Flotation machine fault diagnosis method and system based on periodic impact index

Abstract

The invention provides a flotation machine fault diagnosis method and system based on a periodic impact index. The method comprises the following steps of vibration signal preprocessing and Hilbert envelope demodulation, envelope spectrum local maximum value searching and sorting, periodic impact detection based on a frequency multiplication relation, periodic impact index calculation and fault judgment. According to the method, key information is extracted through vibration signal preprocessing and Hilbert envelope demodulation, periodic impact is detected based on a frequency multiplication relation through envelope spectrum local maximum search sorting, and finally a PII index is calculated to judge a fault. The method can accurately identify periodic impact components, does not need a large number of fault samples, can quantitatively evaluate the severity of faults, is high in anti-interference capability, can carry out real-time online diagnosis, effectively improves the fault diagnosis accuracy and engineering practicability of the flotation machine, reduces non-planned shutdown, and reduces the maintenance cost.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology for mineral processing equipment, and in particular to a method and system for fault diagnosis of flotation machines based on periodic impact indices. Background Technology

[0002] Flotation machines, as core equipment in the mineral processing industry for separating minerals based on differences in the physicochemical properties of their surfaces, are typically composed of single or multiple cells connected in series in the mineral processing flow, forming a flotation system that encompasses roughing, scavenging, and cleaning stages. They mainly consist of the flotation tank, agitation device, aeration device, and motor drive system, with the spindle-bearing system being the critical power transmission component. During long-term operation, due to factors such as slurry corrosion, mechanical wear, and fatigue damage, critical components of the flotation machine, such as bearings and gears, are prone to failure. If these failures are not detected and addressed promptly, they can range from affecting mineral processing indicators to causing equipment downtime and significant economic losses in mineral processing production. Therefore, developing efficient and reliable flotation machine fault diagnosis technology has significant engineering application value.

[0003] Fault diagnosis technology for mechanical equipment has developed over decades, resulting in various technical approaches. Traditional signal processing methods extract fault features based on time-domain, frequency-domain, and time-frequency-domain analysis. Commonly used time-domain features include root mean square (RMS) values ​​and peak values, while frequency-domain features include band energy. Time-frequency-domain features are typically extracted using methods such as EMD and wavelet transform. However, these traditional indicators have significant limitations. For example, while kurtosis values ​​can reflect the impulse component in a signal, they are easily affected by various excitation sources or background noise, leading to misdiagnosis or missed diagnosis. In recent years, fault diagnosis models based on deep learning have made significant progress. Models such as convolutional neural networks (CNN), recurrent neural networks (RNN), and autoencoders (AE) have achieved high diagnostic accuracy under laboratory conditions. However, these methods face many challenges in practical applications of flotation machine fault diagnosis, such as the difficulty in obtaining training samples. As flotation machines are key production equipment, it is impossible to artificially create faults to collect data, and actual fault samples are extremely scarce. The operating conditions are complex and variable, with the load, speed, pulp concentration, and other operating parameters of the flotation machine frequently changing, leading to non-stationarity of vibration signals. The model has poor generalization ability, and models trained based on limited samples are difficult to adapt to the complex operating conditions in actual production. The interpretability is insufficient, as the "black box" nature of deep learning models makes it difficult for maintenance personnel to understand the basis of the diagnostic results.

[0004] In summary, the core technical challenges in flotation machine fault diagnosis include: how to accurately extract fault feature information from complex vibration signals; how to design diagnostic indicators that are sensitive to periodic impacts and have strong anti-interference capabilities; how to achieve real-time online diagnosis without requiring a large number of fault samples; and how to establish a quantitative relationship between fault severity and diagnostic indicators. Summary of the Invention

[0005] The object of the present invention is to provide a fault diagnosis method and system for a flotation machine based on periodic shock indicators, aiming to solve the problems in the fault diagnosis of flotation machines, such as the difficulty in accurately extracting fault characteristic information, the weak anti-interference ability of diagnosis indicators, the need for a large number of fault samples, and the inability to establish a quantitative relationship between the fault severity and diagnosis indicators.

