Intelligent prediction method of lead ions on soil fracture fractal dimension under dry-wet cycle

Abstract

The invention discloses a method for intelligently predicting the fractal dimension of a soil fracture by lead ions under a dry-wet cycle, and relates to the technical field of prediction of the fractal dimension of the soil fracture. According to the technical scheme, sample data are collected for standardization processing; the sample data is divided into prediction samples and training samples; optimizing BiLSTM, GRU, Xgboost and RVM model parameters by the training sample through a particle swarm optimization algorithm and a sparrow optimization algorithm, and establishing a soil fracture fractal dimension prediction model meeting requirements on the basis of optimal solutions of the particle swarm optimization algorithm and the sparrow optimization algorithm; and the prediction sample is substituted into BiLSTM, GRU, Xgboost and RVM model parameters, an obtained prediction result is compared with an actual value for fractal, and the feasibility of the model is verified. The method has the beneficial effects that the prediction precision and efficiency are effectively improved, the research cost and time are reduced, and soil scientific research and technical innovation are promoted; not only is the development and innovation of soil scientific research promoted, but also powerful technical support is provided for environmental protection and realization of sustainable development targets.

Description

Technical Field

[0001] The present invention relates to the technical field of the intersection of civil engineering and artificial intelligence, specifically to the technical field of soil crack fractal dimension prediction, and in particular to an intelligent prediction method for the fractal dimension of soil cracks by lead ions under dry-wet cycles. Background Art

[0002] In recent years, the problem of heavy metal pollution in mining soils has become increasingly serious worldwide, becoming a major problem that needs to be solved by the world. Heavy metals have many effects on soil, including the physical properties, chemical properties, biological activity and ecosystem of soil. Therefore, the study of the effects of heavy metals on soil properties has become a hot topic in the environmental field in recent years. For example, Za studied the effects of long-term Zn and Cu pollution on water-soluble organic matter and soil biological activity in Spolic Technosols; Huang conducted in-depth research on how soil particle size affects the environmental behavior of heavy metals in soil; Song studied the effects of dry-wet cycles and cadmium pollution on the mechanical properties and organization of red clay. In addition, heavy metal pollution will aggravate the formation and distribution of soil cracks, thereby inducing problems such as the destruction of soil integrity, reduced soil strength and increased soil permeability, posing a serious threat to local engineering construction and long-term sustainable development. Therefore, it is of great significance to study the influence of heavy metals on soil cracks.

[0003] Soil cracks are affected by climate and undergo repeated dry-wet cycles, such as rainfall, rise and fall of groundwater levels, and evaporation of surface water. Rayhani et al. reported that with the increase of plasticity index and clay content, the crack size and permeability of soil samples after dry-wet cycles increased. Lu explored the microstructure under dry-wet cycles and found that the cracks increased significantly after dry-wet cycles. Xu proved that the internal cracks of loess were more developed when the salt content was high after dry-wet cycles. In previous studies, most scholars focused on the impact of dry-wet cycles on crack development, but in heavy metal polluted areas, as dry-wet cycles continue, soil integrity is destroyed, resulting in an increase in the diffusion range and concentration of metal ions, which further affects the development of cracks. Therefore, studying the development law of soil cracks under the coupling of dry-wet cycles and different heavy metal ions can provide a more reliable scientific basis for the management of heavily polluted soils. How to accurately and quickly predict the changing parameters of soil cracks under dry-wet cycles is an important basis for further studying the development of soil cracks. Early studies mainly used soil slices, sand filling and other measurement tools to obtain crack-related parameters, but these methods were inefficient and had poor accuracy. The development of digital imaging provides new ways to obtain soil crack parameters, such as radar method and fiber optic method, but these methods are expensive, and more efficient and economical methods need to be sought to obtain and predict soil crack parameters under dry-wet cycle conditions.

[0004] With the rapid development of computer technology, artificial intelligence algorithms have become the key driving force for promoting technological innovation in the field of soil science research by virtue of their ability to self-learn and improve efficiency, as well as their advantages in reducing costs. For example, Prasad et al. used hybrid intelligent extreme learning machines to predict soil moisture; Araghi predicted soil temperature based on surface air temperature based on wavelet artificial neural network (WNN); Zhang et al. proposed an intelligent method to quickly identify soil particle size distribution using convolutional neural network (CNN) under the framework of deep learning. Therefore, it has become an inevitable trend to use artificial intelligence algorithms to predict the evolution law of soil crack parameters under dry-wet cycle conditions. As an improved version of LSTM (Long Short-Term Memory, LSTM), BiLSTM (Bi-directional Long Short-Term Memory, BiLSTM) not only inherits the core advantage of LSTM in processing sequence data, but also effectively overcomes its limitations in contextual prediction. GRU (Gate Recurrent Unit, GRU) occupies an important position in the prediction model with its fewer parameters and higher efficiency. Xgboost (eXtremeGradient Boosting, Xgboost) has performed well in many machine learning tasks with its high flexibility and fast computing speed. RVM (Relevance Vector Machine, RVM) is known for its simple control parameters and efficient sample fitting capabilities. These BiLSTM, GRU, Xgboost and RVM algorithms have been widely used and verified in many fields. Fractal dimension is an important parameter for studying the evolution of soil cracks. It provides an effective means for quantitative description of crack morphology, evaluation of development degree, quantification of roughness and analysis of crack network connectivity. Therefore, a fractal dimension intelligent prediction model of BiLSTM, GRU, Xgboost and RVM is constructed to provide a new way to study the evolution law of soil crack parameters. However, the parameter setting of BiLSTM, GRU, Xgboost and RVM algorithms often relies on manual attempts, which not only increases subjectivity, but also affects the accuracy and prediction ability of the model. Summary of the invention

[0005] In order to solve the above technical problems existing in the prior art, the present invention provides an intelligent prediction method for the fractal dimension of soil cracks under dry-wet cycles by lead ions, which effectively improves the accuracy and prediction performance of BiLSTM, GRU, Xgboost and RVM models by applying PSO and SSA algorithms to parameter optimization of these models, providing strong support for the realization of efficient and intelligent fractal dimension prediction.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles, the steps are as follows:

[0008] S1, collect sample data for standardization;

[0009] S2, the sample data after standardization is divided into prediction samples and training samples;

[0010] S3. The training samples are optimized for the parameters of BiLSTM, GRU, Xgboost and RVM models through the particle swarm optimization algorithm and the sparrow optimization algorithm, and a prediction model of the fractal dimension of soil cracks that meets the requirements is established based on the optimal solutions of the particle swarm optimization algorithm and the sparrow optimization algorithm;

[0011] S4. Bring the predicted samples into the BiLSTM, GRU, Xgboost and RVM model parameters, compare the predicted results with the actual values, and verify the feasibility of the model.

[0012] Furthermore, the particle swarm optimization algorithm steps are as follows:

[0013] T1, initialize the position, fitness and speed of the particle swarm;

[0014] T2, determine the optimal position and fitness of the particle swarm;

[0015] T3. When the number of iterations is less than the maximum number of iterations, use formula (1) to update the particle's velocity and position:

[0016]

[0017] Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors used to adjust the optimal weights, and r1 and r2 are random numbers between [0,1];

[0018] T4. Calculate the fitness of the next generation population;

[0019] T5. Update the optimal position and fitness of the particle swarm.

