Multi-stage and multi-target vibration parameter optimization method for coarse-grained soil compaction process

Abstract

The invention belongs to the technical field of civil engineering roadbed compaction, and particularly discloses a multi-stage and multi-target vibration parameter optimization method for a coarse-grained soil compaction process, and the method comprises the following steps: S1, obtaining multi-working-condition dynamic response data, and constructing a training set, a verification set and a test set after standardization processing; s2, establishing a dry density dynamic evolution model based on the BO-FCNN, and analyzing key parameters influencing compaction deformation in combination with an SHAP value; s3, multi-stage and multi-target vibration parameter optimization is completed, specifically, S3.1, multi-stage division and dynamic constraint transfer are carried out; s3.2, constructing a multi-objective function; s3.3, adopting MC-NSGA-II to generate a Pareto frontier solution set; and S3.4, outputting an optimal vibration parameter combination based on the weight decision. According to the method, closed-loop optimization from data modeling to parameter decision making is achieved, the optimization strategy is dynamically adjusted according to actual engineering requirements, and the construction efficiency is improved to the maximum extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of subgrade compaction in civil engineering, and particularly relates to a multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil. Background Art

[0002] As the core filler for coarse-grained soil filling projects such as high embankment subgrades and rockfill dams, the compaction quality of coarse-grained soil directly affects the structural stability and service life. Although the existing technology improves the density through vibration compaction, there are still the following key defects: 1. Insufficient prediction accuracy of compaction deformation: Traditional compaction deformation models rely on empirical formulas or simplified assumptions, or only consider the relationship between a single parameter and deformation, and cannot meet the requirements of high-precision prediction. It is difficult to describe the non-linear coupling between vibration parameters and dry density and adapt to the compaction characteristics of coarse-grained soil under complex conditions.

[0003] 2. Limitations of parameter optimization: Most of the existing optimization methods are single-objective static optimizations, without considering the multi-stage dynamic characteristics of the compaction process and the multi-objective trade-off of energy-time.

[0004] 3. Lack of optimization scheme selection according to decision-making requirements: The existing methods lack the flexibility to select solutions according to the preferences of decision-makers, which limits their ability to meet the diverse actual engineering needs.

[0005] Therefore, it is necessary to design a new multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil. Summary of the Invention

[0006] The purpose of the present invention is to provide a multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil, so as to solve the problems of insufficient prediction accuracy of compaction deformation, limitations of parameter optimization, and lack of optimization scheme selection according to decision-making requirements in the current compaction process of coarse-grained soil proposed in the background art.

[0007] To achieve the above purpose, the present invention provides a multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil, including the following steps: S1. Obtain multi-condition dynamic response data through vibration compaction tests, and construct a training set, a validation set, and a test set after standardization processing; S2. Establish a dynamic evolution model of dry density based on the Bayesian optimization fully connected neural network algorithm, and analyze the key parameters affecting compaction deformation in combination with SHAP values; S3. Complete the multi-stage and multi-objective vibration parameter optimization, specifically including: S3.1. Divide the compaction process into multiple stages and transfer through dynamic constraints; S3.2. Construct a multi-objective function of energy and time; S3.3. Generate the Pareto front solution set using the non-dominated sorting genetic algorithm with multi-stage compaction; S3.4. Adjust the energy and time weight coefficients according to the engineering priority and output the optimal vibration parameter combination.

[0008] In a specific implementation manner, in step S1, the test equipment used in the vibration compaction test includes a UTM-250 testing machine; the vibration compaction test uses sinusoidal vibration loading.

[0009] In a specific implementation manner, in step S1, the multi-condition dynamic response data obtained from the vibration compaction test includes the initial dry density, excitation force, frequency, number of vibrations, and real-time dry density.

[0010] In a specific implementation manner, in step S2, the initial dry density, excitation force, frequency, and number of vibrations are used as the input data of the dry density dynamic evolution model; the real-time dry density is used as the output data of the dry density dynamic evolution model.