[0006] According to an object of the present invention, the present invention provides a fault diagnosis method for a flotation machine based on periodic shock indicators, including the following steps: S1: Preprocessing of vibration signals and Hilbert envelope demodulation Collect the vibration signals during the operation of the flotation machine, perform Hilbert transform and envelope demodulation processing on the vibration signals to obtain the time-domain envelope signal, and perform FFT transform on the time-domain envelope signal to obtain the envelope spectrum; S2: Searching and sorting of local maxima of the envelope spectrum Search for local maximum points in the envelope spectrum, sort them from largest to smallest in amplitude, and select the first n local maximum points to form a candidate point set P = {(f1,A1), (f2,A2),..., (f n ,A n )}, where fi is the frequency and Ai is the corresponding amplitude, and Ai≥Aj (i<j); S3: Detection of periodic shocks based on frequency multiple relationship Select the first m points from the candidate point set P as candidate fundamental frequencies, where m<n; for each candidate fundamental frequency fc, detect whether its first k harmonics exist in the candidate point set P, count the number of times the harmonics of each candidate fundamental frequency appear in the set P, and select the one with the most occurrences as the fundamental frequency of the periodic shock, and record the maximum intersection number as x; S4: Calculation of periodic shock indicators and fault determination Calculate the periodic shock indicator PII according to the maximum intersection number x. When x is greater than or equal to the preset threshold t, calculate PII = RMS({A_base, A_2f, A_3f,..., A_xf}), where A_base is the fundamental frequency amplitude and A_if is the amplitude of the i-th harmonic; when x is less than the preset threshold t, set PII = 0; determine the fault state of the flotation machine according to the PII value.

[0007] Furthermore, in step S1, the Hilbert transform and envelope demodulation processing specifically includes: Perform Hilbert transform on the original vibration signal to obtain ; Utilize the original vibration signal and transformation result Construct an analytical signal ; Calculate the time-domain envelope signal .

[0008] Furthermore, in step S2, the method for searching for local maximum points is as follows: Set the search window width w. For the frequency point fi in the envelope spectrum S(f), if S(fi) > S(fj), where fj ∈ [fi - w / 2, fi + w / 2], then fi is a local maximum point.

[0009] Furthermore, in step S2, the value range of the search window width w is 0.5% to 2% of the sampling frequency.

[0010] Furthermore, in step S3, the method for detecting the existence of harmonics is as follows: For the candidate fundamental frequency fc, for i = 2, 3,..., k, check whether there exists (fj, Aj) ∈ P such that |fj - i×fc| < δ, where δ is the frequency tolerance; the value range of the frequency tolerance δ is 1% to 3% of the candidate fundamental frequency fc.

[0011] Furthermore, the value range of the parameters is as follows: n takes values from 20 to 50; m takes values from 3 to 5; k takes values from 4 to 8; t takes values from 3 to 4.

[0012] Furthermore, in step S4, the standard for determining the fault status according to the PII value is as follows: When PII = 0, it is determined that the device is normal;​​​​​​​​​​​​​​​​​​​The feature extraction module is used to extract local maxima from the envelope spectrum and detect periodic shocks based on frequency harmonic relationships; The fault diagnosis module is used to calculate the periodic impact index (PII) and determine the fault status based on the PII value. The system implements the flotation machine fault diagnosis method based on the periodic impact index.

[0015] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described flotation machine fault diagnosis method based on periodic impact indicators.

[0016] The technical solution of this invention. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the system structure according to an embodiment of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0021] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0022] Example 1 like Figure 1 As shown, a fault diagnosis method for flotation machines based on periodic impact index is proposed. This method is based on the understanding that when rotating parts such as bearings and gears of a flotation machine suffer local damage, they will generate periodic impact vibrations during rotation. The frequency of this periodic impact is related to the rotation frequency of the parts and its fault characteristic frequency, and is expressed as the fundamental frequency and its harmonic components in the spectrum. The specific technical solution is as follows: 1. Vibration signal preprocessing and Hilbert envelope demodulation: For the original vibration signal Perform the Hilbert transform to obtain the transform result. The transformation formula is shown in equation (1); Equation (1); In equation (1), It can be interpreted as the input signal The output of a linear time-invariant system is given by the impulse response of that system. ; Then, using the original vibration signal Combining the transformation results Constructing analytic signals in the complex field As shown in equation (2); Equation (2); The time-domain envelope signal is obtained by using the real and imaginary parts of the analytic signal. As shown in equation (3); Equation (3); Finally, the obtained time-domain envelope signal Perform an FFT transform to obtain the envelope spectrum.

[0023] Generally, if there are periodic vibration shock components in the original signal, the frequencies corresponding to the shocks (the reciprocals of the periods) will be relatively obvious in the envelope spectrum, and there will be integer multiple harmonics.

