Apparatus and method for generating anomalous time-series data

The method generates abnormal time series data using probability density functions and latent vectors to enhance AI model performance in anomaly detection, addressing the lack of available abnormal data.

WO2026095189A1PCT designated stage Publication Date: 2026-05-07POSCO HLDG INC
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Patent Information

Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
POSCO HLDG INC
Filing Date
2024-12-19
Publication Date
2026-05-07

AI Technical Summary

Technical Problem

Existing methods for generating abnormal time series data are inadequate, leading to AI models being primarily trained on normal data, which hinders accurate detection of abnormal conditions in equipment.

Method used

A method and device for generating abnormal time series data using probability density functions and latent vectors, even with only normal data available, by calculating potential vectors, integrated probability density functions, and reflecting probability variable values in modified latent vectors through an AI model.

Benefits of technology

Enables the generation of realistic abnormal time series data without actual abnormal data, enhancing the performance verification of AI models for anomaly detection.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

The present disclosure relates to a technology for generating anomalous time-series data and provides an apparatus and a method for generating anomalous time-series data, the method comprising: receiving time-series data; dividing the time-series data according to a preset criterion; calculating a latent vector including a probability density function for each of the divided time-series data; calculating a probability variable value for each probability density function for a specific probability in an integrated probability density function in which a plurality of probability density functions are integrated; and generating anomalous time-series data on the basis of a modified latent vector obtained by reflecting the probability variable value for each probability density function on the latent vector and an artificial intelligence model trained through a preset first algorithm.
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Description

Device and method for generating abnormal time series data

[0001] The present disclosure relates to a technique for generating abnormal time series data.

[0002] Artificial intelligence is a field that performs repetitive learning in a manner similar to human intelligence and makes judgments based on the results of that learning. Artificial intelligence is a broad concept that includes machine learning and deep learning, and machine learning is used as a broad concept that includes deep learning.

[0003] Machine learning is a field of artificial intelligence (AI) that develops algorithms and technologies enabling computers to learn from data. It serves as a core technology in various fields such as image processing, video recognition, speech recognition, and internet search, demonstrating outstanding performance in prediction and anomaly detection.

[0004] Recently, research on technologies utilizing artificial intelligence models to detect abnormalities in manufacturing equipment is actively underway.

[0005] It is necessary to utilize various data to train or improve the performance of artificial intelligence models used for anomaly detection, but conventionally, data augmentation has been performed by transforming the original data.

[0006] However, relying solely on a method of simply converting original data makes it difficult to obtain sufficient abnormal time-series data necessary to detect abnormal conditions in the equipment, and there is a problem in that the AI ​​model applied to the equipment is trained primarily on normal data, resulting in an inability to accurately detect abnormal situations.

[0007] The present disclosure aims to provide a technology for generating abnormal time series data used for performance verification in order to solve the problem of difficulty in acquiring abnormal time series data and to more efficiently verify the performance of artificial intelligence models applied to equipment.

[0008] In one aspect, the present embodiments provide an abnormal time series data generation device comprising: a data receiving unit for receiving time series data; a potential vector calculating unit for dividing time series data according to a preset standard and calculating a potential vector including a probability density function for each divided time series data; a probability variable value calculating unit for calculating a probability variable value for each probability density function for a specific probability in an integrated probability density function that integrates a plurality of probability density functions; a modified potential vector that reflects the probability variable value for each probability density function in the potential vector; and an abnormal time series data generation unit that generates abnormal time series data based on an artificial intelligence model learned through a preset first algorithm.

[0009] In another aspect, the present embodiments provide a method for generating abnormal time series data, comprising: a data receiving step for receiving time series data; a potential vector calculation step for dividing the time series data according to a preset criterion and calculating a potential vector including a probability density function for each divided time series data; a probability variable value calculation step for calculating a probability variable value for each probability density function for a specific probability in an integrated probability density function that integrates a plurality of probability density functions; and an abnormal time series data generation step for generating abnormal time series data based on a modified potential vector that reflects the probability variable value for each probability density function in the potential vector and an artificial intelligence model learned through a preset first algorithm.

[0010] The present disclosure may provide a technology for generating abnormal time series data.

[0011] FIG. 1 is a drawing for explaining the configuration of a device for generating abnormal time series data according to one embodiment.

[0012] FIG. 2 is a flowchart for schematically explaining the process of generating abnormal time series data according to one embodiment.

[0013] FIGS. 3a and 3b are drawings illustrating a preprocessing method for univariate time series data according to one embodiment.

[0014] FIGS. 4a, FIGS. 4b, FIGS. 5a, and FIGS. 5b are drawings for explaining a preprocessing method for multivariate time series data according to one embodiment.

[0015] FIG. 6 is an example diagram for explaining the calculation of a potential vector according to one embodiment.

[0016] FIG. 7 is a diagram for explaining the formula for calculating a potential vector according to one embodiment.

[0017] FIG. 8 is a diagram for explaining an integrated probability density function according to one embodiment.

[0018] FIG. 9 is a graph for explaining the method of calculating a modified potential vector according to one embodiment.

[0019] FIG. 10 is a flowchart for explaining a method for generating abnormal time series data according to one embodiment.

[0020] Hereinafter, some embodiments of the present disclosure will be described in detail with reference to the exemplary drawings. In assigning reference numerals to the components of each drawing, the same components may have the same reference numeral as much as possible, even if they are shown in different drawings. Furthermore, in describing the embodiments, if it is determined that a detailed description of related known components or functions may obscure the essence of the technical concept, such detailed description may be omitted. Where terms such as "comprising," "having," or "consisting of" are used in this specification, other parts may be added unless "only" is used. Where a component is expressed in the singular, it may include a plural unless otherwise specified.

[0021] Additionally, terms such as first, second, A, B, (a), (b), etc., may be used to describe the components of the present disclosure. These terms are used merely to distinguish the components from other components, and the nature, order, sequence, or number of the components are not limited by such terms.

[0022] In describing the positional relationship of components, where it is stated that two or more components are "connected," "combined," or "joined," it should be understood that while the two or more components may be directly "connected," "combined," or "joined," they may also be "connected," "combined," or "joined" with other components "intervened." Here, the other components may be included in one or more of the two or more components that are "connected," "combined," or "joined" with one another.

[0023] In describing the temporal flow relationship regarding components, methods of operation, or methods of production, for example, when the temporal or sequential relationship is described using "after," "following," "next," or "before," it may include cases where the relationship is not continuous unless "immediately" or "directly" is used.

