A tailings cementitious material setting time prediction method and system
By acquiring the target parameter set and training a setting time prediction model using an orthogonal experimental dataset, the problem of accurately predicting the setting time of tailings cementitious materials was solved, achieving efficient and accurate setting time prediction, and improving construction efficiency and material performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CENT SOUTH UNIV
- Filing Date
- 2026-01-23
- Publication Date
- 2026-05-29
AI Technical Summary
In existing technologies, the setting time of tailings cementitious materials is affected by many factors, making it difficult to predict efficiently and accurately. This results in low construction efficiency and high costs, hindering the application of tailings cementitious materials in engineering projects.
By acquiring a set of target parameters, including water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature and humidity, a setting time prediction model trained on an orthogonal experimental dataset is used. A machine learning algorithm is then employed to generate a prediction model, outputting the predicted values for initial and final setting times.
It enables rapid prediction of the setting time of tailings cementitious materials with high precision and strong engineering applicability, thereby improving construction efficiency and the stability of material performance.
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Figure CN122117167A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of tailings recycling, specifically to a method and system for predicting the setting time of tailings cementitious materials. Background Technology
[0002] Tailings are a major solid waste generated during mining and mineral processing. Their large-scale accumulation not only occupies land resources but also poses environmental pollution and safety hazards. How to achieve large-scale, high-value-added resource utilization of tailings has always been a pressing technical challenge for the mining and building materials industries. Tailings ponds primarily contain zinc and lead. Lead-zinc tailings, as typical heavy metal tailings, have limited applications in building materials due to their complex composition and low reactivity. Developing them into cementitious materials for use in underground filling, roadbed construction, and other projects represents a promising technological approach.
[0003] However, the setting behavior of lead-zinc tailings cementitious materials exhibits high complexity in practical applications. Its setting time is not only closely related to internal proportioning factors such as the water-cement ratio and the amount of fly ash and tailings added, but is also significantly affected by dynamic environmental factors such as temperature and humidity at the construction site. In related technologies, to obtain materials that meet specific construction requirements, technicians have to rely on experience for repeated trial mixing or conduct numerous time-consuming comparative tests. This method is not only inefficient and costly, but also suffers from poor repeatability and extrapolation of test results due to the difficulty in fully simulating and quantifying the coupling effects of multiple factors, severely restricting the performance stability and engineering applicability of tailings cementitious materials.
[0004] Currently, the industry generally lacks a systematic, efficient, and reliable analytical and predictive method for regulating the properties of materials affected by multiple factors. This hinders the transition from "experience-based exploration" to "precise design," impeding the large-scale promotion and application of this resource utilization technology. Therefore, there is an urgent need for a method that can scientifically predict the setting time of tailings cementitious materials under different conditions. Summary of the Invention
[0005] The purpose of this invention is to provide a method and system for predicting the setting time of tailings cementitious materials, aiming to solve at least one of the technical problems existing in the prior art.
[0006] The technical solution of this invention is: a method for predicting the setting time of tailings cementitious materials, comprising the following steps: Obtain a target parameter set, which includes at least target mix ratio parameters and construction environment parameters. The target mix ratio parameters include at least water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameters include at least one of ambient temperature and ambient humidity. The target parameter set is input into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. Output the setting time prediction results calculated by the setting time prediction model, the prediction results including at least the initial setting time prediction value and the final setting time prediction value.
[0007] In some embodiments of the present invention, the target parameter set further includes tailings activity parameters, and obtaining the target parameter set includes: Pretreatment parameters for lead-zinc tailings are obtained, including thermal activation temperature, thermal activation time, and sieve mesh size. The tailings activity parameters of the lead-zinc tailings are obtained by material characterization methods, and the tailings activity parameters are used to represent the cementing activity of the lead-zinc tailings.
[0008] In some embodiments of the present invention, the steps for constructing the condensation time prediction model include: An orthogonal experimental dataset of lead-zinc tailings cementitious materials was obtained. The orthogonal experimental dataset included multiple sets of proportion training parameters and the measured setting time corresponding to each set of proportion training parameters. The proportion training parameters were combinations of at least three factors at different levels among the water-cement ratio, the fly ash content, the lead-zinc tailings content, the ambient temperature, the ambient humidity, and the tailings activity parameters. Based on the orthogonal experimental dataset, the influence of each of the ratio training parameters on the setting time is determined, and the influence of the first interaction term, the second interaction term, and the third interaction term on the setting time is quantified; wherein, the first interaction term represents the interaction between the water-cement ratio and the fly ash content, the second interaction term represents the interaction between the water-cement ratio and the lead-zinc tailings content, and the third interaction term represents the interaction between the fly ash content and the lead-zinc tailings content; Based on the orthogonal experimental dataset and according to the influence degree and the influence law, a machine learning algorithm is used to train and generate the condensation time prediction model.
[0009] In some embodiments of the present invention, determining the degree of influence of each of the ratio training parameters on the coagulation time includes: The influence of the water-cement ratio, the lead-zinc tailings content, and the fly ash content on the setting time was ranked by range analysis. The ranking of influence was as follows: the influence of the water-cement ratio was greater than that of the lead-zinc tailings content, and the influence of the lead-zinc tailings content was greater than that of the fly ash content.
[0010] In some embodiments of the present invention, the quantification of the influence of the first interaction term, the second interaction term, and the third interaction term on the condensation time includes: Quantify the first influence of the first interaction term on condensation time; Quantify the second influence of the second interaction term on condensation time; The third interaction term is quantified to determine the third influence of the condensation time; wherein the first, second, and third influence rules are used as constraints in the training process of the machine learning algorithm.
[0011] In some embodiments of the present invention, the method further includes: Obtain the target setting time range and the target parameter fluctuation range, wherein the target parameter fluctuation range is the allowable variation range of the target mix ratio parameter and the construction environment parameter; Using the target condensation time range as a constraint, a reverse search is performed using the condensation time prediction model within the target parameter fluctuation range; Output one or more recommended ratio parameter ranges that satisfy the target condensation time range.
