A multi-stage and multi-objective vibration parameter optimization method for coarse-grained soil compaction process

Abstract

The present invention belongs to the technical field of civil engineering roadbed compaction, and specifically discloses a multi-stage and multi-objective vibration parameter optimization method for the coarse-grained soil compaction process, comprising the following steps: S1, obtaining dynamic response data of multiple working conditions, constructing a training set, a validation set, and a test set after standardization; S2, establishing a dry density dynamic evolution model based on BO-FCNN, and analyzing the key parameters affecting compaction deformation in combination with SHAP values; S3, completing multi-stage and multi-objective vibration parameter optimization, specifically including: S3.1, multi-stage division and dynamic constraint transfer; S3.2, constructing a multi-objective function; S3.3, using MC-NSGA-II to generate a Pareto front solution set; S3.4, outputting the optimal vibration parameter combination based on weighted decision-making. The present invention realizes closed-loop optimization from data modeling to parameter decision-making, and dynamically adjusts the optimization strategy according to actual engineering needs to maximize construction efficiency.

Description

Technical Field

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

[0002] Coarse-grained soil is the core filler in coarse-grained soil filling projects such as high-fill roadbeds and rockfill dams. Its compaction quality directly affects the structural stability and service life. Although existing technologies use vibration compaction to improve density, they still have the following key drawbacks:

[0003] 1. Insufficient compaction deformation prediction accuracy: Traditional compaction deformation models rely on empirical formulas or simplified assumptions, or only consider the relationship between a single parameter and deformation. They cannot meet the needs of high-precision prediction, and it is difficult to characterize the nonlinear coupling between vibration parameters and dry density and adapt to the compaction characteristics of coarse-grained soil under complex conditions.

[0004] 2. Limitations of parameter optimization: Most existing optimization methods are single-objective static optimization, which does not consider the multi-stage dynamic characteristics of the compaction process and the energy-time multi-objective trade-off.

[0005] 3. Lack of optimization of solution selection according to decision-making requirements: Existing methods lack the flexibility to select solutions according to decision-makers' preferences, which limits their ability to meet diverse practical engineering needs.

[0006] 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

[0007] The purpose of the present invention is to provide a multi-stage and multi-objective vibration parameter optimization method for the coarse-grained soil compaction process, so as to solve the problems raised in the background technology of the current coarse-grained soil compaction process, such as insufficient compaction deformation prediction accuracy, parameter optimization limitations, and lack of optimization scheme selection according to decision-making requirements.

[0008] To achieve the above objectives, the present invention provides a multi-stage and multi-objective vibration parameter optimization method for a coarse-grained soil compaction process, comprising the following steps:

[0009] S1. Obtain dynamic response data of multiple working conditions through vibration compaction tests, and construct training sets, validation sets, and test sets after standardization.

[0010] S2. Based on the Bayesian optimization fully connected neural network algorithm, a dynamic evolution model of dry density is established, and the key parameters affecting compaction deformation are analyzed in combination with the SHAP value;

[0011] S3. Complete multi-stage and multi-objective vibration parameter optimization, including:

[0012] S3.1, divide the compaction process into multiple stages and transfer them through dynamic constraints;

[0013] S3.2. Construct a multi-objective function of energy and time;

[0014] S3.3, Generate Pareto front solution set using non-dominated sorting genetic algorithm with multi-stage compaction;

[0015] S3.4. Adjust the energy and time weight coefficients according to the project priority and output the optimal vibration parameter combination.

[0016] In a specific embodiment, in step S1, the test equipment used in the vibration compaction test includes a UTM-250 testing machine; the vibration compaction test uses sinusoidal wave vibration loading.

[0017] In a specific embodiment, in step S1, the multi-operation-condition dynamic response data obtained from the vibration compaction test include initial dry density, exciting force, frequency, number of vibrations, and real-time dry density.

[0018] In a specific embodiment, in step S2, the initial dry density, exciting force, frequency, and number of vibrations are used as input data of the dry density dynamic evolution model; and the real-time dry density is used as output data of the dry density dynamic evolution model.

