Time series prediction device, time series prediction method and program

Abstract

To realize highly accurate time series prediction of a target exhibiting nonlinear behavior even when learning data is insufficient.SOLUTION: A time series prediction device according to one aspect of the present disclosure is a time series prediction device that predicts an output time series, which is time series data of output variables output from a target, and includes: a model creation unit that takes as input a first input time series, which is time series data of input variables of the target, and a first output time series corresponding to the first input time series, and creates a feature model that models a relationship between a first input feature of the first input time series and a first output feature of the first output time series; and a time series prediction unit that takes as input a second input time series and an output reference value, and predicts a second output feature from a second input feature of the second input time series using the feature model, and predicts time series data that has a feature represented by the predicted second output feature and is represented by a predetermined trajectory starting from the output reference value, as a second output time series corresponding to the second input time series.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present disclosure relates to a time series prediction device, a time series prediction method, and a program.

Background Art

[0002] As a method for predicting the response of a plant, for example, linear methods such as Fourier transform, ARMA (autoregressive moving average) model, and Kalman filter are known. Also, for example, non-linear methods such as neural networks such as SVR (Support Vector Regression), Gaussian process regression, and Transformer are known.

[0003] In addition, as a method for predicting the class to which data after a certain point in time is classified, a method using feature amounts of time series data is also known (Patent Document 1).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, conventional linear methods for predicting the response of a plant have a problem that the prediction accuracy is poor when the response of the plant has strong non-linearity. On the other hand, conventional non-linear methods for predicting the response of a plant have a problem that the prediction accuracy is poor when the learning data is insufficient.

[0006] The present disclosure has been made in view of the above points, and an object thereof is to realize accurate time series prediction of an object having non-linear behavior even when the learning data is insufficient.

Means for Solving the Problems

[0007] A time series prediction device according to an aspect of the present disclosure is a time series prediction device that predicts an output time series that is time series data of an output variable output from a target, and includes a first input time series that is time series data of an input variable input to the target, and a first output time series that is an output time series output from the target when the first input time series is input to the target. A model creation unit that creates a feature quantity model that models the relationship between a first input feature quantity that represents the feature of the first input time series and a first output feature quantity that represents the feature of the first output time series; and a second input time series that is time series data of an input variable that is a prediction target of the output time series, and an output reference value that is a reference value of the output variable. Using these as inputs, a second output feature quantity is predicted from a second input feature quantity that represents the feature of the second input time series by the feature quantity model, and the predicted second output feature quantity has a feature represented by the second output feature quantity, and time series data represented by a predetermined trajectory starting from the output reference value is used as a second output time series that is predicted to be output from the target when the second input time series is input to the target. It has a time series prediction unit for predicting.

Advantages of the Invention

[0008] Even when the learning data is insufficient, accurate time series prediction of a target with non-linear behavior is realized.

Brief Description of the Drawings

[0009]

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Modes for Carrying Out the Invention

[0010] Hereinafter, each embodiment of the present invention will be described in detail with reference to the drawings. In each of the following embodiments, mainly for a process such as a plant having non-linear behavior, a time series prediction device 10 that can accurately predict time series data representing the response of the plant or the like even when the learning data is insufficient will be described.

[0011] Here, in the conventional non-linear method for predicting the response of a plant, in addition to the problem that the prediction accuracy is poor when the learning data is insufficient, for example, the performance changes depending on hyperparameters such as the number of layers of a neural network, and there are also problems such as a relatively large amount of calculation and difficulty in real-time performance. On the other hand, in the time series prediction device 10 described in each of the following embodiments, adjustment of complicated hyperparameters is unnecessary, and real-time performance of time series prediction is also ensured. That is, according to the time series prediction device 10 described in each of the following embodiments, even when the learning data is insufficient, it is possible to predict the time series data of a non-linear process at high speed and with high accuracy.

