A three-dimensional representation method of univariate time series

Abstract

This invention discloses a three-dimensional representation method for univariate time series, comprising: acquiring the original univariate time series to be processed; performing periodic analysis on the sampled data to determine the period number and position of each sample point within its respective period; constructing a three-dimensional mapping relationship, including: determining the height coordinates of the sample points based on the period number, obtaining the phase angle of the XY plane based on the position of the sample point within its respective period, and obtaining the radial distance of the XY plane based on the observed amplitude; obtaining the three-dimensional spatial coordinates corresponding to each sample point based on the phase angle, radial distance, and height coordinates of the sample points; and connecting the three-dimensional spatial coordinates of all sample points sequentially to generate a three-dimensional spiral time series curve, thus completing the three-dimensional representation of the univariate time series. In practice, this invention can be used for the intuitive visualization of periodic time series, facilitating the discovery of periodic evolution patterns, identification of phase shifts and amplitude anomalies, and simultaneously outputting standardized three-dimensional structured data directly for use by the target model, assisting the model in efficiently learning the periodic characteristics of the time series. It is suitable for various univariate time series processing scenarios with periodic variation patterns.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence data processing and information visualization technology, and in particular to a three-dimensional representation method for a single-variable time series. Background Technology

[0002] Univariate time series data, as the most common form of time series data, are widely distributed across various industries such as power load monitoring, traffic flow statistics, and meteorological and environmental observation. This type of data consists of timestamps and single observation values, and generally contains periodic evolution patterns such as daily, weekly, and monthly. For univariate time series data, various representation and visualization methods have been developed, such as one-dimensional line graphs, periodically layered two-dimensional plots, and time series matrix transformations.

[0003] One-dimensional line graphs, as a basic time series representation method, can only express the continuous trend of numerical changes over time. When there is data with multiple overlapping periods, the information between periods is easily confused, making it difficult to distinguish the inherent relationship between adjacent moments within the same period and the same phase in different periods. Two-dimensional plotting of overlapping periods draws curves for each period separately, which can distinguish different periods, but visual occlusion can easily occur between multiple curves, and the inherent temporal continuous evolution relationship of the original data is severed. Processing periodic time series into two-dimensional matrices is often used as input for deep learning models, completing the data structure transformation. However, the matrix form lacks intuitive visualization capabilities, and padding values ​​are needed for data with variable period lengths, easily introducing additional data noise. The continuous temporal relationship is also severed by the matrix's row and column structure. Most existing representation methods compress multiple types of information, such as amplitude, phase, and period levels, into one-dimensional or two-dimensional space for expression. Multiple features are coupled and interfere with each other, and fixed-period and variable-period time series often require two independent processing logics, limiting overall versatility.

[0004] Existing representation and visualization schemes for univariate time series, while capable of reflecting some characteristics of time series data from a certain perspective, struggle to simultaneously preserve temporal continuity, present periodic hierarchical relationships, and decouple multiple features within a single representation system. For univariate time series with periodic characteristics, how to achieve decoupled representation of periodic layering, phase information, and amplitude information while preserving the original temporal evolution continuity, and simultaneously being compatible with both fixed-period and variable-period time series data, is a pressing technical problem in this field. Summary of the Invention

[0005] This invention provides a three-dimensional representation method for univariate time series to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A three-dimensional representation method for univariate time series, comprising: S1. Obtain the original univariate time series to be processed, which includes several sampled data carrying the observed amplitude; S2. Perform periodic analysis on the sampled data to determine the period number corresponding to each sampling point and its position within the period. S3. Constructing a three-dimensional mapping relationship, including: determining the height coordinates of the sampling point based on the period number, obtaining the phase angle of the XY plane based on the position of the sampling point within the period, and obtaining the radial distance of the XY plane based on the observation amplitude; S4. Based on the phase angle, radial distance, and height coordinates of the sampling points, obtain the three-dimensional spatial coordinates corresponding to each sampling point; S5. Connect the three-dimensional spatial coordinates of all sampling points sequentially according to the original sampling time order to generate a three-dimensional spiral time series curve, thus completing the three-dimensional representation of the univariate time series.