[0024] The physical meaning of envelope demodulation is that when there are periodic shocks caused by faults in the vibration signal, these shocks will amplitude-modulate the carrier signals (such as gear meshing frequency, bearing passing frequency, etc.). Hilbert envelope demodulation can demodulate this amplitude-modulation information, making the frequency components of the periodic shocks clearly appear in the envelope spectrum.

[0025] 2. Searching and sorting local maxima of the envelope spectrum: (1) Searching for local maxima Set the search window width w (it is recommended to take 0.5% - 2% of the sampling frequency), and perform a local maximum search on the envelope spectrum S(f). For the frequency point fi, if it satisfies: S(fi) > S(fj), ∀fj ∈ [fi - w / 2, fi + w / 2], then fi is a local maximum point; (2) Amplitude sorting Sort all local maximum points in descending order of amplitude, and take the first n points to form a set: P = {(f1,A1), (f2,A2),..., (f n ,A n )}; where, A i ≥ A j (i < j), n is an algorithm hyperparameter, and it is recommended to take 20 - 50.

[0026] 3. Detection of periodic shocks based on frequency multiple relationships: (1) Traversing candidate fundamental frequencies Traverse the first m points (m < n, it is recommended to take m as 3 - 5) in the set P, and take the frequency of each point as a candidate fundamental frequency; (2) Harmonic detection For the candidate fundamental frequency fc, detect whether its first k harmonics (it is recommended to take k as 4 - 8) exist in the set P: That is, for i = 2, 3,..., k, check whether there exists (fj,Aj) ∈ P such that |fj - i×fc| < δ; where, δ is the frequency tolerance, and it is recommended to take 1% - 3% of fc; (3) Calculating the number of intersections Count the number of times the harmonics of each candidate fundamental frequency appear in the set P, and select the one with the most occurrences as the fundamental frequency of the periodic shock, and record the maximum number of intersections as x.

[0027] 4. Calculation of Periodic Impact Index and Fault Judgment: (1) Index Calculation If x ≥ t (t is the judgment threshold, recommended to take 3 - 4), it indicates that there is an obvious periodic impact, then calculate the periodic impact index: PII = RMS ({A _ base, A _ 2f, A _ 3f,..., A _ xf}); Among them, RMS represents the calculation of the effective value, A_base is the amplitude of the fundamental frequency, and A_if is the amplitude of the i-th harmonic; If x < t, it is considered that there is no obvious periodic impact, and set PII = 0; (2) Fault Judgment Judge the fault status according to the value of PII: When PII = 0, the device is normal; When 0 < PII < 0.5, it is the initial stage of the fault, and close attention is required; When 0.5 ≤ PII < 2.0, it is the development stage of the fault, and planned maintenance is recommended; When PII ≥ 2.0, the fault is serious, and it is recommended to stop the machine for repair immediately.

[0028] As Figure 2 shown, an embodiment of the present invention also provides a flotation machine fault diagnosis system based on a periodic impact index, which is used to execute the above-mentioned flotation machine fault diagnosis method based on a periodic impact index. The system includes: A vibration signal acquisition module, which is used to acquire the vibration signal during the operation of the flotation machine; A signal processing module, which is used to perform Hilbert envelope demodulation on the vibration signal to obtain an envelope spectrum; A feature extraction module, which is used to extract local maximum points from the envelope spectrum and detect periodic impacts based on the frequency multiple relationship; A fault diagnosis module, which is used to calculate the periodic impact index PII and judge the fault status according to the value of PII.

[0029] An embodiment of the present invention also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it realizes the above-mentioned flotation machine fault diagnosis method based on a periodic impact index.

[0030] Embodiment 2 As Figure 1As shown in the figure, this embodiment provides a flotation machine fault diagnosis method based on periodic impact index, and the specific steps are as follows: Step 1: Vibration signal preprocessing and Hilbert envelope demodulation The original vibration signal x(t) during the operation of the flotation machine is collected and subjected to Hilbert transformation. The transformation formula is shown in equation (1): Equation (1); In equation (1), It can be interpreted as the input signal The output of a linear time-invariant system is given by the impulse response of that system. ; Then, using the original vibration signal Combining the transformation results Constructing analytic signals in the complex field As shown in equation (2): Equation (2); The time-domain envelope signal is obtained by using the real and imaginary parts of the analytic signal. As shown in equation (3): Equation (3); Finally, the obtained time-domain envelope signal Perform an FFT transform to obtain the envelope spectrum.

[0031] For example, when a bearing in a flotation machine experiences a minor pitting fault, the original vibration signal will contain a periodic impact component caused by the fault. After Hilbert envelope demodulation, the frequency and harmonic components corresponding to the periodic impact will be clearly displayed in the envelope spectrum.

