Unsaturated soil parameter inversion method based on machine learning

Abstract

The invention discloses an unsaturated soil parameter inversion method based on machine learning, and belongs to the technical field of soil seepage measurement and control. The method comprises the following steps: firstly, measuring soil body water outlet time under different compaction degrees and initial saturation degrees through a seepage experiment, and establishing a boundary condition driven soil column seepage finite element model; a Van Genuchten model is adopted to describe a relationship between a soil-water characteristic curve and a permeability coefficient, and a value combination of pressure P0 and a dimensionless parameter a is designed and set through an orthogonal test. The water outlet time, the compaction degree and the initial saturation degree obtained through numerical simulation serve as input, P0 and a serve as output, normalization processing is carried out, and then a training data set is constructed. And learning a mapping relation between input and output by using a machine learning model, and optimizing parameters to minimize a prediction error. And finally, inputting measured data into the trained model, and carrying out inversion to obtain target parameters P0 and a. According to the invention, the time for specific unsaturated soil humidification or dehumidification test and penetration test is saved, and the cost is low.

Description

Technical Field

[0001] The present invention relates to the technical field of unsaturated soil seepage coefficient measurement and control, and in particular to a method for inverting unsaturated soil parameters based on machine learning. Background Art

[0002] Unsaturated soil is a three-phase soil. Unlike saturated soil, it contains not only solid and liquid phases but also a gas phase. The presence of the gas phase greatly complicates the soil's properties, and its fundamental characteristics differ from those of saturated soil. These characteristics make it difficult to integrate the theory and practice of unsaturated soils. Determining the parameters of the soil-water characteristic curve and permeability coefficient for unsaturated soils is crucial for the practical application of unsaturated soil theory. To determine these parameters, direct methods are generally used: wetting or dehumidification tests and permeability tests. However, these tests are long and costly, which greatly hinders the application of unsaturated soil theory in practical production. Furthermore, the complexity and nonlinear relationships of soil parameters make traditional numerical methods sometimes difficult to apply. Therefore, finding a conventional method to determine these parameters is an urgent problem. Summary of the Invention

[0003] In order to solve the above problems, the present invention proposes a parameter inversion method based on machine learning to determine these parameters. At the same time, machine learning is a multivariate nonlinear dynamic system algorithm with good adaptability, self-organization, and strong self-learning, association, fault tolerance, and anti-drying capabilities. It can easily model and analyze complex unknown systems with multiple causes. Compared with other neural network models, the model used in machine learning has great advantages in approximation ability, classification ability, and learning speed, and can avoid the occurrence of local minima. In the problem of unsaturated soil parameter inversion, these characteristics of machine learning enable it to better handle complex nonlinear relationships and data uncertainty, and can automatically capture the inherent connections and laws between soil parameters, thereby achieving accurate inversion and prediction of unsaturated soil parameters. Therefore, the present invention establishes a finite element model for forward modeling of unsaturated seepage in two phases of water and gas, and assumes that the functional relationship between the unsaturated soil-water characteristic curve and the permeability coefficient satisfies the Van Genuchten model to invert the unsaturated parameters.

[0004] The technical solution adopted by the present invention is: a method for inverting unsaturated soil parameters based on machine learning, comprising the following steps:

[0005] Step S1: Conducting a soil seepage test using an experimental device. Each soil compaction degree is tested at different initial saturations, and the time for water seepage is recorded.

[0006] Step S2: performing finite element numerical simulation of the soil seepage test process based on boundary conditions and verifying the reliability of the numerical simulation;

[0007] Step S3: Call the Van Genuchten model function to describe the relationship between the soil-water characteristic curve and the permeability coefficient, assume the values ​​of the pressure P0 and the dimensionless parameter a in the Van Genuchten model and adopt the orthogonal method to set the working conditions;

[0008] Step S4: The numerical simulation water seepage time, compaction coefficient, and initial saturation are used as input vectors, and the pressure P0 and dimensionless parameter a in the VanGenuchten model function are used as output vectors for normalization processing;

[0009] Step S5: extract the normalized input vector and output vector to form training data and substitute them into machine learning for training, so that the gap between the fitted value and the true value is minimized;

[0010] Step S6: Substitute the normalized test input vector into the trained neural network model for prediction, and perform denormalization to obtain the target P0 and a value.

