Estimation method, control method, and apparatus

Abstract

To provide an estimation method control method and apparatus that improve the accuracy of estimated values output from a learning model.SOLUTION: A learning processing method comprises: calculating a plurality of types of statistics φ1 to φ5 for a predetermined number of continuous input value groups Vs included in time series data V(t); and inputting the plurality of types of statistics φ1 to φ5 to the learning model M created by machine learning so as to output the estimated value Ve from the learning model M. The plurality of types of statistics include at least the first statistic φ1 indicating the kurtosis of the input value groups Vs, and the second statistic φ2 indicating the skewness of the input value groups Vs. Thereby, the accuracy of the estimated value Ve output from the learning model M is improved compared to the case where the input value V itself of the time series data V(t) is used as an explanatory variable.SELECTED DRAWING: Figure 6

Description

Technical Field

[0001] The present invention relates to an estimation method for outputting an estimated value based on time-series data of input values, a control method for controlling the operation of a device, and a device.

Background Art

[0002] Conventionally, industrial devices such as printing devices, semiconductor manufacturing devices, and display manufacturing devices always measure the state of the device by sensors provided in the device. In recent years, in order to accurately control the device, it has been proposed to use machine learning. Conventional techniques for controlling a device using machine learning are described in, for example, Patent Document 1.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In this type of device, measurement values are output from the sensor at very short time intervals. When using machine learning, such measurement values, which are time-series data, are input into the learning model as explanatory variables, and a desired estimated value is output from the learning model. At that time, in order to improve the estimation accuracy by the learning model, the measurement values of the sensor are subjected to processing such as normalization and noise removal, and then input into the learning model. However, even when such processing is performed, there are cases where accurate estimated values cannot be obtained from the learning model.

[0005] The present invention has been made in view of such circumstances, and an object thereof is to provide a technique capable of improving the accuracy of the estimated value output from the learning model.

Means for Solving the Problems

[0006] To solve the above problems, the first invention of this application is: In a printing apparatus that transports a long, strip-shaped substrate while printing on the surface of the substrate, An estimation method for outputting estimated values ​​based on time-series data of input values, comprising: a) a step of calculating multiple types of statistics for a predetermined number of consecutive input values ​​included in the time-series data; and b) a step of inputting the multiple types of statistics into a learning model created by machine learning and outputting estimated values ​​from the learning model. The computer executes Furthermore, the multiple types of statistics include at least the kurtosis of the input value group and the skewness of the input value group. The input value is a value based on the measurement value of a sensor that measures the tension applied to the substrate in the transport direction, and the estimated value is an estimated value of the input value after a predetermined time from the reference measurement time of the input value group. .

[0007] The second invention of this application is the estimation method of the first invention, wherein the plurality of types of statistics further include the mean value of the input value group.

[0008] The third invention of this application is an estimation method of the first or second invention, wherein the plurality of types of statistics further include the standard deviation of the input value group.

[0009] The fourth invention of this application is a method for estimating any one of the first to third inventions, wherein the plurality of types of statistics further include the integral value of the input value group.

[0010] The fifth invention of this application is a method for estimating any one of the first to fourth inventions, wherein in step b), the input value and the multiple types of statistics are input to the learning model.

[0012] This application 6 The invention is, printing A control method for controlling the operation of a device, wherein x) the printing A step of accumulating the time-series data of the input values ​​based on the measured values ​​of the sensors that the device has, and y) based on the time-series data, First Invention The estimation method involves the steps of outputting the estimated value and z) based on the estimated value, printing A process for controlling the operation of the device, The computer executes do.

[0013] This application 7 The invention is, A printing apparatus that prints on the surface of a substrate while conveying a long, strip-shaped substrate, wherein the tension applied to the substrate in the conveying direction A sensor that measures, a data storage unit that stores time-series data of input values ​​based on the measured values ​​output from the sensor, an estimation unit that calculates multiple types of statistics for a predetermined number of consecutive input value groups included in the time-series data, inputs the calculated multiple types of statistics into a learning model created by machine learning, and outputs estimated values ​​from the learning model, and based on the estimated values, printing The device comprises an operation control unit that controls the operation of the device, wherein the plurality of statistical quantities include at least the kurtosis of the input value group and the skewness of the input value group. Furthermore, the estimated value is an estimated value of the input value after a predetermined time from the reference measurement time of the input value group. . [Effects of the Invention]

[0014] The first invention of this application to the first invention 6 According to the invention, statistical quantities including kurtosis and skewness are input to the learning model as explanatory variables. This improves the accuracy of the estimates output by the learning model compared to when the input values ​​of the time series data themselves are used as explanatory variables.

