KR20220123845A - Meathod and device for measuring similarity between time series data - Google Patents

Abstract

Disclosed is a method for measuring a similarity between time series data. According to the present invention, the method for measuring a similarity between time series data includes: a step of collecting first time series data; a step of splitting the first time series data into a section in a certain size and acquiring a main symbol based on a measurement value of the section; a step of acquiring at least one pattern symbol presenting a structural pattern of the first time series data from the section; and a step of calculating a similarity between the first time series data and second time series data by using the main symbol and the at least one pattern symbol coupled with the main symbol.

Description

Method and apparatus for measuring similarity between time series data

The present invention relates to a method and apparatus for measuring the degree of similarity between time series data, which can calculate the degree of similarity between time series data using a main symbol and a pattern symbol representing a variation pattern of time series data, and represent the degree of similarity between time series data as a normalized value will be.

Due to the recent development of technology, the utilization of edge computing devices such as IOT sensors has been greatly increased.

Specifically, with the development of microprocessor manufacturing technology, the hardware specifications have been improved, and the computing power of edge devices has been strengthened.

For example, due to the development of sensors and the improvement of penetration rates, the size of sensor data collected or analyzed for monitoring and control of building energy has greatly increased, and it is predicted that the increase will be very large in the future.

On the other hand, due to the increase in edge devices and the expansion of complex operations such as sensor AI and machine learning, a lot of data is received in the central cloud connected to a number of edge devices, and complex calculations are performed using a lot of data. should be carried out

In addition, in order to reduce data omissions and delays, traffic, and computational load of the central cloud due to network delay and network stability problems, it is necessary to distribute the computational load of the central cloud to edge devices.

However, even though the performance of the edge device has improved a lot compared to the past, the performance of the edge device is still limited due to cost problems, and therefore, efficient computational technology is required for data processing and analysis in the edge device.

The present invention is to solve the above-described problems, and an object of the present invention is to calculate the similarity between time series data using a main symbol and a pattern symbol representing a variation pattern of time series data, and convert the similarity between time series data to a normalized value. It is to provide a method and apparatus for measuring the similarity between time series data that can be represented.

The method for measuring the similarity between time series data according to the present invention comprises the steps of collecting first time series data, dividing the first time series data into sections of a certain size, and obtaining a main symbol based on the measured value of the section; In the section, obtaining one or more pattern symbols representing a structural pattern of the first time series data, and using the main symbol and one or more pattern symbols combined with the main symbol, the first time series data and the second and calculating a similarity between the two time series data.

In this case, the pattern symbol may include an increase symbol, a decrease symbol, a maintenance symbol, and a noise symbol.

In this case, the step of obtaining the pattern symbol may include calculating a standard deviation using differences between the measurement value at a previous time and the measurement value at the current time of the first time series data, and if the standard deviation is greater than a noise threshold , determining that the pattern symbol is a noise symbol.

In this case, the obtaining of the pattern symbol includes: if the standard deviation is smaller than the noise threshold, calculating average values of detailed sections within the section; The method may further include determining any one of the reduction symbol and the maintenance symbol.

Meanwhile, the noise symbol may have the largest distance from other symbols, and the maintenance symbol may have the smallest distance from the increment symbol or the decrement symbol, except for distances between the same symbols.

Meanwhile, calculating the degree of similarity between the first time series data and the second time series data includes a first combined symbol that is a combination of the main symbol and the pattern symbol of the first time series data, and a second main of the second time series data. and calculating a distance between a second combined symbol that is a combination of a symbol and a second pattern symbol.

In this case, the calculating of the distance between the combined symbol and the second combined symbol includes calculating the main symbol distance between the main symbol and the second main symbol using a comparison table of main symbols, Comparison of pattern symbols calculating a pattern symbol distance between the pattern symbol and the second pattern symbol using a table, and adding the main symbol distance and the pattern symbol distance to the distance between the first combined symbol and the second combined symbol It may include the step of calculating

Meanwhile, calculating the similarity between the first time series data and the second time series data includes generating a DTW matrix using a distance between the first combining symbol and the second combining symbol in each section, and the DTW matrix The method may further include selecting an optimal warping path in which the similarity between the first time series data and the second time series data is most closely mapped using the method.

In this case, the calculating of the similarity between the first time series data and the second time series data may include asynchronously mapping the first time series data and the second time series data using a plurality of index pairs constituting the optimal warping path. It may further include the step of

In this case, the calculating of the similarity between the first time series data and the second time series data may include: using the asynchronously mapped values of the first time series data and the second time series data, the first time series data and calculating a normalized statistical similarity indicating a correlation between the second time series data and the second time series data.

Meanwhile, the apparatus for measuring similarity between time series data according to the present invention includes a data collection unit that collects first time series data, and divides the first time series data into sections of a predetermined size and selects a main symbol based on the measured value of the section obtaining, in the section, one or more pattern symbols representing a structural pattern of the first time series data, and using the main symbol and one or more pattern symbols combined with the main symbol, the first time series data and the second and a control unit for calculating a degree of similarity between the two time series data.

In this case, the pattern symbol may include an increase symbol, a decrease symbol, a maintenance symbol, and a noise symbol.

In this case, the control unit calculates a standard deviation by using differences between the measurement value of the previous time and the measurement value of the current time of the first time series data, and if the standard deviation is greater than a noise threshold, the pattern symbol is a noise symbol it can be decided that

In this case, when the standard deviation is smaller than the noise threshold, the control unit calculates average values of detailed sections within the section, and uses a slope between the average values to select any one of the increase symbol, the decrease symbol, and the maintenance symbol. You can decide one.

Meanwhile, the noise symbol may have the largest distance from other symbols, and the maintenance symbol may have the smallest distance from the increment symbol or the decrement symbol, except for distances between the same symbols.

On the other hand, the control unit, between a first combination symbol that is a combination of the main symbol and the pattern symbol of the first time series data, and a second combination symbol that is a combination of a second main symbol and a second pattern symbol of the second time series data distance can be calculated.

In this case, the control unit calculates a main symbol distance between the main symbol and the second main symbol using a comparison table of main symbols, and uses the comparison table of pattern symbols to determine the pattern symbol and the second pattern symbol. The distance between the first combined symbol and the second combined symbol may be calculated by calculating a pattern symbol distance between the first and second combined symbols by summing the main symbol distance and the pattern symbol distance.

Meanwhile, the controller generates a DTW matrix by using the distance between the first combined symbol and the second combined symbol of each section, and the similarity between the first time series data and the second time series data is the most by using the DTW matrix. It is possible to select an optimal warping path that is closely mapped.

In this case, the controller may asynchronously map the first time series data and the second time series data using a plurality of index pairs constituting the optimal warping path.

Meanwhile, the computer program includes the steps of collecting first time series data, dividing the first time series data into sections of a certain size, and obtaining a main symbol based on the measurement value of the section, in the section, the first obtaining one or more pattern symbols representing a structural pattern of time series data, and calculating a degree of similarity between the first time series data and the second time series data by using the main symbol and one or more pattern symbols combined with the main symbol It may be stored in a medium in order to perform a similarity measurement method between time series data comprising the step of:

According to the present invention, there is an advantage in that the amount of computation is significantly reduced through symbolization, information distortion is minimized by symbolization, and thus the accuracy of determining the similarity of time series data can be improved.

In addition, according to the present invention, similarity between time series data can be expressed as a normalized value, and a state can be classified or anomaly detected using only the normalized value. For example, the controller 120 may determine that the normalized statistical similarity is 0.7 or more as normal, 0.5 to 0.7 as an abnormal symptom, and 0.5 or less as abnormal occurrence. That is, since it is not necessary to store a plurality of time series data to be compared or to calculate distance values of time series data to be compared by calculating the absolute distance between time series data, there is an advantage in that the required memory and the amount of calculation can be reduced.

