JP6623977B2 - Time axis expansion / contraction device, batch process monitoring device, time axis expansion / contraction system and program - Google Patents

Description

  The present invention relates to a time axis expansion / contraction device, a batch process monitoring device, a time axis expansion / contraction system, and a program.

  2. Description of the Related Art Conventionally, in a plant or the like that manufactures a product, a method of monitoring a process such as a manufacturing process using a sensor or the like is known. Then, a method of detecting an abnormality in a process using data sensed by a sensor is known.

  For example, in order to detect an abnormality in a process, modeling is first performed. Specifically, in modeling, a normal model is generated using data in a state where no abnormality has occurred, that is, in a normal state. Then, in an evaluation phase for actually detecting an abnormality, a normal model generated in advance and data acquired by sensing are compared to evaluate and diagnose whether the process is normal or abnormal. Specifically, for example, the following modeling phase and evaluation phase are performed.

  FIG. 1 is a diagram illustrating respective examples of a modeling phase and an evaluation phase in abnormality detection. In the illustrated example, the horizontal axis represents temperature, and the vertical axis represents pressure. First, in the modeling phase, as shown in FIG. 1A, a model MDL is generated from a set of data in a normal state. Next, in the evaluation phase, as shown in FIG. 1B, whether each data is normal or abnormal is determined based on the model MDL generated in the modeling phase. Specifically, if the data is a value belonging to the model MDL as in the illustrated first data D1, the first data is determined to be “normal”. On the other hand, if the data has a value outside the model MDL as in the illustrated second data D2, the second data is determined to be “abnormal”.

  Further, a method of detecting an abnormality in a batch process is known. For example, in this method, each time series data of each batch is treated as a different variable, and each batch is sampled. Next, variable × sample is calculated to be two-dimensional data, and principal component analysis is performed. Then, normalization is performed so that the average is “zero” and the variance is “1”, as is also performed in general principal component analysis. This can be calculated by calculating an average value between batches and a standard deviation at each sampling time in a batch, subtracting each average value at each sampling time, and dividing by the standard deviation. This is called "batch-wise normalization" or the like. In addition, the average and standard deviation between batches at each sampling point in the batch become the same time-series data as the length of the batch when arranged. As such, the mean and standard deviation between batches are referred to as the "mean profile" and "standard deviation profile." Thus, a method of detecting an abnormality in a batch process is known (for example, Non-Patent Document 1).

  Also, a DTW (Dynamic Time Warping) method is known for detecting an abnormality in a batch process or the like. Specifically, when there is waveform data of two different lengths, the DTW method converts the waveform data in the time direction so that the shape indicated by one waveform data matches the shape indicated by the other waveform data. It is a method of expanding and contracting. As described above, a method of making two waveform data easy to compare or process by expanding and contracting the waveform data even for waveform data of a batch process having different time lengths is known (for example, Non-Patent Document 2).

"Multivariate Personal Computer Charts for Monitoring Batch Processes", Paul Nomikos and John F. MacGregor, Technologies, February 1995. 37, no. 1 "Synchronization of Batch Trajectories Using dynamic Time Warping", Athanasios Cassidas, John F. MacGregor, and Paul A. Taylor, Process Systems Engineering (AIChE Journal) April (1998) Vol. 4 864-875

  However, in the conventional method, if the waveform data is expanded or contracted on the time axis, the data indicating the process abnormality included in the waveform data may be lost due to the expansion or contraction. Therefore, when a plant or the like is monitored based on the expanded and contracted waveform data, a process abnormality may be overlooked.

  One aspect of the present invention has been made in view of such a problem, and has as its object to reduce loss of data due to expansion and contraction of waveform data on the time axis.

In order to solve the above-described problems and achieve the object, in one embodiment of the present invention, a time axis expansion / contraction device that expands / contracts waveform data indicating a physical quantity with respect to time in a batch processing process includes:
An input unit for inputting test data indicating a waveform that expands and contracts to the length of the reference data, among the waveform data, reference data indicating a waveform of a reference length and the waveform data.
A progress calculating unit that calculates a first progress of a first process in the reference data and a second progress of a second process in the test data,
A warping path generation unit that generates a warping path that associates the reference data with the test data based on the first progress degree and the second progress degree;
And a telescopic part for expanding and contracting the test data based on the warping path.

  According to the present invention, loss of data due to expansion and contraction of waveform data on the time axis can be reduced.

It is a figure which shows each example of a modeling phase and an evaluation phase in abnormality detection. It is a figure which shows each example of a continuous system process and a batch system process. FIG. 3 is a diagram illustrating an example of a monitoring method of a batch process. FIG. 3 is a diagram illustrating an example of a DTW method and a warping path. FIG. 9 is a diagram illustrating an example of expansion and contraction of waveform data based on a warping path. FIG. 2 is a block diagram illustrating an example of a hardware configuration of a time axis expansion / contraction device according to an embodiment of the present invention. It is a flowchart which shows an example of the whole process by the time axis expansion / contraction apparatus in one Embodiment of this invention. It is a figure showing the example of calculation of the progress by the time axis expansion and contraction device in one embodiment of the present invention. It is a figure showing an example of generation of a warping path based on a 1st progress and a 2nd progress by a time axis expansion and contraction device in one embodiment of the present invention. It is a figure showing an example of a processing result of whole processing by a time axis expansion and contraction device in one embodiment of the present invention. FIG. 4 is a diagram illustrating an example of a warping path generated by a time axis expansion / contraction device according to an embodiment of the present invention. FIG. 9 is a diagram illustrating an example of a warping path used in a comparative example. FIG. 9 is a diagram illustrating an example of a processing result of a comparative example. It is a functional block diagram showing an example of functional composition of a time axis expansion and contraction device in one embodiment of the present invention. It is a figure showing an example of the processing result by the time axis expansion and contraction device in a 2nd embodiment of the present invention. It is a figure showing an example of a progress in a 3rd embodiment of the present invention. It is a functional block diagram showing an example of functional composition of a time axis expansion and contraction device in a 3rd embodiment of the present invention.