[0024] Meanwhile, where numerical values ​​or corresponding information regarding a component (e.g., levels, etc.) are mentioned, even without separate explicit notation, the numerical values ​​or corresponding information may be interpreted as including a range of error that may occur due to various factors (e.g., process factors, internal or external shocks, noise, etc.).

[0025] The embodiments are described in detail below with reference to the drawings.

[0026]

[0027] FIG. 1 is a drawing for explaining the configuration of a device for generating abnormal time series data according to one embodiment.

[0028] Referring to FIG. 1, the device (100) for generating abnormal time series data of the present disclosure includes a data receiving unit (110) for receiving time series data.

[0029] In fields where operations are performed sequentially according to pre-set processes, such as manufacturing, the information used can primarily take the form of time series data. Additionally, manufacturing processes may be executed by inputting time series data into an artificial intelligence model that includes an autoencoder.

[0030] To identify process issues where AI models are utilized, it is necessary to verify the performance of the models in advance using various data, including anomalous time series data. However, since normal data generally outnumbers anomalous time series data available in actual processes, it is difficult to acquire a large volume of anomalous time series data alone.

[0031] Accordingly, the present disclosure proposes a method for generating abnormal time series data.

[0032] For example, time series data received through the data receiving unit (110) of the present disclosure may include only normal data.

[0033] Time series data is a collection of data sets that can be collected over a certain period of time. It is also possible to predict future data changes through the rules or distributions of time series data.

[0034] The present disclosure proposes a method for generating abnormal time series data by utilizing probability density functions and latent vectors, even with time series data composed solely of normal data.

[0035] As another example, time series data received through the data receiving unit (110) of the present disclosure may include data preprocessed based on at least one of a neural network, a 1D (1-Dimensional) Convolution operation, and a 2D (2-Dimensional) Convolution operation.

[0036] Time series data received through the data receiving unit (110) of the present disclosure may be preprocessed univariate data. Specifically, the data receiving unit (110) of the present disclosure may receive a single-dimensional vector as time series data, or receive data output by passing it through a pre-set neural network as time series data. The aforementioned neural network may include at least one of LSTM (Long Short-Term Memory), CNN (Convolutional Neural Network), RNN (Recurrent Neural Network), and DNN (Deep Neural Network).

[0037] Additionally, the time series data received through the data receiving unit (110) of the present disclosure may be preprocessed multivariate data. Specifically, the preprocessing of the time series data may be performed through a method of outputting the time series data through 1D Convolution or 2D Convolution operations, a method of outputting the time series data through an RNN-based architecture, and a method of outputting the time series data through a Transformer-based architecture.

[0038] However, the aforementioned model is merely one example as a target for preprocessing time-series data and is not limited thereto, and can be configured in various ways as needed.

[0039] The apparatus (100) for generating abnormal time series data of the present disclosure includes a potential vector calculation unit (120) that divides the time series data according to a preset standard and calculates a potential vector including a probability density function for each of the divided time series data.

[0040] For example, a preset criterion may include at least one of a criterion for the number of data and a criterion for a unit of time. For example, if the time series data received through the data receiving unit (110) consists of 10 data generated over 10 seconds, the potential vector calculation unit (120) of the present disclosure may divide the time series data into two groups based on a criterion of 5 units or divide the time series data into two groups based on a criterion of 5 seconds. The aforementioned criteria for dividing the time series data according to time and number are merely examples and may be set in various ways as needed.

[0041] As another example, the latent vector calculation unit (120) of the present disclosure may calculate the mean and variance for each of the divided time series data and calculate the noise for each of the divided time series data based on a preset second algorithm.

[0042] In time-series data, noise refers to unintended data distortion caused by interference from external factors. In other words, it can be defined as a factor that distorts some of the data within a time-series. For example, interference with signal data output from objects such as sensors, or bugs frequently found in specific programs, can be considered noise.

[0043] The abnormal time series data generation device (100) of the present disclosure can generate abnormal time series data by calculating a numerical potential vector based on a distribution of groups divided according to a preset standard for time series data.

[0044] A second algorithm including at least one of Gaussian filtering, bidirectional filtering, and Kalman filtering may be used as a method for calculating noise in time series data.

[0045] As another example, the latent vector calculation unit (120) of the present disclosure calculates a plurality of probability density functions based on the mean and variance for each of the divided time series data, and the plurality of probability density functions may include at least one of a normal distribution and a uniform distribution.

[0046] The ideal time series generating device (100) of the present disclosure can calculate the mean and variance for each of the divided time series data and calculate a probability density function for each group of time series data based on the calculation results. Each of the calculated probability density functions may include a random variable.

[0047] As another example, the potential vector calculation unit (120) of the present disclosure can calculate a potential vector based on the mean, variance, and noise calculated for each of the divided time series data.

[0048] In that the probability density function of the present disclosure may include at least one of a normal distribution and a uniform distribution, it is proposed to use a second algorithm that includes a Gaussian filter based on a normal distribution or a uniform distribution among the methods for calculating the noise described above.

[0049] A latent vector may refer to a set of functions that, when each divided time series data group is input into a preset model, produce data identical to the input time series data group. Accordingly, the latent vector calculation unit (120) of the present disclosure may use an autoencoder having a latent space that makes the input data and the output data identical. A latent vector may be calculated through the aforementioned latent space. Additionally, the aforementioned preset model may include an autoencoder.

[0050] The abnormal time series data generation device (100) of the present disclosure may perform not only the calculation of a latent vector but also the process of generating abnormal time series data using the latent vector using an autoencoder. The autoencoder is composed of an encoder into which time series data is input, a latent space for calculating a latent vector, and a decoder from which time series data is output. When a modified latent vector is calculated, the calculated modified latent vector is input into the decoder to generate abnormal time series data through the decoder. An autoencoder including the aforementioned encoder and decoder as well as a latent space may be referred to as a Variational Autoencoder (VAE) in the present disclosure.

[0051]

[0052] Even when using an autoencoder, the input time series data can consist solely of normal data, and latent vectors can be generated through the latent space during the autoencoder's training process. Additionally, abnormal time series data can be generated by inputting the quantified latent vectors into the decoder of the trained autoencoder.

[0053] The latent vector of the present disclosure can be calculated based on Equation 1, which takes the mean μ, the variance σ, the noise ε, the group number i, and the latent vector z as factors for each of the divided time series data.

