Patent Publication Number: US-2023140271-A1

Title: Data processing apparatus, method, and program

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2021-179004, filed Nov. 1, 2021, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a data processing apparatus, a method, and a program. 
     BACKGROUND 
     A system such as a power plant, a water treatment plant, and a manufacturing apparatus includes a plurality of devices. If the system is a system used for an infrastructure, the stop of the system adversely affects a social function. Further, even if the system is not used for an infrastructure, stoppage of the system causes an economic loss. Accordingly, it is important to keep the system in a healthy state. 
     Therefore, in many cases, one or more sensors are installed at various places in the system for monitoring the system. The state of the system can be monitored by using the measurement values of the one or more installed sensors. However, if the system is large or complicated, the number of sensors required for monitoring increases. Therefore, it is difficult to monitor all the sensors simultaneously with a limited number of people. 
     Therefore, a monitoring apparatus that assists or automates monitoring of a system is known. For example, in a case where a deviation between a predicted value obtained by predicting a measured value of a sensor from a machine learning model and an actual measurement value is detected, there is a method of regarding that an anomaly is detected. However, a degree of deterioration of the machine learning model due to a change in environment or data is unknown, and it is difficult to determine the update timing. Furthermore, erroneous detection increases by continuously using the deteriorated machine learning model. 
     On the other hand, there is also a method of detecting a drift of a sensor measurement value and detecting a drift of a sensor measurement value due to aged deterioration of a measuring instrument. However, since the drift of an instantaneous value called the sensor measurement value is detected, it is not possible to detect a time differential value which is a change amount of the sensor measurement value per predetermined time, that is, the drift with respect to a time derivative, and there is a possibility that erroneous detection is performed even in a case where an operation is normal only because the time derivative is different. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram illustrating a data processing apparatus according to a first embodiment. 
         FIG.  2    is a flowchart illustrating an operation of the data processing apparatus according to the first embodiment. 
         FIG.  3    is a diagram illustrating a display example of a first differential value distribution according to the first embodiment. 
         FIG.  4    is a diagram illustrating a display example of a second differential value distribution according to the first embodiment. 
         FIG.  5    is a diagram illustrating a modification of a display example of the first differential value distribution and the second differential value distribution. 
         FIG.  6    is a conceptual diagram illustrating a case where a user designates a differential step. 
         FIG.  7    is a diagram illustrating a display example of a trend graph based on first output information according to a second embodiment. 
         FIG.  8    is a diagram illustrating a display example of a trend graph based on the first output information according to the second embodiment. 
         FIG.  9    is a diagram illustrating a display example of a trend graph based on second output information according to the second embodiment. 
         FIG.  10    is a diagram illustrating a display example of a trend graph based on the second output information according to the second embodiment. 
         FIG.  11    is a diagram illustrating a first modification of the display example of the trend graph according to the second embodiment. 
         FIG.  12    is a diagram illustrating a second modification of the display example of the trend graph according to the second embodiment. 
         FIG.  13    is a block diagram illustrating a data processing apparatus according to a third embodiment. 
         FIG.  14    is a block diagram illustrating a data processing apparatus according to a fourth embodiment. 
         FIG.  15    is a diagram illustrating a first display example of first output information according to a sixth embodiment. 
         FIG.  16    is a diagram illustrating a second display example of the first output information according to the sixth embodiment. 
         FIG.  17    is a diagram illustrating a first display example of second output information according to the sixth embodiment. 
         FIG.  18    is a diagram illustrating a second display example of the second output information according to the sixth embodiment. 
         FIG.  19    is a diagram illustrating a third display example of the first output information and the second output information according to the sixth embodiment. 
         FIG.  20    is a block diagram illustrating a data processing apparatus according to a seventh embodiment. 
         FIG.  21    is a diagram illustrating a first display example of scatter diagram data according to the seventh embodiment. 
         FIG.  22    is a diagram illustrating a second display example of the scatter diagram data according to the seventh embodiment. 
         FIG.  23    is a diagram illustrating an example of a graph showing a change in the number of sensors in which a drift in a time derivative is detected. 
         FIG.  24    is a block diagram illustrating a data processing apparatus according to a ninth embodiment. 
         FIG.  25    is a diagram illustrating an example of a trend graph of a measurement value and a predicted value for a certain sensor of interest according to the ninth embodiment. 
         FIG.  26    is a diagram illustrating an example of a trend graph of a period of training data and a measurement value of a period C for a certain sensor of interest according to the ninth embodiment. 
         FIG.  27    is a block diagram illustrating a data processing apparatus according to a tenth embodiment. 
         FIG.  28    is a diagram illustrating a display example of a detection signal according to the tenth embodiment. 
         FIG.  29    is a diagram illustrating an example of a hardware configuration of the data processing apparatus. 
     
    
    
     DETAILED DESCRIPTION 
     In general, according to one embodiment, a data processing apparatus includes a processor. The processor acquires first measurement data that is a set of measurement values in a first period among time series data of measurement values of a sensor of interest. The processor acquires second measurement data that is a set of measurement values in a second period different from the first period among the time series data of the measurement values of the sensor of interest. The processor calculates, from the first measurement data, a first differential value set that is a set of first differential values in a time direction at a time included in the first period of the measurement values of the sensor of interest. The processor calculates, from the second measurement data, a second differential value set that is a set of second differential values in a time direction at a time included in the second period of the measurement values of the sensor of interest. The processor generates a first differential value distribution using the first differential value set. The processor generates a second differential value distribution using the second differential value set. The processor outputs the first differential value distribution and the second differential value distribution. 
     Hereinafter, a data processing apparatus, a method, and a program according to the present embodiments will be described in detail with reference to the drawings. Note that, in the following embodiments, parts denoted by the same reference signs perform the same operation, and redundant description will be appropriately omitted. 