[0020] Furthermore, the steps of the sparrow optimization algorithm are as follows:

[0021] U1, initialize the position and fitness of the sparrow population;

[0022] U2, sort the fitness values ​​and determine the first generation of discoverers, followers and scouts;

[0023] U3. When the number of iterations is less than the maximum number of iterations, for each discoverer, i from 1 to DN, a random number R2 is generated and the discoverer position is updated using formula (2):

[0024]

[0025] Where: DN is the number of discoverers, t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1;

[0026] U4. For each follower, i from 1 to FN, update the follower position using formula (3):

[0027]

[0028] Where: FN is the number of followers, X B The finder obtains the optimal position, X w Represents the global worst value; A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food;

[0029] U5. For each detector, i from 1 to VN, update the detector position using formula (4):

[0030]

[0031] Where: VN is the number of detectors, X gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, ε is a constant to avoid the denominator being 0, f i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively;

[0032] U6. Update the optimal fitness and position of the sparrow population.

[0033] Furthermore, in step S1, the normalization process is performed by formula (5):

[0034]

[0035] Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, and s is the sample standard deviation.

[0036] Furthermore, the following steps are included: the mean square error of the prediction result is analyzed by formula (6):

[0037]

[0038] Where MSE stands for mean square error, y 0,i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

[0039] Furthermore, the following steps are included: Analyze the root mean square error of the prediction result by formula (7):

[0040]

[0041] Where RMSE represents the root mean square error, y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

[0042] Furthermore, the following steps are included: the mean absolute error of the prediction results is analyzed by formula (8):

[0043]

[0044] Where MAE stands for mean absolute error, y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

[0045] Furthermore, the following steps are included: the mean absolute percentage error of the prediction results is analyzed by formula (9):

[0046]

[0047] Where MAPE stands for mean absolute percentage error, y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

[0048] Furthermore, in step S1, sample data collection is performed through the following steps:

[0049] S1.1. Select silty clay, red clay and expansive soil 5 to 7 meters below the ground at the construction site;

[0050] S1.2, Sample preparation: The soil samples were air-dried and crushed, and then passed through a 2mm sieve. The sieved soil samples were placed in a 105℃ oven and dried to constant weight; then a lead ion solution was prepared and sprayed evenly into the soil sample for thorough stirring. The lead-contaminated soil samples were prepared with an initial moisture content of 20%, and the lead ion contents were 0%, 0.03%, 0.06%, 0.09% and 0.12% of the dry soil mass, respectively; contaminated soil samples with a dry density of 1.45g / cm3, a diameter of 61.8mm and a height of 20mm were prepared according to the static method; the vacuum saturation method was used to humidify the sample for 12h, and then the sample was dehumidified in a 45℃ constant temperature box for 24h, which was one dry-wet cycle;

[0051] S1.3, Digital Image Processing: First, the collected sample image is precisely cropped to ensure that the edge of the cropped image is perfectly aligned with the inner wall of the ring knife; then, the image is imported using software and grayscale conversion is performed; advanced noise reduction algorithms are implemented on the grayscale image to improve image quality, and crack recognition technology is used to accurately extract crack features; finally, key parameters such as crack area and fractal dimension are calculated using image analysis technology to obtain high-precision analysis results.

[0052] Furthermore, in step S1.3, two key indicators are selected: crack area and fractal dimension. The crack area is defined as the projection area of ​​the crack on a two-dimensional plane. The fractal dimension is used to quantify complex geometric structures with self-similar characteristics. The fractal dimension of soil crack patterns is determined by the box dimension method, which is calculated as shown in formula (10):

[0053] n i =A-Dlnε i (10)

[0054] Where: A is a constant; D is the fractal dimension; ε i and N i are the i-th level segmentation size and the corresponding number of self-similar blocks. i and lnε i It shows a linear relationship, and its slope D is the fractal dimension of the crack. The larger the fractal dimension of the crack network, the denser the crack distribution and the more complex the crack structure distribution characteristics.

[0055] Beneficial effects of the present invention:

[0056] Compared with the prior art, the intelligent prediction method of lead ion on soil crack fractal dimension under dry-wet cycle described in the present invention has the following technical characteristics or beneficial effects:

[0057] (1) Improve forecasting accuracy and efficiency

[0058] Application of intelligent prediction model: This paper introduces advanced intelligent algorithms such as BiLSTM, GRU, Xgboost and RVM to construct a prediction model for the effect of lead ions on soil crack fractal dimension under dry-wet cycles. These algorithms can significantly improve the accuracy of predictions by virtue of their powerful self-learning and data processing capabilities. The model parameters are optimized by particle swarm optimization algorithm (PSO) and sparrow optimization algorithm (SSA), which further improves the prediction performance of the model and makes the prediction results more accurate and reliable.

[0059] Standardization and error analysis: Standardization of the collected sample data eliminates the dimensional differences between different data and improves the generalization ability of the model. The prediction results are comprehensively evaluated through error analysis indicators such as mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), ensuring the accuracy and reliability of the prediction results.

[0060] (2) Reduce research costs and time

[0061] Efficient data processing: This invention uses intelligent algorithms to quickly process and analyze large amounts of data. Compared with traditional research methods (such as soil slicing, sand filling and other measurement tools), it significantly improves data processing efficiency and reduces research costs. The optimization algorithm automatically optimizes model parameters, avoiding the tedious process of manual attempts and further shortening the research cycle.

[0062] Reduce experimental resource consumption: The use of intelligent prediction methods can reduce dependence on actual soil samples, reduce the consumption and waste of experimental resources. At the same time, intelligent prediction methods can also provide guidance for experimental design, optimize experimental plans, and improve experimental efficiency.

[0063] (3) Promote soil science research and technological innovation

[0064] Innovative research method: This invention applies advanced intelligent algorithms to the field of soil science research, providing a new approach and method for studying the evolution of soil crack parameters. This innovative research method not only improves the accuracy and efficiency of the research, but also promotes technological innovation and progress in soil science research.

[0065] Promoting interdisciplinary and fusion: The implementation of this invention involves the intersection and fusion of multiple disciplines such as computer science, artificial intelligence, and environmental science, which promotes communication and cooperation between these disciplines. This interdisciplinary research model helps to expand the research horizon and promote the development and innovation of related disciplines.