[0011] In a specific implementation manner, in step S2, the mean square error is used as the loss function during the training process of the dry density dynamic evolution model, and the model parameters are dynamically updated in combination with the Adam optimizer; at the same time, to suppress overfitting, an early stopping strategy is adopted, that is, when the loss of the validation set does not decrease for 5 consecutive rounds, the training is terminated; to optimize the network structure, the Bayesian hyperparameter optimization tool is used to dynamically tune the FCNN model; during the process of optimizing the network structure, the hyperparameters include the number of hidden layers, the number of nodes, the learning rate, the dropout rate, and the activation function; Bayesian optimization uses a surrogate model to predict the performance of each set of hyperparameters and selects the next set of hyperparameters for evaluation through an acquisition function; after each training and validation of the model, the optimization process updates the surrogate model according to the evaluation results, so as to gradually find the optimal combination of hyperparameters; the test set of the optimized model meets the following requirements: the coefficient of determination ≥ 0.85, the mean absolute error ≤ 0.05 g / cm 3 , the root mean square error ≤ 0.08 g / cm 3 . The absolute value of the SHAP value is used to quantify the degree of influence of each vibration parameter on the compaction deformation, and the key influencing factors are identified.

[0012] In a specific implementation manner, in step S3.1, the compaction process is discretized into n optimization stages; the basis for stage division is the dry density increment threshold Δ ρ min = 0.01 g / cm 3 , that is, within each stage, by adjusting the vibration parameters, the dry density of the current stage is gradually increased from the initial value to the target value; (1) The constraint conditions to be satisfied are: (2) In the formula, Δ ρ min is the minimum increment of dry density, and Δ ρ i is the dry density increment in the i-th stage, ρ i , ρ i-1 are the target dry density and the initial dry density in the i-th stage, respectively, ρ target is the target dry density; k is the dry density increment coefficient; m is a positive integer.

[0013] In a specific implementation manner, in step S3.1, the dynamic constraint transfer is specifically as follows: Define the stage sequence i = 1, 2, 3,…, n, and the dynamic association is transferred through the dry density state ρ i : (3) In the formula, g() is the dry density evolution function based on data.

[0014] In a specific implementation manner, in step S3.2, the specific steps for constructing the multi-objective function of energy and time are as follows: Adopt the equivalent energy model, quantify the relative efficiency of energy input through the combined relationship of exciting force, frequency and vibration times, and provide a trade-off index for multi-objective optimization; on the premise of satisfying the dry density increment Δ ρ i , the vibration energy E i required in the i-th optimization stage depends on the exciting force F i and its vibration time T i , where T i is the vibration times N i and the vibration frequency f i ratio; taking the total energy E total and the total time T total as the optimization objectives, establish a double-objective function: (4) (5).

[0015] In a specific embodiment, in step S3.3, a non-dominated sorting genetic algorithm with multi-stage compaction is used to generate a Pareto front solution set of minimum energy and minimum time; the specific steps are as follows: First, set the population size and randomly generate initial individuals within the vibration parameter space. The parameters include the exciting force F , the vibration frequency f and the number of vibrations N ; Then, use BO-FCNN to predict the compaction deformation and calculate the energy consumption and vibration time; Next, through non-dominated sorting and crowding distance, generate a Pareto front solution set of non-dominated sorting with uniform distribution, that is, the vibration parameter combination of minimum energy and time.

[0016] In a specific embodiment, in step S3.4, the priority is adjusted through the weight coefficients ω 1 (energy weight) and ω 2 (time weight): (8) In the formula, ω 1 + ω 2 = 1, E norm , T norm are normalization factors to ensure dimensional consistency.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention realizes the closed-loop optimization from data modeling to parameter decision-making through the method of coupling BO-FCNN compaction deformation prediction and MC-NSGA-II parameter optimization.

[0018] The present invention proposes a multi-stage division method, optimizes energy and time simultaneously, and dynamically adjusts the optimization strategy according to the actual engineering requirements to maximize the construction efficiency.

[0019] The weight decision-making mechanism of the present invention supports flexibly adjusting the energy and time priorities according to the construction conditions, improving the universality of the method.

[0020] Through multi-stage progressive compaction and multi-objective optimization, the present invention can effectively reduce energy consumption and construction time, thereby reducing project costs and improving construction efficiency.