[0032] Step 2: Search and sorting of local maxima in the envelope spectrum Set the search window width w to 1% of the sampling frequency, and perform a local maximum search on the envelope spectrum S(f). For a frequency point fi, if S(fi)>S(fj) and ∀fj ∈ [fi-w / 2, fi+w / 2], then fi is a local maximum point. Sort all local maxima points in descending order of magnitude, and select the top 30 points to form a set P = {(f1,A1),(f2,A2), ...,(f...}. 30 A 30 )}, where A i ≥ A j (i <j)。

[0033] Step 3: Periodic impact detection based on frequency harmonic relationships Traverse the top 4 points in set P, and use the frequency of each point as the candidate fundamental frequency. For each candidate fundamental frequency fc, detect whether its first 6 harmonics exist in set P, where the frequency tolerance δ is taken as 2% of fc, that is, for i = 2, 3,..., 6, check whether there exists (fj, Aj) ∈ P such that |fj - i×fc| < 0.02fc.

[0034] Count the number of occurrences of the harmonics of each candidate fundamental frequency in set P, and select the one with the most occurrences as the fundamental frequency of the periodic shock, and record the maximum number of intersections as x.

[0035] Step 4: Calculation of periodic shock index and fault determination Set the determination threshold t to 3. If x ≥ 3, it means there is an obvious periodic shock, then calculate the periodic shock index PII = RMS ({A_base, A_2f, A_3f,..., A_xf}), where RMS represents the calculation of the effective value, A_base is the fundamental frequency amplitude, and A_if is the amplitude of the i-th harmonic; if x < 3, it is considered that there is no obvious periodic shock, and set PII = 0.

[0036] Determine the fault status according to the value of PII: when PII = 0, determine that the equipment is normal; when 0 < PII < 0.5, it is determined as the initial stage of the fault and needs to be closely monitored; when 0.5 ≤ PII < 2.0, it is determined as the development stage of the fault, and planned maintenance is recommended; when PII ≥ 2.0, it is determined as a serious fault, and immediate shutdown for maintenance is recommended.

[0037] At the same time, judge the fault type by analyzing the magnitude of the fundamental frequency. When the fundamental frequency matches the bearing characteristic frequency, it is judged as a bearing fault; when the fundamental frequency matches the gear characteristic frequency, it is judged as a gear fault.

[0038] As Figure 2 shown, this embodiment also provides a flotation machine fault diagnosis system based on the periodic shock index, including a vibration signal acquisition module, a signal processing module, a feature extraction module and a fault diagnosis module. This system executes the above-mentioned flotation machine fault diagnosis method based on the periodic shock index.

[0039] This embodiment also provides a computer-readable storage medium. This storage medium stores a computer program, and when the computer program is executed by a processor, it implements the above-mentioned flotation machine fault diagnosis method based on the periodic shock index. The computer-readable storage medium is a hard disk, a flash memory, an optical disc or a USB flash drive.

[0040] Compared with the prior art, the present invention has the following beneficial effects: High diagnostic accuracy: High sensitivity in early-stage fault detection, capable of issuing early warnings in the early stages of faults (minor pitting of bearings, initial wear of gears); accurate fault type identification, able to determine whether it is a bearing fault or a gear fault by analyzing the fundamental frequency; quantitative assessment of fault severity, with the PII index showing a positive correlation with the severity of the fault.

[0041] Highly practical for engineering applications: It has strong real-time performance, low computational complexity of the entire algorithm, and can achieve millisecond-level response on ordinary industrial control computers; it has simple parameter settings, and the algorithm parameters have clear physical meanings, making it easy for field engineers to understand and adjust; it has good compatibility, can be integrated into existing equipment monitoring systems, and supports a variety of data acquisition hardware.

[0042] Significant economic benefits: Reduces unplanned downtime by transforming unplanned flotation machine downtime into planned maintenance through early fault warning; extends equipment lifespan by timely detection and handling of early-stage flotation machine faults, preventing the faults from escalating; reduces maintenance costs by accurately locating the faulty part of the flotation machine, reducing maintenance time and spare parts consumption.