[0019] In a specific embodiment, in step S2, the mean square error is used as the loss function in the training process of the dynamic evolution model of dry density, and the model parameters are dynamically updated in combination with the Adam optimizer; at the same time, in order to suppress overfitting, an early stopping strategy is adopted, that is, when the loss of the validation set does not decrease in 5 consecutive rounds, the training is terminated; in order to optimize the network structure, the FCNN model is dynamically tuned using the Bayesian hyperparameter optimization tool; in 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 proxy model to predict the performance of each set of hyperparameters, and selects the next set of hyperparameters for evaluation through the acquisition function; after each training and verification of the model, the optimization process will update the proxy model according to the evaluation results, so as to gradually find the optimal hyperparameter combination; the optimized model test set meets the following requirements: determination coefficient ≥ 0.85, mean absolute error ≤ 0.05 g / cm 3 , root mean square error ≤ 0.08g / cm 3 The absolute value of the SHAP value is used to quantify the degree of influence of each vibration parameter on compaction deformation and identify the key influencing factors.

[0020] In a specific embodiment, in step S3.1, the compaction process is discretized into n optimization stages; the stage division is based on the dry density increment threshold Δ r min = 0.01g / cm3 , that is, in 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;

[0021] (1)

[0022] The constraints that need to be met are:

[0023] (2)

[0024] Where, Δ r min is the minimum increment of dry density, Δ r i is the dry density increment in stage i, r i 、 r i-1 are the target dry density and initial dry density of stage i, r target is the target dry density; k is the dry density increment coefficient; m Is a positive integer.

[0025] In a specific implementation, in step S3.1, dynamic constraint transfer is specifically as follows:

[0026] Define a sequence of stages i = 1, 2, 3,…, n, with the dry density state between stages r i Transfer dynamic associations:

[0027] (3)

[0028] Where g() is the dry density evolution function based on the data.

[0029] In a specific embodiment, in step S3.2, the specific steps of constructing the multi-objective function of energy and time are:

[0030] The equivalent energy model is used to quantify the relative efficiency of energy input through the combined relationship of exciting force, frequency and vibration number, providing a trade-off indicator for multi-objective optimization; r i Under the premise of E i Depends on the exciting force at this stage F i and its vibration time T i ,in T i The number of vibrations Ni and vibration frequency f i The ratio of total energy E total and total time T total To optimize the goal, a dual objective function is established:

[0031] (4)

[0032] (5).

[0033] In a specific embodiment, in step S3.3, a multi-stage compacted non-dominated sorting genetic algorithm is used to generate a Pareto front solution set with minimum energy and minimum time; the specific steps are:

[0034] First, the population size is set, and the initial individuals are randomly generated in the vibration parameter space. The parameters include the excitation force F , vibration frequency f and vibration frequency N ;

[0035] Then, BO-FCNN is used to predict compaction deformation, calculate energy consumption and vibration time;

[0036] Then, through non-dominated sorting and crowding distance, the Pareto front solution set of balanced non-dominated sorting is generated, that is, the vibration parameter combination with minimum energy and time.

[0037] In a specific embodiment, in step S3.4, the weight coefficient oh 1 (energy weight) and oh 2 (Time Weight) Adjust Priority:

[0038] (8)

[0039] Where, oh 1+ oh 2=1, E norm 、 T norm is a normalization factor to ensure dimensional consistency.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention realizes closed-loop optimization from data modeling to parameter decision-making by coupling BO-FCNN compaction deformation prediction with MC-NSGA-II parameter optimization.

[0042] The present invention proposes a multi-stage division method to optimize energy and time simultaneously, and dynamically adjusts the optimization strategy according to actual engineering needs to maximize construction efficiency.

[0043] The weighted decision-making mechanism of the present invention supports flexible adjustment of energy and time priorities according to construction conditions, improving the universality of the method.

[0044] The present invention can effectively reduce energy consumption and construction time through multi-stage progressive compaction and multi-objective optimization, thereby reducing project costs and improving construction efficiency.

[0045] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention is further described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0047] Figure 1 This is a flow chart of coarse-grained soil compaction deformation prediction and parameter optimization according to one embodiment of the present invention;

[0048] Figure 2 The present invention is an embodiment of the coarse-grained soil vibration compaction optimization flow chart. DETAILED DESCRIPTION

[0049] The embodiments of the present invention are described in detail below. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0050] A multi-stage and multi-objective vibration parameter optimization method for a coarse-grained soil compaction process according to the present invention comprises the following steps:

[0051] S1. Obtain dynamic response data of multiple working conditions through vibration compaction tests, and construct training sets, validation sets, and test sets after standardization.

[0052] S2. Based on the Bayesian Optimization Fully Connected Neural Network (BO-FCNN) algorithm, a dynamic evolution model of dry density was established, and the key parameters affecting compaction deformation were analyzed in combination with the SHAP value.

