Joint inversion method of seepage parameters for earth-rockfill dam considering flow-heat coupling effect

Abstract

The application discloses a soil and rock dam seepage parameter joint inversion method considering flow-heat coupling effect, and comprises the following steps: obtaining sample points of seepage parameters to be inverted, calculating water head and temperature monitoring point simulation values corresponding to each sample point; performing data dimension reduction on the water head and temperature monitoring point simulation values; respectively establishing objective functions with water head and temperature as observation information, and converting the objective functions into a single objective function; performing optimization and solving on the single objective function; and obtaining the seepage parameters to be inverted in combination with a universal kriging proxy model. The soil and rock dam seepage parameter joint inversion method considering flow-heat coupling effect not only improves the parameter inversion efficiency, but also avoids the problem of poor generalization ability of the proxy model caused by data multicollinearity, so that the accuracy of the parameter inversion result is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of seepage behavior analysis methods, and relates to a joint inversion method for seepage parameters of earth-rock dams that considers the flow-heat coupling effect. Background Technology

[0002] Earth-rock dams are the most widely constructed dam type in the world. For water storage and power generation, these dams generate very large hydrostatic pressure differences between their upstream and downstream sides, posing a significant challenge to their seepage resistance. More than one-third of earth-rock dam failures are caused by abnormal seepage, making accurate assessment of seepage behavior crucial for ensuring the safe operation of dams. In seepage analysis of earth-rock dams, seepage parameters are usually determined through laboratory geotechnical tests or engineering analogies. However, these parameters are influenced by geological conditions, operating environment, and construction quality, and may not reflect the true performance of the dam's fill materials. Inversion analysis effectively addresses this issue and has become an important method for determining seepage parameters in earth-rock dam seepage calculations.

[0003] Inversion analysis typically requires defining an objective function between simulated and measured values, and then using optimization algorithms to find the minimum value of the objective function—that is, the minimum difference between the simulated and measured values. The parameters corresponding to this minimum value are the optimal parameters obtained through inversion. Initially, inversion analysis requires multiple calls to numerical simulation programs, which is a very time-consuming process. Establishing surrogate models to replace complex numerical simulation programs significantly improves the speed of inversion analysis and reduces computational costs. Commonly used surrogate models include the Kriging model, response surface methodology, radial basis function (RBF), and extreme learning machine. Over the decades, researchers have made considerable progress in this field, but some key issues remain to be addressed. First, traditional parametric inversion mostly uses the seepage pressure or flow rate at monitoring points as the response of dam seepage. However, the seepage process also leads to changes in the temperature of porous media, and the coupling effect between the dam seepage field and temperature field has been proven. Constructing a joint inversion model using multiple types of monitoring information has not yet been considered. Furthermore, in traditional parametric inversion processes, surrogate models are usually built separately for the observation data of each monitoring point. Such a massive workload significantly impacts the efficiency of inversion analysis. The advantage of machine learning is its ability to establish mappings between multiple inputs and multiple outputs. However, the monitoring value sequences from multiple observation points exhibit multicollinearity. Directly using these as output values ​​not only increases the complexity of the machine learning surrogate model but also reduces its generalization ability, thus affecting the accuracy of the inversion results. Summary of the Invention

[0004] The purpose of this invention is to provide a joint inversion method for seepage parameters of earth-rock dams that considers the flow-heat coupling effect, which solves the problems of low inversion efficiency and accuracy in the prior art.

[0005] The technical solution adopted in this invention is a joint inversion method for seepage parameters of earth-rock dams considering the flow-heat coupling effect, including: obtaining sample points of seepage parameters to be inverted, calculating the simulated values ​​of head and temperature monitoring points corresponding to each sample point; performing data dimensionality reduction on the simulated values ​​and measured values ​​of head and temperature monitoring points; establishing objective functions for head and temperature as observed information respectively, linearly adding the objective functions corresponding to head and temperature to obtain a single objective function, optimizing the single objective function, and combining it with a universal Kriging surrogate model to obtain the seepage parameters to be inverted.

[0006] The invention is further characterized by:

[0007] Includes the following steps:

[0008] Step 1: Obtain the sample points of the seepage parameters to be inverted, and calculate the simulated values ​​of the water head and temperature monitoring points corresponding to each sample point through flow-thermal coupled finite element numerical simulation.

