Weighted evaluation method for detecting periodicity in multi-period time series and storage medium

Abstract

The application is a kind of weighted evaluation detection multi-period time sequence period method and storage medium, the method includes calculating and determining multiple candidate period sequences by periodogram and autocorrelation function; then weighted evaluation is carried out on each candidate period area to determine the detection period; finally, the period detection of multi-period time sequence is realized. On the basis of using periodogram and autocorrelation function, the peak value characteristics of periodogram and autocorrelation function are used to screen and narrow the candidate period area. Since the candidate period is processed in blocks, the whole periodogram or autocorrelation diagram does not need to be calculated, thereby reducing the period detection time complexity and calculation time. In addition, the period is detected by using the weighted evaluation method, the characteristics of periodogram and autocorrelation coefficient are comprehensively combined, the best period in the candidate area is selected, the robustness of the detected period is ensured, and the influence of spectrum leakage and noise on the detection result is minimized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of digital signal processing, and particularly relates to a method for detecting multiple periodic time series periods by weighted evaluation and a storage medium. BACKGROUND

[0002] There are generally two kinds of traditional time series period detection algorithms, one is a frequency domain method of converting time series from time domain to frequency domain by periodogram to detect the period, and the other is a time domain method of detecting the period by the peak value of autocorrelation function (ACF). However, the detection result of the periodogram alone will have certain errors from the real period due to the influence of spectral leakage and noise; the autocorrelation function alone will also lead to the detection of an incorrect period or missed detection due to the influence of detecting integer multiples of the real period and noise. The current time series period detection method combines periodogram and autocorrelation function for period detection, and the evaluation method based on clustering or local maximum value can be used to detect a single period of time series. However, for a multiple period sequence, the existing method is time-consuming or is specific to economic, financial and other scenes, and there is no good general, fast and accurate multiple period time series period detection algorithm at present. For example, the wavelet transform-based period detection method in the Robust-period method can realize the detection of multiple periods. It decomposes a single time series into multiple time series of different frequencies, and then uses periodogram and autocorrelation function to detect the period of each time series. However, for the numerous time series decomposed, some may have no period, and the period detection on them will cause invalid calculation. The method detects the period of each time series, which is time-consuming and cannot guarantee the real-time performance of period detection in practice. SUMMARY

[0003] The method for detecting multiple periodic time series periods by weighted evaluation and the storage medium can solve the above technical problems

[0004] To achieve the above purpose, the present application adopts the following technical solutions:

[0005] A method for detecting multiple periodic time series periods by weighted evaluation, comprising the following steps: calculating and determining multiple candidate period sequences by periodogram and autocorrelation function;

[0006] Then, weighted evaluation is performed on each candidate period region to determine the detected period;

[0007] Finally, the period decomposition of the multiple periodic time series is realized.

[0008] Further, the calculation and determination of multiple candidate period regions by periodogram and autocorrelation function are as follows:

[0009] The time series is firstly subjected to a discrete Fourier transform, and then a periodogram is obtained by dividing the square of the discrete Fourier transform by the number of sequences, and an autocorrelation function is obtained by inverse discrete Fourier transform of the product of the discrete Fourier transform and the conjugate of the discrete Fourier transform.

[0010] Further, the multiple candidate period regions are determined according to the periodogram and the autocorrelation function, and the determination of the multiple candidate period regions according to the periodogram and the autocorrelation function obtained in the first step comprises:

[0011] In the periodogram, the region lower than 1 / 5 of the maximum peak value of the periodogram is directly discarded, and the region higher than 1 / 5 of the maximum peak value of the periodogram is the candidate period region, 1 / 5 is an empirical value, and the recommended value range is [1 / 20, 1 / 2], and then the slope of the boundary of each candidate period region in the autocorrelation function is calculated, wherein the region with a left boundary slope less than 0 and a right boundary slope greater than 0 is the valley bottom, and the region with the valley bottom in the autocorrelation function is discarded; in each of the remaining candidate period regions, 1 / 2 of the peak value of the autocorrelation function in the region is calculated, and the candidate period lower than the value is discarded, and finally the processed candidate period region is obtained.

