Method, device, medium and equipment for predicting granulation performance of phosphate tailings

Abstract

The invention discloses a method, a device, a medium and equipment for predicting the granulation performance of phosphate tailings. The method comprises the steps that multiple technological parameters and multiple attributes of a binder serve as explanatory variables, phosphate tailing particle performance serves as response variables, and a database is built based on the explanatory variables and the response variables; performing importance sorting on the explanatory variables in the database by using a random forest algorithm, and selecting the first n explanatory variables as final explanatory variables according to a sorting result; taking the final explanation variable as input, taking the response variable as output, and training a random forest algorithm to obtain a random forest model; and performing quantitative prediction on the performance of the phosphate tailing particles produced under the attributes of the target process parameters and the target binder by using the random forest model. According to the scheme, the problems that the granulation effect is difficult to predict and the process control is inaccurate due to various types and characteristics of binders and complex processes can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical equipment working condition detection, and in particular to a method, device, medium and equipment for predicting phosphate tailings granulation performance. Background Art

[0002] With the continuous expansion of the phosphorus chemical industry, the accumulation of phosphate tailings has continued to increase. Currently, the annual production of phosphate tailings has reached 7 million tons, but its utilization rate is only 20%. The storage of phosphate tailings occupies a large amount of land and poses a significant potential threat to the environment. At the same time, the country is actively promoting the full utilization of this major by-product. Phosphate tailings are rich in calcium and magnesium nutrients and have a certain alkalinity, showing potential for the preparation of soil conditioners and medium-element fertilizers. Phosphate tailings are typically in powder form. Although powdered form can produce better fertilizer effects in agricultural applications due to the easier release of nutrients, it is not suitable for the requirements of agricultural mechanization. In addition, if the granulated products do not disintegrate in the soil, the fertilizer efficiency will be affected. Therefore, how to granulate this raw material and ensure high granule strength and rapid disintegration rate is a difficult problem that urgently needs to be solved.

[0003] However, phosphate tailings, as a typical sandy material, share the difficulty of granulation with other sandy materials, such as calcium magnesium phosphate fertilizer, potassium chloride, and ammonium chloride. For example, phosphate tailings, whose primary component is dolomite (CaMg(CO3)2), exhibits strong electrostatic attraction between positive and negative ions, resulting in higher ionic bond energy. Furthermore, due to its hexagonal crystal structure, the ions are densely packed within the lattice, resulting in strong overall ionic bonds. This results in insufficient hydration energy to overcome the strong lattice energy, further rendering the material insoluble in water and hindering the formation of liquid bridges during granulation. Furthermore, the low surface activity of phosphate tailings weakens the mutual attraction between particles during granulation, making it difficult for particles to naturally bond. In summary, due to their dense ionic structure and low viscosity, phosphate tailings and other sandy materials are difficult to granulate and exhibit poor granulation results. Currently, phosphate tailings are mostly granulated by adding high-viscosity materials and adjusting disc granulation process parameters to achieve high particle strength and dissolution efficiency.

[0004] However, due to the wide variety of binder products on the market, their effective ingredients and functional effects vary greatly, and the effect of optimizing granulation with different binders is difficult to predict. Some indicators such as viscosity and swelling lack method support. In addition to the binder, the disc granulation process parameters also have a great influence on the results. However, the numerous process combinations make the final results complicated, making the granulation rate, particle strength, solubility and other indicators of the phosphate tailings granule products erratic, making it difficult to meet product requirements.

[0005] In summary, the existing technology is unable to consider the impact of different binder characteristics and granulation processes on the final performance of the granular product, resulting in the inability to accurately predict the granulation performance of phosphate tailings. Summary of the Invention

[0006] Based on this, it is necessary to provide a method, device, medium and equipment for predicting the granulation performance of phosphate tailings to address the technical problem that the existing technology cannot accurately predict the granulation performance of phosphate tailings.

[0007] The present invention adopts the following technical solutions: In a first aspect, the present invention provides a method for predicting phosphate tailings granulation performance, the method comprising: Taking various process parameters and various properties of the binder as explanatory variables and the properties of the phosphate tailings particles as response variables, a database is constructed based on the explanatory variables and the response variables; Using a random forest algorithm to rank the importance of the explanatory variables in the database, and selecting the top n explanatory variables as final explanatory variables according to the ranking results; using the final explanatory variables as input and the response variable as output, training the random forest algorithm to obtain a random forest model; The random forest model is used to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties.