[0011] Specifically, in step 1, the seepage time of each soil with different initial saturation is obtained through a soil seepage test; wherein, the seepage test device includes a water inlet, a water outlet, a soil sample placement area above the water inlet and outlet, an external water source inlet, an electronic valve, a water level controller, an electronic trigger, and an electronic meter.

[0012] Specifically, in step 2, a finite element numerical simulation model for forward modeling of unsaturated water-gas two-phase seepage is established based on the water outlet time parameter sample of the seepage test, and then the rationality of the model is verified.

[0013] Specifically, in step 3, after calling the Van Genuchten model, the unknown parameters P0 and a are set up with multiple groups of working conditions using the orthogonal method, and the test process is numerically simulated. During the test, a pressure head h is applied to the bottom, and the top is the leakage boundary. At the same time, the top gas pressure is kept constant at zero, and the gas phase is allowed to flow. The calculation process adopts a conditional cycle mode to perform iterative operations for the next period. Otherwise, it is considered that the top node is saturated and water is seeping out of the top.

[0014] Specifically, in step 4, the numerically simulated water seepage time, compaction coefficient, and initial saturation at different saturations are used as input vectors, and their corresponding parameters P0 and a are used as output vectors. The water seepage time at different initial saturations obtained through the experiment is used as the test input vector and normalized by quoting the formula to process the data between [0, 1]. The formula is as follows:

[0015]

[0016] Where: x max is the longest water seepage time; x min The shortest water seepage time.

[0017] Specifically, in step 5, the entire machine learning project process is divided into three stages:

[0018] The first stage is Lasso regularization, which removes low-variance features and uses penalty terms to force some weights to 0 to achieve feature selection.

[0019] The second stage is to select an appropriate algorithm based on the task type. Each task type has a corresponding model framework. The characteristics of the data are summarized, and the feature type and interpretability requirements are determined. The selected model algorithm is then initialized by substituting the data parameters. The weights and biases are initialized randomly or using a specific initialization method.

[0020] The third stage is to define the loss function, optimize the algorithm and perform iterative training. The defined loss function is minimized through the optimization algorithm, driving the gap between the predicted value and the measured value to continuously decrease, and updating the model parameters according to the learning rate. In each iteration, the performance of the model is evaluated based on the gap between the predicted results of the neural network model and the true value.

[0021] Specifically, in step 6, the test results of the neural network model are used as the test input variables, and the parameters are inverted using machine learning. The measured water discharge time (normalized) of the neural network model is input into the trained machine learning network. Finally, the results are denormalized to obtain the actual unsaturated soil parameters P0 and a value.

[0022] Compared with existing technologies, the present invention offers the following advantages: It provides a method for inverting unsaturated soil parameters based on machine learning. This method aims to minimize the discrepancy between predicted and true values ​​by substituting test results as a training set into a model. The measured model water release time is then substituted into the trained machine learning neural network for denormalization to obtain the actual unsaturated soil parameters. This method reduces the time and expense of specific unsaturated soil wetting or dehumidification tests and permeability tests. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of the method for inverting unsaturated soil parameters based on machine learning according to the present invention;

[0024] Figure 2 This is a diagram of the device for the unsaturated soil seepage test of the present invention;

[0025] Figure 3 This is a diagram of the electronic trigger in the experiment;

[0026] Figure 4 This is the model grid division diagram for the numerical simulation of soil seepage test;

[0027] Figure 5 A diagram of the neuron computation process in machine learning;

[0028] Figure 6 A data propagation diagram for machine learning;

[0029] Figure 7 Update the graph for machine learning weights. DETAILED DESCRIPTION

[0030] The specific implementation of the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0031] Example 1: Figure 1 As shown in FIG, a method for inverting unsaturated soil parameters based on machine learning includes the following steps:

[0032] Step S1: Conducting a soil seepage test using an experimental device. Each soil compaction degree is tested at different initial saturations, and the time for water seepage is recorded.