[0012] In some embodiments of the present invention, after the output satisfies one or more recommended ratio parameter ranges within the target condensation time range, the method further includes: The predicted intensity index and / or raw material cost estimate corresponding to each of the recommended ratio parameter ranges are output synchronously.
[0013] This invention provides a tailings cementitious material setting time prediction system, the system comprising: The parameter set acquisition module is used to acquire a target parameter set, which includes at least a target mix ratio parameter and a construction environment parameter. The target mix ratio parameter includes at least a water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameter includes at least one of ambient temperature and ambient humidity. The data input module is used to input the target parameter set into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. The result output module is used to output the condensation time prediction results calculated by the condensation time prediction model. The prediction results include at least the initial condensation time prediction value and the final condensation time prediction value.
[0014] This invention obtains a target parameter set, which includes at least target mix proportion parameters and construction environment parameters. The target mix proportion parameters include at least the water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameters include at least one of ambient temperature and ambient humidity. The target parameter set is input into a setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. The model outputs the setting time prediction results calculated by the setting time prediction model, which includes at least the predicted values of the initial setting time and the final setting time. By comprehensively considering the material mix proportions and construction environment parameters, and utilizing a prediction model trained based on orthogonal experiments, this invention achieves rapid prediction of the setting time of tailings cementitious materials with high accuracy and strong engineering applicability. Attached Figure Description
[0015] Figure 1 This is a flowchart of the steps of a method for predicting the setting time of tailings cementitious materials provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the initial setting time of the proportioning training parameters provided in this embodiment of the invention at different levels; Figure 3 This is a schematic diagram of the final setting time of the proportioning training parameters provided in this embodiment of the invention at different levels; Figure 4a This is a three-dimensional curve of the initial setting time of the first interaction term provided in an embodiment of the present invention; Figure 4b This is a three-dimensional curve of the final solidification time of the first interaction term provided in an embodiment of the present invention; Figure 5a This is a three-dimensional curve of the initial setting time of the second interaction item provided in an embodiment of the present invention; Figure 5b This is a three-dimensional curve of the final solidification time of the second interaction item provided in an embodiment of the present invention; Figure 6a This is a three-dimensional curve of the initial setting time of the third interaction item provided in the embodiments of the present invention; Figure 6b This is a three-dimensional curve of the final solidification time of the third interaction item provided in the embodiments of the present invention; Figure 7 This is a schematic diagram of a tailings cementitious material setting time prediction system provided in an embodiment of the present invention. Detailed Implementation
[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0017] With the continuous deepening of my country's industrialization, the non-ferrous metal mining industry generates and stores massive amounts of tailings annually, with lead-zinc tailings accounting for a significant proportion. These tailings are typically considered solid waste, and their traditional storage methods not only consume vast amounts of land resources but also pose a long-term threat to the ecological environment due to the migration of residual heavy metal ions, leading to serious soil and groundwater pollution. The reprocessing and reuse of lead-zinc tailings have seen some development, forming a preliminary resource utilization system. The main components of lead-zinc tailings are oxides of Si, Al, Fe, and Ca, making them suitable for direct application in the preparation of building materials and filling materials. The preparation of cementitious materials from tailings has become a major pathway for tailings resource utilization in recent years.
[0018] Therefore, this invention provides a method and system for predicting the setting time of tailings cementitious materials. By comprehensively considering the material ratio and construction environment parameters, and using a prediction model based on orthogonal experimental training, it achieves rapid prediction of the setting time of tailings cementitious materials with high accuracy and strong engineering applicability, providing a scientific solution for tailings resource utilization.
[0019] Reference Figure 1 The diagram shows a flowchart of the steps in a method for predicting the setting time of tailings cementitious materials according to an embodiment of the present invention.
[0020] The method may specifically include the following steps: Step 101: Obtain the target parameter set. The target parameter set includes at least the target mix ratio parameter and the construction environment parameter. The target mix ratio parameter includes at least the water-cement ratio, fly ash content and lead-zinc tailings content. The construction environment parameter includes at least one of the following: ambient temperature and ambient humidity.
[0021] The target parameter set serves as the input basis for the setting time prediction model. It encompasses target proportion parameters that reflect the intrinsic composition of the material and construction environment parameters that reflect external operating conditions, thereby ensuring that the subsequent setting time prediction model can simultaneously respond to the dual influences of the material's own characteristics and the actual application environment.
[0022] In the specific implementation of this invention, the target proportioning parameters refer to the key formulation variables that determine the composition and performance of the cementitious material. Among them, the water-cement ratio, which is the ratio of total water consumption to the total solid mass of the cementitious material, is a key factor affecting the fluidity of the slurry, the setting and hardening process, and the final pore structure; the fly ash content refers to the proportion of fly ash in the total solid mass of the cementitious material; and the lead-zinc tailings content refers to the proportion of lead-zinc tailings in the total solid mass. Lead-zinc tailings, as a major silica-alumina raw material and a potential active component, directly affect the chemical environment, reaction pathway, and setting characteristics. These three parameters together constitute the core variables characterizing the material formulation.
[0023] Meanwhile, this invention further introduces construction environment parameters to capture the influence of external conditions on the setting behavior of lead-zinc tailings cementitious materials in actual engineering projects. Ambient temperature refers to the air or matrix temperature in which the lead-zinc tailings cementitious materials are mixed and cured, which significantly alters the setting process by affecting the hydration reaction rate. Ambient humidity refers to the relative humidity of the surrounding air, which affects the evaporation rate of water on the slurry surface and the internal hydration environment, thereby regulating the setting time. By incorporating at least one construction environment parameter into the target parameter set, the prediction model possesses applicability and robustness under different seasons, regions, and construction scenarios.
[0024] Specific methods for obtaining the target parameter set include, but are not limited to: reading proportioning parameters from engineering design documents, collecting construction environment parameters in real time through temperature and humidity sensors, or obtaining activity parameters from material testing reports. All parameters are input into the subsequent setting time prediction model in numerical form, providing a reliable data foundation for accurate prediction.