[0054] [Mathematical Formula 1]

[0055]

[0056] As described above, a latent vector is a set of functions that output time series data identical to the input time series data, and can be calculated through the aforementioned mathematical formula 1 based on the mean, variance, and noise of each divided time series data.

[0057] The device for generating abnormal time series data (100) of the present disclosure includes a probability variable value calculation unit (130) that calculates a probability variable value for each probability density function for a specific probability in an integrated probability density function that integrates a plurality of probability density functions.

[0058] For example, the same probability variable may be included in a plurality of probability density functions, potential vectors, and integrated probability density functions produced through the abnormal time series data generation device (100) of the present disclosure.

[0059] As another example, the probability variable value calculation unit (130) of the present disclosure can calculate a single integrated probability density function based on the sum of a plurality of probability density functions.

[0060] As another example, the probability variable value calculation unit (130) of the present disclosure may display a plurality of probability density functions in a preset space and calculate an integrated probability density function based on the center position of the plurality of probability density functions displayed in the space and a preset third algorithm. The center position of the aforementioned probability density function refers to the average of each probability density function.

[0061] For example, the probability variable value calculation unit (130) of the present disclosure may display points corresponding to the average of a plurality of probability density functions of the present disclosure on a preset two-dimensional plane, generate regions based on each point based on the variance for each probability density, and calculate a single probability density function integrated through a preset third algorithm.

[0062] However, the aforementioned two-dimensional plane is merely an example for explaining the generation of the integrated probability density function, and the space in which the average of multiple probability density functions is displayed and the integrated probability density function is generated therefrom may be a high-dimensional space of three dimensions or more.

[0063] The integrated probability density function reflects the characteristics of multiple probability density functions. In addition, the integrated probability density function also reflects the characteristics of each data included in the input time series data. Utilizing these properties, the present disclosure proposes using an expectation-maximization algorithm (EM algorithm) as a third algorithm for calculating the aforementioned integrated probability density function.

[0064] The present disclosure calculates the probability that each data included in the input time series data belongs to each probability density function through an expectation maximization algorithm, and determines a probability distribution with high probability for each data to calculate a single integrated probability distribution. For example, the probability that each data included in the aforementioned time series data belongs to each probability density function may be determined based on the distance between each data and the center locations of a plurality of probability density functions.

[0065] When the integrated probability density function is calculated, the probability variable value calculation unit (130) of the present disclosure can calculate a plurality of probability variable values ​​corresponding to a specific probability based on the integrated probability density function.

[0066] As previously mentioned, since the integrated probability density function can be calculated based on the sum of each probability density function, the random variables included in each probability density function are also included in the integrated probability density function. Furthermore, the same random variables are included in the latent vector. Therefore, the aforementioned multiple random variables can correspond, respectively, to the random variables included in each probability density function and the random variables included in the latent vector.

[0067] The abnormal time series data generation device (100) of the present disclosure includes an abnormal time series data generation unit (140) that generates abnormal time series data based on a modified potential vector in which the probability variable value for each probability density function is reflected in the potential vector and an artificial intelligence model learned through a preset first algorithm.

[0068] When multiple probability variable values ​​corresponding to a specific probability are calculated based on an integrated probability density function, the abnormal time series data generation unit (140) of the present disclosure can reflect each probability variable value in a potential vector. The present disclosure may refer to the potential vector in which each probability variable value is reflected as a modified potential vector.

[0069] The aforementioned specific probability is a value that is pre-set according to the degree of abnormality of the data required for generation; the lower the specific probability is set, the more abnormal data with a high degree of abnormality is generated, and the higher the specific probability is set, the more normal data with a low degree of abnormality is generated.

[0070] When a modified latent vector is generated, the modified latent vector can be input into an artificial intelligence model trained through a preset first algorithm to generate anomalous time series data. Additionally, as described above, the modified latent vector can be input into a decoder of an autoencoder trained through a preset first algorithm to generate anomalous time series data.

[0071] The aforementioned artificial intelligence model may include at least one autoencoder or at least one variational autoencoder, and the artificial intelligence model may be trained through a first algorithm.

[0072] The first algorithm used for training an artificial intelligence model may include a Gradient Descent Algorithm that minimizes the loss occurring during the training process of the artificial intelligence model. The aforementioned Gradient Descent Algorithm can minimize the loss arising from the difference between the data output through the artificial intelligence model and the actual data during the training process of the artificial intelligence model. The present disclosure may refer to the aforementioned Gradient Descent Algorithm as a Gradient Optimization Algorithm.

[0073] The present disclosure proposes a method for generating abnormal time series data using only normal data even in situations where abnormal time series data is not available, comprising receiving time series data, dividing the time series data according to a preset criterion, calculating a probability density function for each of the divided time series data, calculating a latent vector and an integrated probability density function based on the calculation result, calculating multiple probability variable values ​​based on the integrated probability density function and reflecting them in the latent vector, and generating abnormal time series data based on a modified latent vector and an artificial intelligence model learned through a preset first algorithm.

[0074]

[0075] The present disclosure has the advantage of being able to generate abnormal time series data that may occur in an actual process without abnormal time series data by calculating a potential vector based on time series data and calculating a probability variable value having a low probability density value and reflecting it in the potential vector.

[0076]

[0077] Below, the overall process of generating abnormal time series data is explained in more detail with reference to flowcharts and diagrams.

[0078]

[0079] FIG. 2 is a flowchart for schematically explaining the process of generating abnormal time series data according to one embodiment.

[0080] Referring to FIG. 2, the abnormal time series data generation device of the present disclosure receives time series data and can generate abnormal time series data by calculating the value of a probability variable included in a potential vector calculated based on the received data.

[0081] Specifically, the abnormal time series data generating device of the present disclosure receives time series data (S200).

[0082] For example, the received time series data may consist only of normal data, or it may include both normal and abnormal time series data.

[0083] As another example, the received time series data may be time series data obtained from the actual process, as well as data received after being converted into a single-dimensional vector, or data preprocessed through a neural network, 1D (1-Dimensional) Convolution operation, 2D (2-Dimensional) Convolution operation, RNN-based architecture, or Transformer-based architecture. The preprocessed time series data may be in the form of univariate time series data having a single feature or multivariate time series data having multiple features.

[0084] When time series data is received, the ideal time series data generating device of the present disclosure can calculate a potential vector including a plurality of probability density functions (S210).