In addition, when the similarity measuring apparatus 100 between time series data is implemented in the form of an edge device, the similarity measuring apparatus 100 between time series data performs state classification or anomaly detection based on the time series data, resulting in a cloud server or network. It has the advantage of reducing the traffic load, the computational load of the cloud server, and data omission and delay.

In addition, when the similarity measuring apparatus 100 between time series data is implemented in the form of an edge device, it is possible to reduce the specifications of the edge device based on a low amount of computation, so that it is possible to secure price competitiveness.

1 is a diagram for explaining problems of conventional statistical similarity, distance-based similarity, and asynchronous distance-based similarity measurement.
2 is a diagram for explaining a limitation of an asynchronous distance-based similarity measurement method.
3 is a diagram for explaining a description of the structural characteristics of time series data according to the related art.
4 is a block diagram for explaining the components of an apparatus for measuring similarity between time series data according to the present invention.
5 is a flowchart illustrating a method for measuring similarity between time series data according to the present invention.
6 to 7 are diagrams for explaining a method of obtaining a symbol according to the present invention.
8 is a diagram for explaining a comparison table of a main symbol and a comparison table of a pattern symbol according to the present invention.
9 is a diagram for explaining a general dynamic time warping (DTW).
10 is a diagram for explaining a method of calculating a normalized similarity according to the present invention.
11 is an example of calculating a normalized statistical similarity between asynchronously mapped first time series data and second time series data based on DTW.
12 is a view for explaining the effect according to the present invention.

Hereinafter, the embodiments disclosed in the present specification will be described in detail with reference to the accompanying drawings, but the same or similar components are assigned the same reference numerals regardless of reference numerals, and redundant description thereof will be omitted. The suffixes "module" and "part" for components used in the following description are given or mixed in consideration of only the ease of writing the specification, and do not have distinct meanings or roles by themselves. In addition, in describing the embodiments disclosed in the present specification, if it is determined that detailed descriptions of related known technologies may obscure the gist of the embodiments disclosed in this specification, the detailed description thereof will be omitted. In addition, the accompanying drawings are only for easy understanding of the embodiments disclosed in this specification, and the technical idea disclosed herein is not limited by the accompanying drawings, and all changes included in the spirit and scope of the present invention , should be understood to include equivalents or substitutes.

Terms including ordinal numbers such as first, second, etc. may be used to describe various elements, but the elements are not limited by the terms. The above terms are used only for the purpose of distinguishing one component from another.

When a component is referred to as being “connected” or “connected” to another component, it may be directly connected or connected to the other component, but it is understood that other components may exist in between. it should be On the other hand, when it is said that a certain element is "directly connected" or "directly connected" to another element, it should be understood that the other element does not exist in the middle.

The singular expression includes the plural expression unless the context clearly dictates otherwise. In the present application, terms such as “comprises” or “have” are intended to designate that a feature, number, step, operation, component, part, or combination thereof described in the specification exists, but one or more other features It is to be understood that this does not preclude the possibility of the presence or addition of numbers, steps, operations, components, parts, or combinations thereof.

In implementing the present invention, components may be subdivided for convenience of description, but these components may be implemented in one device or module, or one component may be divided into a plurality of devices or modules. It can also be implemented in

1 to 3 are diagrams for explaining the problems of the conventional method for determining the time series similarity.

As an analysis technology for time series data (for example, sensor data such as temperature, humidity, gas flow rate, electric energy, cold/hot water flow rate, wind speed, pressure, etc.), statistical analysis (Mean, Max, Min, Mode, Median, Correlation Analysis, Principal Component) Analysis, etc.), frequency analysis (Discrete Wavelet Transform (DWT), Fast Fourier Transform (FFT), etc.), and time series analysis (Seasonal and Trend decomposition using Loess (STL), Pattern Recognition/Matching, etc.).

In addition, pattern matching, a time series analysis technique, is mainly used to classify states or detect anomalies by analyzing time series data.

1 is a diagram for explaining problems of conventional statistical similarity, distance-based similarity, and asynchronous distance-based similarity measurement.

Similarity measurement technology is a technology that is the basis for various purposes such as classification of time series data, anomaly detection, and prediction, and is an essential operation for intelligent analysis in edge devices.

1A illustrates a method of calculating statistical similarity using Pearson's correlation.

This method expresses the strength of the relationship with normalized (-1, 1) numerical values, and has the advantage of easy understanding of the relationship and simple operation. There is a downside to that.

1B illustrates a general distance-based similarity measurement method using the Euclidean distance.

This method has the advantage that it can be intuitively compared and can be used as a general similarity comparison with an easy calculation method, but has a disadvantage in that it is not suitable for similarity comparison of time series data patterns with different time lags or different data lengths.

In addition, in order to overcome the shortcomings of the previous similarity measurement method, an asynchronous distance-based similarity (eg, dynamic time warping) technique has emerged as shown in FIG. 1C .

This method has the advantage that it is possible to measure the distance between asynchronous viewpoints and compare data of different lengths, and has excellent ability to compare time series patterns. , and also has a disadvantage that a large number of comparison data is required to determine the degree of similarity.

This will be described with reference to FIG. 2 .

2 is a diagram for explaining a limitation of an asynchronous distance-based similarity measurement method.

In the existing distance calculation methods (Euclidean, Manhattan, Mahalanobis, etc.), the result range appears as a positive real number, and the distance values between time series data are not standardized.

Therefore, even if the distance value between time series data is calculated, the degree of similarity cannot be determined only by this distance value, and the degree of similarity cannot but be determined through a relative comparison with the distance between other time series data.

Therefore, it is impossible to determine a similar degree using only the distance value, and there is a disadvantage that an accurate determination is possible only when the number of data to be compared increases.

For example, with reference to FIG. 2 , it is assumed that the degree of similarity between the first time series data S1 and the second time series data S2 is determined.

Referring to the table of FIG. 2B , the Euclidean distance between the first time series data S1 and the second time series data S2 is 8.48.

However, it is not possible to determine how similar the first time series data (S1) and the second time series data (S2) are with only 8.48. .

For example, the Euclidean distance 22.35 between the first time series data S1 and the third time series data S3, and the Euclidean distance 23.05 between the first time series data S1 and the fourth time series data S4 (23.05) It is possible to understand that the two time series data are quite similar data by about 8.48 if they are relatively compared in the state of knowing .

Also, it is assumed that new fifth time series data S2 is additionally collected, and the similarity between the first time series data S1 and the fifth time series data S5 is 2.23. In this case, the judgment that “the two time series data are very similar data around 8.48” is wrong.

That is, the Euclidean distance between the first time series data S1 and the second time series data S2 is 8.48. In order to accurately determine the degree of similarity between the first time series data S1 and the second time series data S2, A large number of time series data to be compared are required.

Therefore, according to the prior art, in order to store the time series data to be compared and to calculate the distance value of the time series data to be compared and to store the result value, there may be a problem in that the required memory and the amount of calculation are increased.

Also, as described above, the asynchronous distance-based similarity measurement method itself requires a very large amount of computation, and the increase in the amount of computation may be further increased.

3 is a diagram for explaining a description of the structural characteristics of time series data according to the related art.

SAX (Symbolic Aggregate Approximation) is a technology that extracts structural features of data and abbreviates them in the form of symbols (eg, Alphamet).

Specifically, using a piecewise aggregate approximation (PAA) technique, time series data may be divided into W segments of the same size and converted into W vectors having average values of each segment. In this case, data compressed into W sections may be expressed as a discretized sequence of L symbols.

For example, referring to FIG. 3A , it can be seen that symbols (b, a, e, d, c, b, b, a) corresponding to the average value of the Z values for each section are expressed.

However, SAX (Symbolic Aggregate Approximation) cannot include change information within each segment in the process of abbreviating information into segments. Therefore, as long as the symbol corresponding to the average value is the same, even if the detailed patterns in the interval are time series data different from each other, there is a possibility of distorting the different time series data into very similar ones.