[0012] Further, the detection period is determined by performing a weighted evaluation on each of the candidate period regions.

[0013] In each of the processed candidate period regions, each period is first sorted in descending order according to the power size of the candidate period in the periodogram, and then sorted according to the size of the autocorrelation coefficient in the autocorrelation function.

[0014] A best candidate period is obtained for each weighted evaluation of the candidate period region, and finally all the best candidate periods are obtained, and the period detection task is completed.

[0015] Further, the weighted evaluation is performed on the sorting according to the periodogram and the autocorrelation diagram, and the final score equation is:

[0016]

[0017] wherein, Rank periodogram is the ranking of the periodogram in the candidate period region according to the energy, Rank acf is the ranking of the autocorrelation coefficient in the autocorrelation diagram in the candidate period region, and r is a weight coefficient, and the value range is [0, +∞).

[0018] Further, the periodogram and the autocorrelation function of the multiple period time series signal are calculated as follows:

[0019] First, the time series x(n) is subjected to a discrete Fourier transform (DFT) to obtain X(k)

[0020]

[0021] Then, a periodogram P(k) is obtained according to the result of the discrete Fourier transform

[0022]

[0023] The autocorrelation function ACF(τ) is calculated from the result of the discrete Fourier transform:

[0024] ACF(τ) = IDFT[X(k) * X(k) * ]

[0025] where IDFT represents an inverse discrete Fourier transform, X(k) * represents the conjugate of X(k), and the periodogram and the autocorrelation function of the multi-period time series are obtained.

[0026] In another aspect, the application further discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above method.

[0027] According to the above technical solution, the method for detecting the periods of a multi-period time series by weighted evaluation in the application, in the case that the actual time series contains multiple periods, combines the periodogram and the autocorrelation function, and proposes a method for detecting multiple periods by weighted evaluation to realize the period detection of the multi-period time series in sequence and ensure the real-time performance and accuracy of the period detection.

[0028] The application has the following beneficial effects:

[0029] On the basis of using the periodogram and the autocorrelation function, the application uses the peak value characteristics of the periodogram and the autocorrelation function to screen and narrow the candidate period region, and since the candidate period is subjected to a block processing, the periodogram or the autocorrelation graph does not need to be calculated, thereby reducing the period detection time complexity and the calculation time. In addition, the period is detected by using the method for weighted evaluation, the characteristics of the periodogram and the autocorrelation coefficient are comprehensively combined, the best period in the candidate region is selected, the robustness of the detected period is ensured, and the influence of the spectrum leakage and the noise on the detection result is minimized. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a logic block diagram of the application;

[0031] Figure 2 is a general block diagram of the application;

[0032] Figure 3is a screening process schematic diagram of the present application;

[0033] Figure 4 is a comprehensive evaluation schematic diagram of the present application;

[0034] Figure 5 is a taylor power demand data decomposition diagram. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments.

[0036] In the case that the actual periodic signal contains multiple periods and the actual period detection needs to ensure real-time. In order to realize accurate and real-time multi-period time series period detection, the embodiments of the present application use periodogram and autocorrelation function at the same time, first rely on periodogram and autocorrelation function to determine multiple candidate period regions, then perform weighted evaluation on each candidate period region to determine the detection period. Finally realize the period decomposition of multi-period time series. The specific method is described as follows:

[0037] (1) First, the present application calculates the periodogram and autocorrelation function of the multi-period time series signal. Specifically, first perform discrete Fourier transform (DFT) on the time series x(n) to obtain X(k)

[0038]

[0039] Then get the periodogram P(k) according to the result of discrete Fourier transform

[0040]

[0041] At the same time, in order to avoid the increase of algorithm complexity caused by secondary calculation in time domain, the present application directly calculates the autocorrelation function ACF(τ) through the result of discrete Fourier transform:

[0042] ACF(τ)=DFT[X(k)*X(k) * ]

[0043] Where IDFT represents inverse discrete Fourier transform, X(k) * represents the conjugate of X(k). In this way, the periodogram and autocorrelation function of the multi-period time series are obtained.