[0085] For example, when time series data is received, the abnormal time series data generating device of the present disclosure may divide the time series data based on a preset number or time unit. For each divided time series data, the abnormal time series data generating device of the present disclosure may calculate the mean, variance, and noise, calculate a probability density function for each divided group based on the mean and variance, and calculate a latent vector based on the mean, variance, and noise.

[0086] As described above, the present disclosure proposes using a second algorithm that is pre-set for the calculation of noise, wherein the algorithm includes a Gaussian filter in that the probability density function is a normal distribution or a random distribution.

[0087] As another example, the anomalous time series data generation device of the present disclosure may perform the partitioning of time series data, the calculation of a plurality of probability density functions, and the calculation of a latent vector using a pre-designed autoencoder.

[0088] When a latent vector is calculated, the abnormal time series data generation device of the present disclosure can calculate an integrated probability density function and calculate a probability variable value for which a specific probability is calculated for the integrated probability density function (S220).

[0089] The purpose of calculating the integrated probability density function is to generate a latent vector that reflects the values ​​of random variables. For example, if the integrated probability density function takes the form of a normal distribution, multiple random variable values ​​can be generated where the probability falls below a specific threshold, and these values ​​can be reflected in a latent vector containing the same random variables as those included in the integrated probability density function. The aforementioned probability below a specific threshold is a value that can be pre-set. Conversely, if the values ​​of random variables having probabilities above a certain threshold are reflected in the latent vector, time series data resembling normal time series data may be generated.

[0090] A plurality of probability density functions, latent vectors, and integrated probability density functions calculated by the abnormal time series data generation device of the present disclosure may all include a common random variable. For example, when there are three groups of partitioned time series data, three probability density functions may be calculated based on the mean and variance of each group, and each probability density function may include one random variable (A, B, C). Additionally, a latent vector calculated based on the mean, variance, and noise of each group may include three elements, and each element may include the aforementioned one random variable (A, B, C). Furthermore, an integrated probability density function calculated based on the sum of each probability density function may include three random variables (A, B, C). Additionally, values ​​for random variables A, B, and C may be calculated based on a preset specific probability value of the integrated probability density function, and abnormal time series data may be generated by reflecting the values ​​corresponding to random variables A, B, and C in the aforementioned latent vector.

[0091] When the value of each random variable included in the latent vector is calculated, the abnormal time series data generation device of the present disclosure can reflect the value of the corresponding random variable in a modified latent vector and input the modified latent vector with the reflected value into an artificial intelligence model learned through a preset first algorithm to generate time series data (S230).

[0092] The artificial intelligence model described above may include an autoencoder or a variational autoencoder, and the first algorithm described above may include a Gradient Descent Algorithm that minimizes the loss occurring during the learning process of the artificial intelligence model.

[0093]

[0094] For example, the abnormal time series data generating device of the present disclosure, having received one time series data, can divide it into four time series data according to a preset criterion. Furthermore, the abnormal time series data generating device of the present disclosure can calculate the mean for each divided time series data as [0.1, 1.2, 0.2, 0.8] and the variance as [0.2, 0.5, 0.8, 1.3], and based on each calculated mean and variance, a probability density function It can be calculated as follows. In addition, the abnormal time series data generation device of the present disclosure can calculate noise for each time series data, calculate a latent vector based on the mean, variance, and noise, calculate an integrated probability density function based on four probability density functions to calculate a probability variable value from which a characteristic probability is calculated, and by corresponding the probability variable value to the latent vector again, a modified latent vector such as [0.28, 1.65, 0.92, 1.98] can be calculated. The abnormal time series data generation device of the present disclosure can generate abnormal time series data by applying the modified latent vector to an artificial intelligence model learned through a preset first algorithm. The aforementioned numerical values ​​of the mean, variance, and modified latent vector are merely examples to explain the abnormal time series data generation process, and each numerical value can be calculated in various ways.

[0095]

[0096] FIGS. 3a and 3b are drawings illustrating a preprocessing method for univariate time series data according to one embodiment.

[0097] Referring to FIGS. 3a and 3b, the ideal time series data generating device of the present disclosure can receive preprocessed univariate time series data through a data receiving unit.

[0098] Data preprocessing refers to the process of transforming pre-prepared data into data that reflects specific characteristics as needed. Alternatively, it may refer to the process of removing unnecessary data from pre-prepared data.

[0099] Therefore, since univariate time series data is data that has a single characteristic, if the time series data already has a single characteristic, it can be received through a preprocessing process that converts the time series data into a single-dimensional vector as shown in Fig. 3a.

[0100] Alternatively, as shown in Fig. 3b, the data may be received through a preprocessing process in which it is passed through a neural network such as LSTM or CNN to be processed into data that reflects the necessary characteristics.

[0101] For example, time series data X n According to this preset time unit standard, t w When divided into parts, the divided univariate time series data (n is an integer greater than or equal to 1, the number of time series data, x (n-1) is partitioned time series data, t s is based on a preset time unit, t w It can be expressed as the number of partitioned time series data.

[0102]

[0103] FIGS. 4a, FIGS. 4b, FIGS. 5a, and FIGS. 5b are drawings for explaining a preprocessing method for multivariate time series data according to one embodiment.

[0104] Referring to FIGS. 4a, 4b, 5a, and 5b, the ideal time series data generating device of the present disclosure can receive multivariate time series data output through a preprocessing process.

[0105] The preprocessing of multivariate time series data input to the ideal time series data generation device of the present disclosure described above may be performed through 1D Convolution operation or 2D Convolution operation, through an RNN-based architecture including a plurality of LSTM models, or through a Transformer-based architecture.

[0106] Multivariate time series data is time series data having multiple characteristics, and according to FIG. 4a, the ideal time series data generating device of the present disclosure can receive multivariate time series data in which a preprocessing process is performed through a 1D Convolution operation based on multiple data in the form of a one-dimensional array.

[0107] Alternatively, according to FIG. 4b, the ideal time series data generating device of the present disclosure may receive multivariate time series data in which a preprocessing process is performed through a 2D Convolution operation based on a plurality of data in the form of a two-dimensional array.

[0108] Alternatively, according to FIG. 5a, the abnormal time series data generation device of the present disclosure can receive multivariate time series data that has undergone a preprocessing process through an RNN-based architecture including a plurality of LSTM models.

[0109] Alternatively, according to FIG. 5b, the abnormal time series data generation device of the present disclosure may receive multivariate time series data in which a preprocessing process is performed through a transformer-series architecture including a plurality of encoder layers.