For example, the patterns of the first time series data S1 of FIG. 3B and the second time series data s2 of FIG. 3C are very different. However, when data is expressed by SAX (Symbolic Aggregate Approximation), the symbols of the first time series data (S1) and the second time series data (S2) are all expressed as C-C-C-C-C-C-C-C. A problem occurs in that the data S1 and the second time series data S2 are determined to be very similar.

Therefore, a method for extracting time-series structural feature information that minimizes information distortion due to information reduction is required.

Considering the problems of the prior art described above, an object of the present invention is to reduce the computational load when measuring time series similarity and to increase the accuracy of time series similarity measurement while using less time series data.

In the present invention, distortion is minimized while abbreviated information of time series data, and similarity determination is possible without using a plurality of time series data through absolute distance comparison rather than relative distance comparison between time series data.

4 is a block diagram for explaining the components of an apparatus for measuring similarity between time series data according to the present invention.

The apparatus 100 for measuring the similarity between time series data may include a data collection unit 110 , a control unit 120 , a communication unit 130 , and a memory 140 .

The data collection unit 110 may collect time series data.

Here, the time series data may be sensor data. For example, the time series data may be sensor data such as temperature data, humidity data, gas flow data, wattage data, cold/hot water flow data, wind speed data, pressure data, vibration data, and the like. In this case, the data collection unit 110 may include a sensor for collecting the corresponding time series data.

However, the time series data is not limited to the sensor data, and various data that is the target of determining the similarity with other time series data may be used as the time series data.

Meanwhile, time series data may be received from an external device, and in this case, the data collection unit 110 may include a communication unit for communicating with the external device.

The controller 120 may control the overall operation of the apparatus 100 for measuring the similarity between time series data.

Also, the controller 120 may divide the time series data into sections of a predetermined size, and obtain a main symbol based on measurement values of the sections.

In addition, the controller 120 may acquire one or more pattern symbols indicating a variation pattern of the time series data in the section.

Also, the controller 120 may calculate a similarity between the time series data and other time series data by using the main symbol and one or more pattern symbols combined with the main symbol.

Meanwhile, the controller 120 may be used interchangeably with terms such as a processor, a microprocessor, a controller, and a microcontroller.

The communication unit 130 may support wired or wireless communication between external devices.

Specifically, the communication unit 130 may provide an interface for connecting the apparatus 100 for measuring the similarity between time series data with a wired/wireless network including an Internet network. In addition, the communication unit 130 may transmit/receive data to and from an external device through a network connected to the communication unit 130 or another network linked to the connected network.

The memory 130 may store programs, contents, signal-processed images, audio or data signals, and other data for each signal processing and control in the controller 120 .

Also, the memory 130 may store an application program or data for the operation of the apparatus 100 for measuring the similarity between time series data.

Meanwhile, the apparatus 100 for measuring the similarity between time series data may be an edge device. For example, the apparatus 100 for measuring the similarity between time series data may be an IOT device. In this case, the communication unit 130 may communicate with a cloud server connected to a plurality of edge devices.

In addition, the control unit 120 may transmit at least one of the time series data and the similarity between the time series data to the cloud server through the communication unit 130 .

Also, the controller 120 may acquire information on a classification of a current state or an abnormal state based on the similarity between time series data. In this case, the controller 120 may transmit the classification of the current state or information on the abnormal state to the cloud server through the communication unit 130 .

Meanwhile, the cloud server may perform operations such as obtaining status information and detecting anomalies based on data received from a plurality of edge devices.

5 is a flowchart illustrating a method for measuring similarity between time series data according to the present invention.

The method for measuring the similarity between time series data according to the present invention includes the steps of collecting first time series data (S510), dividing the first time series data into sections of a predetermined size, and obtaining a main symbol based on the measured values of the sections (S530), in the section, obtaining one or more pattern symbols representing a variation pattern of the first time-series data (S550), and using the main symbol and one or more pattern symbols combined with the main symbol, the first time-series data and calculating a similarity between the and second time series data ( S570 ).

6 to 7 are diagrams for explaining a method of obtaining a symbol according to the present invention.

The data collection unit 110 may collect time series data (S510). In this case, the controller 120 may normalize the time series data for comparison with other time series data.

Then, the controller 120 may divide the time series data into sections of a predetermined size (S530). Specifically, the controller 120 may divide the time series data into a plurality of time sections 610 , 620 , 630 , 640 , 650 , 660 , 670 , and 680 having a predetermined size.

In this case, the controller 120 may acquire the main symbol based on the level of the section.

Specifically, there are measured values constituting time series data within the section. In this case, the controller 120 may calculate an average value of the measured values within the section, and obtain a main symbol corresponding to the average value.

That is, the main symbol may be a symbol representing the level of the measurement values of each section. For example, the main symbol of the first section 610 may be an E symbol representing the level of the measurement values of the first section. For another example, the main symbol of the second section 620 may be an E symbol representing the level of the measurement values of the second section.

Meanwhile, the controller 120 may acquire one or more pattern symbols indicating a structural pattern of the time series data in the section (S570).

Referring to FIG. 7A , the pattern symbol may include an increase symbol (u), a decrease symbol (d), a maintenance symbol (s), and a noise symbol (n).

Here, the increase symbol u may indicate that the level of the measurement value increases, that is, the slope of the measurement value is greater than zero.

In addition, the decrease symbol d may indicate that the level of the measured value is decreasing, that is, the slope of the measured value is less than zero.

In addition, the holding symbol s may indicate that there is no significant change in the level of the measured value, that is, the measured value is maintained within a threshold.

In addition, the noise symbol n may represent a state in which the level of the measurement value is highly variable, such as noise.

Meanwhile, one or more pattern symbols may be obtained in one section. Hereinafter, it will be described that two pattern symbols are obtained in one section, but the present invention is not limited thereto, and one or three or more pattern symbols may be obtained in one section.

The following describes a procedure for obtaining a pattern symbol.

First, the controller 120 may determine whether a pattern symbol corresponds to a noise symbol.

In more detail, the controller 120 may calculate the standard deviation by using the differences between the measured value at the previous time and the measured value at the current time.

For example, in FIG. 7B , measured values 1, 9, 2, 8, 3, 7, 4, 6, 5, and 10 at first to tenth time points are shown.

In this case, the controller 120 determines the differences between the measured value of the previous time and the measured value of the current time (9-1=8, 2-9=-7, 8-2=6, 3-8=-5, 7- 3=4, 4-7=-3, 6-4=2, 5-6=-1, 10-5=5) can be calculated.

Then, the controller 120 may calculate a standard deviation for differences between the measured value at the previous time and the measured value at the current time. That is, referring to FIG. 6 , in the case of noise (refer to section 670), fluctuations are severe up and down within the section, and the degree of volatility can be determined by calculating the standard deviation for the increase or decrease of the measured value at each time point.

Meanwhile, the controller 120 may determine whether the calculated standard deviation is greater than (or greater than or equal to) a noise threshold. And if the calculated standard deviation is greater than the noise threshold, the controller 120 may determine that the pattern symbol is a noise symbol.

Meanwhile, when two pattern symbols are allocated to one section, the controller 120 may divide one section into two subsections of the same size and determine whether each of the two subsections corresponds to a noise symbol.

Meanwhile, when the standard deviation is less than (or less than or equal to) the noise threshold, the controller 120 may determine which symbol the pattern symbol corresponds to among an increase symbol, a decrease symbol, and a maintenance symbol.

Specifically, when the standard deviation is smaller than the noise threshold, the controller 120 may calculate average values of detailed sections within the time section.

In more detail, the controller 120 may divide the first section into a plurality of detailed sections having the same size. For example, referring to the enlarged image 610 - 1 of the first section of FIG. 6 , when two pattern symbols are allocated to one section, the controller 120 divides the first section into three subsections having the same size. , and it is possible to calculate average values of the measured values in each sub-section.

In addition, the controller 120 may determine any one of an increase symbol, a decrease symbol, and a maintenance symbol by using the slope between average values in the detailed sections.

