A multi-objective optimization method for the design of modified asphalt binder composition

Abstract

This invention discloses a multi-objective optimization method for the composition design of modified asphalt binders, relating to the field of road engineering material design technology. The method first obtains multiple sets of material composition and performance data based on indoor experiments to construct a snapshot matrix. Then, singular value decomposition is performed on the snapshot matrix to extract intrinsic orthogonal decomposition bases, and an AdaBoost algorithm is used to construct a reduced-order model that characterizes the nonlinear mapping relationship between material composition and performance. Based on this, a multi-objective optimization mathematical model incorporating performance indicators, cost objectives, and component constraints is established. Finally, a non-dominated sorting genetic algorithm with an elitist strategy is used to solve the model to output the Pareto front, thereby selecting the optimal formulation. This invention effectively solves the problem of balancing softening point, ductility, and cost by replacing traditional massive trial-and-error experiments with a reduced-order model, achieving global optimization of the comprehensive performance of modified asphalt binders.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of road engineering material design, in particular to a multi-objective optimization method for composition design of modified asphalt binder. BACKGROUND

[0002] As the core pavement material of modern transportation infrastructure construction, the road performance of modified asphalt binder directly determines the service life and service level of road engineering. In the process of road construction, the composition design of modified asphalt binder material is the key link to ensure the quality of pavement. The core goal is to scientifically and reasonably determine the ratio of base asphalt and various asphalt modification admixtures, so that the modified asphalt binder formed finally can meet the requirements of strict engineering design specifications and actual service environment in multiple dimensions such as high temperature stability, low temperature crack resistance, construction and workability, and price.

[0003] In the existing engineering practice and material research and development system, the ratio design of modified asphalt binder mainly follows the traditional semi-empirical method or the experimental design method based on statistics, such as orthogonal experimental design or uniform design. The technical personnel usually need to preset several groups of grading schemes and oil-stone ratio gradients according to engineering experience, prepare a large number of physical test pieces in the laboratory environment through entity weighing, mixing, molding and curing processes, then strictly detect the physical and chemical performance indicators of the test pieces according to the standard test procedures, and finally select the best component amount that meets the requirements of various indicators according to the experimental feedback data.

[0004] However, this design mode which relies heavily on physical test greatly reveals obvious limitations in the face of increasingly complex material systems. Since the preparation of test pieces and performance maintenance tests consume a long period and a large amount of raw material resources, the trial-and-error cost of material design is extremely high and inefficient. Under the constraints of limited time and funds, designers can only verify a few points in the vast design space. This screening method based on limited physical samples is difficult to fully capture the complex nonlinear response law between material components and performance, making the research and development cycle of new materials long and difficult to quickly adapt to the increasingly refined and customized needs of material performance in engineering. SUMMARY

[0005] In view of the shortcomings of the prior art, the present application provides a multi-objective optimization method for composition design of modified asphalt binder, which solves the problems of low accuracy, long design cycle and difficult to maximize comprehensive benefits of composition design of modified asphalt binder.

[0006] To achieve the above purpose, the present application is implemented by the following technical scheme: a multi-objective optimization method for composition design of modified asphalt binder, comprising the following steps: Step 1: Data Acquisition and Snapshot Construction: Based on engineering requirements, determine material properties and constraints, develop a plan using experimental design methods, and conduct indoor material tests. Acquire multiple sets of material composition and corresponding performance data, defining each set of material composition and its corresponding performance data as a snapshot.

[0007] Step 2: Model Reduction Construction: Based on the acquired snapshots, a snapshot matrix is ​​constructed. Multiple sets of data are arranged so that each column of the snapshot matrix represents a snapshot, and the minimum value within the matrix corresponds to the material performance index. Singular value decomposition (SVD) is performed on the snapshot matrix, decomposing it into a product of a left singular matrix, a diagonal matrix composed of singular values, and a right singular matrix. Intrinsic orthogonal decomposition basis (EOB) is extracted according to the energy ratio rule, i.e., the ratio of the sum of squares of the first few singular values ​​to the sum of squares of all singular values ​​meets a preset tolerance standard, and a corresponding number of left singular vectors are selected as the EOB. The linear combination of the EOB and the expansion coefficient vector is used to approximate the material performance, establishing a nonlinear mapping relationship between material composition and performance. For unknown material compositions, the AdaBoost algorithm is used to establish a mapping relationship between material components and the expansion coefficient vector, thereby obtaining the coefficient vector corresponding to the new material composition, and combining this with the EOB to predict its performance.