     First Embodiment 
       FIG.  1    is a block diagram illustrating a data processing apparatus  100  according to a first embodiment. The data processing apparatus  100  includes a first period setting unit  101 , a second period setting unit  102 , a first acquisition unit  103 , a second acquisition unit  104 , a first differential unit  105 , a second differential unit  106 , a first distribution generation unit  107 , a second distribution generation unit  108 , a first output unit  119 , and a second output unit  120 . 
     Note that, in the following description, when contents are common to a first configuration and a second configuration, ordinal numbers are omitted. For example, contents common to the first differential unit  105  and the second differential unit  106  will be described as “the differential unit is”. 
     The first period setting unit  101  sets a predetermined first period, and sends the first predetermined period to the first acquisition unit  103 . 
     The second period setting unit  102  sets a predetermined second period different from the first period, and sends the second period to the second acquisition unit  104 . 
     The first acquisition unit  103  receives information regarding the first period from the first period setting unit  101 , and acquires, from the outside, first measurement data that is a set of measurement values in the first period of a sensor of interest that is a sensor of interest among one or more sensors installed in a system. The first acquisition unit  103  sends the first measurement data to the first differential unit  105 . 
     The second acquisition unit  104  receives information regarding the second period from the second period setting unit  102 , and acquires, from the outside, second measurement data that is a set of measurement values in the second period of the sensor of interest. The second acquisition unit  104  sends the second measurement data to the second differential unit  106 . 
     Here, the sensors of interest from which the first measurement data and the second measurement data are acquired are the same. The first acquisition unit  103  and the second acquisition unit  104  may be synchronized with each other with respect to information of a sensor of interest for acquiring measurement data, and may acquire the first measurement data and the second measurement data from the same sensor of interest. Alternatively, without synchronization between the first acquisition unit  103  and the second acquisition unit  104 , information regarding sensor ID may be assigned to a measurement value, and the first measurement data and the second measurement data may be acquired based on the measurement value of each sensor. Thereafter, for example, after acquiring the first measurement data and the second measurement data, a data control unit (not illustrated) may associate the first measurement data and the second measurement data related to the same sensor of interest, and send the first measurement data to the first differential unit  105  and the second measurement data to the second differential unit  106 . 
     The first differential unit  105  receives the first measurement data from the first acquisition unit  103 , and calculates a first differential value in a time direction at a first time included in the first period of the measurement value of the first measurement data. The first differential unit  105  transmits, to the first distribution generation unit  107 , a first differential value set that is a set of first differential values calculated by changing the first time in the first period. At this time, all the elements of the first differential value set may be collectively sent to the first distribution generation unit  107 , or each element of the first differential value set may be sequentially sent to the first distribution generation unit  107 . The first differential value in the time direction at the first time is calculated, for example, by calculating a difference between measurement values at a first attention time near the first time and at a first calculation target time separated from the first attention time by s unit time. “s” represents a value of a differential step, and is, for example, “1”. 
     The first attention time is a time to which attention is paid in order to calculate the first differential value at the first time. The first attention time may or may not coincide with the first time. The first calculation target time is, for example, ahead of the first attention time by s unit time. The first calculation target time may be after the first attention time by s unit time. The first differential value in the time direction of the measurement value of the sensor of interest represents a time derivative near the first time of the measurement value of the sensor of interest. 
     The second differential unit  106  receives the second measurement data from the second acquisition unit  104 , and calculates a second differential value in the time direction at a second time included in the second period of the measurement value of the second measurement data. The second differential unit  106  transmits, to the second distribution generation unit  108 , a second differential value set that is a set of second differential values calculated by changing the second time in the second period. At this time, all the elements of the second differential value set may be collectively sent to the second distribution generation unit  108 , or each element of the second differential value set may be sequentially sent to the second distribution generation unit  108 . 
     The second differential value in the time direction at the second time is calculated, for example, by calculating a difference between measurement values at a second attention time near the second time and at a second calculation target time separated from the second attention time by s unit time. The second attention time is a time to which attention is paid in order to calculate the second differential value at the second time. The second attention time may or may not coincide with the second time. The second calculation target time is, for example, ahead of the second attention time by s unit time. The second calculation target time may be after the second attention time by s unit time. The second differential value in the time direction of the measurement value of the sensor of interest represents a time derivative near the second time of the measurement value of the sensor of interest. 
     The first distribution generation unit  107  receives the first differential value set from the first differential unit  105 , generates a distribution or a cumulative distribution related to the differential value, and sends the distribution to the first output unit  119  as a first differential value distribution. 
     The second distribution generation unit  108  receives the second differential value set from the second differential unit  106 , generates a distribution or a cumulative distribution related to the differential value, and sends the distribution to the second output unit  120  as a second differential value distribution. Here, each of the first differential value distribution and the second differential value distribution is assumed to be, for example, a histogram, but is not limited thereto, and may be a discrete probability distribution, a probability density function, a cumulative histogram, a discrete cumulative probability distribution, a cumulative probability density function, or the like. 
     The first output unit  119  receives the first differential value distribution from the first distribution generation unit  107 , and outputs first output information regarding the first differential value distribution to the outside of the data processing apparatus  100 . Note that, when the first output unit  119  is a display apparatus such as a monitor, the first differential value distribution may be displayed as the first output information. 
     The second output unit  120  receives the second differential value distribution from the second distribution generation unit  108 , and outputs second output information representing the second differential value distribution to the outside of the data processing apparatus  100 . Note that, when the second output unit  120  is a display apparatus such as a monitor, similarly to the first output unit  119 , the second differential value distribution may be displayed as the second output information. 
     Next, an operation of the data processing apparatus  100  according to the first embodiment will be described with reference to a flowchart of  FIG.  2   . 
     In step S 201 , the first acquisition unit  103  acquires the first measurement data, and the second acquisition unit  104  acquires the second measurement data. 
     In step S 202 , the first differential unit  105  calculates the first differential value of the measurement value at the first time within the first period. 
     In step S 203 , the first differential unit  105  determines whether or not the first differential value has been calculated at all times at which the first differential value can be calculated in the first period. In a case where the first differential value has been calculated at all times, the process proceeds to step S 205 . In a case where there is an unprocessed time, the process proceeds to step S 204 . 