[0009] Step 2: Obtain the weighting coefficients of the simulated values ​​of water head and temperature at each monitoring point and the measured values ​​of water head and temperature at the monitoring point using the entropy weighting method, and obtain the weighted simulated values ​​and weighted measured values ​​of water head and temperature at the monitoring point by weighted summation.

[0010] Step 3: Establish objective functions for water head and temperature as observed information, and linearly add the objective functions corresponding to water head and temperature to obtain a single objective function;

[0011] Step 4: Combining the universal kriging surrogate model, the multi-island genetic optimization algorithm is used to optimize the single objective function and obtain the seepage parameters to be inverted.

[0012] Step 2 specifically includes the following steps:

[0013] Step 2.1: Assuming the sample points consist of n groups, and each group includes m monitoring point values, then x ij Let be the value of the j-th monitoring point in the i-th group (i = 1, 2, ..., n; j = 1, 2, ..., m);

[0014] Step 2.2: Standardize the monitoring sequences:

[0015]

[0016] Step 2.3: Calculate the entropy of the monitoring sequence:

[0017]

[0018] Step 2.4, Calculate the weights:

[0019]

[0020] Step 2.5: Calculate the weighted values:

[0021]

[0022] The mathematical expression for the universal kriging surrogate model is:

[0023]

[0024] In the formula, x is the seepage parameter to be inverted, Y(x) is the simulated head or temperature value at the monitoring point, α is the regression coefficient, P is the number of polynomial functions, and Z(x) is the random term of the universal kriging surrogate model, whose covariance function is:

[0025] Cov[Z(x (i) ),Z(x (j) )]=σ 2 R ij (6);

[0026] In the formula, σ 2 Let R be the variance of Z(x). ij For any two samples x (i) and x (j) Spatial correlation functions:

[0027]

[0028] In the formula, l is the length scaling parameter, Γ is the gamma function, v is the positive parameter controlling the smoothness of the function, and K v It is a Bessel function of the second kind.

[0029] In step 4, the objective functions for water head and temperature, based on the observed information, are as follows:

[0030]

[0031] In the formula, e is the number of time points selected for inversion, n is the number of head monitoring points, and H is... i,t * H represents the simulated head data of the i-th monitoring point at time t. i,t The measured head data of the i-th monitoring point at time t.

[0032]

[0033] In the formula, l represents the number of time points selected for inversion, m represents the number of temperature monitoring points, and T represents the number of temperature monitoring points. j,t * Let T be the simulated temperature data of the j-th monitoring point at time t. j,tThis represents the measured temperature data of the j-th monitoring point at time t.

[0034] The single objective function in step 4 is:

[0035]

[0036] In the formula, w1 and w2 are weighting coefficients, satisfying w1 + w2 = 1.

[0037] The beneficial effects of this invention are as follows: The joint inversion method for seepage parameters of earth-rock dams, which considers the flow-thermal coupling effect, can fully combine observation information from different categories of earth-rock dams to accurately and efficiently obtain seepage parameters, thus improving the inversion accuracy and providing reliable support and basis for dam seepage behavior analysis. The entropy weight method is used to preprocess the head and temperature observation information from multiple monitoring points, effectively reducing the data dimensionality. This not only improves the efficiency of parameter inversion but also avoids the problem of poor generalization ability of surrogate models caused by multicollinearity, thereby improving the accuracy of parameter inversion results. Furthermore, this method can be applied not only to earth-rock dam engineering but also to slope, tunnel, and embankment engineering, demonstrating strong scalability. Attached Figure Description

[0038] Figure 1 This is a flowchart of the joint inversion method for seepage parameters of earth-rock dams considering the flow-heat coupling effect of the present invention;

[0039] Figure 2 This is a dam structure diagram of an embodiment of the joint inversion method for seepage parameters of earth-rock dams that considers the flow-heat coupling effect of the present invention. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0041] Example 1

[0042] The joint inversion method for seepage parameters of earth-rock dams considering flow-thermal coupling effects includes the following steps:

[0043] Step 1: Obtain the sample points of the seepage parameters to be inverted, and calculate the simulated values ​​of the water head and temperature monitoring points corresponding to each sample point through flow-thermal coupled finite element numerical simulation.

