Pumping and injecting unit economic intelligent evaluation method based on Lie group

Abstract

The invention relates to an intelligent economic evaluation method for a pumping and injecting unit based on a Lie group. The method comprises the following steps: S1, inputting parameters; s2, data preprocessing; s3, dividing a data set; s4, performing Lie group space mapping; s5, constructing a dynamic scoring model; s6, performing a Lie group optimization algorithm; and S7, judging by combining a static threshold value with a dynamic correction factor. According to the economic intelligent evaluation method driven by the Lie group, the cost change trend can be predicted more accurately, resource allocation can be optimized, the operation cost can be reduced, and the economic benefit of the mine can be improved. Meanwhile, the method supports the multi-objective decision of the mining scheme, evaluates the long-term economic influence of the irreversible mining decision, and provides powerful support for the sustainable development of the mine.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of mine informatization and data technology, and specifically relates to a Li group-based economic intelligent evaluation method for pumping and injection units. BACKGROUND

[0002] In the field of mine exploitation, the efficiency and economic evaluation accuracy of pumping and injection units have a decisive impact on ensuring the sustainable development of mines. As key facilities for underground water management in mines, pumping and injection units not only regulate the underground water power field and ensure the stability of ore body mining, but also significantly improve leaching efficiency by optimizing the migration path of leaching solution. At the same time, they play an irreplaceable role in preventing the spread of radioactive substances and controlling environmental risks. In addition, a reasonable balance between injection and pumping can also effectively reduce energy consumption costs during operation and improve resource utilization efficiency.

[0003] Economic evaluation also plays a strategic role in mine development. It is not only an important means to achieve dynamic balance between resource development and economic benefits, but also guides the optimization of pumping and injection parameters, reduces the cost of per ton of uranium production, and thus improves the overall competitiveness of mines. Economic evaluation also supports multi-objective decision-making of mine exploitation schemes, helping decision-makers make scientific and reasonable decisions in complex mining environments. Most importantly, economic evaluation can assess the long-term economic impact of irreversible mining decisions, providing strong protection for the sustainable development of mines. However, traditional economic evaluation methods have many limitations in dealing with the multi-dimensional variables and complex relationships of pumping and injection units. The accuracy and completeness of cost data, especially the price fluctuations of raw material power costs, make traditional cost management methods unable to accurately estimate and control. In addition, the accuracy and method of data collection may result in missing or omitted cost data, further affecting the accuracy of economic evaluation.

[0004] To solve these problems, the present application proposes a Li group-driven economic intelligent evaluation method for pumping and injection units. SUMMARY

[0005] The purpose of the present application is to overcome the shortcomings of the prior art and provide a Li group-based economic intelligent evaluation method for pumping and injection units. This method uses the multi-dimensional construction capability and group operation of Li group to bring the economic evaluation of pumping and injection units into a unified mathematical framework. By representing variables such as raw material cost, energy consumption, and environmental impact as elements in Li group, it can explore the potential relationships and interactions between them, reveal complex relationships that traditional methods cannot discover, and improve the accuracy of economic evaluation. In addition, the Li group method can also handle nonlinear relationships and dynamic changes, effectively dealing with complex changes in market supply and demand, power costs, and price fluctuations.

[0006] Through the Lie group driven economic intelligent evaluation method, the cost change trend can be more accurately predicted, resource allocation can be optimized, operation cost can be reduced, and economic benefit of the mine can be improved. Meanwhile, the method supports multi-objective decision of the mining scheme, evaluates long-term economic influence of the irreversible mining decision, and provides strong support for sustainable development of the mine.

[0007] The present application solves its technical problems by the following technical solutions:

[0008] A Lie group-based pumping and injection unit economic intelligent evaluation method, steps of the method are:

[0009] S1, parameter input: parameters include block segment name, pumping and injection unit number, metal amount Uranium content per square meter ρ u , average grade α and uranium concentration

[0010] S2, data preprocessing: including outlier cleaning, parameter normalization and feature correlation analysis, and calculating economic-environmental comprehensive index η, specifically:

[0011] Outlier cleaning: based on 3σ principle to remove outliers, and Kringing interpolation method is used to fill in missing values;

[0012] Parameter normalization:

[0013] (Continuous parameters: uranium content per square meter ρ u , average grade α, uranium concentration )

[0014] (Cumulative parameters: metal amount )

[0015] Wherein, μ x is the parameter mean, σ x is the standard deviation, and x max is the maximum value of the parameter;

[0016] Feature correlation analysis: mutual information entropy (MI) is used to screen key parameters and remove redundant variables;

[0017] Economic-environmental comprehensive index η represents resource enrichment degree under unit grade:

[0018]

