Time-series data monitoring system and time-series data monitoring method
The system addresses the challenge of determining the optimal window width for pattern extraction by automating the process, enhancing accuracy and reducing costs in time-series data monitoring.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- HITACHI LTD
- Filing Date
- 2022-11-22
- Publication Date
- 2026-05-15
AI Technical Summary
Existing time-series data monitoring systems face challenges in determining the optimal window width for pattern extraction, which affects the accuracy and computational cost, and require multiple trial-and-error settings for users to identify multiple patterns, leading to high analysis costs.
A system that automatically determines the optimal window width for pattern extraction by calculating the difference between the desired pattern length and the calculated pattern length using an objective function, reducing user burden and computational costs.
Automatically determines the optimal window width for pattern extraction, reducing user effort and analysis costs while ensuring accurate pattern monitoring.
Smart Images
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Abstract
Description
Technical Field
[0001] The present invention relates to a time-series data monitoring system and a time-series data monitoring method.
Background Art
[0002] In the industrial field, it is necessary to perform maintenance inspections to prevent malfunction due to aging deterioration of machine tools. Since regular maintenance inspections are costly, it is ideal not to perform inspections when the equipment is operating normally and to perform inspections at an early stage when signs of failure appear.
[0003]
[0004] Therefore, in recent years, sensors are installed on target equipment, operation data of the equipment such as current, torque, and speed obtained from the sensors is monitored, and when a sign is detected from the data, maintenance inspections are increasingly carried out.
[0005] As an example of a device for monitoring equipment using time-series data, in Patent Document 1, a monitoring device is proposed that creates a histogram from the operation data of the equipment to be monitored and searches for similar past data and determines the presence or absence of a precedent by comparing it with a histogram created from the data accumulated in the past.
Prior Art Documents
Patent Documents
[0006]
Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0007] In Patent Document 1, data for which the presence or absence of precedents is to be searched is divided using a predetermined window width to create a histogram, and this plays the role of a pattern in time-series data. In this case, the histogram created will differ depending on the length of the window width, and this may affect the final search results, so how to determine the length of the window width becomes a challenge.
[0008] Furthermore, if the window width is too short, it becomes impossible to extract patterns that adequately represent time changes. Also, the extracted patterns become more susceptible to data noise. On the other hand, if the window width is too long, it becomes difficult to extract characteristic patterns. Additionally, it increases computational cost. Therefore, it is necessary to set an appropriate window width when performing pattern extraction.
[0009] Furthermore, molding machines and other processing machines used in industrial fields repeatedly perform fixed operations, resulting in time-series data that combines several fixed patterns. When monitoring such data, users have some knowledge of the patterns they want to monitor, and there may be multiple patterns they wish to monitor. Therefore, users need to set a window size that allows them to extract the desired patterns and perform analysis. However, the relationship between the extractable patterns and the window size is not clear, so multiple window sizes must be repeatedly set until the desired pattern is obtained. This creates a problem where the analysis cost for the user becomes very high when there are multiple patterns they wish to monitor.
[0010] The present invention aims to provide a monitoring system and time-series data monitoring method that automatically determines the optimal window width for extracting patterns that the user wants to monitor, and monitors the patterns obtained using that window width. [Means for solving the problem]
[0011] To achieve the above objective, the time-series data monitoring system of the present invention comprises a window width search unit that searches for a window width for extracting patterns from time-series data acquired from target equipment from information on input patterns, and a pattern extraction unit that extracts patterns from the time-series data using the window width search unit. The information relating to the pattern is the length of the pattern and the data interval to be extracted from the pattern. The window width search unit calculates the window width such that the objective function, which is the difference between the length of the pattern and the length of the pattern calculated from the window width in the data interval, is less than or equal to a predetermined value. This invention is characterized by the following embodiments. Other aspects of the present invention will be described in the embodiments described below. [Effects of the Invention]
[0012] According to the present invention, the window width for extracting a time-series data pattern desired by the user can be automatically determined, and the pattern obtained using that window width can be monitored. [Brief explanation of the drawing]
[0013] [Figure 1] This diagram shows the overall configuration of the time-series data monitoring system according to the embodiment. [Figure 2] This flowchart shows an overview of the processing of the time-series data monitoring system according to the embodiment. [Figure 3] This flowchart shows the window width determination and pattern extraction process according to the embodiment. [Figure 4A] This figure shows an example of the execution screen (part 1) of the window width search according to the embodiment. [Figure 4B] This figure shows an example of the execution screen (part 2) of the window width search according to the embodiment. [Figure 4C] This figure shows an example of the execution screen (part 3) of the window width search according to the embodiment. [Figure 5A] This figure shows an example of the execution screen (part 1) of pattern extraction according to the embodiment. [Figure 5B] This figure shows an example of the execution screen (part 2) of pattern extraction according to the embodiment. [Figure 6] This is a flowchart showing the window width determination process according to the embodiment. [Figure 7] This is a flowchart showing the anomaly detection process according to the embodiment. [Figure 8] This figure shows an example of the execution screen for anomaly detection according to the embodiment. [Figure 9] This figure shows an example of a display screen for anomaly detection results according to the embodiment. [Modes for carrying out the invention]
[0014] Embodiments of the present invention will be described in detail below with reference to the drawings. The same components will be denoted by the same reference numerals, and descriptions may be omitted if they are redundant. Furthermore, the present invention is not limited to the following embodiments.
