Intelligent sensing-based methods, devices, and systems for controlling drill bit attitude.
Patent Information
- Application Number
- CN202610970405.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-01
- Publication Date
- 2026-09-01
- Estimated Expiration
- 2046-07-01
AI Technical Summary
但是,由于钻探地层结构复杂,使得通过实时采集的角度进行钻头姿态控制调整钻探轨迹时,未能够考虑到地质条件突变,钻头受力状态发生变化,使得钻探轨迹出现偏差
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Figure CN122467151B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of drill bit attitude control technology, specifically to a method, device, and system for controlling the attitude of drilling bits based on intelligent sensing. Background Technology
[0002] Directional drilling is a drilling technique that allows for precise control of the borehole trajectory. By controlling the attitude of the drill bit, it ensures that the drill bit excavates along a predetermined path. This technology can traverse complex geological layers and is therefore widely used in oilfield development, mineral exploration, and geological exploration. In precisely controlling the borehole trajectory, the attitude of the drill bit determines its direction of movement and the actual borehole location. Therefore, real-time dynamic adjustment of the drill bit's attitude ensures that the borehole follows the predetermined path, allowing it to accurately reach the target stratum as designed, thus improving drilling success rate and resource recovery rate.
[0003] Current drilling bit attitude control typically involves acquiring the bit's inclination angle (the angle between the plumb line and the tangent to the wellbore trajectory) and the high-side tool angle (the angle between the bit's directional direction and the end point of the wellbore trajectory within the plane of the bit's central axis). The bit's attitude is then controlled via an angle controller by calculating the angular deviation between the measured wellbore trajectory and the preset wellbore trajectory. However, due to the complex geological structures encountered during drilling, adjusting the drilling trajectory by controlling bit attitude using real-time acquired angles fails to account for sudden changes in geological conditions and the resulting shifts in the bit's stress state, leading to deviations in the drilling trajectory. Summary of the Invention
[0004] In view of the above, it is necessary to provide a method, device and system for controlling the attitude of drilling bits based on intelligent sensing to solve the above problems.
[0005] According to one aspect of this application, a method for controlling the attitude of a drilling bit based on intelligent sensing is provided, the method comprising: The triaxial acceleration and triaxial force data of the drill collar are collected in real time at various moments, and the well inclination angle, high-side tool angle and radial force on the drill bit are calculated. Analyze the changes in radial force, well inclination angle, and high-side tool angle of the drill bit at each moment compared to the previous moment to determine the degree of force and angle change of the drill bit at each moment. Correlation analysis was performed on the degree of force change and the degree of angle change at each moment within a preset time period. Based on the numerical characteristics of the two, the parameter correlation synchronization degree of the drill bit at each moment was determined. Analyze the numerical trend of the force variation of the drill bit within a preset time period, and combine it with the synchronization degree of the parameters to obtain the error ratio coefficient of the drill bit; based on the error ratio coefficient, obtain the control angle deviation of the well inclination angle and the high-side tool angle at each time. Angle control commands are generated based on the control angle deviation, and the rotational torque of the drill bit is adjusted according to a preset adjustment cycle to adjust the attitude of the drilling bit.
[0006] Preferably, the radial force on the drill bit is obtained by synthesizing the lateral force components of the short section section.
[0007] Preferably, the degree of force variation is specifically: Calculate the difference between the radial force of the drill bit at each moment and the radial force at the previous moment, and positively fuse the negative correlation mapping results of the difference with the radial force at each moment to obtain the force variation at each moment.
[0008] Preferably, the degree of angular change is specifically: Calculate the difference between the well inclination angle at each moment of the drill bit and the well inclination angle at the previous moment, and record it as the first difference; Calculate the difference between the high-side tool angle at each time point and the high-side tool angle at the previous time point, and record it as the second difference; multiply the second difference by the sine trigonometric function value of the well inclination angle at each time point, and then add it to the first difference to obtain the degree of angle change.
