Gravel thermal conductivity coefficient prediction method and system based on hippo optimization algorithm optimizing MLP

Abstract

The embodiment discloses a gravel thermal conductivity coefficient prediction method and system based on hippo optimization algorithm optimization MLP, based on the measured data of the gravel thermal conductivity coefficient, taking the dry density, water content and temperature of the gravel as the input, taking the thermal conductivity coefficient of the gravel as the output, constructing the MLP neural network prediction model specially for the gravel, and adopting the three-stage search mechanism of the hippo optimization algorithm (HO) to automatically optimize the hyperparameter configuration of the MLP. The three stages of river exploration, defense behavior and escape behavior of the HO algorithm can realize global exploration, jump out of local optimization and local fine development respectively, significantly improve the prediction accuracy and stability of the MLP, and realize the rapid and accurate prediction of the thermal physical parameters of the gravel. The present application is suitable for railway ballast thermal stability analysis, ground source heat pump design, cold region engineering thermal protection and the like.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of geotechnical engineering and artificial intelligence, and in particular to a method and system for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo optimization algorithm. Background Technology

[0002] Gravel is a type of rock or mineral debris with a particle size greater than 2 mm and less than 60 mm. Compared to fine-grained soils such as sand and silt, gravel is characterized by larger particle size, more complex interparticle contact patterns, larger pore size, and uneven pore distribution. Under humid conditions, its pores contain different media such as water and air. When the ambient temperature drops to a freezing point, the pore water undergoes a phase change and forms ice, significantly altering the heat transfer path and thermal conductivity conditions within the gravel. Therefore, the thermal conductivity of gravel is not only related to the particle composition of the material itself but is also influenced by factors such as dry density, moisture content, and temperature, exhibiting particularly complex nonlinear characteristics during the transition between frozen and unfrozen states.

[0003] Gravel, along with similar coarse-grained materials such as sand, gravel, crushed stone, and ballast, is widely used in underground and railway engineering. For projects involving low temperatures, freezing, and freeze-thaw processes, thermal conductivity is a crucial thermophysical property parameter for temperature field analysis, and its accuracy directly impacts the results of thermal analysis. Compared to general ambient-temperature projects, the thermal conductivity of gravel materials varies more significantly with temperature and moisture content in artificial freezing construction and high-speed railway projects in cold regions. Therefore, rapid and accurate prediction of its thermal conductivity is of paramount engineering importance.

[0004] In the construction of subway tunnel connecting passages, when the project traverses water-rich sand and gravel, artificial freezing is often used to reinforce and stop water in the strata. The thermal conductivity of the sand and gravel strata directly affects the cold transfer and temperature field development during freezing, thus influencing the formation of the frozen wall. Due to the large particle size and complex pore structure of sand and gravel, their thermal conductivity is affected by factors such as dry density, moisture content, and temperature. In particular, the thermal conductivity changes significantly after pore water freezes. Therefore, accurately obtaining the thermal conductivity of sand and gravel under different conditions is of great significance for temperature field analysis during freezing construction.

[0005] Furthermore, in ballasted tracks for high-speed railways in cold and seasonally frozen soil regions, ballast, as a typical coarse-grained material, significantly affects temperature transfer and freeze-thaw processes in the track and subgrade due to its thermal conductivity. The particle contact state, density, and moisture content of ballast vary considerably, and its thermal conductivity also changes with dry density, moisture content, and temperature. Therefore, rapid and accurate prediction of the thermal conductivity of coarse-grained materials such as gravel strata and railway ballast is crucial for artificial freezing construction and thermal stability analysis of railways in cold regions.

[0006] Currently, the main methods for obtaining the thermal conductivity of gravel include laboratory testing and empirical formulas. Laboratory testing methods, such as the transient hot wire method and the transient plane heat source method, are used to determine the thermal conductivity of gravel. While this method offers high accuracy, it has the following drawbacks: the gravel particles are large, making representative sampling difficult; the testing equipment requirements are high, necessitating large-scale testing devices; the testing cycle is long, requiring several hours for each sample; and repeated testing is required under different temperature conditions.

[0007] Regarding empirical formulas, in 1949 Kersten, based on experimental data from the University of Minnesota, proposed an empirical formula for sandy soil: However, this formula is mainly designed for sandy soils. For gravel with larger particle sizes, direct application will result in significant errors due to differences in particle contact characteristics and pore structure. In addition, while models such as the Johansen model and the Côté-Konrad model perform well for fine-grained soils, none of them have been specifically calibrated for gravel.

[0008] In recent years, machine learning methods have been widely used in the field of geotechnical engineering parameter prediction. Support Vector Regression (SVR), Random Forest (RF), and Gradient Boosting Tree (XGBoost) have been successfully applied to predict the thermal conductivity of soil. Multilayer Perceptron (MLP) neural networks, due to their powerful nonlinear fitting capabilities and flexible network structure, have the potential to build models for predicting the thermal conductivity of gravel. However, the predictive performance of MLPs largely depends on the hyperparameter configuration (such as hidden layer structure, learning rate, activation function, etc.). Traditional grid search and random search methods are inefficient in high-dimensional hyperparameter spaces and struggle to find the globally optimal configuration.