[0019] S3, data set division: the preprocessed data is divided into training set, validation set and test set according to the proportion of 70%, 15% and 15%, the training set is stratified sampled according to the sample sequence, the validation set is used for hyperparameter tuning, and the test set is used for performance evaluation;

[0020] S4, Lie group space mapping: construct SE(2) Lie group space, map the shot unit parameters to group elements:

[0021]

[0022] where: represents the economic dimension

[0023] represents the resource richness dimension (η);

[0024] represents the environmental risk dimension due to uranium concentration may be zero or a very small value, directly calculated will cause a division by zero error when , represents an extremely high environmental risk, such as a complete loss of control of radioactive material leakage, when , ∈ has a very small effect on the result;

[0025] Project the parameters to the tangent space T g E(2) through exponential mapping, calculate the geodesic distance to measure unit similarity;

[0026] S5, construct a dynamic scoring model, the model is

[0027]

[0028] Use the analytic hierarchy process (AHP) to construct a judgment matrix through expert scoring, calculate the weight w1 = 0.7, λ = 0.3, η0 = median(η) as the normalization reference;

[0029] S6, Lie group optimization algorithm

[0030] S5 determines the weight according to the analytic hierarchy process, but the parameter mapping relationship of the model still needs to be optimized through data driving, for example, the generation of Lie group element g i depends on the parameter ξ i in the Lie group space, which needs to be optimized to better fit the actual data distribution, and the nonlinear term in the scoring model needs to adjust the parameters to improve the generalization ability, so a loss function is constructed:

[0031]

[0032] partly by minimizing the current group element g i and the ideal group element g optThe geodesic distance (based on Lie algebraic tangent space) ensures the optimality of the parameters on the group manifold, γ·det(Ad g )Constraint adjoint matrix Ad g The determinant value of , prevents the group structure from degenerating (such as irreversible operations) and ensures mathematical consistency;

[0033] Mine economic evaluation needs to respond to price fluctuations (such as uranium prices and energy costs) in real time. S6 dynamically adjusts the optimization step size through adaptive learning rate to optimize the Lie group element g i The generating parameter ξ i and the regularization coefficient γ, which enables the model to quickly adapt to data changes and avoids the performance degradation of static models caused by environmental changes;

[0034]

[0035] Where a0 represents the initial learning rate, β represents the momentum factor, k represents the parameter index, distinguishes the gradient adjustment of different parameters, and T represents the iteration step index, which accumulates historical gradient information.

[0036] S7, static threshold combined with dynamic correction factor determination,

[0037]

[0038] Where S is the score output by the dynamic scoring model of S5, and the threshold function is:

[0039]

[0040] The baseline threshold θ0 was determined by the ROC curve, corresponding to approximately 90% specificity; the dynamic correction coefficient γ responded to the trend change of the score; it was calculated using the exponentially weighted moving average (EWMA) The numerator is the current moment S t and the previous moment score S t-1 The difference between the two represents the instantaneous change in the score. The denominator β is the attenuation factor (0<β<1), which controls the weight of historical information. t is the time step. As time goes by, β t It gradually approaches 0 and the denominator approaches 1, which amplifies the initial changes and stabilizes the long-term trends, and enhances the adaptability of the model to dynamic environments.

[0041] The advantages and beneficial effects of the present invention are:

[0042] 1、The present application utilizes the multi-dimensional construction ability of Lie group and group operation to incorporate the economic evaluation of pumping and injection units into a unified mathematical framework. By representing variables such as raw material cost, energy consumption, and environmental impact as elements in the Lie group, potential correlations and interactions between them can be explored, revealing complex relationships that traditional methods cannot discover, thereby improving the accuracy of economic evaluation. In addition, the Lie group method can handle nonlinear relationships and dynamic changes, effectively addressing price fluctuations due to complex changes in market supply and demand, power costs, etc.

[0043] 2、The Lie group-driven economic intelligent evaluation method can more accurately predict cost trends, optimize resource allocation, reduce operating costs, and improve the economic benefits of mines. At the same time, this method supports multi-objective decision-making for mining plans and evaluates the long-term economic impact of irreversible mining decisions, providing strong support for the sustainable development of mines.

