Production facility monitoring methods, production facility monitoring devices and procedures

Abstract

The production facility monitoring method is a method for monitoring the production facility using Mahalanobis distance calculated based on multiple variable data representing the state of the production facility. The production facility monitoring method includes: an acquisition step, acquiring data for a first period up to the current time point, i.e., first data; a prediction step, predicting data for a second period after the current time point, i.e., second data; and a unit space creation step, creating a unit space as the basis for calculating the Mahalanobis distance based on the first data and the second data. In the prediction step, the second data is predicted based on data for a third period (shifting the first period forward by a predetermined number of periods), i.e., third data; data for a fourth period (shifting the second period forward by the predetermined number of periods), i.e., fourth data; and the first data.

Description

Technical Field

[0001] This invention relates to a method, device, and procedure for monitoring production facilities.

[0002] This application claims priority based on Japan Patent Application No. 2021-082212 filed with the Japan Patent Office on May 14, 2021, the contents of which are incorporated herein by reference. Background Technology

[0003] Sometimes, the Mahalanobis distance, which represents the deviation between a standard dataset of variables (such as state quantities that can be acquired by sensors) and the measured data for those variables, is used to monitor production facilities.

[0004] Patent Document 1 describes a production facility monitoring method using Mahalanobis distance, in which Mahalanobis distance is calculated using multiple unit spaces defined during operation. Here, the aforementioned unit spaces are datasets used as a reference for determining whether the operating status of the production facility is normal. More specifically, in Patent Document 1, Mahalanobis distance is calculated for data acquired during the start-up operation of the production facility using unit spaces created based on the state variables of the production facility during its start-up operation, and Mahalanobis distance is calculated for data acquired during the load operation of the production facility using unit spaces created based on the state variables of the production facility during its load operation.

[0005] Previous technical documents

[0006] Patent documents

[0007] Patent Document 1: Japanese Patent No. 5031088 Summary of the Invention

[0008] The technical problem to be solved by the invention

[0009] The unit space used to calculate Mahalanobis distance typically consists of data acquired by sensors over a past period (reference data). When using this unit space to calculate the Mahalanobis distance for measured data (evaluation data) at a later point in time (e.g., the current point in time or a recent point in time) than the aforementioned past period (the period in which the reference data was acquired), there is a possibility that the data trend during the past period in which the reference data was acquired is inconsistent with the data trend during the period in which the evaluation data was acquired. In this case, the accuracy of detecting anomalies in production facilities based on the Mahalanobis distance calculated for the evaluation data may be poor.

[0010] In view of the above, the object of at least one embodiment of the present invention is to provide a production facility monitoring method, a production facility monitoring device, and a production facility monitoring program capable of detecting anomalies in production facilities with high precision.

[0011] means for solving technical problems

[0012] At least one embodiment of the present invention relates to a production facility monitoring method that uses Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein...

[0013] The production facility monitoring method includes:

[0014] The acquisition step involves acquiring the data from the first period up to the current time point, i.e., the first data.

[0015] The prediction step involves predicting the data for the second period after the current time point, i.e., the second data; and

[0016] The unit space creation step involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data.

[0017] In the prediction step, the second data is predicted based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data.

[0018] Furthermore, at least one embodiment of the present invention relates to a production facility monitoring device that uses a Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein...

[0019] The production facility monitoring device includes:

[0020] The acquisition unit is configured to acquire the data of the first period up to the current time, namely the first data;

[0021] The prediction unit is configured to predict the data, i.e., the second data, for a second period after the current time point; and

[0022] The unit space creation unit is configured to create a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data.

[0023] The prediction unit is configured to predict the second data based on the data of the third period (which is the third data, shifted a predetermined length of time in the past from the first period), the data of the fourth period (which is the fourth data, shifted a predetermined length of time in the past from the second period), and the first data.

[0024] Furthermore, at least one embodiment of the present invention relates to a production facility monitoring program that uses Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein...

[0025] The monitoring program causes the computer to perform the following steps:

[0026] The acquisition process involves acquiring the data from the first period up to the current time point, i.e., the first data.

[0027] The prediction process involves predicting the data for the second period after the current time point, i.e., the second data; and

[0028] The unit space creation process involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data.

[0029] In the process of predicting the second data, the second data is predicted based on the data of the third period (which is the data of the first period shifted back by a predetermined length of time), the data of the fourth period (which is the data of the second period shifted back by the predetermined length of time), and the first data.

[0030] Invention Effects

[0031] According to at least one embodiment of the present invention, a production facility monitoring method, a production facility monitoring device, and a production facility monitoring program are provided that can detect anomalies in production facilities with high precision. Attached Figure Description

[0032] Figure 1 This is a schematic structural diagram of a gas turbine included in a production facility to which monitoring methods are applied in some embodiments.

[0033] Figure 2 This is a schematic structural diagram of a production facility monitoring device according to one embodiment.

[0034] Figure 3 This is a flowchart of a production facility monitoring method according to one embodiment.

[0035] Figure 4A This is a diagram illustrating a production facility monitoring method according to one embodiment.

[0036] Figure 4B This is a diagram illustrating a production facility monitoring method according to one embodiment.

[0037] Figure 5 This is a diagram that schematically represents an example of a unit space created based on multiple variables representing the state of a production facility.

[0038] Figure 6 This is a schematic diagram representing an example of measurement data for variables representing the status of a production facility.

[0039] Figure 7 This is a schematic diagram representing an example of measurement data for variables representing the status of a production facility.

[0040] Figure 8 This is a schematic diagram representing an example of measurement data for variables representing the status of a production facility.

[0041] Figure 9 This is a schematic diagram representing an example of measurement data for variables representing the status of a production facility.

[0042] Figure 10 This is an example of a table representing the correspondence between multiple variables indicating the status of a production facility and a specified length of time (the period of variation of the measured data). Detailed Implementation

[0043] Hereinafter, some embodiments of the present invention will be described with reference to the accompanying drawings. The dimensions, materials, shapes, and relative arrangements of the structural components described or illustrated as embodiments are not intended to limit the scope of the present invention, but are merely illustrative examples.

[0044] (Structure of the production facility monitoring device)

[0045] Figure 1 This is a schematic structural diagram of a gas turbine, an example of equipment included in a production facility that employs monitoring methods applicable to some embodiments. Figure 2 This is a schematic structural diagram of a production facility monitoring device according to one embodiment.