[0009] Hippopotamus Optimization (HO) is a metaheuristic optimization algorithm based on population search. Its search process includes position update mechanisms at different stages and enhances its exploration and development capabilities within the search space through global exploration, Levy-based jump search, and local fine-grained search near the optimal solution. Coupled with the MLP model, which possesses strong nonlinear mapping capabilities, the HO algorithm can automatically search for hyperparameters such as hidden layer structure, learning rate, activation function, regularization coefficient, and batch size. This reduces the subjectivity of manually determining hyperparameters and enhances the MLP's ability to characterize the complex nonlinear relationships between gravel dry density, moisture content, temperature, and thermal conductivity.

[0010] However, current technologies lack a method specifically tailored to the characteristics of coarse-grained gravel materials. This method uses dry density, moisture content, and temperature as primary input parameters and leverages the HO algorithm to co-optimize the hyperparameters of the MLP model, thus enabling rapid prediction of gravel thermal conductivity under both frozen and unfrozen conditions. Particularly important is the need for a method to predict gravel thermal conductivity in artificially frozen construction of subway tunnel connecting passages and in the thermal conduction analysis of ballasted track ballast in cold-region high-speed railways. This method should reduce the need for numerous repetitive thermal conductivity tests, overcome the limitations of traditional empirical formulas, and characterize the nonlinear relationships between multiple coupled factors. Summary of the Invention

[0011] This invention discloses a method and system for predicting the thermal conductivity of gravel based on the Hippo optimization algorithm-optimized MLP, in order to overcome the above-mentioned technical problems.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows: A method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm includes the following steps: S1: Based on the dry density, moisture content, and temperature of the gravel, construct the input features of the gravel and obtain the thermal conductivity corresponding to the input features of the gravel to construct a thermal conductivity dataset of the gravel; and divide the thermal conductivity dataset into a training set and a validation set; S2: Determine the set of hyperparameters to be optimized for the MLP gravel thermal conductivity prediction model, and use the set of hyperparameters to be optimized as individual hippos to initialize the hippo population; S3: Using the training set to analyze the first... The MLP gravel thermal conductivity prediction model for each individual hippopotamus was trained, and the predicted thermal conductivity values ​​were obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Then, based on the fitness evaluation function, the hippopotamus individual with the lowest fitness value in the hippopotamus population was identified as the dominant hippopotamus. An index for individual hippos. , Population size; S4: Based on the dominant hippopotamus, the hippopotamus optimization algorithm is used to obtain the set of hyperparameters after three-stage iterative optimization in order to obtain the optimal hyperparameters; S5: Based on the optimal hyperparameters, construct the final MLP gravel thermal conductivity prediction model, and use the gravel thermal conductivity dataset to train the final MLP gravel thermal conductivity prediction model; based on the trained final MLP gravel thermal conductivity prediction model, obtain the predicted thermal conductivity value of the new gravel sample to be predicted.

[0013] Furthermore, the method used to obtain the set of hyperparameters after the three-stage iterative optimization is as follows: S41: Obtain the time decay factor to get the position of the hippopotamus individual after the first stage update; The formula used to obtain the time decay factor is as follows:

[0014] In the formula: This is the time decay factor; This represents the current iteration number; This represents the maximum number of iterations. It is an exponential function; The formula used to obtain the position of an individual hippopotamus after the first stage update is as follows:

[0015] In the formula: For the first The number of individual hippos after the first phase update Dimensional position; This is the position before the update; The first dominant hippopotamus Dimensional position; , The numbers are mutually independent uniform random numbers in the interval [0,1]. , All are integers randomly selected from {1,2}; To randomly select a subset of hippos from the current population at the th The arithmetic mean of the dimensional position coordinates, i.e. ,in, This is a randomly selected set of indexes for individual hippos; The total number of randomly selected hippopotamus individuals; Index of randomly selected individual hippos; S42: Based on the hippopotamus's position after the first phase update, the Levy flight mechanism is used to obtain the hippopotamus's position after the second phase update; the formula used is as follows:

[0016]

[0017] In the formula: For the first The number of individual hippos after the second phase update Dimensional position; For predator location and The distance between them; It is the absolute value; In the first The predator's position is randomly generated within the dimensional search boundary; For the first Levy's flight stride length; This is the predator position control constant; For the direction parameters of defensive behavior; These are random perturbation parameters; These are the step size control parameters; in,

[0018] In the formula: and Let be mutually independent normally distributed random variables, where , ; for Theoretical standard deviation for The variance; Levy index;

[0019] In the formula: It is the Gamma function; S43: Based on the position of the hippopotamus individual after the second stage update, obtain the position of the hippopotamus individual after the third stage update, so as to obtain the hyperparameter set after three-stage iterative optimization; the formula used is as follows:

[0020] In the formula: For the first The number of individual hippos after the third phase update Dimensional position; The first dominant hippopotamus Dimensional position; This is the step size scaling factor that decreases with the number of iterations; A uniformly random number within the interval [0,1];

[0021] In the formula: This is the current iteration number, and This represents the maximum number of iterations. This is the initial value of the step scaling factor; This is the final value of the step scaling factor.