     In step S 204 , the first differential unit  105  determines a new first time from the unprocessed times, returns to step S 202 , and repeats the same processing. 
     In step S 205 , the first distribution generation unit  107  generates the first differential value distribution from the first differential value set obtained in step S 203 . 
     In step S 206 , the second differential unit  106  calculates the second differential value of the measurement value at the second time within the second period. 
     In step S 207 , the second differential unit  106  determines whether or not the second differential value has been calculated at all times at which the second differential value can be calculated in the second period. In a case where the second differential value has been calculated at all times, the process proceeds to step S 209 . In a case where there is an unprocessed time, the process proceeds to step S 208 . 
     In step S 208 , the second differential unit  106  determines a new second time from the unprocessed times, returns to step S 206 , and repeats the same processing. 
     In step S 209 , the second distribution generation unit  108  generates the second differential value distribution from the second differential value set obtained in step S 207 . 
     In step S 210 , the first output unit  119  and the second output unit  120  output the first differential value distribution and the second differential value distribution. The first differential value distribution and the second differential value distribution may be displayed on separate monitors, or may be displayed as different graphs on the same monitor. 
     Next, a display example of the first differential value distribution is illustrated in  FIG.  3   . 
       FIG.  3    is a graph of the first differential value distribution  30 , where a horizontal axis represents a frequency and a vertical axis represents the first differential value in the time direction. The first differential value distribution  30  is a histogram of the first differential value in the time direction. Note that the vertical axis and the horizontal axis may be interchanged. As illustrated in  FIG.  3   , three frequency peaks exist according to the first differential value. That is, when the first differential value is zero, it indicates that the sensor value does not substantially change, and thus the state is a steady state. When the first differential value is positive or negative, it indicates that the time rate of change is positive or negative. 
     Next, a display example of the second differential value distribution is illustrated in  FIG.  4   . 
       FIG.  4    is a graph of the second differential value distribution  40 , and similarly to  FIG.  3   , the horizontal axis represents a frequency, and the vertical axis represents the differential value in the time direction. The second differential value distribution  40  is a histogram of the second differential value in the time direction. Note that the vertical axis and the horizontal axis may be interchanged. Similarly to the first differential value distribution, three frequency peaks exist according to the second differential value. Here, it is assumed that an absolute value of the differential value is larger in the second differential value than in the first differential value. 
     In this case, comparing  FIGS.  3  and  4   , since the differential value in the time direction is a time derivative, it can be said that an absolute value of the time derivative is larger in the second period than in the first period. When the first differential value distribution matches the second differential value distribution, there is no change between the first period and the second period, that is, no drift occurs at the time derivative. However, a user who compares  FIG.  3    with  FIG.  4    can understand that the absolute value of the time derivative is different between the first differential value and the second differential value, and thus a drift regarding the time derivative occurs between the first period and the second period. 
     The drift of the time derivative will be described. For example, it is assumed that a measurement value of a device measured by a sensor changes from 1 to 10 by an operation of an operator. In this case, an amount of change per predetermined time, that is, a rate is different between the case where an operator A changes the measurement value by one step from 1, 2, 3, . . . , 10 and the case where an operator B changes the measurement value from 1 to 10 at once. Therefore, comparing the operations of the operator A and the operator B, it can be said that the time derivative is drifting. Furthermore, regardless of the operator, for example, when closing an open valve installed in the system, if a frictional force, a pressure, and the like around the valve are different between the first period and the second period, the time taken until the valve is closed may be different. In this case, it can be said that the time derivative of a valve opening degree indicating how much the valve is opened is drifting. 
     Note that the first differential value distribution  30  and the second differential value distribution  40  may be displayed as one graph. 
       FIG.  5    illustrates a modification of a display example of the first differential value distribution and the second differential value distribution. 
     As illustrated in  FIG.  5   , by superimposing and displaying the first differential value distribution  30  and the second differential value distribution  40 , it is possible to easily grasp a difference between peaks of differential values. 
     Furthermore, in the above example, a case where the differential step is “1” has been assumed, but it is not limited thereto, and for example, the differential step may be designated by the user. 
     A case where the user designates the differential step will be described with reference to  FIG.  6   . 
       FIG.  6    illustrates an example of a graphical user interface (GUI) for adjusting the differential step. A slider  61  for determining the differential step is set. The user adjusts the differential step, for example, by moving a knob of the slider  61  with a mouse cursor  62  or a finger. The adjusted value is displayed in a text box  63 . 
     Note that the user may directly input a value of the differential step to the text box  63  instead of setting the differential step by the slider  61 . 
     The value input by the user may be given to the first differential unit  105  and the second differential unit  106 , and set as the value of the differential step. 
     Note that the differential step may be determined based on a machine learning model to be applied to the measurement value of the sensor, which determines whether or not an anomaly has occurred in the system by the sensor. Specifically, a time window length may be set to a value smaller than the time window length of input time series data to a trained machine learning model (also referred to as a trained model). For example, when unit time corresponding to the time window length of the machine learning is W, the differential step may be set to a value of “W−1” obtained by subtracting one unit time from “W”, or may be set to a value of 1 or more and less than “W”. By setting the differential step in this manner, the drift of the time derivative can be similarly calculated. 
     Note that, when the differential step is set by the user, a lower limit of the value that can be set as the differential step may be set to 1, and an upper limit may be set to “W−1”. 
     According to the first embodiment described above, the first differential value distribution related to the measurement value of the sensor of interest in the first period and the second differential value distribution related to the measurement value of the sensor of interest in the second period are generated. As a result, the user can easily compare the time derivatives, and it is possible to easily detect that the drift regarding the time derivative has occurred. Further, in a case where the drift related to the time derivative occurs, the user can determine whether or not detection of the system in which the sensor of interest is installed is appropriate. As a result, usability can be improved. 