[0015] In particular, according to the second invention of this application, statistics including kurtosis, skewness, and mean are input to the learning model as explanatory variables. This makes it possible to further improve the accuracy of the estimates output from the learning model.

[0016] In particular, according to the third invention of this application, statistics including kurtosis, skewness, and standard deviation are input to the learning model as explanatory variables. This makes it possible to further improve the accuracy of the estimates output from the learning model.

[0017] In particular, according to the fourth invention of this application, statistical quantities including kurtosis, skewness, and integral values ​​are input to the learning model as explanatory variables. This makes it possible to further improve the accuracy of the estimates output from the learning model.

[0018] In particular, the first of the present application 6 According to the invention, input values ​​after a predetermined time can be accurately estimated, and the operation of the device can be accurately controlled based on the obtained estimated values.

[0019] Further, according to the invention of the present application, a statistic including kurtosis and skewness is input into the learning model as an explanatory variable. Thereby, the accuracy of the estimated value output from the learning model can be improved compared to the case where the input value itself of the time series data is used as the explanatory variable. Therefore, based on the obtained estimated value, the operation of the device can be accurately controlled. 7

Brief Description of the Drawings

[0020] [Figure 1] It is a diagram showing the configuration of a printing device. [Figure 2] It is a partial top view of the printing device near the printing unit. [Figure 3] It is a block diagram showing the connection between a computer and each part of the printing device. [Figure 4] It is a block diagram conceptually showing the functions of a computer. [Figure 5] It is a flowchart showing the flow of learning processing. [Figure 6] It is a graph showing an example of time series data stored in the data storage unit. [Figure 7] It is a flowchart showing the flow of printing processing. [Figure 8] It is the result of a demonstration experiment showing that the estimation accuracy is improved [Figure 9] It is the result of a demonstration experiment showing that the estimation accuracy is improved

Embodiments for Carrying Out the Invention

[0021] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0022] <1. Configuration of the Printing Device> Figure 1 shows the configuration of a printing apparatus 1, which is an example of the "apparatus" according to the present invention. This printing apparatus 1 is a device that prints an image on the surface of a substrate 9 by transporting a long, strip-shaped substrate 9 and ejecting ink droplets from a plurality of heads 21 to 24 toward the substrate 9. The substrate 9 may be printing paper, or a resin film. The substrate 9 may also be a metal foil or a glass substrate. As shown in Figure 1, the printing apparatus 1 includes a transport mechanism 10, a printing unit 20, a tension sensor 30, and a computer 40.

[0023] The conveying mechanism 10 is a mechanism for conveying the base material 9 in a conveying direction along its longitudinal direction. The conveying mechanism 10 of this embodiment has an unwinding section 11, a plurality of conveying rollers 12, and a winding section 13. The base material 9 is unwound from the unwinding section 11 and conveyed along a conveying path formed by the plurality of conveying rollers 12. Each conveying roller 12 rotates about an axis extending in a direction perpendicular to the conveying direction, thereby guiding the base material 9 to the downstream side of the conveying path. The base material 9 is stretched over the plurality of conveying rollers 12 under tension. This suppresses sagging and wrinkling of the base material 9 during conveying. After conveying, the base material 9 is collected in the winding section 13.

[0024] The transport mechanism 10 has a motor (not shown) that rotates some of the rollers (hereinafter referred to as "drive rollers"). The drive rollers are arranged at multiple locations along the transport path. When the printing device 1 is in operation, the multiple drive rollers rotate due to the drive of the motor. This transports the substrate 9 from the unwinding section 11 to the winding section 13. The transport mechanism 10 can also adjust the tension applied to the substrate 9 by adjusting the rotation speed of the multiple drive rollers.

[0025] The printing unit 20 is a processing unit that ejects ink droplets (hereinafter referred to as "ink droplets") onto the substrate 9 transported by the transport mechanism 10. The printing unit 20 in this embodiment has a first head 21, a second head 22, a third head 23, and a fourth head 24. The first head 21, the second head 22, the third head 23, and the fourth head 24 are arranged at intervals along the transport direction of the substrate 9. The substrate 9 is transported below the four heads 21 to 24 with the printing surface facing upward.

