Charging station load clustering method based on curve elastic shape analysis

Abstract

The invention discloses a charging station load clustering method based on curve elastic shape analysis, and the method comprises the following specific steps: setting the maximum number n of iterations in an iteration process, determining the number K of clusters, and describing a daily load curve of a charging pile; randomly dividing the curves into K groups as initial groups; respectively calculating the Karcher Mean of each group as the average value of each group; respectively calculating the distance between each curve and the K Karcher Means; adding each curve into the group to which the minimum distance Karcher Mean belongs so as to update the group; outputting the group, and returning to the step 3; and if the cycle in the step 6 reaches the maximum number of iterations or the output group does not change any more, exiting the cycle, and outputting the current group. The method has the advantages that charge load analysis accuracy is improved; the power grid dispatching is effectively optimized; the construction of the charging station can be scientifically planned; the charging experience of the vehicle owner is improved; and electricity market stability is promoted.

Description

Technical Field

[0001] The invention relates to the field of charge load analysis, and in particular to a charging station load clustering method based on curve elastic shape analysis. Background Art

[0002] In modern power systems, the analysis and management of charge loads are crucial to ensure stable and efficient operation of the power grid. However, charge loads present complex changing characteristics, among which time factors such as sunshine and weather have a particularly prominent impact on them. With the change of seasons, the duration of sunshine in different seasons varies greatly. In summer, the sunshine duration is long and the light intensity is high, while in winter, the sunshine duration is short and relatively weak. In terms of weather, the temperature, humidity, light penetration, etc. will change significantly under different weather conditions such as sunny, cloudy, rainy, and snowy days.

[0003] Changes in these time factors directly affect the electricity demand side. For example, in the hot summer, the extensive use of cooling equipment such as air conditioners leads to a sharp increase in residential and commercial electricity loads; in the cold winter, the widespread use of heating equipment such as electric heaters will also significantly increase electricity demand. In the industrial field, some production processes are affected by weather temperature and humidity, and their production plans and equipment operating power will also be adjusted accordingly, thus affecting the overall charge load.

[0004] In academic research and practical application scenarios, although a large number of methods for charge load analysis have emerged, such as horizontal comparison method, elastic coefficient method, expert system method, etc. Unfortunately, most of the existing methods do not fully consider the impact of time factors. At the same time, the external conditions such as sunshine and weather in winter and summer may be different, resulting in different demands in the power grid, which has a great impact on charge load analysis. Inaccurate charge load analysis may cause unreasonable grid scheduling, insufficient power supply or redundant power supply during peak periods, affecting the reliability and economy of power supply. For charging stations, unreasonable load analysis will also cause a series of problems such as errors in the layout planning of charging stations, failure to meet the charging needs of car owners or waste of resources. Therefore, there is an urgent need for a method that can effectively eliminate the interference of time factors and accurately analyze charge loads to improve the level of power grid operation and charging station planning and management. Summary of the invention

[0005] In order to solve the above problems, especially to address the deficiencies in the prior art, the present invention provides a charging station load clustering method based on curve elastic shape analysis to solve the above problems.

[0006] To achieve the above purpose, the present invention adopts the following technical means:

[0007] A charging station load clustering method based on curve elastic shape analysis, the specific steps are as follows:

[0008] Step 1: Set the maximum number of iterations n in the iteration process, determine the number of clusters K, and draw the daily load curve of the charging pile based on the historical daily load data of the charging pile for half a year;

[0009] Step 2: Randomly divide these curves into K groups as initial groups;

[0010] Step 3: Calculate the Karcher Mean of each group as the average value of each group;

[0011] Step 4: Calculate the distance between each curve and K Karcher Means respectively;

[0012] Step 5: Add each curve to the group with the smallest distance to the Karcher Mean to update the group;

[0013] Step 6: Output the grouping and return to step 3 for iterative optimization;

[0014] Step 7: If the loop of step 6 reaches the maximum number of iterations n or the output group no longer changes, exit the loop and output the current group.

[0015] A further solution of the present invention is that in step 1, the number of clusters K is determined comprehensively based on the power consumption scale, power consumption characteristics and surrounding environmental factors of the area where the charging station is located.