[0008] Furthermore, the random forest algorithm is used to rank the importance of the explanatory variables in the database, specifically including: Calculate the indicator value of the increase in the mean square error of the explanatory variables of each category and the indicator value of the improvement in node purity; Determining the importance index of each category explanatory variable based on the indicator value of the increase in mean square error and the indicator value of the improvement in node purity; The importance of each category explanatory variable in the database is ranked according to the importance index of each category explanatory variable.

[0009] Furthermore, before using the random forest model to quantitatively predict the performance of the phosphate tailings particles produced under the target process parameters and the properties of the target binder, the parameters of the random forest model are optimized, specifically including: Use the grid parameter adjustment method to optimize the optimal number of variables mtry for the binary tree in the specified node in the random forest model; The optimal number of decision trees ntree contained in the specified random forest in the random forest uses a fixed value.

[0010] Furthermore, after optimizing the parameters of the random forest model, the method further includes: The prediction accuracy of the optimized random forest model was evaluated by the root mean square error and the coefficient of determination.

[0011] Furthermore, the various process parameters specifically include rotation speed, granulation temperature, stirring rate, granulation time and water addition amount; the various types of binders specifically include carboxymethyl cellulose, sodium carboxymethyl cellulose, polyacrylamide, and starch; the various properties of the binder specifically include binder dosage, viscosity, molecular weight, solid content, swelling properties, specific surface area and porosity; the performance of the phosphate tailings particles specifically include formation rate, large particle rate, small particle rate, particle strength and dissolution rate.

[0012] Furthermore, before using the random forest algorithm to rank the importance of the explanatory variables in the database, the method further includes: The data in the database are normalized, and the normalized data are cleaned.

[0013] In a second aspect, the present invention provides a device for predicting the granulation performance of phosphate tailings, comprising: A database construction module is used to use multiple process parameters and multiple properties of the binder as explanatory variables and the properties of the phosphate tailings particles as response variables, and to construct a database based on the explanatory variables and response variables; A model building module is used to use a random forest algorithm to rank the importance of the explanatory variables in the database, select the top n explanatory variables as the final explanatory variables according to the ranking results; use the final explanatory variables as input and the response variable as output, train the random forest algorithm, and obtain a random forest model; The performance prediction module is used to quantitatively predict the performance of phosphate tailing particles produced under target process parameters and target binder properties using the random forest model.

[0014] At least one technical solution adopted by the present invention can achieve the following beneficial effects: the present invention constructs a database by taking multiple process parameters and multiple properties of binders as explanatory variables and the performance of phosphate tailings particles as response variables; uses a random forest algorithm to sort the importance of the explanatory variables in the database, and selects the top n explanatory variables as the final explanatory variables according to the sorting results; uses the final explanatory variables as input and the response variables as output to train the random forest algorithm to obtain a random forest model; uses the random forest model to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties, which can solve the problems of difficult to predict granulation effects and inaccurate process control caused by diverse binder types, numerous characteristics, and complex processes, and achieve accurate prediction of the performance of phosphate tailings particles manufactured under conditions of different process parameters and different binder properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0016] Figure 1 A flow chart of a method for predicting granulation performance of phosphate tailings provided by the present invention; Figure 2 A schematic diagram of a framework process for predicting phosphate tailings granulation performance provided by the present invention; Figure 3 The effects of the characteristics of the screening binder and the key process indicators on the granulation performance of phosphate tailings provided by the present invention; Figure 4 A correlation analysis diagram of the predicted value and actual value of the phosphate tailings granulation performance in the granulation test in Example 1 provided by the present invention; Figure 5 A schematic diagram of a device for predicting granulation performance of phosphate tailings provided by the present invention; Figure 6 A schematic diagram of a computer device for implementing a method for predicting phosphate tailings granulation performance provided by the present invention. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0018] The server mentioned in the present invention can be a server installed on a business platform, or a device such as a desktop computer or laptop computer capable of executing the solution of the present invention. For ease of explanation, the following description will only use the server as the execution entity. The following, combined with the accompanying drawings, details the technical solutions provided by various embodiments of the present invention.

[0019] refer to Figure 1 The present invention provides a method for predicting the granulation performance of phosphate tailings, which specifically comprises the following steps: S10: Taking multiple process parameters and multiple properties of binders as explanatory variables and the properties of phosphate tailings particles as response variables, a database is constructed based on the explanatory variables and response variables.

[0020] In this embodiment, multiple process parameters include but are not limited to rotation speed, granulation temperature, stirring rate, release angle, granulation time and water addition amount; binders include but are not limited to carboxymethyl cellulose, sodium carboxymethyl cellulose, polyacrylamide, starch; the properties of the binder include but are not limited to binder dosage, viscosity, molecular weight, solid content, swelling property, specific surface area and porosity; the performance of phosphate tailings particles include but are not limited to formation rate, large particle rate, small particle rate, particle strength and solubility rate.

