A method for non-destructive determination of dielectric constant of undisturbed permafrost

Abstract

This invention discloses a non-destructive method for determining the dielectric constant of undisturbed permafrost, belonging to the technical field of permafrost dielectric property measurement. The method includes: experimentally measuring the dielectric constants of single-phase dry soil, pure water, and ice in undisturbed permafrost; non-destructively obtaining the porosity of undisturbed permafrost specimens; establishing calculation formulas for the volume ratios of ice, unfrozen water, and soil with respect to unfrozen water content and porosity, respectively; preparing a series of frozen specimens with different porosity ratios using thawed soil samples from the same source as the undisturbed permafrost; experimentally measuring the unfrozen water content at different sub-zero temperatures, obtaining a bivariate prediction model through quadratic fitting, and outputting the unfrozen water content corresponding to any temperature and porosity, thereby obtaining the volume ratios of ice, unfrozen water, and soil; and obtaining the overall dielectric constant of the same type of permafrost in the same region at a fixed temperature using a three-phase dielectric mixing model or a deep neural network model. This invention improves testing accuracy without damaging the permafrost structure.

Description

Technical Field

[0001] This invention belongs to the technical field of dielectric property determination of permafrost, and relates to a non-destructive method for determining the dielectric constant of undisturbed permafrost. Background Technology

[0002] In the fields of cold-region engineering construction, permafrost resource exploration, and global climate change research, the dielectric constant of undisturbed permafrost is a key parameter reflecting its moisture distribution, freeze-thaw state, and mechanical properties. Accurate testing of this parameter is crucial for assessing the stability of permafrost engineering projects and providing early warning of cold-region disasters. However, current techniques for testing the dielectric constant of undisturbed permafrost have significant limitations, making it difficult to simultaneously meet the dual requirements of testing accuracy and preserving the original structure of the permafrost.

[0003] Traditional testing methods can damage the integrity of permafrost. When measuring the water-to-soil volume ratio in permafrost using the drying method, the permafrost must be dried, directly destroying its frozen state and internal structure, making subsequent tests for mechanical strength, frost heave characteristics, and other key properties impossible. Similarly, traditional time-domain reflectometry (TDR) dielectric testing requires drilling holes in the permafrost specimen and inserting probes, which also damages the internal pore structure and ice-water distribution, affecting the accuracy of the test results. TDR testing methods are unsuitable for undisturbed permafrost specimens that need to be preserved intact. Existing non-destructive testing methods have low accuracy and limited applicability. Coaxial probe-based non-destructive testing methods can only probe the surface area of ​​permafrost, failing to reflect the overall dielectric properties of the permafrost, and are prone to large errors due to uneven ice-soil distribution on the surface.

[0004] In summary, current techniques for testing the dielectric constant of undisturbed permafrost suffer from technical bottlenecks, including destructive testing that damages the structure, insufficient accuracy of non-destructive testing, and high testing costs. There is an urgent need for a high-precision, non-destructive method for determining the dielectric constant of undisturbed permafrost that combines non-destructive testing, high accuracy, low cost, and dynamic adaptability. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a non-destructive method for determining the dielectric constant of undisturbed permafrost, which improves testing accuracy without damaging the permafrost structure and solves the problems existing in the prior art.

[0006] The technical solution adopted in this invention is a non-destructive method for determining the dielectric constant of undisturbed permafrost, comprising the following steps:

[0007] S1, the dielectric constants of single-phase dry soil, pure water and ice in undisturbed permafrost were measured by the experiment;

[0008] S2, non-destructive acquisition of the void ratio of undisturbed permafrost specimens;

[0009] S3, establish the calculation formulas for the volume ratios of ice, unfrozen water, and soil with respect to the unfrozen water content and void ratio, respectively;

[0010] S31: Decide the volume of the soil. =1, then the volume of ice and unfrozen water is obtained. ;

[0011] S32: Based on unfrozen water content empirical formula The volume of unfrozen water was obtained. and ice volume The ratio;

[0012] S33: The final formulas for calculating the volume ratios of ice, unfrozen water, and soil with respect to the unfrozen water content and void ratio are as follows:

[0013] ;

[0014] ;

[0015] ;

[0016] in, Indicates the void ratio;

[0017] S4 uses thawed soil samples from the same source as the original frozen soil to prepare a series of frozen specimens with different void ratios; at different negative temperatures, the unfrozen water content is experimentally determined, and a bivariate prediction model is obtained through quadratic fitting to output the unfrozen water content corresponding to any temperature and void ratio, thereby obtaining the volume ratio of ice, unfrozen water and soil through the calculation formula in S3.