[0016] A further solution of the present invention is that in step one, the daily load curve is drawn based on the historical daily load data of the charging piles for half a year and arranged in chronological order.

[0017] A further solution of the present invention is that in step 2, the random method adopts a random seed algorithm.

[0018] A further solution of the present invention is that, in step 3, an iterative algorithm is used when calculating the Karcher Mean, and an iteration termination condition is that the difference between two adjacent calculation results is less than a set accuracy value.

[0019] A further solution of the present invention is that the distance calculation adopts a distance measurement function based on the elastic shape of the curve, which takes into account the shape similarity of the curve and the elastic deformation on the time axis.

[0020] Beneficial effects of the present invention:

[0021] 1. The present invention improves the accuracy of charge load analysis. Based on the elastic shape analysis of the curve, the present invention effectively eliminates the influence of time factors such as sunshine and weather on the charge load. By drawing a curve based on six months of historical daily load data and performing elastic shape analysis, the inherent characteristics and changing laws of the load curve can be accurately captured to avoid misjudgments caused by seasonal and weather changes. Compared with traditional methods that do not fully consider time factors, the accuracy of charge load analysis is significantly improved, providing more reliable data support for power grid dispatching.

[0022] 2. The present invention effectively optimizes grid dispatching. Accurate charge load analysis helps the grid dispatching department to reasonably arrange the grid load during peak hours. It can predict the load demand of different charging stations and regions in advance, allocate power resources in a targeted manner, avoid excessive power supply pressure or power waste in local areas, ensure stable operation of the grid, reduce the risk of power outages caused by improper dispatching, improve the safety and reliability of the overall operation of the grid, and enhance the grid's adaptability to complex power consumption environments.

[0023] 3. The present invention can scientifically plan the construction of charging stations. Provide scientific guidance for the construction planning of charging stations. Through load clustering analysis, the distribution characteristics of charging demand in different regions and different time periods can be clarified. For example, it is possible to determine which areas have concentrated charging demand in a specific time period, so as to reasonably determine the location, scale and number of charging piles of the charging station, avoid idle resources or insufficient charging facilities caused by blind construction, improve the utilization rate and return on investment of charging stations, and promote the rational layout and orderly development of electric vehicle charging infrastructure.

[0024] 4. The present invention improves the charging experience of car owners. Based on the results of the present invention, car owners can be guided to disperse charging. Through the reasonable regulation and information guidance of the charging station load, car owners can more conveniently find idle charging piles for charging, reduce waiting time, improve charging efficiency, improve the convenience and satisfaction of electric vehicle use, further promote the popularization and application of electric vehicles, and help achieve energy conservation and emission reduction goals in the transportation field.

[0025] 5. The present invention promotes the stability of the power market. It is conducive to the stable operation of the power market. Accurate charge load analysis and reasonable grid dispatching and charging station planning can balance the power supply and demand relationship and stabilize power price fluctuations. It avoids large price fluctuations caused by power supply shortages or surpluses due to inaccurate load forecasts, protects the interests of power market participants, and promotes the healthy and sustainable development of the power industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0027] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Example

[0029] like Figure 1 As shown in FIG. 1 , a charging station load clustering method based on curve elastic shape analysis is shown in FIG. 1 . The specific steps are as follows:

[0030] Step 1: Set the maximum number of iterations n in the iteration process, determine the number of clusters K, and draw the daily load curve of the charging pile based on the historical daily load data of the charging pile for half a year;

[0031] Step 2: Randomly divide these curves into K groups as initial groups;

[0032] Step 3: Calculate the Karcher Mean of each group as the average value of each group;

[0033] Step 4: Calculate the distance between each curve and K Karcher Means respectively;

[0034] Step 5: Add each curve to the group with the smallest distance to the Karcher Mean to update the group;

[0035] Step 6: Output the grouping and return to step 3 for iterative optimization;

[0036] Step 7: If the loop of step 6 reaches the maximum number of iterations n or the output group no longer changes, exit the loop and output the current group.

[0037] How it works

[0038] First, by collecting the historical daily load data of charging piles for half a year, these data contain load information at different times (covering different seasons and weather conditions). The daily load curve is drawn with time as the horizontal axis and load as the vertical axis. Due to time factors (such as sunshine and weather), the load curve will be deformed, but these deformations have similar laws from the perspective of elastic shape analysis that removes the influence of time.