[0046] Figure 1 The gas turbine 10 shown includes a compressor 12 for compressing air, a combustor 14 for burning compressed air and fuel from the compressor 12, and a turbine 16 driven by combustion gases generated in the combustor 14. A generator 18 is connected to the rotor 15 of the gas turbine 10, and the generator 18 is driven by the rotation of the gas turbine 10.

[0047] In some embodiments, the production facility of the monitored object includes the aforementioned gas turbine 10. In some embodiments, the production facility of the monitored object may include other equipment (e.g., a steam turbine).

[0048] Figure 2 The production facility monitoring device 40 shown is configured to monitor the production facility based on the measured values ​​of multiple variables representing the state of the production facility measured by the measurement unit 30.

[0049] The measurement unit 30 is configured to measure multiple variables representing the state of the production facility. The measurement unit 30 may include multiple sensors configured to measure the multiple variables representing the state of the production facility respectively.

[0050] When the production facility includes a gas turbine 10, the measurement unit 30 may include a sensor configured to measure any one of the following as variables representing the state of the production facility: the rotor rotation speed of the gas turbine 10, the temperature of each section of the turbine blade passage, the average temperature of the turbine blade passage, the turbine inlet pressure, the turbine outlet pressure, the generator power, the inlet pressure of the air filter, or the outlet pressure of the air filter.

[0051] The production facility monitoring device 40 is configured to receive signals from the measurement unit 30 that display measured values ​​of variables representing the status of the production facility. The production facility monitoring device 40 may be configured to receive signals displaying measured values ​​from the measurement unit 30 according to a predetermined sampling period. Furthermore, the production facility monitoring device 40 is configured to process the signals received from the measurement unit 30 to determine whether there are any abnormalities in the production facility. The determination result based on the production facility monitoring device 40 may be displayed on the display unit 60 (such as a monitor).

[0052] like Figure 2 As shown, the production facility monitoring device 40 according to one embodiment includes a data acquisition unit (acquisition unit) 42, a prediction unit 44, a unit space creation unit 46, a Mahalanobis distance calculation unit 48, and an anomaly determination unit 50.

[0053] The production facility monitoring device 40 includes a computer equipped with a processor (CPU, etc.), main storage (memory device; RAM, etc.), auxiliary storage, and an interface. The production facility monitoring device 40 receives signals from the measurement unit 30 via the interface, displaying measured values ​​of variables indicating the status of the production facility. The processor is configured to process these received signals. Furthermore, the processor is configured to process programs running in the storage device. Thus, the functions of each of the aforementioned functional units (data acquisition unit 42, etc.) are realized.

[0054] The processing content in the production facility monitoring device 40 is installed as a program executed by the processor. The program can also be stored in an auxiliary storage unit. When the program is executed, it is expanded in the storage device. The processor reads the program from the storage device and executes the commands contained within the program.

[0055] The data acquisition unit 42 is configured to acquire data (first data, third data, and fourth data) of multiple variables (V1, V2, ..., Vn) representing the state of the production facility at each of multiple times t (t1, t2, ..., tn) within a specified period prior to the current time (the first period, the third period, and the fourth period described below). When the production facility includes a gas turbine 10, the variables (V1, V2, ..., Vn) representing the state of the production facility may include any one of the following: the rotor rotation speed of the gas turbine 10, the temperature of each section of the turbine blade passage, the average temperature of the turbine blade passage, the turbine inlet pressure, the turbine outlet pressure, the generator power, the inlet pressure of the intake filter, or the outlet pressure of the intake filter. Furthermore, the data of the aforementioned variables at time t may be representative values ​​(e.g., average values) of the measured values ​​of the aforementioned variables within a specified period based on time t.

[0056] The data acquisition unit 42 can be configured to acquire the aforementioned data based on the measured values ​​of multiple variables measured by the measurement unit 30. The measured values ​​of the multiple variables or data based on the measured values ​​can be stored in the storage unit 32. The data acquisition unit 42 can also be configured to acquire the aforementioned measured values ​​or data based on the measured values ​​from the storage unit 32.

[0057] Additionally, storage unit 32 may include the main storage device or auxiliary storage device of the computer constituting the production facility monitoring device 40. Alternatively, storage unit 32 may also include a remote storage device connected to the computer via a network.

[0058] The prediction unit 44 is configured to predict the multiple variable data (second data) for a specified period (the second period described below) after the current time point based on the multiple variable data acquired by the data acquisition unit 42 for a specified period prior to the current time point.

[0059] The unit space creation unit 46 is configured to create a unit space that serves as the basis for calculating Mahalanobis distance based on the first data acquired by the data acquisition unit 42 and the second data acquired by the prediction unit 44.

[0060] The aforementioned unit space refers to a homogeneous set (normal dataset). The Mahalanobis distance is calculated as the distance from the center of the unit space containing the data that serves as the evaluation object (diagnostic object). A smaller Mahalanobis distance indicates a higher probability that the data of the evaluation object is normal, while a larger Mahalanobis distance indicates a higher probability that the data of the evaluation object is abnormal.

[0061] Mahalanobis distance calculation unit 48 is configured to use the unit space created by unit space creation unit 46 to calculate Mahalanobis distance for the data of the evaluation object.

[0062] The anomaly determination unit 50 is configured to determine whether there is an anomaly in the production facility based on the Mahalanobis distance calculated by the Mahalanobis distance calculation unit 48.

[0063] (Production facility monitoring process)

[0064] The following provides a more detailed description of some of the production facility monitoring methods described in the embodiments. Furthermore, the following describes the use of the production facility monitoring device 40 described above to perform one embodiment of the production facility monitoring method; however, in some embodiments, other devices may also be used to perform the production facility monitoring method.

[0065] Figure 3 This is a flowchart of a production facility monitoring method involved in some implementation methods. Figure 4A and Figure 4B This is a diagram used to illustrate a method for monitoring production facilities involved in some implementation methods.

[0066] like Figure 3 As shown, in some embodiments, firstly, the data acquisition unit 42 acquires the first past period T1 up to the current time point (refer to...). Figure 4A The data representing the state of the production facility at multiple times within the first period T1 is called the first data (S2). That is, the first data includes the dataset of multiple variables (V1, V2, ..., Vn) at each time point within the first period T1.

[0067] In addition, in this specification, "current time point" refers to a specific time point (baseline time point), and is not limited to the present, but can also be a time point earlier than the present.