[0044] Step 2: Obtain the weighting coefficients of the simulated values ​​of water head and temperature at each monitoring point and the measured values ​​of water head and temperature at the monitoring point using the entropy weighting method, and obtain the weighted simulated values ​​and weighted measured values ​​of water head and temperature at the monitoring point by weighted summation.

[0045] Step 3: Establish objective functions for water head and temperature as observed information, and linearly add the objective functions corresponding to water head and temperature to obtain a single objective function;

[0046] Step 4: Combining the universal kriging surrogate model, the multi-island genetic optimization algorithm is used to optimize the single objective function and obtain the seepage parameters to be inverted.

[0047] Example 2

[0048] A joint inversion method for seepage parameters of earth-rock dams considering flow-thermal coupling effects, such as Figure 1 As shown, it includes the following steps:

[0049] Step 1: Based on engineering experience and data from indoor and in-situ tests, determine the range of values ​​for the seepage parameters to be inverted and the type of distribution function they follow. Use orthogonal experimental methods to obtain n sets of sample points for the seepage parameters from within the range of values ​​to be inverted, such as... Figure 2 As shown;

[0050] Step 2: Calculate the simulated values ​​of water head and temperature monitoring points corresponding to each sample point using a fluid-thermal coupled finite element numerical simulation model;

[0051] Step 3: Obtain the weight coefficients of the simulated and measured values ​​of each monitoring point through the entropy weight method, and obtain the weighted simulated values ​​of the head and temperature monitoring points and the weighted measured values ​​of the head and temperature monitoring points by weighted summation, thereby achieving data dimensionality reduction; "entropy" is a measure of the degree of disorder of a system. If the information entropy of a monitoring sequence is smaller, the amount of information provided by the monitoring sequence is greater, and its role in the new weighted sequence should be greater, and its weight should be higher.

[0052] Step 3.1: Each sample group includes the values ​​of m monitoring points, then x ij Let be the value of the j-th monitoring point in the i-th group (i = 1, 2, ..., n; j = 1, 2, ..., m);

[0053] Step 3.2: Standardize the monitoring sequences:

[0054]

[0055] Step 3.3: Calculate the entropy of the monitoring sequence:

[0056]

[0057] Step 3.4: Calculate the weights:

[0058]

[0059] Step 3.5: Calculate the weighted values:

[0060]

[0061] Step 4: Combine the seepage parameter sample points and their corresponding weighted simulated values ​​of head or temperature into sample pairs. Take a set proportion of these sample pairs as training samples, and the remaining sample pairs as test samples. Input the training samples into the universal kriging surrogate model for training to obtain the trained universal kriging surrogate model.

[0062] The mathematical expression for the universal kriging surrogate model is:

[0063]

[0064] In the formula, x is the seepage parameter to be inverted, Y(x) is the simulated head or temperature value at the monitoring point, α is the regression coefficient, P is the number of polynomial functions, and Z(x) is the random term of the universal kriging surrogate model, whose covariance function is:

[0065] Cov[Z(x (i) ),Z(x (j) )]=σ 2 R ij (6);

[0066] In the formula, σ 2 Let R be the variance of Z(x). ij For any two samples x (i) and x (j) The spatial correlation function is expressed using the Matérn correlation function:

[0067]

[0068] In the formula, l is the length scaling parameter, Γ is the gamma function, v is the positive parameter controlling the smoothness of the function, and K v It is a Bessel function of the second kind.

[0069] Step 5: Establish objective functions for water head and temperature as observed information, and linearly add the objective functions corresponding to water head and temperature to obtain a single objective function;

[0070] Specifically, in step 5.1, the objective functions for water head and temperature, based on the observed information, are as follows:

[0071]

[0072] In the formula, e is the number of time points selected for inversion, n is the number of head monitoring points, and H is... i,t * H represents the simulated head data of the i-th monitoring point at time t. i,t The measured head data of the i-th monitoring point at time t.

[0073]

[0074] In the formula, l represents the number of time points selected for inversion, m represents the number of temperature monitoring points, and T represents the number of temperature monitoring points. j,t * Let T be the simulated temperature data of the j-th monitoring point at time t. j,t This represents the measured temperature data of the j-th monitoring point at time t.