Embodiments of the present invention will be described in the following order.

1. 1. Overall configuration example of abnormality detection 2. Hardware configuration example of time axis expansion / contraction device 3. Example of overall processing by time axis expansion / contraction device Comparative Example 5 Functional configuration example of time axis expansion / contraction device

(1st Embodiment)
≪ 1. Example of overall configuration of abnormality detection ≫
Hereinafter, an example in which abnormality detection is performed based on data periodically sensed in a plant will be described. First, the types of processes performed in the plant can be classified, for example, as follows.

  FIG. 2 is a diagram illustrating an example of each of a continuous process and a batch process. For example, in a petrochemical process, physical quantities such as temperature, pressure, and flow rate are sensed by a sensor installed in a plant, as shown in FIG. Then, as shown, each physical quantity acquired by the sensor is continuously shown for each time. In such a continuous process, in a state where there is no abnormality such as a failure of the device or the like, that is, a so-called steady state, each physical quantity often has a substantially constant value near an average value. Therefore, in a continuous process, it is often possible to determine whether the process is abnormal or normal depending on whether or not the physical quantity is near the average value, regardless of the time. The continuous process is, for example, a process of continuously producing the same type of product, such as an ethylene plant of petrochemical.

  On the other hand, the batch-based process is, for example, a process for steel, casting, food, medicine, semiconductor, or general chemistry, and is a process in which the process is repeated from the start to the end in a batch processing unit. That is, in the batch process, batch processing is performed for each lot. The batch process is, for example, a process having physical quantities as shown in FIG. As shown in the figure, in a batch-based process, even in a process under a normal state, the physical quantity is not always near the average value and is often not a constant value. That is, in the batch process, the physical quantity changes with time based on the content of the process to be performed and a preset value.

  More specifically, in the illustrated example, first, at the start of the batch processing, the temperature is around room temperature. Next, when the process is started and a process such as heating is started, the temperature rises. When the temperature reaches a predetermined temperature, the temperature is maintained so as to maintain the temperature for a certain time. Subsequently, after the temperature is maintained at a high temperature for a certain period of time, when a predetermined time has elapsed, a process such as cooling is started. Thus, when a process such as cooling starts, the temperature decreases. Then, when the batch processing is cooled to a predetermined temperature, the batch processing ends.

  For example, assuming that a batch process is performed to manufacture one lot of products, the batch process is repeatedly performed according to the number of product lots to be manufactured, as illustrated. That is, in a so-called lot production method or the like, a process is performed for each lot in which a fixed amount of a raw material, an intermediate product, or the like is used as an input unit. In such a batch process, the physical quantity is often not constant, unlike the continuous process. That is, in a batch-based process, the value of the physical quantity increases or decreases depending on the process.

  In addition, a continuous process is often performed in a large-scale facility, whereas a batch process is a process often performed in a small-scale facility or the like. Further, a process similar to a batch-based process may be performed. For example, a reciprocating pump or a compressor is a facility that performs reciprocating motion, and thus is an example of a facility that performs reciprocating motion repeatedly as in a batch process.

  In addition, refrigeration and freezing equipment may perform defrosting at regular intervals. In such a case, the refrigeration and freezing facilities are examples of facilities that repeatedly perform defrosting and the like for each preset defrosting period.

  In such a batch process, data is sensed by a sensor, and the data is stored in a measurement database. Then, in the plant, using the accumulated data, each process is monitored for abnormality.

  Therefore, the time-series data related to the batch process often becomes data having a value that is repeated at a constant cycle. In particular, when a product is manufactured by performing a batch process, the physical quantity is often set to have a constant pattern as the process of the batch process proceeds. In this way, a product is often manufactured by basically repeating the same pattern. In addition, the pattern of the physical quantity used in the batch process is called a “profile”.

  In order to monitor the above batch process, for example, a multi-way method is used. The multi-way method is described in "P. Nomikos, J. F. MacGregor:" Monitoring Batch Processes Using Multiway Principal Component Analysis ", AIChE Journal, Vol. 40, No. 13, p. P. Nomikos, J. F. MacGregor: "Multi-way partial last squares in monitoring batch processes", described in Chemometrics and Intelligent Laboratories, "Methods and Methods" in Chemometrics and Intelligent Laboratories, Inc. is there. Specifically, for example, a batch process is monitored as follows.

  FIG. 3 is a diagram illustrating an example of a method of monitoring a batch process. In the following example, first, it is assumed that a process is performed in a plant or the like, and waveform data relating to temperature and pressure as shown in FIG. 3A is generated by a sensor. Specifically, in this example, the first waveform data DW1 is data indicating the temperature with respect to time for each batch. The second waveform data DW2 is data indicating pressure with respect to time for each batch.

  When the lengths of the respective waveform data are substantially the same, the respective waveform data of the respective batches can be overlapped as shown in FIG. In this way, as shown in FIG. 3C, the average value and the standard deviation of each physical quantity in each batch can be calculated.