[0012] [First Embodiment] First, the first embodiment will be described. Here, in the time series prediction device 10 according to the first embodiment, there are "model learning time" for creating a feature quantity model that models the relationship between the feature quantity of the input time series, which is the time series data of the operation amount of the plant, and the feature quantity of the output time series, which is the time series data of the control amount of the plant, and "time series prediction time" for predicting a simple output time series called a simple output time series from the given input time series using the feature quantity model.

[0013] At the time of model learning, in the time series prediction device 10, the input time series u s (t) and the output time series y s (t) are given as learning data. Let s represent the sample number of the learning data, and assume that s ∈ {1, ···, S}. Also, S represents the total number of samples, and t represents the index of time.

[0014] On the other hand, at the time of time series prediction, in the time series prediction device 10, the input time series u k (t) and the control amount y0 called the output reference value are given. Let k represent the number of the input time series to be predicted, and assume that k = 1, 2, 3, ···.

[0015] For simplicity, hereinafter, it is assumed that the time widths of each input time series and each output time series are the same width, the index representing the start time is t = 0, and the index representing the time immediately after the end time is t = t end . That is, the time intervals of each input time series and each output time series are [0, t end )].

[0016] Also, as an example, the input time series u s (t) is time series data of a two-dimensional vector composed of two operation amounts u s,1 (t) and u s,2 (t), and the output time series y s (t) is time series data of a one-dimensional scalar value. However, this is just an example, and when the input time series u s (t) is time series data of a scalar value or time series data of a vector of three or more dimensions, or when the output time series ys Even when (t) is time-series data of a vector of two or more dimensions, the embodiments described below can be similarly applied.

[0017] <Hardware configuration example of the time series prediction device 10 according to the first embodiment> A hardware configuration example of the time series prediction device 10 according to the first embodiment will be described with reference to FIG. 1. FIG. 1 is a diagram showing an example of the hardware configuration of the time series prediction device 10 according to the first embodiment.

[0018] As shown in FIG. 1, the time series prediction device 10 according to the first embodiment includes an input device 101, a display device 102, an external I / F 103, a communication I / F 104, a RAM (Random Access Memory) 105, a ROM (Read Only Memory) 106, an auxiliary storage device 107, and a processor 108. These hardware components are communicably connected to each other via a bus 109.

[0019] The input device 101 is, for example, a keyboard, a mouse, a touch panel, a physical button, etc. The display device 102 is, for example, a display, a display panel, etc. Note that the time series prediction device 10 may not have at least one of the input device 101 and the display device 102.

[0020] The external I / F 103 is an interface with an external device such as a recording medium 103a. Examples of the recording medium 103a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, etc.

[0021] The communication I / F 104 is an interface for connecting to a communication network or the like. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily holds programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can hold programs and data even when the power is turned off. The auxiliary storage device 107 is a non-volatile storage device such as an HDD (Hard Disk Drive), an SSD (Solid State Drive), or a flash memory, for example. The processor 108 is various arithmetic devices such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit), for example.

[0022] Note that the hardware configuration shown in FIG. 1 is an example, and the hardware configuration of the time series prediction device 10 is not limited to this. For example, the time series prediction device 10 may have a plurality of auxiliary storage devices 107 and a plurality of processors 108, may not have a part of the illustrated hardware, or may have various hardware other than the illustrated hardware.

[0023] <Functional configuration example of the time series prediction device 10 according to the first embodiment> A functional configuration example of the time series prediction device 10 according to the first embodiment will be described with reference to FIG. 2. FIG. 2 is a diagram showing an example of the functional configuration of the time series prediction device 10 according to the first embodiment.

[0024] As shown in FIG. 2, the time series prediction device 10 according to the first embodiment includes a model learning unit 201 and a simple output prediction unit 202. Each of these units is realized, for example, by a process in which one or more programs installed in the time series prediction device 10 are executed by a processor 108 or the like.