[0015] <Overall Structure> Figure 1 shows the overall configuration of the time-series data monitoring system 100 according to this embodiment. The time-series data monitoring system 100 includes a processing unit 10, a storage unit 20, an input unit 31, a display unit 32, and a communication unit 33. The processing unit 10 includes a data acquisition unit 11, a window width search unit 12, a pattern extraction unit 13, an analysis unit 14, a display processing unit 15, etc. The storage unit 20 stores a time-series data management database 21, a results management database 22, etc.
[0016] In Figure 1, the processing unit 10 is a central processing unit (CPU) that executes various programs stored in RAM, HDD, etc. The storage unit 20 is an HDD that stores various data for the time-series data monitoring system 100 to execute processing. The input unit 31 is a device for inputting instructions to the computer, such as a keyboard or mouse, and inputs instructions such as program startup. The display unit 32 is a display, etc., that displays the execution status and execution results of processing by the time-series data monitoring system 100. The communication unit 33 is a device that exchanges various data and commands with other devices (for example, target equipment 50) via a network NW.
[0017] The data acquisition unit 11 acquires time-series data measured by the target equipment 50. The data acquisition unit 11 records the acquired data in the time-series data management database 21.
[0018] The window width search unit 12 searches for the optimal window width to extract the pattern desired by the user, based on time-series data obtained from the time-series data management database 21 and information about the pattern entered by the user.
[0019] The pattern extraction unit 13 extracts patterns from the window width entered in the input unit 31 and the data to be extracted, and records the extracted patterns in the result management database 22.
[0020] The analysis unit 14 retrieves the extracted patterns or window widths stored in the results management database 22, calculates statistics using them, creates graphs, and records these in the results management database 22.
[0021] The display processing unit 15 displays the search results from the window width search unit 12, the statistics or graphs obtained by the analysis unit 14, etc., on the display unit 32.
[0022] The input unit 31 receives input such as data used by the user required for window width search, information about the pattern to be extracted, the window width used by the pattern extraction unit 13, and the data to be analyzed by the analysis unit 14.
[0023] Figure 2 is a flowchart showing the processing overview of the time-series data monitoring system 100 according to the embodiment. First, the time-series data monitoring system 100 performs a window width search in the window width search unit 12 (step S1). The window width search takes information about the pattern that the user wants to extract as input, and searches for and determines the window width from which the pattern that best matches the input information can be extracted. Details will be described later using Figures 3 and 4A to 4C.
[0024] Next, the pattern extraction unit 13 performs pattern extraction (step S2). While the window width used for pattern extraction is usually the one determined in step S1, it is also possible to set a different window width for pattern extraction. Details will be described later using Figures 3, 5A, and 5B.
[0025] Next, the analysis unit 14 performs the analysis (step S3). The analysis targets the data stored in the time-series data management database 21 and the patterns extracted by the pattern extraction unit 13. The analysis involves visualizing the data and patterns and calculating statistics. The most basic analysis is the plotting of graphs of the extracted patterns for display to the user. Furthermore, anomaly detection can be performed using the data stored in the time-series data management database 21 as part of monitoring. Details will be described later using Figures 8 and 9.