[0026] Figure 2 is a partial top view of the printing apparatus 1 near the printing section 20. As shown by the dashed lines in Figure 2, multiple nozzles 201 are provided on the underside of each head 21-24, arranged parallel to the width direction of the substrate 9. Each head 21-24 ejects ink droplets of the respective colors C (cyan), M (magenta), Y (yellow), and K (black), which are the color components of a multicolor image, from the multiple nozzles 201 toward the upper surface of the substrate 9.

[0027] Specifically, the first head 21 ejects a droplet of C-colored ink onto the upper surface of the substrate 9 at the first printing position P1 on the transport path. The second head 22 ejects a droplet of M-colored ink onto the upper surface of the substrate 9 at the second printing position P2, which is downstream of the first printing position P1. The third head 23 ejects a droplet of Y-colored ink onto the upper surface of the substrate 9 at the third printing position P3, which is downstream of the second printing position P2. The fourth head 24 ejects a droplet of K-colored ink onto the upper surface of the substrate 9 at the fourth printing position P4, which is downstream of the third printing position P3.

[0028] Furthermore, a drying section may be provided downstream of the heads 21-24 in the transport direction to dry the ink discharged onto the printed surface of the substrate 9. The drying section dries the ink by, for example, blowing heated gas toward the substrate 9 to vaporize the solvent in the ink adhering to the substrate 9. However, the drying section may also cure or dry the ink by other methods such as light irradiation.

[0029] The tension sensor 30 is a measuring instrument that measures the tension applied to the substrate 9 in the conveying direction. The tension sensor 30 has load cells connected to the rotation axes of some of the conveying rollers 12. The load cells measure the load applied to the rotation axes of the conveying rollers 12. The tension sensor 30 calculates the tension applied to the substrate 9 based on the load measured by the load cells. While the substrate 9 is being conveyed by the conveying mechanism 10, the tension sensor 30 constantly measures the current tension of the substrate 9. The tension sensor 30 then outputs a signal indicating the obtained measurement value to the computer 40.

[0030] Computer 40 is an information processing device for controlling the printing device 1. Figure 3 is a block diagram showing the connections between computer 40 and the various parts of the printing device 1. As conceptually shown in Figure 3, computer 40 has a processor 401 such as a CPU, memory 402 such as RAM, and storage unit 403 such as a hard disk drive. The storage unit 403 stores a computer program P for executing the learning process and printing process described later.

[0031] Furthermore, as shown in Figure 3, the computer 40 is communicated with the transport mechanism 10, the four heads 21-24, and the tension sensor 30. The computer 40 controls the operation of each of these parts based on the computer program P and various data. This allows the transport and printing process of the substrate 9 to proceed.

[0032] <2. About computer functions> In this printing apparatus 1, four heads 21-24 eject ink droplets to print a single-color image on the upper surface of the substrate 9. A multi-color image is then formed on the upper surface of the substrate 9 by superimposing the four single-color images. Therefore, if the positions of the ink droplets ejected from the four heads 21-24 on the substrate 9 are misaligned, the image quality of the printed material will deteriorate. Such misalignment of single-color images is called "registration error." Misregistration can occur due to various factors, but one of the main factors is fluctuations in the tension applied to the substrate 9.

[0033] Therefore, the computer 40 of this printing apparatus 1 has a function to estimate the tension on the substrate 9 after a predetermined time in order to suppress the above-mentioned misregistration, and to control the operation of the transport mechanism 10 based on the estimated value.

[0034] Figure 4 is a block diagram conceptually illustrating the function of the computer 40. As shown in Figure 4, the computer 40 has a data storage unit 41, a learning unit 42, an estimation unit 43, and an operation control unit 44. The functions of the data storage unit 41, the learning unit 42, the estimation unit 43, and the operation control unit 44 are realized by the computer 40 operating according to the computer program P.

[0035] The data storage unit 41 is a processing unit for storing time-series data V(t) based on the measured values ​​output from the tension sensor 30. The tension sensor 30 outputs measured tension values ​​at minute time intervals (for example, 0.5 millisecond intervals). The computer 40 processes the measured values ​​output from the tension sensor 30, such as normalization and noise reduction. The processed measured values ​​are then used as input values ​​V. The input values ​​V are used as explanatory variables for the learning model M, which will be described later. The computer 40 stores the input values ​​V obtained sequentially, along with the measurement time t, in the data storage unit 41. Therefore, the data stored in the data storage unit 41 is time-series data V(t) of the input values ​​V.