[0021] The data source for the database is based on batch granulation experiments. The specific granulation experiment plan is as follows: After setting specific process parameters in the disc granulator, the phosphate tailings granulation raw materials are added to the granulation disc. As the granulation disc rotates, a portion of the binder head is evenly sprinkled on the raw material mixture to form small particles. The remaining raw material mixture and the remaining binder are then added simultaneously and granulation continues until the predetermined granulation time is reached to obtain phosphate tailings particles. The specific culture test plan is shown in Table 1, with a total of 113 groups of experiments: Table 1 Granulation test with different binder parameters and process parameters The method for testing the performance of phosphate tailings particles is as follows: Granulation rate: Use a 2-4mm square hole sieve for screening, and particles with a particle size between 2-4.75mm are qualified products.

[0022] Granulation rate = m1 / m2*100%; Where m1 is the mass of the phosphate tailings particles with a particle size between 2 and 4 mm, and m2 is the total mass of the mixed powder materials before granulation.

[0023] The large particle rate and small particle rate refer to particles with a diameter greater than 4.75 mm and less than 2 mm, respectively.

[0024] Particle strength: Take 30 fertilizer particles of uniform size and measure them using a KQ-3 particle strength meter.

[0025] Solubility: Take a certain amount of phosphate tailings particle product, record the mass as m1, soak it in still water at room temperature for 10 minutes, weigh the mass of the sample that does not pass through the 1.00mm test sieve, record the mass as m2.

[0026] Dissolution rate = (m1-m2) / m1*100%.

[0027] This embodiment uses the performance of phosphate tailing particles as a response indicator, which is more conducive to guiding the granulation practice of phosphate tailing sandy materials in factory production.

[0028] S20: Use the random forest algorithm to sort the importance of the explanatory variables in the database, and select the top n explanatory variables as the final explanatory variables according to the sorting results; use the final explanatory variables as input and the response variables as output, train the random forest algorithm, and obtain a random forest model.

[0029] In this embodiment, reference Figure 2 ,After using the random forest algorithm to screen the importance of the ,explanatory variables, the random forest model is trained using the ,response variables and the screened explanatory variables.

[0030] Specifically, 70% of the data set (i.e., database) was used as a training set, and 30% of the data set was used as a test set. The random forest algorithm was simulated and trained to obtain a random forest model for predicting the performance of phosphate tailings particles.

[0031] In this embodiment, before using the random forest algorithm to rank the importance of the explanatory variables in the database, the following steps are also included: The data in the database are normalized, and the normalized data are cleaned.

[0032] Specifically, after normalizing the data, the data in the database is read in the R language environment and data cleaning is performed to remove outliers. The data cleaning method is:

[0033] Check the missing values ​​in the database and fill in the missing values ​​in the variable indicators: use clustering methods to detect outliers, and complete the data cleaning after deleting the outliers.

[0034] The missing values ​​were filled using one of the following methods: mean value, median simple filling, K-nearest neighbor algorithm, random forest filling missing values ​​and multiple imputation method.

[0035] In this embodiment, the random forest algorithm is used to rank the importance of the explanatory variables in the database, specifically including: Calculate the indicator value of the increase in the mean square error of the explanatory variables for each category and the indicator value of the improvement in node purity.

[0036] The importance index of each category explanatory variable is determined based on the indicator value of the increase in mean square error and the indicator value of the improvement in node purity.

[0037] The importance of each category explanatory variable in the database is ranked according to the importance index of each category explanatory variable.

[0038] Specifically, all explanatory variable indicators in the random forest are ranked by importance. The importance of the predictive explanatory variable is determined by two indicators: the increase in mean squared error and the improvement in node purity. The larger the indicator value, the greater the importance of the explanatory variable. Then, the explanatory variables for constructing the random forest model are determined through four-fold cross-validation.

[0039] In this embodiment, n is a positive integer, Figure 3 , the final screened explanatory variables are 8, including: binder dosage, viscosity, swelling, specific surface area, porosity, rotation speed, granulation time, and water addition amount.

[0040] S30: Use random forest models to quantitatively predict the properties of phosphate tailings particles produced under target process parameters and target binder properties.

