Frozen soil zone thickness evolution analysis method based on sparrow search algorithm optimization

Abstract

The invention relates to the technical field of frozen soil zone evolutionary analysis, in particular to a frozen soil zone thickness evolutionary analysis method based on sparrow search algorithm optimization, which comprises the following steps: dividing a frozen soil layer according to historical formation temperature data, and determining frozen soil zone thickness data; external factors influencing the thickness of the frozen soil zone are collected within the recording time of the historical formation temperature data, and the correlation degree among the recording time, the external factors and the thickness of the frozen soil zone is analyzed; and a machine learning algorithm is combined with a sparrow search algorithm to construct an optimal prediction model for predicting the thickness of the frozen soil zone based on the external factors. The optimal prediction model formed through the machine learning model and the sparrow search algorithm can more accurately describe the complex nonlinear mapping relation between the external factors and the thickness of the frozen soil zone, the fitting degree of the prediction result and the real thickness is higher, the relative standard error is remarkably reduced, the correlation coefficient is further improved, and the method has good application prospects. And the reliability and scientificity of the prediction result are higher.

Description

Technical Field

[0001] This invention relates to the field of permafrost evolution analysis technology, specifically to a permafrost thickness evolution analysis method based on the sparrow search algorithm. Background Technology

[0002] Permafrost, especially permafrost, is a crucial component of the Earth system and is often referred to as an "amplifier of climate change." Its thickness evolution directly reflects regional and even global climate change trends, and has profound impacts on infrastructure stability, the carbon cycle (particularly methane release), ecosystems, and water resource distribution. Therefore, accurate monitoring and prediction of permafrost thickness changes are essential for understanding global climate change, assessing engineering risks, and developing environmental protection policies.

[0003] Traditional methods for monitoring permafrost thickness primarily rely on in-situ borehole temperature measurements and geophysical exploration (such as seismic and resistivity methods). While these methods are direct, they are costly, have limited spatial coverage, are difficult to conduct long-term continuous observations, and are not effective for predicting future trends. Existing prediction models are mostly based on simplified physical equations or statistical regressions. These models are inadequate when dealing with the complex nonlinear processes of permafrost systems driven by multiple environmental factors (such as soil temperature, soil moisture, and atmospheric composition), and struggle to capture their inherent dynamic evolution patterns.

[0004] Therefore, existing technologies have poor nonlinear processing capabilities in analyzing the evolution of permafrost zones and limited ability to grasp evolution laws, ultimately resulting in insufficient reliability and accuracy in predicting permafrost thickness. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm, so as to solve the technical problems of poor nonlinear processing capability and limited ability to grasp evolution law in the existing technology.

[0006] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution:

[0007] A method for analyzing the evolution of permafrost thickness based on a sparrow search algorithm includes the following steps:

[0008] Based on historical stratigraphic temperature data, the permafrost layer was divided, and the thickness of the permafrost zone was determined.

[0009] During the recording period of historical stratigraphic temperature data, external factors affecting the thickness of the permafrost zone were collected, and the correlation between recording time, external factors, and permafrost zone thickness was analyzed.

[0010] An optimal prediction model for predicting the thickness of the permafrost zone based on external factors was constructed by combining machine learning algorithms with the sparrow search algorithm.

[0011] As a preferred embodiment of the present invention, the method for delineating the frozen soil layer includes:

[0012] A graph showing the temperature variation with depth was created based on historical stratigraphic temperature data.

[0013] By analyzing the temperature variation with depth, the seasonally frozen soil layer, the perennial frozen soil layer, and the non-frozen soil layer were identified.

[0014] Among them, the depths where the temperature of the strata changes significantly across the entire time domain during the recording period, exhibit obvious seasonality, and where the temperature change gradually decreases with increasing depth are defined as seasonal permafrost strata.

[0015] The depths where the temperature of the strata is below 0℃ throughout the entire recording time, the temperature is stable, and the temperature gradually increases with increasing depth are defined as permafrost strata.

[0016] Depths where the ground temperature is above 0°C throughout the entire recording period are considered as non-permafrost strata.

[0017] As a preferred embodiment of the present invention, external factors include: soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content.

[0018] As a preferred embodiment of the present invention, the method for constructing the optimal prediction model includes:

[0019] Three prediction models for predicting the thickness of permafrost based on external factors were constructed using Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively.

[0020] The parameters of three prediction models were optimized using the sparrow search algorithm;

[0021] The performance of the three optimized prediction models is evaluated, and the prediction model with the best performance is selected as the optimal prediction model.

[0022] As a preferred embodiment of the present invention, the method for constructing the prediction model includes:

[0023] Soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content were used as feature inputs for Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively. The thickness of the permafrost zone was used as the prediction output for SVM, RF, and DNN. Prediction models based on SVM, RF, and DNN were trained to obtain prediction models.

[0024] As a preferred embodiment of the present invention, the loss functions of the prediction models based on SVM, RF, and DNN are the mean squared error and mean absolute error between the predicted output and the true value.

[0025] As a preferred embodiment of the present invention, the optimization method of the sparrow search algorithm includes:

[0026] The hyperparameters in the SVM-based prediction model are optimized by using the sparrow search algorithm: the penalty parameter C and the parameter gamma of the RBF kernel function. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are determined. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are then substituted into the SVM-based prediction model to obtain the optimized SVM-based prediction model.

[0027] The hyperparameters in the RF-based prediction model are optimized using the Sparrow Search algorithm: the number of decision trees (n_estimators), the number of randomly selected features per decision tree (max_features), and the maximum depth of the tree (max_depth). The optimal values ​​of these parameters are then determined and substituted into the RF-based prediction model to obtain the optimized RF-based prediction model.