[0043] Key technological innovations include: targeted fault feature extraction, specifically designed for the periodic impact characteristics generated by faults in the rotating components of flotation machines, and a detection algorithm based on envelope spectrum harmonic relationships, which is more targeted than general statistical indicators; a multi-parameter adaptive algorithm framework, which can adapt to the diagnostic needs of different flotation machine models and different fault types by setting multiple adjustable parameters such as n, m, k, and t, demonstrating good flexibility; strong anti-interference ability, with a detection mechanism based on frequency harmonic relationships that can effectively distinguish between periodic and random impacts, reducing the false positive rate; and no need for training samples, as the entire diagnostic process is based on signal processing and feature extraction, without relying on historical fault data, solving the problem of scarce fault samples in industrial fields.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features; and these 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 the present invention.

Claims

1. A flotation machine fault diagnosis method based on periodic impact index, characterized in that, It includes the following steps: S1: Vibration signal preprocessing and Hilbert envelope demodulation Collect the vibration signal during the operation of the flotation machine, perform Hilbert transform and envelope demodulation processing on the vibration signal to obtain the time-domain envelope signal, and perform FFT transform on the time-domain envelope signal to obtain the envelope spectrum; S2: Search and sort the local maximum values of the envelope spectrum Local maxima are searched in the envelope spectrum, and the points are sorted from largest to smallest amplitude. The top n local maxima are selected to form a candidate point set P = {(f1,A1), (f2,A2), ..., (f...}. n A n )}, where fi is the frequency, Ai is the corresponding amplitude, and Ai≥Aj(i <j); S3: Periodic impact detection based on frequency multiple relationship Select the top m points from the candidate point set P as candidate fundamental frequencies, where m < n; for each candidate fundamental frequency fc, detect whether its first k harmonics exist in the candidate point set P, count the number of occurrences of the harmonics of each candidate fundamental frequency in the set P, and select the one with the most occurrences as the fundamental frequency of the periodic impact, and record the maximum intersection number as x; S4: Calculation of periodic impact index and fault determination Calculate the periodic impact index PII according to the maximum intersection number x. When x is greater than or equal to the preset threshold t, calculate PII = RMS({A_base, A_2f, A_3f,..., A_xf}), where A_base is the fundamental frequency amplitude and A_if is the amplitude of the i-th harmonic; when x is less than the preset threshold t, set PII = 0; determine the fault state of the flotation machine according to the PII value.

2. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, In step S1, the Hilbert transform and envelope demodulation processing specifically includes: For the original vibration signal Perform Hilbert transform to obtain ; Using the original vibration signal and transformation results Constructing analytic signals ; Calculate the time-domain envelope signal .

3. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, In step S2, the method for searching local maximum points is: Set the search window width w. For the frequency point fi in the envelope spectrum S(f), if S(fi)>S(fj), where fj ∈ [fi - w / 2, fi + w / 2], then fi is the local maximum point.

4. The flotation machine fault diagnosis method based on periodic impact index according to claim 3, characterized in that, In step S2, the value range of the search window width w is 0.5% - 2% of the sampling frequency.

5. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, In step S3, the method for detecting the existence of harmonics is: For the candidate fundamental frequency fc, for i = 2, 3,..., k, check whether there exists (fj, Aj) ∈ P such that |fj - i×fc| < δ, where δ is the frequency tolerance; the value range of the frequency tolerance δ is 1% - 3% of the candidate fundamental frequency fc.

6. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, The value ranges of the parameters are: n takes values from 20 to 50; m takes values from 3 to 5; k takes values from 4 to 8; t takes values from 3 to 4.

7. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, In step S4, the standard for determining the fault state according to the PII value is: When PII = 0, it is determined that the equipment is normal; When 0 < PII < 0.5, it is determined as the initial stage of the fault; When 0.5 ≤ PII < 2.0, it is determined as the development stage of the fault; When PII ≥ 2.0, it is determined as a serious fault.

8. The flotation machine fault diagnosis method based on periodic impact index according to claim 1, characterized in that, It further includes a fault type judgment step: Judge the fault type according to the size of the detected periodic impact fundamental frequency. When the fundamental frequency matches the bearing characteristic frequency, it is determined as a bearing fault. When the fundamental frequency matches the gear characteristic frequency, it is determined as a gear fault.

9. A fault diagnosis system for performing the flotation machine fault diagnosis method based on periodic impact index as described in any one of claims 1-8, characterized in that, It includes: A vibration signal acquisition module for collecting the vibration signal during the operation of the flotation machine; A signal processing module for performing Hilbert envelope demodulation on the vibration signal to obtain the envelope spectrum; A feature extraction module for extracting local maximum points from the envelope spectrum and detecting periodic impacts based on the frequency multiple relationship The fault diagnosis module is used to calculate the periodic impact index (PII) and determine the fault status based on the PII value.

10. A storage medium for storing computer-executable instructions, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 8.

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