[0039] Next, the number of clusters K is determined, and the daily load curves are randomly initially divided into K groups. For each group of curves, its Karcher Mean (a special mean that can represent the central trend of the curve group) is calculated. The distance between each curve and the Karcher Mean of each group is calculated. The distance calculation here uses a metric function designed specifically for the elastic shape of the curve. This function takes into account the similarity of the curve in shape and the elastic deformation on the time axis. That is, even if the curve has deformation caused by time factors such as stretching or compression on the time axis, it can still accurately measure the degree of difference from the mean curve.

[0040] Then, based on the calculated distance, each curve is classified into the group to which the Karcher Mean closest to it belongs, completing a group update. After that, the updated Karcher Mean of each group is calculated again, and the distance between the curve and the new Karcher Mean and the regrouping process are repeated to form an iterative cycle.

[0041] When the loop reaches the preset maximum number of iterations n, or the output grouping no longer changes (i.e., the grouping reaches a stable state), the iteration ends, and the grouping result obtained at this time is the final charging station load clustering result. In this way, curves with similar elastic shape characteristics (i.e., similar load change laws after removing the influence of time factors) are clustered into one category, thereby realizing effective clustering analysis of charging station loads, providing a basis for applications such as power grid dispatching and charging station planning. For example, power grid dispatching can predict the load change trends of different categories and reasonably allocate power resources based on clustering results, and charging station planning can refer to clustering conditions to determine the construction scale and layout of charging stations in different regions.

[0042] The number of clusters K is determined comprehensively based on the power consumption scale, power consumption characteristics and surrounding environmental factors of the area where the charging station is located.

[0043] The advantages of the above settings are:

[0044] Accurately adapt to regional electricity demand

[0045] Determining the number of clusters K based on the scale of electricity consumption in the area where the charging station is located can make the clustering results better adapt to electricity consumption scenarios of different scales. For example, in a commercial area with a large scale of electricity consumption, there may be a large number of electric vehicles charging at the same time, and more detailed clustering is needed to accurately grasp the load conditions of charging stations in different time periods and locations. By considering the scale of electricity consumption, the load curve can be divided into an appropriate number of categories to avoid the situation where too few clusters lead to too general information and cannot effectively guide power grid scheduling and charging station planning, or too many clusters lead to waste of computing resources and overly complex analysis.

[0046] Power consumption characteristics are also an important factor. The power consumption characteristics of different regions vary significantly. For example, in residential areas, charging time may be concentrated at night; while in industrial parks, charging time may be related to the company's working hours and production plans. Considering power consumption characteristics to determine K can group the load curves of charging stations with similar charging time patterns and load change trends into one category, thereby more accurately predicting and managing loads.

[0047] The surrounding environmental factors cannot be ignored. If there are large-scale event venues, tourist attractions, etc. around the charging station, the charging demand will surge during a specific time period. For example, the charging demand for charging stations near stadiums will increase significantly during sports events. By comprehensively determining K based on the surrounding environmental factors, reasonable clustering can be performed for these special situations, and preparations can be made in advance for the allocation of power resources and the adjustment of charging station operation strategies.

[0048] Improving the scientific nature of charging station planning

[0049] For the construction planning of charging stations, a reasonable K value helps to determine the appropriate layout of charging stations and the number of charging piles. By comprehensively considering the number of clusters determined by various factors, the distribution of charging demand in different regions can be clarified. For example, if an area is divided into multiple clusters with significantly different load characteristics based on its electricity consumption scale, characteristics and surrounding environment, then charging stations of different sizes and types can be planned according to the characteristics of these clusters. In cluster areas with higher loads, large charging stations with a higher proportion of fast charging piles can be built; in cluster areas with lower loads, the number of charging piles can be appropriately reduced or the proportion of slow charging piles can be increased to improve the scientificity and economy of charging station construction.

