Time series similarity measure method based on component period matching

Abstract

The application discloses a time series similarity measurement method based on component period matching, and belongs to the technical field of data processing, and comprises the following steps: S1, EMD decomposition of an original time series; S2, calculation of periods of each component; S3, calculation of the shortest distance of the periods; S4, shortest distance merging; a similarity value set is calculated according to the shortest distance of each member of PA and PB, and is merged in a weighted average manner, and a similarity measurement value S between the time series A and the time series B is obtained. The application not only performs frequency domain decomposition on the original time series, but also utilizes the period characteristics of each component, avoids the blindness of matching between the components, realizes the consistency of the periods in signal decomposition and period matching, performs similarity measurement of the time series through period matching of each component, reduces the calculation times in the similarity analysis process, further reduces the time complexity of the distance measurement process, and enhances the applicability.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a time series similarity measurement method based on component period matching. Background Technology

[0002] Time series are random sequences of values ​​for the same indicator arranged in chronological order. Their application in data mining is increasingly widespread. For example, in the networking field, time series are commonly used to represent the state and trend of network traffic over time. Time series similarity measurement, as an important aspect of data mining, is crucial for uncovering the intrinsic relationships between time series.

[0003] Common time series similarity metrics include: Euclidean distance, cosine similarity, singular value decomposition, dynamic time curvature distance, trend distance, edit distance, feature subsequence distance, subsequence matching, Friesian distance, and Hausdorff distance. These metrics mostly match and calculate distances between two different time series from the perspectives of spatial distribution and time period. Their commonality lies in matching and similarity analysis based on the original values ​​of the time series, with less consideration given to similarity measurement based on the internal components of the time series. However, many time series are actually formed by the superposition of multiple independent sub-components; for example, backbone network traffic is the result of the superposition of traffic from multiple independent network nodes. Therefore, decomposing the original time series into multiple independent sub-components and performing similarity analysis on these independent sub-components can help to more accurately discover hidden connections between two seemingly unrelated time series.

[0004] Decomposition methods for time series generally employ frequency domain decomposition, which involves breaking down the original time series into multiple independent sub-components with different frequency periods. Common decomposition methods include Discrete Fourier Transform (DFT), Wavelet Transform (WT), and Empirical Mode Decomposition (EMD). Current research has shifted its focus to time series similarity methods based on signal decomposition, including EMD-based time series similarity measurement algorithms, wavelet transform-based time series clustering methods, methods for time series similarity matching based on Weighted Intrinsic Mode Function (IMF), hierarchical similarity matching algorithms for time series based on EMD, and time series similarity matching methods based on wavelets and dynamic time warping.

[0005] In summary, existing time series similarity measurement methods can be broadly categorized into two types: direct measurement methods, which measure similarity directly on the original time series, and decomposition measurement methods, which decompose the original time series before measuring similarity. Direct measurement methods typically employ absolute value similarity and shape similarity methods, neglecting the characteristics of each component within the original signal, inevitably leading to ambiguity in the evaluation results. While decomposition measurement methods consider the characteristics of each component, they do not examine or compare the periodicity of each component. Instead, they either directly accumulate and restore some components, perform sequential one-to-one measurement of components, or only select some components for similarity measurement, all of which have certain limitations.

[0006] Chinese patent document CN115659160A, published on January 31, 2023, discloses a data quality measurement method for optimizing digital twin models. The method is characterized by the following steps:

[0007] Acquire multiple time-series data in any industrial scenario;

[0008] For any type of time series data, seasonal curves are obtained through time series decomposition. The seasonal curves are then transformed into the frequency domain space to obtain several amplitudes. Several process cycles are obtained based on the frequencies corresponding to different amplitudes. The seasonal curves are divided into several segments based on different process cycles. Several process cycle curves corresponding to the same process cycle are obtained based on the similarity between different segments within the same process cycle. Continuous different process cycle curves are taken as a life cycle curve.

[0009] For each lifecycle curve, several IMF components of each process cycle are obtained through mode decomposition and process cycle. Based on the matching relationship between each IMF component of each process cycle and the process cycle curve, several feature point sequences and several component similarities of each process cycle are obtained. Based on several feature point sequences of the same process cycle in adjacent lifecycles, the first similarity of two adjacent process cycle curves with the same segment is obtained.

[0010] Based on the first similarity of each process cycle in adjacent life cycles, obtain the stability parameters of each process cycle, obtain the stability parameters of each process cycle in different types of time series data, obtain several standard cycles based on several process cycles in different types of time series data, and obtain the data quality index of each standard cycle based on the stability parameters of the process cycles in different types of time series data corresponding to each standard cycle.