[0021] In addition to the purposes, features and advantages described above, the present invention has other purposes, features and advantages. The present invention will be further described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings, which form a part of this application, are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a flowchart for predicting the compaction deformation of coarse-grained soil and optimizing parameters in an embodiment of the present invention; Figure 2 is a flowchart for optimizing the vibration compaction of coarse-grained soil in an embodiment of the present invention. Detailed Description of the Invention

[0023] The following is a detailed description of the embodiments of the present invention. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0024] A multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to the present invention includes the following steps: S1. Obtain multi-condition dynamic response data through vibration compaction tests, and construct a training set, a validation set, and a test set after standardization processing; S2. Establish a dry density dynamic evolution model based on the Bayesian optimization fully connected neural network algorithm (BO-FCNN), and analyze the key parameters affecting compaction deformation in combination with SHAP values; S3. Complete the multi-stage and multi-objective vibration parameter optimization, specifically including: S3.1. Divide the compaction process into multiple stages and transfer through dynamic constraints; S3.2. Construct a multi-objective function of energy and time; S3.3. Use the multi-stage compaction non-dominated sorting genetic algorithm (MC-NSGA-II) to generate a Pareto front solution set; S3.4. Adjust the energy and time weight coefficients according to the engineering priority, and output the optimal vibration parameter combination.

[0025] Embodiment 1 1. Data collection and experimental design: Experimental equipment: UTM-250 testing machine (load 0-250 kN, frequency 0-70 Hz), equipped with a hydraulic loading system and high-precision sensors; the measurement accuracy of the high-precision sensors is 0.5%.

[0026] Specimen preparation: Gradation gravel filler ( C u = 15, C c = 2.5, particle size d = 2~30 mm), filled in layers into a steel cylindrical mold (diameter × height = 160 mm × 250 mm); Operating condition setting: The test adopts sinusoidal vibration loading, with exciting forces (2, 4, 6, 8, 10, 12 kN), frequencies (20, 23, 26, 29, 32, 35 Hz), and an initial dry density of 1.55 - 1.6 g / cm³. Two parallel tests are set for each group, and the total number of data sets is 72 groups; Data acquisition: The dry density is recorded in real-time within 1 - 1000 vibration cycles to form a time series data set.

[0027] Construction of the BO - FCNN prediction model: (1) Data processing: The input data of the input layer of the initial model is set as the initial dry density, exciting force, frequency, and number of vibrations, and the output data of the output layer is set as the real-time dry density. To ensure data consistency, both the input and output data are standardized. The standardized time series data set is divided into a training set, a validation set, and a test set in the ratio of 80%, 10%, and 10%.

[0028] (2) Model optimization: The initial model is trained and validated using the training set and the validation set. The mean squared error (MSE) is used as the loss function during the model training process, and the Adam optimizer is combined to dynamically update the model parameters. At the same time, to suppress overfitting, an early stopping strategy is adopted, that is, when the loss of the validation set does not decrease for 5 consecutive rounds, the training is terminated. To optimize the network structure, a Bayesian hyperparameter optimization tool is used to dynamically tune the FCNN model. The hyperparameters of FCNN mainly include the number of hidden layers (1 - 30), the number of nodes (10 - 50), the learning rate (1e - 4 ~ 1e - 2), the dropout rate (0.1 - 0.3), and the activation function (Sigmoid, ReLU, Linear Activation Function). Bayesian optimization efficiently searches the hyperparameter space of the FCNN model by constructing a surrogate model (usually Gaussian process regression). During the optimization process, the hyperparameter ranges are first defined, such as the number of hidden layers, the number of nodes, the learning rate, the dropout rate, and the activation function. Bayesian optimization uses the surrogate model to predict the performance of each set of hyperparameters and selects the next set of hyperparameters for evaluation through an acquisition function (such as expected improvement). After each training and validation of the model, the optimization process updates the surrogate model according to the evaluation results, thereby gradually finding the optimal combination of hyperparameters. The architecture of the initial model adopts the FCNN model architecture, including the connection methods of all its layers and the hyperparameter configuration; before the initial model is trained, all the weights and biases of the model are initialized to random values; the training set and the validation set are used to optimize these parameters until convergence, so that the model can better fit the data.