[0050] Optimizing the effectiveness of grid dispatch

[0051] From the perspective of power grid dispatching, a suitable K value can help the power grid dispatching department allocate power resources more efficiently. Because the clustered load categories can more accurately reflect the actual power demand and changing patterns of different charging stations, power grid dispatchers can reasonably arrange power supply during peak and trough periods based on the load forecasts of different clusters. For example, for clusters with similar power consumption characteristics and relatively consistent load fluctuations caused by the surrounding environment, a unified dispatching strategy can be formulated to improve the power grid's response speed and regulation capabilities to the charging station load, avoiding power grid overload or power waste due to unreasonable dispatching.

[0052] Enhance the adaptability and flexibility of the model

[0053] This comprehensive way of determining K enables the clustering method to adapt to different geographical areas, different electricity usage scenarios, and changing external environments. With the development of cities, the construction of new commercial areas or residential areas, and changes in people's electricity usage habits, the scale, characteristics, and surrounding environment of electricity usage will change. By comprehensively considering these factors to determine K, the model can be dynamically adjusted according to actual conditions, maintaining the effectiveness and accuracy of charging station load clustering, and enhancing the adaptability and flexibility of the entire load analysis and management system.

[0054] Among them, the daily load curve is drawn based on the historical daily load data of the charging piles for half a year and is organized in chronological order.

[0055] The advantages of the above settings are:

[0056] Comprehensively reflect the load change law

[0057] The half-year time span is long enough to cover the changes in different seasons. For example, in summer, due to the high temperature and frequent use of electric vehicle air conditioning, the charging load may be affected; while in winter, battery performance and the use of in-car heating equipment will also cause changes in the charging load. By collecting data for half a year, these load fluctuations caused by seasonal changes can be captured, fully presenting the load change patterns of charging stations under different climatic conditions.

[0058] It also includes information on different date types (weekdays, weekends, holidays, etc.). The charging peak on weekdays may be concentrated before and after work, while the charging peak on weekends and holidays may occur during periods when people travel more frequently. The six-month historical data can cover various date types, thus fully reflecting the charging load characteristics under different date types.

[0059] The data of half a year can record the impact of some special events or temporary situations on the load. For example, large-scale local events and road construction affecting traffic may change the travel and charging mode of electric vehicles. The historical data of half a year can also include the load changes caused by these accidental factors, making the daily load curve more representative.

[0060] Improve the accuracy of data analysis

[0061] Long-term data accumulation can reduce the impact of randomness and volatility of data on analysis results. When the amount of data is small, individual abnormal data points or short-term irregular fluctuations may lead to misjudgment of load change patterns. The six-month historical daily load data is arranged and plotted in chronological order, which can utilize the statistical characteristics of the data and use smoothing and other methods to more accurately analyze the basic trend and periodic changes of the load.

[0062] Arranging data in chronological order allows for better time series analysis. Many load changes have time series correlations. For example, today's charging load may have a certain correlation with the load on the same day yesterday or last week. By drawing daily load curves in chronological order, time series analysis methods such as the autoregressive moving average model (ARMA) can be easily applied to make more accurate predictions of future loads.

[0063] Provide a reliable basis for subsequent analysis

[0064] For cluster analysis, comprehensive and accurate daily load curves are the prerequisite for effective clustering. In the subsequent steps of calculating Karcher Mean and measuring the distance between curves, these daily load curves drawn based on half-year historical data can provide rich information, so that the clustering results can better reflect the actual load distribution. For example, when calculating the similarity between curves, the complete shape of the curve (including the shape under different seasons and date types) can help determine a more reasonable distance metric, thereby improving the accuracy of clustering.

[0065] It also provides data support for other related analyses. For example, the peak load analysis, valley load analysis, and load change rate analysis of charging stations can all be performed based on these daily load curves. These analysis results can be used to optimize the operation strategy of charging stations, such as formulating time-of-use electricity prices, adjusting the power configuration of charging piles, etc., to improve the economic benefits and service quality of charging stations.

[0066] Among them, the random method adopts a random seed algorithm.

[0067] The advantages of the above settings are:

[0068] Reproducibility of results

[0069] The random seed algorithm ensures that the randomness of the grouping is reproducible each time the clustering algorithm is run, as long as the seed is the same. This is very important in the process of algorithm development, debugging, and verification. For example, when researchers improve the algorithm or optimize the parameters, they need to compare the performance of different versions of the algorithm. If the results of random grouping are different and uncontrollable each time, it is difficult to determine whether the performance change is caused by the improvement of the algorithm itself, or simply due to the difference in random grouping. By setting the random seed, comparisons can be made under the same initial grouping conditions to accurately evaluate the effect of the algorithm improvement.