  Next, at each sampling point of the batch, the average between the batches is subtracted (removal of the average waveform), divided by the standard deviation, and normalized to the average value “0” and the standard deviation “1” at each sampling point. Processing is performed. In this way, an abnormality can be detected based on whether or not each physical quantity deviates from the average value, as in the continuous system process.

  Further, the data of the batch process can be represented by three-dimensional data in which the number of batches is “I”, the variable is “J”, and the time is “K”. Then, the normalization in the batch direction can be expressed as the following equation (1).

なお、上記（１）式では、「μ」は、平均値を示す。また、「σ」は、標準偏差を示す。また、上記（１）式では、「ｘ」は、バッチ系プロセスにおける物理量を示す。

In the above equation (1), “μ” indicates an average value. “Σ” indicates a standard deviation. In the above formula (1), “x” indicates a physical quantity in a batch process.

  As described above, in order to monitor the batch process, it is necessary to equalize the lengths and shapes of the respective waveform data in order to perform normalization. Thus, for example, there is a method using the DTW method to make the length and shape of each waveform data uniform.

  Specifically, first, two or more waveform data having different lengths and shapes are generated by the sensor. The DTW method is a method of aligning the length and shape of other waveform data with certain one of a plurality of waveform data. Further, when the lengths and shapes of the respective waveform data are uniform, the respective waveform data have the same phase in the respective waveforms. Thus, the waveform data can be synchronized by using the DTW method.

  Hereinafter, waveform data serving as a reference for making the length and shape of the waveform data uniform is referred to as “reference data”. On the other hand, waveform data whose length or shape is expanded or contracted so as to match the reference data as much as possible is called “test data”. The waveform indicated by the reference data is referred to as a “reference waveform”. On the other hand, the waveform indicated by the test data is called “test waveform”.

  The DTW method is a method in which, when a function (hereinafter, referred to as “warping path”) for associating reference data with test data is provided, the test data can be made to have the same length and shape as the reference data. Specifically, the DTW method is as follows.

  FIG. 4 is a diagram illustrating an example of the DTW method and the warping path. Hereinafter, a description will be given using reference data indicating the reference waveform WR as shown in FIG. 4A and test data indicating the test waveform WT as shown in FIG. 4B as an example. In FIGS. 4A and 4B, the horizontal axis represents time, and the vertical axis represents a physical quantity for each time.

  In the illustrated example, the reference waveform WR indicates a batch process in which the period from the start to the end of the process is “first time T1”. On the other hand, the test waveform WT indicates a batch process in which the period from the start to the end of the process is “second time T2”. Further, in this example, as illustrated, the first time T1 is assumed to be shorter than the second time T2.

Next, as shown in FIG. 4C, the reference waveform WR is arranged on the vertical axis, and the test waveform WT is arranged on the horizontal axis to obtain two-dimensional coordinates. Also, each coordinate on the vertical axis is “j”, and each coordinate on the horizontal axis is “i”. Then, at each grid point (i, j) in the two-dimensional coordinates, the difference between the value T ₀ (i) of the test waveform WT and the value R ₀ (j) of the reference waveform WR is calculated. The absolute value is “d”. That is, at the grid point (i, j), the absolute value d can be expressed as in the following equation (2).

このように、格子点（ｉ，ｊ）ごとに、絶対値ｄを計算すると、図４（Ｃ）に示すような「距離行列」が生成できる。次に、バッチ処理の開始時点に相当する図４（Ｃ）における左下の座標（以下「スタート座標ＳＴ」という。）から、バッチ処理の終了時点に相当する図４（Ｃ）における右上の座標（以下「エンド座標ＥＤ」という。）まで、各格子点（ｉ，ｊ）おけるそれぞれの絶対値ｄを加算し、累積値「Ｄ_ｉｊ」が、下記（３）式のように計算する。なお、下記（３）式を「Ｓｔｅｐ Ｃｏｎｄｉｔｉｏｎ」と呼び、計算された値を示す行列を「累積距離行列」という。

As described above, when the absolute value d is calculated for each lattice point (i, j), a “distance matrix” as shown in FIG. 4C can be generated. Next, from the lower left coordinates (hereinafter referred to as “start coordinates ST”) in FIG. 4C corresponding to the start of the batch processing, the upper right coordinates (FIG. 4C) corresponding to the end of the batch processing are referred to. The absolute value d at each grid point (i, j) is added up to the “end coordinate ED”, and a cumulative value “D _ij ” is calculated as in the following equation (3). The following equation (3) is referred to as “Step Condition”, and a matrix indicating the calculated values is referred to as a “cumulative distance matrix”.

上記（３）式を図示すると、図４（Ｄ）のように示せる。図４（Ｄ）及び上記（３）式に示すように、累積値「Ｄ_ｉｊ」は、格子点（ｉ，ｊ）に隣接する格子点（ｉ−１，ｊ）、（ｉ，ｊ−１）及び（ｉ−１，ｊ−１）の累積値に基づいて計算される値である。

FIG. 4D shows the above equation (3). As shown in FIG. 4D and the above equation (3), the cumulative value “D _ij ” is _{calculated based} on the grid points (i−1, j), (i, j−1) adjacent to the grid point (i, j). ) And (i-1, j-1).

As described above, the accumulated value “D _ij ” is calculated, and the path having the smallest accumulated value “D _ij ” is the warping path among the paths from the start coordinates ST to the end coordinates ED. That is, as shown in FIG. 4E, the warping path is a path in which the cumulative value “D _ij ” is minimum.