[0026] Finally, the display processing unit 15 displays the analysis results obtained by the analysis unit 14 on the display unit 32 (step S4).
[0027] As a result, patterns can be extracted from pattern information without the user having to determine the window width. This reduces the burden on the user in determining the window width and streamlines the analysis.
[0028] Figure 3 is a flowchart showing the window width determination and pattern extraction process S10 according to the embodiment. Details of the automatic window width determination and pattern extraction by the time-series data monitoring system 100 will be explained with reference to Figure 3. For the explanation of Figure 3, please refer to Figures 4A to 4C, 5A, and 5B. Figures 4A to 4C, 5A, and 5B are display screens shown on the display unit 32.
[0029] First, the user selects the data to be used for pattern extraction from the data stored in the time-series data management database 21 (Step S11: Select data). Specifically, as shown in Figure 4A, the user enters the file path where the data is stored in the file path input section 401.
[0030] Next, the window width search unit 12 reads the data stored in the file path input to the file path input unit 401, creates a graph to visualize the waveform of the time-series data, and the display processing unit 15 displays the graph on the output result screen 402 as shown in Figure 4B (Step S12: Visualize selected data).
[0031] The user refers to the displayed graph and inputs the length of the pattern to be extracted and the target interval for pattern extraction into the value input section 403 and the value input section 404, respectively, as shown in FIG. 4C (step S13: input pattern information). To set the target interval, it is necessary to input the start point and the end point of the interval.
[0032] The window width search section 12 searches for the window width from the data selected in step S11 and the information of the pattern to be extracted input in step S13 (step S14). The display processing section 15 displays the searched window width and the length of the pattern corresponding to the window width on the output result screen 402 as shown in FIG. 4C.
[0033] <Method for Searching Window Width> A specific method for searching the window width in step S14 will be described with reference to FIG. 6. FIG. 6 is a flowchart showing the window width determination process S20 according to the embodiment. Let the length of the pattern to be extracted input by the user be L and the initial value of the window width be w0. This w0 is updated by an algorithm to determine the window width that can obtain a pattern length close to L.
[0034] Let the update counter be k (k = 0, 1, 2,...), the window width after k updates be w k 、w k The length of the pattern (calculated value of the pattern length) calculated by k be τ k ’, the loss function representing the difference between L and τ k ’ be f(L, τ k ’), the threshold value (predetermined value) of the loss function be ε, and the update formula of w k be g(w
[0035] First, set k = 0 and w k = 0 (step S21). Next, calculate τ k ’ using w k (step S22), and calculate f(L, τ k ’) using L and τ k ’ (step S23). f(L, τk Determine if ')<ε (step S24), f(L, τ k When ') < ε is not true (step S24, No), w k+1 ←g(w k ), set k←k+1 (step S25), and return to step S22.
[0036] On the other hand, f(L, τ k When ')<ε (step S24, Yes), w k Determine the optimal window width and end the calculation.
[0037] (τ k (How to calculate the pattern length) Step S22 τ k Let's explain how to calculate '. In this embodiment, it is assumed that the time series data of the target equipment 50 is represented by a combination of solutions to a delayed differential equation, and the time constant of the solution to the delayed differential equation is defined as the length of the pattern τ k Calculate '.
[0038] Let's explain the specific calculation formula. For simplicity, we will use w=w from now on. k , τ ’ =τ k Let's assume that. First, a regression model of the lag coordinate vector is constructed under the window width w, and its coefficient matrix is estimated. The time series data y = [y(1), y(2), ..., y(N)] is used in the window width search. T When y(t) is the t-th data point of y, the t-th lag coordinate vector in the window width w is given by equation (1).
[0039]
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[0040] Now, consider the differential equation (2).
number
[0041] Assume that the differential equation in equation (2) can be expressed as a linear sum of exponential functions and written as in equation (3).
number
[0042] Let's explain the estimation process. First, the coefficient matrix A in equation (2) is estimated using the regression model x(t+1)=Ax(t). Next, the estimated coefficient matrix A is decomposed into eigenvalues as follows.
number
[0043] In this case, x(t) can be expanded starting from t=t0 as follows:
number
[0044] Here... i =-σ i +iω i Let's assume that λ i The real part σ i When is sufficiently small, allow coefficient multiplication and v i The exp(-t / T) in equation (3) i It can be associated with ). Therefore, v i Considering this as a function of t, the time constant T iWe estimate the vector obtained by taking the absolute value of each element. i abs Solve the following using this approach.