[0068] Furthermore, the data acquisition unit 42 acquires the past third period T3 (reference). Figure 4A The third data point involves acquiring data from multiple variables (V1, V2, ..., Vn) representing the state of the production facility at multiple points in time, while simultaneously acquiring data from the fourth past period T4 (see reference). Figure 4A The data (S4) represents the data of multiple variables (V1, V2, ..., Vn) representing the state of the production facility at multiple times within the time frame.

[0069] like Figure 4AAs shown, the third period T3 is a period that shifts the first period T1 forward by a predetermined length of time. That is, the third period T3 corresponds to the first period T1 preceding a predetermined length of time from the current time point. The start time of the third period T3 is a point in time preceding a predetermined length of time from the start time of the first period T1, and the end time of the third period T3 is a point in time preceding a predetermined length of time from the first period T1. Furthermore, the length of the third period T3 is equal to the length of the first period T1.

[0070] like Figure 4A As shown, the fourth period T4 is a period that shifts the second period T2, which is after the current time point, backward by a predetermined length of time. That is, the fourth period T4 corresponds to the second period T2, which is a predetermined length of time prior to the current time point. The start time of the fourth period T4 is a predetermined length of time prior to the start time of the second period T2, and the end time of the fourth period T4 is a predetermined length of time prior to the end time of the second period T2. Furthermore, the length of the fourth period T4 is equal to the length of the second period T2.

[0071] The aforementioned third data (the third data for multiple variables) can be a dataset of each variable in the third period T3, which is a time portion of a predetermined length set for each of the multiple variables, shifting the first period T1 backwards. Similarly, the aforementioned fourth data (the fourth data for multiple variables) can be a dataset of each variable in the fourth period T4, which is a time portion of a predetermined length set for each of the multiple variables, shifting the second period T2 backwards. That is, for each of the multiple variables, a time shift amount (the length of the retrospective time; i.e., the aforementioned predetermined length of time) can be set from the first period T1 and the second period T2 to the third period T3 and the fourth period T4.

[0072] For example, such as Figure 4B As shown, the third data for multiple variables (including Va and Vb) may include data for variable Va in the third period T3 (Va) where variable Va is a specified time Ta (e.g., 1 year) moving forward from the first period T1, and data for variable Vb in the third period T3 (Vb) where variable Vb is a specified time Tb (e.g., 1.5 years) moving forward from the first period T1. The fourth data for multiple variables may include data for variable Va in the fourth period T4 (Va) where variable Va is a specified time Ta moving forward from the second period T2, and data for variable Vb in the fourth period T4 (Vb) where variable Vb is a specified time Tb moving forward from the second period T2.

[0073] That is, the third data for multiple variables (V1, V2, ..., Vn) includes a dataset for each of the multiple times within the third period T3 for each of the multiple variables (V1, V2, ..., Vn). Furthermore, the fourth data for multiple variables (V1, V2, ..., Vn) includes a dataset for each of the multiple times within the fourth period T4 for each of the multiple variables (V1, V2, ..., Vn).

[0074] In this specification, the third data of multiple variables that pertains to a specific variable will sometimes be referred to as the third data of that variable. Similarly, the fourth data of multiple variables that pertains to a specific variable will sometimes be referred to as the fourth data of that variable.

[0075] Next, the prediction unit 44, based on the first data of the first period T1 obtained in step S2 and the third data of the third period T3 and the fourth data of the fourth period T4 obtained in step S4, predicts the second period T2 after the current time point (refer to...). Figure 4A , 4B The data representing the status of the production facility (V1, V2, ..., Vn) within the period T2 is called the second data (S6). Here, the second data includes multiple datasets of multiple variables (V1, V2, ..., Vn) within the second period T2. Typically, the length of the second period T2 is equal to the length of the first period T1. Furthermore, the process of predicting the second data in step S6 will be explained later.

[0076] Next, the unit space creation unit 46 creates a unit space (S8) that forms the basis for calculating the Mahalanobis distance in the subsequent step S10, based on the first data obtained in step S2 and the second data predicted in step S6. That is, in step S8, data constituting the unit space is selected from the first data and the second data.

[0077] In step S8, at least a portion of the first data obtained in step S2 and at least a portion of the second data obtained in step S6 can be used to create the aforementioned unit space. Furthermore, in step S8, in addition to using at least a portion of the first data and at least a portion of the second data, the period T0 preceding the first period up to the period in which the first data was obtained (refer to...) can also be used. Figure 4A , 4B The above unit space is created by using the data of multiple variables (V1, V2, ..., Vn) obtained.

[0078] Then, the Mahalanobis distance calculation unit 48 uses the unit space created by the unit space creation unit 46 to calculate the Mahalanobis distance for the data (signal space data) of the evaluation object (diagnosis object) (S10). Typically, in step S10, the measured values ​​(Y1, Y2, ..., Yn) of multiple variables (V1, V2, ..., Vn) acquired during the period after the current time point are used as the data (signal space data) of the evaluation object, and the Mahalanobis distance is calculated based on this.

[0079] The Mahalanobis distance for the data of the evaluation object can be calculated using the method described in Patent Document 1. The method for calculating the Mahalanobis distance can be roughly explained as follows: First, a dataset (X1, X2, ..., Xn) consisting of n variables (V1, V2, ..., Vn) constituting a unit space is used. n The average of each item (variable) is calculated using the following formula (A). Additionally, in the following formula, k is the number of data points (data set size) for each of the n variables constituting the unit space.

[0080] [Mathematical Expression 1]

[0081]

[0082] Next, the average of each item (variable) calculated by the above equation (A) is used to obtain the covariance matrix COV (n×n matrix) for the data constituting the unit space by the following equation (B).

[0083] [Mathematical Expression 2]

[0084]

[0085] Then, using the data Y1~Y of the evaluation object. n The squared value of Mahalanobis distance D is calculated using the average obtained from equation (A) above and the inverse of the covariance matrix obtained from equation (B) above, and then using equation (C) below. 2 Furthermore, in the following formula, l represents the data (signal spatial data) Y1 to Y2 for the evaluation object with n variables. n The amount of data (number of datasets).