[0011] The digital twin model is optimized based on data quality metrics for each standard period.

[0012] The data quality measurement method disclosed in this patent document for optimizing digital twin models can be optimized for specific processes. However, because it does not consider the periodicity of each component of the original signal and instead mixes and matches signals with different periods, it fails to identify the inherent correlation between signals, increases the number of calculations in the similarity analysis process, and increases the time complexity of the distance measurement process, resulting in poor applicability. Summary of the Invention

[0013] To overcome the shortcomings of the prior art, this invention provides a time series similarity measurement method based on component period matching. This invention not only performs frequency domain decomposition on the original time series, but also utilizes the periodic characteristics of each component, avoiding the blindness of matching between components. It achieves consistency of period in signal decomposition and period matching, and measures the similarity of time series by matching the period of each component, reducing the number of calculations in the similarity analysis process, thereby reducing the time complexity of the distance measurement process and enhancing its applicability.

[0014] This invention is achieved through the following technical solution:

[0015] A time series similarity measurement method based on component period matching is characterized by the following steps:

[0016] S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms;

[0017] S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB.

[0018] S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB.

[0019] S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B.

[0020] S1 specifically includes:

[0021] S11. Draw the upper envelope and lower envelope based on the upper and lower extreme points of the original signal.

[0022] S12. Find the mean of the upper and lower envelopes, and draw the mean envelope.

[0023] S13. Subtract the mean envelope from the original signal to obtain the intermediate signal;

[0024] S14. Determine whether the intermediate signal meets the two conditions of IMF. If it does, the intermediate signal is an IMF component; otherwise, repeat the analysis of S11-S14 based on the intermediate signal.

[0025] S15. After obtaining the first IMF1, subtract IMF1 from the original signal to obtain the new original signal. Then, through the analysis in S11-S14, obtain IMF2, and so on, to complete the EMD decomposition.

[0026] S2 specifically includes:

[0027] S21. For each component IMF i The average period Th is estimated based on the number and location of the peak points. i ;

[0028] S22, For each component IMF i The average period Tl is estimated based on the number and location of the valley points. i ;

[0029] S23. The average period Th obtained from the calculation i and average period Tl i Take the average value as the component IMF i Average period P i ;

[0030] S24. Based on S21-S23, perform IMF analysis on the M components of time series A respectively. 1-M Calculate the average period, denoted as PA. 1-M ;

[0031] S25. Based on S21-S23, perform IMF analysis on the N components of time series B respectively. 1-N Calculate the average period, denoted as PB. 1-N .

[0032] S3 specifically includes:

[0033] S31. Traverse all members of set PA. 1-M Calculate PA respectively 1-M The relative errors with all members of the PB set are used to find the shortest distance, with the minimum relative error being denoted as DA. 1-MFor PA 1-M Any member PA in i PA i The shortest distance between PB and DA is i =min(|(PA) i -PB1) / max(PA i ,PB1)|,|(PA i -PB2) / max(PA i ,PB2)|,…,|(PA i -PB N ) / max(PA i ,PB N )|);

[0034] S32. Traverse all members of set PB. 1-N Calculate PB respectively 1-N The relative errors with all members of the PA set are used to determine the shortest distance, with the minimum relative error being denoted as DB. 1-N For PB 1-N Any member PB in j PB j The shortest distance between PA and DB is DB. j =min(|(PB) j -PA1) / max(PB j ,PA1)|,|(PB) j -PA2) / max(PB j ,PA2)|,…,|(PB) j -PA M ) / max(PB j PA M )|).

[0035] S4 specifically includes:

[0036] S41. Traverse the set DA, for any member DA i Calculate the corresponding similarity value VA i The formula for calculating the similarity value is: VA i =|1-DA i |; Obtain the similarity value set VA from the DA set. 1-M ;

[0037] S42. Traverse the DB collection, and for any member DB... j Calculate the corresponding similarity value VB j The formula for calculating the similarity value is: VB j =|1-DB j |; Obtain a similarity value set from the DB set (VB) 1-N ;

[0038] S43. IMF of the M components of time series A 1-M Calculate the weight value, denoted as WA. 1-M ;

[0039] S44. IMF for the N components of time series B 1-N Calculate the weight value, denoted as WB. 1-N ;

[0040] S45. Calculate the similarity measure S between time series A and time series B using a weighted average. The formula is S = [(VA1 x WA1 + VA2 x WA2 + ... + VA...]. M xW M )+(VB1 x WB1+VB2 xWB2+…+VB N x WB N )] / (M+N).