[0009] Preferably, determining the parameter correlation synchronization degree of the drill bit at each moment specifically involves: Obtain the similarity between the force change and angle change obtained at all times within a preset time period; count the number of numerical values with the same sign for the force change and angle change obtained at the same time within the preset time period; and use the product of the absolute value of the similarity and the number of numerical values as the parameter correlation synchronization degree of the drill bit at each time.
[0010] Preferably, the error proportionality coefficient for obtaining the drill bit is specifically: Linear fitting is performed on the stress variation obtained at all times within the preset time period. The product of the slope of the linear fitting line and the preset proportional coefficient is calculated. Half of the hyperbolic tangent of the product is multiplied by the product of the parameter correlation synchronization degree and added to the value 1 to obtain the error proportional coefficient of the drill bit.
[0011] Preferably, the control angle deviation of the well inclination angle at each moment is obtained by multiplying the difference between the well inclination angle at each moment and the preset well inclination angle at the current position of the drill bit by the error proportional coefficient.
[0012] Preferably, the control angle deviation of the high-side tool angle at each moment is specifically obtained by multiplying the difference between the high-side tool angle at each moment and the preset high-side tool angle at the current position of the drill bit by the error proportional coefficient.
[0013] According to another aspect of this application, a drilling bit attitude control device based on intelligent sensing is provided, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of any of the methods described above.
[0014] According to another aspect of this application, a drilling bit attitude control system based on intelligent sensing is provided, wherein the system stores a computer program that, when executed by a processor, implements any of the methods described above.
[0015] This application has at least the following beneficial effects: This application first acquires real-time triaxial acceleration and force data of the drill collar to calculate the drill bit's inclination angle, high-side tool angle, and radial force. It then further analyzes the changes in radial force, inclination angle, and high-side tool angle at each moment compared to the previous moment, thereby determining the degree of force and angle variation of the drill bit at each instant. This step accurately captures the dynamic response characteristics of the drill bit during drilling, providing highly timely basic data for subsequent attitude analysis.
[0016] Based on this, this application conducts a correlation analysis on the degree of force change and angle change at each moment within a preset time period, and combines the numerical characteristics of both to determine the parameter correlation synchronization degree of the drill bit at each moment. Through this mechanism, the differences between geologically homogeneous zones and abruptly changing zones during the drilling process can be effectively distinguished, significantly reducing trajectory deviations caused by alternating changes in strata hardness, and greatly improving the accuracy of drill bit attitude control decisions.
[0017] Furthermore, this application analyzes the numerical trend of force variation within a preset time period and, combined with the synchronization of the aforementioned parameters, obtains the error ratio coefficient of the drill bit, and accordingly acquires the control angle deviations of the well inclination angle and the high-side tool angle at each moment. This method can objectively reflect the true force state of the drill bit under complex working conditions, effectively optimize the input evaluation of the angle controller, and thus ensure the reliability of the attitude adjustment results.
[0018] Finally, this application generates angle control commands based on the control angle deviation and adjusts the drill bit's torque according to a preset adjustment cycle to achieve dynamic adjustment of the drill bit's attitude. By combining the error proportional coefficient and the deviation angle, it realizes iterative updating and closed-loop control of the drill bit's attitude, enabling it to flexibly adapt to the fluctuation characteristics of different geological layers. This significantly improves the drilling success rate while accelerating the response speed of drilling trajectory correction. Attached Figure Description
[0019] Figure 1 A flowchart illustrating the steps of the drilling bit attitude control method based on intelligent sensing provided in this application. Detailed Implementation
[0020] In the description of the embodiments in this application, the words "exemplary," "or," and "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of the words "exemplary," "or," and "for example" is intended to present the relevant concepts in a specific manner.