[0086] [Mathematical Expression 3]

[0087]

[0088] Next, the anomaly determination unit 50 determines whether the production facility is abnormal based on the Mahalanobis distance D calculated in step S10 (S12). In step S12, the anomaly determination can also be based on a comparison between the Mahalanobis distance D and a threshold. For example, if the Mahalanobis distance D calculated in step S10 is below the threshold, the production facility can be determined to be normal, and if the Mahalanobis distance D is greater than the threshold, the production facility can be determined to be abnormal.

[0089] Figure 5 This is a diagram that schematically represents an example of a unit space created based on multiple variables representing the state of a production facility. Figure 6 and Figure 7 ,as well as Figure 8 and Figure 9 This is a schematic diagram illustrating an example of measured data for variables representing the status of a production facility. In Figure 6 and Figure 7 ,as well as Figure 8 and Figure 9 In the diagram, the solid line represents the measured data (sensor values) for the variable representing the state of the production facility, and the area between a pair of curves U1 and U2 (dashed lines) is equivalent to the unit space that forms the basis for calculating the Mahalanobis distance.

[0090] like Figure 6 and Figure 7 ,as well as Figure 8 and Figure 9 As shown, the measured data (e.g., temperature, pressure, etc.) for multiple variables representing the status of a production facility include data with periodic variations. Figure 6 and Figure 7 The measured data for the variables shown are accompanied by seasonal variations with a one-year cycle, including, for example, measurement data based on temperature sensors. Figure 8 and Figure 9 The measured data for the variables shown are accompanied by variations within the component replacement cycle of the equipment used in the production facility. For example, this includes measured data obtained by a sensor measuring the outlet pressure of the air intake filter (a component of the equipment used in the production facility). Measured data accompanied by variations within the component replacement cycle refers to data in which the manner of variation is affected by the time elapsed since the component replacement point.

[0091] Here, we consider calculating the Mahalanobis distance based on the measurement data obtained at the current time point (or the nearest time point from the current time point, such as the time point within the second period T2 mentioned above).

[0092] At this point, when creating a unit space using only multiple variable data acquired in the most recent past period (e.g., period 1 above), such as... Figure 7 or Figure 9As shown, a time difference arises between the periodic variation of the measured data (solid line) and the periodic variation of the unit space (the area between curves U1 and U2). As a result, a period occurs where the distance from the center of the unit space of the measured data increases (area A in the figure). During this period, the Mahalanobis distance is easily overestimated, which can lead to misjudgments of anomalies in production facilities and potentially result in poor accuracy in anomaly detection.

[0093] In contrast, in the above embodiment, the second data can be predicted by considering the periodic variations of multiple variable data, based on the third and fourth data obtained in the past periods (the third period T3 and the fourth period T4) preceding a predetermined length of time corresponding to the first period T1 and the immediately following second period T2, and the first data obtained in the first period T1. This is because, for example, as... Figure 5 As shown, for data on a certain variable, the data variation between the first period T1 and the immediately following second period T2 corresponds to the data variation between the third period T3, which is a predetermined length of time (e.g., 1 year or a component replacement cycle) before the first period T1, and the fourth period T4, which is a predetermined length of time before the second period T2. Then, in the above embodiment, by simultaneously using the predicted second data and the first data based on measured values, a unit space that takes into account seasonal variations can be created.

[0094] When creating unit space in this way, such as Figure 6 or Figure 8 As shown, the trend of periodic variation in the measured data (solid line) tends to align with the trend of periodic variation in the unit space (the area between curves U1 and U2). Consequently, the calculated Mahalanobis distance is less affected by the periodic variations in the measured data. For example, in Figure 6 or Figure 8 In the region corresponding to A ( Figure 7 or Figure 9 During the period corresponding to region A, the distance from the center of the unit space of the measurement data is the same as in other periods.

[0095] Therefore, by using the Mahalanobis distance calculated based on the unit space thus created, anomalies in production facilities can be detected with high precision.

[0096] in addition, Figure 5 In the diagram, ellipses Q1 to Q4 schematically represent an example of a unit space created based on each of the first to fourth data points. Each ellipse is the set of points with equal Mahalanobis distances calculated from each unit space. Figure 5 For simplicity, the unit space based on two variables V1 and V2 is roughly shown in the diagram. For example... Figure 5As shown, the change in position of unit space Q2 based on the second data relative to unit space Q1 based on the first data corresponds to the change in position of unit space Q4 based on the fourth data relative to unit space Q3 based on the third data. That is, the change vector v of the center of unit space Q2 relative to the center of unit space Q1... 12 The orientation and the change vector v of the center of unit space Q4 relative to the center of unit space Q3 34 The orientations are almost identical. Furthermore, the lengths of these variation vectors are also affected by the degree of deviation of the data constituting the unit space (the size of the ellipse). Figure 5 In this context, the deviations of the data constituting unit spaces Q3 and Q4 are smaller than the deviations of the data constituting unit spaces Q1 and Q2. Therefore, the change vector v 34 The length ratio of the change vector v 12 The length is short. Therefore, in step S6, by considering the difference in the degree of deviation of the data in each period, the second data can be predicted more accurately.

[0097] In some implementations, the time period specified above (the time shift from the first period T1 and the second period T2 to the third period T3 and the fourth period T4) for at least one variable (e.g. Va) among a plurality of variables (V1, V2, ..., Vn) is 1 year.

[0098] The data representing the status of a production facility typically includes data that varies on a one-year cycle corresponding to the season. In this regard, according to the above embodiment, the second data is predicted using the third and fourth data, which include data for at least one of the aforementioned variables (Va) obtained one year prior to the first period T1 and the second period T2 (the third period T3 and the fourth period T4). Therefore, it is possible to predict the second data with high accuracy by taking into account the seasonal variation of the data for the variable (Va).

[0099] In some implementations, the time period specified above (the time shift from period 1 T1 and period 2 T2 to period 3 T3 and period 4 T4) for at least one of the multiple variables (V1, V2, ..., Vn) (e.g., Vb) is the component replacement cycle of the equipment in the production facility associated with the other variable (Vb). For example, the equipment in the production facility may be an intake filter for a gas turbine.

[0100] Here, Figure 10This is an example of a table showing the correspondence between the sensor number (sensor No.) corresponding to multiple variables (V1, V2, ..., V150) representing the status of the production facility and the time (the amount of time movement from period 1 T1 and period 2 T2 to period 3 T3 and period 4 T4) set for each of the multiple variables (sensors).