[0022] Furthermore, the formula used to initialize the hippopotamus population is as follows:

[0023] In the formula: For the first The first individual hippopotamus The location of the hyperparameters; and The first Lower and upper bounds of the hyperparameters; It is a random number uniformly distributed in the interval [0,1].

[0024] Furthermore, the formula used in the forward propagation of the MLP gravel thermal conductivity prediction model is as follows:

[0025]

[0026] In the formula: For the first The weighted input vector of the layer, i.e., the first layer The input to the layer activation function; For the first The layer's output vector, i.e., the activation values ​​after processing by the activation function; This is the index of the activation function layer. and The first Layer weight matrix and bias vector; This is the activation function.

[0027] Furthermore, the fitness evaluation function is expressed as follows:

[0028] In the formula: The number of samples in the validation set; This is the actual thermal conductivity value; This is the predicted value for thermal conductivity; The fitness function value; This is the root mean square error.

[0029] A prediction system for predicting the thermal conductivity of gravel based on the Hippo Optimization Algorithm-optimized MLP includes: a data input module, a data preprocessing module, a hyperparameter optimization module, a prediction model module, and a result output module. The data input module is used to receive the dry density, moisture content and temperature of the gravel; The data preprocessing module is used to preprocess the dry density, moisture content and temperature of the gravel to construct a dataset of the thermal conductivity of the gravel; and divides the dataset of the thermal conductivity into a training set and a validation set. The hyperparameter optimization module is used to optimize the training set based on the first parameter in the hippopotamus population. The MLP gravel thermal conductivity prediction model for each hippopotamus individual was trained, and the predicted thermal conductivity value was obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Based on the fitness evaluation function, the hippopotamus individual with the smallest fitness value in the hippopotamus population was determined as the dominant hippopotamus. The prediction model module is used to construct the final MLP gravel thermal conductivity prediction model based on the optimal hyperparameters, and to train the final MLP gravel thermal conductivity prediction model using a gravel thermal conductivity dataset; based on the trained final MLP gravel thermal conductivity prediction model, the predicted thermal conductivity value of the new gravel sample to be predicted is obtained. The results output module is used to visualize the predicted thermal conductivity values ​​of new gravel samples to be predicted.

[0030] Beneficial Effects: This invention provides a method and system for predicting the thermal conductivity of gravel based on the Hippo Optimization Algorithm (HO) optimized MLP. Addressing the technical problems of existing gravel thermal conductivity prediction methods, such as long testing cycles, limited accuracy of empirical formulas, lack of dedicated prediction models, and difficulties in MLP hyperparameter optimization, this invention constructs a dedicated MLP neural network prediction model for gravel, using measured gravel thermal conductivity data as input and gravel dry density, moisture content, and temperature as input, with gravel thermal conductivity as output. The Hippo Optimization Algorithm (HO) employs a three-stage search mechanism to automatically optimize the hyperparameter configuration of the MLP. Through the three stages of river exploration, defense behavior, and escape behavior of the HO algorithm, global exploration, escape from local optima, and local refinement are achieved respectively, optimizing the hyperparameters of the MLP gravel thermal conductivity prediction model. This enables rapid prediction of gravel thermal conductivity under different dry densities, moisture contents, and temperatures, significantly improving the prediction accuracy and stability of the MLP and achieving rapid and accurate prediction of gravel thermal properties. This invention is applicable to fields such as thermal stability analysis of railway ballast, design of ground source heat pumps, and thermal protection for cold-region engineering. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of the gravel thermal conductivity prediction method based on the Hippo optimization algorithm to optimize MLP according to the present invention.

[0033] Figure 2 This is a complete technical flowchart of the gravel thermal conductivity prediction method in this embodiment of the invention; Figure 3 This is a schematic diagram of the iterative process of optimizing MLP hyperparameters using the HO algorithm in an embodiment of the present invention, including a schematic diagram of the position update of the three-stage search mechanism of the HO algorithm; Figure 4 This is a schematic diagram of the MLP neural network structure in an embodiment of the present invention, showing the connection relationship between the input layer (dry density, moisture content, temperature), the hidden layer, and the output layer (thermal conductivity); Figure 5 This is a comparison chart of the predicted and actual values ​​of the HO-MLP model on the test set in this embodiment of the invention; Figure 6 This is a comparison chart of the prediction accuracy of the HO-MLP model on the test set in this embodiment of the invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] This embodiment introduces a method for predicting the thermal conductivity of gravel based on the Hippo Optimization Algorithm-optimized MLP, including the following steps: Figure 1 and Figure 2 As shown: S1: Based on the dry density, moisture content, and temperature of the gravel, construct the input features of the gravel and obtain the thermal conductivity corresponding to the input features of the gravel to construct a thermal conductivity dataset of the gravel; and divide the thermal conductivity dataset into a training set and a validation set; Specifically, each thermal conductivity dataset contains input features and output labels, whereby the input features include dry density. Moisture content ,temperature The output label is the thermal conductivity. The input features are subjected to unit conversion and standardization, and the dataset is divided into training set, validation set and test set.