[0008] Step 3: Establishing the Optimization Mathematical Model: Based on the nonlinear mapping relationship determined by the reduced-order model, an optimization mathematical model is constructed, including a set of objective functions and constraints. The set of objective functions consists of multiple single-objective functions that are minimized or maximized, representing the performance or cost indicators to be optimized, respectively. The constraints include performance constraints and component content constraints. Performance constraints limit the material property values ​​predicted by the reduced-order model to be less than or equal to the thresholds required by the design specifications, while component content constraints limit the content of each material component to be within the set upper and lower limits.

[0009] Step 4: Multi-objective solution and optimization: The optimization mathematical model is solved using a non-dominated sorting genetic algorithm with an elitist strategy. The algorithm's population size, maximum number of evaluations, crossover probability, and mutation probability are set. The Pareto front is output, and the final material formulation is selected from the Pareto front based on engineering preferences.

[0010] Furthermore, the modified asphalt binder is a nano-modified asphalt binder; the material components include nano-silica, nano-bentonite, styrene-butadiene rubber (SBR), rubber powder (RP), polyethylene (PE), styrene-butadiene-styrene block copolymer (SBS), and ethylene-vinyl acetate copolymer (EVA), with performance constraints including a viscosity value at 135 degrees Celsius less than a specified limit. The objective function set includes maximizing the softening point temperature, maximizing the ductility value at 5 degrees Celsius, and minimizing the total material price; wherein, minimizing the total material price is defined as the sum of the products of the dosage of all modified materials and their corresponding unit prices.

[0011] This invention provides a multi-objective optimization method for the composition design of modified asphalt binders. It has the following beneficial effects: 1. This invention constructs a reduced-order model based on singular value decomposition and intrinsic orthogonal decomposition basis extraction, uses limited experimental snapshots to capture the complex nonlinear mapping relationship between material composition and performance, and combines the AdaBoost algorithm to predict the performance coefficients of unknown compositions. This avoids the reliance on massive repetitive physical experiments in the traditional design process, thereby significantly shortening the material development cycle while ensuring the accuracy of model prediction, and effectively reducing experimental trial and error costs and resource consumption.

[0012] 2. This invention establishes a multi-objective optimization mathematical model that includes conflicting performance indicators and cost constraints, and uses a non-dominated sorting genetic algorithm with an elitist strategy to solve the model and output a Pareto front solution set. This overcomes the shortcomings of traditional single-objective optimization methods in balancing mutually restrictive attributes such as high-temperature softening point, low-temperature ductility and material cost. It enables designers to flexibly select global non-dominated solutions according to specific engineering priorities, and achieves an effective balance between comprehensive material performance and economic investment.

[0013] 3. This invention uses the energy ratio rule to determine the number of intrinsic orthogonal decomposition bases to effectively retain the key feature information of the original data. It also sets strict component content and performance threshold boundary constraints in the optimization model to ensure that the predicted results of the reduced-order model for material properties are highly consistent with the actual measured values. This ensures that the final optimized modified asphalt binder formulation strictly meets the technical requirements of the design specifications and has high reliability for engineering applications and formulation implementation value. Attached Figure Description

[0014] Figure 1 A schematic diagram illustrating the main components and core processes of a reduced-order model (ROM); Figure 2 Comparison of ROM's predicted and measured results of the performance of nano-modified bitumen binder; Figure 3: Optimal composition determination diagram for modified asphalt binder based on the lowest price standard; Figure 4 Pareto Frontier: Modified Asphalt Binders for Non-Standard D-Conditions Figure 1 ; Figure 5 Pareto Frontier: Modified Asphalt Binders for Non-Standard D-Conditions Figure 2 ; Figure 6 Modified asphalt binder standard D condition Pareto frontier Figure 1 ; Figure 7 Modified asphalt binder standard D condition Pareto frontier Figure 2 ; Figure 8 Details of Determining the Optimal Composition of Modified Asphalt Binder Based on Standard D Figure 1 ; Figure 9 Details of Determining the Optimal Composition of Modified Asphalt Binder Based on Standard D Figure 2 . Detailed Implementation