[0101] like Figure 10 As shown, the time period specified above (the time shift from period 1 T1 and period 2 T2 to period 3 T3 and period 4 T4) can be set individually for each of the multiple variables. Additionally, as... Figure 10 As shown, when setting the specified time based on the component replacement cycle of equipment used in production facilities for multiple variables, the component replacement cycle (i.e., the specified time) can vary depending on the type of component, etc.

[0102] Data representing the status of a production facility sometimes includes data on the variation in the replacement cycle of equipment used in the production facility associated with that variable. In this regard, according to the above embodiment, the second data is predicted using third and fourth data, including data for at least one variable (Va) acquired one year prior to the periods corresponding to the first period T1 and the second period T2 (the third period T3 and the fourth period T4), and data for at least another variable (Vb) acquired before the replacement cycle corresponding to the first period T1 and the second period T2 (the third period T3 and the fourth period T4). Therefore, for data on multiple variables (V1, V2, ..., Vn), it is possible to take into account the periodic (seasonal cycle (i.e., one-year cycle) or replacement cycle) variations corresponding to the characteristics of each variable (Va and Vb), and predict the second data with higher accuracy.

[0103] In some implementations, in step S6, the second data is predicted using values ​​representing the data changes of multiple variables between the third period T3 and the fourth period T4, or between the third period T3 and the first period T1. Here, the values ​​representing the data changes of multiple variables between the two periods can be, for example, the difference between the respective representative values ​​(average, etc.) of the data for the two periods.

[0104] The data change between period 3 (T3) and period 4 (T4) corresponds to the data change between period 1 (T1) and period 2 (T2). In this respect, in the above embodiment, the value representing the data change between period 3 (T3) and period 4 (T4) can be used to accurately predict the second data within period 2 (T2) based on the first data within period 1 (T1). Alternatively, the data change between period 3 (T3) and period 1 (T1) corresponds to the data change between period 4 (T4) and period 2 (T2). In this respect, in the above embodiment, the value representing the data change between period 3 (T3) and period 1 (T1) can be used to accurately predict the second data within period 2 (T2) based on the fourth data within period 4 (T4).

[0105] In some implementations, in step S6, for one of the multiple variables (V1, V2, ..., Vn) (here, Va), the value of the difference (m4-m3) between the average m4 of the fourth data for variable Va and the average m3 of the third data is added to the first data for variable Va to obtain the second data for variable Va.

[0106] Thus, as a value representing the data change between the third period T3 and the fourth period T4, the difference (m4-m3) between the average m4 of the fourth data and the average m3 of the third data is used. This value is added to the first data in the first period T1, thereby enabling accurate prediction of the second data.

[0107] Furthermore, when the first data for variable Va is set as d1 and the second data for variable Va is set as d2, the second data d2 can be represented by, for example, the following formula (a).

[0108] d2=d1+(m4-m3)……(a)

[0109] In some embodiments, the second data for variable Va is obtained by multiplying the value obtained by dividing the difference (m4-m3) by the standard deviation σ3 of the third data for variable Va by the standard deviation σ1 of the first data for variable Va, and then adding the resulting value to the first data for variable Va. In this case, when the first data for variable Va is set as d1 and the second data for variable Va is set as d2, the second data d2 can be represented by the following equation (A).

[0110] d2=d1+(m4-m3) / σ3×σ1……(A)

[0111] Thus, the value obtained by correcting the difference (m4-m3) between the average m4 of the fourth data and the average m3 of the third data by dividing it by the standard deviation σ3 of the third data and multiplying it by the standard deviation σ1 of the first data (i.e., the value obtained by correcting the difference (m4-m3) by the ratio of the standard deviation σ1 of the first data to the standard deviation σ3 of the third data) is added to the first data d1. This allows us to take into account the changes in the data distribution starting from a specified time period (e.g., 1 year or a component replacement cycle). Therefore, by using the Mahalanobis distance calculated based on the unit space created using the second data d2 thus obtained, anomalies in the production facility can be detected with higher precision. Furthermore, it can be assumed that σ1≒σ3 to simplify the calculation.

[0112] In some implementations, in step S6, for one of the multiple variables (V1, V2, ..., Vn) (here, Va), the value of the difference (m1-m3) between the average m1 of the first data for variable Va and the average m3 of the third data is added to the fourth data for variable Va to obtain the second data for variable Va.

[0113] Thus, as a value representing the data change between the third period T3 and the first period T1, the difference (m1-m3) between the average m1 of the first data and the average m3 of the third data is used. This value is added to the fourth data in the fourth period T4, thereby enabling accurate prediction of the second data.

[0114] In addition, when the fourth data for variable Va is set as d4 and the second data for variable Va is set as d2, the second data d2 can be represented by, for example, the following equation (b).

[0115] d2=d4+(m1-m3)……(b)

[0116] In some embodiments, the second data for variable Va is obtained by multiplying the value obtained by dividing the difference (m1-m3) by the standard deviation σ3 of the third data for variable Va by the standard deviation σ4 of the fourth data for variable Va, and then adding the resulting value to the fourth data for variable Va. In this case, when the fourth data for variable Va is set as d4 and the second data for variable Va is set as d2, the second data d2 can be represented by the following equation (B).

[0117] d2=d4+(m1-m3) / σ3×σ4……(B)

[0118] Thus, the second data d2 is obtained by correcting the difference (m1-m3) between the average m1 of the first data and the average m3 of the third data by dividing it by the standard deviation σ3 of the third data and multiplying it by the standard deviation σ1 of the fourth data (i.e., by correcting the difference (m1-m3) by the ratio of the standard deviation σ4 of the fourth data to the standard deviation σ3 of the third data) and adding it to the fourth data d4. This allows us to take into account the changes in the data distribution at the beginning of the preceding period. Therefore, by using the Mahalanobis distance calculated based on the unit space created using the second data d2 obtained in this way, anomalies in the production facility can be detected with higher precision. Furthermore, it can be assumed that σ3≒σ4 to simplify the calculation.

[0119] In some implementations, the number of first data constituting the unit space created in step S8 is greater than the number of second data constituting the unit space. That is, in step S8, data constituting the unit space is selected from the first data and the second data such that the number of first data constituting the unit space is greater than the number of second data constituting the unit space.

[0120] In the above implementation, in the data constituting the unit space, the number of first data based on measured data is greater than the number of predicted data, i.e., second data. Therefore, the reliability of anomaly detection based on Mahalanobis distance calculated from the unit space becomes good.

