A multi-objective optimization method and system for the mix proportion of a composite modified asphalt mixture

Abstract

The present invention discloses a multi-objective optimization method for the mix proportion of a composite modified asphalt mixture, including: S1. determining the optimization objective function and constraint conditions of the composite modified asphalt mixture under different application scenarios, and establishing a multi-objective optimization model; S2. collecting and constructing a data set of volume indexes and performance indexes under different mix proportion design parameters; S3. dividing the training sample set and the test sample set, constructing a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, and training and testing it; S4. based on the multi-objective optimization model, selecting a multi-objective particle swarm optimization method to solve the multi-objective optimization optimal solution of the mix proportion of the composite modified asphalt mixture; the system includes a data acquisition module, a Gaussian process regression prediction model, a prediction model training and testing module, a multi-objective optimization model for the mix proportion of the composite modified asphalt mixture, and a multi-objective particle swarm optimization module; which is beneficial to quickly determine the mix proportion optimization scheme of the composite modified asphalt mixture and improve the R & D efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of asphalt pavement material design, and more specifically, to a multi-objective optimization method and system for the mix proportion of composite modified asphalt mixture. Background Art

[0002] Currently, in the face of the current situation of large traffic flow, heavy axle load, fast vehicle speed, and frequent extreme climates in modern transportation, the performance improvement of single modified asphalt pavement materials is limited and it is difficult to meet the requirements of the current traffic situation. The composite modification method can simultaneously possess the advantages of multiple materials and obtain composite modified asphalt mixtures with higher performance.

[0003] However, there is no clear mathematical relationship between the mix proportion parameters of asphalt mixture and the target performance. The traditional mix proportion of composite modified asphalt mixture is determined based on the "trial and error method" with a large sample size, which not only has many steps, a long cycle, and consumes a large amount of resources, but also it is difficult to uncover the internal relationship between the mix proportion parameters and the performance solely by the experimental analysis method.

[0004] Compared with the traditional method for determining the mix proportion of composite modified asphalt mixture, machine learning, as the core strategy of artificial intelligence, integrates artificial intelligence algorithms and optimization algorithms, and has powerful data analysis and prediction capabilities.

[0005] Therefore, in the face of the complex requirements of application scenario differentiation and performance regulation pertinence, how to drive through a small number of data samples, simultaneously study multiple target variables of the mix proportion of composite modified asphalt mixture, and give the global optimal solution of the mix proportion parameters, so as to improve the R & D efficiency of asphalt pavement materials and the level of engineering application is an urgent problem for those skilled in the art to solve. Summary of the Invention

[0006] In view of this, the present invention provides a multi-objective optimization method and system for the mix proportion of composite modified asphalt mixture to solve the problems mentioned in the background art.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A multi-objective optimization method for the mix proportion of composite modified asphalt mixture, comprising the following steps:

[0009] S1. According to the target requirements of asphalt mixture pavement materials and the technical requirements of mix proportion design parameters under different application scenarios, taking the performance indicators of composite modified asphalt mixture as the optimization objectives and the mix proportion design parameters and volume characteristic indicators as the constraint conditions, establish a multi-objective optimization model for the mix proportion of composite modified asphalt mixture;

[0010] S2. Collect and form a volume index data set and a performance index data set of composite modified asphalt mixture under different mix proportion design parameters;

[0011] S3. Randomly divide the volume index dataset and the performance index dataset into a training sample set and a test sample set according to a ratio, construct a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and test the Gaussian process regression prediction model through the test sample set;

[0012] S4. Based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, select the multi-objective particle swarm optimization method to update the search information in the corresponding search space, and find the multi-objective optimization optimal solution of the mix proportion of the composite modified asphalt mixture through the intelligent random search iteration of the swarm.

[0013] Preferably, the performance indexes include high-temperature stability, low-temperature stability, water stability and economy; the volume characteristic indexes include void ratio, stability, flow value, asphalt saturation and voids in mineral aggregate.