[0033] Step S2: performing finite element numerical simulation of the soil seepage test process based on boundary conditions and verifying the reliability of the numerical simulation;

[0034] Step S3: Call the Van Genuchten model function to describe the relationship between the soil-water characteristic curve and the permeability coefficient, assume the values ​​of the pressure P0 and the dimensionless parameter a in the Van Genuchten model and adopt the orthogonal method to set the working conditions;

[0035] Step S4: The numerical simulation water seepage time, compaction coefficient, and initial saturation are used as input vectors, and the pressure P0 and dimensionless parameter a in the VanGenuchten model function are used as output vectors for normalization processing;

[0036] Step S5: extract the normalized input vector and output vector to form training data and substitute them into machine learning for training, so that the gap between the fitted value and the true value is minimized;

[0037] Step S6: Substitute the normalized test input vector into the trained neural network model for prediction, and perform denormalization to obtain the target P0 and a value.

[0038] Furthermore, in step 1, the compaction degree of each soil is tested at different initial saturations, thereby conducting a seepage test on the soil, recording the water discharge time of the test and stopping the test.

[0039] Furthermore, in step 2, in order to obtain learning samples for training, a finite element analysis is performed on the soil column test process, a numerical simulation is performed on the entire soil column seepage process, and the effectiveness of the numerical simulation is verified.

[0040] Figure 2 The test device for this experiment specifically includes: a water inlet, a water outlet, a soil sample located above the inlet and outlet, an external water inlet, an electronic valve, a water level controller, an electronic trigger, and an electronic meter. During the test, the sample is first placed in the device and the outlet valve is closed. Water is then added from the external water source interface until water begins to seep from the top of the sample. At this point, the two poles of the electronic trigger short-circuit due to contact with water, the electronic meter automatically stops, the water outlet is opened, and the time for water to seep out is recorded.

[0041] Figure 3 It is an electronic trigger. When water starts to emerge from the top of the soil sample, the filter paper is wetted, causing the electronic trigger to short-circuit, and the water outflow time is recorded at this time.

[0042] Furthermore, in step 3, after calling the Van Genuchten model, the unknown parameters P0 and a are set up with a total of 36 groups of working conditions using the orthogonal method, and the test process is numerically simulated. During the test, a pressure head h = 1.3054m is applied to the bottom, and the top is the leakage boundary. At the same time, the top gas pressure is kept constant at zero, and the gas phase is allowed to flow. The calculation process adopts a conditional cycle mode and performs iterative operations for the next period (20s). Otherwise, it is considered that the top node is saturated and water is seeping out of the top.

[0043] The functional relationship between the soil-water characteristic curve and the permeability coefficient of unsaturated soil satisfies the Van Genuchten model, which is expressed as follows:

[0044]

[0045] Where: μ w 、μ g is the dynamic viscosity of the water phase and the gas phase, which is a known value and can be obtained from the manual; is the water phase permeability coefficient with a saturation of "1", which can be obtained from conventional permeability tests; is the residual saturation, which can be determined by conventional seepage test methods.

[0046] Furthermore, in step 4, the numerically simulated water seepage time, compaction coefficient, and initial saturation at different saturations are used as input vectors, and the corresponding parameters P0 and a are used as output vectors. The water seepage time at different initial saturations obtained through the experiment is used as the test input vector and normalized by quoting the formula, and the data is processed between [0, 1]. The formula is as follows:

[0047]

[0048] Where: x max is the longest water seepage time; x min The shortest water seepage time.

[0049] Furthermore, in step 5, the machine learning algorithm structure consists of three layers of neurons, the first layer is the input layer, the second layer is the hidden layer, and the third layer is the output layer. During the neuron calculation process, each neuron in the input layer receives input from the previous layer and performs a weighted summation on these inputs. For the jth neuron, its output is expressed as:

[0050]

[0051] where x i represents the i-th input feature, w ij Represents input x i The weight between neuron j, b j Represents the bias of the neuron; and the weighted summation result z in the activation function j Perform nonlinear transformation through activation function and output the result:

[0052] a j =f(z j )

[0053] Where: a j is the final output value of the jth neuron; f(z j ) means z j Transformed by the activation function f.

[0054] In step 5, the entire machine learning project process is divided into three stages:

[0055] The first stage is Lasso regularization, which removes low-variance features and uses penalty terms to force some weights to 0 to achieve feature selection.

[0056] The second stage is to select an appropriate algorithm based on the task type. Each task type has a corresponding model framework. The characteristics of the data are summarized, and the feature type and interpretability requirements are determined. The selected model algorithm is then initialized by substituting the data parameters. The weights and biases are initialized randomly or using a specific initialization method.