[0053] S3. Complete multi-stage and multi-objective vibration parameter optimization, including:

[0054] S3.1, divide the compaction process into multiple stages and transfer them through dynamic constraints;

[0055] S3.2. Construct a multi-objective function of energy and time;

[0056] S3.3. Generate Pareto front solution set using multi-stage compaction non-dominated sorting genetic algorithm (MC-NSGA-II);

[0057] S3.4. Adjust the energy and time weight coefficients according to the project priority and output the optimal vibration parameter combination.

[0058] Example 1

[0059] 1. Data collection and experimental design:

[0060] Test 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%.

[0061] Sample preparation: Graded crushed stone filler ( C u =15, C c =2.5, particle size d = 2~30mm), and fill in layers into a steel cylindrical mold (diameter × height = 160 mm × 250 mm);

[0062] Working condition settings: The test uses sinusoidal vibration loading with excitation force (2, 4, 6, 8, 10, 12 kN) and frequency (20, 23, 26, 29, 32, 35 Hz). The initial dry density is 1.55-1.6 g / cm3. Each group is set up with two parallel tests, and the total data volume is 72 sets.

[0063] Data collection: The dry density is recorded in real time within the vibration frequency range of 1-1000 times to form a time series data set.

[0064] BO-FCNN prediction model construction:

[0065] (1) Data processing: The input data of the input layer of the initial model are set to the initial dry density, exciting force, frequency, and number of vibrations, and the output data of the output layer are set to the real-time dry density. In order to ensure data consistency, both input and output data are standardized, and the standardized time series data set is divided into training set, validation set, and test set according to the ratio of 80%, 10%, and 10%.

[0066] (2) Model optimization: The initial model is trained and validated using the training set and validation set. The mean square error (MSE) is used as the loss function during model training, 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 in 5 consecutive rounds, the training is terminated. In order to optimize the network structure, the FCNN model is dynamically tuned using the Bayesian hyperparameter optimization tool. 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 proxy model (usually Gaussian process regression). During the optimization process, the hyperparameter range is 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 a surrogate model to predict the performance of each set of hyperparameters and selects the next set of hyperparameters for evaluation using an acquisition function (if improvements are expected). After each model training and validation, the optimization process updates the surrogate model based on the evaluation results, gradually finding the optimal hyperparameter combination. The initial model architecture uses the FCNN model architecture, including the connectivity of all its layers and hyperparameter configuration. Before training, all weights and biases are initialized to random values. These parameters are optimized using the training and validation sets until convergence, ensuring that the model better fits the data.

[0067] (3) Model validation: The test set of the prediction model must meet the following requirements: coefficient of determination ≥ 0.85, mean absolute error ≤ 0.05 g / cm³, and root mean square error ≤ 0.08 g / cm³.

[0068] Interpretability analysis: The absolute value of the SHAP value is used to quantify the degree of influence of each vibration parameter on compaction deformation and identify the key influencing factors.

[0069] Multi-stage and multi-objective optimization model building:

[0070] (1) Multi-stage division rules:

[0071] In order to achieve dynamic optimization of vibration parameters, the compaction process is discretized into n The basis for stage division is the dry density increment threshold Δ r min =0.01g / cm 3 , that is, in 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.

[0072] (1)

[0073] The constraints that need to be met are:

[0074] (2)

[0075] Where, Δ r min is the minimum increment of dry density, Δ r i is the dry density increment in stage i, r i 、 r i-1 are the target dry density and initial dry density of stage i, r target is the target dry density; k is the dry density increment coefficient; m Is a positive integer.

[0076] (2) Dynamic constraint transfer:

[0077] Define a sequence of stages i = 1, 2, 3,…, n, with the dry density state between stages r i Transfer dynamic associations:

[0078] (3)

[0079] Where g() is the dry density evolution function based on the data.

[0080] (3) Construction of multi-objective functions.

[0081] The equivalent energy model is used to quantify the relative efficiency of energy input through the combined relationship between the exciting force, frequency and number of vibrations, providing a trade-off indicator for multi-objective optimization. r i Under the premise of i The vibration energy required for each optimization stage E i Depends on the exciting force at this stage F i and its vibration time T i ,in T i The number of vibrations N i and vibration frequency f i The ratio of total energy E total and total time T total To optimize the goal, a dual objective function is established:

[0082] (4)

[0083] (5).

[0084] The multi-objective function in this embodiment is a dual-objective function.

[0085] MC-NSGA-II optimization algorithm implementation:

[0086] (1) Initialize the population:

[0087] The present invention is based on the improved multi-stage optimization algorithm of NSGA-II (MC-NSGA-II). First, the population size is set to 50~400, and the initial individuals are randomly generated in the vibration parameter space. The parameters include the excitation force F , vibration frequency f and vibration frequency N .