[0014] Preferably, the specific content of constructing the Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture in step S3 is: based on Gaussian process regression for modeling, using the squared exponential SE covariance function as the kernel function, corresponding to the Bayesian linear regression model, the SE covariance function of the multi-input variables is:

[0015]

[0016] where x represents the mix proportion design parameter input variable of the training sample set, x′ represents the mix proportion design parameter input variable of the point to be predicted, n represents the dimension of the mix proportion design parameter input variable, s = 1, 2, …, n, the signal variance and the characteristic vector length l of the s-th input variable s are two hyperparameters;

[0017] For the prior distribution of the t-dimensional training sample set output variable observation value y is:

[0018]

[0019] where K(x, x) represents the t×t order symmetric positive definite covariance matrix with the mix proportion design parameters of the training sample set as the input variables, I t is the t-dimensional identity matrix;

[0020] Given the mix proportion design parameter input variable x * of the test sample set, the predicted value f * is obtained through the joint posterior distribution, and the joint distribution between the training sample set output variable observation value y and the predicted value f * based on the test sample set input variable is:

[0021]

[0022] Among them, K(x, x * ), K(x * , x) and K(x * , x * ) are covariance matrices, and K(x, x * ) = K(x * , x) T .

[0023] Preferably, the specific content of testing the Gaussian process regression prediction model through the test sample set in step S3 is: combining cross-validation with the root mean square error RMSE and the square correlation coefficient R 2 as the evaluation indexes for the accuracy of the Gaussian process regression prediction model;

[0024] The root mean square error RMSE is:

[0025]

[0026] The square correlation coefficient R 2 is:

[0027]

[0028] Among them, is the predicted value based on the input variables of the test sample set, y i is the observed value of the output variable based on the training sample set, is the average value of the predicted values based on the input variables of the test sample set, is the average value of the observed values of the output variable based on the training sample set.

[0029] Preferably, the specific content of step S4 is: based on the particle swarm optimization algorithm, randomly initialize the particle swarm, and use the fitness function to evaluate and judge the particle positions, where the particle positions represent the mix proportion design parameters of the composite modified asphalt mixture;

[0030] Specifically: the particle swarm has p particles in the n-dimensional space. At the t-th iteration, the position and velocity of the i-th particle in the j-th dimension are respectively expressed as and The particle velocity represents the moving direction and distance in the search space. Update the positions and velocities of the particles to obtain the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture.

[0031] Preferably, the positions and velocities of the particles in the mix proportion space of the composite modified asphalt mixture are:

[0032]

[0033]

[0034] Among them, is the position of the i-th particle at the (t + 1)-th iteration, is the velocity of the i-th particle at the (t + 1)-th iteration.

[0035] Preferably, in step S4, the technique for order preference by similarity to an ideal solution (TOPSIS) is selected. The specific content for determining the mix proportion design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set is as follows:

[0036] Perform dimensionless and normalization processing on the volume and performance indexes of the Pareto front optimal solution set of the composite modified asphalt mixture mix proportion to construct a standardized decision matrix Y. Based on the entropy weight w of the volume and performance indexes, determine the Euclidean distances between the Pareto front optimal solution set of the mix proportion and the positive and negative ideal solutions Finally, calculate the relative closeness coefficient R of the Pareto front optimal solution set of the mix proportion to the ideal solution a , select the mix proportion design scheme with the highest relative closeness coefficient to obtain the multi-objective optimization decision of the composite modified asphalt mixture mix proportion.

[0037] Preferably, the multi-objective optimization decision of the composite modified asphalt mixture mix proportion is specifically as follows:

[0038]

[0039]

[0040]

[0041]

[0042] Among them, y ab is the standardized element of the b-th index under the a-th mix proportion scheme in the Pareto front optimal solution set, w b is the entropy weight of the b-th index, e b is the information entropy of the b-th index, z ab = w b × y ab is the weighted decision matrix element, are the positive and negative ideal solutions respectively.

[0043] A multi-objective optimization system for the mix proportion of a composite modified asphalt mixture includes a data acquisition module, a Gaussian process regression prediction model, a prediction model training and verification module, a multi-objective optimization model for the mix proportion of the composite modified asphalt mixture, a multi-objective particle swarm optimization module, and a technique for order preference by similarity to an ideal solution (TOPSIS) module;

[0044] A data acquisition module, which is used to collect and form a data set of volume indexes and a data set of performance indexes of the composite modified asphalt mixture under different mix proportion design parameters;

[0045] A prediction model training and testing module, which is used to randomly divide the data set of volume indexes and the data set of performance indexes into a training sample set and a testing sample set according to a ratio, construct a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and test the Gaussian process regression prediction model through the testing sample set;