[0066] In summary, the beneficial effects of the present invention are mainly reflected in improving prediction accuracy and efficiency, reducing research costs and time, promoting soil science research and technological innovation, etc. These beneficial effects not only help promote the development and innovation of soil science research, but also provide strong technical support for the realization of environmental protection and sustainable development goals. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0068] Figure 1 This is the first post-saturation test group diagram;

[0069] Figure 2 It is a picture of the slit observation photography device;

[0070] Figure 3 is a processing flow chart of the crack image;

[0071] Figure 4 It is a curve diagram showing the change of crack area with dry-wet cycle in silty clay, red clay and expansive soil at different lead ion contents;

[0072] Figure 5 It is the curve diagram of the change of crack fractal dimension with dry-wet cycle in silty clay, red clay and expansive soil at different lead ion contents;

[0073] Figure 6 It is the dry-wet cycle change curve of crack area of ​​silty clay, red clay and expansive soil under the same lead ion content;

[0074] Figure 7 The dry-wet cycle variation curve of the fractal dimension of cracks in silty clay, red clay and expansive soil under the same lead ion content;

[0075] Figure 8 This is the BiLSTM schematic diagram;

[0076] Fig. 9 This is the GRU schematic diagram;

[0077] Fig.10This is the Xgboost schematic diagram;

[0078] Fig.11 This is the RVM schematic;

[0079] Fig.12 It is a model flow chart;

[0080] Fig.13 It is the predicted value of three kinds of soils (a) silty clay (b) red clay (c) expansive soil;

[0081] Fig.14 It is the evaluation index diagram of silty clay (a) MSE (b) RMSE (c) MAE (d) MAPE;

[0082] Fig.15 It is the evaluation index diagram of red clay (a) MSE (b) RMSE (c) MAE (d) MAPE;

[0083] Fig.16 It is the evaluation index diagram of expansive soil (a) MSE (b) RMSE (c) MAE (d) MAPE;

[0084] Fig.17 This is a comparison chart of the effects of dry-wet cycles with different lead ion contents on the development of cracks in silty clay;

[0085] Fig.18 This is a comparison chart of the effects of dry-wet cycles with different lead ion contents on the development of red clay cracks;

[0086] Fig.19 This is a comparison chart of the effects of dry-wet cycles with different lead ion contents on the development of cracks in expansive soil. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Figure 1-19 The intelligent prediction method of the fractal dimension of soil cracks caused by lead ions under dry-wet cycles is further explained, and the technical solutions in the embodiments of the present application are clearly and completely described; obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments, and all other embodiments obtained by ordinary technicians in this field without creative work based on the embodiments in the present application are within the scope of protection of the present application.

[0088] Understanding the changes in soil cracks under dry-wet cycles and heavy metal pollution is crucial to the formulation and implementation of soil management strategies. Therefore, the present invention studies the crack development law of soils contaminated with different degrees of lead ions under the action of dry-wet cycles. For silty clay, red clay and expansive soil samples, different lead ion concentrations were polluted and dry-wet cycle tests were carried out. By using image processing technology, parameters such as crack area and fractal dimension were accurately quantitatively analyzed. The results show that the presence of lead ions has a significant promoting effect on the development of crack area in silty clay, red clay and expansive soil. However, this promoting effect is not unlimited, but there is a specific concentration threshold. Specifically, the lead ion content threshold of silty clay is at a medium level, that is, the lead ion to soil particle mass ratio is 0.09%, while for red clay and expansive soil, the lead ion content thresholds are at a lower level, 0.06% and 0.03%, respectively. At the same time, the fracture fractal dimension prediction models of bidirectional long short-term memory network (BiLSTM), gated recurrent unit (GRU), extreme gradient boosting (Xgboost) and relevance vector machine regression (RVM) were constructed. Among them, the RVM model showed excellent performance in the prediction of fracture fractal dimension. For example, in the prediction of silty clay samples, the RVM model achieved significant reductions in key evaluation indicators such as mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) compared with BiLSTM, GRU and Xgboost models. The most significant reduction indicator was RMSE, which decreased by 56.36%, 37.83% and 61.61% respectively. In order to further improve the prediction accuracy, the sparrow search algorithm (SSA) and particle swarm optimization algorithm (PSO) were introduced to fine-tune the four model parameters. Among the optimized algorithms, the RVM model optimized by the SSA algorithm performed best, that is, the MSE, RMSE and MAPE indicators were reduced by 3.55%, 6.98% and 16.79% respectively compared with the unoptimized RVM model, further verifying the effectiveness of the optimization algorithm in improving the prediction performance of the RVM model. Therefore, the present invention provides an efficient tool for monitoring soil pollution and assessment, which is of great significance to promoting the sustainable use of land.

[0089] Particle Swarm Optimization (PSO) and Sparrow Search Algorithm (SSA) have shown obvious advantages in solving complex optimization problems due to their excellent global optimization capabilities, fast convergence and stability. By applying PSO and SSA algorithms to the parameter optimization of BiLSTM, GRU, Xgboost and RVM models, the accuracy and prediction performance of these models are effectively improved. This provides strong support for the realization of efficient and intelligent fractal dimension prediction.

[0090] The present invention prepares silty clay, red clay and expansive soil samples with different lead ion contents (0%, 0.03%, 0.06%, 0.09%, 0.12%), conducts dry-wet cycle tests, and obtains soil crack parameter data of soil samples in each cycle through digital image analysis and processing technology. Based on the results of the dry-wet cycle test, the change law of crack area and fractal dimension due to soil type and different lead ion contents is systematically analyzed. In order to efficiently and economically obtain the fractal dimension of soil, a crack fractal dimension intelligent prediction model of BiLSTM, GRU, Xgboost and RVM is proposed to achieve high-precision prediction of fractal dimension. In addition, PSO and SSA algorithms are introduced to optimize the model parameters, further enhance the generalization and computational efficiency of the model, and provide an innovative method for obtaining soil crack parameters.

[0091] Example 1

[0092] This embodiment provides a specific test method process.

[0093] (1) Test materials

[0094] The silty clay, red clay, and expansive soil used in this experiment come from 5 to 7 meters underground at the construction site and are not contaminated by heavy metals. The mineral components of silty clay include quartz (94.97%), turbidite (2.46%), and montmorillonite (2.57%); the mineral components of red clay include quartz (80.54%), turbidite (15.05%), montmorillonite (2.99%), and kaolinite (1.43%); the mineral components of expansive soil include quartz (67.13%), montmorillonite (2.6%), and calcite (30.27%). The basic physical properties of the three soils are shown in Table 1. The pollution source used in this experiment is lead nitrate Pb(NO3)2 (analytical purity), which is white crystals, easily soluble in water, with a melting point of 470°C and a density of 4.53g / cm 3 .Its technical components are shown in Table 2.

[0095] Table 1 Basic physical properties of three soils

[0096]

[0097] Table 2 Lead nitrate (Pb(NO3)2) (analytical concentration)

[0098]

[0099] (2) Sample preparation

[0100] The soil samples were air-dried and crushed, then passed through a 2 mm sieve and dried in a 105 ° C oven to constant weight. A lead ion solution was then prepared and sprayed evenly into the soil sample for thorough stirring. The initial moisture content of the lead-contaminated soil samples was 20%, and the lead ion content was 0%, 0.03%, 0.06%, 0.09% and 0.12% of the dry soil mass, respectively. A 1.45 g / cm 3 The contaminated soil sample with a diameter of 61.8 mm and a height of 20 mm was humidified by vacuum saturation method for 12 h, and then the sample was dehumidified in a constant temperature box (45°C) for 24 h, which is one dry-wet cycle. Figure 1 shown.

[0101] During the dry-wet cycle, the sample is weighed and the mass is recorded for each dehumidification process and saturation process. Then the sample is placed in a photo box, the distance between the camera and the sample is adjusted, and the appropriate focal length is selected to obtain a sample photo of each cycle process, such as Figure 2 Each soil was subjected to 21 cycles at different lead ion concentrations.