[0018] S5, the overall dielectric constant of the same type of frozen soil in the same region at a fixed temperature is obtained by using a three-phase dielectric hybrid model or a deep neural network model.

[0019] Furthermore, S1 includes the following steps:

[0020] S11: Take samples of undisturbed permafrost at a specified depth and transport them back to the laboratory while they are frozen.

[0021] S12: Prepare standard specimens from frozen soil samples;

[0022] S13: Dry some frozen soil samples that were not made into standard specimens indoors, and measure the dielectric constant of the single-phase dry soil in the frozen soil samples using a vector network analyzer.

[0023] S14: The dielectric constant of water at room temperature is measured using a vector network analyzer. The water is then frozen, and the dielectric constant of the ice at sub-zero temperatures is measured.

[0024] Furthermore, S2 includes the following steps:

[0025] S21: The standard specimen of frozen soil is quickly placed on a CT scanner from a low-temperature environment for scanning;

[0026] S22: After obtaining the CT scan images of the frozen soil, image processing is performed to improve the quality of the CT scan images;

[0027] S23: Combine CT images from different sections and perform three-dimensional reconstruction to obtain the ratio of water molecule volume to soil volume, i.e., the porosity ratio; compared with the traditional method of drying frozen soil to obtain soil volume and water volume, this method achieves non-destructive and high-precision differentiation of water and soil volume.

[0028] Furthermore, S4 includes the following steps:

[0029] S41, using thawed soil samples from the same source as the original frozen soil, a series of frozen specimens with different porosity ratios were artificially prepared; the unfrozen water content was experimentally determined at different sub-zero temperatures;

[0030] S42, for a fixed void ratio, a bivariate prediction model is fitted using the nonlinear least squares method. The curve of unfrozen water content versus temperature and the fitting parameters were obtained under this fixed porosity; among them, Indicates the unfrozen water content. Indicates temperature. , and These are the fitting parameters;

[0031] S43, repeat operation S42 for multiple different void ratios to obtain multiple curves of unfrozen water content changing with temperature and fitting parameters, thereby obtaining fitting parameters under different void ratios. Fit the fitting parameters to the void ratio respectively to obtain the functional expression of the fitting parameters with respect to the void ratio, thereby obtaining the unfrozen water content of frozen soil at any temperature and any void ratio.

[0032] Furthermore, S5 includes the following steps:

[0033] Establish a three-phase dielectric hybrid model:

[0034] ;

[0035] in, The overall dielectric constant of the frozen soil is . Where is the dielectric constant of ice. The dielectric constant of unfrozen water Let be the dielectric constant of the soil. Indicates the unfrozen water content. Indicates the void ratio. , and These are model parameters;

[0036] The overall dielectric constant of artificially frozen specimens with different porosity ratios were obtained by TDR testing at different negative temperatures. The measured overall dielectric constant, the volume ratio of ice, unfrozen water and soil obtained in S4, and the dielectric constant of single-phase dry soil, pure water and ice obtained in S1 were substituted into the three-phase dielectric mixture model. The optimal model parameters were determined by inversion fitting.

[0037] The specific temperature and void ratio of the undisturbed permafrost obtained in the field were substituted into the bivariate prediction model for the unfrozen water content to calculate the unfrozen water content. The calculated unfrozen water content, the void ratio obtained in the field, and the dielectric constants of single-phase dry soil, pure water, and ice in the permafrost were substituted into the three-phase dielectric mixture model to calculate the overall dielectric constant of the undisturbed permafrost in the field.