[0046] A Gaussian process regression prediction model, which is used to input the mix proportion design parameters of the composite modified asphalt mixture and predict the volume characteristics and high and low temperature performance of the composite modified asphalt mixture;

[0047] The multi-objective optimization model of the mix proportion of the composite modified asphalt mixture includes an optimization objective function of the performance indexes of the composite modified asphalt mixture, and constraint conditions of the mix proportion design parameters and volume characteristic indexes;

[0048] A multi-objective particle swarm optimization module, which is used to select a multi-objective particle swarm optimization method to update search information in the corresponding search space based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, and iteratively find the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture through swarm intelligence random search;

[0049] An approximation ideal solution sorting decision-making module, which is used to select the approximation ideal solution sorting decision-making analysis method based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, and determine the mix proportion design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set.

[0050] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a multi-objective optimization method and system for the mix proportion of a composite modified asphalt mixture. According to the target requirements of the composite modified asphalt mixture under different application scenarios, it reveals the implicit relationship between the volume and performance indexes and the mix proportion of the composite modified asphalt mixture, constructs a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, solves the multi-objective optimization problem of the mix proportion of the composite modified asphalt mixture based on the multi-objective particle swarm optimization algorithm, and realizes the purpose of designing the mix proportion of the composite modified asphalt mixture as required. The present invention not only takes into account multi-objective requirements, but also improves the efficiency of mix proportion design and material research and development, provides technical support for realizing the intelligent design of asphalt pavement materials, and has good application prospects. Description of the Drawings

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0052] Figure 1 The attached drawing is a schematic diagram of a multi-objective optimization method for the mix proportion of a composite modified asphalt mixture provided by the present invention;

[0053] Figure 2 The attached drawing is a schematic diagram of the data set acquisition provided by the present invention;

[0054] Figure 3 The attached drawing is a schematic diagram of the establishment of a Gaussian process regression prediction model provided by the present invention;

[0055] Figure 4 The attached drawing is a schematic diagram of a multi-objective particle swarm optimization method provided by the present invention;

[0056] Figure 5 The attached drawing is a schematic diagram of the void ratio prediction result output by the Gaussian process regression prediction model provided by the embodiment of the present invention;

[0057] Figure 6 The attached drawing is a schematic diagram of the asphalt saturation prediction result output by the Gaussian process regression prediction model provided by the embodiment of the present invention;

[0058] Figure 7 The attached drawing is a schematic diagram of the mineral aggregate void ratio prediction result output by the Gaussian process regression prediction model provided by the embodiment of the present invention;

[0059] Figure 8 The attached drawing is a schematic diagram of the high-temperature performance prediction result output by the Gaussian process regression prediction model provided by the embodiment of the present invention;

[0060] Figure 9 The attached drawing is a schematic diagram of the low-temperature performance prediction result output by the Gaussian process regression prediction model provided by the embodiment of the present invention;

[0061] Figure 10 The attached drawing is a schematic diagram of the result of the multi-objective particle swarm optimization Pareto front optimal solution set and the optimal mix proportion design scheme of the approximation ideal solution ranking decision provided by the embodiment of the present invention;

[0062] Figure 11 The attached drawing is a schematic diagram of the change curve of the high and low temperature performance optimization objective function of the composite modified asphalt mixture during the iteration provided by the embodiment of the present invention. Detailed implementation manners

[0063] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0064] An embodiment of the present invention discloses a multi-objective optimization method for the mix proportion of a composite modified asphalt mixture, as Figure 1 follows:

[0065] S1. According to the target requirements of asphalt mixture pavement materials and the technical requirements of mix proportion design parameters under different application scenarios, taking the performance indexes of the composite modified asphalt mixture as the optimization objectives and the mix proportion design parameters and volume characteristic indexes as the constraint conditions, a multi-objective optimization model for the mix proportion of the composite modified asphalt mixture is established;

[0066] S2. Based on experiments and investigations, collect and form a volume index data set and a performance index data set of the composite modified asphalt mixture under different mix proportion design parameters, as Figure 2 ;

[0067] S3. Randomly divide the volume index data set and the performance index data set into a training sample set and a test sample set according to a ratio, construct a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and test the Gaussian process regression prediction model through the test sample set;

[0068] S4. Based on the multi-objective optimization model for the mix proportion of the composite modified asphalt mixture, select the multi-objective particle swarm optimization method to update the search information in the corresponding search space, and iteratively find the multi-objective optimization optimal solution for the mix proportion of the composite modified asphalt mixture through swarm intelligence random search.

