Unsaturated soil heat conductivity coefficient prediction method driven by data mechanism

Abstract

The invention discloses an unsaturated porous medium soil heat conductivity coefficient prediction method and system based on data mechanism driving, and belongs to the technical field of geotechnical engineering thermophysical property analysis. According to the method, experimental testing, numerical simulation and an intelligent algorithm are integrated, and a research normal form of data and mechanism coupling driving is embodied. The method specifically comprises the following steps: obtaining a heat conductivity coefficient initial data set through a test means; then establishing a finite element model, verifying the reliability of the finite element model through temperature drop comparison, and generating 80 groups of working condition data through a least square finite element method; and finally, an intelligent algorithm is introduced to train a prediction model, BPNN is trained after normalization, and neurons of an input layer 3, neurons of a hidden layer 12 + 6 and neurons of an output layer 1 are included. According to the algorithm, a physical mechanism and data driving are fused, the problem that a traditional model is poor in applicability is solved, prediction precision is high, and the algorithm is suitable for civil engineering thermophysical analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical engineering thermophysical property analysis, and in particular to a data mechanism-driven method for predicting thermal conductivity of unsaturated soil. Background Art

[0002] Soil thermal conductivity is a key parameter in geotechnical engineering thermophysical property analysis, and its accurate prediction is of great significance to civil engineering design and geothermal resource development. The existing technology has the following defects: 1. Limitations of measurement methods: The steady-state method requires a long time to reach thermal equilibrium, which can easily lead to soil moisture migration and affect accuracy. Although the transient method is time-efficient, the amount of single test data is limited and it is difficult to cover complex working conditions.

[0003] 2. Insufficient prediction models: Traditional empirical models, such as the De Vries model, rely on specific soil types and simplify the description of the coupled effects of porosity, saturation, and temperature, making them unable to adapt to the dynamic characteristics of unsaturated porous media. Theoretical models are based on the homogenization assumption and ignore the influence of microscopic pore structure on the heat conduction path.

[0004] 3. Data-driven defects: Pure intelligent algorithms, such as BP neural networks, lack physical mechanism constraints. Under extreme working conditions, the prediction results may deviate from the actual heat conduction laws and have insufficient generalization capabilities.

[0005] Therefore, this application proposes a data mechanism-driven unsaturated soil thermal conductivity prediction method to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a data mechanism-driven unsaturated soil thermal conductivity prediction method to solve the problems raised in the background technology.

[0007] To address the above problems, the present invention proposes a data mechanism-driven unsaturated soil thermal conductivity prediction method, which includes the following steps: Step 1: Determine the equivalent specific heat capacity of the soil using the heat balance method, and combine the point heat source method to obtain initial thermal conductivity data under different porosity, saturation, and temperature conditions to construct an initial data set; Step 2: Use finite element method to establish an unsaturated soil heat conduction model. Set specific geometric dimensions, bury a point heat source in the center, and arrange temperature sensors at preset distances. Solve the inverse heat conduction problem using the least squares finite element method to generate an expanded thermal conductivity coefficient data set. Step 3: Perform standardization processing and construct a back-propagation neural network consisting of an input layer, a double hidden layer, and an output layer. The input layer receives porosity, saturation, and temperature data. The model is iteratively trained through the back-propagation algorithm to achieve thermal conductivity prediction.

[0008] Preferably, when determining the equivalent specific heat capacity by the heat balance method in step 1, the soil is simplified into a solid-liquid two-phase system, and the contribution of the gas phase is ignored. The equivalent specific heat capacity calculation formula is: ; ; ; in, and are the specific heat capacities of the soil solid and liquid phases, respectively; and are the mass fractions of soil solid and liquid, respectively.

[0009] Preferably, when obtaining initial data using the midpoint heat source method in step 1, the thermal conductivity is calculated using the formula by recording the cooling curve within 3 hours after the heat source is removed. The formula is as follows: ; ; Where c is the specific heat capacity; ρ is the density; Q(t) is the heat flux per unit time; λ is the thermal conductivity; is the temperature gradient; A is the heat transfer area.