[0029] (3)Model validation: The test set of the prediction model should meet the following requirements: coefficient of determination ≥ 0.85, mean absolute error ≤ 0.05 g / cm³, root mean square error ≤ 0.08 g / cm³.

[0030] Interpretability analysis: The absolute value of SHAP values is used to quantify the degree of influence of each vibration parameter on compaction deformation and identify key influencing factors.

[0031] Establishment of multi-stage and multi-objective optimization model: (1)Multi-stage division rules: To achieve dynamic optimization of vibration parameters, the compaction process is discretized into n optimization stages. The basis for stage division is the dry density increment threshold Δ ρ min = 0.01 g / cm 3 , that is, within each stage, by adjusting the vibration parameters, the dry density in the current stage is gradually increased from the initial value to the target value.

[0032] (1) The constraint conditions to be met are: (2) In the formula, Δ ρ min is the minimum dry density increment, Δ ρ i is the dry density increment in the i-th stage, ρ i , ρ i-1 are the target dry density and the initial dry density in the i-th stage respectively, ρ target is the target dry density; k is the dry density increment coefficient; m is a positive integer.

[0033] (2)Dynamic constraint transfer: Define the stage sequence i = 1, 2, 3, …, n, and the dynamic association is transmitted through the dry density state ρ i : (3) In the formula, g() is the dry density evolution function based on data.

[0034] (3)Construction of multi-objective function.

[0035] The equivalent energy model is adopted to quantify the relative efficiency of energy input through the combined relationship of exciting force, frequency and vibration times, providing a trade-off index for multi-objective optimization. While meeting the dry density increment Δρ i On the premise that the i vibration energy required for the E i ith optimization stage depends on the F i excitation force and its vibration T i time in this stage, where T i is the ratio of the number of N i vibrations to the vibration f i frequency. Taking the total energy E total and the total time T total as the optimization objectives, a two-objective function is established: The multi-objective function in

[0036] this embodiment is a two-objective function. Implementation of the MC-NSGA-II F optimization algorithm: f (1) Initialize the population: N

[0037] (2) Calculate the fitness value: Use BO-FCNN to predict the

[0038] compaction deformation and calculate the energy and vibration time.

[0039] If the parameter combination x a is the optimal solution, then x a dominates x b if and only if: at least one holds strictly (6) Maintain the diversity of thex k Crowding distance: (7) In the formula and are the adjacent solution values of energy and time on the target respectively, and correspond to the maximum and minimum values of the target. ([[]] j = 1 is energy, j = 2 is time). Prioritize solutions with high crowding distance to avoid over - aggregation of parameter combinations and cover the global optimization potential of amplitude, frequency, and number of vibrations.

[0040] (4) Parameter optimization and output of the optimal solution: According to the optimization iteration stage, dynamically adjust the crossover probability and mutation probability, and optimize the search strategy in stages: Initial stage (iteration < 100 times): Focus on global search, adopt a high mutation probability (0.15 - 0.2) and a low simulated binary crossover index (10), and combine with the tournament selection strategy to improve the diversity of solutions.

[0041] Intermediate stage (100 - 200 times): Balance global search and local search, adopt a crossover probability of 0.7 and a mutation probability of 0.1, and gradually converge to high - quality solutions.

[0042] Late stage (> 200 times): Strengthen the local search ability, reduce the mutation probability (0.01 - 0.05), and increase the simulated binary crossover index (30) to ensure a refined search of the Pareto front solution set.

[0043] (5) Weight decision - making: Adjust the priority through the weight coefficients ω 1 (energy weight) and ω 2 (time weight): (8) In the formula, ω 1 + ω 2 = 1, E norm and T norm are normalization factors to ensure dimensional consistency.

[0044] The MC - NSGA - II vibration parameter optimization process considering weight decision - making is as Figure 2 shown.