[0121] In some implementations, in step S8, for example using random numbers, data for creating the unit space is randomly selected from the second data. Then, the unit space is created using at least a portion of the randomly selected second data and the first data.

[0122] According to the above implementation, a unit space can be accurately created using a portion of the data randomly selected from the second data predicted in step S6 and at least a portion of the first data.

[0123] The contents described in the above embodiments can be understood, for example, as follows.

[0124] At least one embodiment of the present invention relates to a production facility monitoring method that uses Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein...

[0125] The production facility monitoring method includes:

[0126] Step (S2) involves obtaining the data from the first past period (T1) up to the current time point, i.e., the first data.

[0127] Prediction step (S6): Predict the data for the second period (T2) after the current time point, i.e., the second data; and

[0128] The unit space creation step (S8) involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data.

[0129] In the prediction step, the second data is predicted based on the data of the third period (T3) which shifts the first period forward by a predetermined length of time, the data of the fourth period (T4) which shifts the second period forward by the predetermined length of time, and the first data.

[0130] The measured data (e.g., temperature, pressure, etc.) representing the status of a production facility include data that varies periodically at predetermined time intervals. Furthermore, the data variation between the first period and the immediately following second period corresponds to the data variation between the third period (corresponding to the first period) and the fourth period (corresponding to the second period) in the past period preceding the predetermined time interval, respectively. In this regard, in the method described in (1) above, the second data can be predicted by considering the periodic variations of multiple variable data, based on the third and fourth data obtained in the past period (the third and fourth periods) preceding the predetermined time intervals corresponding to the first and the immediately following second period, respectively, and the first data obtained in the first period. Then, by simultaneously using the predicted second data and the first data based on the measured values, a unit space that takes into account the periodic variations of multiple variable data can be created. Therefore, by using the Mahalanobis distance calculated based on the unit space thus created, anomalies in the production facility can be detected with high precision.

[0131] (2) In some embodiments, in the method described in (1) above,

[0132] The third data is a dataset of the variables in the third period, which is a time segment of a predetermined length set for each of the plurality of variables and shifted backwards during the first period.

[0133] The fourth data is a dataset of the variables in the fourth period, which is a time segment of a predetermined length set for each of the plurality of variables, shifted backwards from the second period.

[0134] Multiple variables representing the status of a production facility may have different periods of variation depending on their variable characteristics. According to the method described in (2) above, for each of the multiple variables, a time shift (i.e., a specified length of time) is set from the first and second periods to the third and fourth periods. That is, for each of the multiple variables, a specified length of time corresponding to the period of variation of that variable's data can be defined. Therefore, by using past datasets, i.e., the third and fourth data, which are based on the specified length of time corresponding to the characteristics of each variable, the prediction accuracy of the second data can be improved.

[0135] (3) In some embodiments, in the method described in (1) or (2) above,

[0136] The specified time period, for at least one of the plurality of variables, is one year.

[0137] Data representing the status of a production facility typically includes data that varies on a one-year cycle corresponding to the season. According to the method described in (3) above, the second data is predicted using the third and fourth data, which include data for at least one of the above-mentioned variables obtained one year prior to the first and second periods (the third and fourth periods). Therefore, the second data can be predicted with high accuracy, taking into account the seasonal variation of the data for that variable.

[0138] (4) In some embodiments, in the method described in (3) above,

[0139] The specified length of time set for at least one of the plurality of variables is the component replacement cycle of the equipment in the production facility associated with that other variable.

[0140] Data representing the status of a production facility sometimes includes data on the variation in the replacement cycle of equipment used in the production facility associated with that variable. According to the method described in (4) above, the second data is predicted using third and fourth data, which include data for at least one of the aforementioned variables acquired one year prior to the first and second periods (the third and fourth periods), and data for at least another of the aforementioned variables acquired before the replacement cycle corresponding to the first and second periods (the third and fourth periods). Therefore, for data representing multiple variables, the second data can be predicted with higher accuracy, taking into account periodic (seasonal cycle (i.e., one-year cycle) or replacement cycle) variations corresponding to the characteristics of each variable.

[0141] (5) In some embodiments, in any of the methods described in (1) to (4) above,

[0142] In the prediction step, the second data is predicted using a value representing the data change between the third period and the fourth period or between the third period and the first period.

[0143] The data change between period 3 and period 4 corresponds to the data change between period 1 and period 2. Furthermore, the data change between period 3 and period 1 corresponds to the data change between period 4 and period 2. According to the method described in (5) above, the second data in period 2 can be accurately predicted based on the first data in period 1 using the value representing the data change between period 3 and period 4. Alternatively, according to the method described in (5) above, the second data in period 2 can be accurately predicted based on the fourth data in period 4 using the value representing the data change between period 3 and period 1.

[0144] (6) In some embodiments, in any of the methods described in (1) to (5) above,

[0145] In the prediction step, for one of the multiple variables, the second data is obtained by adding the difference between the average of the fourth data and the average of the third data to the first data.

[0146] According to the method described in (6) above, as a value representing the data change between the third period and the fourth period, the difference between the average of the fourth data and the average of the third data is used, and this value is added to the first data in the first period, thereby accurately obtaining the second data.

[0147] (7) In some embodiments, in the method described in (6) above,

[0148] The second data is obtained by multiplying the value obtained by dividing the difference by the standard deviation of the third data by the standard deviation of the first data, and then adding the resulting value to the first data.

[0149] According to the method described in (7) above, the second data is obtained by adding the value obtained after correcting the difference between the average of the fourth data and the average of the third data by dividing it by the standard deviation of the third data and multiplying it by the standard deviation of the first data, thereby taking into account the changes in the data distribution starting one year ago. Therefore, by using the Mahalanobis distance calculated based on the unit space created using the second data obtained in this way, anomalies in the production facility can be detected with higher precision.

[0150] (8) In some embodiments, in any of the methods described in (1) to (5) above,

[0151] In the prediction step, for one of the multiple variables, the second data is obtained by adding the value of the difference between the average of the first data and the average of the third data to the fourth data.

[0152] According to the method described in (8) above, as a value representing the data change between the third period and the first period, the difference between the average of the first data and the average of the third data is used, and this value is added to the fourth data in the fourth period, thereby accurately obtaining the second data.