[0041] In this embodiment, the target process parameters refer to the process parameters used in the actual production of phosphate tailings particles, and the target type of binder refers to the binder used in the actual production of phosphate tailings particles. By inputting the above parameters into the random forest model in the R language environment, the performance of the phosphate tailings particles after granulation can be predicted. This embodiment relies on the type of binder, the properties of the binder and the process combination to predict the granulation performance of the phosphate tailings, and can produce phosphate tailings particle products at the lowest cost according to the requirements of the actual application scenario. In addition, this method covers all key influencing factors of granulation, and the predicted particle indicators include important particle indicators such as particle strength, granulation rate, dissolution rate, etc., which has important guiding significance for the improvement of powder granulation process.

[0042] based on Figure 1 A method for predicting the granulation performance of phosphate tailings is shown. The present invention constructs a database by taking multiple process parameters and multiple properties of a binder as explanatory variables and the performance of phosphate tailings particles as response variables; uses a random forest algorithm to sort the importance of the explanatory variables in the database, and selects the top n explanatory variables as final explanatory variables according to the sorting results; uses the final explanatory variable as input and the response variable as output to train the random forest algorithm to obtain a random forest model; uses the random forest model to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties, which can solve the problems of difficult prediction of granulation effects and inaccurate process control caused by diverse binder types, numerous properties, and complex processes, and achieve accurate prediction of the performance of phosphate tailings particles manufactured under conditions of different process parameters and different binder properties.

[0043] When applying the method for predicting the granulation performance of phosphate tailings provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0044] In addition, in one or more embodiments of the present invention, before using the random forest model to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties, the parameters of the random forest model are optimized, specifically including: The grid parameter adjustment method is used to optimize the optimal number of variables mtry used for the binary tree in the specified node in the random forest model.

[0045] The optimal number of decision trees ntree contained in the specified random forest in the random forest uses a fixed value.

[0046] Specifically, 70% of the data in the database were selected as training samples, and the remaining 30% of the data were selected as test samples. The binary classification and multi-classification of the grid parameter adjustment method were used to screen and optimize the optimal number of variables (mtry) for the binary tree in the specified node in the random forest, and the optimal parameter mtry was determined to be 3; the fixed value of the optimal number of decision trees (ntree) contained in the specified random forest in the random forest was 500.

[0047] In addition, in one or more embodiments of the present invention, after optimizing the parameters of the random forest model, the method further includes: The prediction accuracy of the optimized random forest model was evaluated by the root mean square error and the coefficient of determination.

[0048] Specifically, the accuracy of the random forest model is evaluated by the accuracy indicators Root Mean Squared Error and Determination Coefficient. When the predicted value is closer to the true value, the accuracy indicator Root Mean Squared Error (RMSE) is closer to 0, and the determination coefficient (R 2 ) is closer to 1, the better the model effect is.

[0049] RMSE and R 2 The calculation formulas are: ; ; Where: c i represents the measured value of the effect of the phosphate tailings particles after the i-th binder and process parameters are treated (such as the change in pH value); c ii represents the predicted value of the effect of the phosphate tailings particles after the i-th binder and process parameters are treated; c m Indicates the average value of the measured values ​​of the particle effect (such as particle intensity).

[0050] refer to Figure 4 , Figure 4 (a) shows the comparison between the predicted and measured values ​​of the particle strength of phosphate tailing particles, R 2The RMSE is 1.7073, which means that the gap between the predicted value and the measured value is very small, and the model prediction accuracy is high. Figure 4 (b) shows the comparison between the predicted and measured values ​​of the dispersion rate of phosphate tailing particles, R 2 The RMSE is 0.1118, which means that the gap between the predicted value and the measured value is very small, and the model prediction accuracy is high. Figure 4 (c) shows the comparison between the predicted value and the measured value of the small particle ratio of phosphate tailing particles, R 2 The RMSE is 0.1142, which means that the gap between the predicted value and the measured value is very small, and the model prediction accuracy is high. Figure 4 (d) shows the comparison between the predicted and measured values ​​of the granulation rate of phosphate tailings particles, R 2 The RMSE is 0.1347, which means that the gap between the predicted value and the measured value is small and the model prediction accuracy is high. Figure 4 (e) shows the comparison between the predicted value and the measured value of the large particle ratio of phosphate tailing particles, R 2 The RMSE is 0.1870, which means that the gap between the predicted value and the measured value is small and the model prediction accuracy is high.

[0051] The above is a method for predicting the granulation performance of phosphorus tailings provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding device for predicting the granulation performance of phosphorus tailings, such as Figure 5 Shown, including: The database construction module is used to take multiple process parameters and multiple properties of the binder as explanatory variables, and the performance of the phosphate tailings particles as response variables, and to construct a database based on the explanatory variables and response variables.