[0015] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] Please see the appendix Figures 1-9 This invention provides a multi-objective optimization method for the composition design of modified asphalt binders, specifically including: Example 1: Overall architecture of a data-driven multi-objective optimization design system and method for modified asphalt binder; This embodiment describes the overall workflow of a data-driven multi-objective optimization design system and method for modified asphalt binder composition. This method combines indoor experimental data, a reduced-order model (ROM) based on intrinsic orthogonal decomposition (POD), and a non-dominated sorting genetic algorithm with an elitist strategy (NSGA-II) to achieve global optimization of material composition under multiple performance index conflicts.

[0017] The method specifically includes the following steps: S101: Define the material design variables and performance index system Based on the application scenario of road engineering, define the input variables and output response in the material design problem.

[0018] Let the material composition variable be the optimization design variable, denoted as a vector. The material component variable C includes, but is not limited to, the amount of polymer modifiers (such as styrene-butadiene-styrene block copolymer SBS, ethylene-vinyl acetate copolymer EVA, polyethylene PE) or the amount of nanomaterials.

[0019] Material properties are set as optimization objectives or constraints. Based on design requirements, material properties are divided into two categories: one category serves as the objective function (such as maximizing the softening point / ductility, minimizing cost), denoted as a vector. Another type serves as a constraint (e.g., viscosity must be within a specific range at 135℃), denoted as a vector. .

[0020] Determine the value range (upper and lower limits of the design space) of each material component variable and the specific threshold of each constraint condition.

[0021] S102: Sample Data Acquisition Based on Experimental Design Experimental design schemes are planned using experimental design methods (DOE), including orthogonal experimental design, Taguchi method, or full factorial design.

[0022] Material specimens were prepared according to the experimental design and tested indoors to obtain the variables of different material components. The corresponding measured values ​​of material properties.

[0023] Construct a snapshot matrix. The component and performance data pairs obtained from the above experiments are defined as snapshots, and the collection of all snapshot data constitutes the sample database used to train the reduced-order model. For specific specimen preparation and performance testing operations, those skilled in the art can refer to current civil engineering material testing standards and specifications, which are well-known techniques in the field and will not be elaborated upon here.

[0024] S103: Constructing a material property reduction model (ROM) based on POD Using the snapshot matrix obtained in S102, construct a model to characterize the material composition variables. A data-driven model that maps the relationship between materials and their properties.

[0025] This step specifically extracts the basis vectors of the snapshot matrix using intrinsic orthogonal decomposition (POD). Singular value decomposition (SVD) is then used to process the snapshot matrix to obtain orthogonal basis vectors that characterize the main features of the material properties, and material composition variables are established. The numerical relationship between the POD coefficient and the POD coefficient.

[0026] The mathematical expression for the completed order reduction model is: in, This represents the predicted performance data output by the reduced-order model. This model can predict performance based on any input material composition variables without requiring physical experiments. It can quickly calculate the corresponding predicted values ​​of material properties.

[0027] S104: Constructing a Multi-Objective Optimization Mathematical Model Establish a multi-objective optimization mathematical model that includes the objective function, design variables, and constraints.

[0028] Define the objective function vector The performance prediction values ​​corresponding to each optimization objective are calculated using the reduced-order model constructed using S103. The mathematical expression is as follows: In the formula, Indicates the first An objective function based on the predicted values ​​of the reduced-order model (e.g., the first objective is the intensity function, and the second objective is the cost function). This represents the total number of objective functions; This represents the transpose of a vector.

[0029] Define constraints. Set the boundaries of the limited material properties and component variables as inequality constraints or equality constraints: In the formula, The number predicted by the reduced-order model is... One limited material performance index; This represents the design threshold for the performance indicator; Indicates the number of performance constraints; Indicates the first One material composition variable; and They represent the first The lower and upper limits of each material component variable; The dimension of the material composition variable.

[0030] S105: Performing Multi-Objective Optimization and Pareto Front Search The mathematical model in S104 is solved using a non-dominated sorting genetic algorithm with an elitist strategy (NSGA-II).