[0028] The hyperparameters of a DNN-based prediction model—network structure parameters and model training parameters—are optimized using a sparrow search algorithm. The optimal values ​​of these parameters are determined, and then substituted into the DNN-based prediction model to obtain the optimized model. The network structure parameters include the number and type of intermediate layers, the number of neurons per layer, and the activation function. The model training parameters include the loss function, optimization method, batch size, number of iterations, learning rate, regularization method and coefficients, and initialization method.

[0029] As a preferred embodiment of the present invention, the performance evaluation indicators include the degree of fit between the model predictions and the true values, the relative standard error RSEM, and the correlation coefficient R.

[0030] As a preferred embodiment of the present invention, the method for analyzing the correlation between recording time, external factors, and permafrost thickness includes:

[0031] The correlation between recording time, soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, nitrogen content and frozen soil thickness was analyzed to obtain a data scatter plot matrix and a related heat map.

[0032] Based on the analysis of the data scatter plot matrix and related heat maps, it was found that the thickness of the frozen soil layer is inversely proportional to the recording time, rainfall, soil temperature and soil moisture, and directly proportional to the sunshine duration, carbon dioxide concentration, hydrogen sulfide concentration and nitrogen content.

[0033] The thickness of the frozen soil layer has the strongest correlation with soil moisture, while soil temperature has the strongest correlation with soil moisture.

[0034] As a preferred embodiment of the present invention, the sparrow search algorithm includes the following steps:

[0035] Step 1: Establish a population X consisting of n sparrows. The expression for population X is:

[0036] ;

[0037] Where d is the number of hyperparameters to be optimized. Let n be the position of the nth sparrow in dimension d;

[0038] Step 2: Set fitness value The fitness value represents an individual sparrow's ability to find food. The expression is:

[0039] ;

[0040] in, For the fitness function, Let be the fitness value of the nth sparrow. Let n be the position vector of the nth sparrow;

[0041] Step 3: Based on population X and fitness value The location update formula for the discoverer is set as follows:

[0042] ;

[0043] in, For the number of iterations, The maximum number of iterations, , They were respectively in the second sequence During the nth iteration, the 1st The sparrow that was the discoverer was in the first The position of the dimension It is a random number in [0,1]. This is the warning value, and its range is [0,1]. The safe value is [0.5, 1], Q is a random number that follows a normal distribution, and L is a 1×d matrix with all elements being 1;

[0044] Step 4: Based on population X and fitness value The location update formula for discoverers is set as follows:

[0045] ;

[0046] in, In the first In the next iteration, the sparrow, as the discoverer, is in the best position. Let A be the worst possible position for the sparrow that discovers the sparrow, and let A be a 1×d matrix where each element is randomly assigned a value of 1 or -1. ;

[0047] Step 5: Set the number of scout sparrows to 10% to 20% of the total population. Their initial positions are randomly generated within the population. The behavioral expression for scout alerts is:

[0048] ;

[0049] in, Let t be the current globally optimal sparrow position in the t-th iteration, β be a control parameter, a random number following a standard normal distribution, K be a uniform random number with a value range of [-1, 1], and ε be a small constant to avoid the denominator being zero; The fitness value of the sparrow acting as a scout. The sparrow in the best position in the whole game fitness value, Sparrow in the worst position globally The fitness value.

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] The optimal prediction model formed by the machine learning model and the sparrow search algorithm in this invention can more accurately characterize the complex nonlinear mapping relationship between external factors and the thickness of the permafrost zone. Its prediction results have a higher degree of fit with the actual thickness, a significantly reduced relative standard error (RSEM), and a further improved correlation coefficient (R), making the prediction results more reliable and scientific. Attached Figure Description

[0052] To more clearly illustrate the embodiments of the present invention or the technical solutions in 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 merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0053] Figure 1 This is a flowchart of a machine learning analysis method for permafrost thickness evolution based on a sparrow search algorithm optimized according to an embodiment of the present invention.

[0054] Figure 2 Formation temperature data diagram provided for embodiments of the present invention;

[0055] Figure 3 A temperature variation diagram as a function of depth is provided for an embodiment of the present invention;

[0056] Figure 4 The scatter plot matrix provided in the embodiments of the present invention;

[0057] Figure 5 Correlation heatmap provided for embodiments of the present invention;

[0058] Figure 6 This is a performance comparison chart of various prediction models provided in the embodiments of the present invention;

[0059] Figure 7 The feature contribution map provided for the embodiments of the present invention. Detailed Implementation

[0060] 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, and 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.

[0061] like Figure 1 As shown, this invention provides a method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm, comprising the following steps:

[0062] Based on historical stratigraphic temperature data, the permafrost layer was divided, and the thickness of the permafrost zone was determined.

[0063] During the recording period of historical stratigraphic temperature data, external factors affecting the thickness of the permafrost zone were collected, and the correlation between recording time, external factors, and permafrost zone thickness was analyzed.

[0064] An optimal prediction model for predicting the thickness of the permafrost zone based on external factors was constructed by combining machine learning algorithms with the sparrow search algorithm.

[0065] This invention generates temperature-depth profiles based on historical stratigraphic temperature data. Based on temperature stability (whether it is consistently below 0°C) and variation characteristics, seasonally frozen soil, permafrost, and non-frozen soil layers are interpreted and delineated, thereby accurately determining the depth of the top and bottom plates of the permafrost zone and calculating its thickness.

[0066] Methods for dividing the permafrost layer include:

[0067] A graph showing the temperature variation with depth was created based on historical stratigraphic temperature data.

[0068] By analyzing the temperature variation with depth, the seasonally frozen soil layer, the perennial frozen soil layer, and the non-frozen soil layer were identified.

[0069] Among them, the depths where the temperature of the strata changes significantly across the entire time domain during the recording period, exhibit obvious seasonality, and where the temperature change gradually decreases with increasing depth are defined as seasonal permafrost strata.