[0036] The learning unit 42 is a processing unit that creates a learning model M for estimating the input value V after a predetermined time Δt, based on the statistical quantities φ1 to φ5 of the input value V. The learning unit 42 creates the learning model M using a machine learning algorithm based on the time series data V(t) accumulated as training data. Examples of machine learning algorithms that can be used include generalized linear models, deep learning, decision trees, random forests, gradient boosting decision trees, and support vector machines. However, the machine learning algorithms used in the learning unit 42 are not limited to these algorithms. The detailed procedure of the learning process and the details of the statistical quantities φ1 to φ5 will be described later.

[0037] The estimation unit 43 is a processing unit that uses a learning model M created by the learning unit 42 to estimate the input value V after a predetermined time Δt. When printing is performed on the substrate 9, the estimation unit 43 sequentially reads the time-series data V(t) stored in the data storage unit 41. The estimation unit 43 then calculates statistical quantities φ1 to φ5 of a predetermined number of consecutive input value groups included in the time-series data V(t), and inputs the calculated statistical quantities φ1 to φ5 to the learning model M. The learning model M then outputs an estimated value Ve of the input value V after the predetermined time. The estimation unit 43 outputs this estimated value Ve to the operation control unit 44.

[0038] The motion control unit 44 is a processing unit for controlling the operation of the transport mechanism 10 and the four heads 21-24. The motion control unit 44 calculates a control value by performing feedback control based on the estimated value Ve obtained from the estimation unit 43 and a preset target value Vt. The motion control unit 44 then outputs a control signal C, which includes the calculated control value, to the motor of the transport mechanism 10. This controls the motor of the transport mechanism 10. The motion control unit 44 also controls the operation of the four heads 21-24 based on the image data to be printed. As a result, ink is ejected from the four heads 21-24.

[0039] <3. About the learning process> Next, the learning process performed by the learning unit 42 described above will be explained in detail. Figure 5 is a flowchart showing the flow of the learning process. This learning process is performed in advance before printing is performed on the substrate 9 as a product.

[0040] As shown in Figure 5, when performing the learning process, first the transport mechanism 10 is operated to transport the substrate 9 while accumulating the data necessary for learning (step S11). Here, the computer 40 performs processing such as normalization and noise reduction on the measured values ​​output from the tension sensor 30. This converts the measured values ​​into input values ​​V suitable for learning. The computer 40 then stores these input values ​​V, along with the measurement time t, in the data storage unit 41. This accumulates time-series data V(t) of the input values ​​V.

[0041] Figure 6 is a graph showing an example of time-series data V(t) stored in the data storage unit 41. The horizontal axis in Figure 6 represents the measurement time t. The vertical axis in Figure 6 represents the input value V. As shown in Figure 6, the time-series data V(t) is data in which the input value V changes as time t progresses.

[0042] Once the necessary amount of time-series data V(t) for learning has been accumulated, the learning unit 42 then reads the time-series data V(t) from the data storage unit 41. The learning unit 42 then prepares a large number of training data based on the time-series data V(t) it has read (step S12).

[0043] Specifically, the learning unit 42 first calculates multiple types of statistics φ1 to φ5 for a predetermined number of input value groups Vs included in the time series data V(t). In the example in Figure 6, 10 consecutive input values ​​V from time t1 to time t10 are set as the input value group Vs. The number of input values ​​V included in the input value group Vs can be stored in the storage unit 403 beforehand. As shown in Figure 6, the learning unit 42 calculates multiple types of statistics φ1 to φ5 for this input value group Vs.

[0044] In this embodiment, the learning unit 42 calculates five types of statistics: the first statistic φ1, the second statistic φ2, the third statistic φ3, the fourth statistic φ4, and the fifth statistic φ5. The first statistic φ1 is the kurtosis of the input value group Vs. The second statistic φ2 is the skewness of the input value group Vs. The third statistic φ3 is the mean value of the input value group Vs. The fourth statistic φ4 is the standard deviation of the input value group Vs. The fifth statistic φ5 is the integral value of the input value group Vs.