[0031] The algorithm performs an optimization iterative process. It randomly generates an initial population (i.e., multiple sets of candidate material component variables). In each generation of evolution, the reduced-order model (ROM) in S103 is directly called to calculate the fitness value (i.e., the corresponding objective function value) of each individual in the population. and constraint state ).

[0032] Based on the calculated fitness values, non-dominated ranking and crowding distance are calculated for individuals in the population. Individuals with high non-dominated levels and large crowding distances are retained for the next generation. After multiple iterations and convergence, a set of non-dominated solutions is obtained.

[0033] This set of non-dominated solutions constitutes the Pareto Front. Each solution on the Pareto Front represents a material composition ratio that achieves an optimal trade-off among all objective functions, meaning that it is impossible to improve the performance of one objective without reducing the performance of another.

[0034] S106: Determine the optimal material formulation Output the Pareto front solution set obtained by S105.

[0035] Based on the specific preferences of the actual project (such as cost priority, strength priority, or balance priority), one or more solutions are selected from the Pareto front solution set as the final modified asphalt binder design scheme.

[0036] Example 2: A method for constructing a material property reduction model (ROM) based on intrinsic orthogonal decomposition (POD); This embodiment describes the specific steps for constructing a performance reduction model (ROM) of modified asphalt binder based on intrinsic orthogonal decomposition (POD). The method for constructing the performance reduction model of materials processes laboratory experimental data, extracts the characteristic basis vectors of material properties, and establishes a numerical representation relationship between material component variables and material performance indicators.

[0037] The method for constructing a material property reduction model includes the following steps: S201: Constructing a snapshot matrix of material properties Define the number of material performance indicators as follows For any given material composition The material property data obtained from laboratory tests are defined as a material property vector, denoted as . .

[0038] Select The material property vectors under different material compositions are used as snapshots to capture these properties. The snapshot vectors are arranged as column vectors and assembled to form a snapshot matrix. Snapshot matrix Each column corresponds to a complete material performance test dataset for a specific material composition.

[0039] S202: Perform singular value decomposition of the snapshot matrix. The snapshot matrix constructed in S201 Perform singular value decomposition (SVD) to decompose material property data into a product of singular and diagonal matrices.

[0040] The mathematical expression for singular value decomposition is: In the formula, Represents a snapshot matrix; Represents a snapshot matrix The left singular matrix, whose column vectors form an orthogonal basis for the data space; Represented by the snapshot matrix singular values The diagonal matrix formed; Represents a snapshot matrix The right singular matrix; This represents the matrix transpose symbol.

[0041] S203: Determine the POD basis vectors According to singular values The energy distribution is used to determine the number of POD basis vectors used to characterize the material properties, denoted as . .

[0042] Number of POD basis vectors The selection of must satisfy the energy cutoff criterion, and the calculation formula is: In the formula, Indicates the first One singular value; Indicates the total number of snapshots; This indicates the number of selected POD basis vectors; This indicates the preset tolerance.

[0043] Selecting the left singular matrix The former The column vectors are used as the basis matrix of POD, denoted as: POD basis matrix Low-dimensional orthogonal bases that constitute the material properties.

[0044] S204: Generating Reduced-Order Model Coefficients and Prediction Equations Using the POD basis matrix Calculate the reduced-order model coefficients corresponding to each snapshot and establish the material property prediction equation.

[0045] First, the snapshot data in S201 is projected onto the POD base matrix. In the defined space, obtain the known material composition The corresponding coefficient vector The calculation formula is: In the formula, This represents the POD coefficient vector corresponding to material component p; This represents the transpose of the POD basis matrix; This represents the measured material property vector corresponding to material composition p, and the coefficient vector obtained here. As training data, it is used to establish material composition in conjunction with machine learning algorithms. To coefficient The mapping relationship is used to predict the performance of unknown components.

[0046] Establish the reconstructed and predictive expressions for the material property reduced-order model (ROM): In the formula, This represents the material property characterization (predicted value) output by the reduced-order model. Represents the basis matrix of POD; Indicates corresponding to material composition The coefficient vector, in the multi-objective optimization process, is obtained by inputting the material composition. Predict the corresponding coefficients Then, the multidimensional material performance indicators are calculated using formulas. .