[0070] In actual application scenarios, when you need to show the algorithm process and results to other departments or partners, repeatability is also critical. By providing the same random seed, the other party can get the same initial grouping as you, which facilitates communication and understanding of the algorithm operation process and the final clustering effect.

[0071] Easy to control the degree of randomness

[0072] The random seed algorithm allows users to control the degree of randomness according to specific needs. For example, the randomness of the initial grouping can be changed by adjusting the seed value or the parameters of seed generation. In some cases, it may be desirable to have a higher degree of randomness in the initial grouping to explore a wider range of clustering possibilities; in other cases, it may be necessary to reduce the randomness so that the initial grouping is closer to a certain expected pattern, providing a relatively stable starting point for subsequent iterative optimization. This flexible control of the degree of randomness can better adapt to different application scenarios and data characteristics.

[0073] Improve algorithm stability and convergence

[0074] Reasonable random seed settings can improve the stability of the algorithm to a certain extent. This is because it avoids the overly random initial grouping that may cause the algorithm to fall into a local optimal solution or abnormal clustering results in the early stages of iteration. For example, if the initial grouping is too disorganized, it may cause large deviations in the subsequent calculation of Karcher Mean and curve distance, affecting the convergence speed of the algorithm and the final clustering effect. By using the random seed algorithm, a relatively reasonable initial grouping can be obtained, making it more likely that the algorithm will converge towards the global optimal solution during the iteration process, reducing the algorithm's running time and the waste of computing resources.

[0075] Among them, an iterative algorithm is used to calculate the Karcher Mean, and the iteration termination condition is that the difference between two consecutive calculation results is less than the set accuracy value.

[0076] The advantages of the above settings are:

[0077] Improve calculation accuracy

[0078] The iterative algorithm can gradually approach the true value of the Karcher Mean. In the process of calculating the Karcher Mean, especially for complex curve data, it is difficult to directly obtain accurate results through simple formulas. Through iteration, each update of the calculation result is like gradually polishing a part, making it closer and closer to the ideal Karcher Mean. For example, when processing load curve data with noise or local fluctuations, the iterative algorithm can effectively filter out these interference factors, so that the final Karcher Mean can more accurately represent the central trend of a set of curves.

[0079] The termination condition is that the difference between two consecutive calculation results is less than the set precision value, which can ensure that the accuracy of the calculation meets the requirements. This precision value is like a standard for measuring the quality of the calculation. Only when the calculation result is stable enough and no longer changes significantly (that is, the difference is less than the precision value), it is considered that a reliable Karcher Mean has been obtained. This is crucial for subsequent operations such as curve distance calculation and grouping update based on Karcher Mean, because accurate Karcher Mean is one of the key factors for effective clustering.

[0080] Effectively control computing resources and time

[0081] Setting such an iteration termination condition can avoid infinite loop calculations. If there is no termination condition, the iterative algorithm may continue to run, constantly consuming computing resources, especially when processing a large amount of daily load curve data of charging piles, which may cause the calculation time to be too long or even system crash. By clearly stipulating that the iteration should be stopped when the difference between two consecutive calculation results is less than the precision value, the consumption of computing time and resources can be reasonably controlled while ensuring the calculation accuracy. For example, when the amount of data increases, it may only take a slight adjustment of the precision value to complete the calculation within an acceptable time and resource range, making the algorithm more scalable.

[0082] Adapt to different data characteristics and application scenarios

[0083] The precision value can be flexibly adjusted according to the specific data characteristics and application scenarios. If the data is highly volatile or the accuracy of the clustering results is required to be high, such as when providing data support for high-precision power grid dispatching decisions, the precision value can be set to a smaller value to obtain a more accurate Karcher Mean. On the contrary, if the data is relatively stable or the accuracy of the clustering results is not particularly high, such as in the preliminary data analysis stage, the precision value can be appropriately increased to speed up the calculation. This flexibility enables the algorithm to perform well in different situations and adapt to diverse needs.