[0045] Furthermore, the learning unit 42 sets the input value V obtained at a predetermined time Δt (for example, 500 milliseconds later) from the reference measurement time of the input value group Vs (in the example in Figure 6, the starting time t1 of the input value group Vs) as the correct answer value Vc. The predetermined time Δt is set to be sufficiently longer than the time range of the measurement time of the input value group Vs. The length of the predetermined time Δt can be stored in the storage unit 403 in advance.

[0046] The learning unit 42 stores a set of five types of statistics φ1 to φ5 and their corresponding correct values ​​Vc as training data. The learning unit 42 stores the above training data while changing the time range of the input value group Vs as t1 to t10, t2 to t11, t3 to t12, t4 to t13, t5 to t14, ... In this way, a large number of training data are prepared.

[0047] The learning unit 42 uses a machine learning algorithm to perform learning on one training data set, with five statistical quantities φ1 to φ5 as explanatory variables and the corresponding ground truth value Vc as the target variable. Specifically, first, the learning unit 42 inputs the five statistical quantities φ1 to φ5 of a certain input value group Vs into the learning model M (step S13). Then, based on the input statistical quantities φ1 to φ5, the learning model M outputs an estimated value Ve of the input value V after a predetermined time Δt from the reference time of the input value group Vs (step S14). The learning unit 42 adjusts the parameters of the learning model M so that the estimated value Ve output from the learning model M approaches the ground truth value Vc (step S15).

[0048] Subsequently, the learning unit 42 determines whether a predetermined termination condition is met (step S16). The termination condition may be, for example, that the difference between the estimated value Ve and the correct value Vc becomes smaller than a predetermined threshold. Alternatively, the termination condition may be that the number of repetitions of steps S13 to S15 reaches a predetermined threshold. If the termination condition is not met (step S16: No), the learning unit 42 repeats the process of steps S13 to S15 described above with different training data than the previous time.

[0049] As the learning process in steps S13 to S15 is repeated, the estimation accuracy of the learning model M improves. Eventually, when the termination condition is met (step S16: Yes), the learning unit 42 terminates the learning process. This creates a trained learning model M that can accurately output an estimated value Ve of the input value V after a predetermined time Δt, based on five types of statistics φ1 to φ5. The learning unit 42 provides the created learning model M to the estimation unit 43.

[0050] <4. Regarding printing> Next, we will explain the printing process that is performed in the printing device 1 after the learning process described above. Figure 7 is a flowchart showing the flow of the printing process.

[0051] As shown in Figure 7, the printing apparatus 1 first starts the operation of the transport mechanism 10 (step S21). This starts the transport of the substrate 9. Once the transport of the substrate 9 begins, the tension sensor 30 measures the tension applied to the substrate 9 at minute time intervals. The tension sensor 30 then outputs the current measured value to the computer 40 (step S22).

[0052] The computer 40 processes the measured values ​​output from the tension sensor 30, performing normalization, noise reduction, and other processing. This processing is the same as the processing performed in step S11 of the learning process. This converts the measured values ​​into input values ​​V suitable for estimation processing using the learning model M. The computer 40 then stores these input values ​​V, along with the measurement time t, in the data storage unit 41. This stores the time-series data V(t) of the input values ​​V (step S23). The estimation unit 43 of the computer 40 then sequentially reads the time-series data V(t) from the data storage unit 41.

[0053] The estimation unit 43 selects a predetermined number of consecutive input value groups Vs included in the time series data V(t). Here, the most recent predetermined number of input value groups Vs are selected. Then, the estimation unit 43 calculates the first statistic φ1, the second statistic φ2, the third statistic φ3, the fourth statistic φ4, and the fifth statistic φ5 for the selected input value groups Vs (step S24).

[0054] The number of input values ​​V included in the input value group Vs is the same as in the learning process. Also, the types of statistics φ1 to φ5 are the same as in the learning process described above. That is, the first statistic φ1 is the kurtosis of the input value group Vs. The second statistic φ2 is the skewness of the input value group Vs. The third statistic φ3 is the mean of the input value group Vs. The fourth statistic φ4 is the standard deviation of the input value group Vs. The fifth statistic φ5 is the integral of the input value group Vs.

[0055] The estimation unit 43 inputs the five calculated statistical quantities φ1 to φ5 to the learning model M (step S25). The learning model M then outputs an estimated value Ve of the input value V after a predetermined time Δt from the reference measurement time of the input value group Vs (for example, the starting time of the input value group Vs) (step S26). The estimation unit 43 outputs the obtained estimated value Ve to the operation control unit 44.