[0047] Example 3: Implementation process of multi-objective optimization (MOO) of material composition based on NSGA-II S301: Variable Encoding and Target Mapping in Configuration Algorithms Based on the mathematical model constructed in step S104 of Example 1, the material design problem is concretized into the solution object of the NSGA-II algorithm, and the algorithm's coding configuration is completed.

[0048] The problem of material proportioning at the physical level is transformed into a mathematical model that can be processed by computer algorithms.

[0049] Encoding is performed by mapping the vector of modified asphalt material components (i.e., the specific dosage of various modifiers) to individual chromosomes in the genetic algorithm. Considering that material dosages in actual engineering are continuously varying values, this embodiment abandons traditional binary encoding and adopts a real-coded mechanism. That is, each gene position on the chromosome is no longer an abstract 0 and 1, but directly represents the actual percentage dosage of a specific material (such as SBS or nanomaterials). This not only avoids the accuracy loss caused by encoding conversion but also greatly improves the efficiency of searching for the optimal material ratio.

[0050] Establish scoring criteria for evaluating the quality of formulas.

[0051] Configure the fitness evaluation interface: Configure the aforementioned material performance objectives (such as maximizing the softening point, minimizing cost, etc.) as the fitness function to evaluate the merits of individual algorithm components. During the algorithm's virtual optimization process, for each new formulation component generated, the reduced-order model (ROM) trained in Example 2 is directly invoked to instantly predict various performance indicators of the formulation. These predicted performance values ​​serve as the "fitness score" of the formulation, which is directly used for subsequent non-dominated ranking (i.e., survival of the fittest) among a massive pool of candidate formulations.

[0052] Set engineering baselines to eliminate substandard formulas.

[0053] Constraint handling rules are set: Technical requirements from actual road engineering specifications (such as viscosity at 135℃ must be less than the specified limit) are set as feasibility judgment criteria for the algorithm. During population initialization and evolution, if the performance predicted by the reduced-order model for a certain formulation exceeds the boundary threshold allowed by the specification, the formulation is directly determined to be an infeasible solution, or it is eliminated by assigning a very large penalty weight during sorting. This mechanism ensures that the final Pareto optimal solution set 100% meets the specifications of actual road engineering and is directly feasible for implementation.

[0054] S302: Initializing Algorithm Parameters and Initial Population Configure the running parameters for the NSGA-II algorithm.

[0055] In this embodiment, the maximum number of evaluations is set to 25,000 to ensure algorithm convergence; the population size is also set. The value is 100, meaning that each generation of the population contains 100 individuals representing different material mixing schemes.

[0056] Set the genetic operator probabilities. Set the crossover probability to 0.9; set the mutation probability to the number of material composition variables. The reciprocal of (i.e.) ).

[0057] An initial population is randomly generated within the range of values ​​for the material composition variables. Initial population Include A randomly generated vector of material composition variables.

[0058] S303: Perform fast non-dominated sorting and crowding distance calculation Fitness assessment and classification of individuals in the population.

[0059] Calculate the objective function value for each individual in the population using the reduced-order model. And the condition that the constraints are met.

[0060] Based on the objective function value, a fast non-dominated sorting is performed on the population. The population is divided into several non-dominated levels, denoted as [levels not specified in the original text]. , ,.....in, The hierarchy is the current set of non-dominated solutions, i.e., Pareto front candidate solutions. Individuals in a hierarchy are not dominated by other individuals in any objective function.

[0061] Calculate the crowding distance. For individuals in the same non-dominated hierarchy, calculate the crowding distance of the individual in the target space. Use the crowding distance to maintain the diversity of solution distribution and avoid the algorithm from converging to a local optimum.

[0062] S304: Perform genetic evolution operations Offspring populations are generated through selection, crossover, and mutation operations.

[0063] Perform the selection operation. Select individuals from the parent population based on non-dominated level and crowding distance. Prioritize individuals with lower non-dominated levels; if two individuals have the same non-dominated level, select the individual with a larger crowding distance.

[0064] Perform crossover and mutation operations. Based on the crossover probability (0.9) and mutation probability (...) set in S302... The selected individuals are subjected to crossover and mutation processes to generate a progeny population. The above operations follow the standard procedure of the NSGA-II algorithm.