     Second Embodiment 
     In a second embodiment, in addition to displaying the first differential value distribution and the second differential value distribution, a trend graph of the first differential value and a trend graph of the second differential value are displayed. 
     The trend graph of the differential value is a graph representing a temporal change (temporal transition) of the differential value. 
     The first output unit  119  receives the first differential value set from the first differential unit  105 , and further outputs a trend graph of the first differential value as the first output information. Similarly, the second output unit  120  receives the second differential value set from the second differential unit  106 , and further outputs a trend graph of the second differential value as the second output information. 
       FIGS.  7  and  8    illustrate an example of the trend graph output from the first output unit  119  according to the second embodiment. 
     In  FIG.  7   , a trend graph  70  in the first period is displayed. A vertical axis represents the first differential value, and a horizontal axis represents time. As a result, a change in the first differential value can be grasped along time series. 
     The trend graph  70  and the first differential value distribution  30  may be displayed in different display regions, or as illustrated in  FIG.  8   , the trend graph  70  of the first differential value and the first differential value distribution  30  may be displayed side by side in one display region. When the trend graph  70  and the first differential value distribution  30  are displayed side by side in one display region, it is easier for the user to see by aligning scales of common axes. 
     Next, an example of the trend graph output from the second output unit  120  according to the second embodiment is illustrated in  FIGS.  9  and  10   . 
     In  FIG.  9   , a trend graph  90  in the second period is displayed. A vertical axis represents the second differential value, and a horizontal axis represents time. As a result, a change in the second differential value can be grasped along time series. 
     As illustrated in  FIG.  10   , the trend graph  90  of the second differential value and the second differential value distribution  40  may be displayed side by side. 
     Next,  FIG.  11    illustrates a first modification of a display example of the trend graph. 
     As illustrated in  FIG.  11   , a trend graph  70  of the first differential value and a trend graph  90  of the second differential value may be displayed in one graph. By displaying the two trend graphs in one graph, it is possible to grasp the trend of the first differential value and the second differential value along time series. 
     Next,  FIG.  12    illustrates a second modification of a display example of the trend graph. 
       FIG.  12    is an example in which both the trend graph illustrated in  FIG.  11    and the differential value distribution illustrated in  FIG.  5    are displayed in the same display area. Note that the trend graph illustrated in  FIG.  11    and any one of the graphs in  FIGS.  3  and  4    may be displayed on one screen. 
     According to the second embodiment described above, in addition to displaying the first differential value distribution and the second differential value distribution, the trend graph of the first differential value and the second differential value is generated and output. As a result, it is possible to detect that the drift of the time derivative has occurred, and in addition, it is easy to notice the time when the drift of the time derivative has occurred, so that it is easy to specify the time when the drift has occurred. 
     Third Embodiment 
     In a third embodiment, a score for determining the drift of the time derivative is calculated. 
     A data processing apparatus  100  according to the third embodiment will be described with reference to a block diagram of  FIG.  13   . 
     The data processing apparatus  100  according to the third embodiment illustrated in  FIG.  13    further includes a score calculation unit  1301  and a score output unit  1302  as compared with  FIG.  1   . 
     The score calculation unit  1301  receives the first differential value distribution from a first distribution generation unit  107  and the second differential value distribution from a second distribution generation unit  108 , and calculates a score regarding a distribution difference. As the score, for example, similarity or dissimilarity between the first differential value distribution and the second differential value distribution may be used. As the similarity, for example, a histogram intersection and a cosine similarity may be used. The dissimilarity may be, for example, Kullback-Leibler divergence or Wasserstein distance, or may be a Euclidean distance, a difference between the maximum values, a difference between the minimum values, a difference between average values, a difference between median values, or a weighted sum of these criteria. 
     The score output unit  1302  receives the score from the score calculation unit  1301 , and outputs the score to the outside. If the score output unit  1302  is a display unit, the score is displayed. 
     According to the third embodiment described above, the score of the sensor of interest can be known by calculating the score. In a case where the score is the degree of similarity, a smaller value of the score indicates a lower degree of similarity, so that the user can grasp that there is a high possibility that a drift regarding the time derivative of the sensor of interest has occurred. In a case where the score is the degree of dissimilarity, the greater the value of the score, the greater the degree of dissimilarity, so that the user can grasp that there is a high possibility that a drift regarding the time derivative of the sensor of interest has occurred. 
     Fourth Embodiment 
     In a fourth embodiment, the occurrence of the drift of the time derivative is detected based on the score. 
     A data processing apparatus  100  according to the fourth embodiment will be described with reference to a block diagram of  FIG.  14   . 
     As compared with  FIG.  1   , the data processing apparatus  100  according to the fourth embodiment illustrated in  FIG.  14    further includes a score calculation unit  1301 , a drift detection unit  1401 , and a drift information output unit  1402 . 
     The score calculation unit  1301  is similar to that of the third embodiment. 
     The drift detection unit  1401  receives the score from the score calculation unit  1301 , and detects whether or not the drift of the time derivative has occurred by determining a magnitude between the score and a threshold value. In a case where the score is the similarity, when the score is smaller than the threshold value, it is regarded that the drift of the time derivative has occurred and detected. In a case where the score is the degree of dissimilarity, in a case where the score is larger than the threshold value, it is regarded that the drift of the time derivative has occurred, and detection is performed. The drift detection unit  1401  generates a drift detection signal indicating whether the drift of the time derivative of the sensor of interest has been detected. 
     The drift information output unit  1402  receives the drift detection signal from the drift detection unit  1401 , and outputs drift information regarding detection of the drift of the time derivative of the sensor of interest to the outside of the data processing apparatus  100 . As the drift information, for example, whether or not the drift of the time derivative of the sensor of interest has occurred in a certain display region on a monitor may be displayed as a text. Alternatively, a sound or an alert sound indicating that the drift of the time derivative has occurred may be output. 
     According to the fourth embodiment described above, the drift detection unit detects whether or not the drift of the time derivative has occurred based on the score, whereby the user can know whether or not the drift related to the time derivative of the sensor of interest has occurred. 