[0038] Furthermore, S5 includes the following steps:

[0039] S51: Constructing a deep neural network model suitable for the dielectric properties of permafrost: using a deep residual fully connected PINN structure, with the porosity as the input. and temperature The output is the overall dielectric constant of the frozen soil. Introducing the GELU activation function and skip connections across layers; embedding a Layer Norm layer at the end of the hidden layer to achieve feature normalization;

[0040] S52: Obtain the measured overall dielectric constant of the artificially frozen specimens from the same source through simultaneous testing using a TDR (Time Domain Reflectometer) and a vector network analyzer; construct a model including porosity... ,temperature and the overall dielectric constant of frozen soil The three-dimensional structured training dataset was augmented with data augmentation techniques to increase the sample size and cover the frozen soil freeze-thaw critical zone and stable freezing zone.

[0041] S53: Constructing a multi-scale physical regularization loss function:

[0042] ;

[0043] in: This is the adaptive weighted mean square error loss term; The loss is due to the three-phase volume conservation constraint; calculated using the Huber loss function. The deviation from 1 results in a penalty for a prediction that violates the law of volume conservation; To constitutive constraint loss based on the bivariate prediction model of unfrozen water content, i.e., to construct residual terms based on the bivariate prediction model of unfrozen water content. ; Loss is due to the constraint of dielectric energy conservation; Data-driven loss; , and These are the physical constraint weighting coefficients;

[0044] S54: Measured porosity of untouched permafrost in the field. and temperature Input the converged PINN model, perform forward inference, estimate the prediction uncertainty through Monte Carlo dropout, and output the overall dielectric constant prediction value of the permafrost and the corresponding 95% confidence interval. If the uncertainty is greater than 5%, trigger the adaptive fine-tuning mechanism to update the model parameters by adding new measured data.

[0045] Furthermore, the temperature of the frozen soil is less than or equal to -0.5℃.

[0046] Furthermore, the porosity of the homologous artificially frozen specimens ranges from 0.6 to 1.

[0047] The beneficial effects of this invention are:

[0048] 1. This invention integrates CT three-dimensional reconstruction, three-phase volume ratio calculation and dielectric hybrid model closed loop to design an overall non-destructive testing method, realizing non-destructive testing of the dielectric constant of undisturbed frozen soil throughout the entire process.

[0049] 2. This invention establishes an exponential prediction model for unfrozen water content with respect to two variables: temperature and porosity. It creates an equivalent formula between unfrozen water, ice, and soil. After completing the calibration test, the unfrozen water content of frozen soil at any temperature can be obtained, thereby obtaining the accurate volume ratio of unfrozen water, ice, and soil at different temperatures. This improves the accuracy of frozen soil dielectric testing. At the same time, it eliminates the need for indoor NMR testing at each temperature to obtain the volume ratio of ice and unfrozen water, reducing equipment investment and operating time, and significantly lowering economic costs.

[0050] 3. This invention integrates a data-driven layer (supported by measured data of the bivariate prediction model) and a physical constraint layer (considering the three-phase volume ratio of porosity) in the physical information neural network model. It captures the nonlinear relationship of the dielectric properties of frozen soil through data learning and avoids the model output from violating common sense through physical constraints. This significantly reduces the mean square error, mean absolute error and mean absolute percentage error of the dielectric constant prediction, thus improving the test accuracy.

[0051] 4. Traditional TDR testing methods require insertion into the permafrost to damage the specimen. Furthermore, non-destructive testing methods based on coaxial probes have very small probe ranges and can only measure the surface of the object, failing to measure its overall structure. During testing, the probe detects only the ice or soil on the specimen surface, leading to significant errors. This invention achieves the definitive measurement of the dielectric constant of undisturbed permafrost without damaging its original structure. The same specimen can then be used for subsequent mechanical and strength tests, improving specimen utilization and the correlation between the dielectric constant and mechanical data of the same specimen, thereby enhancing the comprehensive value of the research data. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart of the measurement method according to an embodiment of the present invention.

[0054] Figure 2 This is a diagram of the internal structure of frozen soil in an embodiment of the present invention.

[0055] Figure 3 This is an error diagram showing the actual and predicted values ​​of the ordinary dielectric hybrid model in an embodiment of the present invention.

[0056] Figure 4 This is an error diagram showing the difference between the actual and predicted values ​​of the optimized dielectric hybrid model in this embodiment of the invention.