[0084] The distance calculation adopts a distance measurement function based on the elastic shape of the curve, which takes into account the shape similarity of the curve and the elastic deformation on the time axis.

[0085] The advantages of the above settings are:

[0086] Accurately measure curve differences

[0087] Considering the shape similarity of the curves can more accurately assess the true difference between the two daily load curves. Because even if the two curves are located differently on the time axis, if their shapes are similar (for example, the charging peak and trough occur at different times but have similar shapes), in actual load clustering analysis, they may belong to the same class or have similar charging behavior patterns. By using a distance metric based on shape similarity, this potential similarity can be mined to avoid incorrectly dividing the curves simply because of differences in the time axis.

[0088] It is a very important advantage to consider the elastic deformation on the time axis at the same time. Due to time factors such as sunshine and weather, as well as changes in users' charging habits, the load curve may be stretched or compressed on the time axis. For example, in summer, due to the long daytime hours, users' charging time may be more dispersed than in winter, resulting in a certain deformation of the load curve on the time axis. The distance measurement function based on the elastic shape of the curve can adapt to this deformation and will not misjudge the distance between the curves due to such changes on the time axis, thereby more accurately measuring the actual difference between the curves.

[0089] Improve the rationality and accuracy of clustering

[0090] In the clustering process, accurate distance calculation is the key to reasonably grouping curves. Using this distance measurement function that takes into account the elastic shape of the curve, curves with similar charging behaviors and load change patterns are more likely to be clustered into one group. For example, for those curves with similar overall load shapes that are advanced or delayed due to special events (such as large-scale events), they can be correctly classified into the same category instead of being divided into different groups due to time differences. This can improve the rationality of the clustering results, make the clustered groups more reflect the actual charging load pattern, and provide a more accurate basis for subsequent power grid scheduling and charging station planning.

[0091] Enhance the versatility and adaptability of the method

[0092] This distance metric function can adapt to various types of load curve changes and has strong versatility. It can effectively handle curve deformations caused by seasonal changes, changes in user behavior habits, or other external factors. For example, in different geographical regions, the charging behavior of electric vehicles may be affected by a combination of factors such as local climate and economic activities, resulting in load curves showing a variety of shapes and time axis deformations. This distance metric function can adapt well to these different situations, enhancing the adaptability of the entire clustering method to different scenarios and enabling it to be effectively applied in a wider range.

[0093] The examples given in the present invention are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here, and the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A charging station load clustering method based on curve elastic shape analysis, characterized in that: The specific steps are as follows: Step 1: Set the maximum number of iterations n in the iteration process, determine the number of clusters K, and draw the daily load curve of the charging pile based on the historical daily load data of the charging pile for half a year; Step 2: Randomly divide these curves into K groups as initial groups; Step 3: Calculate the Karcher Mean of each group as the average value of each group; Step 4: Calculate the distance between each curve and K Karcher Means respectively; Step 5: Add each curve to the group with the smallest distance to the Karcher Mean to update the group; Step 6: Output the grouping and return to step 3 for iterative optimization; Step 7: If the loop of step 6 reaches the maximum number of iterations n or the output group no longer changes, exit the loop and output the current group.

2. The charging station load clustering method based on curve elastic shape analysis according to claim 1 is characterized in that: In step 1, the number of clusters K is determined comprehensively based on the power consumption scale and power consumption characteristics of the area where the charging station is located and the surrounding environmental factors.

3. The charging station load clustering method based on curve elastic shape analysis according to claim 1 is characterized in that: In step 1, the daily load curve is drawn based on the historical daily load data of the charging piles for half a year in chronological order.

4. The charging station load clustering method based on curve elastic shape analysis according to claim 1, characterized in that: In step 2, the random method adopts a random seed algorithm.

5. The charging station load clustering method based on curve elastic shape analysis according to claim 1, characterized in that: In step 3, an iterative algorithm is used to calculate the Karcher Mean, and the iteration termination condition is that the difference between two adjacent calculation results is less than a set accuracy value.

6. The charging station load clustering method based on curve elastic shape analysis according to claim 1, characterized in that: In step 4, the distance calculation uses a distance metric function based on the elastic shape of the curve, which takes into account the shape similarity of the curve and the elastic deformation on the time axis.

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