     Fifth Embodiment 
     In a fifth embodiment, it is detected whether or not the drift of the time derivative has occurred in a plurality of the sensors. 
     A data processing apparatus  100  according to the fifth embodiment may have the same configuration as the data processing apparatus  100  according to the fourth embodiment. 
     In a case where a plurality of sensors are installed in a certain system, the data processing apparatus  100  may execute the processing according to the fourth embodiment using one of the plurality of sensors as a sensor of interest. When detection processing of a drift of the time derivative for one sensor of interest is completed, in the data processing apparatus  100 , for example, a first acquisition unit  103  or a second acquisition unit  104  sets an unprocessed sensor among the plurality of sensors as a new sensor of interest, and acquires the first measurement data and the second measurement data. Similarly, the detection processing of the drift of the time derivative may be executed. Note that, when acquiring the first measurement data and the second measurement data, the first acquisition unit  103  and the second acquisition unit  104  acquire the first measurement data and the second measurement data in association with ID (also referred to as a sensor ID) for uniquely identifying the sensor. 
     A drift detection unit  1401  may send the drift detection signal related to the drift of the time derivative calculated for the sensor of interest to a drift information output unit  1402  each time the drift detection signal is generated, or may calculate the drift detection signals for all the plurality of sensors and then collectively send the plurality of drift detection signals to the drift information output unit  1402 . 
     The drift information output unit  1402  receives the drift detection signal calculated for each sensor from the drift detection unit  1401 , generates a list of sensors in which the drift of the time derivative is detected, and outputs the list to the outside as drift information. 
     Note that, as the drift information, the number of sensors in which the drift of the time derivative is detected may be output. The drift information output unit  1402  may count the number of sensors in which the drift of the time derivative is detected based on the drift detection signal, and output the number of the sensors to the outside. 
     According to the fifth embodiment described above, the drift information output unit outputs at least one of the list of the sensors in which the drift of the time derivative has occurred and the number of the sensors among the plurality of sensors. As a result, the user can easily grasp the sensor in which the drift of the time derivative is detected and the number of the sensors. 
     Sixth Embodiment 
     In a sixth embodiment, a maximum value, a minimum value, an average value, and a median value of the measurement data in the first period and the second period may be displayed on the graph of the first differential value distribution and the second differential value distribution. In order to simplify the description, an example of displaying the maximum value and the minimum value among the maximum value, the minimum value, the average value, and the median value will be described below. 
     A configuration of a data processing apparatus  100  according to the sixth embodiment is similar to that of the above-described embodiments. 
     A first differential unit  105  calculates the maximum value and the minimum value of the first measurement data. 
     A first output unit  119  receives the maximum value and the minimum value from the first differential unit  105 , and outputs the first differential value distribution, and the maximum value and the minimum value as first output information. As a result, the display unit of an output destination or the like can visualize the first differential value distribution while superimposing the maximum value and the minimum value of the first differential value on the first differential value distribution. 
     Similarly, a second differential unit  106  calculates the maximum value and the minimum value of the second measurement data. 
     A second output unit  120  receives the maximum value and the minimum value from the second differential unit  106 , and outputs the second differential value distribution, and the maximum value and the minimum value as second output information. As a result, the display unit of the output destination or the like can visualize the second differential value distribution while superimposing the maximum value and the minimum value of the second differential value on the second differential value distribution. 
     Note that the first differential unit  105  and the second differential unit  106  are not limited to calculating the maximum value and the minimum value, respectively. For example, the first output unit  119  may receive the first measurement data from the first differential unit  105 , and calculate the maximum value and the minimum value of the first measurement data. Similarly, the second output unit  120  may receive the second measurement data from the second differential unit  106 , and calculate the maximum value and the minimum value of the second measurement data. 
     Next, a first display example of the first output information according to the sixth embodiment is illustrated in  FIG.  15   . 
       FIG.  15    illustrates an example in which a maximum value  1501  and a minimum value  1502  of the first measurement data are indicated by broken lines in the first differential value distribution  30  illustrated in  FIG.  3   . 
     Since the maximum value and the minimum value of the measurement data are important in confirming the drift of the time derivative, it is possible to make it easy for the user to visually recognize the maximum value and the minimum value. 
     Note that the maximum value and the minimum value of the second measurement data may be displayed in the first differential value distribution. 
     A second display example of the first output information according to the sixth embodiment is illustrated in  FIG.  16   . 
       FIG.  16    illustrates an example in which a maximum value  1601  and a minimum value  1602  of the second measurement data are displayed by solid lines in the first differential value distribution  30  illustrated in  FIG.  3   . As in the case of  FIG.  15   , it is possible to allow the user to easily visually recognize the maximum value and the minimum value. 
     In this case, the first output unit  119  may acquire the maximum value and the minimum value of the second measurement data from the second differential unit  106 . Alternatively, the second measurement data may be received from the second differential unit  106 , and the first output unit  119  may calculate the maximum value and the minimum value of the second measurement data. 
     Next, a first display example of the second output information according to the sixth embodiment is illustrated in  FIG.  17   . 
       FIG.  17    illustrates an example in which a maximum value  1601  and a minimum value  1602  of the second measurement data are displayed by solid lines in the second differential value distribution  40  illustrated in  FIG.  4   . 
     Note that the maximum value and the minimum value of the first measurement data may be displayed in the second differential value distribution. 
     A second display example of the second output information according to the sixth embodiment is illustrated in  FIG.  18   . 
       FIG.  18    illustrates an example in which a maximum value  1501  and a minimum value  1502  of the first measurement data are indicated by broken lines in the second differential value distribution  40  illustrated in  FIG.  4   . As in the case of  FIG.  17   , it is possible to allow the user to easily visually recognize the maximum value and the minimum value. 
     In this case, the second output unit  120  may acquire the maximum value and the minimum value of the first measurement data from the first differential unit  105 . Alternatively, the first measurement data may be received from the first differential unit  105 , and the second output unit  120  may calculate the maximum value and the minimum value of the first measurement data. 