For example, referring to the enlarged image 610 - 1 of the first section of FIG. 6 , the controller 120 controls the first average value 611 in the first detailed section and the second average value in the second detailed section. A gradient between the first subsection and the second subsection may be obtained using 612 .

In this case, the controller 120 may determine whether the absolute value of the slope between the first subsection and the second subsection is less than (or less than or equal to) the maintenance threshold. In addition, if the absolute value of the slope between the first subsection and the second subsection is less than (or less than or equal to) the maintenance threshold, the controller 120 determines that the pattern symbol between the first subsection and the second subsection is the maintenance symbol. can decide

Meanwhile, when the absolute value of the slope between the first subsection and the second subsection is greater than the maintenance threshold, the controller 120 may determine whether the slope between the first subsection and the second subsection is greater than zero.

And if the slope between the first subsection and the second subsection is greater than 0, the controller 120 may determine that the pattern symbol between the first subsection and the second subsection is the increment symbol u.

Conversely, if the slope between the first subsection and the second subsection is less than 0, the controller 120 may determine that the pattern symbol between the first subsection and the second subsection is the reduction symbol d.

Meanwhile, through the same process, a pattern symbol between the second subsection and the third subsection may be obtained.

For example, referring to the enlarged image 610 - 1 of the first section of FIG. 6 , the controller 120 controls the second average value 612 in the second sub section and the third average value in the third sub section A gradient between the second subsection and the third subsection may be obtained using 613 .

In this case, if the absolute value of the slope between the second subsection and the third subsection is less than (or less than or equal to) the maintenance threshold, the controller 120 controls the pattern between the second subsection and the third subsection It may be determined that the symbol is a holding symbol.

Meanwhile, when the absolute value of the slope between the second subsection and the third subsection is greater than the maintenance threshold, the controller 120 may determine whether the slope between the second subsection and the third subsection is greater than zero.

And when the slope between the second subsection and the third subsection is less than 0, the controller 120 may determine that the pattern symbol between the second subsection and the third subsection is the reduction symbol (d).

In addition, the controller 120 may acquire pattern symbols for each of the plurality of sections in the plurality of sections 610 , 620 , 630 , 640 , 650 , 660 , 670 , and 680 .

That is, the controller 120 may obtain the 1-1 pattern symbol and the 1-2 th pattern symbol for the first section 610 . In this case, according to the above-described order (preferentially determining whether the 1-1 pattern symbol corresponds to a noise symbol, and then determining whether the 1-1 pattern symbol corresponds to any one of a maintenance symbol, an increase symbol, or a decrease symbol) , the control unit 120 may determine which symbol of the 1-1 pattern symbol corresponds to an increase symbol, a decrease symbol, a maintenance symbol, and a noise symbol. Then, in the same manner, the control unit 120 may determine which symbol of the 1-2 th pattern symbol corresponds to an increase symbol, a decrease symbol, a sustain symbol, and a noise symbol.

In the same way, the control unit 120 may obtain a 2-1 pattern symbol and a 2-2 pattern symbol with respect to the second section 620, and the remaining sections 630, 640, 650, 660, 670, 680), by repeating the same process, it is possible to obtain a pattern symbol corresponding to each section.

Meanwhile, the main symbol may be combined with the pattern symbol. For example, the main symbol E of the first section 610 may be combined with the 1-1 pattern symbol u and the 1-2 pattern symbol d to generate a first combined symbol Eud. . For another example, the main symbol (E) of the seventh section 670 is combined with the 7-1 pattern symbol (n) and the 7-2 pattern symbol (n) to generate a seventh combined symbol (Enn). have.

8 is a diagram for explaining a comparison table of a main symbol and a comparison table of a pattern symbol according to the present invention.

A comparison table 810 of a main symbol and a comparison table 820 of a pattern symbol may be stored in the memory 140 of the apparatus 100 for measuring the similarity between time series data.

Here, the comparison table 810 of the main symbols may include information on distances between the main symbols. In this case, the comparison table of the main symbol standardizes the measured values that can be represented by the time series data, and the normalized measured values are the same for the main symbols (A, B, C, D, E, F). It can be obtained by calculating a boundary value assigned as a ratio.

For example, referring to FIG. 8 , the boundary values of the main symbol A are -3.719 and -0.967, the boundary values of the main symbol B are -0.967 and -0.431, the boundary values of the main symbol C are -0.431 and 0.000, and the main symbol D is Boundary values of , may be 0.000 and 0.431, the boundary values of the main symbol E may be 0.431 and 0.967, and the boundary values of the main symbol F may be 0.967 and 3.719.

In this case, the distance between the main symbols included in the comparison table 810 of the main symbols may be defined as a difference between the center value of two boundary values of a specific main symbol and the center value of two boundary values of another main symbol.

For example, if the two boundary values of the main symbol A are -3.719 and -0.967, the median value of the two boundary values of the main symbol A is 2.343. As another example, if the two boundary values of the main symbol D are 0.000 and 0.431, the median value of the two boundary values of the main symbol D is -0.2155. In this case, the distance between the main symbol A and the main symbol D may be defined as 2.5585 (rounded up to 2.559), which is the difference between 2.343 and -0.2155.

Meanwhile, the comparison table 820 of pattern symbols may include information on distances between pattern symbols.

In this case, the distance between pattern symbols may be calculated using a minimum value among distances between main symbols (eg, 0.431, which is a minimum value among distances included in the main symbol table 810 ).

That is, when comparing time series data, since the main symbol compares the level of measured values and the pattern symbol compares the structural pattern (structural variation pattern) of time series data, the degree of reflection of the difference between the main symbols when determining the similarity of time series data should be larger than the degree of reflection of the difference between pattern symbols.

Therefore, in the present invention, the distance between pattern symbols can be calculated using the minimum value among the distances between the main symbols. Here, the minimum value among the distances between the main symbols is defined as m _d .

Specifically, a distance (un, dn, sn) of a noise symbol (n) to other symbols (u, d, s) may be defined as 3*m _d . For example, when the minimum value (m _d ) among the distances between the main symbols is 0.431, the distance the noise symbol (n) has from other symbols (u, d, s) may be 1.293 (rounded up to 1.29).

In addition, the distance (us, ds) that the maintenance symbol (s) has with the increasing symbol (u) or the decreasing symbol (d) may be defined as m _d . For example, if the minimum value (m _d ) among the distances between the main symbols is 0.431, the distance that the maintenance symbol (s) has with the increment symbol (u) or the decrement symbol (d) can be 0.431 (rounded to 0.43). have.

Also, the distance ud between the increment symbol u and the decrement symbol d may be defined as 2*m _d . For example, when the minimum value md among the distances between the main symbols is 0.431, the distance between the increment symbol u and the decrement symbol d may be 0.862 (rounded up to 0.86).

That is, among the distances between symbols, the distance (u-n, d-n, s-n) of the noise symbol (n) to other symbols (u, d, s) is the largest, except for 0, which is the distance between the same symbols, maintain The distance (u-s, d-s) of the symbol (s) to the increasing symbol (u) or the decreasing symbol (d) may be the smallest.

This is because the distance between the pattern symbols indicates a difference in the structural pattern of the time series data.

That is, since the noise symbol n represents a structural pattern with very high variability like noise, the structural pattern difference from other patterns may be the largest.

In addition, the distance (u-s, d-s) that the maintenance symbol (s) has with the increasing symbol (u) or the decreasing symbol (d) is the difference between a structural pattern with a slope of + (or a structural pattern with a slope of -) and a structural pattern with a slope of 0 In contrast, the distance (u-d) between the increment symbol (u) and the decrement symbol (d) compares a structural pattern with a slope of + to a structural pattern with a slope of -. Accordingly, the distance between the maintenance symbol and the increment symbol or the decrement symbol may be smaller than the distance between the increment symbol and the decrement symbol.

Meanwhile, the controller 120 may obtain the distance between the combined symbols by using the comparison table 810 of the main symbol and the comparison table 820 of the pattern symbol.