[0010] Preferably, the geometric dimensions of the finite element model are a radius of 180 mm and a height of 200 mm, a point heat source with a radius of 4 mm is buried in the center, and the distances between the buried points of the temperature sensors and the point heat source are 40 mm, 70 mm, and 100 mm respectively.

[0011] Preferably, when the finite element method is used to solve the inverse problem of heat conduction in step 2, the heat conduction control equation is: ; in, is the initial temperature field; and The first-class boundary 、 The known temperature on By discretizing the space domain using the Galerkin method and the time domain using the difference method, we get the finite element format: ; in, is the specific heat capacity matrix; is the temperature matrix; is the thermal conductivity matrix; coefficient , taking any value between 0 and 1.

[0012] Preferably, the specific heat capacity matrix [C] and thermal conductivity matrix [K] of the finite element model in step 2 are combined through the unit stiffness matrix, and the expression is: ; ; in, is the thermal conductivity function of soil; is the soil specific heat capacity function.

[0013] Preferably, when the numerical simulation in step 3 generates the expanded data set, 8 porosities, i.e., 0.1 to 0.8, and 10 saturations are set, and the finite element optimization module is used to solve the problem, thereby obtaining 80 sets of thermal conductivity data under different working conditions.

[0014] Preferably, the normalization process uses the Max-Min normalization method to map the data to the interval [0, 1], and the formula is: ; 70% of the dataset is used as the training set and 30% as the test set.

[0015] Preferably, the structure of the back propagation neural network in step 3 is: 3 neurons in the input layer, i.e., receiving porosity, saturation, and temperature data; 12 neurons in the first hidden layer; 6 neurons in the second hidden layer; 1 neuron in the output layer, i.e., outputting thermal conductivity; and the activation function adopts the ReLU function, which is expressed as follows: ; .

[0016] Preferably, when the back propagation neural network model is iteratively trained by the back propagation algorithm, the weight update formula is as follows: ; in is the learning rate, and iterates until the mean square error < Or the maximum number of iterations is reached and the average absolute error of the test set is <0.05W / m / K.

[0017] The present invention has the following beneficial effects: 1. This invention significantly improves the prediction accuracy and generalization ability of unsaturated soil thermal conductivity through a multi-stage collaboration of experimentation, numerical simulation, and intelligent algorithms, solving the problems of traditional empirical models with a narrow scope of application and strong data dependence. A core data set of porosity, saturation, and thermal conductivity is obtained through laboratory measurements. This data is expanded by combining finite element multi-physics simulation to generate a variety of working conditions and construct a training library for a large number of parameters. The BPNN prediction model established based on this deeply integrates the dual advantages of physical mechanisms and data-driven development.

[0018] 2. This invention uses finite element simulation to precisely quantify the heat conduction pathways within the microscopic pore structure. BPNN, with its deep nonlinear mapping capabilities, completely overcomes the oversimplification of soil heat conduction mechanisms by traditional empirical formulas. This model, without relying on physical assumptions or homogenization theory, accurately captures the complex coupling effects of multiple factors, including porosity, saturation, and temperature, through an adaptive learning mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Flow chart of the implementation of the present invention; Figure 2 This is a temperature comparison diagram under different porosity conditions in the numerical simulation of the present invention; Figure 3 This is a temperature comparison diagram under different saturation conditions of the numerical simulation of the present invention; Figure 4 It is the prediction result and error diagram of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments: See also Figure 1-4 , introduces a specific embodiment of the present invention, a data mechanism driven unsaturated soil thermal conductivity prediction method, comprising the following steps: Step 1: Determine the specific heat capacity by the heat balance method, which can be used as an input parameter for calculating the thermal conductivity of the soil. In order to calculate the effective specific heat capacity, the soil is defined as a three-phase system consisting of solid, liquid and gas. Considering that the soil behaves as a typical three-phase porous medium, its overall specific heat capacity is generated by the weighted contributions of these three components. Due to its inherent properties, the mass fraction of air in unsaturated soil is the smallest. Therefore, its contribution to the equivalent specific heat capacity can be reasonably ignored without causing significant errors. Its expression is as follows: ; in, and are the specific heat capacities of the soil solid and liquid phases, respectively; and are the mass fractions of soil solid and liquid, respectively.