[0036] This embodiment uses measured gravel thermal conductivity data as the training data source. The gravel used is typical river alluvial gravel, which has good engineering representativeness. The thermal conductivity dataset contains 64 sets of measured data, covering the following parameter range: dry density. Moisture content Test temperature Thermal conductivity The input features for each set of data are: The output labels are .

[0037] This embodiment preprocesses the input features, including converting the input features to the International System of Units (SI) and performing Z-score standardization on the input features: Specifically, the unit conversion of the input features is performed using the following formula: ; ; .

[0038] In the formula: Dry density; Grams per cubic centimeter, the international unit of density; Measured in pounds per cubic foot, density is an imperial unit. For temperature; Fahrenheit; Thermal conductivity; Kelvin per watt is the unit of thermal conductivity. The unit for thermal conductivity is the imperial system. Perform Z-score standardization on the input features:

[0039] In the formula: This is the mean vector of each feature; The standard deviation vector of each feature; standardization parameters and The data is computed and stored on the training set, while the validation and test sets are transformed using the same standardized parameters to avoid data leakage. These are the standardized input feature values; These are the original input feature values.

[0040] In this embodiment, the thermal conductivity dataset is randomly divided into a training set (64 groups) and a test set (20 groups) in a 7:3 ratio.

[0041] S2: Determine the set of hyperparameters to be optimized for the MLP gravel thermal conductivity prediction model, and use the set of hyperparameters to be optimized as individual hippos to initialize the hippo population; In this embodiment, the MLP gravel thermal conductivity prediction model (MLP neural network) is used to predict the thermal conductivity of gravel. The network structure includes: Input layer: 3 neurons, corresponding to dry density. Moisture content ,temperature Three input features; hidden layer: containing 1-2 hidden layers, with the number of neurons in each hidden layer equal to the number of hyperparameters to be optimized; output layer: 1 neuron, outputting the predicted gravel thermal conductivity value, using a linear activation function, such as... Figure 4 As shown.

[0042] Define the set of hyperparameters to be optimized. The hyperparameters in this embodiment include the number of hidden layer neurons, learning rate, activation function type, regularization coefficient, and batch size. The set of hyperparameters and the search range for each hyperparameter are as follows:

[0043] In the formula: The set of hyperparameters to be optimized; The number of neurons in the first hidden layer, with a search range of [4,32]. The number of neurons in the second hidden layer is [0, 16], and 0 indicates that only a single hidden layer is used. The learning rate is [0.001, 0.1]; The activation function type is encoded as a discrete hyperparameter, where 0 represents ReLU and 1 represents Tanh. is the L2 regularization coefficient, with a search range of [1e-5, 0.01]; The batch size is [4, 16].

[0044] Preferably, the population size is set to N (N=20 is recommended in this embodiment), and each hippopotamus individual represents a set of MLP hyperparameter configurations, which are randomly initialized according to the following formula. The first individual hippopotamus Hyperparameters:

[0045] In the formula: For the first The first individual hippopotamus The location of the hyperparameters; and The first Lower and upper bounds of the hyperparameters; It is a random number uniformly distributed in the interval [0,1].

[0046] Specifically, the hippo population is initialized, with each hippo representing a set of MLP hyperparameter configurations; a fitness evaluation function for each hippo is constructed, and a corresponding MLP network is built for each set of hyperparameter configurations. The network is trained using the training set and its prediction performance is evaluated on the validation set.

[0047] S3: Using the training set to analyze the first... The MLP gravel thermal conductivity prediction model for each individual hippopotamus was trained, and the predicted thermal conductivity values ​​were obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Then, based on the fitness evaluation function, the hippopotamus individual with the lowest fitness value in the hippopotamus population was identified as the dominant hippopotamus. An index for individual hippos. , Population size; In this embodiment, the forward propagation calculation of the MLP network is as follows:

[0048]

[0049] In the formula: For the first The weighted input vector of the layer, i.e., the first layer The input to the layer activation function; For the first The layer's output vector, i.e., the activation values ​​after processing by the activation function; This is the index of the activation function layer. and The first Layer weight matrix and bias vector; is the activation function. The network is trained using the Adam optimizer, and the loss function is the mean squared error (MSE).

[0050] After training, the predicted thermal conductivity values ​​are obtained using the validation set and the trained MLP neural network based on individual hippos, i.e., the MLP gravel thermal conductivity prediction model. Based on the fitness evaluation function, the root mean square error is calculated on the validation set as the fitness value; the individual with the smallest fitness value is selected as the dominant hippo. A smaller fitness value indicates a better hyperparameter configuration.

[0051] Preferably, the fitness evaluation function is the root mean square error on the validation set, expressed as follows:

[0052] In the formula: The number of samples in the validation set; This is the actual thermal conductivity value; This is the predicted value for thermal conductivity; The fitness function value is the root mean square error of the validation set in this embodiment. This is the root mean square error; Specifically, the fitness value of all individuals in the hippopotamus population is calculated, and the individual with the lowest fitness value is selected as the dominant hippopotamus. Its position is recorded as ,in For hyperparameter dimensions.