[0025] The model learning unit 201 creates a feature model F from the given input time series u s (t) and the output time series y s (t) during model learning. More specifically, the model learning unit 201 is the output time series y sOutput feature amount Y representing the feature amount from (t) s is generated, and input time series u s Input feature amount U representing the feature amount from (t) s is generated. Then, a feature amount model F that models the relationship between the input feature amount U s and the output feature amount Y s is created.

[0026] The simple output prediction unit 202 predicts a simple output time series v k (t) from the given input time series u k (t) and the output reference value y0 during time series prediction. More specifically, the simple output prediction unit 202 generates an input feature amount U k representing the feature amount from the input time series u k (t), then generates an output feature amount Y k using the feature amount model F, and then predicts the simple output time series v k (t) from the output feature amount Y k and the output reference value y0.

[0027] <Operation example of the model learning unit 201 according to the first embodiment> An operation example of the model learning unit 201 according to the first embodiment will be described with reference to FIG. 3. FIG. 3 is a flowchart showing the operation example of the model learning unit 201 according to the first embodiment.

[0028] Step S101: The model learning unit 201 performs preprocessing on the given input time series u s (t) and the output time series y s (t). Hereinafter, for simplicity, x s (t) ∈ {u s (t), y s (t)}, and the preprocessing for the time series x s (t) will be described with reference to FIG. 4. FIG. 4 is a diagram for explaining an example of preprocessing.

[0029] As shown in FIG. 4, the maximum value of the time series x s (t) is x s,max , and the minimum value is x s,minLet it be so. Also, let r be a constant that is commonly determined among each input time series and each output time series. max ≥ x s,max r min ≤ x s,min Let it be so. When determining r for the input time series, for example, the maximum value u of each input time series u(t) can be set as r. max In the case of determining r for the input time series, for example, the minimum value u of each input time series u(t) can be set as r. s (t) can be set as r. Similarly, when determining r for the output time series, for example, the maximum value y of each output time series y(t) can be set as r. s,max (s = 1, ···, S) can be set as r. Similarly, when determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. max In the case of determining r for the input time series, for example, the minimum value u of each input time series u(t) can be set as r. min In the case of determining r for the input time series, for example, the minimum value u of each input time series u(t) can be set as r. s (t) can be set as r. Similarly, when determining r for the output time series, for example, the maximum value y of each output time series y(t) can be set as r. s,min (s = 1, ···, S) can be set as r. Similarly, when determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. min In the case of determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. max In the case of determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. s (t) can be set as r. Similarly, when determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. s,max (s = 1, ···, S) can be set as r. Similarly, when determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. max In the case of determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. min In the case of determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. s (t) can be set as r. Similarly, when determining r for the output time series, for example, the minimum value y of each output time series y(t) can be set as r. s,min (s = 1, ···, S) can be set as r. min Let it be so.

[0030] At this time, the model learning unit 201 creates the pre-processed time series x'(t) by x'(t)=(x(t)-r) / (r - r). As a result, as shown in Fig. 4, a pre-processed time series normalized to values between 0 and 1 is obtained. Hereinafter, each input time series u(t) and each output time series y(t) are assumed to be pre-processed time series data. s '(t)=(x s (t)-r min ) / (r max -r min ) to create the pre-processed time series x s '(t). As a result, as shown in Fig. 4, a pre-processed time series normalized to values between 0 and 1 is obtained. Hereinafter, each input time series u s (t) and each output time series y s (t) are assumed to be pre-processed time series data.

[0031] Note that the pre-processing in step S101 above is not essential and may not be executed if not necessary. Also, in addition to normalization, known pre-processing such as missing value interpolation and outlier removal may be performed.