[0021] Furthermore, based on the experimentally obtained temperature curve, the specific heat capacities of the solid and gas phases were determined. Through curve fitting, a mathematical model describing the relationship between relative heat capacity and temperature was established: ; ; Furthermore, the point heat source method was used to measure the temperature drop curves at 40, 70, and 100 mm to calculate the thermal conductivity. The relationship between the temperature gradient, thermal conductivity, and heat flux in the soil is: ; ; in, is the specific heat capacity; is the density; is the heat flux per unit time; is the thermal conductivity; is the temperature gradient; is the heat transfer area.

[0022] Step 2, numerical simulation: The finite element model established has the same dimensions as the test. The overall geometric dimensions are 180mm in radius and 200mm in height. A point heat source with a radius of 4mm is buried in the center of the model, and the temperature sensors are buried at distances of 40, 70, and 100mm, respectively. The inverse problem of heat conduction using the least squares finite element method is converted into an optimization problem and solved using the finite element optimization module. The thermal conductivity coefficients for different porosity and saturation are generated. The heat conduction governing equations are: ; in, is the initial temperature field; and The first-class boundary 、 The known temperature on .

[0023] Applying the Galerkin method for discretization in the spatial domain and the difference method in the time domain can obtain the finite element format as follows: ; in, is the specific heat capacity matrix; is the temperature matrix; is the thermal conductivity matrix; coefficient It can take any value between 0 and 1.

[0024] These matrices are combined through the element stiffness matrix and can be expressed as: ; ; in, is the thermal conductivity function of soil; is the soil specific heat capacity function.

[0025] Furthermore, substituting the corresponding temperature vector, we can obtain: ; in, and are the coefficient matrices of specific heat capacity and thermal conductivity, respectively.

[0026] Furthermore, according to the least squares finite element principle, when solving the equation, the residual of the equation is defined as: ; ; The essence of the least-squares finite element method is to minimize the residual of the objective function. To minimize the objective function, the necessary condition is that the derivative of the function with respect to each variable is 0. After obtaining the coefficient matrix of the soil specific heat capacity and the coefficient matrix of the thermal conductivity, the solution is obtained by multiplying the left and right coefficient matrices by the inverse matrix.

[0027] 8 different porosities were set, namely =0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 10 saturations were studied, and 80 groups of thermal conductivity coefficients under different porosity and saturation conditions were obtained.

[0028] Step 3: Prediction model construction and training: The thermal conductivity data obtained after numerical simulation is standardized and divided into training samples and test samples. A prediction model is established based on the BPNN algorithm. The training samples are used to iteratively train the prediction model, and the test samples are used to test the prediction model.

[0029] The thermal conductivity data obtained under different porosity and saturation conditions were normalized and processed using the Max-Min method. ; in, is the original data, and are the minimum and maximum values ​​in the data set, respectively. is the normalized data.

[0030] Furthermore, the specific principle and formula of the back propagation neural network (BPNN) in S3 are as follows: BPNN is a multi-layer feedforward neural network that is trained using the back-propagation algorithm. Its core structure includes: input layer, hidden layer, and output layer.

[0031] Input layer: The input layer is the starting point of the BP neural network and is responsible for receiving external data. Each neuron corresponds to a characteristic value, and data enters the network through these neurons. The input layer has no computational function and only serves as a data transmission channel.