[0053] S4: Based on the dominant hippo, the hippo optimization algorithm is used to obtain the set of hyperparameters after three-stage iterative optimization, in order to obtain the optimal hyperparameters; such as Figure 3 As shown; In this embodiment, the three-stage iterative optimization of the hippo optimization algorithm is performed, including: Phase 1: exploratory position updates of the population through river exploration strategy; Phase 2: escaping local optima by adopting a defense behavior update mechanism based on Levy flight; Phase 3: performing local fine search by performing escape behavior near the dominant hippo's position; boundary processing and greedy selection are performed on the updated position, and the termination condition is judged. If the condition is not met, the iteration continues.

[0054] Specifically, Phase 1: Simulates the position update behavior of a hippopotamus in a river, achieving a global exploration of the hyperparameter space.

[0055] S41: Obtain the time decay factor to get the position of the hippopotamus individual after the first stage update; The formula used to obtain the time decay factor is as follows:

[0056] In the formula: This is the time decay factor; This represents the current iteration number; This represents the maximum number of iterations. Represented by natural constant An exponential function with base 0.

[0057] Specifically, It gradually decreases as the iteration progresses, and is used as the decay coefficient for updating the hippopotamus position in the second half of step S42, so that the search process gradually transitions from the early global exploration to the later local development.

[0058] The formula used to obtain the position of an individual hippopotamus after the first stage update is as follows:

[0059] In the formula: For the first The number of individual hippos after the first phase update Dimensional position; This is the position before the update; The first dominant hippopotamus Dimensional position; , The numbers are mutually independent uniform random numbers in the interval [0,1]. , All are integers randomly selected from {1,2}; To randomly select a subset of hippos from the current population at the th The arithmetic mean of the dimensional position coordinates, i.e. ,in, This is a randomly selected set of indexes for individual hippos; The total number of randomly selected hippopotamus individuals; This is an index of randomly selected individual hippos.

[0060] Specifically, Phase 2: In this embodiment, the first half of the population ( ) and individuals in the latter half of the population ( Different position update methods were adopted: the first half of the individuals mainly learned from the dominant hippopotamus; the second half of the individuals, while introducing random subset mean information to maintain population diversity, were updated by a time decay factor. Gradually reduce the update frequency.

[0061] Specifically, in Phase 2, the defensive behavior phase, we escape local optima: This phase simulates the defensive behavior of a hippopotamus when facing a predator, using the Levy flight mechanism to make large-step jumps, effectively escaping local optima.

[0062] S42: Based on the hippopotamus's position after the first phase update, the Levy flight mechanism is used to obtain the hippopotamus's position after the second phase update; the formula used is as follows: Preferably, the position update formula is:

[0063]

[0064] In the formula: For the first The number of individual hippos after the second phase update Dimensional position; For predator location and The distance between them; It is the absolute value; In the first The predator's position is randomly generated within the dimensional search boundary; For the first Levy's flight stride length; This is the predator position control constant; Parameters for the direction of defensive behavior; These are random perturbation parameters; These are the step size control parameters; The Levy flight step length is calculated as follows:

[0065] In the formula: and Let be mutually independent normally distributed random variables, where , ; for Theoretical standard deviation for The variance, by The following formula is used to determine the result, rather than obtaining it from statistical analysis of sample data; Levy index;

[0066]

[0067] In the formula: It is the Gamma function; In this embodiment, =1.5, will Substituting 1.5 into the above formula yields the result. And generate accordingly .

[0068] S43: Based on the position of the hippopotamus individual after the second stage update, obtain the position of the hippopotamus individual after the third stage update, so as to obtain the hyperparameter set after the three-stage iterative optimization; Specifically, Phase 3 escape behavior: This phase simulates the hippo's danger escape behavior, starting from the updated position in Phase 2, and performing a local fine-grained search around the current dominant hippo's position. The formula used is as follows:

[0069] In the formula: For the first The number of individual hippos after the third phase update Dimensional position; The first dominant hippopotamus Dimensional position; This is the step size scaling factor that decreases with the number of iterations; The values ​​are uniformly random numbers in the interval [0,1]. This update is based on the position of the second stage, allowing for a fine-grained search of candidate solutions near the dominant hippo.

[0070] In this embodiment, the step size scaling factor The current iteration progress is determined using a linear decreasing method, and its calculation formula is as follows:

[0071] In the formula: This is the current iteration number, and This represents the maximum number of iterations. This is the initial value of the step scaling factor; in this embodiment, it is set to 1.0. This is the final value of the step scaling factor; in this embodiment, it is set to 0.1.

[0072] Therefore, in the first iteration When the maximum number of iterations is reached hour, Step scaling factor The search scale decreases linearly with the iteration process, thereby gradually reducing the overall local search scale of Phase 3, while maintaining a non-zero search scale in the final iteration.

[0073] Specifically, in this embodiment, boundary checks are performed after each stage of position update. If any dimension exceeds the search range, it is pruned to the corresponding boundary value. (Number of neurons in the first hidden layer) Number of neurons in the second hidden layer and batch size For hyperparameters of integer type, rounding is used and the parameters are limited to their respective search ranges; the activation function type encoding β is a discrete class hyperparameter, mapped to 0 or 1; the learning rate α and L2 regularization coefficients... Since it is a continuous hyperparameter, its continuous values ​​are retained. Subsequently, a greedy selection strategy is adopted, comparing the fitness of the candidate positions in the current iteration with the positions retained in the previous stage, and only accepting the update when the fitness value of the candidate position is smaller.