[0021] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this application's specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
[0022] It should also be noted that the terms "first" and "second" in this application and its accompanying drawings are used to distinguish similar objects, rather than to describe a specific order or sequence. The methods disclosed in the embodiments of this application or the methods shown in the flowcharts include one or more steps for implementing the method. Without departing from the scope of this application, the execution order of multiple steps can be interchanged, and some steps can also be deleted.
[0023] Please see Figure 1 The diagram illustrates a flowchart of a drilling bit attitude control method based on intelligent sensing according to an embodiment of this application. The method includes the following steps: Step 1: Collect the triaxial acceleration and triaxial force data of the drill collar at each moment in real time, and calculate the well inclination angle, high-side tool angle and radial force on the drill bit.
[0024] A triaxial accelerometer is embedded inside the drill collar, and a triaxial force sensor is installed within the force measurement section of the drill collar. The sensor collects data from the drill bit in real time at a frequency of 10Hz, which can be adjusted by the operator as needed. For the current moment, data from the previous minute is collected as the preset time period. The triaxial accelerometer first collects the triaxial coordinate acceleration at the horizontal and vertical planes, then obtains the triaxial gravitational acceleration through projection. By calculating the triaxial coordinate acceleration and gravitational acceleration, the drill bit's inclination angle and high-side tool angle are obtained. The radial force of the triaxial force is also measured. ,in, , The X-axis and Y-axis force components of the short section section are measured. Radial force can reflect the extrusion pressure of the formation on the drill bit. It should be noted that in this embodiment, the X-axis of the three-axis coordinate system is due north, the Y-axis is due east, and the Z-axis is vertically downward.
[0025] The collected wellbore inclination angle, high-side tool angle, and radial force are arranged in chronological order of acquisition time. The arranged data are then denoised using a mean filter. The denoised data are denoised as wellbore inclination angle sequence, high-side tool angle sequence, and radial force sequence, respectively. The calculation of the three-axis coordinate acceleration and gravitational acceleration, and the mean filtering, are well-known techniques, and the specific calculations will not be detailed here. In this embodiment, the sliding window width for the mean filtering is 3 seconds.
[0026] The drilling trajectory of the drill bit is obtained through the drilling drawings, and the predetermined well inclination angle and predetermined high-side tool angle are obtained at each position in the trajectory through the drilling trajectory.
[0027] Step 2: Analyze the changes in radial force, well inclination angle, and high-side tool angle of the drill bit at each moment compared to the previous moment to determine the degree of force and angle change of the drill bit at each moment.
[0028] When a drill bit advances, if the drilling direction needs to be adjusted, the inclination angle and high-side tool angle of the drill bit must be changed. This change in angle alters the pressure exerted by the geological formation on the drill bit, causing a synchronous change in the radial force measured on the drill bit. Since the adjustment of the drill bit angle corresponds to the change in the formation's reaction force, a higher consistency between the drill bit's advancing angle and the change in radial force indicates a smaller change in the geological structure, suggesting that no geological changes have occurred in the area where the drill bit is advancing, such as changes from rock to soil or soil to rock.
[0029] Since changes in drill bit attitude directly determine changes in various drill bit parameters, this application analyzes these parameter changes to obtain the state of the geological strata where the drill bit is located. This allows for effective adjustment of the drill bit's attitude, ensuring it follows a predetermined trajectory as closely as possible and minimizing deviations from the actual trajectory. Therefore, the degree of force and angle change of the drill bit at each moment is calculated to characterize the force and angle changes after attitude adjustment.