[0025] In some embodiments of this application, the target parameter set further includes tailings activity parameters, and step 101 may specifically include the following sub-steps: Sub-step 11: Obtain the pretreatment parameters of lead-zinc tailings, including thermal activation temperature, thermal activation time, and sieve mesh size; Sub-step 12: Obtain the tailings activity parameters of lead-zinc tailings through material characterization methods. The tailings activity parameters are used to represent the cementing activity of lead-zinc tailings.
[0026] In some embodiments, the target parameter set may be further expanded, for example, to include tailings activity parameters that characterize the cementing activity of the tailings themselves.
[0027] The cementitious activity of lead-zinc tailings is significantly affected by its physical state and pretreatment process. Dosage parameters alone are insufficient to fully reflect its role in the actual system; therefore, specific pretreatment and characterization methods are needed to obtain quantitative indicators of its activity. To this end, some embodiments of this invention further introduce tailings activity parameters into the target parameter set, which can more accurately characterize the intrinsic reactivity of lead-zinc tailings as a cementing component, further improving the accuracy and material specificity of the setting time prediction model.
[0028] In practical implementation, pretreatment parameters refer to the key control variables of the pretreatment process implemented to activate or improve the gelling activity of lead-zinc tailings. Among these, thermal activation temperature refers to the highest heating temperature reached by the tailings during activation and calcination, directly affecting the crystal structure transformation and active site formation of the aluminum-silicon phase in the tailings; thermal activation time refers to the duration of heat preservation at the target thermal activation temperature, and the thermal activation time and activation temperature together determine the sufficiency of the activation reaction; and sieve mesh size refers to the screen specifications selected for screening the tailings raw material, determining the particle size and specific surface area of the activated tailings powder, thus affecting its reaction rate and interfacial effects in the hydration system. Obtaining these pretreatment parameters allows for tracing the pretreatment history of the tailings from a process perspective, providing crucial background information for activity assessment.
[0029] Furthermore, standardized material characterization methods are used to obtain tailings activity parameters of lead-zinc tailings to scientifically characterize their cementing activity. Characterization methods may include, but are not limited to: X-ray diffraction (XRD) analysis to determine changes in mineral composition and crystal structure; thermogravimetric analysis (TGA) to assess mass changes and active component content during heating; or the use of standard mortar strength testing to indirectly evaluate its pozzolanic activity index. Tailings activity parameters can be specifically expressed as one or more quantitative indicators such as the percentage of active component content, the intensity ratio of characteristic diffraction peaks, or the activity index value. This parameter directly relates to the chemical reaction potential of tailings in the cementing system and is an important input variable for constructing accurate prediction models.
[0030] In some embodiments, sub-steps 11 and 12 can be executed sequentially or in parallel. For example, tailings samples can be standardized according to known pretreatment parameters (such as thermal activation temperature of 900°C, time of 60 min, and sieve mesh size of 65 mesh) and then their activity parameters can be obtained through XRD and strength index testing. Alternatively, tailings samples from different batches or different ore sources can be directly characterized to obtain their activity parameters. By incorporating tailings activity parameters into the target parameter set, this invention is compatible with lead-zinc tailings from different sources and processed using different techniques, significantly enhancing the universality and reliability of the setting time prediction method.
[0031] In some embodiments, the target parameter set may be further expanded, for example, to include other process parameters that affect material properties, such as sand-to-binder ratio, type and dosage of admixtures, etc.
[0032] This step aims to obtain comprehensive, multi-level input parameters to achieve accurate prediction of the setting time of tailings cementitious materials.
[0033] Step 102: Input the target parameter set into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials.
[0034] Among them, the condensation time prediction model is a mathematical model based on data analysis and machine learning algorithms that can reflect the law of multi-factor coupling. Its core function is to establish a high-dimensional mapping relationship between the input parameter set and the condensation time, so as to achieve rapid and accurate prediction of material ratio and environmental conditions to performance indicators.
[0035] The predictive model is built upon a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. This dataset was obtained through systematically designed orthogonal experiments, encompassing multiple combinations of mix proportions, construction environment parameters, and corresponding measured setting times. The orthogonal experimental design method in this invention ensures a balanced examination of the effects of various factors, including water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, humidity, and tailings activity parameters, on setting time within a limited number of experiments, and effectively separates the main effects and interactions of each factor. Each set of experimental data includes complete input conditions and the actual measured initial and final setting times, thus providing sufficient and reliable data support for model training.
[0036] In some embodiments of the present invention, the construction step of the "condensation time prediction model" in step 102 includes: Sub-step 21: Obtain the orthogonal experimental dataset of lead-zinc tailings cementitious materials. The orthogonal experimental dataset includes multiple sets of proportion training parameters and the measured setting time corresponding to each set of proportion training parameters. The proportion training parameters are combinations of at least three factors at different levels among water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, ambient humidity and tailings activity parameters. Sub-step 22: Based on the orthogonal experimental dataset, determine the influence of each ratio training parameter on setting time, and quantify the influence of the first interaction term, the second interaction term, and the third interaction term on setting time; wherein, the first interaction term represents the interaction between the water-cement ratio and the fly ash content, the second interaction term represents the interaction between the water-cement ratio and the lead-zinc tailings content, and the third interaction term represents the interaction between the fly ash content and the lead-zinc tailings content; Sub-step 23: Based on the orthogonal experimental dataset and according to the influence degree and influence law, a machine learning algorithm is used to train and generate a condensation time prediction model.
[0037] During model training, an orthogonal experimental dataset of lead-zinc tailings cementitious materials was used. Machine learning algorithms were employed to learn and fit the data, extracting the intrinsic relationship between input parameters and setting time, ultimately generating a setting time prediction model with predictive capabilities. The trained model not only considers the linear influence of single factors but also captures complex nonlinear interactions between factors, thus significantly improving the accuracy and engineering applicability of predictions.
[0038] The orthogonal experimental dataset is the foundation for model construction. This invention systematically combines at least three key factors among water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, ambient humidity, and tailings activity parameters through a designed orthogonal experimental scheme, and conducts limited but representative experiments at different levels of each factor.