  Thus, when a warping path is provided, for example, the test waveform can be expanded or contracted based on the warping path as described below.

  FIG. 5 is a diagram illustrating an example of expansion and contraction of waveform data based on a warping path. For example, an example in which test data shown in FIG. The illustrated example is an example in which the test waveform WT indicated by the input test data is expanded and contracted based on the warping path WPP illustrated in FIG. The warping path WPP is a function for associating the reference waveform WR indicated by the reference data as shown in FIG. 5C with the test waveform WT.

As shown, when the warping path WPP is used, each point T ₀ (i) on the test waveform WT can be associated with each point R ₀ (j) on the reference waveform WR by the warping path WPP.

In the illustrated example, as illustrated, each point T ₀ (i) of the first test section AR11 in the test waveform WT is associated with each point R ₀ (j) of the first reference section AR21 in the reference waveform WR. You. Similarly, each point T ₀ (i) of the second test section AR12 in the test waveform WT is associated with each point R ₀ (j) of the second reference section AR22 in the reference waveform WR. Further, each point T ₀ (i) of the third test section AR13 in the test waveform WT is associated with each point R ₀ (j) of the second reference section AR23 in the reference waveform WR. In this way, the test waveform WT is expanded and contracted to become expanded and contracted data WTA having a length substantially the same as the reference waveform WR, as shown in FIG.

  As described above, when the warping path WPP is obtained, as shown in FIG. 5, even if the waveform data has different lengths, the waveform data expands and contracts based on the warping path WPP, thereby aligning the waveform data with the waveform of the reference data. be able to.

  As described above, it is desirable to use a dynamic time warping method (DTW method) which has high versatility and can be applied to various processes for expansion and contraction on the time axis.

  Hereinafter, an example of a time axis expansion / contraction device that generates a warping path and expands / contracts waveform data will be described.

≪ 2. Example of hardware configuration of time axis telescopic device 装置
The time axis expansion / contraction device is, for example, the following information processing device.

  FIG. 6 is a block diagram illustrating an example of a hardware configuration of the time axis expansion and contraction device according to the embodiment of the present invention. As illustrated, the time axis expansion / contraction device 10 has a CPU (Central Processing Unit) HW1, a communication device HW2, a storage device HW3, a display device HW4, and an input device HW5. That is, the time axis expansion / contraction device 10 is a computer such as a PC (Personal Computer), a server, or a workstation, and the CPU HW1 calculates and controls based on a program installed in advance, thereby processing and processing according to the present embodiment. This is a device that can realize control.

  The CPU HW1 is an arithmetic unit that performs arithmetic and data processing for realizing processing and a control device that controls hardware.

  The communication device HW2 is a device that transmits and receives data to and from an external device via the network NW.

  The storage device HW3 is a main storage device such as a memory. Further, the storage device HW3 may include an auxiliary storage device such as a hard disk.

  The display device HW4 is an example of an output device such as a display. For example, the display device HW4 outputs a processing result and the like to the user.

  The input device HW5 is, for example, a keyboard, a mouse, or a combination thereof. That is, the input device HW5 is a device for inputting an operation from a user.

  Note that the hardware configuration is not limited to the illustrated configuration. For example, the time axis expansion / contraction device 10 may have a hardware configuration further including an arithmetic device, a control device, or a storage device inside or outside.

  Further, an apparatus for implementing the present embodiment may be a time axis expansion / contraction system having one or more information processing apparatuses connected by a network or the like. Further, the time axis expansion / contraction system may be configured to perform a part or all of the processing in a redundant, distributed, or parallel manner.

≪ 3. Example of overall processing using the time axis expansion / contraction device ≫
FIG. 7 is a flowchart illustrating an example of the entire process performed by the time axis expansion / contraction device according to the embodiment of the present invention. For example, when the following processing is performed, the time axis expansion / contraction device can generate a warping path and expand / contract test data.

入 力 Input example of reference data and test data (Step S01) ≫
In step S01, the time axis expansion / contraction device inputs reference data and test data. For example, it is assumed that reference data and test data as shown in FIGS. 5A and 5C are input.

例 Calculation example of first progress of first process indicated by reference data (step S02) ≫
In step S02, the time axis expansion / contraction device calculates a first progress degree of the first process indicated by the reference data. For example, the first degree of progress is calculated as follows.

  FIG. 8 is a diagram illustrating an example of calculating the degree of progress by the time axis expansion and contraction device according to the embodiment of the present invention. For example, it is assumed that waveform data as shown in FIG. 8A is input as reference data to the time axis expansion / contraction device in step S01. The first process is a batch process that can be represented by a reference waveform WR as illustrated.

  In the following description, it is assumed that the first process is a batch process represented by a function f (τ). In this example, the first degree of progress is a value obtained by integrating the values for each time indicated by the function f (τ). That is, assuming that the first degree of progress is “F (t)”, the first degree of progress is a value obtained by calculating the following equation (4).

また、「Ｆ（ｔ）」は、図示すると、図８（Ｂ）のように示せる。上記（４）式に示すように、第１進行度は、関数ｆ（τ）を積分すると計算できる積算値である。なお、上記（４）式は、離散的には、時間ごとの各値を加算する計算となる。

Also, “F (t)” can be illustrated as shown in FIG. 8B. As shown in the above equation (4), the first degree of progress is an integrated value that can be calculated by integrating the function f (τ). Note that the above equation (4) is a calculation that discretely adds each value for each time.

  In this way, the first degree of progress is calculated based on the function f (τ). For example, “F (t)” indicating the first degree of progress is a function as shown in FIG.