[0102] (3) Digital image processing

[0103] In recent years, with the development of computer science, digital image processing technology has been widely used in the quantitative analysis of crack network morphology. First, the collected sample image is accurately cropped to ensure that the edge of the cropped image is perfectly aligned with the inner wall of the ring knife. Subsequently, the image is imported using software and grayscale conversion is performed. On this basis, advanced noise reduction algorithms are implemented on the grayscale image to improve image quality, and crack recognition technology is used to accurately extract crack features. Finally, key parameters such as crack area and fractal dimension are calculated using image analysis technology to obtain high-precision analysis results. The process is as follows: Figure 3 shown.

[0104] In order to accurately quantify the crack development characteristics of soil cracks under different lead ion concentration conditions, two key indicators were selected: crack area and fractal dimension. The crack area is defined as the projected area of ​​the crack on a two-dimensional plane. It is an important parameter for evaluating the degree of crack development. The increase in its value directly reflects the intensification of crack development. Fractal dimension, as a basic concept in fractal geometry, provides a powerful tool for quantifying complex geometric structures with self-similar characteristics. Lu et al. used fractal theory to conduct an in-depth analysis of the morphological characteristics of soil cracks, using fractal dimension as an indicator to quantify the complexity of crack morphology. The increase in fractal dimension indicates an increase in the complexity of the crack structure. At present, the box dimension method has been widely recognized as a standard method for determining the fractal dimension of soil crack patterns. The calculation of this method is as shown in formula (1):

[0105] ni =A-Dlnε i (1)

[0106] Where: A is a constant; D is the fractal dimension; ε i and N i are the i-th level segmentation size and the corresponding number of self-similar blocks. i and lnε i It shows a linear relationship, and its slope D is the fractal dimension of the crack. The larger the fractal dimension of the crack network, the denser the crack distribution and the more complex the crack structure distribution characteristics.

[0107] Example 2

[0108] This example provides analysis of test results.

[0109] (1) Description of specimen crack development

[0110] Fig.17 / 18 / 19 shows the crack development of silty clay, red clay, and expansive soil samples under drying conditions of 0, 5, 10, 15, and 20 dry-wet cycles at different lead ion contents. It can be found that in the absence of dry-wet cycles (N=0), the surface of different soil samples is flat under different lead ion concentrations, and the soil particles are connected to each other; after 5 dry-wet cycles, all three types of soil samples have obvious cracks. After 10, 15, and 20 cycles, silty clay, red clay, and expansive soil continue to deepen and widen along the initial cracks, and the number of cracks continues to increase. In addition, when the soil particles on one side of the expansive soil are severely lost, cracks are also found on the other side, indicating that the cracks have penetrated the soil sample. During the process of dry-wet alternating cycles, white particles appear on the surface of silty clay and red clay samples containing lead ions in the drying stage. The white particles are Pb(NO3)2 crystals. And with the increase of lead ion content, the number of precipitated white particles increases. This is mainly because the soil sample undergoes expansion and contraction during the dry-wet cycle, which leads to changes in internal stress, and then forms cracks that increase the permeability of the soil sample, making the lead ions originally adsorbed by the soil particles more easily migrate and precipitate with water.

[0111] Different lead ion contents have different effects on the development of cracks in silty clay, red clay and expansive soil. (I) In the fifth cycle of silty clay, no significant crack formation was observed in the sample not contaminated by lead ions; when lead ions were added, obvious crack formation was found, indicating that lead ions promoted the development of cracks in silty clay. Because the double electrical layer structure of silty clay is stable when it is not contaminated by lead ions, no obvious crack formation was observed. When lead ions were added, due to their large hydration radius and charge density, they would generate a stronger attraction with the negative charge on the surface of clay particles, thereby compressing the diffusion layer of the double electrical layer, reducing the repulsive force between clay particles, making it easier for clay particles to approach each other, thereby promoting the formation of cracks. When the lead ion content was low (0.03% and 0.06%), the cracks mainly developed at the edges; when the lead ion content increased by 0.09%, the cracks in the sample began to expand from the center to the edge, causing the sample to split into four independent block structures. When the lead ion content continued to increase to a higher level (0.12%), the area of ​​crack formation decreased compared with the medium lead ion content (0.09%). This shows that the lead ion content of 0.09% is the critical point for promoting the development of crack area. After exceeding this concentration, the promoting effect of lead ions on the growth of crack area began to decrease. (II) In the fifth cycle of red clay, no cracks were generated in the middle of the sample that was not contaminated by lead ions, and its cracks mainly developed at the edges; when lead ions were added, the cracks developed from the middle to the edges. When the lead ion content was low (0.03% and 0.06%), tiny cracks were generated in the middle; when the content was medium (0.09%), deep cracks appeared in the middle of the sample. When the content was high (0.12%), the development of cracks was consistent with that of silty clay, that is, compared with the medium lead ion content (0.09%), the area of ​​crack formation was reduced. The crack development law of expansive soil is different from that of silty clay and red clay. Cracks will be generated in the middle of expansive soil samples that are not contaminated by lead ions. This is because the calcite in the expansive soil is easily dissolved and precipitated in the dry-wet cycle. When the water in the soil evaporates, the calcite will dissolve and the soil volume will decrease; and when the soil absorbs water again, the calcite will reprecipitate and the soil volume will increase. This repeated change in volume will cause changes in the stress distribution inside the soil, resulting in cracks developing from the middle. And regardless of whether lead ions are added, cracks are still generated from the middle, indicating that the lead ion concentration has little effect on the development of cracks in expansive soil.

[0112] (2) Influence of different factors on crack indicators

[0113] 2.1 Lead ion concentration

[0114] Figure 4 The curves showing the change of crack area with dry-wet cycles in silty clay, red clay and expansive soil at different lead ion contents. Figure 5The fractal dimension of cracks in silty clay, red clay and expansive soil under different lead ion contents varies with dry-wet cycles. In order to fully demonstrate the variation of fractal dimension with the number of cycles, the adjacent average method is used to smooth the fractal dimension curve ( Figure 5 ).

[0115] (I) Figure 4 In (a), when the number of dry-wet cycles is within the range of 1-18, it is observed that the crack area growth curve of the silty clay sample (0%) that is not contaminated by lead ions is always lower than that of the sample contaminated by lead ions. This phenomenon once again confirms that lead ions have a significant promoting effect on the growth of crack area in silty clay. In particular, in the first four cycles, the medium content (0.09%) of lead ions has the most significant effect on the growth of crack area. Specifically, at the end of the fourth cycle, the crack area of ​​the sample with a lead ion content of 0.09% is 2.81 times, 2.23 times, 1.64 times and 1.72 times that of the samples with a lead ion content of 0%, 0.03%, 0.06% and 0.12%, respectively. These results indicate that the medium level (0.09%) of lead ions is the critical content that promotes the crack area of ​​silty clay. When the lead ion content exceeds this threshold, its promoting effect on the growth of crack area will begin to slow down. Figure 5 In (a), for the silty clay sample that is not contaminated by lead ions, it can be observed that its fractal dimension shows an overall increasing trend with the increasing number of dry-wet cycles. Relatively speaking, when the lead ion content in the sample rises to 0.03%, the fractal dimension shows a change pattern of first decreasing, then increasing, and finally tending to be stable. When the lead ion content is further increased to 0.06% and 0.09%, the change of the fractal dimension is characterized by an initial increase, followed by a decrease, and finally gradually tending to a stable state. For the silty clay sample with a lead ion content of up to 0.12%, the fractal dimension shows a trend of first increasing and then decreasing.