[0057] Figure 5 The error diagram between the actual and predicted values ​​of the PINN model considering composite physical constraints is shown in the embodiments of the present invention. Detailed Implementation

[0058] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0059] Example 1,

[0060] A non-destructive method for determining the dielectric constant of undisturbed permafrost, see [link to relevant documentation]. Figure 1 This includes the following steps:

[0061] S1: Select a rotary drilling rig to take samples of the undisturbed permafrost. After the samples are properly preserved, transport them back to the laboratory for indoor testing to determine the basic properties of the undisturbed permafrost, such as the dielectric constant of the soil, the dielectric constant of the water, and the dielectric constant of the ice.

[0062] S1.1: In the permafrost region to be explored, use a drilling rig to drill permafrost to a specified depth, and wrap and seal the extracted permafrost core sample on site with a polyethylene protective film to keep it in a frozen state before transporting it back to the laboratory.

[0063] S1.2: The core sample taken out by the rotary drilling machine is irregular in shape and cannot meet the requirements of the indoor test. It is necessary to cut and grind the core sample to make a standard part with a diameter of 10cm and a length of 20cm.

[0064] S1.3: Some frozen soil samples that were not made into standard specimens were dried indoors, and the dielectric constant of the dried frozen soil samples was measured using a vector network analyzer. The dielectric constant of the dried soil was found to be 6.5.

[0065] S1.4: The dielectric constant of water at 25℃ was measured to be 81 using a vector network analyzer. The dielectric constant of ice at -2℃ was measured to be 3.5 after freezing the water.

[0066] S2: Taking a undisturbed permafrost specimen as an example, a CT scan is performed, followed by three-dimensional reconstruction to calculate the ratio of water molecule volume to soil volume, i.e., the porosity. The value is 0.708. The volume ratio of water to soil in frozen soil is calculated using a CT scanner. Compared to the traditional method of drying frozen soil to determine soil and water volume, this method achieves a non-destructive and highly accurate distinction between water and soil volume.

[0067] S2.1: Place standard-sized frozen soil specimens quickly on a CT scanner from a low-temperature environment and scan them. Record the specimen corresponding to each scan image.

[0068] S2.2: After obtaining the CT scan image of the frozen soil, conventional image processing such as histogram equalization, image noise reduction, image sharpening, image segmentation, and morphological processing are required to ensure the quality of the CT image scan.

[0069] S2.3: After processing the CT images of the frozen soil samples, the CT images of different sections are combined and three-dimensionally reconstructed to draw the ice structure and soil structure respectively.

[0070] S2.4: Obtain the ratio of ice volume to soil volume from CT scan images, and then calculate the porosity using the formula. The value is 0.708, and its formula is:

[0071]

[0072] in, For the volume of soil, This is the volume of a water molecule (the volume of ice and unfrozen water). , Let the volume of ice be... This represents the volume of unfrozen water.

[0073] S3: Based on the formula for unfrozen water content, and combined with the porosity... The volume ratios of ice, unfrozen water, and soil were derived.

[0074] S3.1: Let the soil volume... =1, then the volume of ice and unfrozen water is obtained. ;

[0075] S3.2: Based on the empirical formula for the unfrozen water content, the volume ratio of unfrozen water to ice is obtained. The formula is as follows:

[0076]

[0077] S3.3: The final volume proportions of soil, ice, and unfrozen water are shown in [reference needed]. Figure 2 The formulas are as follows:

[0078]

[0079]

[0080]

[0081] S4: Artificially frozen specimens were prepared by conducting indoor calibration tests on the thawed frozen soil from S1 to obtain the relationship between unfrozen water content, temperature, and porosity. Empirical formulas are used to obtain the unfrozen water content at different temperatures, and then the volume ratios of ice, unfrozen water, and soil at different temperatures are calculated. The accurate volume ratios of each phase are fully considered and clarified, overcoming the problem that CT (Computed Tomography) struggles to accurately determine the volume ratio of ice and unfrozen water.