[0057] The third stage is to define the loss function, optimize the algorithm and perform iterative training. The defined loss function is minimized through the optimization algorithm, driving the gap between the predicted value and the measured value to continuously decrease, and updating the model parameters according to the learning rate. In each iteration, the performance of the model is evaluated based on the gap between the predicted results of the neural network model and the true value.

[0058] Furthermore, in step 6, the neural network model test results were used as test input variables, and machine learning was used to invert the parameters. The measured water release time (normalized) from the neural network model was input into the trained machine learning network. Finally, the results were denormalized to obtain the actual unsaturated soil parameters. Numerical simulations of water release times corresponding to initial saturation under different compaction conditions were performed and compared with the actual water release times. The maximum error in the water release time was 6.11%, demonstrating the feasibility of inverting unsaturated soil parameters using machine learning.

[0059] The core process of neural network training is divided into four stages.

[0060] The first stage is forward propagation. Forward propagation is the process by which data flows through a machine learning neural network. Starting from the input layer, data undergoes linear calculations and nonlinear activation functions layer by layer, ultimately reaching the output layer. Specifically, the input data is prepared by passing it directly to the neurons in the input layer, with each input corresponding to a neuron. The output is then calculated layer by layer. For each neuron in each layer, the output value of the previous layer is linearly combined with the weight w and bias b of the current layer, and then an activation function is applied to perform a nonlinear transformation:

[0061] z (l) =W (l) a (l-1) +b (l)

[0062] a (l) =f(z (l) )

[0063] Among them, z (l) is the linear combination result of the lth layer; w (l) is the weight matrix of the current layer; b (l) is the bias; a (l-1) is the output of the previous layer (layer 0 is the input data); a (l) is the output of layer l.

[0064] The second stage is loss calculation. After forward propagation, the neural network outputs the predicted value. The difference between the predicted result and the true value y is measured by the loss function, and the choice of loss function depends on the task type: the regression task uses the mean square error (MSE):

[0065]

[0066] Cross-Entropy Loss is suitable for classification tasks:

[0067]

[0068] Where m is the number of samples, is the predicted value of the i-th sample, y (i) is the true label of the i-th sample. The goal of the loss function is to provide a scalar value that represents the performance of the model. The goal of training is to minimize this loss function through an optimization process.

[0069] The third stage is backpropagation. Backpropagation uses the chain rule to calculate the gradient of the loss with respect to each parameter layer by layer, providing a basis for parameter updates. The backpropagation step is to first calculate the error of the output layer. The error of the output layer is the gradient of the loss function with respect to the output layer activation value.

[0070]

[0071] in, is the gradient of the loss function with respect to the output, f′(z (L) ) is the derivative of the activation function. The error is then propagated layer by layer, starting from the output layer and propagating forward layer by layer. The error of the hidden layer is calculated by the chain rule. For the Lth layer, the error is:

[0072] δ (l) =(W (l+1) ) T δ (l+1) ·f′(z (l) )

[0073] Here, δ (l) is the error of the Lth layer, δ (l+1) is the L+1th error, (W (l+1) ) T is the weight transposed matrix of the L+1th layer, f′(z (l) ) is the derivative of the activation function, and finally the gradient calculation is performed. For each layer L, the gradient of the weight and bias is calculated according to the error and activation value of the current layer. The weight gradient is:

[0074]

[0075] Bias gradient:

[0076]

[0077] The fourth stage is weight update. After calculating the gradient of each layer's weights and biases through backpropagation, an optimization algorithm is used to update the parameters. The most common optimization algorithm is gradient descent:

[0078] Weight update:

[0079]

[0080] Bias update:

[0081]

[0082] Where η is the learning rate.

[0083] Figure 4 This is the model grid division diagram for the numerical simulation of soil seepage test. In order to make the numerical simulation effect closest to the actual experiment, after repeated debugging and judgment of the grid sensitivity, the number of grid divisions was finally determined to be 10×100.