In detail, it is assumed that the first combining symbol is Csn and the second combining symbol is Aud.

The controller 120 may calculate the main symbol distance between the main symbols by using the comparison table of the main symbols. For example, the main symbol of the first combining symbol is C, and the main symbol of the second combining symbol is A. In this case, the controller 120 may obtain the distance between C and A of 2.128 from the comparison table 810 of the main symbol.

Next, the controller 120 may calculate the pattern symbol distance between the pattern symbols by using the comparison table of the pattern symbols.

For example, the 1-1 pattern symbol of the first combined symbol is s, and the 2-1 pattern symbol of the second combined symbol is u. In this case, the controller 120 may obtain 0.43, which is the distance between s and u, from the comparison table 820 of pattern symbols.

In addition, the 1-2th pattern symbol of the first combined symbol is n, and the 2-2th pattern symbol of the second combined symbol is d. In this case, the controller 120 may obtain 1.29, which is the distance between n and d, from the comparison table 820 of the pattern symbol.

In this case, the control unit 120 may calculate the distance between the first combining symbol (Csn) and the second combining symbol (Aud). Specifically, the controller 120 may calculate the distance between the first combined symbol Csn and the second combined symbol Aud by summing the main symbol distance and the pattern symbol distance. For example, the controller 120 sums up the main symbol distance (2.128) and the two pattern symbol distances (0.43, 1.29), thereby determining the distance (3.848) between the first combining symbol (Csn) and the second combining symbol (Aud). can be calculated.

Meanwhile, the controller 120 may calculate a similarity between the first time series data and the second time series data by using the main symbol and one or more pattern symbols combined with the main symbol ( S570 ).

Here, the second time series data may be stored in the memory 140 as data indicating a classification of a state or an abnormal state. Also, without the second time series data being stored in the memory 140 , only the combined symbol of each section of the second time series data may be stored in the memory 140 .

In this case, the control unit 120, in each section, a combination symbol that is a combination of a main symbol and a pattern symbol of the collected first time series data, and a second combination that is a combination of a second main symbol and a second pattern symbol of the second time series data The distance between symbols can be calculated.

Specifically, in each section, the control unit 120 calculates a main symbol distance between the main symbol and the second main symbol using the comparison table of the main symbol, and uses the comparison table of the pattern symbol to calculate the distance between the pattern symbol and the second pattern symbol. The distance between the combined symbol and the second combined symbol may be calculated by calculating the pattern symbol distance and summing the main symbol distance and the pattern symbol distance.

Meanwhile, the combined symbol is a combination of a main symbol and a pattern symbol indicating a structural pattern, and may be referred to as P-SAX (Pattern-added SAX).

Meanwhile, the controller 120 may calculate a similarity between the first time series data and the second time series data by using the DTW matrix.

Before describing the similarity calculation method of the present invention, general dynamic time warping (DTW) will be described first.

9 is a diagram for explaining a general dynamic time warping (DTW).

A DTW matrix may be generated through the DTW algorithm.

It is assumed that the first time series data (x) and the second time series data (y) are compared.

The first time series data x is divided into a plurality of sections, and a plurality of measurement values each representing the plurality of sections exist. In the DTW matrix, a plurality of sections are represented by indices 1 to 10, and a plurality of measurement values representing each section are represented by 1, 3, 5, 7, 6, 8, 9, 10, 8, 7 has been

In addition, the second time series data y is divided into a plurality of sections, and a plurality of measurement values each representing the plurality of sections exist. In the DTW matrix, a plurality of sections are represented by indices 1 to 8, and a plurality of measurement values representing the plurality of sections are represented by 1, 2, 6, 6, 7, 9, 8, and 7.

In a general DTW algorithm, a DTW matrix 930 is created according to Equation 1 below.

: 현재 인덱스의 DTW 값,

: 현재 인덱스의 거리 값,

: 이전 인덱스들 중 최소 DTW 값)(

: DTW value of the current index,

: the distance value of the current index,

: Minimum DTW value among previous indexes)

And the distance value of the current index can be expressed as in Equation (2).

: 유클리디안 거리)(

: Euclidean distance)

에 의해,

=1로 계산된다.For example, referring to FIG. 9A , the value of the sixth index of the first time series data x is 8, and the value of the fifth index of the second time series data y is 7. in this case

by,

= 1 is calculated.

=3,

=4,

=5라는 값이 이미 산출된 상태이다.Also, referring to the DTW matrix 930, using Equations 1 and 2,

=3,

=4,

=5 has already been calculated.

는 1+3(3, 4, 5 중 최소 값)이 되어 4로 산출되게 된다. 이 경우 4는

에 해당 하는 칸(931)에 기재되게 된다.therefore

becomes 1+3 (the minimum value among 3, 4, and 5) and is calculated as 4. In this case 4 is

It will be described in the column 931 corresponding to .

If this process is repeated for all indices, the DTW matrix 930 is completed, and the final DTW value can be expressed by Equation (3).

(M: data length of x, N: data length of y)

That is, the first time series data (x) has 10 indexes and the second time series data (y) has 8 indexes.

가 되어 최종 DTW의 값은

에 해당하는 칸(932)에 기재된 5가 될 수 있다.So the final DTW is

and the final DTW value is

It may be 5 described in the column 932 corresponding to .

Meanwhile, FIG. 9B shows graphs of the first time series data (x) and the second time series data (y). As described above, the degree of similarity between two time series data having different lengths may be calculated through the DTW algorithm.

As described above, Dynamic Time Warping (DTW) is a method with excellent asynchronous comparison ability among distance-based similarity methods used for pattern comparison between two time series data.

However, as described above, this method has a disadvantage in that a large number of comparison data is required because similarity determination through relative comparison is required.

Therefore, in the present invention, similarity is standardized by newly mapping time series data using a warping path.

First, the control unit 120 may generate a DTW matrix according to the DTW algorithm in the same manner as described above.

Then, the controller 120 may select an optimal warping path to which the similarity between the first time series data and the second time series data is most closely mapped using the DTW matrix.

Specifically, referring to 9a, an optimal warping path is indicated in the form of an arrow. Here, the optimal warping path may refer to an index path in which the similarity between two time series data is most closely mapped.

에 해당하는 칸(932)에 기재된 5로 산출되게 된다.For example, referring to FIG. 9A , the index path to which the similarity of the two time series data is most closely mapped is (1, 1), (2, 2), (3, 3), (4, 3), (5, 4) ), (6, 5), (7, 6), (8, 6), (9, 7), (10, 8), so the final similarity is

It is calculated as 5 described in the column 932 corresponding to .

In this case the index paths (1, 1), (2, 2), (3, 3), (4, 3), (5, 4), (6, 5), (7, 6), (8, 6) ), (9, 7), and (10, 8) may constitute an optimal warping path.

10 is a diagram for explaining a method of calculating a normalized similarity according to the present invention.

10c shows a general Euclidean distance calculation method. An index-linked pair in a general Euclidean distance calculation method can be expressed by the following equation.

That is, a general method of calculating the Euclidean distance is a method of comparing the distances by pairing the same index of the first time series data (x) and the second time series data (y) as a pair. For example, referring to FIG. 10B , the warping path of the Euclidean distance calculation method is the same as 1010 of FIG. 1-B .

However, in the present invention, the index of the first time series data (x) and the index of the second time series data (x) are asynchronously mapped based on the optimal warping pass 1020 .

That is, although the time series of the two time series data are displaced from each other in FIG. 10A , in the optimal warping pass 1020 of FIG. 10B , a corresponding index pair is obtained despite the time series being displaced from each other.

Accordingly, in the present invention, the first time-series data (x) and the second time-series data (y) are re-mapped using the optimal warping path 1020 derived from the operation process due to the DTW algorithm.

In more detail, the controller 120 may asynchronously map the first time series data x and the second time series data y using a plurality of index pairs constituting the optimal warping path 1020 .

The first time series data x and the second time series data y that are asynchronously remapped based on a plurality of index pairs located in the optimal warping path 1020 are illustrated in FIG. 10D .

