emission path in stage t-1.

4. The method according to claim 1, characterized in that, The formula for the upper-level optimization model described in S3 is as follows: （13）， In the formula: Represent the overall objective function; c(x) represents the path deviation measurement function; c(x) represents the actual carbon emission path function determined by the design variable vector x. Indicates the target carbon emission path; Regularization terms indicating design complexity or cost; This represents the path smoothing penalty term; , >0: Weighting coefficient (taken as 1×10) -3 –1×10 -1 ); The formula for the path deviation metric is as follows: （14）， In the formula: D represents the path deviation metric; This indicates the stage weight, i.e., 1.5–3.0 for the construction stage and 0.8–1.5 for the operation stage; Indicates the actual carbon emission value; Indicates the target carbon emission value; The formula for the complexity regularization term is as follows: （15）， In the formula: Regularization terms indicating complexity; Indicates the first Material density; Indicates the corresponding volume; The formula for the lower-level optimization model is as follows: （16）， （17）， exist Under the constraints, find the optimal response variable. ; In the formula: This represents the subordinate objective function, namely, construction energy consumption / construction period; The function represents the performance constraint; x represents the set of design variables. Indicates a dependent response variable; The convergence condition is formulated as follows: ， （18）， In the formula, J （k+1） J represents the total objective function value obtained in the (k+1)th iteration; (k) This represents the total objective function value obtained in the k-th iteration; Represents all constraint functions The maximum amount of constraint violation in the code is defined as the amount of constraint failure. When the amount of failure is less than or equal to zero, it means that all constraints have been satisfied. Indicates the index of the constraint function; Indicates the iteration count index.

5. The method according to claim 1, characterized in that, The formula for calculating the path deviation mentioned in S4 is as follows: ， （19）， In the formula: D i Indicates path deviation; This represents the actual carbon emission path obtained from the design variables of the i-th sample group. With the target carbon emission pathway The path deviation metric between them; Indicates the actual carbon emission path of the sample; Indicates the target carbon emission path; Indicates the first Group sample design variables; This indicates the sample size, ranging from 200 to 2000. The formula for the reachable region is as follows: （20）， In the formula: This represents a set of designs that can achieve the target path; This represents the path error threshold, taken as 1×10. -2 –5×10 -3 ; The formula for reachability is as follows: （21）， In the formula: This indicates reachability; a larger value indicates that the path is closer to the target path. Indicates the actual carbon emission pathway Target carbon emission pathway Path deviation measurement between; This represents the maximum bias in the sample set.

6. The method according to claim 1, characterized in that, The formulas for updating the path generator parameters and regularization weights as described in S5 are as follows: （22）， （23）， In the formula: Indicates the first Next iteration generator parameters; Represents the learning rate (10) -4 -10 -2 ); Indicates the regularization weight; Indicates the step size; Indicates average reachability; The formula for the closed-loop termination condition is as follows: （24）， In the formula, the threshold x is the current design variable vector; c(x) is its actual carbon emission path; c * The target carbon emission path; when this condition is met or the improvement amount is less than 10 for M=10 consecutive times. -3 When the closed loop terminates, the loop is closed.

7. The method according to claim 1, characterized in that, The consistency metrics described in S6 are as follows: （25）， In the formula: Indicates consistency index; Represents the optimal design variables; This represents the actual carbon emissions obtained from the optimal design variables at time t; This represents the target carbon emission value at time t; This represents the target carbon emission value at time t; This represents the actual carbon emission path function corresponding to the optimal design variables; Indexes representing time or lifecycle stages; This indicates taking the maximum value over the entire time interval; The formula for the sensitivity of the design variable is as follows: ， In the formula, This represents the sensitivity of the j-th design variable to the consistency index; This represents the partial derivative of the consistency index with respect to the j-th optimal design variable; Represents the j-th optimal design variable; Indicates consistency index; Indicates the design variable index.

8. A computer program product comprising a storage medium and computer-readable instructions stored on the medium, which, when executed by a computer, implement the method.

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