[0041] In step S43, the calculation of the weight values ​​specifically refers to calculating the mean AO of the original time series data and the M component IMFs respectively. 1-M Their respective mean A 1-M Using A respectively 1-M Divide the value by AO to obtain the weight value WA of each component's mean relative to the original data. 1-M For any component of the IMF i weight value WA i =A i / AO.

[0042] In step S44, the calculation of weight values ​​specifically refers to calculating the mean BO of the original time series data and the IMF of the N components. 1-N Their respective means B 1-N B respectively 1-N Divide the value by BO to obtain the weight value WB of each component's mean relative to the original data. 1-N For any component of the IMF j weight value WB j =Bj / BO.

[0043] The beneficial effects of this invention are mainly reflected in the following aspects:

[0044] 1. This invention not only performs frequency domain decomposition on the original time series, but also utilizes the periodic characteristics of each component to avoid the blindness of matching between components. It achieves consistency of period in signal decomposition and period matching, and measures the similarity of time series by matching the period of each component. This reduces the number of calculations in the similarity analysis process, thereby reducing the time complexity of the distance measurement process and enhancing its applicability.

[0045] 2. This invention can significantly reduce the time complexity of the distance measurement process by transforming the distance metric of data points in a time series into the distance metric of component periods.

[0046] 3. Compared with the prior art, which does not consider the periodicity of each component of the original signal and mixes and matches signals with different periods, resulting in the inability to identify the intrinsic correlation of the signals, this invention can better reduce the time complexity of the distance measurement process by making full use of the component periods and examining the periodicity similarity of each component.

[0047] 4. Compared with the prior art, which can cause the time axis to be too curved in shape similarity matching, the present invention achieves period consistency in signal decomposition and period matching, which can effectively reduce the curvature of the time axis.

[0048] 5. This invention decomposes behavioral feature time series, calculates the similarity of components, and discovers internal correlations between time series based on component matching. Attached Figure Description

[0049] The present invention will now be further described in detail with reference to the accompanying drawings and specific embodiments:

[0050] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0051] Example 1

[0052] See Figure 1 A time series similarity measurement method based on component period matching includes the following steps:

[0053] S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms;

[0054] S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB.

[0055] S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB.

[0056] S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B.

[0057] This embodiment is the most basic implementation method. It not only performs frequency domain decomposition on the original time series, but also utilizes the periodic characteristics of each component to avoid the blindness of matching between components. It achieves consistency of period in signal decomposition and period matching. By matching the period of each component, the similarity of the time series is measured, which reduces the number of calculations in the similarity analysis process, thereby reducing the time complexity of the distance measurement process and enhancing its applicability.

[0058] Example 2

[0059] See Figure 1 A time series similarity measurement method based on component period matching includes the following steps:

[0060] S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms;

[0061] S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB.

[0062] S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB.

[0063] S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B.

[0064] S1 specifically includes:

[0065] S11. Draw the upper envelope and lower envelope based on the upper and lower extreme points of the original signal.

[0066] S12. Find the mean of the upper and lower envelopes, and draw the mean envelope.

[0067] S13. Subtract the mean envelope from the original signal to obtain the intermediate signal;

[0068] S14. Determine whether the intermediate signal meets the two conditions of IMF. If it does, the intermediate signal is an IMF component; otherwise, repeat the analysis of S11-S14 based on the intermediate signal.

[0069] S15. After obtaining the first IMF1, subtract IMF1 from the original signal to obtain the new original signal. Then, through the analysis in S11-S14, obtain IMF2, and so on, to complete the EMD decomposition.

[0070] This embodiment is a preferred implementation method. By converting the distance metric of data points in the time series into the distance metric of component periods, the time complexity of the distance metric process can be significantly reduced.

[0071] Example 3

[0072] See Figure 1 A time series similarity measurement method based on component period matching includes the following steps:

[0073] S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms;

[0074] S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB.

[0075] S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB.

[0076] S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B.

[0077] S1 specifically includes:

[0078] S11. Draw the upper envelope and lower envelope based on the upper and lower extreme points of the original signal.

[0079] S12. Find the mean of the upper and lower envelopes, and draw the mean envelope.

[0080] S13. Subtract the mean envelope from the original signal to obtain the intermediate signal;

[0081] S14. Determine whether the intermediate signal meets the two conditions of IMF. If it does, the intermediate signal is an IMF component; otherwise, repeat the analysis of S11-S14 based on the intermediate signal.