In this case, a plurality of index pairs constituting the optimal warping path 1020 may be represented by the following example.

)를 구성하는 다른 인덱스 쌍들((1,1), (3,3), (M,M) 등)들 역시 최적 와핑 패스(1020) 상에 위치하는 인덱스 쌍들이다.For example, the index pair (3, 4) means that one pair is generated by mapping the third index of the first time series data (x) and the fourth index of the second time series data (y). And the index pair (3, 4) may be located on the optimal warping pass 1020, DTW pair (

) constituting the other index pairs ((1,1), (3,3), (M,M), etc.) are also index pairs located on the optimal warping path 1020 .

)는 아래와 같이 표현될 수 있다.Also, the number of indices used to calculate normalized statistical similarity (

) can be expressed as follows.

)는 DTW 페어즈(

)의 인덱스 쌍의 개수가 될 수 있다.That is, according to Equation 5, the number of indices of the first time series data (x) before mapping is M, and the number of indices of the second time series data (y) before mapping is also M. In this case, if the Euclidean warping pass 1010 in FIG. 10B is used, the number of index pairs also becomes M, but in the present invention, since the optimal warping pass 1020 is selected, the index used for calculating the normalized statistical similarity number of (

) is the DTW pair (

) can be the number of index pairs.

)는, 제1 시계열 데이터가 가지는 인덱스의 개수보다 크거나 같고, 제2 시계열 데이터가 가지는 인덱스의 개수보다 크거나 같을 수 있다.That is, the number of indexes used to calculate normalized statistical similarity (

) may be greater than or equal to the number of indexes of the first time series data, and greater than or equal to the number of indexes of the second time series data.

Meanwhile, the controller 120 may calculate a normalized statistical similarity by comparing the asynchronously mapped values of the first time series data and the values of the second time series data.

Here, the normalized statistical similarity may mean a value representing a correlation between the first time series data and the second time series data as a normalized numerical value. For example, the Pearson's correlation described above may be used to calculate the normalized statistical similarity.

)를 산출하는 방법은 아래와 같은 수학식으로 표현될 수 있다.On the other hand, the statistical similarity normalized by comparing the asynchronously mapped values of the first time series data and the values of the second time series data (

) can be expressed by the following equation.

) 및 제2 시계열 데이터를 구성하는 인덱스들의 값들의 평균(

)을 산출할 수 있다.Specifically, the controller 120 controls the average (

) and the average of the values of the indices constituting the second time series data (

) can be calculated.

)를 구성하는 특정 인덱스 쌍 내 제1 시계열 데이터의 인덱스의 값(

) 및 제2 시계열 데이터의 인덱스의 값(

)을 수학식 7에 대입할 수 있다. 그리고 이러한 과정을 총

개의 인덱스 쌍에 대하여 반복함으로써, 제어부(120)는 비동기적으로 매핑된 제1 시계열 데이터 및 제2 시계열 데이터의 정규화된 통계적 유사도(

)를 산출할 수 있다.In addition, the control unit 120 DTW pairs (

), the value of the index of the first time series data within a specific index pair (

) and the value of the index of the second time series data (

) can be substituted into Equation 7. And this process

By repeating the index pairs, the control unit 120 determines the normalized statistical similarity (

) can be calculated.

And through this process, a DTW-based correlation normalized to a range of -1 to 1 may be derived.

11 is an example of calculating a normalized statistical similarity between asynchronously mapped first time series data and second time series data based on DTW.

Referring to the graph 1110 before mapping, the time series between the first time series data (x) and the second time series data (y) is out of alignment with each other. And the number (M) of the indices of the first time series data (x) and the second time series data (y) is 10.

First, the controller 120 may generate the DTW matrix 1120 according to the DTW algorithm in the same manner as described above.

Then, the controller 120 may select an optimal warping path to which the similarity between the first time series data and the second time series data is most closely mapped using the DTW matrix 1120 .

)의 인덱스 쌍의 개수는 12개가 될 수 있다.In this case, a plurality of index pairs constituting an optimal warping path are (1,1), (2,2), (3,3), (4,3) as shown in Table 1 (1130). ), (5,4), (6,5), (7,6), (8,6), (9,7), (10,8), (1,9), (10,10) can be i.e. DTW Pairs (

), the number of index pairs may be 12.

In this case, the controller 120 may asynchronously map the first time series data (x) and the second time series data (y) using a plurality of index pairs constituting the optimal warping path.

Referring to the graph 1140 after mapping, the first time series data (x) and the second time series data (y) are asynchronously mapped.

Meanwhile, the controller 120 may obtain a value corresponding to each of a plurality of index pairs constituting an optimal warping path.

For example, referring to Table 1 ( 1130 ) and Table 2 ( 1150 ), the first index pair (pairs NO. 1) constituting the optimal warping path is the first index and the second time series of the first time series data (x). It consists of a first index of the data y, and the value of the first index of the first time series data x before mapping is 1, and the value of the second index of the second time series data y before mapping is 1. Accordingly, the value of the first time series data x corresponding to the first index pair (pairs NO. 1) is 1, and the value of the second time series data (y) corresponding to the first index pair (pairs NO. 1) is 1 can be

For another example, referring to Table 1 1130 and Table 2 1150 , the ninth index pair (pairs NO. 9) constituting the optimal warping path is the ninth index and the second index of the first time series data (x). It consists of a seventh index of the time series data y, and the value of the ninth index of the first time series data x before mapping is 8, and the value of the seventh index of the second time series data y before mapping is 8. Accordingly, the value of the first time series data x corresponding to the ninth index pair (pairs NO. 9) is 8, and the value of the second time series data (y) corresponding to the ninth index pair (pairs NO. 9) is 8 can be

As another example, referring to Table 1 1130 and Table 2 1150 , the eleventh index pair (pairs NO. 11) constituting the optimal warping path is the tenth index and the second index of the first time series data (x). It consists of a ninth index of the time series data y, a value of a tenth index of the first time series data x before mapping has a value of 7, and a value of a ninth index of the second time series data y before mapping has a value of 6. Accordingly, the value of the first time series data x corresponding to the eleventh index pair (pairs NO. 11) is 7, and the value of the second time series data (y) corresponding to the eleventh index pair (pairs NO. 11) is 6 can be

In this case, the controller 120 may calculate the normalized statistical similarity by using the asynchronously mapped values of the first time series data and the second time series data.

Specifically, the controller 120 substitutes the values (the value of the first time series data and the value of the second time series data) corresponding to each of the plurality of index pairs constituting the optimal warping path into Equation 7, and the normalized statistical similarity degree can be calculated.

)는 0.94838으로 산출된다.According to the example of FIG. 11 , the normalized statistical similarity (

) is calculated as 0.94838.

That is, since normalized statistical similarity is calculated, the closer to 1, the more similar the two time series data.

)를 산출함으로써, 유사한 정도를 나타내는 절대 값을 산출할 수 있다. That is, the value calculated according to the conventional asynchronous distance-based similarity measurement method is only a relative value, and thus, a lot of comparison data is needed to determine the degree of similarity of the calculated value. However, in the present invention, the normalized statistical similarity (

), an absolute value representing a similar degree can be calculated.

Meanwhile, in the example of FIG. 11 , the statistical similarity calculated without the asynchronous mapping process (ie, the method of FIG. 10C ) is calculated to be 0.7619. This can only determine that there is a positive correlation between the first time series data and the second time series data, and it is difficult to determine that the two data are very similar.

That is, if the distance is compared by pairing the same index of the first time series data (x) and the second time series data (y) without an asynchronous mapping process (that is, in the method of FIG. 10C ), the accuracy is significantly improved. will fall However, in the present invention, values corresponding to index pairs are calculated through an asynchronous mapping process using an optimal warping path, and normalized statistical similarity is calculated using this. There are advantages.

Next, a method of calculating the normalized statistical similarity between time series data using the symbols described above will be described.