[0070] The depths where the temperature of the strata is below 0℃ throughout the entire recording time, the temperature is stable, and the temperature gradually increases with increasing depth are defined as permafrost strata.

[0071] Depths where the ground temperature is above 0°C throughout the entire recording period are considered as non-permafrost strata.

[0072] This invention transforms raw temperature data into structured thickness-labeled data through rigorous geophysical interpretation methods, ensuring the accuracy of the "true value" in supervised learning, providing high-quality training targets for training high-performance models, and laying a quality foundation for all subsequent machine learning analyses.

[0073] External factors include: soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content.

[0074] Methods for analyzing the correlation between recording time, external factors, and permafrost thickness include:

[0075] The correlation between recording time, soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, nitrogen content and frozen soil thickness was analyzed to obtain a data scatter plot matrix and a related heat map.

[0076] Based on the analysis of the data scatter plot matrix and related heat maps, it was found that the thickness of the frozen soil layer is inversely proportional to the recording time, rainfall, soil temperature and soil moisture, and directly proportional to the sunshine duration, carbon dioxide concentration, hydrogen sulfide concentration and nitrogen content.

[0077] The thickness of the frozen soil layer has the strongest correlation with soil moisture, while soil temperature has the strongest correlation with soil moisture.

[0078] Methods for constructing optimal prediction models include:

[0079] Three prediction models for predicting the thickness of permafrost based on external factors were constructed using Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively.

[0080] The parameters of three prediction models were optimized using the sparrow search algorithm;

[0081] The performance of the three optimized prediction models was evaluated, and the best-performing prediction model was selected as the optimal prediction model.

[0082] Methods for constructing predictive models include:

[0083] Soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content were used as feature inputs for Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively. The thickness of the permafrost zone was used as the prediction output for SVM, RF, and DNN. Prediction models based on SVM, RF, and DNN were trained to obtain prediction models.

[0084] The loss functions for prediction models based on SVM, RF, and DNN are the mean squared error and mean absolute error between the predicted output and the true value.

[0085] Optimization methods for the sparrow search algorithm include:

[0086] The hyperparameters in the SVM-based prediction model are optimized by using the sparrow search algorithm: the penalty parameter C and the parameter gamma of the RBF kernel function. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are determined. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are then substituted into the SVM-based prediction model to obtain the optimized SVM-based prediction model.

[0087] The hyperparameters in the RF-based prediction model are optimized using the Sparrow Search algorithm: the number of decision trees (n_estimators), the number of randomly selected features per decision tree (max_features), and the maximum depth of the tree (max_depth). The optimal values ​​of these parameters are then determined and substituted into the RF-based prediction model to obtain the optimized RF-based prediction model.

[0088] The hyperparameters of a DNN-based prediction model—network structure parameters and model training parameters—are optimized using a sparrow search algorithm. The optimal values ​​of these parameters are determined, and then substituted into the DNN-based prediction model to obtain the optimized model. The network structure parameters include the number and type of intermediate layers (fully connected, dropout, normalized, convolutional, etc.), the number of neurons per layer, and the activation function. The model training parameters include the loss function, optimization method, batch size, number of iterations, learning rate, regularization method and coefficients, and initialization method.

[0089] Performance evaluation metrics include the goodness of fit between model predictions and true values, relative standard error (RSEM), and correlation coefficient (R).

[0090] Among them, the kernel functions of Support Vector Machines (SVM) mainly fall into three categories: polynomial kernel functions, radial basis functions (RBF), and sigmoid functions. This invention uses the radial basis function (RBF), whose expression is: .

[0091] The core approach of using SVM to solve problems encountered in regression fitting has shifted from finding the optimal plane to finding an optimal surface that minimizes the error between all original data and the target classification surface.

[0092] Generally, we assume the dataset contains l training samples. ,in , , This is the corresponding output value.

[0093] Let the regression polynomial established in the new space be: ;

[0094] in, Let ε be a linear loss function in a multinomial nonlinear function mapping expression. ;

[0095] Where f(x) is the predicted value of the objective function; y is the true value. This means that if the difference between the objective expression f(x) and the true value y is less than or equal to ε, then the value of the loss function is equal to 0.

[0096] Slack variables were introduced The mathematical expression for SVM is:

[0097] ;

[0098] Where C is the penalty value, the larger C is, the larger the penalty function is for samples with training error greater than ε, and ε represents the upper limit of the objective function error. The smaller ε is, the smaller the objective function error is.

[0099] Use the Largerange function to solve for the dual form of the above equation:

[0100] ;

[0101] in, This is the kernel function.

[0102] Let the optimal solution obtained by the above equation be Then we can obtain the expressions for w* and b*. Therefore, the regression function is: .

[0103] Random Forest (RF), proposed by Leo Breiman in 2001, is an improvement on Bagging and consists of a large number of decision trees. RF can meet the needs of classification and regression. For classification, voting determines the prediction result of each decision tree, and the class with the most votes is selected. For regression, the mean of all decision trees is selected as the prediction result.

[0104] The RF regression model can be mathematically interpreted as follows: Given a specific dataset, X is the independent variable (input data), and Y is the dependent variable to be predicted (output data). Assuming that the distributions of (X,Y) are independent, a training set is randomly generated from (X,Y), and the prediction result is denoted as g(X). Then, its mean squared generalization error is expressed as: ;

[0105] Assuming there are h decision trees, what is the predicted value of h decision trees? The average value is the prediction result of random forest regression. If Then the following formula holds true: ;

[0106] In the above formula The generalization error is represented by PE.** When h is infinitely large, the average generalization error of a single decision tree is denoted as PE. * PE * satisfy: ;

[0107] The above equation satisfies: ;

[0108] in This represents the weighted correlation coefficient between the residuals. The final regression function for the randomization function is: ;

[0109] The construction steps or process of this algorithm are as follows:

[0110] Step 1: Use the Bootstrap resampling method to randomly select n samples with replacement from the dataset, repeating this sampling K times to obtain K training sample sets, which are independent and identically distributed. Simultaneously, the samples not selected in the K samplings are grouped into K out-of-bag (OOB) data sets, becoming the K test sample sets.