[0039] This invention, through prior thermal activation tests and optimized proportioning tests of lead-zinc tailings cementitious materials, determined that the water-cement ratio, thermal activation temperature of 900℃, thermal activation time of 30 minutes, lead-zinc tailings content, and fly ash content have the greatest impact on the compressive strength of the cementitious materials. Therefore, in the specific implementation of this invention, the water-cement ratio, fly ash content, and lead-zinc tailings content are used as the three most important proportioning training parameters. Orthogonal experiments were designed at four different levels to explore the influence of these three proportioning training parameters on the setting time of lead-zinc tailings cementitious materials. The correspondence between the three proportioning training parameters and the levels in the orthogonal experiments is shown in Table 1.
[0040] Table 1 In a specific implementation of this invention, the mixing ratio training parameters can be the 16 sets of data shown in Table 2, and the measured setting time (including initial setting time and final setting time) corresponding to each set of mixing ratio training parameters is obtained by testing. In the specific implementation, the water-cement ratio, fly ash content, and lead-zinc tailings content are proportioned by mass. First, the lead-zinc tailings are sieved through a 65-mesh sieve and then thermally activated at 900℃ for 30 minutes. According to the experimental mix ratio, the grade I fly ash, the treated lead-zinc tailings, and ordinary silicate 42.5 cement are weighed and mixed evenly. After thorough mixing, the corresponding water is added according to different water-cement ratios. Timing starts at the same time as the water is poured in. After the water is added and the mixture is thoroughly stirred, it is poured into a Vicat apparatus mold and cured at constant temperature and humidity for 30 minutes. Then, the sample is taken out for initial setting test. The initial setting test is then performed every 15 minutes thereafter. After the initial setting is completed, the final setting time is tested.
[0041] Table 2 In some embodiments of the present invention, the "determining the degree of influence of each of the ratio training parameters on the coagulation time" in sub-step 22 may specifically include: The influence of water-cement ratio, lead-zinc tailings content, and fly ash content on setting time was ranked by range analysis. The ranking of influence was as follows: the influence of water-cement ratio is greater than that of lead-zinc tailings content, and the influence of lead-zinc tailings content is greater than that of fly ash content.
[0042] The range is calculated by subtracting the minimum value from the maximum value of each factor at its respective levels. A larger range indicates that the factor produces greater differences at different levels, meaning that the factor is an important factor and has a significant impact on the experimental results.
[0043] In the specific implementation of this application, after the final setting time test is completed, the present invention calculates the average initial setting time for each ratio training parameter at different levels. The calculation results are shown in Table 3. Table 3 includes the average initial setting time of each ratio training parameter at different levels, as well as the range of each ratio training parameter at different levels. The contents of Table 3 are visualized as follows: Figure 2 As shown, Figure 2 This is a schematic diagram of the initial setting time at different levels for the proportioning training parameters provided in this embodiment of the invention.
[0044] Table 3 (min) From Table 3 and Figure 2 It can be seen that, for factor A, the water-cement ratio, the initial setting time is shortest at level 1 (water-cement ratio of 0.3) and longest at level 4 (water-cement ratio of 0.45). Furthermore, the initial setting time increases with increasing water-cement ratio, showing a positive correlation within a certain range. For factor B, the fly ash content, the initial setting time is shortest at level 1 (fly ash content of 5%) and longest at level 4 (fly ash content of 20%). Furthermore, the initial setting time increases with increasing fly ash content, showing a positive correlation within a certain range. For factor C, the lead-zinc tailings content, the initial setting time is shortest at level 4 (lead-zinc tailings content of 45%) and longest at level 1 (lead-zinc tailings content of 15%). Furthermore, the initial setting time decreases with increasing lead-zinc tailings content, showing a negative correlation within a certain range.
[0045] This invention, through range analysis, determined that the range values of the three factors affecting initial setting time, from largest to smallest, are: A. Water-cement ratio > C. Lead-zinc tailings content > B. Fly ash content. Therefore, the influence of water-cement ratio, lead-zinc tailings content, and fly ash content on setting time can be ranked as follows: the influence of water-cement ratio is greater than that of lead-zinc tailings content, which in turn is greater than that of fly ash content. Thus, the influence of the three factors on initial setting time is, in descending order: A. Water-cement ratio > C. Lead-zinc tailings content > B. Fly ash content.
[0046] In a specific implementation of this invention, after analyzing the initial setting time of each proportion training parameter at different levels, the mean of the final setting time of each proportion training parameter at different levels is further calculated. The calculation results are shown in Table 4. Table 4 includes the mean of the final setting time of each proportion training parameter at different levels, as well as the range of the final setting time of each proportion training parameter at different levels. The contents of Table 4 are visualized as follows: Figure 3 As shown, Figure 3 This is a schematic diagram showing the final setting time of the proportioning training parameters provided in this embodiment of the invention at different levels.
[0047] Table 4 From Table 4 and Figure 3 Similar to the initial setting time, the cementitious material of lead-zinc tailings generally undergoes final setting 20-30 minutes after the initial setting. For factor A (water-cement ratio), the shortest final setting time is 153.75 minutes at level 1 (water-cement ratio of 0.3), and the longest is 268.75 minutes at level 4 (water-cement ratio of 0.45). Furthermore, the final setting time increases with increasing water-cement ratio, showing a positive correlation within a certain range. For factor B (fly ash content), the shortest final setting time is 182.5 minutes at level 1 (fly ash content of 5%), and the longest is 217.5 minutes at level 4 (fly ash content of 20%). Again, the final setting time increases with increasing fly ash content, showing a positive correlation within a certain range. Factor C, the final setting time was shortest at level 4 (45% lead-zinc tailings content) at 177.5 min, and longest at level 1 (15% lead-zinc tailings content) at 226.25 min. The final setting time decreased with increasing lead-zinc tailings content, and the two showed a negative correlation within a certain range.
[0048] This invention uses range analysis to determine the range of influence of three factors at different levels on the final setting time of cementitious materials. The order of influence is: A. Water-cement ratio > C. Lead-zinc tailings content > B. Fly ash content. Therefore, the sensitivity of the three factors to the final setting time of lead-zinc tailings cementitious materials is: A. Water-cement ratio > C. Lead-zinc tailings content > B. Fly ash content.