[0065] S305: Executing an elite strategy and iterative population updates The process is iterated cyclically according to the maximum number of evaluations (25,000) set in S302. An elitist strategy is implemented, in which the parent and offspring populations are mixed in each generation of evolution, and the mixed population is sorted non-dominated.

[0066] Generate the next generation population. Based on the ranking results, select and retain individuals with high fitness from the mixed population to enter the next generation, ensuring that excellent non-dominated solutions (elites) are not lost in the evolutionary process. This step utilizes the elite retention mechanism of the NSGA-II algorithm to continuously optimize the population structure until the cumulative number of evaluations reaches the preset 25,000 times.

[0067] S306: Output the Pareto optimal solution set After the algorithm terminates, it outputs the non-dominated solution set of the final generation population.

[0068] The non-dominated solution set constitutes the Pareto front in materials design. Each point on the Pareto front corresponds to a specific material composition vector. This represents the material formulation that achieves the optimal trade-off between various objective functions under current constraints. Designers analyze the trade-offs between different performance indicators based on the Pareto front and select the final material formulation according to actual engineering requirements.

[0069] Example 4: Composition Design of Nano-Modified Asphalt Binder This embodiment applies the system and method described in Embodiments 1 to 3 above to perform multi-objective optimization design of the material composition of nano-modified asphalt binder. This embodiment optimizes performance and cost in a complex multi-component system by introducing an economic cost index.

[0070] S401: Determine the material system and design variables The raw material system for the modified asphalt binder was selected. In this embodiment, the selected raw materials include: two types of nanoparticles (nano silica and nano bentonite) and five polymers (styrene-butadiene-styrene block copolymer SBS, ethylene-vinyl acetate copolymer EVA, polyethylene PE, styrene-butadiene rubber SBR, and rubber powder RP). Material component design variables were set, specifying that each modified asphalt binder formulation consists of a composite of two nanoparticles and two polymers. Specific compositional variables include the content of nano silica, the content of nano bentonite, and the content of the two selected polymers.

[0071] S402: Constructing a Reduced-Order Model and Optimizing the Mathematical Model Based on the laboratory test data obtained according to the method described in Example 1, a reduced-order model was constructed. The test data covered three performance indicators: softening point, ductility at 5℃, and viscosity at 135℃, totaling 72 sets of data (64 sets of snapshot data and 8 sets of validation data). The reduced-order model was verified to meet the required accuracy in predicting material properties. The comparison between the predicted results of the reduced-order model and the measured results is as follows: Figure 2 As shown.

[0072] Establish a multi-objective optimization mathematical model. Based on engineering requirements and economic cost considerations, define the objective function and constraints: Objective function: Set as an optimization objective in three dimensions, namely softening point (maximize), 5℃ ductility (maximize), and material price (minimize).

[0073] Material unit price parameters: Nano silica 60 yuan / kg, Nano bentonite 15 yuan / kg, SBS 22 yuan / kg, EVA 15 yuan / kg, SBR 11 yuan / kg, PE 9 yuan / kg, RP 2 yuan / kg.

[0074] Constraints: The viscosity at 135℃ is set as the constraint index, requiring the viscosity value to be less than 3 Pa·s.

[0075] S403: Obtain the Pareto optimal mix ratio Multi-objective optimization was performed, and Pareto fronts were obtained for eight different polymer combination conditions (including nanomaterials + SBS + EVA, nanomaterials + SBS + SBR, etc.). The obtained Pareto fronts characterize the numerical distribution relationship among the three objective functions: softening point, ductility at 5℃, and price. The Pareto front for the non-standard D condition is shown below. Figure 4 As shown, the Pareto front under standard D condition is as follows: Figure 5 As shown in the figure; the coordinate axes f1 represent the softening point, f2 represent the ductility, and f3 represent the price.

[0076] S404: Optimal Solution Decision The Pareto optimal solution set is output, and the Pareto front consists of multiple non-dominant feasible solutions. Designers select the final formulation from the solution set based on engineering objectives. In this embodiment, the selection strategy is as follows: while meeting the softening point and ductility performance requirements, the lowest-priced composition is selected from the Pareto solution set. The optimal composition determination process based on the lowest price criterion is as follows: Figure 3 As shown, the details of determining the optimal composition based on standard D are as follows: Figure 6 As shown.