[0007] Furthermore, in S2, the sampled data is periodically analyzed to determine the period number corresponding to each sampling point and its position within the period, including: S21. Based on the sampling frequency and variation pattern of the sampled data, the sampled data is divided into fixed-period time-series sampled data and variable-period time-series sampled data; S22. Determine the first [number] in the sampled data. The period number corresponding to each sampling point is: and position within the corresponding period ,include: For time-series sampling data with a fixed period, where the first... The period number corresponding to each sampling point and position within the corresponding period The expression is: ; ; in: For a fixed period length; This is the floor function operator; This is the modulo operator; For variable-period time-series sampling data, the first The period number corresponding to each sampling point and within the corresponding period The expression is: ; ; ; in: This indicates that the year and month of the sample are returned, which corresponds to the period number of the sample. This indicates that the number of days in the corresponding month, i.e., the period length, is returned. This is a timestamp, indicating the [number]th [item]. The actual time corresponding to each sampling point.

[0008] Furthermore, the height coordinates of the sampling points determined based on the aforementioned period number are expressed as follows: ; in: and These correspond to the height coordinates of sampling points in fixed-period and variable-period time-series sampling data, respectively. For fixed step size.

[0009] Furthermore, the phase angle of the XY plane is obtained based on the position of the sampling point within its period, including: For fixed-period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ; For variable period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ; in: This is the initial phase angle.

[0010] Furthermore, the radial distance in the XY plane is obtained based on the observed amplitude, including: The observed amplitudes are normalized: set up and Let be the minimum and maximum observed amplitudes in the sampled data, respectively. Then the th k Normalized value of the observed amplitude at each sampling point for: ; in: For the first k The observed amplitude corresponding to each sampling point k This is the global sampling sequence number for the time series, which is applicable to both fixed-period and variable-period time series sampling data. Based on the k The normalized value of the observed amplitude at each sampling point determines the radial distance between the sampling points, expressed as: ; in: Indicates the base radius; This represents the scaling factor.

[0011] Furthermore, in S4, the three-dimensional spatial coordinates corresponding to each sampling point are obtained based on the phase angle, radial distance, and height coordinates of the sampling point. , is represented as: ; ; .

[0012] Beneficial Effects: This invention acquires the original univariate time series, performs periodic analysis on the sampled data to obtain the period number and position of each sampling point within the period, constructs a three-dimensional mapping relationship of height coordinates, XY plane phase angle, and radial distance, solves for the three-dimensional spatial coordinates of each sampling point, and generates a three-dimensional spiral time series curve by connecting the original sampling time sequence. This can map the periodic level, phase information, and observed amplitude of the time series to different geometric dimensions in three-dimensional space, highlighting its periodic characteristics while maintaining the continuity of the univariate time series, and is compatible with both fixed-period and variable-period sample data, providing a structured three-dimensional data representation for univariate time series. In practice, this invention can be used for the intuitive visualization of periodic time series, facilitating the discovery of periodic evolution patterns, identification of phase shifts and amplitude anomalies, and can output standardized three-dimensional structured data directly for use by the target model, assisting the model in efficiently learning the periodic characteristics of the time series. It is suitable for various univariate time series processing scenarios with periodic variation patterns. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the 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 based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of a three-dimensional representation method for a univariate time series according to the present invention; Figure 2 This is a schematic diagram of the spatial spiral structure in an embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0016] This embodiment provides a three-dimensional representation method for univariate time series, such as... Figure 1 As shown, it includes: S1. Obtain the original univariate time series to be processed, which includes several sampled data carrying observed amplitudes; the sampled data is power load data. Specifically, obtain the original univariate time series to be processed. : ; in: This represents the total number of sampling points; For the first The observed amplitude corresponding to each sampling point. Depending on the specific application scenario, the sampling frequency can be divided into 15 minutes, 1 hour, 1 day, and other time intervals.