[0074] Specifically, the current iteration count has reached the maximum iteration count. (Recommended value 50-100), or consecutively (Recommended) If the optimal fitness value does not improve, the iteration is terminated, and the optimal hyperparameter set is obtained.

[0075] S5: Based on the optimal hyperparameters, construct the final MLP gravel thermal conductivity prediction model, and use the gravel thermal conductivity dataset to train the final MLP gravel thermal conductivity prediction model; based on the trained final MLP gravel thermal conductivity prediction model, obtain the predicted thermal conductivity value of the new gravel sample to be predicted.

[0076] Specifically, the dry density and moisture content of the new gravel sample to be predicted are measured, and the specified temperature conditions for the new gravel sample are used. The final MLP gravel thermal conductivity prediction model after training is then used to output the predicted thermal conductivity value.

[0077] Specifically, the optimal hyperparameter configuration corresponding to the dominant hippopotamus is output, and the hidden layer structure, learning rate, activation function, regularization coefficient, and batch size of the final MLP neural network are determined accordingly. The optimal hyperparameters are only used to determine the network structure and training rules and are not equivalent to the already trained network weights. Therefore, after selecting the hyperparameters, the training and validation sets are merged, and the network is retrained once using all the data from both sets (37 groups) according to the optimal hyperparameters to fully utilize the modeling data and obtain the final model weights; the test set is not involved in this retraining. After training, the model weights and the standardized parameters determined by the modeling data are saved to form the final MLP gravel thermal conductivity prediction model.

[0078] For the gravel sample to be predicted, its dry density is measured. and moisture content Specified temperature conditions The input parameters are preprocessed by unit conversion (if necessary) and standardization before being input into the model. The predicted thermal conductivity value is then calculated and output through forward propagation.

[0079] Specifically, this embodiment can predict the thermal conductivity of gravel under both frozen and unfrozen conditions, and automatically distinguish between the two conditions based on temperature input characteristics.

[0080] In this embodiment, the gravel includes coarse-grained soil with a particle size greater than 2mm, such as river alluvial gravel, crushed stone, and ballast.

[0081] This embodiment also discloses a prediction system for a gravel thermal conductivity prediction method based on the Hippo optimization algorithm to optimize MLP, including: a data input module, a data preprocessing module, a hyperparameter optimization module, a prediction model module, and a result output module; The data input module is used to receive the dry density, moisture content and temperature of the gravel, and supports manual input and batch import. The data preprocessing module is used to preprocess the dry density, moisture content and temperature of the gravel to construct a dataset of the thermal conductivity of the gravel; and divides the dataset of the thermal conductivity into a training set and a validation set. Specifically, the input parameters are subjected to unit conversion and Z-score standardization, using the standardized parameters saved during the training phase.

[0082] The hyperparameter optimization module is used to optimize the training set based on the first parameter in the hippopotamus population. The MLP gravel thermal conductivity prediction model for each hippopotamus individual was trained, and the predicted thermal conductivity value was obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Based on the fitness evaluation function, the hippopotamus individual with the smallest fitness value in the hippopotamus population was determined as the dominant hippopotamus. Specifically, the hyperparameter optimization module uses the Hippo optimization algorithm to search for the optimal hyperparameter configuration of the MLP neural network, including the population initialization unit, fitness evaluation unit, three-stage position update unit, and termination judgment unit.

[0083] The prediction model module is used to construct the final MLP gravel thermal conductivity prediction model based on the optimal hyperparameters, and to train the final MLP gravel thermal conductivity prediction model using a gravel thermal conductivity dataset; based on the trained final MLP gravel thermal conductivity prediction model, the predicted thermal conductivity value of the new gravel sample to be predicted is obtained. Specifically, an MLP neural network is constructed based on the optimal hyperparameter configuration, and forward propagation calculation is performed on the standardized input data to output the predicted value of the gravel thermal conductivity. The results output module is used to visualize the predicted thermal conductivity values ​​of new gravel samples to be predicted.

[0084] Specifically, the results output module displays the prediction results, supports single-sample prediction and batch prediction, and provides visualization and export functions for the prediction results.

[0085] Example 1: Construction of a gravel thermal conductivity prediction model based on HO-MLP This embodiment, based on measured data of gravel thermal conductivity, details the complete construction process of the HO-MLP gravel thermal conductivity prediction model. The experimental environment was as follows: Windows 10 operating system, Intel Core i7-12700H processor, 32GB memory, Python 3.9 programming language, PyTorch 2.0.1 deep learning framework, and NumPy 1.24 and Scikit-learn 1.3 scientific computing libraries.

[0086] (a) Data Acquisition and Preprocessing: Sixty-four sets of measured data on the thermal conductivity of gravel were selected. The original data were in imperial units. First, the units were converted, and the statistical characteristics of the converted data are shown in Table 1.