[0111] Step 2: Construct a decision tree using the K training samples extracted in Step 1. A random subspace method is used to select the node feature variables of the decision tree; that is, when a sample has n features, m features are randomly selected from each node of the decision tree. Then, the information values ​​contained in these features are calculated, and the most representative feature and its corresponding value are selected from the m features for node splitting.

[0112] Step 3: Each tree will grow to its maximum extent until the number of samples in a node is less than the originally set threshold or the minimum mean square error is less than the set threshold, at which point the decision tree terminates.

[0113] Step 4: Based on the above steps, K decision trees were obtained. Combining these K decision trees can construct a random forest regression model. Then, inputting the data will yield... ,Will average As a prediction result of the random forest regression model.

[0114] After generating pre-pruned decision trees, feature importance can be obtained using the Gini index of each decision tree in the random forest. Let G be the Gini index, and if dataset A has M classes in a classification problem, the probability that a subset belongs to the Mth class is... Then the Gini index is: ;

[0115] In a decision tree, the change in the Gini index before and after pruning a certain internal node is denoted as V. Suppose that after pruning, two new nodes appear, and the Gini indexes of these two new nodes are denoted as . Then we have the following formula: ;

[0116] Let feature N be in the decision tree. Let S be the set of nodes that appear in the decision tree. Then, the feature N in the decision tree... The importance of is recorded as follows: ;

[0117] If there are K decision trees in a random forest, then the Gini score of feature N in the random forest algorithm is: ;

[0118] Finally, after normalizing the Gini indices obtained from different features, the importance ranking of the different features is obtained by sorting them.

[0119] Neural networks are products derived from the analysis, abstraction, and imitation of the operation of biological neural networks. They are network structures that connect a large number of individual neurons according to certain rules, forming a network capable of processing information in parallel. They belong to a type of intelligent mathematical operation model. This model was first proposed by an American psychologist who analyzed the characteristics of biological neurons and, after combining them with mathematical theory, proposed the first mathematical model of an artificial neuron.

[0120] A neural network consists of a large number of processing units called neurons (corresponding to nerve cells in the human brain). The function of a neuron is to calculate the inner product of the input vector and the weight vector, and then pass it through a nonlinear transfer function to obtain a scalar result.

[0121] ;

[0122] ;

[0123] Commonly used activation functions include:

[0124] (1) Sigmoid function: ;

[0125] (2) tanh function: ;

[0126] (3) ReLU function: ;

[0127] (4) Leaky ReLU function: ;

[0128] Taking a neural network model containing an input layer, two hidden layers, and an output layer as an example, the first... The linear coefficient from the i-th neuron in layer 1 to the j-th neuron in layer 1 is defined as... The bias of the j-th neuron in the l-th layer is defined as The bias of the j-th neuron in the l-th layer is defined as The output of the first hidden layer is calculated as shown in the following equation:

[0129] ;

[0130] Suppose that the activation function we choose is The output of the j-th neuron in the (l+1)-th layer is defined as Then the input to the second hidden layer is:

[0131] ;

[0132] The output calculation for the second hidden layer is shown in the following formula:

[0133] ;

[0134] The input to the output layer is: ;

[0135] The output of the output layer is then: ;

[0136] The general expression for the loss function of a neural network is: The loss function is used to measure the degree of inconsistency between the true value y and the predicted value f(x), and generally, a smaller value is better. A small loss function indicates that the machine learning model closely approximates the true distribution of the data, indicating good model performance; a large loss function indicates that the machine learning model deviates significantly from the true distribution of the data, indicating poor model performance. For regression problems, the loss function is: ;

[0137] in, y represents the predicted result, and y represents the actual result.

[0138] Gradient descent is one of the most commonly used optimization algorithms and currently the most frequently used method for optimizing neural networks. It is an algorithm that reaches the minimum value of a function through iterative steps. To find a local minimum of a function using gradient descent, steps can be taken that are proportional to the negative value of the function's gradient (or approximate gradient) at the current point.

[0139] The gradient represents the directional derivative of a function at a given point, where the directional derivative along that direction reaches its maximum value; in other words, it is the derivative of the function at the current position. ;

[0140] In the formula, As the independent variable, For about The function, Let represent the gradient. Then the independent variable parameter in the i-th step should be equal to: ;

[0141] η is the learning rate. When the learning rate is too low, many steps are needed to converge. Conversely, when the learning rate is too high, gradient descent will fail to reach the minimum value.

[0142] The learning process of BP neural network reservoir modeling consists of two stages: The first stage is forward propagation, which involves inputting known reservoir geological information as training samples. Using the established network structure and the thresholds and weights obtained from the previous training step, the output of each neuron is calculated from the first layer onwards. This process processes the input geological variable data and outputs the results. The second stage is backpropagation, where the output error is propagated back through the hidden layers to the input layers, distributing the error to all units in each layer. This yields the error signal for each unit, which serves as the basis for adjusting the weights. Specifically, by comparing the deviation between the actual output and the expected parameters, the network error is determined and propagated back to the reservoir attribute data processing units, thus readjusting their connections. This process of forward and backward propagation of signals and adjustment of layer weights is repeated continuously. This continuous adjustment of weights is the network's learning and training process. This continues until the network's output error is reduced to an acceptable level or until a predetermined number of training iterations are completed.