[0032] Step S102: The model learning unit 201 generates the output feature amount Y from the output time series y s (t). s

[0033] For example, as shown in FIG. 5, the initial value of the output time series y s (t) (i.e., the value at t = 0) is y s,0 , the elapsed time when the output time series y s (t) takes the minimum value (the elapsed time from t = 0) is t s,1 , the difference between the minimum value of the output time series y s (t) and the initial value y s,0 is d s,1 . Also, the elapsed time when the output time series y s (t) takes the maximum value (the elapsed time from t = 0) is t s,2 , the difference between the maximum value of the output time series y s (t) and the initial value y s,0 is d s,2 . Further, the difference between the final value of the output time series y s (t) (i.e., the value that y end (t) takes as t approaches t s (hereinafter, this is represented as y s (t end )) and the initial value y s,0 is d s,3 . Note that d s,1 and d s,2 take positive values, and d s,3 considers positive and negative values (i.e., d s,3 = y s (t end ) - y s,0 ). This is because the minimum value is always less than or equal to the initial value, the maximum value is always greater than or equal to the initial value, so the positive and negative are obvious, but the positive and negative of the difference between the final value and the initial value are not constant.

[0034] At this time, the model learning unit 201 generates the output feature amount Y of the output time series y s (t) as follows, for example. s

Equation

[0035] Step S103: The model learning unit 201 generates an input feature amount U s from the input time series u s .

[0036] For example, as shown in FIG. 6, regarding the manipulated variable u s (t) of the input time series u s,1 (t), let the elapsed time from time t = 0 to the time when the change in the manipulated variable starts be tb s,1 . Also, regarding the manipulated variable u s,1 (t), let the elapsed time from time t = 0 to the time when the change in the manipulated variable ends be te s,1 . Similarly, regarding the manipulated variable u s,2 (t), let the elapsed time from time t = 0 to the time when the change in the manipulated variable starts be tb s,2 , and the elapsed time from time t = 0 to the time when the change in the manipulated variable ends be te s,2 . Further, let the time when u s,1 (t)=u s,2 (t) be tc s .

[0037] At this time, the model learning unit 201 generates the input feature amount U s of the input time series u s for example, as follows.

Number

[0038] Alternatively, the model learning unit 201 may generate the input feature amount U s of the input time series u s for example, as follows.

Number

[0039] In addition to the above, for example, as shown in FIG. 7, the maximum value of the operation amount u s,1 (t) is u s,1,max , and the minimum value is u s,1,min . Similarly, the maximum value of the operation amount u s,2 (t) is u s,2,max , and the minimum value is u s,2,min . Also, among the change rates of the operation amount u s,1 (t), the value with the maximum absolute value is du s,1 . Similarly, among the change rates of the operation amount u s,2 (t), the value with the maximum absolute value is du s,2 .

[0040] At this time, the model learning unit 201 may generate the input feature amount U s of the input time series u s in the following manner, for example.

Number

[0041] Alternatively, the model learning unit 201 may generate the input feature amount U s of the input time series u s in the following manner, for example.

Number

[0042] However, the methods for generating the output feature amount Y s and the input feature amount U s described in steps S102 and S103 above are merely examples, and there are various other methods for generating the output feature amount Y s and the input feature amount Us may be generated. For example, the output feature quantity Y s may be generated by the method described in step S103 above. Conversely, the input feature quantity U s may be generated by the method described in step S102 above. Or, for example, the input feature quantity U s and the output feature quantity Y s may be generated.

[0043] Step S104: The model learning unit 201 creates a feature model F from the input feature quantity U s and the output feature quantity Y s . That is, the model learning unit 201 uses the input feature quantity U s and the output feature quantity Y s for s = 1, ···, S, and uses the existing prediction model creation method to create the feature model F so that when the input feature quantity U s is input to the feature model F, the output feature quantity Y s can be accurately predicted.

[0044] As the feature model F, for example, the linear model shown in the following example (part 1) or the non-linear model shown in the example (part 2) can be used. Each input feature quantity U s is an m-dimensional vector, and each output feature quantity Y s is assumed to be represented by an n-dimensional vector.

[0045] · Example of a feature model (part 1) F: Y s = A·U s + b Here, A is an n × m matrix, and b is an n-dimensional vector.