[0088] (2) Calculate the fitness value:

[0089] BO-FCNN is used to predict compaction deformation, calculate energy and vibration time.

[0090] (3) Non-dominated sorting and crowding distance calculation:

[0091] Through non-dominated sorting and crowding distance, a Pareto front solution set of balanced non-dominated sorting is generated to screen vibration parameter combinations that perform well in both energy and time targets.

[0092] If the parameter combination x a is the optimal solution, then x a Dominate x b If and only if:

[0093] At least one strictly holds (6)

[0094] Maintaining the diversity of Pareto front solutions by crowding distance, calculating x k Crowding distance:

[0095] (7)

[0096] In the formula 、 are the adjacent solution values of energy and time on the target, 、 The maximum and minimum values of the corresponding targets. j =1 for energy, j=2 for time). Prioritize solutions with high crowding distance to avoid excessive aggregation of parameter combinations and cover the global optimization potential of amplitude, frequency, and number of vibrations.

[0097] (4) Parameter optimization and output optimal solution:

[0098] According to the optimization iteration stage, the crossover probability and mutation probability are dynamically adjusted to optimize the search strategy in stages:

[0099] Initial stage (iterations < 100): Focus on global search, use high mutation probability (0.15~0.2) and low simulated binary crossover index (10), combined with tournament selection strategy to improve solution diversity.

[0100] Intermediate stage (100-200 times): Balance global search and local search, use a crossover probability of 0.7 and a mutation probability of 0.1, and gradually converge to a high-quality solution.

[0101] Late stage (>200 times): Strengthen local search capability, reduce mutation probability (0.01~0.05), improve simulated binary crossover index (30), and ensure refined search of Pareto front solution set.

[0102] (5) Weight decision:

[0103] By weight coefficient oh 1 (energy weight) and oh 2 (Time Weight) Adjust Priority:

[0104] (8)

[0105] Where, oh 1+ oh 2=1, E norm 、 T norm is a normalization factor to ensure dimensional consistency.

[0106] The MC-NSGA-II vibration parameter optimization process considering weighted decision is as follows: Figure 2 shown.

[0107] The effectiveness of the optimized parameters was verified by experiments:

[0108] This study validated the effectiveness of the optimized vibration parameters through indoor vibration compaction tests and compared the compaction performance of the MC-NSGA-II optimization scheme with that of a traditional empirical scheme. Seven control schemes were used in the experiment, with schemes 1 through 5 adopting alternating combinations and schemes 6 and 7 adopting fixed parameters. The details are as follows:

[0109] (1) Alternating combination scheme:

[0110] Solution 1: First, perform two vibrations (excitation force 15kN, frequency 28Hz), and then perform two vibrations (excitation force 8kN, frequency 32Hz).

[0111] Solution 2: First perform two vibrations (excitation force 12kN, frequency 28Hz), and then perform one vibration (excitation force 6kN, frequency 32Hz).

[0112] Solution 3: First perform three vibrations (excitation force 14kN, frequency 34Hz), then perform one vibration (excitation force 7kN, frequency 38Hz).

[0113] Solution 4: First perform two vibrations (excitation force 6kN, frequency 36Hz), then perform three vibrations (excitation force 12kN, frequency 32Hz).

[0114] Solution 5: First perform one vibration (excitation force 13kN, frequency 38Hz), then perform one vibration (excitation force 6kN, frequency 34Hz).

[0115] The number of single-pass vibrations in each scheme was 20 times, and the combinations were alternating until the target dry density was reached.

[0116] (2) Fixed parameter scheme:

[0117] Solution 6: Use fixed vibration parameters (excitation force 14kN, frequency 36Hz) and uniform vibration.

[0118] Solution 7: Use fixed vibration parameters (excitation force 12kN, frequency 38Hz) and uniform vibration.

[0119] 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 was verified and the effectiveness of the optimized vibration parameters was ensured.

[0120] Engineering application example: Optimization of compaction of coarse-grained soil in a railway subgrade:

[0121] (1) Project background:

[0122] This example uses 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 vibration compaction parameters is to improve construction efficiency while reducing energy consumption and ensuring that the final compaction quality meets project requirements.

[0123] (2) Stage division:

[0124] Based on the MC-NSGA-II multi-stage optimization method, the minimum dry density increment Δρ is set. min =0.01g / cm 3, the optimal number of stages is calculated. During the optimization process, vibration parameters (excitation force, frequency, and number of vibrations) are dynamically adjusted at each stage to achieve the Pareto front optimal solution that minimizes energy consumption and maximizes construction efficiency.