[0082] S4.1: Conduct indoor calibration tests by artificially freezing the dried soil. The indoor calibration tests use thawed undisturbed frozen soil to prepare artificially frozen specimens, ensuring that the soil composition and porosity characteristics of the artificially frozen specimens are consistent with those of the undisturbed frozen soil. This avoids model parameter deviations caused by material differences between the calibration specimens and the target specimens, ensuring the applicability of the optimized model to undisturbed frozen soil testing. The unfrozen water content of the artificially frozen specimens under different void ratios (0.6~1.0) and different temperature conditions (-5℃~-0.5℃) is measured to obtain the unfrozen water content. Measured data for temperature T. The freezing temperatures of artificially frozen specimens are defined under different temperature conditions (-5℃ to -0.5℃). If the freezing time is long enough, the internal temperature of the specimen stabilizes at -5℃. At this temperature, the measured unfrozen water content is equal to the freezing temperature. Specific testing methods for unfrozen water content include nuclear magnetic resonance (NMR) testing, low-temperature vacuum distillation, and centrifugation.

[0083] S4.2: Experiment with various function forms and calculate the goodness of fit. The exponential form shows the best fit, thus establishing a bivariate prediction model for unfrozen water content:

[0084]

[0085] in, Indicates the void ratio; Indicates temperature; , and For the fitting parameters, Characterizing the residual unfrozen water content at the low-temperature limit, This reflects the total potential of freezeable water in permafrost. This indicates the sensitivity of water in permafrost to temperature changes.

[0086] S4.3: For a fixed porosity, a bivariate prediction model for unfrozen water content is fitted using the nonlinear least squares method to obtain the curve of unfrozen water content as a function of temperature under this fixed porosity and its fitting parameters. , and Repeat the process for multiple different porosities to obtain multiple curves and fitting parameters, such as... Figure 3 As shown, this yields results for different porosity ratios. , and , fit parameters , and By fitting the porosity ratio separately, the functional expressions of the fitting parameters are obtained:

[0087]

[0088]

[0089]

[0090] This invention establishes fitting parameters. , , Compared with porosity The quadratic fitting relationship makes the unfrozen water content Porosity ,temperature It directly analyzes the data to obtain the unfrozen water content of frozen soil at any temperature and porosity; it breaks through the limitation of traditional models that only correlate with a single temperature, and eliminates the need for additional NMR experiments at different temperatures, thus reducing costs.

[0091] S5: Destructive dielectric testing was performed on the artificially frozen specimens used for calibration tests. The dielectric constants of different porosity ratios (0.6~1.0) and different temperatures (-5℃~-0.5℃) were substituted into the power-law dielectric mixture model, and the mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) were minimized when the model was fitted. , and The value of is used to obtain a dielectric hybridization optimization model applicable to a certain region, see [reference]. Figure 3 .

[0092] S5.1: Specimens with different porosity ratios (0.6~1.0) and different temperatures (-5℃~-0.5℃) prepared for indoor calibration tests were drilled with holes of the same size as the probe of the TDR dielectric tester.

[0093] S5.2: Insert the probe into the artificially calibrated specimen and perform a destructive test to obtain the dielectric constant of the artificially calibrated specimen (i.e., the overall dielectric constant of the frozen soil).

[0094] S5.3: Based on the power-law dielectric mixing model, the dielectric constants at different porosity ratios (0.6~1.0) and temperatures (-5℃~-0.5℃), as well as the corresponding porosity ratios and temperatures, are substituted into the three-phase dielectric mixing model:

[0095]

[0096] Inversion fitting yields the model parameters in the dielectric hybrid model. , and Thus, a dielectric hybridization optimization model applicable to a certain region is obtained:

[0097]

[0098] in, The overall dielectric constant of the frozen soil is . Where is the dielectric constant of ice. The dielectric constant of unfrozen water is the dielectric constant of the soil.

[0099] The specific temperature of the undisturbed permafrost obtained in the field, -2℃, and the void ratio, 0.708, were substituted into the permafrost dielectric mixing optimization model to calculate the dielectric constant of the undisturbed permafrost at a certain temperature. Specifically, the model parameters of the dielectric mixing optimization model applicable to a certain region were obtained through S5.3. , and And S4.3 obtains the fitting parameters , and After fitting the formula, the void ratio of the undisturbed permafrost was obtained through S2.4. Substituting 0.708 into the formula in S5.3, we can finally obtain the actual dielectric constant of the undisturbed permafrost at a temperature of -2℃ without any destructive testing, which is 9.41.

[0100] In practical implementation, if the dielectric constant of the same type of frozen soil in the same region is tested, the fitting parameters... , and and model parameters , and It remains unchanged. If you want to measure the dielectric constant of frozen soil in another area, and the soil type and temperature range vary greatly, you need to recalibrate and refit.