[0017] S2. Perform periodic analysis on the sampled data to determine the period number corresponding to each sampling point and its position within the period. In a specific embodiment, S2 involves performing periodic analysis on the sampled data to determine the period number corresponding to each sampling point and its position within the period, including: S21. Based on the sampling frequency and variation pattern of the sampled data, the sampled data is divided into fixed-period time-series sampled data and variable-period time-series sampled data; Specifically, time series data with different sampling frequencies often exhibit certain periodic patterns. For example, for 15-minute and 1-hour power load data, 96 and 24 sampling points per day can be used as the period, respectively. For daily power load data, a week or a calendar month can be used as the period.

[0018] Fixed period: refers to a period in which each period contains the same number of sampling points, such as 24 hours a day, 7 days a week, or 12 months a year.

[0019] Variable period: Different periods may include periods with different numbers of sampling points, such as 28, 29, 30 or 31 days per month, or 365 or 366 days per year.

[0020] S22. To characterize the periodic hierarchical relationship of the time series in the spiral structure, a two-level index of loop number-loop position is introduced to determine the first... The period number corresponding to each sampling point is: and position within the corresponding period ,include: For fixed-cycle time-series sampling data that spans 24 hours a day, 7 days a week, and 12 months a year, the first... The period number corresponding to each sampling point and position within the corresponding period The expression is: ; ; in: For a fixed period length, for a 24-hour day, T=24; This is the floor function operator; This is the modulo operator. For time-series sampling data with variable periods, taking daily sampling frequency and monthly sampling period as an example, since the number of days in each month is not fixed, the sampling data will contain data from the first day of each month. Period length of each sampling point It changes over time, therefore it cannot be relied upon Inferring the location index of the sample. This embodiment introduces a timestamp. The concept that represents the first The real time corresponding to each sampling point is used to obtain the month number, number of days in the month, and location within the month from the calendar information, thereby achieving adaptive encoding of the natural month cycle.

[0021] No. The period number corresponding to each sampling point and within the corresponding period The expression is: ; ; ; in: This indicates that the year and month of the sample are returned, which corresponds to the period number of the sample. This indicates that the number of days in the corresponding month, i.e., the cycle length, can be 28, 29, 30, or 31.

[0022] S3. Constructing a three-dimensional mapping relationship, including: determining the height coordinates of the sampling point based on the period number, obtaining the phase angle of the XY plane based on the position of the sampling point within the period, and obtaining the radial distance of the XY plane based on the observation amplitude; In a specific embodiment, the height coordinates of the sampling point determined based on the period number are expressed as: ; in: and These correspond to the height coordinates of sampling points in fixed-period and variable-period time-series sampling data, respectively. A fixed step size is used to describe the evolution of the spiral in the height direction, such that adjacent period sampling points are within the range of the spiral. The height difference in the direction remains constant; Specifically, the height coordinates can be determined based on the period number, or jointly based on the period number and the position within the period, so that the sampling points rise continuously in three-dimensional space along the time direction. In this case, sampling points within the same period are located at the same or corresponding height layers; different periods are arranged sequentially along the height direction; and sampling points at the same time position in different periods form a vertical correspondence. Thus, the temporal evolution information of the time series data is continuously encoded through the height coordinates, ensuring that the sampling points within the same period maintain a temporal adjacency relationship in three-dimensional space, and that sampling points of the same phase across periods are vertically aligned. This facilitates intuitive comparison of data differences at the same phase position in different periods, quickly identifying periodic features such as phase shifts and amplitude anomalies; and ensures that the constructed three-dimensional spiral structure has no time dimension breakpoints, fully preserving the continuous evolution characteristics of the original time series, providing a structured geometric basis for subsequent visualization and extraction of periodic features from the time series model.

[0023] In a specific embodiment, the phase angle of the XY plane is obtained based on the position of the sampling point within its period, including: For fixed-period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ; For variable period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ; in: This is the initial phase angle.

[0024] Specifically, through the above processing, the sampling points in the same cycle are distributed in chronological order within a 360-degree angle range.