[0110] For example, time series data X n According to this preset time unit standard, t w When divided into parts, the divided multivariate time series data (n is an integer greater than or equal to 1, the number of time series data, x (n-1) is partitioned time series data, t s is based on a preset time unit, t wcan be expressed as the number of partitioned time series data, and x representing the partitioned time series data n Depending on each characteristic It can be expressed as (k is the number of data features).

[0111] The aforementioned preprocessing method is merely one example for receiving input data suitable for generating abnormal time series data of the present disclosure, but is not limited thereto; various preprocessing methods may be performed as needed, and preprocessing may be performed through two or more models.

[0112]

[0113] FIG. 6 is an example diagram for explaining the calculation of a potential vector according to one embodiment.

[0114] Referring to FIG. 6, the ideal time series generating device of the present disclosure can calculate a latent vector based on information about divided time series data.

[0115] As described above, the ideal time series data generation device of the present disclosure receives time series data, divides the time series data to calculate a plurality of probability density functions based on the mean and variance for each divided group, and calculates a latent vector based on the mean, variance, and noise for each group.

[0116] According to FIG. 6, an example of a model for calculating a latent vector is illustrated. The aforementioned model may be a model comprising a data receiving unit and a latent vector generating unit of an ideal time series data generating device. Alternatively, it may be an autoencoder comprising an encoder, a decoder, and a latent space. The aforementioned autoencoder is merely one example used for calculating a latent vector and is not limited thereto, and various models may be used.

[0117] For convenience of explanation, the present disclosure describes an autoencoder (600) as an example.

[0118] The autoencoder (600) may be composed of an encoder (630) into which time series data is input, a latent space (640) into which a latent vector is calculated and output, and a decoder (650) into which time series data (620) identical to the time series data (610) input to the encoder (630) is output.

[0119] Specifically, time series data (610) can be input through the encoder (630) of the autoencoder (600). As described above, the input time series data (610) may be either preprocessed univariate time series data or preprocessed multivariate time series data.

[0120] When time series data (610) is input to the encoder (630), the latent space (640) can produce a latent vector that causes data (620) identical to the time series data (610) input to the encoder (630) to be output through the decoder (650). Variational Bayes inference may be utilized for the production of the latent vector using the autoencoder (600).

[0121] The latent space (640) can divide the input time series data (610) according to preset criteria and calculate the mean, variance, and noise for each divided group. Accordingly, the latent space (640) can calculate a probability density function for each group based on the mean and variance, and can calculate a latent vector that allows the same probability density function as the calculated probability density function to be output.

[0122]

[0123] FIG. 7 is a diagram for explaining the formula for calculating a potential vector according to one embodiment.

[0124] Referring to FIG. 7, the abnormal time series generating device of the present disclosure can calculate a latent vector based on the mean, variance, and noise of the divided time series data.

[0125] As described above, the latent vector of the present disclosure refers to a set of functions that enable an output value identical to the input value. The ideal time series data generating device of the present disclosure can calculate the set of functions through the aforementioned mathematical formula 1.

[0126] The ideal time series generation device of the present disclosure can calculate a latent vector according to the conceptual diagram shown in FIG. 7.

[0127] For example, the ideal time series generating device of the present disclosure can divide the time series data (700) according to preset conditions when time series data is input. As described above, the time series data may be divided based on the number of data units or based on time units.

[0128] The time series data generation device of the present disclosure can calculate the mean, variance, and noise for each of the divided time series data (710). As described above, the calculation of the noise of the divided time series data is performed using a preset second algorithm, wherein the second algorithm may include at least one of Gaussian filtering, a bidirectional filter, and a Kalman filter. Once the mean, variance, and noise are calculated, the variance and noise corresponding to each of the divided time series data can be multiplied, and the mean can be summed.

[0129] Through this, a latent vector for the divided time series data can be calculated (720). The latent vector may have as many elements as the number of divided time series data. Additionally, the latent vector may have multiple random variables for each element that are included in multiple probability density functions calculated based on the mean and variance.

[0130]

[0131] FIG. 8 is a diagram for explaining an integrated probability density function according to one embodiment.

[0132] Referring to FIG. 8, the ideal time series data generation device of the present disclosure can display a location corresponding to the mean or a plurality of probability density functions of each of the divided time series data in a preset space, and each region can be displayed based on the variance of each of the divided time series data centered on each location.

[0133] In addition, the ideal time series data generation device of the present disclosure can calculate the sum of a plurality of probability density functions, calculate an integrated probability density function through a preset third algorithm, and display the integrated probability density function in a preset space.

[0134] As described above, the third algorithm used to calculate the integrated probability density function may include an expectation-maximization algorithm (EM algorithm).

[0135]

[0136] Figure 8 is an example of an implementation of an integrated probability density function. For convenience of explanation, assuming a pre-set space as a two-dimensional space, the dotted line shown in Figure 8 represents the integrated probability density function, and the five circular dots represent the mean or probability density function of each of the divided time series data. Additionally, the space colored in blue, red, and light green represents the area calculated based on the variance of each of the divided time series data centered around the five circular dots.

[0137] A modified potential vector may be located inside, on, or outside the dotted line. A probability variable value for which a specific probability can be calculated for an integrated probability density function is calculated through the abnormal time series data generation device of the present disclosure, and when the calculated probability variable value is reflected in the modified potential vector, the modified potential vector may be located inside the dotted line, on the dotted line, or outside the dotted line depending on the reflected probability variable value.

[0138] The further the correction potential vector is located from the dotted line, the more the time series data generated by the abnormal time series data generation device of the present disclosure can be viewed as data similar to abnormal data that may actually be generated during the process. Conversely, the further the correction potential vector is located from the dotted line, the more the time series data generated by the abnormal time series data generation device of the present disclosure can be viewed as data similar to actual normal data.

[0139] However, the two-dimensional space shown in FIG. 8 is merely an example for convenience of explanation regarding the integrated probability density function and the modified potential vector, and is not limited thereto; it may also be displayed in a space of three or more dimensions as needed, and the aforementioned point is also merely an example for convenience of explanation and may be displayed in various forms such as a two-dimensional figure or a three-dimensional sphere as needed.

[0140]

[0141] FIG. 9 is a graph for explaining the method of calculating a modified potential vector according to one embodiment.

[0142] Referring to FIG. 9, the ideal time series data generation device of the present disclosure can calculate an integrated probability density function based on the sum of a plurality of probability density functions, and can calculate the value of a probability variable for each probability density function based on the integrated probability density function.