[0075] Step 5.2: Joint inversion requires satisfying both objective functions in Equations 8 and 9 simultaneously. This is a typical multi-objective optimization problem. To simplify the optimization algorithm and avoid a large number of non-dominated solutions that may be generated by multi-objective optimization, a linear weighting method is used to transform the multi-objective optimization problem into a single-objective optimization problem. That is, the objective functions corresponding to water head and temperature are linearly added to obtain the single objective function:

[0076]

[0077] In the formula, w1 and w2 are weighting coefficients, satisfying w1 + w2 = 1.

[0078] Step 6: Combining the universal kriging surrogate model, the multi-island genetic optimization algorithm is used to optimize the single objective function and obtain the seepage parameters to be inverted.

[0079] Through the above methods, the joint inversion method for seepage parameters of earth-rock dams considering the flow-heat coupling effect of this invention can fully combine observation information of different types of earth-rock dams to accurately and efficiently obtain seepage parameters, which helps to improve the inversion accuracy and thus provides reliable support and basis for the analysis of dam seepage behavior. By using the entropy weight method to preprocess the head and temperature observation information of multiple monitoring points, the data dimensionality is effectively reduced, which not only improves the efficiency of parameter inversion but also avoids the problem of poor generalization ability of surrogate models caused by multicollinearity of data, thereby improving the accuracy of parameter inversion results. It can be used not only for earth-rock dam engineering but also for slope, tunnel, embankment and other engineering fields, and has strong scalability.

[0080] Example 3

[0081] The effectiveness and superiority of the proposed method are demonstrated by inverting the dam's permeability coefficient. For simplified calculation, the dam foundation is not considered. The dam body comprises three parts: a rockfill zone, a transition layer, and a clay core. Each part is designed as an isotropic, homogeneous, porous medium, with a total of nine monitoring points. The parameters for the fluid-thermal coupling numerical simulation are shown in Table 1.

[0082] Table 1. Parameters of the Flow-Thermal Coupling Numerical Simulation Model

[0083]

[0084]

[0085] In the table, n is porosity, θ s It is the saturated volumetric water content, θ r ρ is the residual volumetric water content, k is the permeability coefficient, and its theoretical value is considered the "true value." Correspondingly, the results calculated by its numerical simulation model are considered the "measured value." s It is the density of the solid, C s It is the specific heat capacity of the solid, α and n v These are the parameters of the vG model. Regions 1, 2, and 3 represent the rockfill zone, transition zone, and core wall zone, respectively. The upstream head H1 = 55m, the downstream head H2 = 0m, the water temperature is 28℃, and the initial temperature of the dam body is 16.5℃. The permeability coefficients of each part are set as the seepage parameters to be inverted, and the following processing is performed:

[0086] Within the range of values, nine levels of permeability coefficient were selected for each region, and 81 sets of sample points were generated through orthogonal design. These 81 sets of permeability coefficient sample points were input into the dam flow-heat coupled numerical model for simulation calculation. Assuming that the upstream water level does not change, 12 time control points were selected to obtain the simulated values ​​of water head and temperature at each monitoring point corresponding to each set of permeability coefficient sample points. The weighting coefficients of the response values ​​of each monitoring point were obtained by entropy weighting method, and the weighted simulated values ​​of water head and temperature monitoring points were obtained by weighted summation. The permeability coefficient sample points and the weighted simulated values ​​of monitoring points were combined to form 81 sample pairs. 60 sample pairs from the 81 sample pairs were used as training samples to train the universal kriging surrogate model, and the remaining 21 sample pairs were used as test samples. The trained surrogate model was used to replace the computationally time-consuming flow-heat coupled numerical simulation model. The objective function was optimized and solved by the multi-island genetic optimization algorithm to obtain the inverted values ​​of permeability coefficient in each region of the dam body.

[0087] To further verify the superiority of the proposed method for inverting seepage parameters using observation information from different types of earth-rock dams, the inverted seepage parameter values ​​and relative errors of w2 in the interval [0,1] were calculated, as shown in Table 2:

[0088] Table 2. Results of seepage parameter inversion

[0089]

[0090]

[0091] As shown in Table 2, compared to relying on single-category observation information, using both temperature and head observation information for joint inversion of dam seepage parameters helps improve inversion accuracy to some extent. Specifically, the optimal weight of w2 is approximately 0.6, meaning that when temperature observation information is relatively dominant, the inverted permeability coefficient is closest to the theoretical value. This demonstrates the superiority of the joint inversion method for seepage parameters of earth-rock dams considering the flow-thermal coupling effect proposed in this invention.