[0032] Hidden layer: The hidden layer is the core of the BP neural network, responsible for extracting features from the input data and performing nonlinear transformations. Each hidden layer consists of multiple neurons, each of which performs a weighted summation of the output of the previous layer and transforms it using an activation function. The choice of activation function has a significant impact on network performance.

[0033] Assume the input of the hidden layer is , and its calculation formula is: ; in, Is the connection input layer neurons and hidden layers The weights of neurons; The input layer The output of a neuron; The hidden layer The bias term of a neuron.

[0034] Activation Function The ReLU function is usually used, and its formula is: ; Output layer: The output layer is the end point of the BP neural network and is responsible for generating the final prediction results. For regression problems, no activation function is used or a linear activation function is used.

[0035] ; in, Is the connection hidden layer neurons and the output layer The weights of neurons; is the output of the hidden layer; The output layer The bias term of a neuron.

[0036] Furthermore, if the output error does not reach the threshold, in the forward propagation, the input information is calculated layer by layer from the input layer to the output layer through the hidden layer, and each neuron in the output layer outputs the network response corresponding to the input pattern.

[0037] The gradient of loss with respect to weights is calculated by chain rule and propagated back from the output layer to the input layer. Partial derivative of: ; For the gradient of the hidden layer, calculate the loss versus the hidden layer input Partial derivative of: ; Furthermore, once we have the gradient, we can update the weights and biases of the network: ; ; wherein, is the learning rate; is the weight matrix; is the bias vector.

[0038] The forward propagation, loss calculation, and back propagation are repeated until convergence or the maximum number of iterations is reached. The learning rate, weight, and other parameters in the network model can be fine-tuned to minimize the prediction error. Embodiment 1: A data mechanism-driven unsaturated soil thermal conductivity prediction method, specifically comprising the following steps: Step one, obtaining experimental data: before the experiment, the basic physical parameters of the test soil body need to be determined. According to the soil test standard GB / T50123—2019, the particle size distribution curve and soil particle density are obtained.

[0040] Further, the specific heat capacity of the soil is determined by the heat balance method. When the specific heat capacity test is carried out, the specific heat capacity of water is considered as known. 50g of soil sample and 200g of water are weighed, and the initial temperature of the water in the insulation barrel is measured in advance. The soil sample is placed in a drying oven and heated to a specified temperature, and the specified temperature is set to 24℃, 33℃, 38℃, 43℃, 48℃, 53℃, 58℃, and 63℃, respectively. When the temperature on the temperature sensor reaches the specified temperature, the soil sample is quickly placed in the insulation barrel and sealed with an insulation cover. After reaching thermal equilibrium, the reading of the temperature sensor does not change basically, and the final temperature of the temperature sensor is recorded.

[0041] Further, the specific heat capacity obtained is then used to conduct a thermal conductivity test by the point heat source method. The test equipment is made of a sample loading barrel with an inner diameter of 180mm, a wall thickness of 40mm, and a height of 200mm, with a heat source in the center. The temperature sensor is buried at a distance of 40, 70, and 100mm from the point heat source, and the heating time is 3h. The temperature time series is recorded for 3h after the point heat source is removed to calculate the thermal conductivity. The formulas for calculating the porosity and saturation of the soil are: ; ; wherein, is the dry density of the soil; is the specific gravity of the soil particles; is the density of water; ω is the water content of the soil; e is the porosity.

[0042] This test uses different times of compaction, namely 0, 30, 60, and 90 times, to control the porosity of the soil and thus the saturation of the soil. The target heating temperature is set with a temperature difference of 60°C. That is, when the initial temperature of the soil is 18°C, the heating temperature of the heating rod is set to 78°C. At the same time, the ambient temperature is controlled to minimize the interference of the ambient temperature on the test process. After heating for 3 hours, stop heating, open the temperature acquisition module software, and record the cooling curve of each measuring point for 3 hours at an interval of 1 minute to provide test data for the calculation of the thermal conductivity of the soil under this condition. The steps are as follows: S1.1. First, dry and crush the test soil sample. Based on the size of the sample container, the total mass of the soil sample is 25,000 g. Fill and compact the soil in five layers, with each layer weighing 5,000 g. For thermal conductivity tests of soils at varying degrees of saturation, prepare soil samples with a 10% moisture content. Each layer contains 500 g of water. Cover the sample with a transparent film for 24 hours.