[0045] Verify the effectiveness of the optimized parameters through experiments: The present invention verifies the effectiveness of the optimized vibration parameters through indoor vibration compaction tests, and compares the compaction performance differences between the MC-NSGA-II optimization scheme and the traditional empirical scheme. Seven control schemes are set in the test. Among them, Schemes 1-5 adopt the alternating combination scheme, and Schemes 6 and 7 adopt the fixed parameter scheme, which are specifically as follows: (1) Alternating combination scheme: Scheme 1: First, perform 2 passes of vibration (exciting force 15 kN, frequency 28 Hz), and then perform 2 passes of vibration (exciting force 8 kN, frequency 32 Hz).

[0046] Scheme 2: First, perform 2 passes of vibration (exciting force 12 kN, frequency 28 Hz), and then perform 1 pass of vibration (exciting force 6 kN, frequency 32 Hz).

[0047] Scheme 3: First, perform 3 passes of vibration (exciting force 14 kN, frequency 34 Hz), and then perform 1 pass of vibration (exciting force 7 kN, frequency 38 Hz).

[0048] Scheme 4: First, perform 2 passes of vibration (exciting force 6 kN, frequency 36 Hz), and then perform 3 passes of vibration (exciting force 12 kN, frequency 32 Hz).

[0049] Scheme 5: First, perform 1 pass of vibration (exciting force 13 kN, frequency 38 Hz), and then perform 1 pass of vibration (exciting force 6 kN, frequency 34 Hz).

[0050] The number of single-pass vibrations for each scheme is 20 times, and the alternating combination is carried out until the target dry density is reached.

[0051] (2) Fixed parameter scheme: Scheme 6: Adopt fixed vibration parameters (exciting force 14 kN, frequency 36 Hz) for uniform vibration.

[0052] Scheme 7: Adopt fixed vibration parameters (exciting force 12 kN, frequency 38 Hz) for uniform vibration.

[0053] By comparing the performance of each scheme in terms of compaction efficiency, energy consumption, and final dry density, the superiority of the MC-NSGA-II scheme is verified to ensure the effectiveness of the optimized vibration parameters.

[0054] Engineering application example: Optimization of the compaction of coarse-grained soil for a railway subgrade: (1) Engineering background: This embodiment takes a railway subgrade project as the research object, with a target dry density of 1.88 g / cm³ and an initial dry density of 1.70 g / cm³. The goal of optimizing the vibration compaction parameters is to improve the construction efficiency, reduce energy consumption, and ensure that the final compaction quality meets the engineering requirements.

[0055] (2) Stage division: Based on the MC-NSGA-II multi-stage optimization method, the minimum dry density increment Δρ is set min = 0.01 g / cm 3 , and the optimal number of stages is calculated. During the optimization process, the vibration parameters (exciting force, frequency, number of vibrations) are dynamically adjusted in each stage to achieve the Pareto front optimal solution of minimizing energy consumption and maximizing construction efficiency.

[0056] (3) Optimization results: Through multi-objective optimization by MC-NSGA-II, weights are selected from the Pareto front solution set, and finally the optimal combination of vibration parameters is obtained.

[0057] The above content is a further detailed description of the present invention in combination with specific preferred implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions and substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil, characterized in that, It includes the following steps: S1. Obtain multi-condition dynamic response data through vibration compaction tests, and construct a training set, a validation set, and a test set after standardization processing; S2. Establish a dry density dynamic evolution model based on the Bayesian optimization fully connected neural network algorithm, and analyze the key parameters affecting compaction deformation in combination with SHAP values; S3. Complete the optimization of vibration parameters for multiple stages and multiple objectives, specifically including: S3.

1. Divide the compaction process into multiple stages and transfer through dynamic constraints; S3.

2. Construct a multi-objective function of energy and time; S3.

3. Use the non-dominated sorting genetic algorithm for multi-stage compaction to generate a Pareto front solution set; S3.

4. Adjust the energy and time weight coefficients according to the engineering priority, and output the optimal vibration parameter combination.

2. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 1, characterized in that In step S1, the test equipment used in the vibration compaction test includes a UTM-250 testing machine; the vibration compaction test uses sinusoidal vibration loading.

3. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 1, characterized in that In step S1, the multi-condition dynamic response data obtained from the vibration compaction test includes the initial dry density, excitation force, frequency, number of vibrations, and real-time dry density.

4. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 3, wherein In step S2, the initial dry density, excitation force, frequency, and number of vibrations are used as the input data of the dry density dynamic evolution model; the real-time dry density is used as the output data of the dry density dynamic evolution model.

5. The multi-stage and multi-objective vibration parameter optimization method for the coarse-grained soil compaction process according to claim 1, characterized in that In step S2, during the training process of the dry density dynamic evolution model, the mean square error is used as the loss function, and the model parameters are dynamically updated in combination with the Adam optimizer; at the same time, to suppress overfitting, an early stopping strategy is adopted, that is, when the loss of the validation set does not decrease for 5 consecutive rounds, the training is terminated; to optimize the network structure, the Bayesian hyperparameter optimization tool is used to dynamically tune the FCNN model; during the process of optimizing the network structure, the hyperparameters include the number of hidden layers, the number of nodes, the learning rate, the dropout rate, and the activation function; Bayesian optimization uses a surrogate model to predict the performance of each set of hyperparameters and selects the next set of hyperparameters for evaluation through an acquisition function; after each training and validation of the model, the optimization process updates the surrogate model according to the evaluation results, so as to gradually find the optimal combination of hyperparameters; the test set of the optimized model meets the following requirements: the coefficient of determination ≥ 0.85, the mean absolute error ≤ 0.05 g / cm 3 , the root mean square error ≤ 0.08 g / cm 3 ; the absolute value of the SHAP value is used to quantify the degree of influence of each vibration parameter on the compaction deformation, and the key influencing factors are identified.

6. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 1, characterized in that In step S3.1, the compaction process is discretized into n optimization stages; the basis for stage division is the dry density increment threshold Δ ρ min = 0.01 g / cm 3 , that is, within each stage, by adjusting the vibration parameters, the dry density of the current stage is gradually increased from the initial value to the target value; (1) The constraint conditions to be satisfied are: (2) Where, Δ ρ min is the minimum increment of dry density, and Δ ρ i is the dry density increment at the i stage; ρ i , ρ i-1 are the target dry density and the initial dry density at the i stage respectively; ρ target is the target dry density; k is the dry density increment coefficient; m is a positive integer.

7. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 6, characterized in that In step S3.1, the dynamic constraint transfer is specifically: Define the phase sequence i = 1, 2, 3, …, n. The phases are dynamically associated through the dry density state ρ i Transfer dynamic association: (3) In the formula, g() is a data-based dry density evolution function.

8. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 1, characterized in that In step S3.2, the specific steps for constructing the multi-objective function of energy and time are: Using the equivalent energy model, the relative efficiency of energy input is quantified through the combined relationship of exciting force, frequency, and number of vibrations, providing a trade-off index for multi-objective optimization; on the premise of meeting the dry density increment Δ ρ i , the vibration energy i required for the E i th optimization stage depends on the exciting force F i at this stage and its vibration time T i , where T i is the ratio of the number of vibrations N i to the vibration frequency f i ; With the total energy E total and the total time T total as the optimization objectives, a two-objective function is established: (4) (5)。 9. The multi-stage and multi-objective vibration parameter optimization method for the compaction process of coarse-grained soil according to claim 1, characterized in that In step S3.3, use the non-dominated sorting genetic algorithm for multi-stage compaction to generate a Pareto front solution set of minimum energy and minimum time; the specific steps are: First, set the population size and randomly generate initial individuals within the vibration parameter space. The parameters include the exciting force F , the vibration frequency f , and the number of vibrations N ; Then use BO-FCNN to predict compaction deformation, calculate the energy consumption and vibration time; Then, through non-dominated sorting and crowding distance, generate a well-distributed non-dominated sorted Pareto front solution set, that is, the vibration parameter combination of minimum energy and time.

10. The multi-stage and multi-objective vibration parameter optimization method for the coarse-grained soil compaction process according to claim 1, characterized in that In step S3.4, the priority is adjusted by weight coefficients ω 1 (energy weight) and ω 2 (time weight): (8) In the formula, ω 1 + ω 2 = 1, E norm , T norm are normalization factors to ensure dimensional consistency.

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