     Next, a third display example of the first output information and the second output information according to the sixth embodiment is illustrated in  FIG.  19   . 
       FIG.  19    is a graph in which a first differential value distribution  30 , a second differential value distribution  40 , a maximum value  1501  and a minimum value  1502  of the first measurement data, and a maximum value  1601  and a minimum value  1602  of the second measurement data are displayed in a superimposed manner. 
     For example, if the drift of the time derivative does not occur, it is assumed that the maximum value  1501  and the maximum value  1601  are close to each other, but since the maximum value  1501  and the maximum value  1601  are separated as illustrated in  FIG.  19   , it is possible to grasp a possibility that the drift of the time derivative occurs. Of course, in the comparison between the minimum value  1502  and the minimum value  1602 , it is possible to similarly grasp a possibility that the drift of the time derivative occurs. 
     According to the sixth embodiment described above, the maximum value and the minimum value of the measurement data that cannot be confirmed only by the histogram or the probability density function of the differential value distribution are calculated and superimposed and displayed on the graph, so that the user can easily confirm the maximum value and the minimum value. 
     Seventh Embodiment 
     In a seventh embodiment, a scatter diagram is created and output based on the differential value. 
     A data processing apparatus according to the seventh embodiment will be described with reference to  FIG.  20   . 
     As compared with  FIG.  1   , a data processing apparatus  100  according to the seventh embodiment illustrated in  FIG.  20    further includes a scatter diagram creation unit  2001  and a scatter diagram output unit  2002 . 
     The scatter diagram creation unit  2001  receives the first measurement data from a first acquisition unit  103  and the second measurement data from a second acquisition unit  104 , and creates scatter diagram data of the first measurement data and the second measurement data. 
     The scatter diagram output unit  2002  outputs scatter diagram data from the scatter diagram creation unit  2001  to the outside. 
     Next, a first display example of the scatter diagram data created by the scatter diagram creation unit according to the seventh embodiment will be described with reference to  FIG.  21   . 
     In a scatter diagram illustrated in  FIG.  21   , a vertical axis represents the measurement value at a time of interest, and a horizontal axis represents the measurement value at a time that is s unit time before the time of interest. 
     A time of interest is set from among a plurality of times corresponding to measurement values included in measurement data, and a time of a combination of a measurement value at the time of interest and a measurement value at a time that is s unit time before the time of interest is plotted. In the example of  FIG.  21   , black circles are plots relating to the first measurement data, and black triangles are plots relating to the second measurement data. Note that the plots of the first measurement data and the plots of the second measurement data are not limited to the black circle and the black triangle, and the plots of the first measurement data and the plots of the second measurement data may be displayed in any display mode as long as the plots of the first measurement data and the plots of the second measurement data are displayed in different display modes and can be distinguished from each other. 
     A region  2101  indicates that the measurement value at the time of interest of the measurement data and the measurement value before the s unit time are close to each other, and indicates a steady state. In other words, the value obtained by differentiating the measured value in the time direction in the differential step s is close to zero, indicating a steady state in which the time derivative is close to zero, that is, no drift of the time derivative occurs. 
     On the other hand, in a region  2102 , it is indicated that the measured value at the time of interest of the measurement data is larger than the measured value before the s unit time, and it is indicated that the measured value is in a transient state of increasing with time. In other words, it represents a transient state in which the value obtained by differentiating the measured value in the time direction in the differential step s is positive and the time derivative is positive. 
     Further, in an area  2103 , it is indicated that the measured value at the time of interest of the measurement data is smaller than the measured value before the s unit time, and it is indicated that the measured value is in a transient state of decreasing with time. In other words, it represents a transient state in which the value obtained by differentiating the measured value in the time direction in the differential step s is negative and the time derivative is negative. By referring to the scatter diagram illustrated in  FIG.  21   , it can be grasped from the scatter diagram that the drift of the time derivative occurs. 
     Next, a second display example of scatter diagram data according to the seventh embodiment is illustrated in  FIG.  22   . 
       FIG.  22    is an example in which the scatter diagram illustrated in  FIG.  21    and the differential value distribution illustrated in  FIG.  5    are displayed side by side. 
     A correspondence relationship is illustrated so as to connect corresponding data groups between the plot of the scatter diagram and the histogram of the differential value distribution. 
     Note that in  FIGS.  21  and  22   , a vertical axis and a horizontal axis of the scatter diagram may be interchanged. Further, the horizontal axes of the scatter diagrams in  FIGS.  21  and  22    indicate the measurement value corresponding to the time that is s unit time before the time of interest, but the measurement value corresponding to the time that is s unit time after the time of interest may be used. 
     According to the seventh embodiment described above, the user can grasp the drift of the time derivative from both the scatter diagram and the histogram. 
     Eighth Embodiment 
     In an eighth embodiment, a case where values of one or more sensors installed in a system are monitored by a machine learning model will be described. 
     If the first period is a period of training data of the machine learning model, and the second period is a period after the first period, a data processing apparatus  100  can monitor the number of sensors in which the drift of the time derivative is detected among the one or more sensors to be monitored in the period of the training data and the period after the period of the training data. 
     Further, by shifting the second period in the latest time direction and acquiring the second measurement data in a second acquisition unit  104 , it is also possible to monitor a change in the number of sensors in which the drift regarding the time derivative is detected. 
     Here, an example of a graph representing a change in the number of sensors in which the drift of the time derivative is detected is illustrated in  FIG.  23   . 
     In the graph illustrated in  FIG.  23   , a horizontal axis represents time, and a vertical axis represents the number of sensors in which the drift of the time derivative is detected. A drift information output unit  1402  may generate, as the drift information, information regarding the time series change in the number of sensors in which the drift of the time derivative is detected, and output the information as a graph illustrated in  FIG.  23    or as a list. 