The descriptions of FIGS. 9 to 11 may be applied here as well, and below, different points will be mainly described.

The controller 120 may generate a DTW matrix by using a distance between a combined symbol of each section of the first time series data and a combined symbol of each section of the second time series data.

Specifically, referring back to FIG. 9 , the first time series data x is divided into a plurality of sections, and in this case, a plurality of measurement values representing the plurality of sections may be combined symbols of the first time series.

In addition, the second time series data y is divided into a plurality of sections, and in this case, a plurality of measurement values representing the plurality of sections may be combined symbols of the second time series.

Meanwhile, referring to Equation 2 again, the distance value of the current index may be calculated as the Euclidean distance. And when the DTW matrix is generated using the combining symbol, the distance value of the current index is . Instead of the Euclidean distance, it may be the distance between the combined symbols described in FIG. 8 .

는 심볼 Csn와 심볼 Aud 간의 거리인 3.848로 산출될 수 있다. 그리고 제어부(120)는 현재 인덱스의 거리

및 이전 인덱스들 중 최소 DTW 값을 이용하여 현재 인덱스의 DTW 값을 산출할 수 있다.For example, it is assumed that the value of the sixth index of the first time series data (x) is the symbol Csn, and the value of the fifth index of the second time series data (y) is the symbol Aud. in this case

may be calculated as 3.848, which is the distance between the symbol Csn and the symbol Aud. And the control unit 120 is the distance of the current index

and the DTW value of the current index may be calculated using the minimum DTW value among the previous indices.

And by repeating this process, the controller 120 may generate the DTW matrix.

Also, the controller 120 may select an optimal warping path in which the similarity between the first time series data and the second time series data is most closely mapped using the DTW matrix.

Also, the controller 120 may asynchronously map the first time series data and the second time series data using a plurality of index pairs constituting the optimal warping path.

For example, the ninth index pair (pairs NO. 9) constituting the optimal warping path is composed of the ninth index of the first time series data (x) and the seventh index of the second time series data (y), and before mapping The value of the ninth index of the first time series data (x) is Ass, and the value of the seventh index of the second time series data (y) before mapping is Bnn. In this case, the value of the first time series data x corresponding to the ninth index pair (pairs NO. 9) is Ass, and the value of the second time series data (y) corresponding to the ninth index pair (pairs NO. 9) is It can be Bnn.

Also, the controller 120 may calculate the normalized statistical similarity by using the asynchronously mapped values of the first time series data and the second time series data.

) 및 제2 시계열 데이터를 구성하는 인덱스들의 값들의 평균(

)을 산출해야 한다.Specifically, referring to Equation 7, the control unit 120 controls the average (

) and the average of the values of the indices constituting the second time series data (

) should be calculated.

)은, 제1 시계열 데이터를 구성하는 인덱스(구간)들의 결합 심볼들의 평균이 될 수 있다. In this case, the average of the values of the indexes constituting the first time series data (

) may be an average of combined symbols of indices (intervals) constituting the first time series data.

Specifically, the average of the combined symbols of indices (intervals) constituting the first time series data may mean a combined symbol of the most frequent symbol among the main symbols included in the first time series data and the most frequent symbol among the pattern symbols. .

For example, when the first to ninth combined symbols exist in the first time series data, the first time series data includes 9 main symbols and 18 pattern symbols. And when the main symbol that appears the most in the 9 main symbols is C and the pattern symbol that appears the most in the 18 pattern symbols is n, the average of the combined symbols of the indices (intervals) constituting the first time series data can be Cnn. have.

In the same way, the average of the combined symbols of the indices (intervals) constituting the second time series data may also be calculated.

,

)는, 도 8에서 설명한 결합 심볼 간의 거리에 기반하여 산출될 수 있다.On the other hand, in Equation 7, the difference between the value of the index and the average of the values of the indexes (

,

) may be calculated based on the distance between the combined symbols described with reference to FIG. 8 .

For example, it is assumed that the values of the ninth index pair (pairs NO. 9) are substituted in Equation (7). In addition, the value of the first time series data (x) corresponding to the ninth index pair (pairs NO. 9) is Ass, and the value of the second time series data (y) corresponding to the ninth index pair (pairs NO. 9) is Bnn to be. Also, an average of values of indices constituting the first time series data is Cnn, and an average of index values constituting the second time series data is Bss.

)는 Ass와 Cnn의 거리로써 산출될 수 있다.In this case, the difference between the value of the first time series data in the ninth index pair and the average of the first time series data (

) can be calculated as the distance between Ass and Cnn.

)는 Bnn과 Bss의 거리로써 산출될 수 있다.In addition, the difference between the value of the second time series data in the ninth index pair and the average of the second time series data (

) can be calculated as the distance between Bnn and Bss.

That is, according to the present invention, even when structural features of time series data are extracted as symbols, a normalized statistical similarity between two time series data can be calculated.

Next, the computational complexity by the conventional time-series distance-based pattern comparison method (Dynamic Time Warping technology) is compared with the computational complexity by the structural feature-based pattern comparison method of the present invention.

N is the length of the time series, W is the number of sections, S is the number of types of main symbols, P is the number of types of pattern symbols, and O(*) may mean a method for comparing the efficiency of operations between algorithms.

In this case, in the conventional time series distance-based pattern comparison method (Dynamic Time Warping technology), the computational complexity can be calculated as O(N2), and in the structural feature-based pattern comparison method of the present invention, the computational complexity is O( N + W*log(S*2P)).

For example, when N = 288, W = 8, S = 6, and P = 4, according to the conventional time-series distance-based pattern comparison method (Dynamic Time Warping technique), operation is performed as O(288·288). The complexity may be O(82944).

On the other hand, according to the structural feature-based pattern comparison method of the present invention, the computational complexity may be about O(325) as O(288 + 8·log(6, 4)).

Therefore, according to the present invention, compared with the conventional time-series distance-based pattern comparison method (Dynamic Time Warping technology), the computational complexity can be reduced by 99.61%.

In addition, in the normalized statistical similarity calculation based on the conventional DTW, the computational complexity can be calculated as O(N ² +N), and in the regularized statistical similarity calculation based on the structural feature-based pattern comparison method of the present invention, the computational complexity is It becomes O(N + W*log(S*2P)+W ² +W).

Therefore, when N = 288, W = 8, S = 6, P = 4, according to the conventional DTW-based normalized statistical similarity calculation, the computational complexity is O(288·288+288) and O(83232). have. On the other hand, according to the structural feature-based pattern comparison method of the present invention, the computational complexity may be about O(397) as O(325 + 8·8 + 8). Accordingly, the computational complexity according to the present invention can be reduced by 99.52%.

12 is a view for explaining the effect according to the present invention.

The patterns of the first time series data S1 and the second time series data S2 are very different.

However, when data is expressed by SAX (Symbolic Aggregate Approximation), the symbols of the first time series data (S1) and the second time series data (S2) are all expressed as C-C-C-C-C-C-C-C. A problem occurs in that the data S1 and the second time series data S2 are determined to be very similar.

However, the method of extracting and symbolizing the structural pattern according to the present invention (Pattern-added SAX, P-SAX) is Cnn-Cnn-Cnn-Cnn-Cnn-Cnn-Cnn-Cnn in the case of the first time series data S1. , the second time series data (S2) is symbolized as Css-Css-Css-Css-Css-Css-Css-Css, and accordingly, the first time series data (S1) and the second time series data (S2) are mutually It is considered to have a different pattern.

That is, according to the present invention, there is an advantage in that the amount of computation is significantly reduced through symbolization, information distortion is minimized by symbolization, and thus the accuracy of determining the similarity of time series data can be improved.

In addition, according to the present invention, similarity between time series data can be expressed as a normalized value, and a state can be classified or anomaly detected using only the normalized value. For example, the controller 120 may determine that the normalized statistical similarity is 0.7 or more as normal, 0.5 to 0.7 as an abnormal symptom, and 0.5 or less as abnormal occurrence. That is, since it is not necessary to store a plurality of time series data to be compared or to calculate distance values of time series data to be compared by calculating the absolute distance between time series data, there is an advantage in that the required memory and the amount of calculation can be reduced.