[0043] S1.2. During the soil sample filling process, adhere to the principle of layered compaction, using a compacting hammer to perform different compaction times to control the soil porosity. After each layer is compacted, use a soil scraper to roughen the surface of the soil sample before adding the next layer. This ensures that the soil between adjacent layers is in full contact.

[0044] S1.3. After compacting the third layer, bury a heating rod in the center of the soil sample and, using a tape measure, bury temperature sensors at different distances from the point heat source: 40, 70, and 100 mm. Two temperature sensors are buried at each distance to ensure reliable temperature data collection at that distance. After the equipment is installed, proceed to compacting the next layer.

[0045] S1.4. After the five layers of soil are compacted, replace the insulation cover and check that the circuit connections of the temperature controller and temperature acquisition module are intact, and that the data displayed by the temperature sensor and heating rod are normal. Once all checks are complete, the test can begin.

[0046] S1.5. Set the target heating temperature with a temperature difference of 60°C. That is, when the initial soil temperature is 18°C, set the heating temperature of the heating rod to 78°C. Simultaneously, control the ambient temperature to minimize its interference with the test process. Click the heating button on the temperature controller to begin the test, and the point heat source begins to apply temperature interference to the soil. After 3 hours of heating, stop heating, open the temperature acquisition module software, and record the cooling curve at each measuring point at 1-minute intervals over a 3-hour period to provide test data for calculating the soil thermal conductivity under these conditions.

[0047] Step 2: Numerical simulation: The finite element model and the test model have the same size, see the attached Figure 2 . It consists of a circle with a radius of 180 mm and a height of 200 mm. A point heat source with a radius of 4 mm is placed in the center of the circle. The temperature measurement points are placed at 40 mm, 70 mm, and 100 mm away from the heat source. The initial temperature of the soil is controlled at 18°C, and the heating rod operates at 78°C for 3 hours before being deactivated. The heat source material is Ni80Cr20. According to the specification "GB / T1234-2012", the density of this material is 8.4 g / cm³, the specific heat capacity is 440 J / (kg·℃), and the thermal conductivity is 15 W / m / K.

[0048] In order to verify the accuracy and reliability of the least squares finite element method, temperature change data under three different conditions of porosity and saturation at a depth of 70 mm were selected. The calculated values ​​were compared with the measured data. Figure 3 Under different porosity and saturation conditions, the experimental and calculated temperature curves showed high consistency. The goodness of fit for all models exceeded 0.988, confirming the high reliability of the method. By setting up the numerical model and performing numerical simulations, the data was expanded to 80 groups, providing a data set for the prediction model.

[0049] Step 3: Prediction Model Construction and Training: The 80 data sets obtained from the numerical simulation were standardized. The thermal conductivity data were converted to the (0, 1) interval using the Max-Min normalization method. This ensured comparability of data of different dimensions and improved the training efficiency and convergence speed of the subsequent neural network. 70% of the standardized data was then divided into a training set for model training, and 30% was divided into a test set for evaluating the model's final performance.

[0050] The BPNN input consists of three neurons, representing porosity, saturation, and temperature. The hidden layer uses a two-layer structure, with 12 neurons in the first hidden layer and 6 neurons in the second hidden layer. The output layer consists of one neuron, corresponding to the predicted thermal conductivity value. The ReLU function is used as the activation function to enhance nonlinear expression capabilities.

[0051] The trained model is verified using the test set, and the error indicators between the predicted results and the actual values ​​are calculated, such as the mean square error (MSE) and the mean absolute error (MAE).