[0087] Table 1 Statistical characteristics of the measured gravel dataset

[0088] The input features were Z-score standardized, and the standardized parameters calculated on the training set were: μ = [1.92, 2.37, -1.8], σ = [0.17, 1.54, 18.7]. The dataset was divided into 64 training sets and 20 test sets in a 7:3 ratio, and a random seed of 42 was used to ensure repeatability.

[0089] (II) HO Algorithm Parameter Settings: The parameter settings for the hippo optimization algorithm are shown in Table 2.

[0090] Table 2 HO Algorithm Parameter Settings

[0091] (III) Optimization process and results: The HO algorithm converged after 80 iterations, with the fitness (RMSE on the validation set) gradually decreasing from 0.312 W / (m·K) in the initial generation to a final 0.067 W / (m·K). Based on the records of the optimal fitness in each generation, it can be seen that the HO algorithm rapidly decreased fitness in the first 20 generations, demonstrating the efficiency of the global exploration in Phase 1; several fitness jumps occurred between generations 20 and 50, reflecting the role of Phase 2's levy flight in escaping local optima; after generation 50, the algorithm stabilized, and Phase 3 further fine-tuned the hyperparameters through a refined search.

[0092] The optimal hyperparameter configuration obtained from the final search is shown in Table 3.

[0093] Table 3. Optimal hyperparameter configurations obtained by the HO algorithm.

[0094] As shown in Table 3, the optimal network structure obtained by the HO algorithm is 3-24-12-1 (input layer - hidden layer 1 - hidden layer 2 - output layer), with the activation function Tanh, a learning rate of 0.008, an L2 regularization coefficient of 0.0003, and a batch size of 8. The dual-hidden-layer structure has stronger feature extraction capabilities compared to the single-hidden-layer structure. The Tanh activation function outperforms ReLU in this task, possibly due to the presence of negative temperature values ​​in the input data.

[0095] (iv) Test set prediction results: After retraining the optimal MLP structure using all the training data, predictions were performed on 20 test datasets. The prediction results are as follows: Figure 5 and Figure 6 As shown.

[0096] Depend on Figure 5 and Figure 6 It can be seen that the predicted values ​​of the HO-MLP model on the test set are highly consistent with the measured values, and the relative error of the 20 test samples is within 10%, which shows good generalization ability.

[0097] This embodiment has the following beneficial effects: (1) Improve the relevance and applicability of gravel thermal conductivity prediction. This invention addresses the characteristics of gravel particles, such as large particle size, complex particle contact and pore structure, and thermal conductivity affected by dry density, moisture content and temperature. It uses three easily obtainable physical parameters, such as dry density, moisture content and temperature, as model inputs to establish a nonlinear mapping relationship between the above parameters and gravel thermal conductivity. It can also predict the thermal conductivity of gravel in both frozen and unfrozen states, thereby reducing the need to conduct repeated thermal conductivity tests under different working conditions. It can provide thermal conductivity parameters for gravel strata in the artificial freezing construction of subway tunnel connecting passages and for the thermal conduction analysis of ballast in high-speed railways in cold regions.

[0098] (2) Improve the prediction accuracy and stability of the MLP model. This invention uses the Hippo optimization algorithm to automatically optimize the hyperparameters of the MLP gravel thermal conductivity prediction model, such as the hidden layer structure, learning rate, activation function, regularization coefficient, and batch size. Through a three-stage search mechanism, it realizes global exploration of the hyperparameter space, escape from local optima, and local fine search, reducing the influence of manual parameter tuning and traditional grid search and random search on hyperparameter selection, thereby improving the fitting ability and prediction stability of the MLP model for the complex nonlinear relationship of gravel thermal conductivity.

[0099] (3) Improve the efficiency of obtaining the thermal conductivity of gravel and its engineering application capability. After the model training is completed, only the dry density, moisture content and corresponding temperature conditions of the gravel sample to be predicted need to be obtained. The corresponding thermal conductivity can be obtained by using the trained HO-MLP gravel thermal conductivity prediction model. There is no need to conduct indoor thermal conductivity tests for each combination of dry density, moisture content and temperature. This shortens the time for obtaining the thermal conductivity of gravel under different working conditions and can provide thermophysical parameters for the analysis of artificial freezing temperature field, the analysis of the freezing wall formation process and the thermal stability analysis of ballast track of high-speed railway in cold regions.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm, characterized in that, Includes the following steps: S1: Based on the dry density, moisture content, and temperature of the gravel, construct the input features of the gravel and obtain the thermal conductivity corresponding to the input features of the gravel to construct a thermal conductivity dataset of the gravel; and divide the thermal conductivity dataset into a training set and a validation set; S2: Determine the set of hyperparameters to be optimized for the MLP gravel thermal conductivity prediction model, and use the set of hyperparameters to be optimized as individual hippos to initialize the hippo population; S3: Using the training set to analyze the first... The MLP gravel thermal conductivity prediction model for each individual hippopotamus was trained, and the predicted thermal conductivity values ​​were obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Then, based on the fitness evaluation function, the hippopotamus individual with the lowest fitness value in the hippopotamus population was identified as the dominant hippopotamus. An index for individual hippos. , Population size; S4: Based on the dominant hippopotamus, the hippopotamus optimization algorithm is used to obtain the set of hyperparameters after three-stage iterative optimization considering time decay, so as to obtain the optimal hyperparameters; S5: Based on the optimal hyperparameters, construct the final MLP gravel thermal conductivity prediction model, and use the gravel thermal conductivity dataset to train the final MLP gravel thermal conductivity prediction model; based on the trained final MLP gravel thermal conductivity prediction model, obtain the predicted thermal conductivity value of the new gravel sample to be predicted.