[0069] To further implement the above technical solution, the performance indexes include high-temperature stability, low-temperature stability, water stability and economy; the volume characteristic indexes include void ratio, stability, flow value, asphalt saturation and mineral aggregate void ratio.

[0070] To further implement the above technical solution, as Figure 3 , the specific content of constructing the Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture in step S3 is: based on Gaussian process regression for modeling, using the squared exponential SE covariance function as the kernel function, corresponding to the Bayesian linear regression model, the SE covariance function of multiple input variables is:

[0071]

[0072] Among them, \(x\) represents the mix proportion design parameter input variable of the training sample set, \(x'\) represents the mix proportion design parameter input variable of the point to be predicted, \(n\) represents the dimension of the mix proportion design parameter input variable, \(s = 1, 2, \cdots, n\), the signal variance and the eigenvector length \(l\) of the \(s\)-th input variable s are two hyperparameters;

[0073] The prior distribution of the observed value \(y\) of the output variable of the \(t\)-dimensional training sample set is:

[0074]

[0075] Among them, \(K(x, x)\) represents a \(t\times t\) order symmetric positive definite covariance matrix with the mix proportion design parameters of the training sample set as input variables, \(I\) t is a \(t\)-dimensional identity matrix;

[0076] Given the mix proportion design parameter input variable \(x\) of the test sample set * , the predicted value \(f\) is obtained through the joint posterior distribution * , the joint distribution between the observed value \(y\) of the output variable of the training sample set and the predicted value \(f\) based on the input variable of the test sample set * is:

[0077]

[0078] Among them, \(K(x, x\) * ), \(K(x\) * , \(x)\) and \(K(x\) * , \(x\) * ) are covariance matrices, \(K(x, x\) * ) = \(K(x\) * , \(x)\) T .

[0079] To further implement the above technical solution, the specific content of testing the Gaussian process regression prediction model through the test sample set in step S3 is: combining cross-validation with the root mean square error RMSE and the squared correlation coefficient \(R\) 2 as the evaluation indexes for the accuracy of the Gaussian process regression prediction model;

[0080] The root mean square error RMSE is:

[0081]

[0082] The squared correlation coefficient \(R\) 2 is:

[0083]

[0084] Among them, is the predicted value of the input variable based on the test sample set, y i is the observed value of the output variable based on the training sample set is the average value of the predicted values of the input variables based on the test sample set is the average value of the observed values of the output variables based on the training sample set

[0085] To further implement the above technical solution, as Figure 4 , the specific content of step S4 is: Based on the particle swarm optimization algorithm, randomly initialize the particle swarm, and use the fitness function to evaluate and judge the particle positions, where the particle positions represent the mix proportion design parameters of the composite modified asphalt mixture

[0086] Specifically: The particle swarm has p particles in the n-dimensional space. At the t-th iteration, the position and velocity of the i-th particle in the j-th dimension are respectively expressed as and The particle velocity represents the moving direction and distance in the search space. Update the positions and velocities of the particles to obtain the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture

[0087] To further implement the above technical solution, the positions and velocities of the particles in the mix proportion space of the composite modified asphalt mixture are

[0088]

[0089]

[0090] where is the position of the i-th particle at the (t + 1)-th iteration is the velocity of the i-th particle at the (t + 1)-th iteration

[0091] To further implement the above technical solution, in step S4, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is selected. The specific content of determining the mix proportion design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set is

[0092] Perform dimensionless and normalization processing on the volume and performance indicators of the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture, construct the standardized decision matrix Y, and based on the entropy weight w of the volume and performance indicators, determine the Euclidean distances between the Pareto front optimal solution set of the mix proportion and the positive and negative ideal solutions Finally, calculate the relative closeness coefficient R of the Pareto front optimal solution set of the mix proportion to the ideal solution a , select the mix proportion design scheme with the highest relative closeness coefficient to obtain the multi-objective optimization decision of the mix proportion of the composite modified asphalt mixture

[0093] To further implement the above technical solution, the multi-objective optimization decision of the composite modified asphalt mixture mix proportion is specifically as follows:

[0094]

[0095]

[0096]

[0097]

[0098] Among them, y ab is the standardized element of the b-th index under the a-th mix proportion scheme in the Pareto front optimal solution set, w b is the entropy weight of the b-th index, e b is the information entropy of the b-th index, z ab = w b × y ab is the element of the weighted decision matrix, are the positive and negative ideal solutions respectively.