[0030]
[0031] In the formula, This represents the degree of change in force on the drill bit at time i. , Represents the i-th and (i-1)-th elements in the radial force sequence; This represents a preset first constant to prevent the denominator from being 0. In this embodiment, it is set to 0.1, and its dimensions are the same as those of the elements in the radial force sequence. , Let i and i-1 represent the i-th element and the (i-1)-th element in the drill bit inclination sequence, respectively. , Let i and i-1 represent the i-th and (i-1)-th elements in the drill bit high-side tool angle sequence, respectively. This represents the degree of angular change of the drill bit at time i, specifically the angle between the spatial displacement of the drill bit's pointing vector at the current time and the pointing vector at the previous time; sin represents the sine trigonometric function. The weight used to characterize the influence of changes in the high-side tool angle on the actual spatial orientation increases with increasing well inclination angle. In the vertical segment ( When the tool face rotation has a minimal impact on the radial force, this weighting factor can correct for the physical boundary. It should be noted that when... When the difference is such that the modulus is taken, then the difference is taken as a modulus. The supplementary angle, i.e., the difference adjustment, is... This ensures that the high-side tool face uses the shortest rotation path. , These are denoted as the first difference and the second difference, respectively.
[0032] In this embodiment, the difference between the radial force at the current moment and the radial force at the previous moment, compared with the radial force at the current moment, can characterize the change in the drill bit's state relative to the previous moment. The greater the change in force and angle, the greater the magnitude of the drill bit's attitude adjustment and the greater the change in the radial force on the drill bit, effectively characterizing the changing trend and dynamic response characteristics of the drill bit parameters.
[0033] Step 3: Perform correlation analysis on the degree of force change and angle change at each moment within the preset time period, and determine the parameter correlation synchronization degree of the drill bit at each moment by combining the numerical characteristics of the two.
[0034] A higher correlation between the stress variation and angle variation of the drill bit indicates that the drill bit is operating within the same geological stratum. In strata with similar and homogeneous geological conditions, the compression and stress states exerted on the drill bit by the formation remain relatively stable. However, a significant decrease in the correlation between stress and angle variation indicates that the drill bit is traversing a soft-hard interface, encountering localized hard rock, or entering a heterogeneous stratum, resulting in a sudden change in geological conditions. In this case, the compression force exerted on the drill bit by the formation exhibits irregular fluctuations, and the radial force and angle variations are no longer synchronized.
[0035] Based on the force and angle changes obtained in the previous step, arrange them in chronological order according to their corresponding moments to obtain the force change sequence and angle change sequence. If the data in the two sequences have the same sign at the same moment, it indicates that the parameter data are synchronous, and the force change is partly or entirely caused by the angle change. Count the number of identical signs at the same moment in the force change sequence and angle change sequence, denoted as n. This can characterize the length of the synchronous change of the drill bit; the larger the value, the higher the synchronization state of the drill bit parameters.
[0036] Furthermore, the parameter correlation synchronization degree of the drill bit is calculated to characterize the synchronization and correlation of drill bit parameter changes. The specific formula is as follows:
[0037] In the formula, This indicates the degree of synchronization of drill bit parameters; Indicates a sequence of force changes; Represents a sequence of angle changes; This indicates the number of elements in the force change sequence; The correlation coefficient is represented by , and in this embodiment, the Pearson correlation coefficient is used. This indicates the sign of the absolute value. The correlation coefficient is one of the factors considered. The calculation window length is consistent with the preset time period length at the current moment, and each The update is performed once per second, and in this embodiment, M is set to 10.
[0038] In this embodiment, the degree of synchronization of data changes characterizes the geological change state of the drill bit. The parameter correlation synchronization degree of the drill bit... The larger the value, the more uniform the current geological conditions, and the more linear the dynamic response of the formation reaction force to the drill bit attitude adjustment. Adjusting the error ratio coefficient The aim is to stabilize local geological conditions. When the geological conditions are large, it provides more accurate correction gain; when the geological conditions change abruptly ( When significantly reduced, by adjusting Reduce the weight of blind corrections to prevent the drill bit from oscillating violently or overshooting in heterogeneous formations.
[0039] Step 4: Analyze the numerical trend of the force variation of the drill bit within a preset time period, and obtain the error ratio coefficient of the drill bit by combining the parameter correlation synchronization degree; based on the error ratio coefficient, obtain the control angle deviation of the well inclination angle and the high-side tool angle at each time.