[0143] Assumption It is known that the following can be calculated using the chain rule:

[0144] ;

[0145] and ;

[0146] Therefore, as long as the error of the l-th layer is known... Then you can calculate , , , and Used to update the parameters w and b of the l-th layer. It is passed to the (l-1)th layer to further calculate the derivatives of the parameters of the (l-1)th layer.

[0147] In the Sparrow Search Algorithm (SSA), sparrows can be categorized into three types: leaders, followers, and alerters. Within the population, leaders play a role in finding resources, providing clues such as foraging areas and directions. Followers, with their keen observation skills, capture the leader's movements to obtain food. Sparrows primarily utilize both leader and follower strategies for foraging, maintaining a cooperative yet competitive relationship. Alerters typically reside on the periphery of the population, where they are more vulnerable to predators, thus requiring them to constantly adjust their position to secure safer areas. Based on this brief overview, the following principles can be summarized:

[0148] (1) Resource reserve principle: Leaders usually control more food resources and are responsible for finding more favorable areas for the population, that is, areas with abundant food, and contacting followers to provide relevant foraging areas and directions.

[0149] (2) The principle of constant proportion: As long as a better resource is found, every sparrow can become a leader. However, the overall proportion of the two remains constant. That is to say, for every sparrow whose status changes to a leader, there must be another sparrow whose status changes to a follower. In other words, the status of leaders and followers is in a dynamic switching process.

[0150] (3) Warning and escape principle: If a sparrow discovers a predator, it will issue a warning. Once the warning value exceeds the warning threshold, the followers will escape to other safe areas to forage under the guidance of the leader.

[0151] (4) The principle of surveillance and plunder: When sparrows are foraging, they will always find the discoverer with the best food resources and obtain food from that area or forage around the leader. At the same time, if the followers want to improve their foraging rate, they will monitor the leader in real time in order to plunder food resources.

[0152] (5) The principle of flying towards the best: The scarcer the resources available to followers, the worse their foraging locations will be within the population. Some followers who are starving are more likely to fly to areas with more resources to forage.

[0153] (6) Warning and transfer principle: When a danger is sensed, sparrows on the periphery will immediately move to a safe location, while those in the middle of the population will adopt a random movement strategy to move closer to other individuals.

[0154] The process of the sparrow search algorithm includes:

[0155] Step 1: Establish a population X consisting of n sparrows. The expression for population X is:

[0156] ;

[0157] where \(d\) is the number of hyperparameters to be optimized, is the position of the \(n\)th sparrow in the \(d\)-dimensional space;

[0158] Step 2: Set the fitness value represents the ability of a sparrow individual to find food, and the fitness value is expressed as:

[0159] ;

[0160] where is the fitness function, is the fitness value of the \(n\)th sparrow, is the position vector of the \(n\)th sparrow;

[0161] Step 3: According to the population \(X\) and the fitness value , set the position update formula for the discoverer as:

[0162] ;

[0163] where is the iteration number, is the maximum iteration number, , are respectively the positions of the \(m\)th and \(k\)th sparrows acting as discoverers in the \(j\)th dimension at the th and th iterations, is the \(n\)th sparrow, is the \(j\)th dimension, is a random number in \([0, 1]\). is the warning value, with a value range of \([0, 1]\), is the safety value, with a value range of \([0.5, 1]\), \(Q\) is a random number following a normal distribution, and \(L\) is a \(1\times d\) matrix with all elements equal to 1;

[0164] When \(R2 < ST\), it indicates that the foraging environment is safe at this time, no predators are detected, and the discoverer can perform extensive search operations;

[0165] When \(R2 > ST\), it indicates that an individual in the sparrow population has detected a predator and issued an alarm. At this time, all sparrows will perform anti-predation behaviors and quickly move to other safe places to continue foraging;

[0166] Step 4: According to the population \(X\), the fitness value and the position update formula of the discoverer, set the position update formula for the joiner as:

[0167] ;

[0168] in, In the first In the next iteration, the sparrow, as the discoverer, is in the best position. Let A be the worst possible position for the sparrow that discovers the sparrow, and let A be a 1×d matrix where each element is randomly assigned a value of 1 or -1. ;

[0169] When it appears In this case, it indicates that the entrant with low fitness has not found food in the current state and needs to go to other areas to forage in order to improve its survival rate.

[0170] Step 5: Set the number of scout sparrows to 10% to 20% of the total population. Their initial positions are randomly generated within the population. The behavioral expression for scout alerts is:

[0171] ;

[0172] in, Let t be the current globally optimal sparrow position in the t-th iteration, β be a control parameter, a random number following a standard normal distribution, K be a uniform random number with a value range of [-1, 1], and ε be a small constant to avoid the denominator being zero; The fitness value of the sparrow acting as a scout. The sparrow in the best position in the whole game fitness value, Sparrow in the worst position globally The fitness value.

[0173] When f appears i =f g In this situation, it indicates that the sparrow in question is in the optimal position globally and will move closer to other sparrows to reduce the risk of being preyed upon.

[0174] When f appears i >f g In this situation, it indicates that the sparrow in question is on the edge of the population and is more vulnerable to predators, and will quickly move to the current optimal position.

[0175] Methods for optimizing the penalty parameter C and the gamma parameter of the RBF kernel function in Support Vector Machines (SVM) using the sparrow search algorithm include:

[0176] Each sparrow's position is represented as a (C, gamma) combination. The initial position is randomly generated within a preset range. The fitness value of the population is calculated using the relative standard error RSEM or the correlation coefficient R2 as the fitness function. The population size and maximum number of iterations of the sparrow search algorithm SSA are set.