[0025] In a specific embodiment, obtaining the radial distance in the XY plane based on the observed amplitude includes: To reflect the influence of sample size on the spiral radius, the observed amplitudes were normalized: set up and Let be the minimum and maximum observed amplitudes in the sampled data, respectively. Then the th k Normalized value of the observed amplitude at each sampling point for: ; in: For the first k The observed amplitude corresponding to each sampling point k This is the global sampling sequence number for the time series, which is applicable to both fixed-period and variable-period time series sampling data. Specifically, the normalization result is used to control the radial position of the sampling point in the spiral layer.

[0026] Based on the k The normalized value of the observed amplitude at each sampling point determines the radial distance between the sampling points, expressed as: ; in: This represents the basic radius, used to ensure that the spiral structure has a basic spatial dimension; This represents the scaling factor, used to adjust the effect of changes in sample values ​​on the radial distance.

[0027] Specifically, in this embodiment, the larger the sample value, the greater the distance from the sampling point to the central axis of the spiral; the smaller the sample value, the smaller the distance from the sampling point to the central axis of the spiral. The base radius and scaling factor can be preset or adaptively determined according to the numerical range of the sample data, the display scale, or subsequent data processing requirements.

[0028] S4. Based on the phase angle, radial distance, and height coordinates of the sampling points, obtain the three-dimensional spatial coordinates corresponding to each sampling point; In a specific embodiment, in step S4, the three-dimensional spatial coordinates corresponding to each sampling point are obtained based on the phase angle, radial distance, and height coordinates of the sampling point. , is represented as: ; ; ; At this point, each sampling point k was Mapped to a three-dimensional point in spiral space .

[0029] S5. Connect the three-dimensional spatial coordinates of all sampling points sequentially according to the original sampling time order to generate a three-dimensional spiral time series curve, thus completing the three-dimensional representation of the univariate time series. This will assist analysts in conducting visualization analysis and help artificial intelligence models extract periodic features.

[0030] Specifically, the sampling points are connected sequentially according to their time order. This forms a three-dimensional spatial spiral structure in time series, such as Figure 2 As shown, global sampling data is connected in 3D coordinates according to the original sampling time sequence to generate a continuous spiral curve, which does not sever the continuous evolution relationship of time as in periodic layered plots and time series matrices. Adjacent time points in the same period and points with the same phase across periods are close in 3D space, intuitively highlighting the short-term continuous dependence and long-term periodic repetition of time series. For example, in the power load scenario, it is convenient for operation and maintenance personnel to intuitively compare load differences at the same time over multiple days, identify load peak and valley changes, capture phase shifts and abnormal power consumption phenomena, support the fine-grained scheduling of the power grid and distribution network operation and maintenance decisions, optimize power resource allocation, reduce power loss, and provide structured feature support for load forecasting and distribution network anomaly detection algorithms.

[0031] Specifically, this embodiment adopts a three-dimensional spiral geometric architecture, which independently maps the three types of core temporal features to different three-dimensional dimensions, eliminating the problems of mutual occlusion and overlapping interference, and greatly improving the visualization and recognition.

[0032] Specifically, this embodiment first obtains the complete original univariate time series, and divides it into two categories based on the data sampling frequency and fluctuation pattern: fixed-period time series sampling data and variable-period time series sampling data. For the two types of time series, period analysis is performed respectively: for fixed-period time series, the period number and position index within the period are obtained by rounding and other operations. For variable-period time series, the calendar information is retrieved based on the real timestamp corresponding to the sampling point, and the period number, current period length and position index within the period are adaptively obtained. In this way, the two-level encoding of period level and phase position is completed, and the period phase characteristics are explicitly characterized.

[0033] Secondly, a three-dimensional spatial mapping rule is constructed: the z-axis height coordinate is mapped by the period number, and different periods are arranged in layers along the height direction; the XY plane phase angle is converted based on the position of each sampling point within the period, so that the samples in the same period are distributed at equal angles along the circumference; after global normalization of the sampling observation amplitude, the radial distance of the XY plane is solved by combining the preset base radius and scaling factor, and then the three-dimensional spatial coordinates corresponding to each sampling point are obtained by converting the phase angle, radial distance and height coordinates through the polar coordinate to rectangular coordinate formula.