[0056] The motion control unit 44 controls the operation of the transport mechanism 10 based on the estimated value Ve output from the estimation unit 43 (step S27). The motion control unit 44 has a preset target value Vt for the input value V. The motion control unit 44 provides feedback control to the transport mechanism 10 so that the estimated value Ve output from the estimation unit 43 approaches the target value Vt.

[0057] For feedback control, PID control is used, for example. That is, the motion control unit 44 calculates the control value for each motor based on the deviation between the estimated value Ve and the target value Vt, the derivative of the deviation, and the integral of the deviation. The motion control unit 44 then supplies a control signal C representing the control value to each motor of the transport mechanism 10. Each motor of the transport mechanism 10 is driven according to the control signal C supplied from the motion control unit 44. This makes it possible to transport the substrate 9 while suppressing fluctuations in the tension of the substrate 9.

[0058] Furthermore, the motion control unit 44 transports the substrate 9 using the control described above, while also controlling the operation of the four heads 21-24. Each of the four heads 21-24 ejects ink droplets toward the upper surface of the substrate 9 (step S28). As a result, an image is printed on the upper surface of the substrate 9.

[0059] Subsequently, the computer 40 determines whether or not to terminate the printing process (step S29). If there is still image data to be printed, the computer 40 continues the printing process (step S29: No). In this case, the computer 40 repeats the processes described in steps S22 to S28. In this way, the computer 40 proceeds with the printing process while suppressing fluctuations in the measured value of the tension sensor 30 by repeating the processes in steps S22 to S28. This suppresses the occurrence of misregistration.

[0060] Eventually, when there is no more image data to print, the computer 40 terminates the printing process (Step S29: Yes). In this case, the printing device 1 stops the operation of the transport mechanism 10 and terminates the transport of the substrate 9 (Step S30).

[0061] As described above, this printing device 1 inputs the statistical quantities φ1 to φ5 of a predetermined number of input value groups Vs into the learning model M as explanatory variables. Therefore, the accuracy of the estimated value Ve output from the learning model M can be improved compared to when the input value V itself is used as the explanatory variable.

[0062] In particular, in this embodiment, five types of statistics φ1 to φ5—kurtosis, skewness, mean, standard deviation, and integral—are input to the learning model M as explanatory variables. Therefore, the accuracy of the estimated value Ve output from the learning model M can be improved compared to when only one statistic is used as an explanatory variable.

[0063] The printing apparatus 1 then controls the operation of the transport mechanism 10 based on the obtained estimated value Ve. This allows for highly accurate suppression of tension fluctuations in the substrate 9. As a result, high-quality printed materials with minimal misregistration can be obtained.

[0064] The first statistic φ1 (kurtosis), the second statistic φ2 (skewness), the third statistic φ3 (mean), the fourth statistic φ4 (standard deviation), and the fifth statistic φ5 (integral value) are all statistics that emphasize the characteristics of the data distribution of the input value group Vs. For example, the fourth statistic φ4 (standard deviation) and the second statistic φ2 (skewness) provide information about the width of the data distribution of the input value group Vs and whether it spreads to the left or right. The first statistic φ1 (kurtosis) provides information that emphasizes the frequency (height) of the values ​​in the data distribution of the input value group Vs. The fifth statistic φ5 (integral value) provides information that emphasizes the characteristics of the vertical axis of the data distribution of the input value group Vs. The third statistic φ3 (mean) provides global waveform information of the data distribution by smoothing the values ​​of the input value group Vs.

[0065] Therefore, including these statistics as explanatory variables can improve the estimation accuracy of the learning model M. Furthermore, since these statistics can all be calculated using simple calculations, the computational burden on the computer 40 can be reduced, making it practical.

[0066] In the above embodiment, five types of statistics φ1 to φ5 of the input value group Vs were input to the learning model M as explanatory variables. However, the statistics input to the learning model M may be only a portion of the five types of statistics φ1 to φ5. Furthermore, not only statistics, but the input value V itself may also be input to the learning model M as an explanatory variable.