[0116] (II) Figure 4In the data shown in (b), in the first four cycles, the crack area of ​​the red clay samples increased significantly, especially the samples contaminated by lead ions, whose crack area growth rate was significantly higher than that of the uncontaminated samples. That is, at the end of the fourth cycle, the crack areas of the samples with lead ion content of 0.03%, 0.06%, 0.09% and 0.12% reached 2.39 times, 6.75 times, 5.19 times and 2.20 times the crack areas of the samples not contaminated by lead ions, respectively. These data show that when the lead ion content reaches 0.06%, the effect of increasing the crack area is most significant. However, as the lead ion content increases further, its promoting effect on the growth of the crack area shows a decreasing trend. This phenomenon shows that the lead ion content of 0.06% constitutes a critical threshold, under which lead ions play a significant catalytic role in the expansion of the red clay crack area. When the lead ion concentration exceeds this threshold, the effect of promoting the development of the crack area will begin to weaken. In cycles 1-21, the crack area growth curves of red clay samples with lead ion content of 0.03% and 0.06% were always above the curves of samples not contaminated by lead ions, indicating that during the dry-wet cycle, lead ions continued to promote the growth of crack area in red clay. Figure 5 In (b), during the 2nd to 18th cycles, the fractal dimensions of the red clay samples with lead ion contents of 0.06% and 0.09% were higher than the fractal dimensions of the samples not contaminated by lead ions, indicating that at this lead ion content, the crack morphology of the red clay tends to evolve in a more complex trajectory.

[0117] (III) Figure 4 In (c), it is observed that the crack area of ​​the expansive soil sample shows an increasing trend in the first four cycles. It is worth noting that the crack area curve of the sample contaminated with a lead ion content of 0.03% is always above the curve of the uncontaminated sample. This phenomenon reveals that at this specific content, the presence of lead ions significantly promotes the development of the crack area. However, when the lead ion content is increased to 0.06% and 0.09%, its crack area curve is below the crack area curve of the uncontaminated sample, indicating that at this level, the growth of the crack area is inhibited. In particular, when the lead ion content reaches 0.09%, the crack area is the smallest. This is because in expansive soil, at a low content (0.03%), the free expansion rate of the sample will be increased, thereby promoting the development of the crack area. As the lead ion content increases, the free expansion rate of the expansive soil decreases, thereby inhibiting the development of the crack area. In the first 12 cycles, the crack area of ​​the expansive soil develops slowly. After 12 cycles of development, its crack area first increases rapidly and then fluctuates. Figure 5(c) The fractal dimension of the cracks in the expansive soil increases as the number of cycles increases. In the first three cycles, the fractal dimension of the expansive soil sample that was not contaminated by lead ions showed an upward trend, while the fractal dimension curve of the sample contaminated by lead ions showed a downward trend, indicating that in the first three cycles, the presence of lead ions caused the fractal dimension to decline. This is because in the first three cycles, the presence of lead ions affects the surface charge of the sample particles, thereby changing the interaction between the particles, resulting in the rearrangement and distribution of the particles. This rearrangement affects the pore structure of the sample, resulting in a decrease in the fractal dimension. After 17 cycles, it was found that the fractal dimension curve of the sample contaminated by lead ions was below the uncontaminated curve, revealing that after 17 cycles, the lead ion concentration has an inhibitory effect on the fractal dimension.

[0118] 2.2 Soil Type

[0119] Figure 6 The crack area of ​​silty clay, red clay and expansive soil changes with dry-wet cycles under the same lead ion content. (I) Figure 6It can be found that in the first three cycles, the curve of the crack area of ​​the expansive soil is always above the curve of the crack area of ​​the silty clay and red clay, indicating that the crack area of ​​the expansive soil expands faster than that of the silty clay and red clay. For example, in the first three cycles, when the lead ion content was 0%, 0.03% and 0.12%, the crack area of ​​the expansive soil was 2.63 times, 1.21 times and 1.75 times that of the silty clay, and 5.31 times, 3.33 times and 3.69 times that of the red clay. This is because calcite (30.27%) and kaolinite (2.6%) account for a large proportion in the expansive soil, montmorillonite has high expansibility and ion exchange capacity, and the presence of calcite can provide additional cation exchange points, which enables faster adsorption of lead ions, resulting in double layer compression, thereby reducing the repulsive force between particles, and thus the crack area grows rapidly. Moreover, after 14 dry-wet cycles, the crack area of ​​expansive soil increased significantly, exceeding that of silty clay and red clay. Silty clay and red clay contain a higher proportion of quartz. The high chemical stability of this mineral helps the soil to maintain a stable microstructure of silty clay and red clay during dry-wet cycles. It is not easy to produce significant changes in the crack area in the late cycle, so the crack area of ​​silty clay and red clay changes less in the late cycle. In contrast, montmorillonite and calcite account for a large proportion in expansive soil. The water absorption and water loss shrinkage characteristics of montmorillonite directly promote the formation of cracks, while the dissolution-precipitation behavior of calcite in dry-wet cycles indirectly promotes crack expansion by changing the pore structure. The synergistic effect of the two leads to a significant increase in the crack area of ​​expansive soil. In addition, it can be observed that in the early stage, the crack area of ​​silty clay is generally higher than that of red clay, but in the later stage, the crack area of ​​red clay generally exceeds that of silty clay. The mineral composition of silty clay is mainly quartz, accounting for 94.97%, and there are also small amounts of lauric zeolite (2.46%) and montmorillonite (2.57%). Quartz is a mineral with high hardness and good stability. In the early stage of the cycle, the silty clay sample maintains structural stability when drying, reducing the water retention capacity, so it is easier to form cracks in the early stage of the cycle. The lauric zeolite (15.05%), montmorillonite (2.99%) and kaolinite (1.42%) in the red clay will produce water absorption expansion and water loss shrinkage. With the accumulation of cycles, this expansion and contraction will weaken the bonding force between soil particles, thereby destroying the soil structure and increasing the crack area.

[0120] Figure 7The fractal dimension curves of silty clay, red clay and expansive soil with dry-wet cycles under the same lead ion content are shown. (I) Under the condition of no lead ion contamination (0%), the fractal dimensions of silty clay, red clay and expansive soil all show an increasing trend with the increase of dry-wet cycles, which reflects that the complexity of the soil crack structure increases with the progress of the cycle. However, with the accumulation of the number of cycles, the fractal dimension changes of different samples begin to differ. Especially after the completion of the 4th cycle, the fractal dimension of expansive soil is significantly higher than that of silty clay and red clay. By the 21st cycle, the fractal dimension of expansive soil increased by 5% and 4% compared with silty clay and red clay, respectively. (II) Under the condition of 0.03% lead ion content, silty clay showed a higher fractal dimension than red clay and expansive soil in the first 10 dry-wet cycles. However, this trend changed after the number of cycles exceeded 10, when the fractal dimensions of expansive soil and red clay surpassed those of silty clay. (III) Under the condition of 0.06% lead ion content, the fractal dimensions of red clay and expansive soil showed a continuous growth trend, while the fractal dimension of silty clay was relatively stable. After 4 dry-wet cycles, the fractal dimension of red clay significantly surpassed that of silty clay and expansive soil. With the accumulation of cycles, by the 21st cycle, the fractal dimension of expansive soil finally surpassed that of red clay, indicating that the complexity of its crack development increased during the cycle. (IV) When the lead ion content was increased to 0.09%, the fractal dimension of red clay surpassed that of silty clay and expansive soil after the 4th dry-wet cycle. Furthermore, at the end of 21 cycles, the fractal dimension of red clay increased by 8% and 5% compared with silty clay and expansive soil, respectively. This phenomenon shows that under the action of lead ions, the complexity of the crack structure of red clay increased significantly after multiple dry-wet cycles compared with silty clay and expansive soil. (V) When the lead ion content was 0.12%, after 8 dry-wet cycles, the fractal dimension of expansive soil was higher than that of red clay and silty clay. This phenomenon indicates that at this lead ion level, the complexity of the crack network of expansive soil increased significantly in the later stages of dry-wet cycles, indicating that the crack development trend of expansive soil is more complicated.