     Further, a threshold value  2301  of the predetermined number of sensors is set, and in a case where the number of sensors is larger than or equal to the threshold value  2301  in the time series change in the number of sensors, the drift information output unit  1402  may output information prompting update of the machine learning model. This is because the generated machine learning model can be determined to be a model not suitable for the current sensor value in a case where the number of sensors in which the drift of the time derivative occurs is larger than or equal to the threshold value. 
     That is, the user can determine to update the trained model when the number of sensors in which the drift regarding the time derivative is detected exceeds the predetermined value. 
     Note that, if the period during which the number of sensors in which the drift has occurred exceeds the threshold value  2301  is less than a predetermined period, it may be determined that the trained model is not updated. For example, if the period during which the number of sensors in which the drift has occurred exceeds the threshold value  2301  is less than a predetermined period  2302 , it is conceivable that the sensor value has temporarily fluctuated due to a defect of a product or the like. Therefore, the drift information output unit  1402  may not output information prompting update of the trained model. 
     According to the eighth embodiment described above, it is possible to determine the necessity of updating the trained model in a case where the trained model based on the values of the plurality of sensors is designed by detecting whether or not the drift of the time derivative occurs for the plurality of sensors. 
     Ninth Embodiment 
     In a ninth embodiment, for example, a prediction value regarding a measurement value of a sensor is calculated using a machine learning model. 
     A data processing apparatus  100  according to the ninth embodiment will be described with reference to a block diagram of  FIG.  24   . 
     As compared with  FIG.  1   , the data processing apparatus  100  according to the ninth embodiment illustrated in  FIG.  24    further includes a third acquisition unit  2401 , a model acquisition unit  2402 , a predicted value generation unit  2403 , and a third output unit  2404 . 
     The third acquisition unit  2401  acquires time series data including measurement values at a plurality of times of one or more sensors installed in a system. 
     The model acquisition unit  2402  acquires a machine learning model trained with training data whose data period is the first period. The machine learning model is, for example, a model or a regression model of a neural network including an auto encoder model. Machine learning models for monitoring a system often determine periods of training data excluding periods of anomaly state by the system. In a case where the period of the training data does not include a period in which the system is anomaly, when time series data including measurement values of a plurality of times of the one or more sensors when the system is in a normal state is input to the machine learning model, a value close to the measurement value of the time of interest of the one or more sensors when the system is in a normal state is output from the trained model as a predicted value. 
     Further, when time series data including measurement values of one or more sensors at a plurality of times when the system is in an anomaly state is input to the machine learning model, it is expected that a value substantially different from a measurement value of a time of interest of one or more sensors when the system is in an anomaly state is output as a predicted value from the trained model. 
     The predicted value generation unit  2403  receives time series data from the third acquisition unit  2401  and a machine learning model from the model acquisition unit  2402 . The predicted value generation unit  2403  generates a predicted value of the one or more sensors installed in the system by inputting the time series data to the machine learning model. 
     The third output unit  2404  outputs third output information related to the predicted value and the measurement value to the outside. The third output information is, for example, information indicating a trend graph of the measurement value and the predicted value regarding the one or more sensors. 
     Next, a display example regarding the third output information according to the ninth embodiment will be described with reference to  FIGS.  25  and  26   . 
       FIG.  25    is an example of a trend graph of the measurement value and the predicted value for a certain sensor of interest. In the graph illustrated in  FIG.  25   , a horizontal axis represents time and a vertical axis represents a value. A dashed line indicates a predicted value  2501  and a solid line indicates a measurement value  2502 . 
       FIG.  26    is an example of a graph in which the period of the training data and the trend graph of a period C in  FIG.  25    are displayed in a superimposed manner for the measurement value of the sensor of interest. A horizontal axis represents relative time, and a vertical axis represents a value. A dashed line indicates a measurement value  2601  for the period of the training data, i.e., the first period, and a solid line indicates a measurement value  2602  for the period C. 
     Referring to  FIGS.  25  and  26   , it can be seen that the sensor of interest takes a value around a value “A” or “B” in the steady state, and takes a value between the value “A” and the value “B” in the transient state. From  FIG.  26   , it can be seen that the time derivative of the measurement value in the transient state is faster in the period C than in the period of the training data, that is, the first period. Since the machine learning model has trained that the time derivative of the measurement value of the sensor of interest is similar to that of the training data, the time derivative of the predicted value of the period C tends to be similar to that of the training data. Therefore, a curve of the predicted value  2501  in the period C illustrated in  FIG.  25    has a shape delayed as compared with a curve of the measurement value  2502 . In a case where an absolute value of the difference between the predicted value  2501  and the measurement value  2502  is larger than the threshold value, it is considered that the anomaly is easily detected in the transient state when the anomaly is detected as the anomaly (or the anomaly candidate). 
     Note that the sensor of interest may be displayed via a GUI that can be switched to a measurement value of another sensor. 
     By displaying  FIG.  25    together with  FIGS.  3  and  4    or by displaying  FIG.  25    together with  FIG.  5   , it can be easily grasped that the reason why the time derivative of the measurement value  2502  is faster than the predicted value  2501  is the drift of the time derivative. If the drift in the time derivative is not anomaly, the user can be aware that the deviation between the predicted value  2501  and the measurement value  2502  in the transient state is a false detection and the system is not anomaly. 
     According to the ninth embodiment described above, for example, by displaying the first and second differential value distributions in addition to the trend graph comparing the measurement value and the predicted value in the first period, the user can grasp that the deviation of the transient state of the trend graph is caused by the drift of the time derivative. As a result, since the user can notice the cause without stopping the system and investigating the cause, it is possible to avoid a loss of cost and time due to the system stop. 
     Tenth Embodiment 
     In a tenth embodiment, for example, a predicted value regarding a measurement value of a sensor is calculated using a machine learning model. 
     A data processing apparatus  100  according to the tenth embodiment will be described with reference to a block diagram of  FIG.  27   . 