[0045]
number
[0046] , ||Series|| 2 refers to the square norm, c i is, v i abs These are coefficient parameters for fitting the function. argmin represents the parameter that minimizes the given function, and here it is the parameter that minimizes the squared norm of equation (6). i , c i This refers to T i ’ (i=1, 2, ..., w) are found, and in equation (5), v has a large contribution to x(t). i T corresponding to i ’ to τ ’ Let's assume that.
[0047] The loss function used in step S23 is the following formula.
number
[0048] The update formula for step S25 will be explained. The update formula is based on the gradient method and uses the following equation.
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[0049] Regarding the second term of equation (8)
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[0050] As a result, users do not need to pre-set window widths; they can check the time-series data of the 50 target facilities and automatically determine the optimal window width based on the information of the patterns they want to monitor.
[0051] Returning to Figure 3, the user then inputs the window width obtained in step S14 into the value input unit 501 in Figure 5A, inputs the data to be pattern extracted into the file path input unit 502 in Figure 5A, and performs pattern extraction (step S15). In pattern extraction, the pattern length calculated from the input window width and the basis vector corresponding to the pattern length are calculated using the method of step S22 of the window width search. The window width entered in step S15, the calculated pattern length, and the basis vector are recorded in the result management database 22.
[0052] The display processing unit 15 uses the pattern extraction results recorded in the results management database 22 to display a graph as shown in Figure 5B that clearly indicates the portion of the time-series data corresponding to the extracted pattern (step S16).
[0053] I will now explain how to identify the relevant section. First, the pattern extraction unit 13 retrieves data from the time-series data management unit 3 based on the file path entered in the file path input unit 502 in Figure 5A, and retrieves the window width and basis vector recorded in step S15 from the result management database 22. The data is converted to lag coordinates by the window width to obtain a lag coordinate vector x(t) (t=w, w+1, ..., N). The dot product of each lag coordinate vector and the basis vector is calculated, and the interval of the lag coordinate vector with the maximum dot product is taken as the corresponding part of the extracted pattern. By calculating the dot product, the degree of dependence of the two vectors can be calculated, and data intervals that have a similar trend to the extracted pattern interval can be identified.
[0054] This section explains how to clearly indicate the relevant part. The display processing unit 15 creates a waveform graph of the selected time-series data and draws only the partial waveform corresponding to the extracted pattern in a different line format from the other waveforms. In the output result screen 503 of Figure 5B, only a portion of the waveform section is shown as a solid line, indicating that this section has been extracted as a pattern.
[0055] Furthermore, as an application of the window width search and pattern extraction described above, it is possible to automate the automatic determination of window width and pattern extraction by combining it with change point detection. Specifically, data is input to the file path input unit 401, and change point detection is performed on the input data. Since the interval between the detected change points can be made to correspond to the pattern length in the value input unit 403 and the pattern extraction interval in the value input unit 404, by combining it with change point detection, it becomes possible to automatically determine the window width and extract patterns with only data input.
[0056] Figure 7 is a flowchart showing the anomaly detection process S30 according to the embodiment. Figure 8 is a diagram showing an example of the execution screen for anomaly detection according to the embodiment.
[0057] The analysis unit 14 has the function of learning an anomaly detection model using the window width searched by the window width search unit 12 and performing anomaly detection on the target equipment 50. The function of the analysis unit 14 will be explained using the anomaly detection process S30 in Figure 7 and the example execution screen in Figure 8.
[0058] First, the user sets the data and window width required for training the anomaly detection model (step S31). Specifically, the user inputs the file path of the data to be used as training data in the file path input section 701 in Figure 8, the file path of the data to be used as validation data in the file path input section 702, and the window width in the value input section 703. The validation data is used to calculate the threshold used by the anomaly detection model to determine whether or not an anomaly exists. Setting the validation data is not always necessary, and if the file path of the validation data is not set, the threshold will not be calculated.
[0059] The analysis unit 14 reads the training data entered by the user and trains an anomaly detection model (step S32). The training data is transformed into delayed coordinates using a window width, and the transformed data is trained. If the data path of the validation data is entered in the file path input unit 702, a threshold is calculated from the trained model and the validation data. The trained anomaly detection model, the window width used during training, and the threshold are recorded in the results management database 22.