[0082] S15. After obtaining the first IMF1, subtract IMF1 from the original signal to obtain the new original signal. Then, through the analysis in S11-S14, obtain IMF2, and so on, to complete the EMD decomposition.

[0083] S2 specifically includes:

[0084] S21. For each component IMF i The average period Th is estimated based on the number and location of the peak points. i ;

[0085] S22, For each component IMF i The average period Tl is estimated based on the number and location of the valley points. i ;

[0086] S23. The average period Th obtained from the calculation i and average period Tl i Take the average value as the component IMF i Average period P i ;

[0087] S24. Based on S21-S23, perform IMF analysis on the M components of time series A respectively. 1-M Calculate the average period, denoted as PA. 1-M ;

[0088] S25. Based on S21-S23, perform IMF analysis on the N components of time series B respectively. 1-N Calculate the average period, denoted as PB. 1-N .

[0089] S3 specifically includes:

[0090] S31. Traverse all members of set PA. 1-M Calculate PA respectively 1-M The relative errors with all members of the PB set are used to find the shortest distance, with the minimum relative error being denoted as DA. 1-M For PA 1-M Any member PA in i PA iThe shortest distance between PB and DA is i =min(|(PA) i -PB1) / max(PA i ,PB1)|,|(PA i -PB2) / max(PA i ,PB2)|,…,|(PA i -PB N ) / max(PA i ,PB N )|);

[0091] S32. Traverse all members of set PB. 1-N Calculate PB respectively 1-N The relative errors with all members of the PA set are used to determine the shortest distance, with the minimum relative error being denoted as DB. 1-N For PB 1-N Any member PB in j PB j The shortest distance between PA and DB is DB. j =min(|(PB) j -PA1) / max(PB j ,PA1)|,|(PB) j -PA2) / max(PB j ,PA2)|,…,|(PB) j -PA M ) / max(PB j PA M )|).

[0092] This embodiment is another preferred implementation. Compared with the prior art, which does not consider the periodicity of each component of the original signal and mixes and matches signals with different periods, resulting in the inability to identify the intrinsic correlation of the signals, by making full use of the component periods and examining the periodicity similarity of each component, the time complexity of the distance measurement process can be better reduced.

[0093] Example 4

[0094] See Figure 1 A time series similarity measurement method based on component period matching includes the following steps:

[0095] S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms;

[0096] S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB.

[0097] S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB.

[0098] S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B.

[0099] S1 specifically includes:

[0100] S11. Draw the upper envelope and lower envelope based on the upper and lower extreme points of the original signal.

[0101] S12. Find the mean of the upper and lower envelopes, and draw the mean envelope.

[0102] S13. Subtract the mean envelope from the original signal to obtain the intermediate signal;

[0103] S14. Determine whether the intermediate signal meets the two conditions of IMF. If it does, the intermediate signal is an IMF component; otherwise, repeat the analysis of S11-S14 based on the intermediate signal.

[0104] S15. After obtaining the first IMF1, subtract IMF1 from the original signal to obtain the new original signal. Then, through the analysis in S11-S14, obtain IMF2, and so on, to complete the EMD decomposition.

[0105] S2 specifically includes:

[0106] S21. For each component IMF i The average period Th is estimated based on the number and location of the peak points. i ;

[0107] S22, For each component IMF i The average period Tl is estimated based on the number and location of the valley points. i ;

[0108] S23. The average period Th obtained from the calculation i and average period Tl i Take the average value as the component IMF iAverage period P i ;

[0109] S24. Based on S21-S23, perform IMF analysis on the M components of time series A respectively. 1-M Calculate the average period, denoted as PA. 1-M ;

[0110] S25. Based on S21-S23, perform IMF analysis on the N components of time series B respectively. 1-N Calculate the average period, denoted as PB. 1-N .

[0111] S3 specifically includes:

[0112] S31. Traverse all members of set PA. 1-M Calculate PA respectively 1-M The relative errors with all members of the PB set are used to find the shortest distance, with the minimum relative error being denoted as DA. 1-M For PA 1-M Any member PA in i PA i The shortest distance between PB and DA is i =min(|(PA) i -PB1) / max(PA i ,PB1)|,|(PA i -PB2) / max(PA i ,PB2)|,…,|(PA i -PB N ) / max(PA i ,PB N )|);

[0113] S32. Traverse all members of set PB. 1-N Calculate PB respectively 1-N The relative errors with all members of the PA set are used to determine the shortest distance, with the minimum relative error being denoted as DB. 1-N For PB 1-N Any member PB in j PB j The shortest distance between PA and DB is DB. j =min(|(PB) j -PA1) / max(PB j ,PA1)|,|(PB) j -PA2) / max(PB j ,PA2)|,…,|(PB) j -PA M ) / max(PB j PAM )|).