     The data processing apparatus  100  according to the tenth embodiment illustrated in  FIG.  27    further includes an anomaly detection unit  2701  as compared with  FIG.  24   . 
     The anomaly detection unit  2701  receives the time series data of the sensor of interest from a third acquisition unit  2401  and the predicted value from a predicted value generation unit  2403 , and generates a detection signal that detects whether or not an absolute value of a difference between the predicted value and the measurement value at each time is larger than a threshold value. When an absolute value of the difference is larger than the threshold value, it is determined that there is an anomaly or an anomaly candidate. The detection signal is transmitted to a first acquisition unit  103 , a second acquisition unit  104 , and the third acquisition unit  2401 . 
     Next, a display example of the detection signal according to the tenth embodiment is illustrated in  FIG.  28   . 
     In a graph illustrated in  FIG.  28   , a horizontal axis represents time and a vertical axis represents a value of the detection signal. For example, when a value of the detection signal is zero, it indicates that it has not been detected as an anomaly or an anomaly candidate, and when the value is not zero, it indicates that it has been detected as an anomaly or an anomaly candidate. 
     Here, the first acquisition unit  103  and the second acquisition unit  104  may receive an anomaly signal from the anomaly detection unit  2701 , identify a sensor detected to be anomaly or an anomaly candidate, and set the sensor as a sensor of interest that acquires the first measurement data and the second measurement data. 
     Note that by matching the period of the training data of the machine learning model acquired by a model acquisition unit  2402  with the first period, the first output information can correspond to the period of the training data of the machine learning model. Similarly, by matching the period in which the predicted value is generated by a predicted value generation unit  2403  with the second period, the second output information can correspond to the period in which the predicted value is generated. Note that, in a case where the period for generating the predicted value of the sensor of interest is the second period, the second period is a period of the training data, that is, a period after the first period in the time direction. 
     According to the tenth embodiment described above, an anomaly or an anomaly candidate is detected by comparing the measurement value of the sensor of interest with the predicted value of the machine learning model, and the measurement value of the sensor is made to correspond to the first period corresponding to the period of the training data and the second period corresponding to the period in which the predicted value is generated. This makes it easier for the user to grasp, from the first and second differential value distributions, whether or not the time derivative of the measurement value of the sensor in which the anomaly or the anomaly candidate is detected has drifted between the period of the training data and the period in which the predicted value is generated. 
     Here, an example of a hardware configuration of the data processing apparatus  100  according to the above-described embodiments is illustrated in a block diagram of  FIG.  29   . 
     The data processing apparatus  100  includes a central processing unit (CPU)  2901 , a random access memory (RAM)  2902 , a read only memory (ROM)  2903 , a storage  2904 , a display device  2905 , an input device  2906 , and a communication device  2907 , which are each connected by a bus. 
     The CPU  2901  is a processor that executes arithmetic processing, control processing, and the like according to a program. The CPU  2901  uses a predetermined area of the RAM  2902  as a work area, and executes processing of each unit of the data processing apparatus  100  described above in cooperation with programs stored in the ROM  2903 , the storage  2904 , and the like. 
     The RAM  2902  is a memory such as a synchronous dynamic random access memory (SDRAM). The RAM  2902  functions as a work area of the CPU  2901 . The ROM  2903  is a memory that stores programs and various types of information in a non-rewritable manner. 
     The storage  2904  is an apparatus that writes and reads data in and from a magnetic recording medium such as a hard disc drive (HDD), a semiconductor storage medium such as a flash memory, an optically recordable storage medium, or the like. The storage  2904  writes and reads data to and from the storage medium under the control of the CPU  2901 . 
     The display device  2905  is a display device such as a liquid crystal display (LCD). The display device  2905  displays various types of information based on a display signal from the CPU  2901 . 
     The input device  2906  is an input device such as a mouse and a keyboard. The input device  2906  receives information input by operation from the user as an instruction signal, and outputs the instruction signal to the CPU  2901 . 
     The communication device  2907  communicates with an external device via a network in accordance with the control from the CPU  2901 . 
     The instruction illustrated in the processing procedure illustrated in the above-described embodiments can be executed based on a program that is software. By storing this program in advance and reading this program, a general-purpose computer system can obtain an effect similar to the effect of the control operation of the data processing apparatus described above. The instructions described in the above-described embodiments are recorded in a magnetic disk (flexible disk, hard disk, etc.), an optical disk (CD-ROM, CD-R, CD-RW, DVD-ROM, DVD±R, DVD±RW, Blu-ray (registered trademark) Disc, and the like), a semiconductor memory, or a recording medium similar thereto as a program that can be executed by a computer. A storage format may be any form as long as it is a recording medium readable by a computer or an embedded system. When the computer reads a program from the recording medium and causes the CPU to execute instructions described in the program based on the program, it is possible to realize an operation similar to the control of the data processing apparatus of the above-described embodiment. Of course, when the computer acquires or reads the program, the program may be acquired or read through a network. 
     Further, an operating system (OS) running on a computer, database management software, middleware (MW) such as a network, or the like based on an instruction of a program installed from a recording medium to the computer or an embedded system may execute a part of each processing for realizing the present embodiments. 
     Furthermore, the recording medium in the present embodiments is not limited to a medium independent of a computer or an embedded system, and includes a recording medium that downloads and stores or temporarily stores a program transmitted via a LAN, the Internet, or the like. 
     Further, the number of recording media is not limited to one, and a case where the processing in the present embodiments is executed from a plurality of media is also included in the recording media in the present embodiments, and the configuration of the media may be any configuration. 
     Note that the computer or the embedded system in the present embodiments is for executing each processing in the present embodiments based on a program stored in a recording medium, and may have any configuration such as an apparatus including one such as a personal computer or a microcomputer, or a system in which a plurality of apparatuses are connected to a network. 
     Further, the computer in the present embodiments is not limited to a personal computer, and includes an arithmetic processing apparatus, a microcomputer, and the like included in an information processing device, and collectively refers to a device and an apparatus capable of realizing a function in the present embodiments by a program. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.