[0067] <5. Results of demonstration regarding improvement in estimation accuracy> Figures 8 and 9 show the results of an experimental demonstration demonstrating that the estimation accuracy of the input value V is improved by the estimation method described above. In the experimental demonstration in Figures 8 and 9, time-series data V(t) of the input value V was created based on the measured tension of the actual printing device 1, and the estimated value Ve was output from the learning model M using the method of the embodiment described above. However, the explanatory variables input to the learning model M were set to five different cases, from Case 1 to Case 5 below. Case 1: Input value V only Case 2: Input value V and first statistic φ1 (kurtosis) Case 3: Input value V and second statistic φ2 (skewness) Case 4: Input value V, first statistic φ1 (kurtosis), and second statistic φ2 (skewness) Case 5: Input value V, 1st statistic φ1 (kurtosis), 2nd statistic φ2 (skewness), 3rd statistic φ3 (mean), 4th statistic φ4 (standard deviation), and 5th statistic φ5 (integral value)

[0068] In the demonstration experiments shown in Figures 8 and 9, the interval between output of measurement values ​​from the tension sensor 30 was set to 0.5 milliseconds. The time range of the input value group Vs for calculating the statistics φ1 to φ5 was set to 5 milliseconds. That is, the number of input values ​​V required to calculate one statistic was set to 10. Furthermore, the input value V after a predetermined time Δt was estimated based on the measurement time of the starting point of the input value group Vs. The length of the predetermined time Δt was set to 500 milliseconds. A gradient boosting decision tree was used as the machine learning algorithm.

[0069] Figure 8 shows the correlation between the estimated value Ve and the correct value Vc. Figure 9 shows the error between the estimated value Ve and the correct value Vc.

[0070] As can be seen from the results in Figures 8 and 9, the correlation value is improved and the error is reduced in cases 2 to 5 compared to case 1. In other words, by including statistics containing the first statistic φ1 (kurtosis) or the second statistic φ2 (skewness) as explanatory variables, the estimation accuracy by the learning model M is improved compared to when only the input value V is used as an explanatory variable.

[0071] Furthermore, looking at the results in Figures 8 and 9, we can see that in cases 4 and 5, the correlation value is improved and the error is reduced compared to cases 1 to 3. In other words, by including at least two types of statistics, the first statistic φ1 (kurtosis) and the second statistic φ2 (skewness), in the explanatory variables, the estimation accuracy by the learning model M is improved.

[0072] Furthermore, looking at the results in Figures 8 and 9, it can be seen that in Case 5, the correlation value is even better and the error is even lower than in Cases 1 to 4. In other words, by including five types of statistics—the first statistic φ1 (kurtosis), the second statistic φ2 (skewness), the third statistic φ3 (mean), the fourth statistic φ4 (standard deviation), and the fifth statistic φ5 (integral value)—in the explanatory variables, the estimation accuracy by the learning model M is further improved.

[0073] Furthermore, based on the results for cases 4 and 5, it can be inferred that the estimation accuracy of the learning model M can be improved when the explanatory variables include three types of statistics: the first statistic φ1 (kurtosis), the second statistic φ2 (skewness), and the third statistic φ3 (mean); when the explanatory variables include three types of statistics: the first statistic φ1 (kurtosis), the second statistic φ2 (skewness), and the fourth statistic φ4 (standard deviation); and when the explanatory variables include three types of statistics: the first statistic φ1 (kurtosis), the second statistic φ2 (skewness), and the fifth statistic φ5 (integral value).

[0074] <6. Variation> Although one embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment.

[0075] In the above embodiment, the input value V was a value based on the measurement value of the tension sensor 30. However, the input value in the present invention may be a value based on the measurement value of another sensor that measures the state of the device. For example, the input value V may be a value based on the measurement value output from a sensor such as a displacement sensor, meandering sensor, torque sensor, speed sensor, temperature sensor, or image sensor. Furthermore, the input value V does not necessarily have to be a value based on the measurement value of a sensor; it may be any value that constitutes time-series data.

[0076] Furthermore, in the above embodiment, the input value V after a predetermined time Δt was estimated based on the time of the starting point of the input value group Vs. However, the time used as the reference for the input value group Vs does not necessarily have to be the time of the starting point. For example, the input value after a predetermined time Δt may be estimated based on the time of the ending point of the input value group Vs or the time in the middle of the input value group Vs.

[0077] Furthermore, in the above embodiment, the input value V after a predetermined time Δt was estimated based on the statistics φ1 to φ5 of the input value group Vs. However, a value other than the input value V may be estimated based on the statistics φ1 to φ5 of the input value group Vs. For example, an estimated value of the misalignment may be output based on the statistics φ1 to φ5 of the input value group Vs based on the measured tension value.