[0044] (2) Then, the application determines multiple candidate periodic regions by the periodogram and the autocorrelation function obtained in the first step. Specifically, first, a real period will generate multiple candidates in the periodogram, so the application uses 1 / 5 of the maximum power in the periodogram as a threshold to quickly narrow down the range of the candidate period, and each part in the periodogram that is higher than the threshold is a candidate periodic region. 1 / 5 is an empirical value, and the recommended value range is [1 / 20, 1 / 2]. Then, since the real period is always located at the peak of the autocorrelation function, the application eliminates the candidate periodic regions corresponding to the valleys of the autocorrelation function and retains the candidate periodic regions corresponding to the peaks of the autocorrelation function. Specifically, the slope of the upper boundary of the corresponding region on the autocorrelation function is calculated. If the left slope is less than 0 and the right slope is greater than 0, the region is a valley. For the remaining candidate periodic regions, the application eliminates the candidate periods that are lower than 1 / 2 of the peak height of the autocorrelation function in each candidate periodic region for further screening. Finally, multiple screened candidate periodic regions are obtained.

[0045] (3) Finally, the application realizes multiple period detection by weighted evaluation of each candidate periodic region. Specifically, for all candidate periods x i (=1, 2, …, n) of any candidate periodic region, the application first respectively ranks them in descending order according to their power in the periodogram and the correlation coefficient of the autocorrelation function, and assigns each candidate period a serial number 0, 1, 2, …, k-1. In this way, each candidate period has two rankings. Then, the rankings of each candidate period are weighted to obtain a new ranking. The smaller the new ranking, the greater the probability that the corresponding candidate period is the real period. The period corresponding to the smallest ranking is the best candidate period in the candidate periodic region. For each candidate periodic region, a best candidate period is obtained by weighted evaluation. Finally, all best candidate periods are obtained to complete the period detection task.

[0046] The above content can be explained as:

[0047] As shown in Figure 1 and Figure 2 , the weighted evaluation detection multiple period time series period technology proposed by the embodiment of the application mainly includes the following parts: screening candidate period sequences through a periodogram and an autocorrelation function, and determining a best candidate period by weighted evaluation. The technology mainly includes the following steps:

[0048] (1) Time series processing

[0049] The time series is first processed by Fourier transform. Then, the periodogram is obtained by squaring the discrete Fourier transform and dividing by the number of sequences, and the autocorrelation function is obtained by discrete Fourier inverse transform of the product of the discrete Fourier transform and the conjugate of the discrete Fourier transform.

[0050] (2) Determine the candidate periodic region

[0051] In the periodic graph, the region below 1 / 5 of the peak value of the periodic graph is directly discarded, and the region above 1 / 5 of the peak value of the periodic graph is the candidate periodic region. 1 / 5 is an empirical value, and the recommended value range is [1 / 20, 1 / 2]. Then calculate the slope of the boundary of each candidate periodic region in the autocorrelation function, where the region with a left boundary slope less than 0 and a right boundary slope greater than 0 is the valley bottom, and the region with a valley bottom in the autocorrelation function is discarded. In each of the remaining candidate periodic regions, calculate 1 / 2 of the peak value of the autocorrelation function in the region, and discard the candidate period below this value. Finally, the processed candidate periodic region is obtained.

[0052] (3) Weighted evaluation

[0053] In each processed candidate periodic region, first, according to the power size of the candidate period in the region on the periodic graph, each period is sorted in descending order, and then sorted according to the size of the autocorrelation coefficient on the autocorrelation function.