[0177] During the iteration process of the Sparrow Search Algorithm (SSA):

[0178] Update the position of the leading sparrow based on the discoverer's updated formula, and explore new (C, gamma) combinations;

[0179] The position of the following sparrow is updated according to the formula for updating the position of the introducer, so as to move closer to the high-quality solution;

[0180] The position of the early warning sparrow is updated based on the behavior formula of the reconnaissance and early warning system to avoid getting trapped in local optima.

[0181] The fitness values ​​of all sparrows are recalculated after each iteration;

[0182] The sparrow position with the highest fitness that reaches the maximum number of iterations is taken as the optimal combination solution (C, gamma).

[0183] Methods for optimizing the number of decision trees (n_estimators), the number of randomly selected features (max_features) for each decision tree, and the maximum depth (max_depth) in Random Forest (RF) using the Sparrow Search algorithm include:

[0184] Each sparrow's position is represented as a (n_estimators, max_features, max_depth) combination. The initial position is randomly generated within a preset range. The fitness value of the population is calculated using the relative standard error RSEM or the correlation coefficient R2 as the fitness function. The population size and maximum number of iterations of the sparrow search algorithm SSA are set.

[0185] During the iteration process of the Sparrow Search Algorithm (SSA):

[0186] Update the position of the leading sparrow according to the discoverer's update formula, and explore new combinations of (n_estimators, max_features, max_depth);

[0187] The position of the following sparrow is updated according to the formula for updating the position of the introducer, so as to move closer to the high-quality solution;

[0188] The position of the early warning sparrow is updated based on the behavior formula of the reconnaissance and early warning system to avoid getting trapped in local optima.

[0189] The fitness values ​​of all sparrows are recalculated after each iteration;

[0190] The position of the sparrow with the highest fitness that reaches the maximum number of iterations is taken as the optimal combination solution of (n_estimators, max_features, max_depth).

[0191] The methods for optimizing network structure parameters and model training parameters in a neural network (DNN) using the sparrow search algorithm include:

[0192] Each sparrow's position is represented as a combination of (network structure parameters, model training parameters). The initial position is randomly generated within a preset range. The fitness value of the population is calculated using the relative standard error RSEM or the correlation coefficient R2 as the fitness function. The population size and maximum number of iterations of the sparrow search algorithm SSA are set.

[0193] During the iteration process of the Sparrow Search Algorithm (SSA):

[0194] Update the position of the leading sparrow according to the discovery formula, and explore new combinations of (network structure parameters, model training parameters);

[0195] The position of the following sparrow is updated according to the formula for updating the position of the introducer, so as to move closer to the high-quality solution;

[0196] The position of the early warning sparrow is updated based on the behavior formula of the reconnaissance and early warning system to avoid getting trapped in local optima.

[0197] The fitness values ​​of all sparrows are recalculated after each iteration;

[0198] The sparrow position with the highest fitness that reaches the maximum number of iterations is taken as the optimal combination of (network structure parameters, model training parameters).

[0199] This invention cleverly balances global search and local exploitation capabilities through the SSA algorithm. Its watchdog mechanism effectively avoids getting trapped in local optima, which is difficult to achieve with traditional optimization methods. The resulting hyperparameters (such as the complex three-layer neuron structure in the DNN stress model) are often difficult to design manually, fully tapping the potential performance of the machine learning model.

[0200] This invention automates the entire process from model training and hyperparameter optimization to performance comparison. By setting the population and number of iterations of the SSA (Self-Assessing and Optimizing) model, parallel optimization and evaluation of three machine learning models can be automatically completed, significantly reducing manual intervention and computational time costs. This makes it possible to quickly select the optimal prediction model for the permafrost thickness prediction task, thus improving analysis efficiency.

[0201] Example: This invention establishes an optimal machine learning model to learn the variation patterns of permafrost thickness data, enabling predictive analysis of permafrost thickness, as detailed below:

[0202] Permafrost refers to various bedrock and loose sediments containing ice at or below 0°C, commonly found in high-altitude and cold regions. Based on the freezing time, permafrost is classified into perennial permafrost (several to tens of thousands of years or more), seasonal permafrost (half a month to several months), and transient permafrost (several hours, several days to half a month). The formation environment of permafrost is unique, and its development is influenced by natural geographical environment, geological environment, and human activities. Factors affecting permafrost development include external and internal factors. External factors include climate change (temperature, precipitation, radiation balance), topography (altitude, slope aspect), surface hydrogeological conditions, Quaternary tectonic movements, and human activities (mining activities, construction). Internal factors include soil and rock properties, water content, ice content, and annual average ground temperature.

[0203] To determine the depth of the top boundary of the permafrost layer, the thickness of the active layer near the surface that freezes in winter and thaws in summer must first be determined. By recording ground temperature data for the entire year of 2021, it can be known that... Figure 2 As shown, surface temperature varies considerably with the seasons, dropping below 0℃ at the beginning and end of the year, reaching a maximum of 7.4℃ in summer, with an annual average temperature of -2.021℃. As the depth of the strata increases, the overall stratum temperature rises, reaching nearly 20℃ at a depth of 600m.

[0204] The temperature variation with depth throughout the year is as follows: Figure 3 As shown, the temperature of the strata at depths of 0-10m varies considerably, exhibiting a clear seasonality. The temperature variation gradually decreases with increasing depth; at 10m, the temperature remains below 0℃ throughout the year, thus this 0-10m stratum is classified as seasonally frozen soil. The strata at depths of 10-100m maintain a year-round temperature below 0℃, classifying them as permafrost. The temperature remains stable throughout the year, gradually increasing with depth, reaching near 0℃ at 100m. When the strata depth exceeds 110m, the temperature is above 0℃, meaning the strata below 110m are not considered frozen soil. The bottom of the permafrost zone is primarily located between 100-110m underground.