[0040] If the trend of element changes in the stress change sequence of the drill bit is downward, it indicates that the geology where the drill bit is located is transitioning from hard geology (such as rock) to softer geology (such as soil). The constraint and squeezing force on the drill bit is weakened, and the drill bit can cut into the formation more easily under the same drilling pressure. The deviation of the geology from the drill bit angle is smaller. If the trend is upward, it indicates that the geology that the drill bit needs to explore is becoming harder and harder. The greater the influence of the geology on the drill bit, the larger the angle is needed to ensure that the deviation of the drilling trajectory from the predetermined trajectory is smaller.
[0041] Therefore, the force change sequence is used as the input of the linear least squares method, where the independent variable is the index of the element in the sequence, the dependent variable is the value of the element in the sequence, and the output of the algorithm is the fitted line of the force change sequence. The slope of the fitted line is obtained to characterize the changing trend of the force change sequence. The larger the absolute value of the slope, the stronger the changing trend of the elements in the force change sequence.
[0042] Furthermore, the control angle error of the drill bit is calculated, which characterizes the angle error that needs to be input when controlling the drill bit angle. The specific formula is as follows:
[0043]
[0044] In the formula, This represents the error proportionality coefficient of the drill bit; It represents the slope of the straight line fitted to the force change sequence; Represents the hyperbolic tangent function; This represents a preset scaling factor, which is set to 10 in this embodiment. 3 ; This indicates the control angle error of the well inclination angle at the current moment; Indicates the inclination angle at the current moment; The predetermined well inclination angle indicates the current position of the drill bit; This indicates the control angle error of the upper edge tool angle at the current moment; Indicates the high-side tool angle at the current moment; This indicates the predetermined high-side tool angle representing the current position of the drill bit.
[0045] It should be understood that when the drill bit enters a harder formation ( And it has good synchronization. (High) If the value is significantly greater than 1, the correction force is automatically increased to overcome the high resistance of hard formations; when the drill bit enters softer formations ( And it has good synchronization. (High) If the value is less than 1, the system automatically reduces the convergence control intensity to prevent trajectory serpentination due to excessive sensitivity in soft strata; when geological changes cause a decrease in synchronization ( When it approaches 0, regardless of the trend, All values return to 1, and the system maintains basic feedback control to avoid blind and excessive compensation caused by geological anomalies.
[0046] In this embodiment, by considering the trend of force changes on the drill bit and combining the synchronization degree of the drill bit parameters, an error proportionality coefficient of the drill bit is obtained. This coefficient is used to characterize the adjustment intensity of the difference between the actual angle and the predetermined angle of the drill bit. The larger the value, the greater the adjustment intensity of the drill bit angle. The product of the error proportionality coefficient and the deviation angle between the actual angle and the predetermined angle of the drill bit represents the angle that should be adjusted to the drill bit at the current moment.
[0047] Step 5: Generate angle control commands based on the control angle deviation, adjust the drill bit's rotational torque according to the preset adjustment cycle, and adjust the drill bit's attitude.
[0048] The control angle error obtained at the moment preceding each adjustment is used as the input to the angle controller. The angle controller generates a corresponding control signal, which, after modulating the PWM pulse width, enters the control drive module to control the armature current of the lower turbine motor, thereby adjusting the drill bit's torque and ensuring that the drill bit's attitude reaches the predetermined well inclination angle and high-side tool angle. Attitude adjustment is performed every M seconds, where M is set to 10 in this embodiment. The PWM pulse is a known technique, and its specific calculation steps will not be detailed here.
[0049] Based on the same concept as the method embodiments of this application, a drilling bit attitude control device based on intelligent sensing is provided, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any of the methods described above.
[0050] Based on the same concept as the method embodiments of this application, a drilling bit attitude control system based on intelligent perception is provided. The system stores a computer program, which, when executed by a processor, implements any of the methods described above.