[0054] Then, the sorting according to the periodic graph and the autocorrelation graph is weighted and evaluated, and the final score equation is:

[0055]

[0056] where Rank periodogram is the ranking of the periodic graph in the candidate periodic region according to the energy, Rank acf is the ranking of the autocorrelation coefficient in the autocorrelation graph in the candidate periodic region, and r is the weight coefficient, with a value range of [0, +∞).

[0057] As shown in Figure 4 , the evaluation method is as follows:

[0058] 1. Then, the periods that meet the conditions in the screening process are calculated in the sorting of the periodic graph and the autocorrelation graph, respectively.

[0059] 2. Select an appropriate weight coefficient r, generally recommended r = 1, indicating that the weights of the periodic graph and the autocorrelation graph are the same.

[0060] 3. According to the two sorts of the previous step, and according to the weight coefficient r, calculate the final ranking of each period, and select the highest ranking as the final candidate period.

[0061] 4. The above is the process of obtaining a candidate periodic region. If there are multiple candidate periodic regions, only the same 1-3 processes need to be performed.

[0062] The following is an example:

[0063] As shown in Figure 1Shown:

[0064] 1. Calculate periodogram and autocorrelation plot for the time series of England electricity data with period 48 and 336 respectively.

[0065] 2. Screening according to the periodogram and autocorrelation plot, the specific steps are as follows: Figure 1

[0066] a) Regional division: Since there are multiple periods in the multi-period time series, multiple peaks will be shown in the periodogram. Each peak is taken as a candidate region, which divides the candidate period into multiple regions, avoiding sorting the entire periodogram of the candidate period and reducing the time complexity.

[0067] b) Periodogram screening: The multiple candidate periods divided by the peak value of the periodogram cannot be used immediately and need to be screened. Generally, 1 / 5 of the maximum power of the periodogram is selected as the threshold. 1 / 5 is an empirical value, and the recommended value range is [1 / 20, 1 / 2]. It is generally believed that if the power corresponding to a period is less than 1 / 5 of the maximum power in the periodogram, the power corresponding to this period is too small, and it may not be the main component of the multi-period time series, i.e. it is not an important period and can be discarded. Figure 3 The periodogram in the periodogram only has three regions centered on 24, 48, and 336 with power values greater than 1 / 5 of the maximum power;

[0068] c) Autocorrelation plot screening: For candidate period regions with power greater than 1 / 5 in the periodogram, further screening is needed due to noise and spectral leakage. First, discard the candidate periods in the valley of the autocorrelation plot. Then, discard the periods in the autocorrelation plot that are less than 1 / 2 of the peak value.

[0069] i.The periodogram in the periodogram only has three regions centered on 24, 48, and 336 with power values greater than 1 / 5 of the maximum power; Figure 3 The region around 24 in the periodogram is in the valley of the autocorrelation plot and is discarded. At this point, the candidate region becomes two, i.e. the regions centered on 48 and 336.

[0070] ii. 348 in the region centered on 336 has an autocorrelation coefficient less than 1 / 2 of the peak value in the autocorrelation plot, so it is discarded.

[0071] d) For multi-period time series, there may be multiple candidate regions. For each candidate region, repeat steps b and c to obtain the screened candidate period.

[0072] 3. Comprehensive ranking of each candidate region to obtain the best period of each candidate region

[0073] a) For the period of each candidate region, calculate the ranking in the autocorrelation plot and the periodogram respectively

[0074] b) Then select a suitable weight value r, r is an empirical value, the range is [0, +∞), the recommended value is r = 1. If you want to give more weight to the periodogram, r can take a small value, for example, r = 0.1. If you want to give more weight to the autocorrelation graph, r can take a larger value, for example: r = 100.

[0075] c) According to the weight r and the comprehensive evaluation formula, the final ranking is obtained. Select the highest ranking period as the best period of the region.

[0076] 4. Collect each candidate best period to get the period of the multi-period time series.

[0077] The following is an example:

[0078] In daily life, many time series of data have multi-period properties, such as household electricity consumption and office electricity consumption in power data, network traffic in network data, and traffic flow and passenger flow in traffic data.