[0049] Based on the above analysis, it can be determined that the ranking of the influence of the three factors on the final setting time is consistent with the ranking of their influence on the initial setting time. Therefore, it can be determined that the final ranking of the influence of the three factors on the setting time is that the influence of the water-cement ratio is greater than that of the lead-zinc tailings content, and the influence of the lead-zinc tailings content is greater than that of the fly ash content.
[0050] Meanwhile, this invention also pays special attention to the interaction between key factors. The first interaction term reflects the synergistic or antagonistic effect on setting time when the water-cement ratio and fly ash content are adjusted together; the second interaction term characterizes the coupling effect between the water-cement ratio and the lead-zinc tailings content; and the third interaction term describes the interaction law when fly ash and lead-zinc tailings, two types of active components, coexist.
[0051] In some embodiments of the present invention, the "quantification of the influence of the first interaction term, the second interaction term, and the third interaction term on the condensation time" in sub-step 22 may specifically include the following sub-steps: Sub-step 111: Quantify the first influence of the first interaction term on condensation time; Sub-step 112: Quantify the second influence of the second interaction term on condensation time; Sub-step 113: Quantify the third influence of the third interaction term on condensation time; wherein the first, second and third influence laws are used as constraints for the training process of the machine learning algorithm.
[0052] In its specific implementation, this invention employs three-dimensional curves to quantify the influence of the first, second, and third interaction terms on setting time. The three-dimensional curves illustrating the influence of the first interaction term on initial setting time and final setting time quantify the first influence of the first interaction term on setting time; the three-dimensional curves illustrating the influence of the second interaction term on initial setting time and final setting time quantify the second influence of the second interaction term on setting time; and the three-dimensional curves illustrating the influence of the third interaction term on initial setting time and final setting time quantify the third influence of the third interaction term on setting time.
[0053] Figure 4a This is a three-dimensional curve of the initial setting time of the first interaction item provided in an embodiment of the present invention. Figure 4b The three-dimensional curve of the final solidification time of the first interaction item provided in the embodiments of the present invention is composed of... Figure 4a and Figure 4bIt can be seen that the interaction between factor A (water-cement ratio) and factor B (fly ash content) on the initial and final setting times of lead-zinc tailings cementitious materials is basically consistent. When factor B remains constant, the setting time first decreases and then increases with the increase of factor A level. This trend is obvious when factor B level is less than 2. When factor A water-cement ratio is between 1 and 2, each increase of 0.01 in water-cement ratio reduces the setting time by about 20 minutes, while when factor A water-cement ratio is between 2 and 4, each increase of 0.01 in water-cement ratio increases the setting time by about 30 minutes. This again proves that water-cement ratio is highly sensitive to lead-zinc tailings cementitious materials. When factor B level is greater than 2, increasing factor A water-cement ratio increases the setting time. The changes in the time between factors were not significant, with setting times consistently above 220 minutes. At this point, excessive moisture made cementation difficult. When factor A remained constant, the cementing time increased slowly with the increase in fly ash content (factor B), showing a positive correlation, but the increase was slightly smaller. When factor A was at levels 2-3, each 2% increase in fly ash content increased the cementing time by approximately 10 minutes. When factor A was at levels 1-2 and 3-4, the increase in factor B had little sensitivity to cementing time, indicating that fly ash content had a relatively small impact on cementing time.
[0054] Figure 5a This is a three-dimensional curve of the initial setting time of the second interaction item provided in an embodiment of the present invention. Figure 5b The three-dimensional curve of the final solidification time of the second interaction item provided in the embodiments of the present invention is composed of... Figure 5a and Figure 5b It can be seen that the interaction between the water-cement ratio (factor A) and the lead-zinc tailings content (factor C) on the initial and final setting times of lead-zinc tailings cementitious materials is basically consistent.
[0055] When factor C is at levels 1-2, the setting time of lead-zinc tailings cementitious materials first decreases and then increases with the increase of factor A. At factor A levels 1-2, each increase of 0.01 in the water-cement ratio decreases the setting time by approximately 10 minutes; at factor A levels 2-4, each increase of 0.01 in the water-cement ratio increases the setting time by approximately 15 minutes. Compared to factor B, factor C more strongly promotes the cementing effect of factor A, resulting in relatively less variation in setting time. When factor C is at levels 2-4, the setting time gradually increases with the increase of factor A, with each increase of 0.01 in the water-cement ratio increasing the setting time by approximately 8 minutes.
[0056] When factor A is at level 1-2, the setting time of the cementitious material decreases with the increase of factor C; for every 2% increase in fly ash content (C), the setting time decreases by approximately 9 minutes. When factor A is at level 2-3.5, the setting time of the cementitious material increases with the increase of factor C; for every 2% increase in fly ash content (C), the setting time increases by approximately 8 minutes. However, when factor A is at level 3.5-4, the setting time of the cementitious material changes very little, with an initial setting time of approximately 219 minutes and a final setting time of approximately 247 minutes. In conclusion, the interaction between A and C has a greater impact on the setting time of lead-zinc tailings cementitious materials, further demonstrating the stronger sensitivity of A and C.
[0057] Figure 6a This is a three-dimensional curve of the initial setting time of the third interaction item provided in an embodiment of the present invention. Figure 6b The three-dimensional curve of the final solidification time of the third interaction item provided in the embodiments of the present invention is... Figure 6a and Figure 6b It can be seen that the interaction effects of fly ash content (factor B) and lead-zinc tailings content (factor C) on the initial and final setting times of lead-zinc tailings cementitious materials are different.
[0058] When factor C is at levels 1-2, an increase in factor B will increase the initial setting time of the cementitious material, approximately 6 minutes for every 2% increase in fly ash content. When factor C is at levels 2-4, the initial setting time of the cementitious material first decreases and then increases with the increase of factor B, reaching its minimum at factor B level 3. At factor B levels 1-3, the initial setting time decreases by approximately 8 minutes for every 2% increase in fly ash content; at factor B levels 3-4, the initial setting time increases by approximately 4 minutes for every 2% increase in fly ash content. However, when factor B is at levels 1-3, the initial setting time of the cementitious material first increases, then decreases, and then increases again with the increase of factor C. When factor B is at levels 3-4, the initial setting time of the lead-zinc tailings cementitious material first decreases and then increases with the increase of factor C. This indicates that factor C, the lead-zinc tailings content, has a significant impact on the initial setting time, and an excessive increase in C will lead to a decrease in the cementing effect of the cementitious material.