[0121] Example 3

[0122] This embodiment provides a specific description of the construction of an intelligent prediction model for soil crack fractal dimension.

[0123] Fractal dimension, as a key indicator to quantify the complexity of fracture systems, can accurately describe the self-similarity and scale invariance characteristics of fracture networks. In-depth analysis of the dynamic changes of fractal dimension is crucial to revealing the evolutionary patterns of fractures under diverse environmental conditions, and thus provides a scientific basis for understanding the internal mechanism of fracture development and its evolution law. Despite this, traditional fracture fractal dimension measurement techniques often introduce significant random errors due to the subjectivity of human operation. In contrast, artificial intelligence algorithms significantly enhance the accuracy and stability of prediction results by virtue of their ability to identify complex patterns from large data sets. Therefore, using artificial intelligence algorithms to predict the fractal dimension of soil fractures can not only effectively improve the accuracy and efficiency of prediction work, but also deepen the understanding of fracture complexity. This has significant application value in deepening the understanding of fracture development mechanisms, optimizing engineering design schemes, and improving the safety of engineering structures.

[0124] (1) Basic principles

[0125] 1.1BiLSM

[0126] BiLSTM (Bi-directional Long Short-Term Memory, BiLSTM) is composed of two LSTM units, which process the forward and reverse sequences of data respectively. Data first enters the network through the input layer and is then processed by the forward and reverse LSTM units; then, the outputs of the two directional LSTM units are merged to generate the final output. In BiLSTM, x t represents the input at time point t, and h t Represents the network output at time point t. This structure enables BiLSTM to consider context information at the same time, thereby improving the model's ability to understand sequence data. Figure 8 As shown, the architecture of BiLSTM allows it to effectively integrate information from both directions to generate a more comprehensive output.

[0127] 1.2GRU

[0128] GRU (Gated Recurrent Unit, GRU) is an advanced recurrent neural network that introduces a gating mechanism based on the traditional RNN, which enables it to effectively process long sequence data while alleviating the problem of gradient disappearance. The core of GRU is two key gating units: update gate and reset gate. The update gate is responsible for deciding which information to keep and which information to discard; while the reset gate determines whether to ignore the previous memory. Fig. 9 Shows the basic structure of GRU, where x t represents the input at different time points; h t-1 and ht Represents the hidden state at the corresponding time point; Gr represents the reset gate value, σ represents the sigmoid activation function, and Gu represents the update gate value. Represents the network hidden layer output.

[0129] 1.3Xgboost

[0130] Xgboost (eXtreme Gradient Boosting, Xgboost) is an efficient machine learning algorithm based on gradient boosting. It optimizes GBDT, introduces the second-order Taylor expansion to deal with the loss function, and enhances the stability and expressiveness of the model. Xgboost accelerates the construction of the tree through the greedy algorithm and the quantile approximation algorithm, and uses hyperparameters to strictly control the complexity of the model to effectively prevent overfitting. In addition, it also has the ability to automatically handle missing values, support sparse data and parallel computing, which improves the efficiency and scalability of the algorithm. Its principle is as follows Fig.10 shown.

[0131] 1.4RVM

[0132] RVM (Relevance Vector Machine) is an innovative machine learning algorithm that combines Bayesian statistics and sparse optimization to automatically select "relevant vectors" that are critical to prediction from the data. These vectors play a core role in the model, while the weights of the remaining data points are close to zero, making the model sparse. During the training process, RVM optimizes the weight and precision parameters by maximizing the marginal likelihood function, screens out key vectors, reduces model complexity and improves computational efficiency. In addition, RVM can quantify prediction uncertainty and provide confidence assessment, which is suitable for scenarios that need to deal with uncertainty. Its principle is as follows Fig.11 shown.

[0133] (2) Optimization algorithm

[0134] 2.1 Particle Swarm

[0135] Particle Swarm Optimization (PSO) is an evolutionary computing technology based on swarm intelligence methods. It randomly generates a group of particles in the solution space, each particle represents a solution to a problem. These particles use their own best position and the best position information of the entire group to continuously iterate and adjust their position and speed through equation (2), thereby gradually exploring and approaching the optimal solution. Due to its easy-to-set parameters, efficient search capabilities and fast convergence, PSO has been widely adopted in many fields such as pattern recognition and parameter optimization. Its pseudo code is shown in Table 3

[0136]

[0137] Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors, which are often used to adjust the optimal weights, r1 and r2 are random numbers between [0,1]. The code running steps are shown in Table 3.

[0138] Table 3 Pseudo code of particle swarm algorithm

[0139]

[0140] 2.2 Sparrow Optimization Algorithm

[0141] Sparrow Search Algorithm (SSA) is an optimization algorithm that simulates the behavior of sparrows foraging and escaping predators. It has attracted attention for its simplicity, efficiency and fast convergence. In this algorithm, the sparrow population is divided into three roles according to a specific ratio: finders, followers and scouts, each of which undertakes different tasks to achieve the optimization goal. The finder is responsible for finding food and guiding the population, the follower forages according to the information of the finder, and the scout is responsible for monitoring the surrounding environment and warning of potential dangers. The finder, follower and scout update their positions through equations 3, 4 and 5 respectively. Its pseudo code is shown in Table 4.

[0142]

[0143] Where: t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1. B is the optimal position obtained by the finder, Xw represents the global worst value. A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food. gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, and ε is a constant to avoid the denominator being 0. i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively.

[0144] Table 4 Pseudocode of sparrow optimization algorithm

[0145]

[0146]

[0147] (3) Constructing a fractal dimension prediction model for soil cracks

[0148] The geometric parameters of soil cracks provide a comprehensive description of the cracks, such as the crack area describes the projected area of ​​the cracks in two-dimensional space, the perimeter and length describe the boundaries and one-dimensional dimensions of the cracks, and the inclination and shape factor provide the complexity information of the crack direction and shape. These features are indirectly potentially related to the fractal dimension, and the number of cycles and lead ion content will also affect the fractal dimension. Therefore, the present invention selects the number of cycles, lead ion concentration, area, inclination, shape factor, perimeter, length, and width of soil cracks as input parameters, and the fractal dimension as output parameter. In the process of dry-wet cycle tests on silty clay, red clay and expansive soil, each sample has undergone 21 dry-wet cycles, each cycle includes a dry-wet alternation stage, and each alternation stage produces 10 groups of data. Based on this, for each type of soil, a total of 210 groups of sample data are obtained. The present invention selects the first 190 groups of crack data of dry-wet cycles as training samples, and the last 20 groups of data as test samples. Prediction models for constructing fractal dimensions for silty clay, red clay and expansive soil are established respectively.