[0084] Figure 5 、 6 ,7 are the machine learning neuron calculation process diagram, propagation process diagram and weight update diagram, where w1, w2, ..., w n is the coefficient of the independent variable, b is the bias, and the goal of linear regression is to find the optimal coefficient and intercept to minimize the error between the predicted value of the neural network model and the true value. The mean square error (MSE) is often used as the error indicator:

[0085] y=w1x1+w2x2+…+w n x n +b

[0086]

[0087] Where J(θ) represents the loss function; x (i) is the input feature; h θ (x (i) ) is the model prediction value; y (i) is the actual value of the i-th training sample; θ is the parameter vector, and m is the number of samples. In order to find the parameter θ that minimizes the loss function, the gradient descent method is used, and the update rule of the gradient descent method is:

[0088]

[0089] Among them, α is the learning rate, and the loss function is calculated based on θ j Partial derivatives of :

[0090]

[0091] Therefore, the parameter update formula for gradient descent is:

[0092]

[0093] Where: is the jth eigenvalue of the i-th training sample; h θ (x (i) )-y (i) Represents the error between the predicted value and the actual value of the i-th sample.

[0094] Logistic regression is a classification algorithm used in neural network algorithms for machine learning, mainly used for binary classification problems. Logistic regression uses the Sigmoid function to map the output of linear regression to between 0 and 1, indicating the probability that the sample belongs to a certain class:

[0095]

[0096] The goal of logistic regression is to maximize the likelihood function, which is the product of the probabilities that all training examples belong to their true categories:

[0097]

[0098] Taking the logarithm gives the log-likelihood function:

[0099]

[0100] In order to maximize the log-likelihood function, the gradient descent method is also used. Calculate the log-likelihood function for θ j Partial derivatives of :

[0101]

[0102] Therefore, the parameter update formula of gradient ascent is:

[0103]

[0104] Decision trees, a machine learning algorithm, are a type of tree-structured classification and regression algorithm. The basic idea is to partition a dataset into subsets using a series of feature tests, with each internal node representing a feature test and each leaf node representing a category or value. Decision trees are typically constructed using criteria such as information gain, gain ratio, or the Gini index to select the optimal partitioning features. Information gain is the metric used in the ID3 decision tree algorithm to select partitioning features, and its calculation formula is:

[0105] Gain(D,a)=Ent(D)-Ent(D|a)

[0106] Among them, Ent(D) is the information entropy of data set D, Ent(D|a) is the condition of data set D after the value of attribute a is known, and the CART decision tree uses the Gini index to select the optimal partitioning feature. The calculation formula of the Gini index is:

[0107]

[0108] Among them, p k is the proportion of category k in the dataset D. For attribute a, its Gini index is:

[0109]

[0110] Among them, D v It is a subset of the set whose attribute a takes the value v.

[0111] In this embodiment, the sample soil in step S1 was red bed mudstone crushed and then passed through a 2 mm sieve. A heavy compaction test was performed on the test soil in accordance with the "Soil Testing Code" (SL237-1999), resulting in a maximum dry density of 1.855 g / cm3 and an optimal moisture content of 12.81%. Furthermore, with reference to the "Highway Subgrade Design Manual," permeability tests were performed on samples with compaction degrees of 87%, 90%, 93%, 95%, and 98%. Two sets of tests were conducted for each compaction degree at different initial saturations. The test results are shown in Table 1.

[0112] Table 1 Test results

[0113]

[0114] The numerically simulated water seepage time under various parameter combinations at different initial saturations and various compaction degrees in step S2 of this embodiment is shown in Tables 2 and 3.

[0115] Table 2 Numerical simulation of water seepage time under various parameters combinations at different initial saturations and various compaction degrees

[0116]

[0117]

[0118] Table 3 Numerical simulation of water seepage time under various parameters combinations at different initial saturations and various compaction degrees

[0119]

[0120]

[0121] In steps S3, S4, S5, and S6 of this embodiment, the correctness of the inversion parameters is evaluated. The water seepage time corresponding to the initial saturation under different compactions is trained and compared with the actual water seepage time. The maximum error of the water seepage time is 6.11%, which proves the feasibility of inversion of unsaturated parameters based on the machine learning algorithm, as shown in Tables 4 and 5.

[0122] Table 4 Prediction parameter values ​​under different compaction degrees

[0123] parameter 87％ 90％ 93％ 95％ 98％ <![CDATA[P0 / Kpa]]> 48.62 50.09 52.64 57.07 66.68 a 0.324 0.305 0.297 0.283 0.278

[0124] Table 5 Comparison of predicted and actual water seepage time under different compaction degrees

[0125]

[0126]

[0127] The above describes in detail the specific embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the purpose of the present invention. In addition, the meanings of the various letters in the present invention that are not separately explained are well known in the prior art and will not be repeated here.