例 Example of calculating second progress of second process indicated by test data (step S03) ≫
Returning to FIG. 7, in step S03, the time axis expansion / contraction device calculates a second progress degree of the second process indicated by the test data. For example, the second degree of progress is calculated by a method as shown in FIG. 8, similarly to the first degree of progress. In the following description, the first degree of progress and the second degree of progress may be simply referred to as “degree of progress”.

<< Example of Generating Warping Path Based on First Progress and Second Progress (Step S04) >>
In step S04, the time-axis expansion / contraction device generates a warping path based on the first progress degree and the second progress degree. For example, the time axis expansion / contraction device generates a warping path as follows.

  FIG. 9 is a diagram illustrating an example of generation of a warping path based on the first progression degree and the second progression degree by the time axis expansion and contraction device according to the embodiment of the present invention. For example, suppose that the first progression degree “F1 (t)” as shown in FIG. 9A is calculated in step S02 based on the reference data. On the other hand, it is assumed that the second progression degree “F2 (t)” as shown in FIG. 9B is calculated based on the test data in step S03.

The warping path is generated by a method similar to the method shown in FIG. Compared to FIG. 4, FIG. 9C is different in that the value of each waveform data is used for generating the warping path, but the progress is used. As shown in the drawing, the warping path WPP has a path in which the cumulative value “D _ij ” (see FIG. 4) of the first progression “F1 (t)” and the second progression “F2 (t)” is minimum. Can be generated by calculating

伸縮 Example of expansion / contraction of test data based on warping path (Step S05) ≫
Returning to FIG. 7, in step S05, the time axis expansion / contraction device expands / contracts the test data based on the warping path. For example, the time axis expansion / contraction device expands / contracts the test data based on the warping path generated in step S04 so that the length of the test data is equal to the length of the reference data, as shown in FIG.

  As described above, by using the warping path generated based on the degree of progress, the time axis expansion / contraction device can expand / contract test data as follows, for example.

  FIG. 10 is a diagram illustrating an example of a processing result of the entire processing by the time axis expansion / contraction device according to the embodiment of the present invention. In the figure, the waveform data before expansion / contraction, that is, the waveform data input to the time axis expansion / contraction device is referred to as “pre-expansion / reduction waveform data”. The figure shows the experimental results obtained by simulation.

  On the other hand, in the figure, one of the waveform data is used as reference data, a warping path is generated by the entire process shown in FIG. 7, and test data that is waveform data other than the reference data is generated based on the warping path. To expand and contract. In the figure, the processing result of such overall processing is indicated as “waveform data after expansion and contraction”.

  Specifically, as shown in the figure, the process to be sensed by the waveform data is from the start of the process (when the time is “0”) to the time when the time becomes approximately “10”. , A “start-up” process of increasing the physical quantity is performed.

  Next, after the “start-up”, a “steady-state” process of maintaining the physical quantity constant is performed. In the figure, the “steady” process is started when the time becomes about “10”. The time at which the “steady” process ends depends on the process. In the case shown in FIG. 10A, the “steady” process is any time between “30” and “40”. Ends.

  Subsequently, after the “steady state”, a “falling” process of lowering the physical quantity is performed. Since the “falling” process is started from the time when the “steady” process ends, the time when the “falling” process starts is different as shown in FIG.

  In other words, the “waveform data before expansion / contraction” is not synchronized because the latter half of the batch processing, that is, the point at which the “falling” process starts is different for each waveform data. Therefore, the “waveform data before expansion / contraction” is a case where the lengths of the respective waveform data are different. Specifically, in the case shown in FIG. 10A, the length of the waveform data is different between “40” and “50”. Hereinafter, examples of a case where there is no abnormality in the process and a case where there is an abnormality of the process will be described.

  First, FIGS. 10A and 10B show examples of processing results in a state where there is no abnormality in the process, that is, a state where the process is being performed normally (in the figure, “abnormal” is shown). As shown in FIG. 10 (A), even when the lengths of the respective waveform data are different, if the entire processing is performed as shown in FIG. 7, the time-axis expansion / contraction device becomes as shown in FIG. 10 (B). In addition, the length of the test data can be set to a length substantially matching the length of the reference data. Therefore, as shown in FIG. 10B, the time axis expansion and contraction device can make the lengths of the respective waveform data uniform.

  Next, FIGS. 10C and 10D show examples of processing results in a state in which the process has an abnormality, that is, a state in which the process has an abnormality (shown as “abnormal” in the figure). Specifically, an example will be described in which abnormal data ANM as shown in FIG. 10C is present on the waveform data before expansion and contraction. In this example, as shown in FIG. 10A, it is normal for the waveform data to maintain the physical quantity in a state close to “1” when the time is around “20” to “30”.

  On the other hand, as shown in FIG. 10 (C), for some reason such as a failure of an apparatus related to a process, an abnormality in which the physical quantity temporarily drops during a period in which the physical quantity is kept substantially close to “1”. Is generated. When such an abnormality occurs, the abnormality appears on the waveform data as abnormal data ANM, as shown in FIG.

  As shown in FIG. 10 (C), when the time-axis expansion / contraction device performs the entire process shown in FIG. 7 on the waveform data having the abnormal data ANM, the case shown in FIG. 10 (A) and FIG. Similarly to the above, the length of each waveform data can be made uniform. Specifically, when the time axis expansion / contraction device performs the entire process illustrated in FIG. 7, the following warping path can be generated.