[0060] Next, the user sets the test data for anomaly detection and the model to be used for anomaly detection (step S33). Specifically, the user inputs the file path of the test data and the file path of the anomaly detection model to be used in the file path input sections 704 and 705 in Figure 8.
[0061] The analysis unit 14 retrieves test data from the time-series data management database 21 and an anomaly detection model from the results management database 22, and performs anomaly detection (step S34). The test data undergoes a delayed coordinate transformation, similar to the training data, and the anomaly detection model performs inference on the transformed test data. The anomaly detection model calculates an anomaly score for each data point in the test data and stores it in the results management database 22. When saving the anomaly score to the results management database 22, information about the anomaly detection model used for inference is also recorded.
[0062] The display processing unit 15 visualizes and displays the abnormal score (step S35). The display processing unit 15 displays a graph of the abnormal score calculated in step S34 on the result display screen 706 in Figure 8. If a threshold exists, the threshold is also plotted on the graph, allowing the user to recognize data points where the abnormal score exceeds the threshold as abnormal.
[0063] <Abnormal Score> This section explains how the anomaly score is calculated. The anomaly score is calculated by determining the difference between the training data and the test data. The lag coordinate vector of the test data at time t is x test Let (t), x test The lag coordinate vector of the training data to compare the difference with (t) is x train Let's assume that x train x does not necessarily have to be the delayed coordinate at time t and varies depending on the anomaly detection model. For example, in the case of the k-nearest neighbor method, x test The value closest to (t) is x train This is how it works. At this point, the abnormal score (score(t)) at time t is calculated using the following formula.
[0064]
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[0065] Typical distance functions include the L2 norm and the L1 norm. By plotting the resulting score(t) (t=w, w+1, ..., N), the graph shown in display screen 706 of Figure 8 is obtained.
[0066] Furthermore, the anomaly score can also be calculated using the basis vectors calculated by the pattern extraction unit 13. The basis vectors for the training data and the test data are respectively v train , v test Therefore, the abnormal score is score(vtrain , v test In this case, the anomaly score will be 1, and it will be possible to reduce the dimensionality of the training data and perform anomaly detection more quickly.
[0067] When calculating the threshold, an anomaly score is calculated using formula (10) on the validation data selected in the file path input section 702. Then, the threshold is calculated based on the obtained anomaly score. Various methods are possible for calculating the threshold, with typical methods including using quantiles and the variance of the anomaly score.
[0068] Figure 9 shows an example of a display screen for anomaly detection results according to the embodiment. In the visualization of anomaly scores, multiple anomaly scores stored in the result management database 22 can be visualized simultaneously, allowing for comparison of each anomaly detection result. This will be explained in detail using Figure 9.
[0069] When a user enters the file path of the anomaly score they want to visualize in the file path input section 801 in Figure 9, the display processing unit 15 displays a graph of the selected anomaly score on the output result screen 802. If a threshold exists, the threshold is also displayed. The output result screen 802 displays graphs of the anomaly scores for Model 1, which was created with a window width of 100, and Model 2, which was created with a window width of 500. In the graph of the anomaly score for Model 1, anomalies are detected in the range of 1000 to 1500, while in Model 2, anomalies are detected in the range of 2500 to 3000. Models with a shorter window width are more likely to detect anomalies in fine waveforms, while models with a longer window width are more likely to detect anomalies in long waveforms.
[0070] If multiple anomalies occur in the window width test data, and these anomalies are of different types, checking the anomaly scores of multiple models allows for detection without missing any anomalies. Furthermore, as shown in output result screen 802, it is possible to classify anomalies by utilizing the fact that different models, i.e., different window widths, can detect different anomalies.
[0071] The time-series data monitoring system 100 has been described above, and the time-series data monitoring method is as follows:
[0072] (1) The time-series data monitoring method comprises a window width search step, which searches for a window width for extracting patterns from time-series data acquired from the target equipment based on input pattern information, and a pattern extraction step, which extracts patterns from the time-series data using the window width search step. This allows for the automatic determination of a window width for extracting time-series data patterns desired by the user, and enables monitoring of patterns obtained using that window width.