[0099] A multi-objective optimization system for the mix proportion of composite modified asphalt mixture includes a data acquisition module, a Gaussian process regression prediction model, a prediction model training and verification module, a multi-objective optimization model for the mix proportion of composite modified asphalt mixture, a multi-objective particle swarm optimization module, and an approximation ideal solution ranking decision module;

[0100] The data acquisition module is used to collect and form a volume index data set and a performance index data set of composite modified asphalt mixture under different mix proportion design parameters;

[0101] The prediction model training and verification module is used to randomly divide the volume index data set and the performance index data set into a training sample set and a test sample set according to a ratio, construct a Gaussian process regression prediction model for the volume and performance indexes of composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and verify the Gaussian process regression prediction model through the test sample set;

[0102] The Gaussian process regression prediction model is used to input the mix proportion design parameters of composite modified asphalt mixture and predict the volume characteristics and high and low temperature performance of composite modified asphalt mixture;

[0103] The multi-objective optimization model for the mix proportion of composite modified asphalt mixture includes an optimization objective function for the performance indexes of composite modified asphalt mixture, and constraint conditions for mix proportion design parameters and volume characteristic indexes;

[0104] The multi-objective particle swarm optimization module is used to select the multi-objective particle swarm optimization method to search for information update in the corresponding search space based on the multi-objective optimization model of the composite modified asphalt mixture ratio, and find the Pareto front optimal solution set of the composite modified asphalt mixture ratio through swarm intelligence random search iteration;

[0105] The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) decision-making module is used to select the TOPSIS analysis method based on the multi-objective optimization model of the composite modified asphalt mixture ratio, and determine the optimal mixture ratio design scheme with the best comprehensive multi-objective performance in the Pareto front optimal solution set.

[0106] Example Two

[0107] S1. Taking the diatomite and basalt fiber composite modified asphalt mixture as an example, aiming at the target requirements of the application scenario in the seasonal freezing area with hot summers and cold winters in Northeast China, combined with the Chinese specification JTGF40 - 2004, determine the high and low temperature pavement performance of the composite modified asphalt mixture as the optimization objectives, and the mixture ratio design parameters and volume characteristics as the constraints. Use polynomial equations to establish a multi-objective optimization mathematical model for the composite modified asphalt mixture ratio. The multi-objective function and constraints are as follows:

[0108] maxF(x)=max(Y4 + Y5)

[0109]

[0110] In the formula, F1 is the high temperature performance objective function, F2 is the low temperature performance objective function, F3 is the economic objective function, X1 is the diatomite content, X2 is the basalt fiber content, X3 is the asphalt-aggregate ratio, Y1 is the void ratio, Y2 is the asphalt saturation, Y3 is the mineral aggregate void ratio, Y4 is the high temperature performance MS, and Y5 is the low temperature performance S b .

[0111] S2. Based on the orthogonal experiment L 16 (4 3 ), with the mixture ratio design parameters X1, X2, and X3 as input variables, and the asphalt mixture volume characteristics and high and low temperature performances Y1, Y2, Y3, Y4, and Y5 as output variables, collect the test results of the void ratio, asphalt saturation, mineral aggregate void ratio, and high and low temperature performances of the diatomite and basalt fiber composite modified asphalt mixture. The volume and performance index data set is as follows:

[0112]

[0113] S3. Randomly divide the dataset of volume and performance indicators obtained from the orthogonal experimental design in S2 into a training sample set and a test sample set at a ratio of 3:1; construct a Gaussian process regression prediction model for the volume and performance indicators of the composite modified asphalt mixture, and train the Gaussian process regression prediction model through the training sample set;

[0114] Use the test sample set divided in S3 to test the Gaussian process regression prediction model for the volume and performance indicators of the composite modified asphalt mixture constructed and trained in S3, and combine cross-validation with the root mean square error RMSE and the square correlation coefficient R 2 As the evaluation indicators for the accuracy of the Gaussian process regression prediction model, the results are shown in the following table:

[0115]

[0116] Analysis shows that the constructed Gaussian process regression prediction model can better learn the relationship between the input and output variables of the mix proportion design of the composite modified asphalt mixture, can accurately predict the volume characteristics and high and low temperature performance of the diatomite and basalt fiber composite modified asphalt mixture, and output the prediction results of the Gaussian process regression prediction model, such as Figures 5 - 9 .