Claims

1. A method for inverting unsaturated soil parameters based on machine learning, characterized in that: The following steps are involved: Step S1: Conducting a soil seepage test using an experimental device. Each soil compaction degree is tested at different initial saturations, and the time for water seepage is recorded. Step S2: performing finite element numerical simulation of the soil seepage test process based on boundary conditions and verifying the reliability of the numerical simulation; Step S3: Call the Van Genuchten model function to describe the relationship between the soil-water characteristic curve and the permeability coefficient, assume the values ​​of the pressure P0 and the dimensionless parameter a in the Van Genuchten model and adopt the orthogonal method to set the working conditions; Step S4: using the numerically simulated water seepage time, compaction coefficient, and initial saturation as input vectors, and the pressure P0 and dimensionless parameter a in the Van Genuchten model function as output vectors for normalization; Step S5: extract the normalized input vector and output vector to form training data and substitute them into machine learning for training, so that the gap between the fitted value and the true value is minimized; Step S6: Substitute the normalized test input vector into the trained neural network model for prediction, and perform denormalization to obtain the target P0 and a value.

2. The method for inversion of unsaturated soil parameters based on machine learning according to claim 1, characterized in that: In step 1, the seepage time of each soil with different initial saturation is obtained through a soil seepage test; wherein, the seepage test device includes a water inlet, a water outlet, a soil sample placement area above the water inlet and outlet, an external water source inlet, an electronic valve, a water level controller, an electronic trigger, and an electronic meter.

3. The method for inversion of unsaturated soil parameters based on machine learning according to claim 1 is characterized in that: In step 2, a finite element numerical simulation model for forward modeling of unsaturated water-gas two-phase seepage is established based on the water outlet time parameter sample of the seepage test, and then the rationality of the model is verified.

4. The method for inversion of unsaturated soil parameters based on machine learning according to claim 1, characterized in that: In step 3, after calling the Van Genuchten model, the unknown parameters P0 and a are set up with multiple groups of working conditions using the orthogonal method, and the test process is numerically simulated. During the test, a pressure head h is applied to the bottom, the top is the leakage boundary, and the top gas pressure is kept constant at zero, allowing the gas phase to flow. The calculation process adopts a conditional cycle mode and performs iterative calculations for the next period. Otherwise, it is considered that the top node is saturated and water is seeping out of the top.

5. The method for inversion of unsaturated soil parameters based on machine learning according to claim 1, characterized in that: In step 4, the numerically simulated water seepage time, compaction coefficient, and initial saturation at different saturations are used as input vectors, and the corresponding parameters P0 and a are used as output vectors. The water seepage time at different initial saturations obtained through the experiment is used as the test input vector and normalized by quoting the formula to process the data between [0, 1]. The formula is as follows: Where: x max is the longest water seepage time; x min The shortest water seepage time.

6. The method for inversion of unsaturated soil parameters based on machine learning according to claim 1, characterized in that: In step 5, the entire machine learning project process is divided into three stages: The first stage is Lasso regularization, which removes low-variance features and uses penalty terms to force some weights to 0 to achieve feature selection. The second stage is to select an appropriate algorithm based on the task type. Each task type has a corresponding model framework. The characteristics of the data are summarized, and the feature type and interpretability requirements are determined. The selected model algorithm is then initialized by substituting the data parameters. The weights and biases are initialized randomly or using a specific initialization method. The third stage is to define the loss function, optimize the algorithm and perform iterative training. The defined loss function is minimized through the optimization algorithm, driving the gap between the predicted value and the measured value to continuously decrease, and updating the model parameters according to the learning rate. In each iteration, the performance of the model is evaluated based on the gap between the predicted results of the neural network model and the true value.

7. The method for inverting unsaturated soil parameters based on machine learning according to claim 1, characterized in that: In step 6, the test results of the neural network model are used as the test input variables, and the parameters are inverted using machine learning. The normalized water discharge time of the measured neural network model is input into the trained machine learning network. Finally, the results are denormalized to obtain the actual unsaturated soil parameters P0 and a value.

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