[0073] (2) A time-series data monitoring method described in (1), wherein the information relating to the pattern is the length of the pattern and the data interval to be extracted, and the window width search step is an objective function (for example, f(L, τ)) consisting of the difference between the length of the pattern and the length of the pattern calculated from the window width in the data interval. k A window width can be calculated such that ')) is less than or equal to a predetermined value (for example, a threshold ε).
[0074] (3) A time-series data monitoring method according to (1), comprising an analysis step that performs analysis of the patterns extracted by the pattern extraction step and the time-series data.
[0075] (4) The time series data monitoring method of (3) above, wherein the analysis step involves learning an anomaly detection model using the time series data and the window width, and performing inference using the anomaly detection model.
[0076] (5) A time-series data monitoring method described in (4), comprising a display processing step of displaying the analysis results obtained by the analysis step on a display unit.
[0077] (6) The time-series data monitoring method described in (5), wherein the display processing step can display the inference results of the anomaly detection model performed in the analysis step together on the display unit using multiple window widths. [Explanation of Symbols]
[0078] 10 Processing Unit 11 Data Acquisition Unit 12 Window width search section 13 Pattern extraction unit 14 Analysis Department 15 Display Processing Unit 20 Memory section 21. Time-series data management database 22 Results Management Database 31 Input section 32 Display section 33 Communications Department 50 Target equipment 100 Time-series data monitoring system (time-series data monitoring device) k update counter L pattern length w0 Initial value of window width w k Window width after k updates τ k ' w k The length of the pattern calculated by (calculated value of the pattern length) f(L, τ) k ') L and τ k Loss function (objective function) that represents the difference of ' ε is the threshold value (predetermined value) of the loss function. g(w k )w k Update formula
Claims
1. A window width search unit that searches for a window width for extracting a pattern of time-series data acquired from the target equipment from information about the input pattern, The system includes a pattern extraction unit that extracts patterns from the time-series data using the window width searched by the window width search unit, The information regarding the pattern includes the length of the pattern and the data interval from which the pattern is extracted. The window width search unit calculates a window width such that the objective function, which is the difference between the length of the pattern and the length of the pattern calculated from the window width in the data interval, is less than or equal to a predetermined value. A time-series data monitoring system characterized by the following features.
2. A time-series data monitoring system according to claim 1, The system includes an analysis unit that performs analysis of the patterns extracted by the pattern extraction unit and the time-series data. A time-series data monitoring system characterized by the following features.
3. A time-series data monitoring system according to claim 2, The analysis unit learns an anomaly detection model using the time-series data and the window width, and performs inference using the anomaly detection model. A time-series data monitoring system characterized by the following features.
4. A time-series data monitoring system according to claim 3, The system includes a display processing unit that displays the analysis results obtained from the analysis unit. A time-series data monitoring system characterized by the following features.
5. A time-series data monitoring system according to claim 4, The display processing unit displays the inference results of the anomaly detection model performed by the analysis unit using multiple window widths, all together on the display unit. A time-series data monitoring system characterized by the following features.
6. A window width search step that searches for a window width for extracting a pattern of time-series data acquired from the target equipment from information about the input pattern, The system includes a pattern extraction step which extracts a pattern from the time-series data using the window width found in the window width search step, The information regarding the pattern includes the length of the pattern and the data interval from which the pattern is extracted. The window width search step calculates a window width such that the objective function, which is the difference between the length of the pattern and the length of the pattern calculated from the window width in the data interval, is less than or equal to a predetermined value. A time-series data monitoring method characterized by the following features.
7. A time-series data monitoring method according to claim 6, The analysis step includes an analysis step for analyzing the patterns extracted by the pattern extraction step and the time-series data. A time-series data monitoring method characterized by the following features.
8. A time-series data monitoring method according to claim 7, The analysis step involves training an anomaly detection model using the time-series data and the window width, and performing inference using the anomaly detection model. A time-series data monitoring method characterized by the following features.
9. A time-series data monitoring method according to claim 8, The system includes a display processing step in which the analysis results obtained in the above analysis step are displayed on a display unit. A time-series data monitoring method characterized by the following features.
10. A time-series data monitoring method according to claim 9, The display processing step displays the inference results of the anomaly detection model performed in the analysis step, using a plurality of window widths, together on the display unit. A time-series data monitoring method characterized by the following features.