[0153] (9) In some embodiments, in the method described in (8) above,

[0154] The second data is obtained by multiplying the value obtained by dividing the difference by the standard deviation of the third data by the standard deviation of the fourth data, and then adding the resulting value to the fourth data.

[0155] According to the method described in (9) above, the second data is obtained by adding the value obtained after correcting the difference between the average of the first data and the average of the third data by dividing it by the standard deviation of the third data and multiplying it by the standard deviation of the fourth data, thereby taking into account the changes in the data distribution at the beginning of the preceding period. Therefore, by using the Mahalanobis distance calculated based on the unit space created using the second data obtained in this way, anomalies in the production facility can be detected with higher precision.

[0156] (10) In some embodiments, in any of the methods described in (1) to (9) above,

[0157] The number of the first data constituting the unit space is greater than the number of the second data constituting the unit space.

[0158] According to the method described in (10) above, in the data constituting the unit space, the number of first data based on measured data is greater than the number of predicted data, i.e., second data. Therefore, the reliability of anomaly detection based on Mahalanobis distance calculated from the unit space becomes good.

[0159] (11) In some embodiments, any of the methods in (1) to (10) above includes:

[0160] In the selection step, data for creating the unit space is randomly selected from the second set of data.

[0161] In the unit space creation step, the unit space is created using the data selected in the selection step and at least a portion of the first data.

[0162] According to the method described in (11) above, a unit space can be accurately created using a portion of the data randomly selected from the predicted second data and at least a portion of the first data.

[0163] (12) The production facility monitoring device (40) according to at least one embodiment of the present invention is a monitoring device for the production facility that uses Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein,

[0164] The production facility monitoring device (40) includes:

[0165] The acquisition unit (42) is configured to acquire the data of the past first period (T1) up to the current time point, namely the first data;

[0166] The prediction unit (44) is configured to predict the data for the second period (T2) after the current time point, i.e., the second data; and

[0167] The unit space creation unit (46) is configured to create a unit space that forms the basis for calculating the Mahalanobis distance based on the first data and the second data.

[0168] The prediction unit is configured to predict the second data based on the data of the third period (T3) which shifts the first period forward by a predetermined length of time, the data of the fourth period (T4) which shifts the second period forward by the predetermined length of time, and the first data.

[0169] The measured data (e.g., temperature, pressure, etc.) representing the status of a production facility include data that varies periodically at predetermined time intervals. Furthermore, the data variation between the first period and the immediately following second period corresponds to the data variation between the third period (corresponding to the first period) and the fourth period (corresponding to the second period) in the past period preceding the predetermined time interval, respectively. In this regard, in the configuration described above (12), the second data can be predicted by considering the periodic variations of multiple variable data, based on the third and fourth data obtained in the past period (the third and fourth periods) preceding the predetermined time intervals corresponding to the first and the immediately following second period, respectively, and the first data obtained in the first period. Then, by simultaneously using the predicted second data and the first data based on the measured values, a unit space that takes into account the periodic variations of multiple variable data can be created. Therefore, by using the Mahalanobis distance calculated based on the unit space thus created, anomalies in the production facility can be detected with high precision.

[0170] (13) The production facility monitoring program according to at least one embodiment of the present invention is a monitoring program for the production facility that uses Mahalanobis distance calculated based on multiple variable data representing the state of the production facility, wherein,

[0171] The monitoring program causes the computer to perform the following steps:

[0172] The acquisition process acquires the data from the first past period (T1) up to the current time point, i.e., the first data.

[0173] The prediction process involves predicting the data for the second period (T2) after the current time point, i.e., the second data; and

[0174] The unit space creation process involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data.

[0175] In the process of predicting the second data, the second data is predicted based on the data of the third period (T3) which shifts the first period forward by a predetermined length of time, the data of the fourth period (T4) which shifts the second period forward by the predetermined length of time, and the first data.

[0176] The measured data (e.g., temperature, pressure, etc.) representing the status of a production facility include data that varies periodically at predetermined time intervals. Furthermore, the data variation between the first period and the immediately following second period corresponds to the data variation between the third period (corresponding to the first period) and the fourth period (corresponding to the second period) in the past period preceding the predetermined time interval, respectively. In this regard, in the configuration described above (13), the second data can be predicted by considering the periodic variations of multiple variable data, based on the third and fourth data obtained in the past period (the third and fourth periods) preceding the predetermined time intervals corresponding to the first and the immediately following second periods, respectively, and the first data obtained in the first period. Then, by simultaneously using the predicted second data and the first data based on the measured values, a unit space that takes into account the periodic variations of multiple variable data can be created. Therefore, by using the Mahalanobis distance calculated based on the unit space thus created, anomalies in the production facility can be detected with high precision.

[0177] The embodiments of the present invention have been described above, but the present invention is not limited to the above embodiments, and also includes ways to modify the above embodiments and ways to appropriately combine these methods.

[0178] In this specification, expressions such as "in a certain direction", "along a certain direction", "parallel", "orthogonal", "center", "concentric" or "coaxial" that indicate relative or absolute configuration not only indicate such configuration in a strict sense, but also indicate a state of relative displacement by an angle or distance with tolerances or to the extent that the same function can be obtained.

[0179] For example, expressions such as "same," "equal," and "homogeneous" that indicate things are in the same state not only mean that they are the same in a strict sense, but also that there are differences in the degree to which they can achieve the same function.

[0180] Furthermore, in this specification, the descriptions of shapes such as quadrilaterals and cylinders not only refer to quadrilaterals and cylinders in a strict geometric sense, but also include shapes with concave and convex parts, chamfered parts, etc., within the range where the same effect can be obtained.

[0181] Furthermore, in this specification, the use of terms such as "possessing," "including," or "having" a constituent element is not an exclusive statement that excludes the existence of other constituent elements.

[0182] Symbol Explanation

[0183] 10-Gas turbine, 12-Compressor, 14-Burner, 15-Rotor, 16-Turbine, 18-Generator, 30-Measuring unit, 32-Storage unit, 40-Production facility monitoring device, 42-Data acquisition unit, 44-Forecasting unit, 46-Unit space creation unit, 48-Madara distance calculation unit, 50-Anomaly determination unit, 60-Display unit, A-Area, T1-Period 1, T2-Period 2, T3-Period 3, T4-Period 4.