[0117] S4. Based on the multi-objective optimization mathematical model of the mix proportion of the composite modified asphalt mixture established in S1, select the multi-objective particle swarm optimization method to update the search information in the corresponding search space, and find the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture through the swarm intelligence random search iteration. Select the technique for order preference by similarity to an ideal solution (TOPSIS) to determine the mix proportion design scheme with the best comprehensive performance among the Pareto front optimal solution sets;

[0118] Draw the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture based on the multi-objective particle swarm optimization method and the optimal mix proportion design scheme based on the technique for order preference by similarity to an ideal solution (TOPSIS), such as Figure 10 , the Pareto front optimal solution sets are all distributed within a reasonable range, and the optimal mix proportion design scheme has the highest relative proximity coefficient, taking into account the high temperature performance, low temperature performance and economy; draw the change curve of the high and low temperature performance optimization objective function of the composite modified asphalt mixture during the iteration process, such as Figure 11 . The optimization objective function reaches the local optimal value at the 7th iteration, indicating that the constructed multi-objective optimization method for the mix proportion of the composite modified asphalt mixture based on the machine learning model has a fast iteration convergence speed and can achieve relatively effective optimization results.

[0119] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For related parts, reference can be made to the description in the method section.

[0120] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective optimization method for the mix proportion of a composite modified asphalt mixture, characterized in that, It includes the following steps: S1. Based on the target requirements of asphalt mixture pavement materials under different differential application scenarios and the technical requirements of mix design parameters, taking the performance indicators of the composite modified asphalt mixture as the optimization goal and the mix design parameters and volume characteristic indicators as the constraints, establish a multi-objective optimization model for the mix proportion of the composite modified asphalt mixture; S2. Collect and form a dataset of volume indicators and a dataset of performance indicators of the composite modified asphalt mixture under different mix design parameters; S3. Randomly divide the dataset of volume indicators and the dataset of performance indicators into a training sample set and a test sample set according to a certain proportion, construct a Gaussian process regression prediction model for the volume and performance indicators of the composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and test the Gaussian process regression prediction model through the test sample set; S4. According to the Gaussian process regression prediction model, predict the volume and performance of the composite modified asphalt mixture. Based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, select the multi-objective particle swarm optimization method to update the search information in the corresponding search space, and iteratively find the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture through swarm intelligence random search; select the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to determine the mix design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set.

2. According to the multi-objective optimization method for the mix proportion of a composite modified asphalt mixture described in claim 1, the performance indicators include high-temperature stability, low-temperature stability, water stability, and economy; the volume characteristic indicators include void ratio, stability, flow value, asphalt saturation, and voids in mineral aggregate.

3. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 1, characterized in that The specific content of constructing the Gaussian process regression prediction model for the volume and performance indicators of the composite modified asphalt mixture in step S3 is: Based on Gaussian process regression for modeling, use the squared exponential (SE) covariance function as the kernel function. Corresponding to the Bayesian linear regression model, the SE covariance function for multi-input variables is: where x represents the mix proportion design parameter input variables of the training sample set, x' represents the mix proportion design parameter input variables of the point to be predicted, n represents the dimension of the mix proportion design parameter input variables, s = 1, 2, …, n, the signal variance and the length l of the eigenvector of the s-th input variable s are two hyperparameters; The prior distribution of the observed values y of the output variable of the t-dimensional training sample set is: Among them, \(K(x, x)\) represents a \(t\times t\) order symmetric positive definite covariance matrix with the mix proportion design parameters of the training sample set as input variables, and \(I\) t is a \(t\)-dimensional identity matrix; The mix proportion design parameter input variable x of the given test sample set * , and the predicted value f is obtained through the joint posterior distribution * . The joint distribution between the observed value y of the output variable of the training sample set and the predicted value f based on the input variable of the test sample set * is as follows: Among them, K(x, x * ), K(x * , x) and K(x * , x * ) are covariance matrices, and K(x, x * ) = K(x * , x) T .

4. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 1, wherein, The specific content of testing the Gaussian process regression prediction model with the test sample set in step S3 is as follows: Combining cross-validation, the root mean square error RMSE and the square correlation coefficient R 2 are used as evaluation indicators for the accuracy of the Gaussian process regression prediction model; The root mean square error (RMSE) is: Square correlation coefficient R 2 is as follows: Among them, is the predicted value of the input variable based on the test sample set, y i is the observed value of the output variable based on the training sample set, is the average value of the predicted values of the input variables based on the test sample set, is the average value of the observed values of the output variables based on the training sample set.

5. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 1, characterized in that, The specific content of step S4 is: Based on the particle swarm optimization algorithm, randomly initialize the particle swarm, use the fitness function to evaluate and judge the particle positions, and the particle positions represent the mix design parameters of the composite modified asphalt mixture; Specifically: The particle swarm has p particles in the n-dimensional space. At the t-th iteration, the position and velocity of the i-th particle in the j-th dimension are respectively expressed as and The particle velocity represents the moving direction and distance in the search space. The position and velocity of the particles are updated to obtain the optimal solution set of the Pareto front of the mix proportion of the composite modified asphalt mixture.

6. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 5, characterized in that, The positions and velocities of the particles in the mix proportion space of the composite modified asphalt mixture: wherein, is the position of the i-th particle at the (t + 1)-th iteration, is the velocity of the i-th particle at the (t + 1)-th iteration.

7. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 1, characterized in that, The specific content of selecting the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method in step S4 to determine the mix design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set is: The dimensionless and normalized processing of the volume and performance indicators of the Pareto front optimal solution set of the composite modified asphalt mixture proportion is carried out to construct a standardized decision matrix Y. Based on the entropy weight w of the volume and performance indicators, the Euclidean distances between the Pareto front optimal solution set of the mixture proportion and the positive and negative ideal solutions are determined. Finally, the relative closeness coefficient R of the Pareto front optimal solution set of the mixture proportion to the ideal solution is calculated. a The mixture proportion design scheme with the highest relative closeness coefficient is selected to obtain the multi-objective optimization decision of the composite modified asphalt mixture proportion.

8. The multi-objective optimization method for the mix proportion of a composite modified asphalt mixture according to claim 7, characterized in that The multi-objective optimization decision for the mix proportion of the composite modified asphalt mixture is specifically: Among them, y ab is the standardized element of the b-th index under the a-th mix ratio plan in the Pareto front optimal solution set, w b is the entropy weight of the b-th index, e b is the information entropy of the b-th index, z ab = w b × y ab is the element of the weighted decision matrix, are the positive and negative ideal solutions respectively.

9. A multi-objective optimization system for the mix proportion of a composite modified asphalt mixture, characterized in that, Based on the multi-objective optimization method for the mix proportion of a composite modified asphalt mixture described in any one of claims 1-8, it includes a data acquisition module, a Gaussian process regression prediction model, a prediction model training and testing module, a multi-objective optimization model for the mix proportion of the composite modified asphalt mixture, a multi-objective particle swarm optimization module, and a Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) decision module; A data acquisition module, which is used to collect and form a dataset of volume indexes and a dataset of performance indexes of the composite modified asphalt mixture under different mix proportion design parameters; A prediction model training and testing module, which is used to randomly divide the dataset of volume indexes and the dataset of performance indexes into a training sample set and a testing sample set according to a proportion, construct a Gaussian process regression prediction model for the volume and performance indexes of the composite modified asphalt mixture, train the Gaussian process regression prediction model through the training sample set, and test the Gaussian process regression prediction model through the testing sample set; A Gaussian process regression prediction model, which is used to input the mix proportion design parameters of the composite modified asphalt mixture and predict the volume characteristics and high and low temperature performance of the composite modified asphalt mixture; The multi-objective optimization model of the mix proportion of the composite modified asphalt mixture includes an optimization objective function for the performance indexes of the composite modified asphalt mixture, and constraint conditions for the mix proportion design parameters and volume characteristic indexes; A multi-objective particle swarm optimization module, which is used to, based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, select the multi-objective particle swarm optimization method to update search information in the corresponding search space, and iteratively find the Pareto front optimal solution set of the mix proportion of the composite modified asphalt mixture through swarm intelligence random search; A technique for order preference by similarity to an ideal solution (TOPSIS) decision-making module, which is used to, based on the multi-objective optimization model of the mix proportion of the composite modified asphalt mixture, select the TOPSIS analysis method to determine the mix proportion design scheme with the optimal multi-objective comprehensive performance in the Pareto front optimal solution set.

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