In addition, the control unit 120 may group the time series data by using a combination symbol of the time series data. That is, according to the present invention, a combination symbol of time series data may be used as a criterion for grouping time series data according to structural features.

In addition, when the similarity measuring apparatus 100 between time series data is implemented in the form of an edge device, the similarity measuring apparatus 100 between time series data performs state classification or anomaly detection based on the time series data, resulting in a cloud server or network. It has the advantage of reducing the traffic load, the computational load of the cloud server, and data omission and delay.

In addition, when the similarity measuring apparatus 100 between time series data is implemented in the form of an edge device, it is possible to reduce the specifications of the edge device based on a low amount of computation, so that it is possible to secure price competitiveness.

In addition, the controller 120 may train the artificial intelligence model by using the time series data as training data. In this case, if the training data is stored as time series data, a very large amount of memory is required. However, the control unit 120 stores the combined symbols of the time series data and utilizes the stored combined symbols as training data of the artificial intelligence model, thereby solving the memory shortage problem caused by storing time series data in the past.

In addition, according to the present invention, the controller 120 can train the artificial intelligence model by providing a combination symbol of time series data as an input value and a state classification as an output value. In addition, when new time series data is collected, state prediction based on the newly collected time series data can be performed by providing a combination symbol of the newly collected time series data to the AI model.

The present invention described above can be implemented as computer-readable code on a medium in which a program is recorded. The computer-readable medium includes all kinds of recording devices in which data readable by a computer system is stored. Examples of computer-readable media include Hard Disk Drive (HDD), Solid State Disk (SSD), Silicon Disk Drive (SDD), ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc. There is this. In addition, the computer may include a control unit. Accordingly, the above detailed description should not be construed as restrictive in all respects but as exemplary. The scope of the present invention should be determined by a reasonable interpretation of the appended claims, and all modifications within the equivalent scope of the present invention are included in the scope of the present invention.

100: device for measuring the similarity between time series data

Claims (20)

collecting first time series data;
dividing the first time series data into sections of a predetermined size, and obtaining a main symbol based on a measurement value of the section;
obtaining at least one pattern symbol representing a structural pattern of the first time series data in the section; and
Calculating a degree of similarity between the first time series data and the second time series data by using the main symbol and one or more pattern symbols combined with the main symbol;
A method of measuring the similarity between time series data. The method of claim 1,
The pattern symbol is
including increment symbols, decrement symbols, hold symbols and noise symbols.
A method of measuring the similarity between time series data. 3. The method of claim 2,
The step of obtaining the pattern symbol comprises:
calculating a standard deviation by using differences between a measurement value at a previous time point and a current time point of the first time series data; and
determining that the pattern symbol is a noise symbol if the standard deviation is greater than a noise threshold;
A method of measuring the similarity between time series data. 4. The method of claim 3,
The step of obtaining the pattern symbol comprises:
calculating average values of subsections within the section when the standard deviation is smaller than the noise threshold; and
Determining any one of the increase symbol, the decrease symbol, and the maintenance symbol by using the slope between the average values; further comprising
A method of measuring the similarity between time series data. 3. The method of claim 2,
The noise symbol has the largest distance from other symbols,
Except for the distance between the same symbols, the distance the maintenance symbol has with the increasing symbol or the decreasing symbol is the smallest.
A method of measuring the similarity between time series data. The method of claim 1,
Calculating the degree of similarity between the first time series data and the second time series data includes:
Calculating a distance between a first combined symbol that is a combination of the main symbol and the pattern symbol of the first time series data, and a second combined symbol that is a combination of a second main symbol and a second pattern symbol of the second time series data including;
A method of measuring the similarity between time series data. 7. The method of claim 6,
Calculating the distance between the combined symbol and the second combined symbol comprises:
calculating a main symbol distance between the main symbol and the second main symbol by using a comparison table of the main symbols;
calculating a pattern symbol distance between the pattern symbol and the second pattern symbol by using a comparison table of pattern symbols; and
calculating a distance between the first combined symbol and the second combined symbol by summing the main symbol distance and the pattern symbol distance;
A method of measuring the similarity between time series data. 7. The method of claim 6,
Calculating the degree of similarity between the first time series data and the second time series data includes:
generating a DTW matrix by using a distance between the first combining symbol and the second combining symbol in each interval; and
using the DTW matrix to select an optimal warping path in which the similarity between the first time series data and the second time series data is most closely mapped;
A method of measuring the similarity between time series data. 9. The method of claim 8,
Calculating the degree of similarity between the first time series data and the second time series data includes:
Asynchronously mapping the first time series data and the second time series data using a plurality of index pairs constituting the optimal warping path; further comprising
A method of measuring the similarity between time series data. 10. The method of claim 9,
Calculating the degree of similarity between the first time series data and the second time series data includes:
Calculating a normalized statistical similarity indicating a correlation between the first time series data and the second time series data by using the asynchronously mapped values of the first time series data and the second time series data further containing ;
A method of measuring the similarity between time series data. a data collection unit for collecting first time series data; and
dividing the first time series data into sections of a certain size, obtaining a main symbol based on a measurement value of the section, obtaining one or more pattern symbols representing a structural pattern of the first time series data in the section, and A control unit for calculating a degree of similarity between the first time series data and the second time series data by using a main symbol and one or more pattern symbols combined with the main symbol;
A device for measuring the similarity between time series data. 12. The method of claim 11,
The pattern symbol is
including increment symbols, decrement symbols, hold symbols and noise symbols.
A device for measuring the similarity between time series data. 13. The method of claim 12,
The control unit is
calculating a standard deviation by using the differences between the measurement value of the previous time point and the current time point of the first time series data,
If the standard deviation is greater than a noise threshold, determining that the pattern symbol is a noise symbol
A device for measuring the similarity between time series data. 14. The method of claim 13,
The control unit is
If the standard deviation is less than the noise threshold, calculating average values of detailed sections within the section,
Determining any one of the increment symbol, the decrement symbol, and the maintenance symbol using the slope between the average values
A device for measuring the similarity between time series data. 13. The method of claim 12,
The noise symbol has the largest distance from other symbols,
Except for the distance between the same symbols, the distance the maintenance symbol has with the increasing symbol or the decreasing symbol is the smallest.
A device for measuring the similarity between time series data. 12. The method of claim 11,
The control unit is
Calculating a distance between a first combined symbol that is a combination of the main symbol and the pattern symbol of the first time series data, and a second combined symbol that is a combination of a second main symbol and a second pattern symbol of the second time series data
A device for measuring the similarity between time series data. 17. The method of claim 16,
The control unit is
calculating a main symbol distance between the main symbol and the second main symbol using a comparison table of main symbols,
calculating a pattern symbol distance between the pattern symbol and the second pattern symbol using a comparison table of pattern symbols,
calculating the distance between the first combined symbol and the second combined symbol by summing the main symbol distance and the pattern symbol distance
A device for measuring the similarity between time series data. 17. The method of claim 16,
The control unit is
generating a DTW matrix by using the distance between the first combining symbol and the second combining symbol in each interval;
Selecting an optimal warping path in which the similarity between the first time series data and the second time series data is most closely mapped using the DTW matrix
A device for measuring the similarity between time series data. 19. The method of claim 18,
The control unit is
Asynchronously mapping the first time series data and the second time series data using a plurality of index pairs constituting the optimal warping path
A device for measuring the similarity between time series data. collecting first time series data;
dividing the first time series data into sections of a predetermined size, and obtaining a main symbol based on a measurement value of the section;
obtaining at least one pattern symbol representing a structural pattern of the first time series data in the section; and
Using the main symbol and one or more pattern symbols combined with the main symbol, calculating a degree of similarity between the first time series data and the second time series data; stored computer programs.

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