[0079] In practical applications, the original multi-period time series data can be various types of multi-period time series data, which can include multi-period power time series data such as household electricity consumption and office electricity consumption, multi-period network time series data such as network traffic, and multi-period traffic time series data such as traffic flow and passenger flow. The following takes household electricity as an example to explain. For household electricity, you can observe the power usage in a certain period of time (such as a day, a week, a month, a quarter, or a year) according to the decomposition results.

[0080] In real life, the use of electricity will show certain periodicity in small and large scales. For example, for the household electricity consumption in a day, since most people are at work or school during the day, the household electricity consumption at night is usually greater than that during the day, and after most people rest in the early morning, this data will also decrease. For example, for the household electricity consumption in a week, for the same reason, the household electricity consumption on weekends is usually greater than that on weekdays. For example, for the household electricity consumption in a year, since air conditioners, fans, and other electrical appliances are used more in summer and winter, the household electricity consumption in summer and winter is usually greater than that in spring and autumn. It can be understood that other multi-period time series data also have similar properties, such as network traffic, which is usually more during the day and less at night, and household network traffic is more on weekends and office network traffic is more on weekdays. For example, traffic flow is more on weekdays and less on weekends, and more on holidays.

[0081] It should be clear that this is only an example of household electricity in power data, which does not mean that this method can only be used for this purpose. As long as various time series involving multiple periodic components (such as the above network traffic, traffic, passenger flow and other any time series with multiple periodic properties) can use this method for periodic detection to facilitate subsequent analysis, therefore any time series with multiple periodic properties belongs to the protection scope of the present application.

[0082] The above describes the scenario of periodic time series. For a periodic time series, if we want to further analyze it, taking household electricity as an example, if we want to know the user's electricity usage rules: for example, when is the electricity peak and when is the valley in a day, how much electricity is used in a day, and how much electricity is used in a week. Understanding these rules can provide data support for decision-making by relevant departments.

[0083] Figure 5 It is the electricity demand in England and Wales from Monday, June 5, 2000 to Sunday, August 27, 2000, with a sampling interval of half an hour. The data set has 48 and 336 cycles, corresponding to a day (24x2=48) and a week (48x7=336).

[0084] "Raw data": that is, data without decomposition.

[0085] "Change trend": the change trend of electricity consumption over time, which may be related to the weather, for example: some days in the middle of the rain, the temperature decreases, and the user reduces the use of cooling equipment such as air conditioners, and the electricity consumption decreases.

[0086] "Daily data": daily electricity consumption, showing a periodic fluctuation.

[0087] "weekly data": weekly electricity consumption, showing a periodic fluctuation.

[0088] "noise": some noise data, for example: suddenly use high-power electrical equipment at a certain time, which is not regular.

[0089] Common periodic time series decomposition methods, such as the MSTL method, need to input the period in advance to decompose the periodic time series, such as daily and weekly electricity data. If the result of the period detection tool is not accurate, the time series cannot be well decomposed, which will affect the downstream work, such as data analysis, prediction and anomaly detection.

[0090] For example: if the periodic detection algorithm only detects that the taylor data has a daily change period, and does not detect a weekly change period. Then only the daily change data can be used for prediction, that is, the weekly change trend cannot be well grasped.

[0091] Therefore, cycle detection accuracy is extremely important. Accurate determination of the period of a periodic time series can lay a good foundation for downstream work, such as time series decomposition, anomaly detection, and prediction.

[0092] However, current cycle detection tools can only detect single-period time series, and multi-period detection tools, such as Robust-period, are long in running time and inaccurate. The method is 300 times faster than Robust-period on taylor power data. The cycle accuracy is also better than existing methods.

[0093] It can be seen that the above technical solutions of the embodiments of the present application use the peak characteristics of the periodogram and the autocorrelation function to screen and narrow down the candidate period region on the basis of the periodogram and the autocorrelation function. Since the candidate period is processed in blocks, there is no need to calculate the entire periodogram or autocorrelation diagram, thereby reducing the cycle detection time complexity and calculation time. In addition, the weighted evaluation method is used to detect the period, which can ensure fast and robust detection of multiple periods.