[0114] S4 specifically includes:

[0115] S41. Traverse the set DA, for any member DA i Calculate the corresponding similarity value VA i The formula for calculating the similarity value is: VA i =|1-DA i |; Obtain the similarity value set VA from the DA set. 1-M ;

[0116] S42. Traverse the DB collection, and for any member DB... j Calculate the corresponding similarity value VB j The formula for calculating the similarity value is: VB j =|1-DB j |; Obtain a similarity value set from the DB set (VB) 1-N ;

[0117] S43. IMF of the M components of time series A 1-M Calculate the weight value, denoted as WA. 1-M ;

[0118] S44. IMF for the N components of time series B 1-N Calculate the weight value, denoted as WB. 1-N ;

[0119] S45. Calculate the similarity measure S between time series A and time series B using a weighted average. The formula is S = [(VA1 x WA1 + VA2 x WA2 + ... + VA...]. M xW M )+(VB1 x WB1+VB2 xWB2+…+VB N x WB N )] / (M+N).

[0120] In step S43, the calculation of the weight values ​​specifically refers to calculating the mean AO of the original time series data and the M component IMFs respectively. 1-M Their respective mean A 1-M Using A respectively 1-M Divide the value by AO to obtain the weight value WA of each component's mean relative to the original data. 1-M For any component of the IMF i weight value WA i =A i / AO.

[0121] In step S44, the calculation of weight values ​​specifically refers to calculating the mean BO of the original time series data and the IMF of the N components. 1-N Their respective means B 1-N B respectively 1-N Divide the value by BO to obtain the weight value WB of each component's mean relative to the original data. 1-N For any component of the IMF j weight value WB j =Bj / BO.

[0122] This embodiment is the best implementation method. Compared with the prior art, which can cause the time axis to be too curved in shape similarity matching, the signal decomposition and period matching achieve period consistency, which can effectively reduce the curvature of the time axis.

[0123] By decomposing the time series of behavioral features and calculating the similarity of the components, the internal correlation between time series can be discovered through component-based matching.

[0124] The EMD mentioned in this invention refers to Empirical Mode Decomposition, which is an adaptive signal time-frequency processing method suitable for the analysis and processing of nonlinear and non-stationary signals. It decomposes signals based on the time-scale characteristics of the data itself, without the need to pre-define any basis functions.

[0125] The IMF mentioned in this invention refers to an intrinsic modal component that satisfies the following two constraints: First, the number of extreme points and the number of zero-crossing points must be equal or differ by no more than one throughout the entire data segment; Second, at any given time, the average value of the upper envelope formed by local maxima and the lower envelope formed by local minima is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.

[0126] The residual term in this invention refers to the linear superposition of the original signal decomposed into a series of IMFs and the remaining part by EMD decomposition, and the residual term is the remaining amount after subtracting each IMF component from the original signal.

[0127] The component period described in this invention refers to a continuous time period, denoted as T, during which the IMF component signal is almost identical to the IMF component signal in the next continuous time period, and this continuous time is the shortest continuous time period with this property that can be found.

[0128] The distance described in this invention refers to a distance expressed using relative error.

[0129] The basic principle of this invention is as follows:

[0130] First, based on signal decomposition, instead of directly measuring the distance between each component, we first calculate the period of each component to form a set of periods in the time series. Second, we measure the distance between the periods of components from different time series to obtain the shortest distance between the sets of periods of different time series. Furthermore, we merge the shortest distances of the sets of periods to form a similarity measurement result between time series.