[0052] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A data mechanism driven method for predicting thermal conductivity of unsaturated soil, characterized by: The following steps are involved: Step 1: Determine the equivalent specific heat capacity of the soil using the heat balance method, and combine the point heat source method to obtain initial data on thermal conductivity under different porosity, saturation, and temperature conditions to construct an initial data set; Step 2: Use finite element method to establish an unsaturated soil heat conduction model. Set specific geometric dimensions, bury a point heat source in the center, and arrange temperature sensors at preset distances. Solve the inverse heat conduction problem using the least squares finite element method to generate an expanded thermal conductivity coefficient data set. Step 3: Perform standardization processing and construct a back-propagation neural network consisting of an input layer, a double hidden layer, and an output layer. The input layer receives porosity, saturation, and temperature data. The model is iteratively trained through the back-propagation algorithm to achieve thermal conductivity prediction.

2. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: When determining the equivalent specific heat capacity using the heat balance method in step 1, the soil is simplified into a solid-liquid two-phase system, and the contribution of the gas phase is ignored. The equivalent specific heat capacity calculation formula is: ； ； ； in, and are the specific heat capacities of the soil solid and liquid phases, respectively; and are the mass fractions of soil solid and liquid, respectively.

3. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: When obtaining initial data using the midpoint heat source method in step 1, the thermal conductivity is calculated using the formula by recording the cooling curve within 3 hours after the heat source is removed. The formula is as follows: ； ； Where c is the specific heat capacity; ρ is the density; Q(t) is the heat flux per unit time; λ is the thermal conductivity; is the temperature gradient; A is the heat transfer area.

4. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: The geometric dimensions of the finite element model are a radius of 180 mm and a height of 200 mm. A point heat source with a radius of 4 mm is buried in the center, and the distances between the buried points of the temperature sensors and the point heat source are 40 mm, 70 mm, and 100 mm, respectively.

5. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: When the finite element method is used to solve the inverse problem of heat conduction in step 2, the heat conduction control equation is: ； in, is the initial temperature field; and The first-class boundary 、 The known temperature on By discretizing the space domain using the Galerkin method and the time domain using the difference method, we get the finite element format: ； in, is the specific heat capacity matrix; is the temperature matrix; is the thermal conductivity matrix; coefficient , taking any value between 0 and 1.

6. A data mechanism driven unsaturated soil thermal conductivity prediction method according to any one of claims 1 or 5, characterized in that: The specific heat capacity matrix [C] and thermal conductivity matrix [K] of the finite element model in step 2 are combined through the element stiffness matrix, and the expression is: ； ； in, is the thermal conductivity function of soil; is the soil specific heat capacity function.

7. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: When the numerical simulation in step 3 generates the expanded data set, 8 porosities, i.e., 0.1 to 0.8, and 10 saturations are set, and the finite element optimization module is used to solve the problem, thereby obtaining 80 sets of thermal conductivity data under different working conditions.

8. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: The standardization process uses the Max-Min normalization method to map the data to the interval [0, 1], and the formula is: ； 70% of the dataset is used as the training set and 30% as the test set.

9. The method for predicting thermal conductivity of unsaturated soil driven by a data mechanism according to claim 1, characterized in that: The structure of the back propagation neural network in step 3 is as follows: 3 neurons in the input layer, i.e., receiving porosity, saturation, and temperature data; 12 neurons in the first hidden layer; 6 neurons in the second hidden layer; 1 neuron in the output layer, i.e., outputting thermal conductivity; and the activation function uses the ReLU function, which is expressed as follows: ； 。 10. The data mechanism driven unsaturated soil thermal conductivity prediction method according to claim 9, characterized in that: When the back-propagation neural network model is iteratively trained through the back-propagation algorithm, the weight update formula is as follows: ； in is the learning rate, and iterates until the mean square error < Or the maximum number of iterations is reached and the average absolute error of the test set is <0.05W / m / K.

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