  FIG. 11 is a diagram illustrating an example of a warping path generated by the time axis expansion and contraction device according to the embodiment of the present invention. By using a warping path as shown in the figure, as shown in FIG. 10D, the abnormal data ANM can be stored on the waveform data even if the process of expanding / contracting the waveform data is performed. That is, the time axis expansion / contraction device can reduce the loss of data such as the abnormal data ANM due to expansion / contraction of the waveform data on the time axis.

  Note that the abnormal data ANM is not limited to the data as illustrated. For example, the abnormal data ANM may occur in a “rising” or “falling” process. In addition, the abnormal data ANM may not be an abnormality in which the physical quantity temporarily decreases, for example, may be an abnormality in which the physical quantity temporarily increases.

４ 4. Comparative example ≫
Unlike the processing shown in FIG. 7, a case where a warping path generated without using the progress degree is used will be described below as a comparative example. For example, the comparative example uses the following warping path.

  FIG. 12 is a diagram illustrating an example of the warping path used in the comparative example. The illustrated warping path is a warping path having many parallel portions PR parallel to the horizontal axis as compared with the warping path illustrated in FIG. When such a warping path is used, the parallel portion PR may be associated with the same point on the reference data as shown in the drawing. Therefore, when waveform data is expanded or contracted using a warping path as shown in the figure, the following processing result may be obtained.

  FIG. 13 is a diagram illustrating an example of a processing result of the comparative example. The figure shows the result of the process of expanding and contracting the waveform data on the time axis using the warping path shown in FIG. 12 for the waveform data before expansion and contraction similar to the waveform data shown in FIG.

  As shown in FIGS. 13A and 13B, in a normal state, the waveform data can have the same length as in FIGS. 10A and 10B. . On the other hand, in the case where the waveform data has the abnormal data ANM, as in FIG. 10C, using the warping path shown in FIG. 12, as shown in FIG. , The abnormal data ANM may be missing.

  When FIG. 10 (D) is compared with FIG. 13 (D), in FIG. 13 (D), in the “waveform data before expansion / contraction”, the existing abnormal data ANM is ignored in the expansion / contraction, and the abnormal data ANM is not stored in “Waveform data after expansion / contraction”. As described above, if the abnormal data ANM is missing, the “waveform data after expansion and contraction” becomes waveform data indicating “no abnormality”, as in FIG. 13B. Therefore, when a warping path as shown in FIG. 12 is used, “waveform data after expansion and contraction” as shown in FIG. 13D in which it is difficult to detect an abnormality may be generated.

≪5. Functional configuration example of time axis expansion and contraction device ≫
FIG. 14 is a functional block diagram illustrating an example of a functional configuration of the time axis expansion and contraction device according to the embodiment of the present invention. As shown in the figure, for example, the time axis expansion / contraction device 10 has a functional configuration including an input unit FN1, a progress degree calculation unit FN2, a warping path generation unit FN3, and an expansion / contraction unit FN4.

  The input unit FN1 inputs reference data DR indicating a waveform having a length serving as a reference for expansion and contraction. Further, the input unit FN1 inputs test data DT indicating a waveform to be expanded and contracted. The input unit FN1 is realized by, for example, the input device HW5 (see FIG. 6) or the communication device HW2.

  The progress calculating unit FN2 calculates the first progress “F1 (t)” of the first process indicated by the reference data DR and the second progress “F2 (t)” of the second process indicated by the test data DT. calculate. The progress calculating unit FN2 is realized by, for example, the CPU HW1 (see FIG. 6).

  The warping path generation unit FN3 generates the reference data DR and the test data DT based on the first progression “F1 (t)” calculated by the progression calculation unit FN2 and the second progression “F2 (t)”. And a warping path WPP for associating. Note that the warping path generation unit FN3 is realized by, for example, the CPU HW1 (see FIG. 6).

  The expansion / contraction unit FN4 expands / contracts the test data DT based on the warping path WPP generated by the warping path generation unit FN3. The expansion and contraction unit FN4 is realized by, for example, the CPU HW1 (see FIG. 6).

  First, the time axis expansion / contraction device 10 inputs, via the input unit FN1, waveform data DW indicating a result of sensing a process by a sensor. Then, among the waveform data DW, waveform data DW indicating a waveform serving as a reference for aligning the lengths becomes the reference data DR. On the other hand, the waveform data DW other than the reference data DR becomes the test data DT.

  Next, in the time axis expansion / contraction device 10, the progress degree is calculated by the progress degree calculation unit FN2, for example, as shown in FIG. When the first degree of progress “F1 (t)” and the second degree of progression “F2 (t)” can be calculated, the time-axis expansion / contraction device 10 uses the warping path generation unit FN3 as shown in FIG. , A warping path WPP can be generated. As described above, when the warping path WPP is generated, the time axis expansion / contraction device 10 expands / contracts the test data DT based on the warping path WPP so as to align the test data DT with the reference data DR, for example, as shown in FIG. Can be.

  As described above, when the warping path WPP generated based on the degree of progress is used, as shown in FIG. 10, the time axis expansion / contraction device lacks the abnormal data ANM even if the waveform data is expanded / contracted on the time axis. Can be reduced.

If the process involves batch processing, and if the waveform data is expanded or contracted on the time axis, simply expanding and contracting the waveform data evenly cannot align the phases of the waveforms and synchronize the waveforms. May not be possible. Therefore, the DTW method of expanding and contracting the waveform data using the warping path as described above is used. According to the present embodiment, even when the process indicated by the waveform data includes a batch process and the waveform data is expanded or contracted on the time axis, data such as abnormal data ANM is included in the expanded and contracted waveform data. Can be reduced.
(2nd Embodiment)
The second embodiment is realized by the same hardware configuration and overall processing as the first embodiment. As compared with the first embodiment, the second embodiment differs from the first embodiment in the method of calculating the degree of progress. Hereinafter, points different from the first embodiment will be mainly described, and redundant description will be omitted.