[0143] As mentioned above, each probability density function, integrated probability density function, and latent vector may contain the same random variable.

[0144] For example, if random variables A, B, and C are included in each probability density function, integrated probability density function, and potential vector, X0 = {A0, B0, C0} shown in FIG. 9 can be said to be a random variable or set of random variables in which the probability density of the integrated probability density function is 0.5, X1 = {A1, B1, C1} can be said to be a random variable or set of random variables in which the probability density of the integrated probability density function is the first value, and X2 = {A2, B2, C2} can be said to be a random variable or set of random variables in which the probability density of the integrated probability density function is the second value.

[0145] The set of random variables X0, X1, X2 and random variables A, B, and C included in the integrated probability density function are given as examples of only three for the convenience of explanation, and are not limited to the aforementioned X0, X1, X2, A, B, and C, but can be calculated in various ways depending on the probability density set or the number of partitioned time series data.

[0146] The area under the integrated probability density function represents the probability density or probability.

[0147] For example, the ideal time series data generation device of the present disclosure can calculate A0, B0, and C0 of a set of random variables X0 such that the probability density of the integrated probability density function is 0.5. In other words, the area of ​​the portion of the graph that is larger than the set of random variables X0 can be 0.5 as the probability density.

[0148] As another example, the ideal time series data generating device of the present disclosure can calculate A1, B1, and C1 of a set of random variables X1, where the probability density of the integrated probability density function is the first value. In other words, the area of ​​the portion on the graph that is larger than the set of random variables X1 can be the first value as the probability density.

[0149] As another example, the ideal time series data generating device of the present disclosure can calculate A2, B2, and C2 of a set of random variables X2, where the probability density of the integrated probability density function is the second value. In other words, the area of ​​the portion on the graph that is larger than the set of random variables X2 can be the second value as the probability density.

[0150] In the aforementioned example, it means that the anomalous time series data calculated from a potential vector with X0 or X1 applied, based on a value with a larger probability density, is closer to normal data than the anomalous time series data calculated from a modified potential vector with X2 applied, based on a value with a smaller probability density.

[0151] In addition, the device for generating abnormal time series data of the present disclosure can generate abnormal time series data by calculating A2, B2, and C2 of a set of random variables X2 in which the probability density of an integrated probability density function becomes a second value, reflecting the calculated random variables A2, B2, and C2 in a latent vector to calculate a modified latent vector, and inputting the calculated modified latent vector into an artificial intelligence model learned through a preset first algorithm.

[0152] The device for generating abnormal time series data of the present disclosure can calculate the value of a random variable corresponding to a specific probability of an integrated probability density function and reflect the calculated value of the random variable in each element of a latent vector.

[0153] A latent vector reflecting the value of a random variable may be referred to as a modified latent vector in this disclosure. When a modified latent vector is calculated, the abnormal time series data generation device of this disclosure can generate abnormal time series data based on an artificial intelligence model learned through a preset first algorithm. As described above, the artificial intelligence model learned through the first algorithm may include at least one autoencoder or at least one variational autoencoder, and the first algorithm may include a Gradient Descent Algorithm. Additionally, when a modified latent vector is calculated, the abnormal time series data generation device of this disclosure can generate abnormal time series data by inputting the modified latent vector into a decoder of a designed autoencoder.

[0154] In addition, the abnormal time series data generation device of the present disclosure can set N specific probability values ​​of an integrated probability density function (N is an integer greater than or equal to 2) to generate N probability variables (N is an integer greater than or equal to 2) corresponding to a plurality of specific probabilities, and accordingly, N modified potential vectors (N is an integer greater than or equal to 2) can also be generated. When the N modified potential vectors are input into an artificial intelligence model learned through a first algorithm that is pre-set, N time series data can be generated.

[0155]

[0156] FIG. 10 is a flowchart for explaining a method for generating abnormal time series data according to one embodiment.

[0157] Referring to FIG. 10, the method for generating abnormal time series data of the present disclosure includes a data receiving step of receiving time series data (S1000).

[0158] For example, the time series data received in the data receiving step of the present disclosure may include only normal data.

[0159] As another example, the time series data received in the data receiving step of the present disclosure may include data preprocessed based on at least one of a neural network, a 1D (1-Dimensional) Convolution operation, and a 2D (2-Dimensional) Convolution operation.

[0160] In the data reception step of the present disclosure, the time series data may be preprocessed univariate data. Specifically, the data reception step of the present disclosure may receive a single-dimensional vector as time series data, or receive data output by passing it through a pre-set neural network as time series data. The aforementioned neural network may include at least one of LSTM (Long Short-Term Memory), CNN (Convolutional Neural Network), RNN (Recurrent Neural Network), and DNN (Deep Neural Network).

[0161] In addition, the time series data received through the data receiving step of the present disclosure may be preprocessed multivariate data. Specifically, the preprocessing of the time series data may be performed through a method of outputting the time series data through 1D Convolution or 2D Convolution operations, a method of outputting the time series data through an RNN-based architecture, and a method of outputting the time series data through a Transformer-based architecture.

[0162] However, the aforementioned model is merely one example as a target for preprocessing time-series data and is not limited thereto, and can be configured in various ways as needed.

[0163] The method for generating abnormal time series data of the present disclosure includes a latent vector calculation step of dividing time series data according to a preset criterion and calculating a latent vector including a probability density function for each of the divided time series data (S1010).

[0164] For example, a preset criterion may include at least one of a criterion for the number of data and a criterion for unit time. For example, if the time series data received through the data reception step consists of 10 data points generated over 10 seconds, the latent vector calculation step of the present disclosure may divide the time series data into two groups based on a criterion of 5 units or divide the time series data into two groups based on a criterion of 5 seconds. The aforementioned criteria for dividing the time series data according to time and number are merely examples and may be set in various ways as needed.

[0165] As another example, the latent vector calculation step of the present disclosure may calculate the mean and variance for each of the divided time series data and calculate noise for each of the divided time series data based on a preset second algorithm.

[0166] In time-series data, noise refers to unintended data distortion caused by interference from external factors. In other words, it can be defined as a factor that distorts some of the data within a time-series. For example, interference with signal data output from objects such as sensors, or bugs frequently found in specific programs, can be considered noise.

[0167] Through the method for generating abnormal time series data of the present disclosure, abnormal time series data can be generated by calculating a quantified latent vector based on a distribution of groups divided according to preset criteria.