Claims

1. A method for monitoring a production facility, comprising a method for monitoring the production facility using Mahalanobis distance calculated from data of multiple variables representing the state of the production facility, wherein, The production facility monitoring method includes: The acquisition step involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction step involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation step involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the prediction step, the second data is predicted based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. In the prediction step, the second data is predicted using a value representing the data change between the third period and the fourth period or between the third period and the first period.

2. A method for monitoring a production facility, comprising a method for monitoring the production facility using Mahalanobis distance calculated from data of multiple variables representing the state of the production facility, wherein, The production facility monitoring method includes: The acquisition step involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction step involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation step involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the prediction step, the second data is predicted based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. In the prediction step, for one of the multiple variables, the second data is obtained by adding the difference between the average of the fourth data and the average of the third data to the first data.

3. The production facility monitoring method according to claim 2, wherein, The second data is obtained by multiplying the value obtained by dividing the difference by the standard deviation of the third data by the standard deviation of the first data, and then adding the resulting value to the first data.

4. A method for monitoring a production facility, comprising a method for monitoring the production facility using Mahalanobis distance calculated from data of multiple variables representing the state of the production facility, wherein, The production facility monitoring method includes: The acquisition step involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction step involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation step involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the prediction step, the second data is predicted based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. In the prediction step, for one of the multiple variables, the second data is obtained by adding the value of the difference between the average of the first data and the average of the third data to the fourth data.

5. The production facility monitoring method according to claim 4, wherein, The second data is obtained by multiplying the value obtained by dividing the difference by the standard deviation of the third data by the standard deviation of the fourth data, and then adding the resulting value to the fourth data.

6. The production facility monitoring method according to any one of claims 1 to 5, wherein, The third data is a dataset of the variables in the third period, which is a time segment of a predetermined length set for each of the plurality of variables and shifted backwards during the first period. The fourth data is a dataset of the variables in the fourth period, which is a time segment of a predetermined length set for each of the plurality of variables, shifted backwards from the second period.

7. The production facility monitoring method according to any one of claims 1 to 5, wherein, The specified time period, for at least one of the plurality of variables, is one year.

8. The production facility monitoring method according to claim 7, wherein, The specified length of time set for at least one of the plurality of variables is the component replacement cycle of the equipment in the production facility associated with that other variable.

9. The production facility monitoring method according to any one of claims 1 to 5, wherein, The number of the first data constituting the unit space is greater than the number of the second data constituting the unit space.

10. The production facility monitoring method according to any one of claims 1 to 5, comprising: In the selection step, data for creating the unit space is randomly selected from the second set of data. In the unit space creation step, the unit space is created using the data selected in the selection step and at least a portion of the first data.

11. A production facility monitoring device, which is a monitoring device for said production facility using Mahalanobis distance calculated based on data of multiple variables representing the state of the production facility, wherein, The production facility monitoring device includes: The acquisition unit is configured to acquire the data of the first period up to the current time, namely the first data; The prediction unit is configured to predict the data, i.e., the second data, for a second period after the current time point; and The unit space creation unit is configured to create a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. The prediction unit is configured to predict the second data based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. The prediction unit uses a value representing the data change between the third period and the fourth period or the data change between the third period and the first period to predict the second data.

12. A production facility monitoring device, which is a monitoring device for said production facility using Mahalanobis distance calculated based on data representing the state of a plurality of variables, wherein, The production facility monitoring device includes: The acquisition unit is configured to acquire the data of the first period up to the current time, namely the first data; The prediction unit is configured to predict the data, i.e., the second data, for a second period after the current time point; and The unit space creation unit is configured to create a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. The prediction unit is configured to predict the second data based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. The prediction unit obtains the second data by adding the difference between the average of the fourth data and the average of the third data to the first data for one of the plurality of variables.

13. A production facility monitoring device, which is a monitoring device for the production facility using Mahalanobis distance calculated based on data representing the state of a plurality of variables, wherein, The production facility monitoring device includes: The acquisition unit is configured to acquire the data of the first period up to the current time, namely the first data; The prediction unit is configured to predict the data, i.e., the second data, for a second period after the current time point; and The unit space creation unit is configured to create a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. The prediction unit is configured to predict the second data based on the data of the third period (which is the first period shifted back by a predetermined length of time), the data of the fourth period (which is the second period shifted back by the predetermined length of time), and the first data. The prediction unit obtains the second data by adding the difference between the average of the first data and the average of the third data to the fourth data for one of the plurality of variables.

14. A production facility monitoring program product comprising a monitoring program for the production facility using Mahalanobis distance calculated from data representing a plurality of variables of the production facility's state, wherein, The monitoring program causes the computer to perform the following steps: The acquisition process involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction process involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation process involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the process of predicting the second data, the second data is predicted based on the data of the third period (which is the data of the first period shifted back by a predetermined length of time), the data of the fourth period (which is the data of the second period shifted back by the predetermined length of time), and the first data. In the process of predicting the second data, the second data is predicted using a value that represents the data change between the third period and the fourth period or the data change between the third period and the first period.

15. A production facility monitoring program product comprising a monitoring program for the production facility using Mahalanobis distance calculated from data representing the state of a plurality of variables, wherein, The monitoring program causes the computer to perform the following steps: The acquisition process involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction process involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation process involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the process of predicting the second data, the second data is predicted based on the data of the third period (which is the data of the first period shifted back by a predetermined length of time), the data of the fourth period (which is the data of the second period shifted back by the predetermined length of time), and the first data. In the process of predicting the second data, for one of the plurality of variables, the second data is obtained by adding the value of the difference between the average of the fourth data and the average of the third data to the first data.

16. A production facility monitoring program product comprising a monitoring program for the production facility using Mahalanobis distance calculated from data representing a plurality of variables of the production facility's state, wherein, The monitoring program causes the computer to perform the following steps: The acquisition process involves acquiring the data from the first period up to the current time point, i.e., the first data. The prediction process involves predicting the data for the second period after the current time point, i.e., the second data; and The unit space creation process involves creating a unit space that serves as the basis for calculating the Mahalanobis distance, based on the first data and the second data. In the process of predicting the second data, the second data is predicted based on the data of the third period (which is the data of the first period shifted back by a predetermined length of time), the data of the fourth period (which is the data of the second period shifted back by the predetermined length of time), and the first data. In the process of predicting the second data, for one of the plurality of variables, the second data is obtained by adding the value of the difference between the average of the first data and the average of the third data to the fourth data.

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