[0077] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-objective optimization method for the composition design of modified asphalt binders, characterized in that, Includes the following steps: Step 1: Data Acquisition and Snapshot Construction: Based on the engineering requirements, determine the properties and constraints of the modified asphalt binder, use experimental design methods to determine the experimental scheme and conduct indoor material tests, obtain multiple sets of modified asphalt binder composition and corresponding performance data, and define each set of material composition and corresponding performance data as a snapshot; Step 2, Reduced-order model construction: Based on the multiple snapshots obtained in Step 1, a snapshot matrix is ​​constructed. Singular value decomposition is performed on the snapshot matrix to extract intrinsic orthogonal decomposition basis. The intrinsic orthogonal decomposition basis is then used to establish a nonlinear mapping relationship between material composition and material properties, forming a reduced-order model. Step 3: Establishment of the optimization mathematical model: The design of modified asphalt binder is transformed into a multi-objective optimization problem. Based on the nonlinear mapping relationship determined in Step 2, an optimization mathematical model containing a set of objective functions and constraints is constructed. Step 4, Multi-objective solution and optimization: The optimization mathematical model constructed in Step 3 is solved using a non-dominated sorting genetic algorithm with an elitist strategy, the Pareto front is output, and the final material formulation is selected from the Pareto front according to engineering preferences.

2. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 1, characterized in that, In step two, the snapshot matrix is ​​constructed by arranging the multiple sets of data obtained in step one, with each column of the snapshot matrix representing a snapshot, and the minimum value in the snapshot matrix corresponding to a specific indicator of material performance; the reduced-order model is used to capture the characteristics between material composition and performance contained in the snapshot matrix, and to predict the performance of unknown material compositions.

3. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 2, characterized in that, In step two, the process of performing singular value decomposition on the snapshot matrix includes: decomposing the snapshot matrix into a product of a left singular matrix, a diagonal matrix composed of singular values, and a right singular matrix.

4. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 3, characterized in that, In step two, the step of extracting intrinsic orthogonal decomposition basis includes: determining the number of basis using the energy ratio rule, wherein the energy ratio rule is that the ratio of the sum of squares of the first few singular values ​​to the sum of squares of all singular values ​​reaches a preset tolerance standard, and selecting the corresponding number of left singular vectors as intrinsic orthogonal decomposition basis.

5. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 4, characterized in that, In step two, establishing the nonlinear mapping relationship between material composition and material properties includes the following sub-steps: approximating the material properties using a linear combination of intrinsic orthogonal decomposition basis and expansion coefficient vector; for unknown material compositions, establishing a mathematical mapping relationship between material components and the expansion coefficient vector using the AdaBoost algorithm, thereby obtaining the coefficient vector corresponding to the new material composition, and predicting the material properties of the new material composition by combining the intrinsic orthogonal decomposition basis.

6. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 1, characterized in that, In step three, the objective function set consists of multiple single objective functions that need to be minimized or maximized. Each single objective function represents a material performance index or cost index that needs to be optimized. The objective function set is used to evaluate the merits of the material composition vector.

7. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 6, characterized in that, In step three, the constraints include performance constraints and component content constraints; the performance constraints refer to the material property values ​​predicted by the reduced-order model being less than or equal to the thresholds required by the design specifications; the component content constraints refer to the content of each material component being between the set lower and upper limits of content.

8. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 1, characterized in that, In step four, the parameters of the non-dominated sorting genetic algorithm with elite strategy are configured as follows: the population size is set to a fixed value, the maximum number of evaluations is set to a fixed value, the crossover probability is set to a constant value, and the mutation probability is set to the reciprocal of the number of design variables.

9. The multi-objective optimization method for the composition design of modified asphalt binder according to claim 1, characterized in that, The set of objective functions includes: maximizing the softening point temperature, maximizing the ductility at five degrees Celsius, and minimizing the total material price; wherein, the minimized total material price is defined as the sum of the products of the dosage of all modified materials and the corresponding unit price of the modified materials.

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