[0149] The present invention combines PSO and SSA optimization algorithms with BiLSTM, GRU, Xgboost and RVM models respectively to adaptively obtain the optimal parameter values, and uses the optimized model to establish a nonlinear mapping relationship between the number of cycles, lead ion concentration, area, inclination, shape factor, perimeter, length, width and fractal dimension of soil cracks, and establish a prediction model for the fractal dimension of soil cracks. The prediction steps of the model are as follows:

[0150] Step 1: Divide the collected sample data set into two parts: training set and test set to prevent the dimensional difference of influencing factors from affecting the results. Normalize the samples. The processing formula is:

[0151]

[0152] Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, and s is the sample standard deviation.

[0153] Step 2: Initialize and set the parameters of each model. Optimize the parameters of BiLSTM, GRU, Xgboost and RVM models through PSO and SSA. Based on the optimal solutions of SSA and PSO algorithms, a prediction model of soil crack fractal dimension that meets the requirements is established.

[0154] Step 3: Bring the test data into the prediction model of soil crack fractal dimension, compare the predicted results with the actual values, and verify the feasibility of the model.

[0155] According to the above modeling steps, the soil crack fractal dimension prediction models of BiLSTM, PSO-BiLSTM, SSA-BiLSTM, GRU, PSO-GRU, SSA-GRU, Xgboost, PSO-Xgboost, SSA-Xgboost, RVM, PSO-RVM, and SSA-RVM are compiled. The model process is as follows Fig.12 shown.

[0156] Example 4

[0157] This embodiment provides a specific description of the prediction result analysis.

[0158] In order to better reflect the overall prediction effect of each model, the mean absolute error, mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) of the prediction results of these 12 models are compared and analyzed. The closer the values ​​of MSE, RMSE, MAE, and MAPE are to 0, the better the prediction effect is. The mathematical formulas are as follows: Fig.13 are the predicted values ​​of fractal dimensions of three soils.

[0159]

[0160] Where y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample. n represents the total number of samples.

[0161] Fig.14The evaluation indicators of (silty clay) more intuitively and clearly compare the MSE, RMSE, MAE, and MAPE of the BiLSM, PSO-BiLSTM, SSA-BiLSTM, GRU, PSO-GRU, SSA-GRU, Xgboost, PSO-Xgboost, SSA-Xgboost, RVM, PSO-RVM, and SSA-RVM models. Compared with the BiLSTM, GRU, and Xgboost models, the RVM model has significant improvements in all indicators: the MSE decreased by 33.94%, 21.15%, and 38.04%, respectively; the RMSE decreased by 56.36%, 37.83%, and 61.61%, respectively; the MAE decreased by 17.05%, 9.74%, and 21.88%, respectively; and the MAPE decreased by 21.97%, 15.50%, and 26.54%, respectively. Further comparison shows that the SSA-RVM model and the PSO-RVM model are 23.58% and 18.30% lower in MAE than the RVM model, respectively; and 16.79% and 11.77% lower in MAPE, respectively. And overall, the MSE, RMSE, and MAE indicators of SSA-RVM are the best among all models. Although the PSO-BiLSTM model achieves the best MAPE indicator, it is worth noting that its MAPE value is only 0.14% higher than that of the SSA-RVM model. This slight difference shows that the SSA-RVM model is not only stable in predicting silty clay samples, but also has a high degree of credibility.

[0162] Fig.15 In the evaluation of red clay fractal dimension prediction, the RVM model achieved significant performance improvements on multiple evaluation indicators compared with the BiLSTM, GRU and XGBoost models. Specifically, the RVM model achieved a reduction of 48.46%, 51.82% and 52.70% in mean square error (MSE); 28.21%, 30.58% and 31.22% in root mean square error (RMSE); 8.16%, 17.55% and 12.78% in mean absolute error (MAE); and 10.69%, 17.83% and 14.56% in mean absolute percentage error (MAPE). In addition, the SSA-RVM and PSO-RVM models showed significant reductions of 55.49% and 58.28% and 54.45% and 58.39% in MAE and MAPE indicators compared with the RVM model. Comprehensively considering various indicators, the PSO-RVM model showed the best performance among all models in terms of MSE, RMSE, MAE and MAPE, which verified the excellent effectiveness of the PSO-RVM model in predicting the fractal dimension of red clay.

[0163] Fig.16 In the evaluation of the prediction of fractal dimension of expansive soil presented, the prediction performance of BiLSTM, GRU, XGBoost and RVM was analyzed in depth. The XGBoost algorithm performed outstandingly in the two key evaluation indicators of MAE and MAPE, standing out with the smallest error value. The RVM algorithm achieved the best results in MSE and RMSE, showing its significant advantage in prediction accuracy. However, when PSO and SSA algorithms were applied to the parameter optimization of these models, the SSA-RVM model not only surpassed BiLSTM, GRU, Xgboost and RVM in all evaluation indicators of MSE, RMSE, MAE and MAPE, but also significantly outperformed the BiLSTM, GRU, and Xgboost models optimized by PSO and SSA. This remarkable result highlights the efficiency and reliability of the SSA-RVM model in the prediction of the analytical dimension of expansive soil, and further confirms its excellent performance in this field.

[0164] In the comprehensive analysis of the fractal dimension prediction of silty clay, red clay, and expansive soil samples, the results show that the RVM model has surpassed the BiLSTM, GRU, and XGBoost models in multiple key evaluation indicators. This finding verifies the efficiency and reliability of the RVM model in the prediction of different soil samples. In addition, the RVM model optimized by SSA and particle PSO has achieved significant improvements in prediction performance. In particular, in the prediction of silty clay and expansive soil samples, the SSA-RVM model achieved the best performance in evaluation indicators such as MSE, RMSE, and MAE. In the prediction of red clay samples, the PSO-RVM model showed excellent performance, surpassing all other models. These results not only confirm the potential of combining the optimization algorithm with the RVM model in the prediction of soil crack parameters, but also highlight its important value in practical applications.

[0165] The present invention conducted a systematic dry-wet cycle test on silty clay, red clay and expansive soil samples under different lead ion content conditions, and applied advanced digital image analysis technology to accurately measure the crack parameters of the samples during each dry-wet alternation. The research results revealed that under the same lead ion content environment, the crack development of the three soil samples showed significant differences. Specifically, in the first three cycles of the cycle and after the 14th cycle, the degree of crack development of the expansive soil significantly exceeded that of the silty clay and red clay. Under the condition of no lead ion addition or a lead ion content of 0.12%, the expansive soil showed a more complex crack structure than the silty clay and red clay in the later stage of the cycle. Under the condition of a lead ion content of 0.09%, the crack structure of the red clay was more complex in the later stage of the cycle. In addition, the presence of lead ions has a significant promoting effect on the expansion of the crack area of ​​silty clay, red clay and expansive soil. It is worth noting that this promoting effect does not grow infinitely, but tends to stabilize after reaching a specific content threshold. Specifically, the lead ion content threshold of silty clay is at a medium level (0.09%). In contrast, the lead ion content thresholds of red clay and expansive soil are relatively low, at 0.03% and 0.06% respectively.