[0101] Existing methods for testing dielectric constant include the coaxial probe method and the time-domain reflectometry (TDRS) method. The coaxial probe method can only measure the dielectric constant of the object's surface and cannot fully represent the overall dielectric constant of the frozen soil. The TDRS probe needs to be inserted into the undisturbed frozen soil sample to destroy it. In this invention, embodiment S1 measures the dielectric constant of the dry soil sample using frozen soil samples that have not been made into standard specimens. S4 measures the unfrozen water content, and S5 measures the overall dielectric constant of the specimen using artificially frozen specimens from the same source as the undisturbed frozen soil. By combining CT, NMR, and calibration tests, the proportions of soil, ice, and unfrozen water are obtained without destroying the original sample. This allows for the determination of the overall dielectric constant of undisturbed permafrost in the field at any temperature and with any void ratio. This overcomes the limitations of specifying a temperature, void ratio, or soil type. More importantly, it does not require destroying the original sample, achieving high-precision dielectric constant determination without damage.

[0102] This invention applies the Looyenga model At that time, the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) between the actual and predicted values ​​were 5.050%, 2.114%, and 26.51%, respectively. However, after applying the optimized model of this invention, the MSE, MAE, and MAPE decreased to 0.33%, 0.21%, and 4.61%, respectively. Figure 3 and Figure 4 This invention demonstrates that the model parameters obtained through calibration experiments in the embodiments of the present invention effectively compensate for the dielectric response deviation caused by complex factors such as microstructural inhomogeneity, interface polarization, and phase spatial distribution in real permafrost, thereby improving the accuracy of the overall dielectric constant determination of undisturbed permafrost in the field.

[0103] Example 2,

[0104] Unlike Example 1, S5 uses a deep neural network model to predict the overall dielectric constant of the same type of frozen soil in the same region at a fixed temperature, including the following steps:

[0105] S51: Network topology design; a deep residual fully-connected network (PINN) is used as the basic architecture to construct a hierarchical feature mapping system with physical priors; the input layer has a dimension of 2 (porosity e, temperature T), and the output layer has a dimension of 1 (overall dielectric constant). The hidden layers employ a stacked structure of 4-6 residual blocks, with 128-256 neurons per layer. Cross-layer skip connections are introduced to alleviate the gradient vanishing problem in deep networks. The activation function is the GELU function, a modified ReLU variant, and a Layer Norm layer is embedded at the end of the hidden layers to normalize features and enhance the network's ability to fit the nonlinear dielectric response of permafrost. The output layer uses a Linear activation function to ensure the physical validity range of the dielectric constant prediction.

[0106] S52: Construction and Enhancement of High-Dimensional Training Dataset; Within the parameter space of porosity and temperature, the LatinHypercube sampling method is used for working condition design, and high-precision overall dielectric constant of the homogeneous artificially frozen specimen is obtained through synchronous testing using a TDR time-domain reflectometer combined with a vector network analyzer; Construction ( The three-dimensional structured training dataset is augmented with data enhancement techniques such as Gaussian noise injection (noise intensity 0.01) and temperature-porosity ratio parameter interpolation to increase the sample size to more than 2,000 sets, ensuring coverage of typical physical states such as the frozen soil freeze-thaw critical zone and stable freezing zone, thereby improving the model's generalization ability.

[0107] S53: Multi-physics constraint embedding mechanism; The volume ratios of the three phases (ice, unfrozen water, and soil) of frozen soil derived in S3 of Example 1 are calculated with respect to unfrozen water content and porosity, respectively. The constitutive relationship of unfrozen water content-temperature-porosity (bivariate prediction model of unfrozen water content) and the energy conservation equation of the dielectric properties of frozen soil are used as composite physical constraints and embedded into the loss function of PINN to form a multi-scale physical regularization loss function:

[0108]