[0125] (3) Optimization results:

[0126] Multi-objective optimization is performed through MC-NSGA-II, weights are selected from the Pareto front solution set, and finally the optimal vibration parameter combination is obtained.

[0127] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection 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: The steps include: S1. Obtain dynamic response data under multiple working conditions through vibration compaction tests, and construct training sets, validation sets, and test sets after standardization. S2. Based on the Bayesian optimization fully connected neural network algorithm, a dynamic evolution model of dry density is established, and the key parameters affecting compaction deformation are analyzed in combination with the SHAP value; S3. Complete multi-stage and multi-objective vibration parameter optimization, including: S3.1, divide the compaction process into multiple stages and transfer them through dynamic constraints; In step S3.1, the compaction process is discretized into n optimization stages; the stage division is based on the dry density increment threshold Δ ρ min =0.01g / cm 3 , that is, in 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 constraints that need to be met are: (2) Where, Δ ρ min is the minimum increment of dry density, Δ ρ i For the i Stage dry density increment, ρ i 、 ρ i-1 Respectively i The target dry density and initial dry density of the stage, ρ target is the target dry density; k is the dry density increment coefficient; m is a positive integer; S3.

2. Construct a multi-objective function of energy and time; S3.3, Generate Pareto front solution set using non-dominated sorting genetic algorithm with multi-stage compaction; S3.

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

2. 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 S1, the test equipment used in the vibration compaction test includes a UTM-250 testing machine; the vibration compaction test adopts sinusoidal vibration loading.

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

4. The multi-stage and multi-objective vibration parameter optimization method for the coarse-grained soil compaction process according to claim 3, characterized in that: In step S2, the initial dry density, exciting force, frequency, and vibration times are used as input data of the dry density dynamic evolution model; and the real-time dry density is used as 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, the mean square error is used as the loss function in the training process of the dynamic evolution model of dry density, and the model parameters are dynamically updated in combination with the Adam optimizer; at the same time, in order to suppress overfitting, an early stopping strategy is adopted, that is, when the loss of the validation set does not decrease in 5 consecutive rounds, the training is terminated; in order to optimize the network structure, the FCNN model is dynamically tuned using the Bayesian hyperparameter optimization tool; in 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 proxy model to predict the performance of each set of hyperparameters and selects the next set of hyperparameters for evaluation through the acquisition function; after each training and verification of the model, the optimization process will update the proxy model according to the evaluation results, so as to gradually find the optimal hyperparameter combination; the optimized model test set meets the following requirements: determination coefficient ≥ 0.85, mean absolute error ≤ 0.05 g / cm 3 , root mean square error ≤ 0.08g / cm 3 The absolute value of SHAP value is used to quantify the influence of each vibration parameter on compaction deformation and identify the key influencing factors.

6. 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 S3.1, dynamic constraint transfer is specifically as follows: Defining a Phase Sequence i = 1, 2, 3,…, n, with the stages passing through the dry density state ρ i Transfer dynamic associations: (3) Where g() is the dry density evolution function based on the data; F i For the i The exciting force of each stage; f i For the i The vibration frequency of each stage; N i For the i The number of vibrations in each stage.

7. 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 S3.2, the specific steps for constructing the multi-objective function of energy and time are as follows: The equivalent energy model is used to quantify the relative efficiency of energy input through the combined relationship of exciting force, frequency and vibration number, providing a trade-off indicator for multi-objective optimization; ρ i Under the premise of i The vibration energy required for each optimization stage E i Depends on the exciting force at this stage F i and its vibration time T i ,in T i The number of vibrations N i and vibration frequency f i The ratio of Total energy E total and total time T total To optimize the goal, a dual objective function is established: (4) (5)。 8. 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 S3.3, a multi-stage compacted non-dominated sorting genetic algorithm is used to generate the Pareto front solution set with minimum energy and minimum time. The specific steps are as follows: First, the population size is set, and the initial individuals are randomly generated in the vibration parameter space. The parameters include the excitation force F , vibration frequency f and vibration frequency N ; Then, BO-FCNN is used to predict compaction deformation, calculate energy consumption and vibration time; Then, through non-dominated sorting and crowding distance, the Pareto front solution set of balanced non-dominated sorting is generated, that is, the vibration parameter combination with minimum energy and time.

9. 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 weight coefficient, i.e., the energy weight ω 1 and time weight ω 2 Adjust the priority: (8) Where, ω 1+ ω 2=1, E norm 、 T norm is the normalization factor to ensure dimensional consistency; E total is the total energy, T total For the total time.

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