[0051] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of the systems, methods, and computer program products according to embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different blocks may also occur in a different order than disclosed in the description; sometimes there is no specific order between different operations or steps. For example, two consecutive operations or steps may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. Each block in a block diagram and / or flowchart, and combinations of blocks in a block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.
[0052] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A drilling bit attitude control method based on intelligent sensing, characterized in that, The method includes the following steps: The triaxial acceleration and triaxial force data of the drill collar are collected in real time at various moments, and the well inclination angle, high-side tool angle and radial force on the drill bit are calculated. Analyze the changes in radial force, well inclination angle, and high-side tool angle of the drill bit at each moment compared to the previous moment to determine the degree of force and angle change of the drill bit at each moment. Correlation analysis was performed on the degree of force change and the degree of angle change at each moment within a preset time period. Based on the numerical characteristics of the two, the parameter correlation synchronization degree of the drill bit at each moment was determined. Analyze the numerical trend of the force variation of the drill bit within a preset time period, and combine it with the synchronization degree of the parameters to obtain the error ratio coefficient of the drill bit; based on the error ratio coefficient, obtain the control angle deviation of the well inclination angle and the high-side tool angle at each time. Angle control commands are generated based on the control angle deviation, and the rotational torque of the drill bit is adjusted according to a preset adjustment cycle to adjust the attitude of the drilling bit. The determination of the parameter correlation synchronization degree of the drill bit at each moment is specifically as follows: Obtain the correlation coefficient between the force change and angle change obtained at all times within a preset time period; count the number of values with the same sign for the force change and angle change obtained at the same time within the preset time period; divide the product of the absolute value of the correlation coefficient and the number of values by the total number of force changes obtained at all times within the preset time period and use the result as the parameter correlation synchronization degree of the drill bit at each time. The error proportionality coefficient of the drill bit is specifically as follows: Linear fitting is performed on the force variation obtained at all times within the preset time period. The product of the slope of the linear fitting line and the preset proportional coefficient is calculated. The hyperbolic tangent of the product is added to half of the product of the parameter correlation synchronization degree and the number 1 to obtain the error proportional coefficient of the drill bit.
2. The drilling bit attitude control method based on intelligent sensing as described in claim 1, characterized in that, The radial force on the drill bit is obtained by synthesizing the lateral force components of the cross section of the drill collar force measurement sub.
3. The drilling bit attitude control method based on intelligent sensing as described in claim 1, characterized in that, The degree of force variation is specifically as follows: Calculate the difference between the radial force of the drill bit at each moment and the radial force at the previous moment, and positively fuse the negative correlation mapping results of the difference with the radial force at each moment to obtain the force variation at each moment.
4. The drilling bit attitude control method based on intelligent sensing as described in claim 1, characterized in that, The angle change is specifically as follows: Calculate the difference between the well inclination angle at each moment of the drill bit and the well inclination angle at the previous moment, and record it as the first difference; Calculate the difference between the high-side tool angle of the drill bit at each moment and the high-side tool angle at the previous moment, and record it as the second difference; multiply the second difference by the sine trigonometric function value of the well inclination angle at each moment, and then add it to the first difference to obtain the degree of angle change.
5. The drilling bit attitude control method based on intelligent sensing as described in claim 1, characterized in that, The control angle deviation of the well inclination angle at each moment is specifically obtained by multiplying the difference between the well inclination angle at each moment and the preset well inclination angle at the current position of the drill bit by the error proportional coefficient.
6. The drilling bit attitude control method based on intelligent sensing as described in claim 1, characterized in that, The control angle deviation of the high-side tool angle at each moment is specifically obtained by multiplying the difference between the high-side tool angle at each moment and the preset high-side tool angle at the current position of the drill bit by the error proportional coefficient.
7. A drilling bit attitude control device based on intelligent sensing, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.
8. A drilling bit attitude control system based on intelligent sensing, wherein the system stores a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.
Citation Information
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