[0034] Finally, following the original sampling time sequence, the three-dimensional coordinates of all sampling points are connected sequentially. The time series data is then stretched layer by layer along the z-axis according to the periodic hierarchy, generating a three-dimensional spiral time series curve with continuous evolution characteristics, thus completing the three-dimensional spiral representation of the univariate time series. This three-dimensional spiral spatial structure can achieve decoupled expression of multiple types of features: sampling points that are temporally adjacent within the same period and sampling points of the same phase in different periods are all in close proximity in three-dimensional space, completely preserving the original continuous evolution relationship of the time series. Simultaneously, the layered structure highlights the periodic hierarchy, uniformly adapting to both fixed-period and variable-period time series data. It supports both manual visualization of periodic features and can also be used as structured three-dimensional data input to the target model.

[0035] Example 1: Fixed cycle of hourly power load This embodiment uses hourly electricity load data from Pennsylvania in 2019. After data processing, a total of 8755 valid sampling points were obtained. This data is sampled hourly, with a fixed period of one day; therefore, the period length is set to... ; The parameter settings for this embodiment are as follows:

[0036] Therefore, the radial distance and height position of this set of data are as follows: ; ; Calculation of spatial coordinates of a single sampling point: Taking the sampling point at 05:00 on January 1, 2019 as an example, its load value is MW. The minimum and maximum values ​​of this data set are respectively MW, MW, then: =(1213.596 1027.126) / (2661.935 1027.126)≈0.1141; =0.1 + 0.5 × 0.1141 ≈ 0.1570; Taking 00:00 as the first position of the day, then 05:00 corresponds to =6, this sampling point is located in the first daily cycle, therefore =1; =0+2π·(6 1) / 24 = 5π / 12; =(1 1) × 1 = 0; =0.1570·cos(5π / 12)≈0.0406; =0.1570·sin(5π / 12)≈0.1517; Therefore, the coordinates of this sampling point in the spatial spiral structure are ( , , = (0.0406, 0.1517, 0). Based on this, a daily load spiral is constructed with a 24-hour cycle. This allows for a direct comparison of the peak and valley electricity consumption differences during the same period each day. It can be used to quickly identify load phase shifts, equipment leakage, and abnormal electricity consumption on weekdays / rest days.

[0037] Example 2: Daily Sampling Univariate Natural Month Variable Period Mapping This example uses the PJM dataset, which, after data processing, yields 609 valid sampling points covering the period from January 1, 2015 to August 31, 2016. This data is sampled daily, with a calendar month as the cycle. Since different months may contain 28, 29, 30, or 31 days, a variable cycle processing method is used. The parameter settings for this embodiment are as follows:

[0038] Calculation of spatial coordinates of a single sampling point: Taking the sampling point on February 29, 2016 as an example, its sample value is =1738MW. The minimum and maximum values ​​of this data set are respectively... =1MW =3596MW, then: =(1738 1) / (3596 1)≈0.4832; =0.5 + 1.0 × 0.4832 ≈ 0.9832; February 2016 was a leap year, with 29 days. =29; This sampling point is the 29th day of the month, therefore =29. Taking January 2015 as the first cycle and February 2016 as the 14th calendar month cycle, therefore... =14; =0+2π·(29 1) / 29 = 56π / 29; =(14 1) × 1 = 13; =0.9832·cos(56π / 29)≈0.9602; =0.9832·sin(56π / 29)≈ 0.2114; Therefore, the coordinates of this sampling point in the spatial spiral structure are ( , , )=(0.9602, 0.2114,13). Based on this, adapting to the natural monthly cycle, a spiral layered display shows the total monthly electricity consumption and daily load fluctuations within the month, which can be used to assist in grid capacity planning and peak-valley electricity pricing strategy formulation.

[0039] The two embodiments described above correspond to fixed-period and variable-period data, respectively. Hourly power load data is based on... Establish a daily periodic spatial spiral structure; daily sampling data is obtained through... , and Adaptive encoding of natural monthly cycles is achieved. Both embodiments employ consistent normalization, radial mapping, phase mapping, height hierarchies, and 3D coordinate transformation methods, demonstrating that this invention can handle univariate time series with different sampling frequencies and periodic forms within a unified 3D representation framework.