[0094] In yet another aspect, the present application also discloses a computer readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of any of the above methods.

[0095] In yet another aspect, the present application also discloses a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the computer program, when executed by the processor, causes the processor to perform the steps of any of the above methods.

[0096] In yet another embodiment provided in the present application, a computer program product containing instructions is also provided, which, when running on a computer, causes the computer to perform the steps of any of the above methods.

[0097] It can be understood that the system provided by the embodiments of the present application corresponds to the method provided by the embodiments of the present application, and the explanation, examples and beneficial effects of the related content can refer to the corresponding parts in the above method.

[0098] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The program can be stored in a non-volatile computer readable storage medium, and when the program is executed, the processes of the above-mentioned embodiment methods can be included. Any reference to memory, storage, database or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0099] The technical features of the above embodiments can be combined in any way. In order to make the description simple, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist, they should be considered as the scope of the present application.

[0100] The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for detecting periodicity in a multi-period time series by weighted evaluation, characterized in that, The method comprises the following steps, The periodogram and the autocorrelation function are calculated and used to determine a plurality of candidate period regions; wherein the periodogram and the autocorrelation function of the multi-period power time sequence are calculated as follows: The multi-period power time sequence is subjected to Fourier transform, and then the periodogram is obtained by dividing the square of the discrete Fourier transform by the number of sequences, and the autocorrelation function is obtained by the inverse discrete Fourier transform of the product of the discrete Fourier transform and the conjugate of the discrete Fourier transform; Because multi-period power time series have multiple periods, they will appear as multiple peaks in the periodic chart. In the periodic chart, the peak value is lower than the maximum peak value of the periodic chart. The region was directly discarded, exceeding the maximum peak value of the periodic chart. The region is designated as the candidate periodic region. Then, the slope of the boundary in the autocorrelation function is calculated for each candidate periodic region. Regions with a left boundary slope less than 0 and a right boundary slope greater than 0 are considered valleys and are discarded. In each remaining candidate periodic region, the peak value of the autocorrelation function in that region is calculated. Discard candidate periods below this value to obtain the final processed candidate period region; Then, the weighted evaluation is performed on each candidate period region to determine the detection period of the multi-period power time sequence, comprising: In each processed candidate period region, first, the candidate periods in the region are sorted in descending order according to the power of the candidate periods on the periodogram, and then the autocorrelation coefficients are sorted according to the size of the autocorrelation coefficients on the autocorrelation function; For each candidate period region, a weighted evaluation is performed to obtain a best candidate period, and finally all the best candidate periods are obtained to complete the period detection task of the multi-period power time sequence; Finally, the period detection of the multi-period power time sequence is realized.

2. The method of claim 1, wherein the weighted evaluation detects periodicity in a multi-period time series. The weighted evaluation is performed according to the sorting of the periodogram and the autocorrelation diagram, and the final score equation is: ; wherein, is a ranking of periodic patterns in the candidate periodic region according to energy, is a ranking of autocorrelation coefficients in the autocorrelation pattern in the candidate periodic region, and r is a weight coefficient with a value range of [0, +∞).

3. The method of claim 1, wherein the weighted evaluation detects periodicity in a multi-period time series. The periodogram and the autocorrelation function of the multi-period power time sequence are calculated as follows: The multi-period electric power time series is first divided into a plurality of sub-periods a discrete Fourier transform is performed to obtain The periodogram is then obtained from the results of the discrete Fourier transform Computing the autocorrelation function from the results of a discrete Fourier transform : where IDFT denotes the inverse discrete Fourier transform, denotes the conjugate of the Fourier transform of the time series, and the periodogram and autocorrelation function of the multi-periodic power time series are obtained.

4. A computer readable storage medium storing a computer program, wherein the computer program is executed by a processor to make the processor execute the steps of the method according to any one of claims 1 to 3.

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