  The degree of progress may be calculated as follows. First, each data indicated by the waveform data is defined as “y (i, j, k)”. “I” indicates a batch number, and “1 ≦ i ≦ I”. “J” indicates a variable number and “1 ≦ j ≦ J”. Further, “k” indicates a sampling number, and “1 ≦ k ≦ K”. Next, the minimum value represented by the following equation (5) is defined as “ymin (j)”.

すなわち、上記（５）式で示す最小値「ｙｍｉｎ（ｊ）」は、全バッチ中、かつ、全サンプリング点において、最も小さい値である。次に、時間軸伸縮装置は、上記（５）式に示す最小値を用いて、波形データが示すデータを下記（６）式のように計算する。

That is, the minimum value “ymin (j)” shown in the above equation (5) is the smallest value in all batches and at all sampling points. Next, the time axis expansion / contraction device calculates the data indicated by the waveform data as in the following equation (6) using the minimum value shown in the above equation (5).

進行度を示す関数は、例えば、図９（Ａ）及び図９（Ｂ）に示すように、時間に伴って増加していくのが望ましい。一方で、プロセスにおける物理量は、バッチ処理又は物理量の種類等によって、負の数となる場合がある。そこで、時間軸伸縮装置は、上記のように、波形データにおける最小値を用いて、最小値が「０」以上となるように、波形データの値を変更する。これらの処理は、例えば、以下のように示せる。

It is desirable that the function indicating the degree of progress increase with time, for example, as shown in FIGS. 9A and 9B. On the other hand, the physical quantity in the process may be a negative number depending on the type of the batch processing or the physical quantity. Therefore, as described above, the time axis expansion / contraction device changes the value of the waveform data using the minimum value in the waveform data so that the minimum value is “0” or more. These processes can be shown as follows, for example.

  FIG. 15 is a diagram illustrating an example of a processing result by the time axis expansion / contraction device according to the second embodiment of the present invention. For example, assume that there is waveform data “y (i, j, k)” as shown in FIG. As shown, in the waveform data "y (i, j, k)", at least the minimum value "ymin (j)" is a value smaller than "0" and is a negative number.

  Therefore, when the degree of progress is calculated based on “y (i, j, k)”, the degree of progress is calculated by integrating a negative number near the minimum value “ymin (j)”. The degree “F (t)” may be a value that decreases with time. Therefore, the time axis expansion / contraction device calculates as in the above equation (6). When calculated in this way, the waveform data becomes data as shown in FIG.

  As shown in FIG. 15B, when the above equation (6) is calculated, the minimum value is “0”. Further, the values other than the minimum value are larger than the minimum value, and as shown in the figure, since the value of the minimum value is added to the value other than the minimum value, all the values of the waveform data are positive. Is the number of Therefore, if the progress is calculated after all the values of the waveform data are made positive numbers, the progress “F (t)” becomes a function of a so-called monotonic increase.

  When the processing is performed as described above, the value indicated by the waveform data is adjusted to a positive number, so that each value of the reference data and the test data is a positive number. When such positive reference data and test data are used, the time axis expansion / contraction device performs warping using a function of the degree of progress that increases with time, as shown in FIG. A path can be generated.

The method of adjusting each value of the waveform data to a positive number is not limited to the calculation represented by the above equation (6) or the like. For example, the time axis expansion / contraction device may calculate each square of each value, and set each value of the waveform data to a positive number.
(Third embodiment)
The third embodiment is realized by the same hardware configuration and overall processing as the first embodiment and the second embodiment. As compared with the first embodiment and the second embodiment, the third embodiment differs from the first embodiment and the second embodiment in the method of calculating the degree of progress. Hereinafter, points different from the first embodiment and the second embodiment will be mainly described, and redundant description will be omitted.

  The degree of progress may be a value indicating the degree of progress of the process (hereinafter referred to as “degree of progress”) or the like. For example, the degree of progress has the following values.

  FIG. 16 is a diagram illustrating an example of the degree of progress according to the third embodiment of the present invention. In the illustrated example, the horizontal axis represents time, and the vertical axis represents physical quantities.

  The illustrated process is a process in which time “0” is a start time and time “T” is an end time. As illustrated, the process is a process in which the physical quantity increases in proportion to time from the start point to the end point.

  In such a process, the progress is set such that the start time is “0%” and the end time is “100%”. Specifically, for example, assuming that the process is a process in which “0 min” is the start time and “60 min” is the end time, the time when the time is “0 min” is “the degree of progress z1 = 0%”. Then, in this process, the time point at which the time is “60 min” becomes “progress z1 = 100%”. Further, in this process, the point in time when the time is “30 min” is “progress z1 = 50%”. As described above, the progress degree may be the progress degree of the process using the elapsed time from the start of the process.

  In the case where the physical quantity increases in proportion to the time, the physical quantity at the time when the time reaches “T” is set to “100%”, and the progress may be a value using the amount of change in the physical quantity.

  For example, suppose that the process is to change the temperature from “0 ° C.” to “100 ° C.”. That is, at the start of the process, the physical quantity is “0 ° C.”, and at the end of the process, the physical quantity is “100 ° C.”. In such a case, the degree of progress is the amount of change from “0 ° C.”.