[0078] Furthermore, in the above embodiment, PID control was given as an example of feedback control by the motion control unit 44. However, the feedback control performed by the motion control unit 44 may be other methods such as PI control.

[0079] Furthermore, in the above embodiment, as shown in Figure 2, the nozzles 201 were arranged in a single row in the width direction in each head 21 to 24. However, the nozzles 201 may be arranged in two or more rows in each head 21 to 24.

[0080] Furthermore, the printing apparatus 1 in the above embodiment was equipped with four heads 21 to 24. However, the number of heads equipped in the printing apparatus 1 may be 1 to 3, or 5 or more. For example, the printing apparatus 1 may be equipped with a head that ejects spot color ink in addition to the C, M, Y, and K colors.

[0081] Furthermore, in the above embodiment, a printing apparatus 1 that ejects ink onto the surface of a substrate 9 was described. However, the apparatus of the present invention is not limited to a printing apparatus 1, but may be other apparatus that can obtain time-series input values. For example, the apparatus of the present invention may be an exposure apparatus that exposes the surface of a substrate, a coating apparatus that applies a processing solution to the surface of a substrate, a cleaning apparatus that cleans the surface of a substrate with a processing solution, and so on.

[0082] Furthermore, the elements that appear in the above embodiments and modifications may be combined as appropriate, to the extent that no contradictions arise. [Explanation of Symbols]

[0083] 1 Printing device 9 Base material 10 Conveying mechanism 20 Printing Department 30 Tension Sensor 40 Computers 41 Data Storage Unit 42 Learning Department 43 Estimation part 44 Operation Control Unit M Learning Model V Input Value Vs Input Value Group Vc Correct Value Ve estimate

Claims

1. A printing apparatus that prints on the surface of a substrate while transporting a long strip-shaped substrate, comprising an estimation method that outputs an estimated value based on time-series data of input values, a) A step of calculating multiple types of statistics for a predetermined number of consecutive input values ​​included in the time series data, b) A step of inputting the multiple types of statistics into a learning model created by machine learning and outputting estimated values ​​from the learning model, The computer executes this, The aforementioned multiple types of statistics are, The kurtosis of the aforementioned input value group and The skewness of the aforementioned group of input values, It includes at least, The aforementioned input value is a value based on the measurement of a sensor that measures the tension applied to the substrate in the transport direction. The estimation method is characterized in that the estimated value is an estimated value of the input value after a predetermined time from the reference measurement time of the input value group.

2. The estimation method according to claim 1, The aforementioned multiple types of statistics are, The average value of the aforementioned group of input values An estimation method that further includes the following.

3. An estimation method according to claim 1 or claim 2, The aforementioned multiple types of statistics are, Standard deviation of the aforementioned group of input values An estimation method that further includes the above.

4. An estimation method according to any one of claims 1 to 3, The aforementioned multiple types of statistics are, The integral value of the aforementioned input value group An estimation method that further includes the following.

5. An estimation method according to any one of claims 1 to 4, Step b) above is an estimation method in which the input value and the multiple types of statistics are input to the learning model.

6. A control method for controlling the operation of a printing apparatus, x) A step of accumulating the time-series data of the input values ​​based on the measured values ​​of the sensors of the printing apparatus, y) A step of outputting the estimated value based on the time series data using the estimation method described in claim 1, z) A step of controlling the operation of the printing apparatus based on the estimated value, A control method used by a computer to perform an action.

7. A printing apparatus that performs printing on the surface of a substrate while conveying a long, strip-shaped substrate, A sensor that measures the tension applied to the substrate in the transport direction, A data storage unit that stores time-series data of input values ​​based on the measured values ​​output from the aforementioned sensor, An estimation unit calculates multiple types of statistics for a predetermined number of consecutive input values ​​included in the time series data, inputs the calculated multiple types of statistics into a learning model created by machine learning, and outputs an estimated value from the learning model. Based on the estimated values, an operation control unit controls the operation of the printing device, It has, The aforementioned multiple types of statistics are, The kurtosis of the aforementioned input value group and The skewness of the aforementioned group of input values, It includes at least, The device wherein the estimated value is an estimated value of the input value after a predetermined time from the reference measurement time of the input value group.

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