[0052] The model building module is used to use the random forest algorithm to sort the importance of the explanatory variables in the database, and select the top n explanatory variables as the final explanatory variables according to the sorting results; the final explanatory variables are used as input and the response variables are used as output to train the random forest algorithm and obtain a random forest model.

[0053] The performance prediction module is used to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties using a random forest model.

[0054] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the Figure 1 A method for predicting the pelletizing performance of phosphate tailings is provided.

[0055] The present invention also provides Figure 6 The structural diagram of the computer equipment shown in FIG. Figure 6 As shown, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory, and may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the Figure 1 A message passing method for multi-commodity flow problems in communication networks is provided.

[0056] The specific limitation about a device for predicting the granulation performance of phosphate tailings can refer to the limitation of a method for predicting the granulation performance of phosphate tailings above, which will not be repeated here. Each module in the device for predicting the granulation performance of phosphate tailings can be realized in whole or in part by software, hardware and a combination thereof. Each module can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory in the computer device in software form, so that the processor calls the operation corresponding to each of the above modules.

[0057] Those skilled in the art will appreciate that all or part of the processes in the described method embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the described method embodiments. Any reference to memory, storage, database, or other media used in the embodiments provided herein may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0058] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A method for predicting the granulation performance of phosphate tailings, characterized in that, include: Taking various process parameters and various properties of the binder as explanatory variables and the properties of the phosphate tailings particles as response variables, a database is constructed based on the explanatory variables and the response variables; Random forest algorithm is used to sort the importance of the explanatory variables in the database, and the top n explanatory variables are selected as the final explanatory variables according to the sorting results; Taking the final explanatory variable as input and the response variable as output, training the random forest algorithm to obtain a random forest model; The random forest model is used to quantitatively predict the performance of phosphate tailings particles produced under target process parameters and target binder properties.

2. A method for predicting phosphate tailings granulation performance as claimed in claim 1, characterized in that, The random forest algorithm is used to rank the importance of the explanatory variables in the database, specifically including: Calculate the indicator value of the increase in the mean square error of the explanatory variables of each category and the indicator value of the improvement in node purity; Determining the importance index of each category explanatory variable based on the indicator value of the increase in mean square error and the indicator value of the improvement in node purity; The importance of each category explanatory variable in the database is ranked according to the importance index of each category explanatory variable.

3. A method for predicting phosphate tailings granulation performance as claimed in claim 1, characterized in that, Before using the random forest model to quantitatively predict the performance of the phosphate tailings particles produced under the target process parameters and the properties of the target binder, the parameters of the random forest model are optimized, specifically including: Use the grid parameter adjustment method to optimize the optimal number of variables mtry for the binary tree in the specified node in the random forest model; The optimal number of decision trees ntree contained in the specified random forest in the random forest uses a fixed value.

4. A method for predicting phosphate tailings granulation performance as claimed in claim 3, characterized in that, After optimizing the parameters of the random forest model, the following steps are also included: The prediction accuracy of the optimized random forest model was evaluated by the root mean square error and the coefficient of determination.

5. A method for predicting phosphate tailings granulation performance as claimed in claim 1, characterized in that, The various process parameters specifically include rotation speed, granulation temperature, stirring rate, granulation time and water addition amount; the binder specifically includes carboxymethyl cellulose, sodium carboxymethyl cellulose, polyacrylamide, and starch; the various properties of the binder specifically include binder dosage, viscosity, molecular weight, solid content, swelling property, specific surface area and porosity; the performance of the phosphate tailings particles specifically include formation rate, large particle rate, small particle rate, particle strength and dissolution rate.

6. A method for predicting phosphate tailings granulation performance as claimed in claim 1, characterized in that, Before using the random forest algorithm to rank the importance of the explanatory variables in the database, it also includes: The data in the database are normalized, and the normalized data are cleaned.

7. A device for predicting the granulation performance of phosphate tailings, characterized in that: include: A database construction module is used to use multiple process parameters and multiple properties of the binder as explanatory variables and the properties of the phosphate tailings particles as response variables, and to construct a database based on the explanatory variables and response variables; A model building module is used to use a random forest algorithm to rank the importance of the explanatory variables in the database, and select the top n explanatory variables as the final explanatory variables according to the ranking results; Taking the final explanatory variable as input and the response variable as output, training the random forest algorithm to obtain a random forest model; The performance prediction module is used to quantitatively predict the performance of phosphate tailing particles produced under target process parameters and target binder properties using the random forest model.

8. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by a processor, the method for predicting the granulation performance of phosphate tailings according to any one of claims 1 to 6 is implemented.

9. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, a method for predicting the granulation performance of phosphate tailings as claimed in any one of claims 1 to 6 is realized.

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