  Note that the time axis expansion / contraction device may input an external signal or the like indicating a physical quantity. That is, the time axis expansion / contraction device may calculate the degree of progress based on the value indicated by the external signal.

  FIG. 17 is a functional block diagram illustrating an example of a functional configuration of the time axis expansion / contraction device according to the third embodiment of the present invention. Hereinafter, the same components as those in FIG. 14 are denoted by the same reference numerals, and description thereof will be omitted.

As illustrated, for example, the time axis expansion / contraction device 10 has a functional configuration including an input unit FN1, a warping path generation unit FN3, and an expansion / contraction unit FN4. 14 in that a warping path is generated based on the first progress degree and the second progress degree.
(Other embodiments)
In the description of the above embodiment, an example in which a warping path is used for abnormality detection has been described, but the embodiment is not limited to this. For example, the time-axis expansion / contraction device may perform a prediction of a batch process or the like after performing a preparation process for adjusting the shape.

  All or a part of each processing according to an embodiment of the present invention may be realized by a program for causing a computer described in a low-level language, a high-level language, or a combination thereof to execute a time axis expansion / contraction method. Good. That is, the program is a computer program for causing a computer such as an information processing device to execute all or a part of each process.

  In addition, the program can be stored in a computer-readable recording medium and distributed. The recording medium is a flash memory, a flexible disk, an optical disk such as a CD-ROM or a Blu-ray disk, an SD (registered trademark) card, an auxiliary storage device, an MO, or the like. Furthermore, the program can be distributed through a telecommunication line.

  Further, the processes according to the embodiment of the present invention are not limited to the illustrated order. For example, some or all of the processes may be performed in a different order, parallel, distributed, or omitted.

  Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the above-described embodiments, and various modifications or changes may be made within the scope of the present invention described in the appended claims. It is possible.

10 Time axis expansion / contraction device FN1 Input unit FN2 Progress degree calculation unit FN3 Warping path generation unit FN4 Expansion / contraction unit DR Reference data DT Test data DW Waveform data WPP Warping path ANM Abnormal data

Claims (9)

A time axis expansion / contraction device that expands / contracts waveform data indicating a physical quantity with respect to time in a batch processing process,
An input unit for inputting test data indicating a waveform that expands and contracts to the length of the reference data, among the waveform data, reference data indicating a waveform of a reference length and the waveform data.
A progress calculating unit that calculates a first progress of a first process in the reference data and a second progress of a second process in the test data,
A warping path generation unit that generates a warping path that associates the reference data with the test data based on the first progress degree and the second progress degree;
A time-axis expansion / contraction device including an expansion / contraction unit that expands / contracts the test data based on the warping path.   The time axis expansion and contraction device according to claim 1, wherein the first progress degree and the second progress degree are values obtained by integrating the respective physical quantities at each time. Adjust each physical quantity indicated by the waveform data to be a positive number,
The said progress degree calculation part calculates the said 1st progress degree and the said 2nd progress degree using the said reference data and the said test data which the said physical quantity became a positive number, respectively, The Claims 1 or 2 characterized by the above-mentioned. Time axis telescopic device.   The time axis expansion / contraction device according to claim 1, wherein the first progress degree and the second progress degree are progress degrees of the first process and the second process. When the physical quantity increases in proportion to the time from the start time to the end time of the process,
The time axis expansion / contraction device according to claim 4, wherein the progress degree is an elapsed time from the start time of each of the first process and the second process, or a change amount of the physical quantity from the start time.   The time axis expansion and contraction device according to claim 1, wherein the expansion and contraction unit expands and contracts the test data by a dynamic time warping method. A batch process monitoring device that expands and contracts waveform data indicating a physical quantity with respect to time in a batch processing process, and monitors the process,
An input unit for inputting test data indicating a waveform that expands and contracts to the length of the reference data, among the waveform data, reference data indicating a waveform of a reference length and the waveform data.
A progress calculating unit that calculates a first progress of a first process in the reference data and a second progress of a second process in the test data,
A warping path generation unit that generates a warping path that associates the reference data with the test data based on the first progress degree and the second progress degree;
A batch process monitoring device comprising: an expansion / contraction unit that expands / contracts the test data based on the warping path. A time-axis expansion / contraction system having one or more information processing apparatuses and expanding / contracting waveform data indicating a physical quantity with respect to time in a batch processing process,
An input unit for inputting test data indicating a waveform that expands and contracts to the length of the reference data, among the waveform data, reference data indicating a waveform of a reference length and the waveform data.
A progress calculating unit that calculates a first progress of a first process in the reference data and a second progress of a second process in the test data,
A warping path generation unit that generates a warping path that associates the reference data with the test data based on the first progress degree and the second progress degree;
A time axis expansion / contraction system including an expansion / contraction unit that expands / contracts the test data based on the warping path. A program for causing a computer that expands and contracts waveform data indicating a physical quantity with respect to time in a batch processing process to execute a time axis expansion method,
An input step of inputting test data indicating a waveform that expands and contracts to the length of the reference data, among the waveform data, among the waveform data, the reference data indicating a waveform having a reference length and the waveform data;
A step of the computer calculating a first degree of progress of a first process in the reference data and a second degree of progress of a second process in the test data;
A warping path generation step of generating a warping path for causing the computer to associate the reference data with the test data based on the first progress degree and the second progress degree;
A program for causing the computer to execute an expansion / contraction procedure for expanding / contracting the test data based on the warping path.

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