[0059] When factor C is at levels 1-2, the final setting time of lead-zinc tailings cementitious materials first decreases and then increases with the increase of factor B level. The final setting time is smallest when the fly ash content of factor B reaches level 2. When factor B is at levels 1-2, each 1% increase in fly ash content decreases the final setting time by approximately 20 minutes. When factor B is at levels 2-4, each 1% increase in fly ash content increases the final setting time by approximately 15 minutes. When factor C is at levels 2-4, the final setting time gradually increases with the increase of factor B, with each 1% increase in fly ash content increasing the final setting time by approximately 9 minutes. When factor B is at levels 1-2, the final setting time first increases and then decreases with the increase of factor C. At this point, the final setting time is largest when factor C reaches level 2 (25% content). When factor B is at levels 2-4, the final setting time gradually increases with the increase of factor C, with each 1% increase in lead-zinc tailings content increasing the final setting time by approximately 3 minutes.
[0060] Based on the orthogonal experimental dataset designed in the above steps, and according to the influence of the single factor (i.e. each ratio training parameter) on the condensation time determined in the above steps, and the influence of the multiple interaction terms on the condensation time obtained in the above steps, a machine learning algorithm is used for training to generate a condensation time prediction model that can accurately predict the condensation time.
[0061] In some embodiments of the present invention, the proportioning training parameters can also be combinations of five key factors at different levels: water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, and tailings activity parameters. Based on orthogonal experimental datasets, the influence of each proportioning training parameter on setting time is determined, and the influence of the fourth interaction term (excluding the aforementioned steps) on setting time is quantified. The fourth interaction term characterizes the synergistic influence between ambient temperature and tailings activity parameters. Based on orthogonal experimental datasets and according to the influence degree and influence law, machine learning algorithms are used for training to generate a setting time prediction model that reflects the synergistic effect of material composition, external environment, and material activity.
[0062] Specifically, this invention combines five key factors—water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, and tailings activity parameters—through an orthogonal experimental design. Limited but representative experiments are conducted at different levels for each factor. By introducing ambient temperature and tailings activity parameters, the model can more realistically simulate material behavior changes under actual construction conditions, enhancing the engineering guidance value of the prediction results. The training parameters and levels for the five proportions in the orthogonal experiment are shown in Table 5.
[0063] Table 5 In practice, the proportioning training parameters can be the 16 sets of data shown in Table 6. Each set of experiments records the complete parameter combination and the corresponding measured initial and final setting times. The tailings activity parameters can be determined by the standard mortar strength test method, or calculated based on indicators such as X-ray diffraction peak intensity ratio and thermogravimetric loss rate.
[0064] Table 6 In some embodiments of the present invention, range analysis or variance analysis is used to calculate the ranking of the influence of water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, and tailings activity parameters on setting time. For example, the following ranking may be obtained: water-cement ratio > ambient temperature > lead-zinc tailings content > tailings activity parameters > fly ash content. This ranking result can be used as feature importance weights for training and optimizing machine learning models.
[0065] Furthermore, this invention quantifies the influence of the fourth interaction term (ambient temperature and tailings activity parameters) on setting time. For example, when tailings activity is high, the accelerating effect of ambient temperature on setting time may be more significant; while when activity is low, the effect of temperature change is relatively gradual. This pattern can be visualized and analyzed using a three-dimensional response surface or interaction effect diagram, and can be introduced as prior knowledge into the model training process to enhance the model's predictive robustness under complex conditions.
[0066] Finally, based on a dataset containing five-factor orthogonal experimental data, and combining the quantified single-factor influence and multi-factor interaction patterns, machine learning algorithms such as random forest, neural network, or support vector regression are used for model training.
[0067] The setting time prediction model trained through the above steps can simultaneously receive water-cement ratio, fly ash content, lead-zinc tailings content, ambient temperature, and tailings activity parameters as inputs, and output corresponding predicted values for initial and final setting times, achieving more comprehensive and accurate setting time prediction and material design support.
[0068] The method for constructing the condensation time prediction model of the present invention is a systematic and data-driven process. The construction process first obtains a high-quality training dataset based on orthogonal experimental design, then analyzes the influence degree and interaction law of each factor, and finally uses machine learning algorithms to realize the transformation from experimental data to prediction model, ensuring that the model has both physical interpretability and prediction accuracy.
[0069] Step 103: Output the condensation time prediction results calculated by the condensation time prediction model. The prediction results shall include at least the predicted values of the initial condensation time and the final condensation time.
[0070] The predicted initial setting time characterizes the time required for the cementitious material to initially form a cohesive structure from the start of water mixing. This predicted initial setting time directly guides the material's casting and initial forming processes. The predicted final setting time characterizes the time required for the slurry to fully harden and achieve initial strength from the start of water mixing. This predicted final setting time relates to the timing of subsequent construction procedures, formwork removal, and early strength development assessment. By outputting the predicted initial and final setting times, the entire process of the material transitioning from a plastic to a hardened state is fully covered, providing a continuous time benchmark for project scheduling and quality control.
[0071] The prediction results (including predicted initial and final setting times) are output in a structured data format, which may be expressed as numerical values, charts, or prompts comparing the results to preset thresholds. In some embodiments of the invention, the prediction results may further include a setting time interval estimate or a confidence index to reflect the level of uncertainty or reliability of the prediction results. For example, the model may simultaneously output the standard deviation or prediction interval of the predicted values to help users assess the stability and applicability of the prediction results. Furthermore, the prediction results can also be compared with historical data or industry standards to output performance evaluations or optimization suggestions, further enhancing the engineering applicability of the results.