[0168] A second algorithm including at least one of Gaussian filtering, bidirectional filtering, and Kalman filtering may be used as a method for calculating noise in time series data.

[0169] As another example, the latent vector calculation step of the present disclosure calculates a plurality of probability density functions based on the mean and variance for each of the divided time series data, and the plurality of probability density functions may include at least one of a normal distribution and a uniform distribution.

[0170] The method for generating an anomalous time series of the present disclosure calculates the mean and variance for each of the divided time series data and can calculate a probability density function for each group of time series data based on the calculation results. Each of the calculated probability density functions may include a random variable.

[0171] As another example, a latent vector can be calculated based on the mean, variance, and noise calculated for each of the time series data segmented through the latent vector calculation step of the present disclosure.

[0172] In that the probability density function of the present disclosure may include at least one of a normal distribution and a uniform distribution, it is proposed to use a second algorithm that includes a Gaussian filter based on a normal distribution or a uniform distribution among the methods for calculating the noise described above.

[0173] A latent vector may refer to a set of functions that, when each partitioned time series data group is input into a preset model, output data identical to the input time series data group. Accordingly, the latent vector calculation step of the present disclosure may utilize an autoencoder having a latent space that makes the input data and the output data identical. A latent vector may be calculated through the aforementioned latent space. Additionally, the aforementioned preset model may include an autoencoder or a variational autoencoder.

[0174] The abnormal time series data generation device of the present disclosure may perform not only the calculation of a latent vector but also the process of generating abnormal time series data using the latent vector using an autoencoder. The autoencoder is composed of an encoder into which time series data is input, a latent space for calculating a latent vector, and a decoder into which time series data is output. When a modified latent vector is calculated, the calculated modified latent vector is input into the decoder to generate abnormal time series data through the decoder.

[0175] Even when using an autoencoder, the input time series data can consist solely of normal data, and latent vectors can be generated through the latent space during the autoencoder's training process. Additionally, abnormal time series data can be generated by inputting the quantified latent vectors into the decoder of the trained autoencoder.

[0176] The latent vector of the present disclosure can be calculated based on the aforementioned mathematical formula 1, which takes μ as the mean, σ as the variance, ε as the noise, i as the number of the group, and z as the latent vector for each of the divided time series data.

[0177] As described above, a latent vector is a set of functions that output time series data identical to the input time series data, and can be calculated through the aforementioned mathematical formula 1 based on the mean, variance, and noise of each divided time series data.

[0178] The method for generating abnormal time series data of the present disclosure includes a step of calculating a probability variable value for each probability density function for a specific probability in an integrated probability density function that integrates a plurality of probability density functions (S1020).

[0179] For example, the same random variable may be included in a plurality of probability density functions, latent vectors, and integrated probability density functions calculated through the method for generating abnormal time series data of the present disclosure.

[0180] As another example, the step of calculating the probability variable value of the present disclosure may calculate a single integrated probability density function based on the sum of a plurality of probability density functions.

[0181] As another example, the step of calculating the probability variable value of the present disclosure may display a plurality of probability density functions in a preset space and calculate an integrated probability density function based on the center position of the plurality of probability density functions displayed in the space and a preset third algorithm. The center position of the aforementioned probability density function refers to the mean of each probability density function.

[0182] For example, the step of calculating the probability variable value of the present disclosure may display points corresponding to the average of a plurality of probability density functions of the present disclosure on a preset two-dimensional plane, generate regions based on each point based on the variance for each probability density, and calculate a single probability density function integrated through a preset third algorithm.

[0183] However, the aforementioned two-dimensional plane is merely an example for explaining the generation of the integrated probability density function, and the space in which the average of multiple probability density functions is displayed and the integrated probability density function is generated therefrom may be a high-dimensional space of three dimensions or more.

[0184] The integrated probability density function reflects the characteristics of multiple probability density functions. In addition, the integrated probability density function also reflects the characteristics of each data included in the input time series data. Utilizing these properties, the present disclosure proposes using an expectation-maximization algorithm (EM algorithm) as a third algorithm for calculating the aforementioned integrated probability density function.

[0185] The present disclosure calculates the probability that each data point included in the input time series data belongs to each probability density function through an expectation maximization algorithm, and determines a probability distribution with a high probability for each data point to produce a single integrated probability distribution.

[0186] For example, the probability that each data point included in the aforementioned time series data belongs to each probability density function may be determined based on the distance between each data point and the center locations of multiple probability density functions.

[0187] When the integrated probability density function is calculated, the step of calculating the probability variable value of the present disclosure can calculate a plurality of probability variable values ​​corresponding to a specific probability based on the integrated probability density function.

[0188] As previously mentioned, since the integrated probability density function can be calculated based on the sum of each probability density function, the random variables included in each probability density function are also included in the integrated probability density function. Furthermore, the same random variables are included in the latent vector. Therefore, the aforementioned multiple random variables can correspond, respectively, to the random variables included in each probability density function and the random variables included in the latent vector.

[0189] The method for generating abnormal time series data of the present disclosure includes a step of generating abnormal time series data based on a modified latent vector in which the value of a probability variable for each probability density function is reflected in a latent vector, and an artificial intelligence model learned through a preset first algorithm (S1030).

[0190] When multiple probability variable values ​​corresponding to a specific probability are calculated based on an integrated probability density function, the abnormal time series data generation step of the present disclosure can reflect each probability variable value in a latent vector. The present disclosure may refer to the latent vector reflecting each probability variable value as a modified latent vector.

[0191] The aforementioned specific probability is a value that is pre-set according to the degree of abnormality of the data required for generation; the lower the specific probability is set, the more abnormal data with a high degree of abnormality is generated, and the higher the specific probability is set, the more normal data with a low degree of abnormality is generated.

[0192] When a modified latent vector is generated, the modified latent vector can be input into an artificial intelligence model trained through a preset first algorithm to generate anomalous time series data. Additionally, as described above, the modified latent vector can be input into a decoder of an autoencoder trained through a preset first algorithm to generate anomalous time series data.

[0193] The aforementioned artificial intelligence model may include at least one autoencoder or at least one variational autoencoder, and the artificial intelligence model may be trained through a first algorithm.

[0194] The first algorithm used for training an artificial intelligence model may include a Gradient Descent Algorithm that minimizes the loss occurring during the training process of the artificial intelligence model. The aforementioned Gradient Descent Algorithm can minimize the loss arising from the difference between the data output through the artificial intelligence model and the actual data during the training process of the artificial intelligence model. The present disclosure may refer to the aforementioned Gradient Descent Algorithm as a Gradient Optimization Algorithm.