[0044] 3、The present application maintains SOTA performance in most scenarios through rigorous mathematical reconstruction and experimental verification, providing a new methodology with theoretical depth for economic evaluation of pumping and injection units in mines. The present application uses Lie group theory to conduct in-depth mathematical modeling and intelligent analysis of pumping and injection units in economic activities. This method not only accurately captures the complex relationships between economic variables, but also reveals the internal laws and dynamic changes of economic data using the continuity and group structure characteristics of Lie groups. Compared with traditional economic evaluation methods, the present application has the following advantages:

[0045] Firstly, it improves the accuracy of evaluation. Through the mathematical framework of Lie groups, economic phenomena can be described more comprehensively and accurately. Secondly, it enhances the robustness of the system. Based on the Lie group model, better stability and anti-interference ability are shown when facing complex and variable economic environments. At the same time, the decision-making process is optimized. The intelligent evaluation system can quickly generate evaluation reports, providing timely and accurate data support for decision-makers, shortening the decision-making cycle. Finally, it improves economic benefits. Accurate evaluation results help optimize resource allocation and reduce operating costs, thereby improving overall economic benefits. In summary, the present application has important application value and broad market prospects in the field of economic evaluation. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a flowchart of the present application;

[0047] Figure 2 is a model module diagram of the present application. DETAILED DESCRIPTION

[0048] The present application will be further described in detail below through specific embodiments. The following examples are only descriptive and not limiting, and cannot limit the scope of protection of the present application.

[0049] A Lie group-based economic intelligence evaluation method for pumping units, the innovation of which lies in the following steps:

[0050] S1. Parameter input: Parameters include block name, pumping unit number, metal amount Uranium content per square meter ρ u , average grade α, uranium concentration

[0051] S2. Data preprocessing: including outlier cleaning, parameter normalization, and feature correlation analysis, as well as calculation of the economic-environmental composite index η;

[0052] S3. Dataset division: The preprocessed data is divided into a training set, a validation set, and a test set in a ratio of 70%, 15%, and 15%. The training set is stratified and sampled according to the specimen sequence. The validation set is used for hyperparameter tuning, and the test set is used for performance evaluation.

[0053] S4. Lie group space mapping: Construct the SE(2) Lie group space and map the extraction unit parameters to group elements:

[0054]

[0055] in: Represents the economic dimension

[0056] represents the resource enrichment dimension (η);

[0057] Represents environmental risk dimensions

[0058] Project the parameters to the tangent space T through the exponential mapping g SE(2), calculates the geodesic distance to measure unit similarity;

[0059] S5. Construct a dynamic scoring model. The model is

[0060]

[0061] The analytic hierarchy process (AHP) was used to construct a judgment matrix through expert scoring, and the weights w1 = 0.7, λ = 0.3, and η0 = median (η) were calculated as the normalization benchmark;

[0062] The hyperparameters of the evaluation model are specifically shown in Table 1.

[0063] Table 1

[0064]

[0065] S6, Lie group optimization algorithm

[0066] Constructing loss function:

[0067]

[0068] Where: det(Ad g ) is the reversibility of the constraint group structure;

[0069] · Adaptive learning rate:

[0070]

[0071] Where a0 represents the initial learning rate, and β represents the momentum factor;

[0072] Optimization process hyperparameters are shown in Table 2.

[0073] Table 2

[0074]

[0075] S7, static threshold combined with dynamic correction factor determination,

[0076]

[0077] Where: threshold function

[0078]

[0079] Where: the basic threshold θ0 is determined by the ROC curve, corresponding to about 90% specificity;

[0080] Dynamic correction coefficient γ responds to the change of score trend;

[0081] Using exponential weighted moving average (EWMA) Moreover, the S2 is specifically:

[0082] Outlier cleaning: based on the 3σ principle to remove outliers, and Kringing interpolation method is used to fill in the missing values; parameter normalization:

[0083] (Continuous parameters);

[0084] (Accumulative parameters)

[0085] Feature correlation analysis: use mutual information entropy (MI) to screen key parameters and remove redundant variables;

[0086] Add economic-environmental comprehensive index to represent the resource enrichment degree under unit grade:

[0087]

[0088] Innovative verification

[0089] Baseline:

[0090] Random Forest (RF): Number of trees = 200, max_depth = 8, min_samples_split = 5

[0091] XGBoost: learning_rate = 0.1, max_depth = 6, subsample = 0.8

[0092] Support Vector Machine (SVM): Kernel function = Radial Basis Function (RBF), C = 1.0, gamma ='scale'

[0093] Traditional economic evaluation method: Net Present Value (NPV), discount rate = 8%, project period = 5 years

[0094] Comparison of experimental results:

[0095] Economic classification accuracy: consistency of unit economic status judgment with expert annotation;

[0096] Ton uranium cost error: absolute percentage error of predicted cost and actual cost;

[0097] Decision response time: time consumption from data input to output result calculation.

[0098] Method Accuracy (%) MAPE of cost of uranium per ton (%) Response time (ms) AUC This method (Lie group) 92.1 6.3 120 0.943 XGBoost 85.7 9.8 250 0.872 Random forest 83.2 11.5 180 0.841 SVM 78.9 13.2 350 0.802 Traditional NPV method 71.4 15.6 N / A 0.723

[0099] Verification of the necessity of Lie group structure:

[0100] Experimental group: complete SE(2) Lie group structure;

[0101] Control group 1: only use the translation subgroup (ignore the rotation operation);

[0102] Control group 2: Euclidean space linear model.