[0072] In the specific implementation of this invention, the output forms of the prediction results include, but are not limited to: displaying the predicted values on a computer interface or mobile terminal, generating a report document containing the prediction results, and transmitting the predicted values to a construction control system or material production management system for real-time adjustment. By providing clear, reliable, and operable setting time prediction results, this invention significantly reduces the time and economic costs of traditional trial mixing methods, improves the construction controllability and performance predictability of tailings cementitious materials under complex conditions, thereby supporting their efficient and scientific application in practical engineering.
[0073] In some embodiments of the present invention, the following steps may also be included: Obtain the target setting time range and the target parameter fluctuation range. The target parameter fluctuation range is the allowable variation range of the target mix ratio parameters and construction environment parameters. Using the target condensation time range as a constraint, an inverse search is performed using the condensation time prediction model within the fluctuation range of the target parameters; Output one or more recommended ratio parameter ranges that meet the target condensation time range.
[0074] This invention further provides reverse parameter recommendations through the above three steps, and determines the feasible material ratio and construction environment conditions range in reverse according to the specific requirements of actual engineering for setting time.
[0075] This invention achieves a scientific reverse mapping from performance targets to design parameters by pre-setting the target condensation time range and the allowable variation range of each parameter, and by using a pre-trained condensation time prediction model for reverse search and condition matching, ultimately outputting one or more recommended parameter combination ranges that meet engineering requirements.
[0076] The target setting time range refers to the upper and lower limits of the setting time determined based on actual construction techniques, environmental conditions, or engineering specifications. For example, the initial setting time is required to be between 120-180 minutes, and the final setting time between 240-300 minutes. This range serves as a rigid constraint to screen parameter combinations that meet the requirements. The target parameter fluctuation range refers to the allowable adjustment range of each input parameter in actual engineering practice. For example, the water-cement ratio is allowed to vary between 0.40 and 0.50, the fly ash content can be adjusted within 10%-20%, and the ambient temperature is expected to vary within 15-30℃. The target parameter fluctuation range defines the parameter space boundary for the reverse search, ensuring that the recommended parameter combinations are engineering feasible.
[0077] Based on this, a reverse search is performed within the target parameter fluctuation range using a condensation time prediction model. The search process employs optimization algorithms to generate a large number of candidate parameter combinations, and then calculates the condensation time for each combination using the prediction model. These optimization algorithms include, but are not limited to, genetic algorithms, particle swarm optimization, and Monte Carlo simulations. If the calculated condensation time falls within the target condensation time range, that set of parameters is retained; otherwise, it is excluded. Through this process, all feasible regions meeting the condensation time requirements can be efficiently screened in the multidimensional parameter space.
[0078] Ultimately, this invention can output one or more recommended mixing ratio parameter ranges. Each range corresponds to a set of parameter values that meet the target setting time requirements. For example, the output result might be: "When the water-cement ratio is 0.42-0.46, the fly ash content is 12%-18%, and the ambient temperature is 20-28℃, the predicted initial setting time is 130-170 minutes, and the final setting time is 250-290 minutes." These ranges are presented in the form of data lists, visualization charts, or parameter combination fields, providing engineers with intuitive and flexible material mixing and construction condition selection options.
[0079] Suppose a downhole filling project requires the initial setting time of the cementitious material to be between 150 and 200 minutes, and the ambient temperature at the construction site is expected to fluctuate between 10 and 25°C. It is known that the water-cement ratio in the material mix can be adjusted between 0.38 and 0.45, and the fly ash content can vary between 5% and 15%. This invention first obtains the aforementioned target setting time range and the fluctuation range of each parameter. Then, it generates a large number of candidate combinations within the parameter space and uses a setting time prediction model to calculate the initial setting time for each candidate combination. Through reverse search, the solution of this invention may output the following recommended interval: "When the water-cement ratio is 0.39-0.43, the fly ash content is 8%-12%, and the ambient temperature is 12-22°C, the predicted initial setting time can meet the requirement of 150-200 minutes." Engineers can then determine the specific construction mix based on this recommended interval, combined with actual costs and material conditions.
[0080] In some embodiments of the present invention, after the step "outputting one or more recommended ratio parameter ranges that satisfy the target condensation time range", the following steps may also be included: The system synchronously outputs the predicted intensity index and / or raw material cost estimate corresponding to each recommended ratio parameter range.
[0081] The predicted strength index refers to the predicted mechanical properties calculated using an established strength prediction model (which can be trained based on the same or similar orthogonal experimental data from the aforementioned steps) based on the material mix proportions within the corresponding recommended parameter range. Examples include key indicators such as 3-day compressive strength, 7-day compressive strength, and 28-day compressive strength. These indicators reflect the load-bearing capacity of the material after hardening under this parameter combination. Meanwhile, the raw material cost estimate refers to the estimated production cost per unit volume or unit mass of cementitious material calculated based on the material mix proportions corresponding to each parameter range, combined with current market price information (such as the unit price of cement, fly ash, lead-zinc tailings, etc.). The production cost estimate provides users with the ability to directly select solutions from an economic perspective.
[0082] In actual output, each recommended parameter range can be presented with its corresponding predicted intensity range, or with its corresponding raw material cost estimate. Alternatively, each recommended parameter range can be displayed in conjunction with its corresponding predicted intensity range and cost estimate, for example, in the form of tables, comparison charts, or multi-dimensional radar charts, so that users can intuitively compare the comprehensive performance of different schemes under the multi-dimensional objectives of "condensation time-intensity-cost".
[0083] For example, this invention, through reverse search, outputs two recommended parameter ranges that meet the requirement of an initial setting time of 150-200 minutes. Range A is: water-cement ratio 0.40-0.42, fly ash content 10-12%, tailings content 40-45%, and ambient temperature 15-20℃; Range B is: water-cement ratio 0.43-0.45, fly ash content 8-10%, tailings content 35-40%, and ambient temperature 18-23℃. Furthermore, it simultaneously outputs the predicted performance and economic indicators corresponding to the above two ranges. For Range A, the predicted strength is: 28-day compressive strength 15-18 MPa; estimated raw material cost: 180-200 yuan / cubic meter. For Range B, the predicted strength is: 28-day compressive strength 12-15 MPa; estimated raw material cost: 160-180 yuan / cubic meter. By comparison, engineers can clearly see that although both intervals meet the setting time requirements, interval A exhibits superior strength performance, while interval B offers a greater economic advantage. Users can flexibly select the most suitable mix ratio interval based on their priorities regarding strength and economy in their specific projects, or further fine-tune it within the interval. This method significantly improves the overall decision-making efficiency and scientific rigor of material mix design, achieving multi-objective synergistic optimization of performance, cost, and construction conditions.