[0109] in: The adaptive weighted mean square error loss term dynamically adjusts the weights of samples under different operating conditions, with the weights of frozen critical zone samples being higher than those of unfrozen critical zone samples, thereby reducing prediction bias under extreme operating conditions. The Huber loss function is used to calculate the three-phase volume conservation constraint loss. The deviation from 1 results in a penalty for a prediction that violates the law of volume conservation; The constitutive constraint loss is the residual term constructed based on the bivariate prediction model for unfrozen water content. ( ), to ensure that the prediction results meet the phase transformation law of permafrost moisture; To account for the loss due to dielectric energy conservation, the thermodynamic consistency residual of the dielectric response of frozen soil was calculated, and the output of the constraint model conformed to the law of electromagnetic energy propagation. Data-driven loss focuses on the difference between the model's predicted values ​​and the measured data. It does not involve physical constraints and is the basic loss term for the PINNN model to learn patterns from the data. The smaller the value, the better the model fits the measured data. , and The physical constraint weight coefficients range from 0.2 to 0.8. The optimal combination is determined by adaptive optimization using a Bayesian optimization algorithm.

[0110] S54: Multi-scale reasoning and uncertainty quantification; Measured porosity ratio of undisturbed permafrost in the field. and temperature The PINN model, which has been trained and converged, is input and inferred through forward propagation combined with the Monte Carlo-dropout method. The predicted dielectric constant of the permafrost and the corresponding 95% confidence interval are output. Bayesian posterior estimation is used to quantify the prediction uncertainty. When the uncertainty index is greater than 5%, the model adaptive fine-tuning mechanism is triggered to update the model parameters based on the newly added measured data to ensure the prediction accuracy under extreme conditions.

[0111] Finally, the specific temperature and porosity of undisturbed permafrost obtained in the field are input into a trained physical information neural network, which outputs the overall dielectric constant of the undisturbed permafrost. This eliminates the need to measure the dielectric constants of soil, water, and ice.

[0112] like Figure 5 As shown, the mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) between the true and predicted values ​​are 0.045, 0.023, and 1.57%, respectively, indicating that Example 2 of the present invention improves the accuracy of the determination of the overall dielectric constant of undisturbed permafrost in the field.

[0113] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for non-destructive determination of the dielectric constant of undisturbed permafrost, characterized in that, Comprising the following steps: S1, experimentally measuring the dielectric constants of single-phase dry soil, pure water and ice in the original permafrost; S2, non-destructively obtaining the void ratio of the original permafrost sample; S3, establishing a calculation formula for the volume proportions of ice, unfrozen water and soil body with respect to the unfrozen water content and the void ratio; S31: Let the volume of the soil body = 1, then the volume of ice and unfrozen water is ; S32: According to the unfrozen water content empirical formula , the ratio of the volume of unfrozen water and the volume of ice is obtained; S33: Finally, the calculation formula for the volume proportions of ice, unfrozen water and soil body with respect to the unfrozen water content and the void ratio is obtained: ； ； ； wherein, represents the pore ratio; S4, using the thawed soil sample homologous to the original frozen soil, preparing a series of frozen test pieces with different void ratios; experimentally measuring the unfrozen water content at different negative temperatures, obtaining the bivariate prediction model through quadratic fitting, and outputting the unfrozen water content corresponding to any temperature and void ratio, so as to obtain the volume proportions of ice, unfrozen water and soil body through the calculation formula of S3; S5, obtaining the overall dielectric constant of the frozen soil of the same type in the same region at a fixed temperature through a three-phase dielectric mixing model or a deep neural network model.

2. The method for non-destructive determination of dielectric constant of undisturbed permafrost according to claim 1, characterized in that, The S1 comprises the following steps: S11: sampling the original permafrost at a specified depth and transporting it back to the laboratory in a frozen state; S12: preparing the frozen soil sample into a standard test piece; S13: drying part of the frozen soil sample that has not been prepared into a standard test piece in the laboratory, and measuring the dielectric constant of single-phase dry soil in the frozen soil sample through a vector network analyzer; S14: measuring the dielectric constant of room temperature water through a vector network analyzer, freezing the water, and measuring the dielectric constant of ice at negative temperature.

3. The method for non-destructive determination of dielectric permittivity of undisturbed permafrost according to claim 1, characterized in that, The S2 comprises the following steps: S21: quickly placing the standard test piece of frozen soil from the low-temperature environment on the CT for scanning; S22: after obtaining the CT scan image of the frozen soil, image processing is performed to improve the CT image scanning quality; S23: combining the CT images of different sections and performing three-dimensional reconstruction to obtain the ratio of water molecule volume to soil volume, i.e. the void ratio.