[0195]

[0196] The foregoing description is merely an illustrative explanation of the technical concept of the present disclosure, and those skilled in the art to which the present disclosure pertains may make various modifications and variations within the scope of the essential characteristics of the technical concept. Furthermore, since these embodiments are intended to explain, not limit, the scope of the technical concept is not limited by these embodiments. The scope of protection of the present disclosure shall be interpreted by the claims below, and all technical concepts within an equivalent scope shall be interpreted as being included within the scope of rights of the present disclosure.

[0197]

[0198] CROSS-REFERENCE TO RELATED APPLICATION

[0199] This patent application claims priority pursuant to Section 119(a) of the U.S. Patent Act (35 USC § 119(a)) to Korean Patent Application No. 10-2024-0148828 filed on October 28, 2024, all of which are incorporated by reference into this patent application. Additionally, this patent application claims priority in countries other than the United States for the same reasons as above, all of which are incorporated by reference into this patent application.

Claims

1. A data receiving unit that receives time series data; A latent vector calculation unit that divides the above time series data according to preset criteria and calculates a latent vector including a probability density function for each of the divided time series data; A probability variable value calculation unit that calculates a probability variable value for each of the above probability density functions for a specific probability in an integrated probability density function that integrates the above plurality of probability density functions; and An abnormal time series data generation device comprising an abnormal time series data generation unit that generates abnormal time series data based on an artificial intelligence model learned through a modified potential vector in which the probability variable values ​​for each of the above probability density functions are reflected in the above potential vector and a preset first algorithm.

2. In Paragraph 1, The above time series data is, An abnormal time series data generation device characterized by including only normal data.

3. In Paragraph 1, The above time series data is, An ideal time series data generation device characterized by data preprocessed based on at least one of a neural network, a 1D (1-Dimensional) Convolution operation, and a 2D (2-Dimensional) Convolution operation.

4. In Paragraph 1, The above-mentioned preset criteria are, An ideal time series data generation device characterized by including at least one of a standard for the number of data points and a standard for unit time.

5. In Paragraph 1, The above artificial intelligence model is, It includes at least one autoencoder, and The above-mentioned preset first algorithm is, An abnormal time series data generation device characterized by including a Gradient Descent Algorithm that minimizes loss occurring during the learning process of the above artificial intelligence model.

6. In Paragraph 1, The above potential vector calculation unit is, Calculate the mean and variance for each of the above-mentioned divided time series data, and Noise for each of the divided time series data is calculated based on a preset second algorithm, An ideal time series data generation device characterized by the above-mentioned preset second algorithm including a Gaussian filter.

7. In Paragraph 6, The above potential vector calculation unit is, Calculate the plurality of probability density functions based on the mean and variance for each of the divided time series data, and The above plurality of probability density functions are, An ideal time series data generation device characterized by including at least one of a normal distribution and a uniform distribution.

8. In Paragraph 6, The above potential vector calculation unit is, An ideal time series data generation device characterized by calculating the latent vector based on the mean, the variance, and the noise for each of the divided time series data.

9. In Paragraph 1, The above potential vector calculation unit is, The above latent vector is calculated through an artificial intelligence model into which the above time series data is input, and The data output through the above artificial intelligence model is, An ideal time series data generation device characterized by being identical to the above time series data.

10. In Paragraph 1, The above integrated probability density function is, An ideal time series data generation device characterized by being integrated based on the sum of the above-mentioned plurality of probability density functions.

11. In Paragraph 1, The above probability variable value calculation unit is, Display the above multiple probability density functions in a preset space, and Calculate the integrated probability density function based on the center positions of the plurality of probability density functions displayed in the space and a preset third algorithm, wherein The above-mentioned preset third algorithm is, An ideal time series data generation device characterized by including an expectation-maximization algorithm (EM algorithm) that calculates the integrated probability density function based on the probability that each data included in the received time series data belongs to each of the plurality of probability density functions.

12. Data receiving step for receiving time series data; A latent vector calculation step of dividing the above time series data according to preset criteria and calculating a latent vector including a probability density function for each of the divided time series data; A step for calculating a probability variable value for each of the probability density functions for a specific probability in an integrated probability density function that integrates the plurality of probability density functions; and A method for generating abnormal time series data, comprising a step of generating abnormal time series data based on an artificial intelligence model learned through a modified potential vector in which the probability variable values ​​for each of the above probability density functions are reflected in the above potential vector, and a preset first algorithm.

13. In Paragraph 12, The above time series data is, A method for generating abnormal time series data characterized by including only normal data.

14. In Paragraph 12, The above time series data is, A method for generating abnormal time series data characterized by data preprocessed based on at least one of a neural network, a 1D (1-Dimensional) Convolution operation, and a 2D (2-Dimensional) Convolution operation.

15. In Paragraph 12, The above-mentioned preset criteria are, A method for generating abnormal time series data characterized by including at least one of a criterion for the number of data points and a criterion for a unit time.

16. In Paragraph 12, The above artificial intelligence model is, It includes at least one autoencoder, and The above-mentioned preset first algorithm is, A method for generating abnormal time series data characterized by including a Gradient Descent Algorithm that minimizes loss occurring during the learning process of the above artificial intelligence model.

17. In Paragraph 12, The above potential vector calculation step is, Calculate the mean and variance for each of the above-mentioned divided time series data, and Noise for each of the divided time series data is calculated based on a preset second algorithm, A method for generating abnormal time series data characterized by the above-mentioned preset second algorithm including a Gaussian filter.

18. In Paragraph 12, The above potential vector calculation step is, The above latent vector is calculated through an artificial intelligence model into which the above time series data is input, and The data output through the above artificial intelligence model is, A method for generating abnormal time series data characterized by being identical to the above time series data.

19. In Paragraph 12, The above integrated probability density function is, A method for generating ideal time series data characterized by being integrated based on the sum of the above-mentioned plurality of probability density functions.

20. In Paragraph 12, The above step of calculating the probability variable is, Display the above multiple probability density functions in a preset space, and Calculate the integrated probability density function based on the center positions of the plurality of probability density functions displayed in the space and a preset third algorithm, wherein The above-mentioned preset third algorithm is, A method for generating ideal time series data characterized by including an expectation-maximization algorithm (EM algorithm) that calculates the integrated probability density function based on the probability that each data included in the received time series data belongs to each of the plurality of probability density functions.

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