[0084] In summary, this invention achieves rapid prediction of the setting time of tailings cementitious materials with high accuracy and strong engineering applicability by comprehensively considering material ratios and construction environment parameters and utilizing a prediction model based on orthogonal experimental training.
[0085] Reference Figure 7 The diagram illustrates a structural schematic of a tailings cementitious material setting time prediction system provided in an embodiment of the present invention. The system includes: The parameter set acquisition module 701 is used to acquire a target parameter set, which includes at least a target proportion parameter and a construction environment parameter. The target proportion parameter includes at least a water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameter includes at least one of ambient temperature and ambient humidity. Data input module 702 is used to input the target parameter set into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. The result output module 703 is used to output the condensation time prediction result calculated by the condensation time prediction model. The prediction result includes at least the predicted value of the initial condensation time and the predicted value of the final condensation time.
[0086] As the system implementation is basically similar to the method implementation, it is described in a relatively simple way. For relevant details, please refer to the description of the method implementation.
[0087] This invention also provides an electronic device that may include a processor, a memory, and a computer program stored in the memory and capable of running on the processor. When the computer program is executed by the processor, it implements the method described above.
[0088] This invention also provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the method described above.
[0089] The specific embodiments described above are preferred embodiments of the present invention and are not intended to limit the specific scope of the present invention. The scope of the present invention includes, but is not limited to, these specific embodiments. All equivalent changes made in accordance with the shape and structure of the present invention are within the protection scope of the present invention.
Claims
1. A method for predicting the setting time of tailings cementitious materials, characterized in that, Includes the following steps: Obtain a target parameter set, which includes at least target mix ratio parameters and construction environment parameters. The target mix ratio parameters include at least water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameters include at least one of ambient temperature and ambient humidity. The target parameter set is input into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. Output the setting time prediction results calculated by the setting time prediction model, the prediction results including at least the initial setting time prediction value and the final setting time prediction value.
2. The method according to claim 1, characterized in that, The target parameter set also includes tailings activity parameters, and obtaining the target parameter set includes: Pretreatment parameters for lead-zinc tailings are obtained, including thermal activation temperature, thermal activation time, and sieve mesh size. The tailings activity parameters of the lead-zinc tailings are obtained by material characterization methods, and the tailings activity parameters are used to represent the cementing activity of the lead-zinc tailings.
3. The method according to claim 2, characterized in that, The steps for constructing the condensation time prediction model include: An orthogonal experimental dataset of lead-zinc tailings cementitious materials was obtained. The orthogonal experimental dataset included multiple sets of proportion training parameters and the measured setting time corresponding to each set of proportion training parameters. The proportion training parameters were combinations of at least three factors at different levels among the water-cement ratio, the fly ash content, the lead-zinc tailings content, the ambient temperature, the ambient humidity, and the tailings activity parameters. Based on the orthogonal experimental dataset, the influence of each of the ratio training parameters on the setting time is determined, and the influence of the first interaction term, the second interaction term, and the third interaction term on the setting time is quantified; wherein, the first interaction term represents the interaction between the water-cement ratio and the fly ash content, the second interaction term represents the interaction between the water-cement ratio and the lead-zinc tailings content, and the third interaction term represents the interaction between the fly ash content and the lead-zinc tailings content; Based on the orthogonal experimental dataset and according to the influence degree and the influence law, a machine learning algorithm is used to train and generate the condensation time prediction model.
4. The method according to claim 3, characterized in that, Determining the influence of each of the aforementioned ratio training parameters on the coagulation time includes: The influence of the water-cement ratio, the lead-zinc tailings content, and the fly ash content on the setting time was ranked by range analysis. The ranking of influence was as follows: the influence of the water-cement ratio was greater than that of the lead-zinc tailings content, and the influence of the lead-zinc tailings content was greater than that of the fly ash content.
5. The method according to claim 3, characterized in that, The quantification of the influence of the first, second, and third interaction terms on the condensation time includes: Quantify the first influence of the first interaction term on condensation time; Quantify the second influence of the second interaction term on condensation time; The third interaction term is quantified to determine the third influence of the condensation time; wherein the first, second, and third influence rules are used as constraints in the training process of the machine learning algorithm.
6. The method according to claim 1, characterized in that, The method further includes: Obtain the target setting time range and the target parameter fluctuation range, wherein the target parameter fluctuation range is the allowable variation range of the target mix ratio parameter and the construction environment parameter; Using the target condensation time range as a constraint, a reverse search is performed using the condensation time prediction model within the target parameter fluctuation range; Output one or more recommended ratio parameter ranges that satisfy the target condensation time range.
7. The method according to claim 6, characterized in that, After the output satisfies one or more recommended ratio parameter ranges within the target condensation time range, the method further includes: The predicted intensity index and / or raw material cost estimate corresponding to each of the recommended ratio parameter ranges are output synchronously.
8. A tailings cementitious material setting time prediction system, used to implement the method described in any one of claims 1-7, characterized in that, The system includes: The parameter set acquisition module is used to acquire a target parameter set, which includes at least a target mix ratio parameter and a construction environment parameter. The target mix ratio parameter includes at least a water-cement ratio, fly ash content, and lead-zinc tailings content. The construction environment parameter includes at least one of ambient temperature and ambient humidity. The data input module is used to input the target parameter set into the setting time prediction model, which is trained based on a pre-constructed orthogonal experimental dataset of lead-zinc tailings cementitious materials. The result output module is used to output the condensation time prediction results calculated by the condensation time prediction model. The prediction results include at least the initial condensation time prediction value and the final condensation time prediction value.
9. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the method as described in any one of claims 1-7.