2. The method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm according to claim 1, characterized in that, The method used to obtain the set of hyperparameters after three-stage iterative optimization is as follows: S41: Obtain the time decay factor to get the position of the hippopotamus individual after the first stage update; The formula used to obtain the time decay factor is as follows: In the formula: This is the time decay factor; This represents the current iteration number; This represents the maximum number of iterations. It is an exponential function; The formula used to obtain the position of an individual hippopotamus after the first stage update is as follows: In the formula: For the first The number of individual hippos after the first phase update Dimensional position; This is the position before the update; The first dominant hippopotamus Dimensional position; , The numbers are mutually independent uniform random numbers in the interval [0,1]. , All are integers randomly selected from {1,2}; To randomly select a subset of hippos from the current population at the th The arithmetic mean of the dimensional position coordinates, i.e. ,in, This is a randomly selected set of indexes for individual hippos; The total number of randomly selected hippopotamus individuals; Index of randomly selected individual hippos; S42: Based on the hippopotamus's position after the first phase update, the Levy flight mechanism is used to obtain the hippopotamus's position after the second phase update; the formula used is as follows: In the formula: For the first The number of individual hippos after the second phase update Dimensional position; For predator location and The distance between them; It is the absolute value; In the first The predator's position is randomly generated within the dimensional search boundary; For the first Levy's flight stride length; This is the predator position control constant; Parameters for the direction of defensive behavior; These are random perturbation parameters; These are the step size control parameters; in, In the formula: and Let be mutually independent normally distributed random variables, where , ; for Theoretical standard deviation for The variance; Levy index; In the formula: It is the Gamma function; S43: Based on the position of the hippopotamus individual after the second stage update, obtain the position of the hippopotamus individual after the third stage update, so as to obtain the hyperparameter set after three-stage iterative optimization; the formula used is as follows: In the formula: For the first The number of individual hippos after the third phase update Dimensional position; The first dominant hippopotamus Dimensional position; This is the step size scaling factor that decreases with the number of iterations; A uniformly random number within the interval [0,1]; In the formula: This is the current iteration number, and This represents the maximum number of iterations. This is the initial value of the step scaling factor; This is the final value of the step scaling factor.

3. The method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm according to claim 1, characterized in that, The formula used to initialize the hippopotamus population is as follows: In the formula: For the first The first individual hippopotamus The location of the hyperparameters; and The first Lower and upper bounds of the hyperparameters; It is a random number uniformly distributed in the interval [0,1].

4. The method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm according to claim 1, characterized in that, The formula used in the forward propagation of the MLP gravel thermal conductivity prediction model is as follows: In the formula: For the first The weighted input vector of the layer, i.e., the first layer The input to the layer activation function; For the first The layer's output vector, i.e., the activation values ​​after processing by the activation function; This is the index of the activation function layer. and The first Layer weight matrix and bias vector; This is the activation function.

5. The method for predicting the thermal conductivity of gravel based on MLP optimized by the Hippo Optimization Algorithm according to claim 1, characterized in that, The fitness evaluation function is expressed as follows: In the formula: The number of samples in the validation set; This is the actual thermal conductivity value; This is the predicted value for thermal conductivity; The fitness function value; This is the root mean square error.

6. The prediction system for the gravel thermal conductivity prediction method based on the Hippo Optimization Algorithm-optimized MLP according to any one of claims 1-5, characterized in that, include: Data input module, data preprocessing module, hyperparameter optimization module, prediction model module, and result output module; The data input module is used to receive the dry density, moisture content and temperature of the gravel; The data preprocessing module is used to preprocess the dry density, moisture content and temperature of the gravel to construct a dataset of the thermal conductivity of the gravel; and divides the dataset of the thermal conductivity into a training set and a validation set. The hyperparameter optimization module is used to optimize the training set based on the first parameter in the hippopotamus population. The MLP gravel thermal conductivity prediction model for each hippopotamus individual was trained, and the predicted thermal conductivity value was obtained based on the validation set and the trained MLP gravel thermal conductivity prediction model. Based on the fitness evaluation function, the hippopotamus individual with the smallest fitness value in the hippopotamus population was determined as the dominant hippopotamus. The prediction model module is used to construct the final MLP gravel thermal conductivity prediction model based on the optimal hyperparameters, and to train the final MLP gravel thermal conductivity prediction model using a gravel thermal conductivity dataset. The predicted thermal conductivity of a new gravel sample is obtained using the final MLP gravel thermal conductivity prediction model after training. The results output module is used to visualize the predicted thermal conductivity values ​​of new gravel samples to be predicted.

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