[0092] To further verify the effectiveness of the proposed data dimensionality reduction procedure in improving parameter inversion efficiency and the generalization ability of surrogate models, the correlation coefficients of surrogate models constructed using weighted response values ​​of monitoring points and original data were compared. The former used 24 surrogate models with an average correlation coefficient of 0.961, while the latter used 216 surrogate models with an average correlation coefficient of 0.943. The proposed data dimensionality reduction procedure resulted in fewer surrogate models and higher correlation coefficients. Therefore, it can be concluded that the proposed data dimensionality reduction procedure effectively improves parameter inversion efficiency and the generalization ability of surrogate models.

Claims

1. A joint inversion method for seepage parameters of earth-rock dams considering flow-thermal coupling effects, characterized in that, Includes the following steps: Step 1: Obtain the sample points of the seepage parameters to be inverted, and calculate the simulated values ​​of the water head and temperature monitoring points corresponding to each sample point through flow-thermal coupled finite element numerical simulation. Step 2: Obtain the weighting coefficients of the simulated values ​​of water head and temperature at each monitoring point and the measured values ​​of water head and temperature at the monitoring point using the entropy weighting method, and obtain the weighted simulated values ​​and weighted measured values ​​of water head and temperature at the monitoring point by weighted summation. Step 3: Combine the seepage parameter sample points and their corresponding weighted simulated values ​​of head or temperature into sample pairs. Take a set proportion of the sample pairs as training samples and the remaining sample pairs as test samples. Input the training samples into the universal kriging surrogate model for training to obtain the trained universal kriging surrogate model. Step 4: Establish objective functions for water head and temperature as observed information, and linearly add the objective functions corresponding to water head and temperature to obtain a single objective function; Step 5: Combining the universal kriging surrogate model, the multi-island genetic optimization algorithm is used to optimize the single objective function and obtain the seepage parameters to be inverted.

2. The joint inversion method for seepage parameters of earth-rock dams considering flow-heat coupling effect according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1, Assume the sample points include Groups, each group includes The value of each monitoring point, then For the first Group 1 The values ​​of monitoring points, where i = 1, 2, ..., n; j = 1, 2, ..., m; Step 2.2: Standardize the monitoring sequences: （1）； Step 2.3: Calculate the entropy of the monitoring sequence: （2）； Step 2.4, Calculate the weights: （3）； Step 2.5: Calculate the weighted values: （4）。 3. The joint inversion method for seepage parameters of earth-rock dams considering flow-heat coupling effect according to claim 1, characterized in that, The mathematical expression for the universal kriging proxy model is: （5）； In the formula, For the seepage parameters to be inverted, The simulated water head or temperature value at the monitoring point. For regression coefficients, The number of polynomial functions, For the random term in the universal kriging surrogate model, its covariance function is: （6）； In the formula, for variance For any two samples and Spatial correlation functions: （7）； In the formula, where It is a length scaling parameter. It is the gamma function. It is a positive parameter that controls the smoothness of the function. It is a Bessel function of the second kind.

4. The joint inversion method for seepage parameters of earth-rock dams considering flow-heat coupling effect according to claim 1, characterized in that, In step 4, the objective functions for water head and temperature, based on the observed information, are as follows: （8）； In the formula, The number of time points selected for the inversion. The number of water head monitoring points, For the first Each monitoring point at time point Simulated head data, For the first Each monitoring point at time point The measured head data, （9）； In the formula, The number of time points selected for the inversion. The number of temperature monitoring points, For the first Each monitoring point at time point Simulated temperature data, For the first Each monitoring point at time point The measured temperature data.

5. The joint inversion method for seepage parameters of earth-rock dams considering flow-heat coupling effect according to claim 4, characterized in that, The single objective function mentioned in step 4 is: （10）； In the formula, w1 and w2 are weighting coefficients, satisfying w1+w2=1.

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