Claims

1. A time series similarity measurement method based on component periodic matching, where the time series represents the state and trend of network traffic changes over time, characterized in that... Includes the following steps: S1. EMD decomposition of the original time series: Time series A and time series B are decomposed into multiple components, respectively. Assume time series A is decomposed into M components (IMF). 1-M With residuals, time series B is decomposed into N components IMF. 1-N and residual terms; S2. Calculate the period of each component. Calculate the period of each component in turn. The period is calculated based on the estimation of extreme points. Time series A obtains M periods, forming a period set PA. Time series B obtains N periods, forming a period set PB. S3. Calculate the shortest distance of each periodic set PA and PB. Calculate the shortest distance between each member of each periodic set PA and PB and the other set. The shortest distance is calculated by taking the minimum relative error. The shortest distance between each member of PA and PB and the other set is obtained, and each of them forms sets DA and DB. S4. Shortest distance merging: Calculate the similarity value set based on the shortest distance of each member of PA and PB, and merge them in a weighted average manner to obtain the similarity measure S between time series A and time series B. S3 specifically includes: S31. Traverse all members of set PA. 1-M Calculate PA respectively 1-M The relative errors with all members of the PB set are used to find the shortest distance, with the minimum relative error being denoted as DA. 1-M For PA 1-M Any member PA in i PA i The shortest distance between PB and DA is i =min(|(PA i -PB1) / max(PA i ,PB1)|,|(PA i -PB2) / max(PA i ,PB2)|,…,| (PA i -PB N ) / max(PA i ,PB N )|); S32. Traverse all members of set PB. 1-N Calculate PB respectively 1-N The relative errors with all members of the PA set are used to determine the shortest distance, with the minimum relative error being denoted as DB. 1-N For PB 1-N Any member PB in j PB j The shortest distance between PA and DB is DB. j =min(|(PB j -PA1) / max(PB j ,PA1)|,|(PB) j -PA2) / max(PB j ,PA2)|,…,|(PB) j -PA M ) / max(PB j PA M )|); S4 specifically includes: S41. Traverse the set DA, for any member DA i Calculate the corresponding similarity value VA i The formula for calculating the similarity value is: VA i =|1-DA i |; Obtain the similarity value set VA from the DA set. 1-M ; S42. Traverse the DB collection, and for any member DB... j Calculate the corresponding similarity value VB j The formula for calculating the similarity value is: VB j =|1-DB j |; Obtain a similarity value set from the DB set (VB) 1-N ; S43. IMF of the M components of time series A 1-M Calculate the weight value, denoted as WA. 1-M ; S44. IMF for the N components of time series B 1-N Calculate the weight value, denoted as WB. 1-N ; S45. Calculate the similarity measure S between time series A and time series B using a weighted average. The formula is S = [(VA1 x WA1 + VA2 x WA2 + ... + VA...]. M xW M )+ (VB1 x WB1+ VB2 x WB2+…+ VB N x WB N )] / (M+N).

2. The time series similarity measurement method based on component periodic matching according to claim 1, characterized in that: S1 specifically includes: S11. Draw the upper envelope and lower envelope based on the upper and lower extreme points of the original signal. S12. Find the mean of the upper and lower envelopes, and draw the mean envelope. S13. Subtract the mean envelope from the original signal to obtain the intermediate signal; S14. Determine whether the intermediate signal meets the two conditions of IMF. If it does, the intermediate signal is an IMF component; otherwise, repeat the analysis of S11-S14 based on the intermediate signal. S15. After obtaining the first IMF1, subtract IMF1 from the original signal to obtain the new original signal. Then, through the analysis in S11-S14, obtain IMF2, and so on, to complete the EMD decomposition.

3. The time series similarity measurement method based on component periodic matching according to claim 1, characterized in that: S2 specifically includes: S21. For each component IMF i The average period Th is estimated based on the number and location of the peak points. i ; S22, For each component IMF i The average period Tl is estimated based on the number and location of the valley points. i ; S23. The average period Th obtained from the calculation i and average period Tl i Take the average value as the component IMF i Average period P i ; S24. Based on S21-S23, perform IMF analysis on the M components of time series A respectively. 1-M Calculate the average period, denoted as PA. 1-M ; S25. Based on S21-S23, perform IMF analysis on the N components of time series B respectively. 1-N Calculate the average period, denoted as PB. 1-N .

4. The time series similarity measurement method based on component periodic matching according to claim 1, characterized in that: In step S43, the calculation of the weight values ​​specifically refers to calculating the mean AO of the original time series data and the M component IMFs respectively. 1-M Their respective mean A 1-M Using A respectively 1-M Divide the value by AO to obtain the weight value WA of each component's mean relative to the original data. 1-M For any component of the IMF i weight value WA i =A i / AO.

5. The time series similarity measurement method based on component periodic matching according to claim 1, characterized in that: In step S44, the calculation of weight values ​​specifically refers to calculating the mean BO of the original time series data and the IMF of the N components. 1-N Their respective means B 1-N B respectively 1-N Divide the value by BO to obtain the weight value WB of each component's mean relative to the original data. 1-N For any component of the IMF j weight value WB j =Bj / BO.

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