[0103] Model type Accuracy (%) AUC Full SE(2) 92.1 0.943 Translation subgroup 84.3 0.861 Euclidean space model 76.5 0.794

[0104] Experimental evidence shows that the rotation operation of Lie group can capture the non-commutative relationship between parameters, such as Interaction with η.

[0105] Where: e(t) = actual economic rate - target economic rate; PID control parameters k p = 0.1, k i = 0.05.

[0106] Although the embodiments of the present application and the drawings disclose the present application for illustrative purposes, those skilled in the art can understand that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present application and the appended claims, and therefore the scope of the present application is not limited to the disclosed embodiments and drawings.

Claims

1. A Lie group-based economic intelligence evaluation method for pumping units, characterized by: The steps of the method are: S1. Parameter input: Parameters include block name, pumping unit number, metal amount Uranium content per square meter ρ u , average grade α and uranium concentration S2. Data preprocessing: This includes outlier cleaning, parameter normalization, and feature correlation analysis, as well as calculation of the economic-environmental composite index η. Specifically: Outlier cleaning: outliers are eliminated based on the 3σ principle, and missing values ​​are filled using the Kringing interpolation method; Parameter normalization: (Continuous parameter: Uranium content per square meter ρ u , average grade α, uranium concentration ) (Cumulative parameter: Metal content ) Among them, μ x is the parameter mean, σ x is the standard deviation, x max is the maximum value of the parameter; Feature association analysis: Use mutual information entropy (MI) to screen key parameters and eliminate redundant variables; The economic-environmental comprehensive index η represents the resource richness per unit grade: S3. Dataset division: The preprocessed data is divided into a training set, a validation set, and a test set in a ratio of 70%, 15%, and 15%. The training set is stratified and sampled according to the specimen sequence. The validation set is used for hyperparameter tuning, and the test set is used for performance evaluation. S4. Lie group space mapping: Construct the SE(2) Lie group space and map the extraction unit parameters to group elements: in: Represents the economic dimension represents the resource enrichment dimension (η); Represents environmental risk dimensions Due to the uranium concentration It may be zero or a very small value, so calculate it directly will cause a division by zero error when hour, Indicates extremely high environmental risks, such as the complete uncontrolled release of radioactive materials. When ∈ has little effect on the results; Project the parameters to the tangent space T through the exponential mapping g SE(2), calculates the geodesic distance to measure unit similarity; S5. Construct a dynamic scoring model. The model is The analytic hierarchy process (AHP) was used to construct a judgment matrix through expert scoring, and the weights w1 = 0.7, λ = 0.3, and η0 = median (η) were calculated as the normalization benchmark; S6, Lie group optimization algorithm S5 determines the weights according to the hierarchical analysis method, but the parameter mapping relationship of the model still needs to be optimized through data drive, such as the Lie group element g i The generation of depends on the parameter ξ in the Lie group space i , it is necessary to optimize it to make it more consistent with the actual data distribution, and the nonlinear terms in the scoring model Parameters need to be adjusted to improve generalization ability, so the loss function is constructed: Partially by minimizing the current group element g i and the ideal group element g opt The geodesic distance (based on Lie algebraic tangent space) ensures the optimality of the parameters on the group manifold, γ·det(Ad g )Constraint adjoint matrix Ad g The determinant value of , prevents the group structure from degenerating (such as irreversible operations) and ensures mathematical consistency; Mine economic evaluation needs to respond to price fluctuations (such as uranium prices and energy costs) in real time. S6 dynamically adjusts the optimization step size through adaptive learning rate to optimize the Lie group element g i The generating parameter ξ i and the regularization coefficient γ, which enables the model to quickly adapt to data changes and avoids the performance degradation of static models caused by environmental changes; Where a0 represents the initial learning rate, β represents the momentum factor, k represents the parameter index, distinguishes the gradient adjustment of different parameters, and T represents the iteration step index, which accumulates historical gradient information. S7, static threshold combined with dynamic correction factor determination, Where S is the score output by the dynamic scoring model of S5, and the threshold function is: The baseline threshold θ0 was determined by the ROC curve, corresponding to approximately 90% specificity; the dynamic correction coefficient γ responded to the trend change of the score; it was calculated using the exponentially weighted moving average (EWMA) The numerator is the current moment S t and the previous moment score S t-1 The difference between the two represents the instantaneous change in the score. The denominator β is the attenuation factor (0<β<1), which controls the weight of historical information. t is the time step. As time goes by, β t It gradually approaches 0 and the denominator approaches 1, which amplifies the initial changes and stabilizes the long-term trends, and enhances the adaptability of the model to dynamic environments.

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