[0205] Besides temperature, other external factors also significantly impact permafrost. Therefore, data on surface temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content in 2021 were collected. These data were then used to construct a scatter plot matrix (e.g.,...). Figure 4 (as shown) and correlation heatmaps (such as) Figure 5 As shown in the figure, the thickness of the permafrost layer is inversely proportional to time, rainfall, soil temperature, and soil moisture, and directly proportional to sunshine duration, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content. The correlations between these parameters and the permafrost layer thickness are relatively low, with soil moisture showing the strongest correlation. Among the many parameters, soil temperature and soil moisture exhibit the highest correlation, reaching 0.9.

[0206] First, the data is divided into training, testing, and prediction sets in a ratio of 0.8, 0.1, and 0.1, respectively. The training set is used to train the machine learning model, the testing set is used to calculate the fit index of the SSA model and optimize the model parameters, and the prediction set is used for on-site prediction.

[0207] The SVM, RF, and DNN models are coupled into the SSA optimization algorithm, with a population size of 30 and a maximum number of iterations of 30. For the SVM model, c ∈ [0.01, 30] and gamma ∈ [0.01, 100]; for the RF model, n_estimators ∈ [1, 100] and max_features ∈ [1, 7]; for the DNN model, the learning rate η ∈ [0.001 0.01], the maximum number of iterations Epoch ∈ [10, 100], and the neural network has three hidden layers with the number of neurons num ∈ [1, 100]. The batch size for the DNN model is [1, 100], and the optimization algorithm is Adam.

[0208] The change in the fit index during the SSA optimization of hyperparameters for SVM, RF, and DNN models is as follows: Figure 6 As shown in Figure a, the vertical axis represents the Fitness Value, and the horizontal axis represents the number of iterations. The SVM model's hyperparameters reached their minimum value of 0.07250144849656637 after one iteration, with optimal variables c = 0.7182434927274329 and gamma = 0.4045428527904793. The RF model's hyperparameters underwent two adjustments, reaching a final value of 0.03726805416647596, with optimal variables n_estimators = 4 and max_features = 2. The DNN model's hyperparameters reached their minimum value of 3.078409 × 10⁻⁶ after three adjustments. -5 The optimal learning rate is 0.00621829093, the number of iterations is 98, the batch size is 34, the number of neurons in the first hidden layer is 43, the number of neurons in the second hidden layer is 93, and the number of neurons in the third hidden layer is 98.

[0209] The prediction set data is input into the optimized SVM, RF, and DNN models, namely SSA-SVM, SSA-RF, and SSA-DNN, and the prediction results are as follows. Figure 6 As shown in Figure b, the SSA-DNN model has the best prediction performance, followed by the SSA-RF model, and the SSA-SVM model has the worst performance.

[0210] Furthermore, by analyzing the contribution of the input parameters, it can be concluded that, for example... Figure 7As shown, soil temperature and nitrogen contribution were the highest, both exceeding 30%, while soil moisture and carbon dioxide concentration contributed moderately, exceeding 10%. Rainfall, sunshine duration, and hydrogen sulfide concentration were lower, with hydrogen sulfide contributing the least and making no contribution.

[0211] Table 1 shows the RMSE and R values ​​of the prediction results from the SSA-SVM, SSA-RF, and SSA-DNN models. Among the three machine learning models, the SSA-DNN model has the lowest RMSE, followed by SSA-RF, and then SSA-SVM. The correlation coefficient is lowest for the SSA-SVM method (0.9427), followed by SSA-RF (0.9481), and highest for the SSA-DNN method (0.9769). Considering both the R value and RMSE, the SSA-DNN model is the best.

[0212] Table 1. Model prediction results and RMSE and R of monitoring data for permafrost thickness: Evaluation indicators SSA-SVM SSA-RF SSA-DNN RMSE 0.1910 0.1589 0.1139 R 0.9427 0.9481 0.9769

[0213] Therefore, this invention uses the SSA-DNN model as the optimal prediction model for predicting the thickness of the permafrost zone.

[0214] In summary, the surface temperature in Muli area varies significantly with the seasons, with an annual average temperature of -2.021℃. The surface temperature generally increases with depth, reaching nearly 20℃ at a depth of 600m. The strata from 0 to 10m in Muli area are seasonally frozen, from 10 to 100m are perennially frozen, and the strata below 110m are not frozen. The bottom of the permafrost zone is mainly distributed between 100 and 110m underground. Permafrost thickness is inversely proportional to time, rainfall, soil temperature, and soil moisture, and directly proportional to sunshine duration, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content. The correlation between these parameters and permafrost thickness is relatively low, while soil moisture shows the strongest correlation. Among the models, the SSA-DNN model has the lowest RMSE, followed by SSA-RF, and the SSA-SVM model has the highest. The SSA-SVM method has the lowest correlation coefficient at 0.9427, the SSA-RF method has a correlation coefficient of 0.9481, and the SSA-DNN method has the highest correlation coefficient at 0.9769. Considering both the correlation coefficient R and the RMSE index, the SSA-DNN model is the optimal choice.

[0215] The optimal prediction model formed by the machine learning model and the sparrow search algorithm in this invention can more accurately characterize the complex nonlinear mapping relationship between external factors and the thickness of the permafrost zone. Its prediction results have a higher degree of fit with the actual thickness, a significantly reduced relative standard error (RSEM), and a further improved correlation coefficient (R), making the prediction results more reliable and scientific.

[0216] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for analyzing the evolution of permafrost thickness based on a sparrow search algorithm, characterized in that, Includes the following steps: Based on historical stratigraphic temperature data, the permafrost layer was divided, and the thickness of the permafrost zone was determined. During the recording period of historical stratigraphic temperature data, external factors affecting the thickness of the permafrost zone were collected, and the correlation between recording time, external factors, and permafrost zone thickness was analyzed. An optimal prediction model for the thickness of the permafrost zone based on external factors was constructed by combining machine learning algorithms with the sparrow search algorithm.

2. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 1, characterized in that: Methods for dividing the permafrost layer include: A graph showing the temperature variation with depth was created based on historical stratigraphic temperature data. By analyzing the temperature variation with depth, the seasonally frozen soil layer, the perennial frozen soil layer, and the non-frozen soil layer were identified. Among them, the depths where the temperature of the strata changes significantly across the entire time domain during the recording period, exhibit obvious seasonality, and where the temperature change gradually decreases with increasing depth are defined as seasonal permafrost strata. The depths where the temperature of the strata is below 0℃ throughout the entire recording time, the temperature is stable, and the temperature gradually increases with increasing depth are defined as permafrost strata. Depths where the ground temperature is above 0°C throughout the entire recording period are considered non-permafrost strata.

3. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 2, characterized in that: External factors include: soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content.

4. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 3, characterized in that: The method for constructing the optimal prediction model includes: Three prediction models for predicting the thickness of permafrost based on external factors were constructed using Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively. The parameters of three prediction models were optimized using the sparrow search algorithm; The performance of the three optimized prediction models is evaluated, and the prediction model with the best performance is selected as the optimal prediction model.

5. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 4, characterized in that: The method for constructing the prediction model includes: Soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, and nitrogen content were used as feature inputs for Support Vector Machine (SVM), Random Forest (RF), and Distributed Neural Network (DNN), respectively. The thickness of the permafrost zone was used as the prediction output for SVM, RF, and DNN. Prediction models based on SVM, RF, and DNN were trained to obtain prediction models.

6. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 5, characterized in that: The loss functions of the prediction models based on SVM, RF, and DNN are the mean squared error and mean absolute error between the predicted output and the true value.

7. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 6, characterized in that: The optimization methods for the sparrow search algorithm include: The hyperparameters in the SVM-based prediction model are optimized by using the sparrow search algorithm: the penalty parameter C and the parameter gamma of the RBF kernel function. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are determined. The optimal values ​​of the penalty parameter C and the parameter gamma of the RBF kernel function are then substituted into the SVM-based prediction model to obtain the optimized SVM-based prediction model. The hyperparameters in the RF-based prediction model are optimized using the Sparrow Search algorithm: the number of decision trees (n_estimators), the number of randomly selected features per decision tree (max_features), and the maximum depth of the tree (max_depth). The optimal values ​​of these parameters are then determined and substituted into the RF-based prediction model to obtain the optimized RF-based prediction model. The hyperparameters of a DNN-based prediction model—network structure parameters and model training parameters—are optimized using a sparrow search algorithm. The optimal values ​​of these parameters are determined, and then substituted into the DNN-based prediction model to obtain the optimized model. The network structure parameters include the number and type of intermediate layers, the number of neurons per layer, and the activation function. The model training parameters include the loss function, optimization method, batch size, number of iterations, learning rate, regularization method and coefficients, and initialization method.

8. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 7, characterized in that: The performance evaluation metrics include the degree of fit between the model's predicted values ​​and the true values, the relative standard error (RSEM), and the correlation coefficient (R).

9. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 8, characterized in that: Methods for analyzing the correlation between recording time, external factors, and permafrost thickness include: The correlation between recording time, soil temperature, rainfall, sunshine duration, soil moisture, carbon dioxide concentration, hydrogen sulfide concentration, nitrogen content and frozen soil thickness was analyzed to obtain a data scatter plot matrix and a related heat map. Based on the analysis of the data scatter plot matrix and related heat maps, it was found that the thickness of the frozen soil layer is inversely proportional to the recording time, rainfall, soil temperature and soil moisture, and directly proportional to the sunshine duration, carbon dioxide concentration, hydrogen sulfide concentration and nitrogen content. The thickness of the frozen soil layer has the strongest correlation with soil moisture, while soil temperature has the strongest correlation with soil moisture.

10. The method for analyzing the evolution of permafrost thickness based on the sparrow search algorithm as described in claim 9, characterized in that: The process of the sparrow search algorithm includes: Step 1: Establish a population X consisting of n sparrows. The expression for population X is: ； Where d is the number of hyperparameters to be optimized. Let n be the position of the nth sparrow in dimension d; Step 2: Set fitness value The fitness value represents an individual sparrow's ability to find food. The expression is: ； in, For the fitness function, Let be the fitness value of the nth sparrow. Let be the position vector of the nth sparrow; Step 3: Based on population X and fitness value The location update formula for the discoverer is set as follows: ； in, For the number of iterations, The maximum number of iterations, , They were respectively in the second sequence During the nth iteration, the 1st The sparrow that was the discoverer was in the first The position of the dimension It is a random number in [0,1]. This is the warning value, and its range is [0,1]. The safe value is [0.5, 1], Q is a random number that follows a normal distribution, and L is a 1×d matrix with all elements being 1; Step 4: Based on population X and fitness value The location update formula for discoverers is set as follows: ； in, In the first In the next iteration, the sparrow, as the discoverer, is in the best position. Let A be the worst possible position for the sparrow that discovers the sparrow, and let A be a 1×d matrix where each element is randomly assigned a value of 1 or -1. ; Step 5: Set the number of scout sparrows to 10% to 20% of the total population. Their initial positions are randomly generated within the population. The behavioral expression for scout alerts is: ； in, Let t be the current globally optimal sparrow position in the t-th iteration, β be a control parameter, a random number following a standard normal distribution, K be a uniform random number with a value range of [-1, 1], and ε be a small constant to avoid the denominator being zero; The fitness value of the sparrow acting as a scout. The sparrow in the best position in the whole game fitness value, Sparrow in the worst position globally The fitness value.

Images