[0040] This invention selects only power load data as a demonstration case to clearly illustrate the technical calculation process. However, the technical implementation logic of this invention is not limited to the power load data scenario. As long as it is a single variable time series containing only a single observation indicator and having periodic evolution characteristics, regardless of the industry, sampling interval length, or whether the period is fixed, the scheme proposed in this invention can be used to complete the three-dimensional spiral structured representation. It is not constrained by the data industry attributes and has universal adaptability across all industries.

[0041] 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 three-dimensional representation method for univariate time series, characterized in that, include: S1. Obtain the original univariate time series to be processed, which includes several sampled data carrying the observed amplitude; S2. Perform periodic analysis on the sampled data to determine the period number corresponding to each sampling point and its position within the period. S3. Constructing a three-dimensional mapping relationship, including: determining the height coordinates of the sampling point based on the period number, obtaining the phase angle of the XY plane based on the position of the sampling point within the period, and obtaining the radial distance of the XY plane based on the observation amplitude; S4. Based on the phase angle, radial distance, and height coordinates of the sampling points, obtain the three-dimensional spatial coordinates corresponding to each sampling point; S5. Connect the three-dimensional spatial coordinates of all sampling points sequentially according to the original sampling time order to generate a three-dimensional spiral time series curve, thus completing the three-dimensional representation of the univariate time series.

2. The three-dimensional representation method for univariate time series according to claim 1, characterized in that, In S2, the sampled data is periodically analyzed to determine the period number corresponding to each sampling point and its position within the period, including: S21. Based on the sampling frequency and variation pattern of the sampled data, the sampled data is divided into fixed-period time-series sampled data and variable-period time-series sampled data; S22. Determine the first [number] in the sampled data. The period number corresponding to each sampling point is: and position within the corresponding period ,include: For time-series sampling data with a fixed period, where the first... The period number corresponding to each sampling point and position within the corresponding period The expression is: ； ； in: For a fixed period length; This is the floor function operator; This is the modulo operator; For variable-period time-series sampling data, the first The period number corresponding to each sampling point and within the corresponding period The expression is: ； ； ； in: This indicates that the year and month of the sample are returned, which corresponds to the period number of the sample. This indicates that the number of days in the corresponding month, i.e., the period length, is returned. This is a timestamp, indicating the [number]th [item]. The actual time corresponding to each sampling point.

3. The three-dimensional representation method for univariate time series according to claim 2, characterized in that, The height coordinates of the sampling points determined based on the aforementioned period number are expressed as follows: ； in: and These correspond to the height coordinates of sampling points in fixed-period and variable-period time-series sampling data, respectively. For fixed step size.

4. The three-dimensional representation method for univariate time series according to claim 3, characterized in that, The phase angle of the XY plane is obtained based on the position of the sampling point within its period, including: For fixed-period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ； For variable period time-series sampling data, according to the first... Position of each sample within the period The phase angle is determined by the following formula: ； in: This is the initial phase angle.

5. The three-dimensional representation method for univariate time series according to claim 4, characterized in that, The radial distance in the XY plane is obtained based on the observed amplitude, including: The observed amplitudes are normalized: set up and Let be the minimum and maximum observed amplitudes in the sampled data, respectively. Then the th k Normalized value of the observed amplitude at each sampling point for: ； in: For the first k The observed amplitude corresponding to each sampling point k This is the global sampling sequence number for the time series, which is applicable to both fixed-period and variable-period time series sampling data. Based on the k The normalized value of the observed amplitude at each sampling point determines the radial distance between the sampling points, expressed as: ； in: Indicates the base radius; This represents the scaling factor.

6. The three-dimensional representation method for univariate time series according to claim 5, characterized in that, In S4, the three-dimensional spatial coordinates corresponding to each sampling point are obtained based on the phase angle, radial distance, and height coordinates of the sampling point. , is represented as: ； ； 。

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