[0166] In order to obtain the fractal dimension in an efficient and economical way, the fractal dimension intelligent prediction models of BiLSTM, GRU, Xgboost and RVM are proposed. At the same time, in order to improve the accuracy of these models, SSA and PSO algorithms are introduced to optimize the parameters of these four models. The results show that compared with BiLSTM, GRU and Xgboost models, the RVM model performs well in predicting the fractal dimension of cracks, and its prediction accuracy is significantly enhanced after parameter optimization. In silty clay, compared with the RVM model, the SSA-RVM model reduced MSE by 6.88%, RMSE by 3.54%, and MAE by 23.59%; in red clay, compared with the RVM model, the PSO-RVM model reduced MSE by 76.84%, RMSE by 51.87%, and MAE by 58.28%; in expansive soil, compared with the SSA-RVM model, the SSA-RVM model reduced MSE by 20.96%, RMSE by 11.05%, and MAE by 32.19%. Through comparative analysis, the potential of combining the optimization algorithm with the RVM model to predict soil crack parameters was verified.

[0167] In view of the influence of lead ions on the development of soil cracks, it is necessary to formulate and implement differentiated management strategies based on the specific characteristics of the soil and the differences in lead content. Effectively control the development of cracks, reduce the risks of damage to soil structural integrity, decrease in soil bearing capacity, and increase in soil permeability caused by them, ensure the stability of local infrastructure construction, and promote the realization of the long-term goal of sustainable development. And future research should focus on expanding the range of soil types and pollutants to verify the universality of the model developed in this invention. In addition, long-term field studies can further understand the applicability of research results and models in the real world and improve their predictive accuracy under different environmental conditions, thereby providing policymakers and environmental management experts with crucial decision-making basis to ensure the sustainable use of soil resources.

[0168] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. An intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles, characterized in that: Here are the steps: S1, collect sample data for standardization; S2, the sample data after standardization is divided into prediction samples and training samples; S3. The training samples are optimized for the parameters of BiLSTM, GRU, Xgboost and RVM models through the particle swarm optimization algorithm and the sparrow optimization algorithm, and a prediction model of the fractal dimension of soil cracks that meets the requirements is established based on the optimal solutions of the particle swarm optimization algorithm and the sparrow optimization algorithm; S4. Bring the predicted samples into the BiLSTM, GRU, Xgboost and RVM model parameters, compare the predicted results with the actual values, and verify the feasibility of the model.

2. The intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles as claimed in claim 1, characterized in that: The particle swarm optimization algorithm steps are as follows: T1, initialize the position, fitness and speed of the particle swarm; T2, determine the optimal position and fitness of the particle swarm; T3. When the number of iterations is less than the maximum number of iterations, use formula (1) to update the particle's velocity and position: Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors used to adjust the optimal weights, and r1 and r2 are random numbers between [0,1]; T4. Calculate the fitness of the next generation population; T5. Update the optimal position and fitness of the particle swarm.

3. The intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles as claimed in claim 1, characterized in that: The steps of the sparrow optimization algorithm are as follows: U1, initialize the position and fitness of the sparrow population; U2, sort the fitness values ​​and determine the first generation of discoverers, followers and scouts; U3. When the number of iterations is less than the maximum number of iterations, for each discoverer, i from 1 to DN, a random number R2 is generated and the discoverer position is updated using formula (2): Where: DN is the number of discoverers, t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1; U4. For each follower, i from 1 to FN, update the follower position using formula (3): Where: FN is the number of followers, X B The finder obtains the optimal position, X w Represents the global worst value; A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food; U5. For each detector, i from 1 to VN, update the detector position using formula (4): Where: VN is the number of detectors, X gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, ε is a constant to avoid the denominator being 0, f i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively; U6. Update the optimal fitness and position of the sparrow population.

4. The intelligent prediction method for the fractal dimension of soil cracks by lead ions under dry-wet cycles as claimed in claim 1, characterized in that: In step S1, normalization is performed using formula (5): Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, and s is the sample standard deviation.

5. The intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles as claimed in claim 1, characterized in that: The following steps are also included: The mean square error of the prediction results is analyzed by formula (6): Where MSE stands for mean square error, y 0,i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

6. The intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles as claimed in claim 1, characterized in that: The following steps are also included: The root mean square error of the prediction results is analyzed by formula (7): Where RMSE represents the root mean square error, y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

7. The intelligent prediction method for lead ion effect on soil crack fractal dimension under dry-wet cycle as claimed in claim 1, characterized in that: The following steps are also included: The mean absolute error of the prediction results is analyzed by formula (8): Where MAE stands for mean absolute error, y 0,i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

8. The intelligent prediction method for lead ion effect on soil crack fractal dimension under dry-wet cycle as claimed in claim 1, characterized in that: The following steps are also included: The mean absolute percentage error of the prediction results is analyzed by formula (9): Where MAPE stands for mean absolute percentage error, y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample, and n represents the total number of samples.

9. The intelligent prediction method for lead ion effect on soil crack fractal dimension under dry-wet cycle as claimed in claim 1, characterized in that: In step S1, sample data collection is performed through the following steps: S1.

1. Select silty clay, red clay and expansive soil 5 to 7 meters below the ground at the construction site; S1.2, Sample preparation: The soil samples were air-dried and crushed, and then passed through a 2mm sieve. The sieved soil samples were placed in a 105℃ oven and dried to constant weight; then a lead ion solution was prepared and sprayed evenly into the soil sample for thorough stirring. The lead-contaminated soil samples were prepared with an initial moisture content of 20%, and the lead ion contents were 0%, 0.03%, 0.06%, 0.09% and 0.12% of the dry soil mass, respectively; contaminated soil samples with a dry density of 1.45g / cm3, a diameter of 61.8mm and a height of 20mm were prepared according to the static method; the vacuum saturation method was used to humidify the sample for 12h, and then the sample was dehumidified in a 45℃ constant temperature box for 24h, which was one dry-wet cycle; S1.3, Digital Image Processing: First, the collected sample image is precisely cropped to ensure that the edge of the cropped image is perfectly aligned with the inner wall of the ring knife; then, the image is imported using software and grayscale conversion is performed; advanced noise reduction algorithms are implemented on the grayscale image to improve image quality, and crack recognition technology is used to accurately extract crack features; finally, key parameters such as crack area and fractal dimension are calculated using image analysis technology to obtain high-precision analysis results.

10. The intelligent prediction method for the fractal dimension of soil cracks caused by lead ions under dry-wet cycles as claimed in claim 9, characterized in that: In step S1.3, two key indicators are selected: crack area and fractal dimension. The crack area is defined as the projected area of ​​the crack on a two-dimensional plane. The fractal dimension is used to quantify complex geometric structures with self-similar characteristics. The fractal dimension of soil crack patterns is determined by the box dimension method, which is calculated as shown in formula (10): <h2 style=";text-align:left;direction:ltr">lnN<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> (A-Dlnε)<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> (10) Where: A is a constant; D is the fractal dimension; ε i and N i are the i-th level segmentation size and the corresponding number of self-similar blocks. i and lnε i It shows a linear relationship, and its slope D is the fractal dimension of the crack. The larger the fractal dimension of the crack network, the denser the crack distribution and the more complex the crack structure distribution characteristics.

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