4. The method for non-destructive determination of dielectric constant of undisturbed permafrost according to claim 1, characterized in that, The S4 comprises the following steps: S41, using the thawed soil sample homologous to the original frozen soil to artificially prepare a series of frozen test pieces with different void ratios; experimentally measuring the unfrozen water content at different negative temperatures; S42, for a fixed void ratio, fitting the bivariate prediction model by nonlinear least squares to obtain the curve of unfrozen water content versus temperature and the fitting parameters for the fixed void ratio; wherein, UFC represents the unfrozen water content, T represents the temperature, , and are fitting parameters; S43, repeating S42 for multiple different void ratios to obtain multiple curves of unfrozen water content changing with temperature and fitting parameters, thereby obtaining the fitting parameters under different void ratios, fitting the fitting parameters with respect to the void ratio to obtain a functional expression of the fitting parameters with respect to the void ratio, and thereby obtaining the unfrozen water content of the frozen soil at any temperature and any void ratio.

5. The method for non-destructive determination of dielectric constant of undisturbed permafrost according to claim 1, characterized in that, The S5 comprises the following steps: Establishing a three-phase dielectric mixing model: ； wherein, is the bulk dielectric constant of frozen soil, is the dielectric constant of ice, is the dielectric constant of unfrozen water, is the dielectric constant of the soil, denotes the unfrozen water content, denotes the porosity, , and are model parameters; At different negative temperatures, the overall dielectric constant of the homologous artificial frozen test piece with different void ratios is obtained through TDR testing; the measured overall dielectric constant, the volume proportions of ice, unfrozen water and soil body obtained by S4, and the dielectric constants of single-phase dry soil, pure water and ice obtained by S1 are brought into the three-phase dielectric mixing model, and the optimal model parameters are determined through inversion fitting; The specific temperature and the porosity ratio of the field-acquired original permafrost are substituted into the double-variable prediction model of unfrozen water content to calculate the unfrozen water content; the calculated unfrozen water content, the field-acquired porosity ratio, and the dielectric constants of the single-phase dry soil, pure water and ice in the frozen soil are substituted into the three-phase dielectric mixing model to calculate the overall dielectric constant of the field-acquired original permafrost.

6. The method for non-destructive determination of dielectric permittivity of undisturbed permafrost according to claim 1, characterized in that, The S5 comprises the following steps: S51: Constructing a deep neural network model suitable for the dielectric properties of frozen soil: using a deep residual fully connected PINN structure, the input is the void ratio and temperature , and the output is the overall dielectric constant of frozen soil ; introduce GELU activation function and cross-layer skip connection; embed Layer Norm layer at the end of the hidden layer to realize feature normalization; S52: Obtain the measured value of the overall dielectric constant of the same source artificial frozen test piece by synchronous testing of the TDR time domain reflectometer and the vector network analyzer; construct a three-dimensional structured training data set including the pore ratio , temperature and the overall dielectric constant of frozen soil , improve the sample size through data enhancement technology, and cover the freezing and thawing critical zone and stable frozen zone of frozen soil; S53: constructing a multi-scale physical regularization loss function: ； wherein: is an adaptive weighted mean squared error loss term; is a three-phase volume conservation constraint loss; is a constitutive relation constraint loss based on a two-variable prediction model of unfrozen water content; is a dielectric energy conservation constraint loss; is a data-driven loss; , and are physical constraint weight coefficients; S54: measured porosity ratio of field undisturbed permafrost and temperature Input the PINN model trained to converge, perform forward inference, estimate the prediction uncertainty by Monte Carlo-dropout, output the predicted value of the dielectric constant of the whole permafrost and the corresponding 95% confidence interval, if the uncertainty is greater than 5%, trigger the adaptive fine-tuning mechanism, update the model parameters by adding new measured data.

7. The method for non-destructive determination of dielectric constant of undisturbed permafrost according to claim 1, characterized in that, The temperature of the frozen soil is less than or equal to-0.5℃.

8. The method according to claim 5, wherein, The porosity ratio of the artificial frozen test piece is 0.6-1. The temperature of the frozen soil is less than or equal to-0.5℃. The porosity ratio of the artificial frozen test piece is 0.6-1.

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