[0046] · Example of a feature model (part 2) F: Y s = NN(U s ) Here, NN is a neural network. As the neural network, a neural network with a general configuration (for example, a neural network composed of an input layer, a predetermined number of fully connected layers, and an output layer, etc.) can be used. However, it is not limited to neural networks, and for example, known non-linear functions such as SVR and random forest may be used.

[0047] Hereinafter, a feature model for predicting the output feature amount Y with the input feature amount U as the input will be expressed as Y = F(U).

[0048] Note that in the above example (Example 1), the matrix A and the n-dimensional vector b are the parameters to be learned. On the other hand, in the above example (Example 2), the learnable parameters of the neural network are the parameters to be learned.

[0049] <Operation example of the simple output prediction unit 202 according to the first embodiment> An operation example of the simple output prediction unit 202 according to the first embodiment will be described with reference to FIG. 8. FIG. 8 is a flowchart showing an operation example of the simple output prediction unit 202 according to the first embodiment.

[0050] Step S201: The simple output prediction unit 202 performs preprocessing on the input time series u k (t) by the same process as step S101 in FIG. 3. Hereinafter, it is assumed that the input time series u k (t) is the time series data after preprocessing.

[0051] Step S202: The simple output prediction unit 202 generates the input feature amount U k from the input time series u k by the same process as step S103 in FIG. 3.

[0052] Step S203: The simple output prediction unit 202 uses the feature model F created by the model learning unit 201 to obtain the output feature amount Y k from the input feature amount U kto predict. That is, the simple output prediction unit 202 predicts the output feature amount Y k = F(U k ) to predict the output feature amount Y k .

[0053] Step S204: The simple output prediction unit 202 predicts the simple output time series v k (t) from the output feature amount Y k and the output reference value y0.

[0054] For example, assume that the output feature amount Y k predicted in step S203 above is as follows.

Number

Number

[0055] [Second Embodiment] Next, the second embodiment will be described. In the second embodiment, when generating the output feature amount, a case where the output time series is divided into a plurality of sections and the output feature amount is generated for each section will be described.

[0056] In the second embodiment, mainly, the differences from the first embodiment will be described, and the description of the components that may be the same as those in the first embodiment will be omitted or simplified.

[0057] <Operation Example of Model Learning Unit 201 According to Second Embodiment> The operation example of the model learning unit 201 according to the second embodiment will be described with reference to FIG. 11. FIG. 11 is a flowchart showing the operation example of the model learning unit 201 according to the second embodiment.

[0058] Step S301: The model learning unit 201 performs preprocessing on the given input time series u s (t) and output time series y s (t) in the same process as step S101 in FIG. 3.

[0059] Step S302: The model learning unit 201 performs the same process as step S103 in FIG. 3 on the input time series u sInput feature quantity U is generated from (t). s Generate it.

[0060] Step S303: The model learning unit 201 divides the time interval [0, t end ) into two or more intervals. Hereinafter, the number for identifying each divided interval is called an interval number, and the interval number is represented by i. Also, the number of divided intervals is set to I (≥2). Furthermore, for simplicity, the interval of interval number i is also referred to as "interval i", and the time interval represented by interval i is set to [T i-1 , T i ). At this time, T0 = 0, T I = t end .

[0061] Note that each interval i (i = 1, ···, I) may be an equal interval or an unequal interval. Also, the length of each interval may be variable according to the value of the output time series y s (t). For example, in a time interval where the value of the output time series y s (t) fluctuates greatly, it may be divided into fine intervals, and in a time interval where it does not, it may be divided into coarse intervals.

[0062] Step S304: The model learning unit 201 initializes the interval number i to 1. That is, the model learning unit 201 sets i ← 1.

[0063] Step S305: The model learning unit 201 generates the output feature quantity Y s,i in interval i. That is, the model learning unit 201 generates the output feature quantity Y s from the output time series y i-1 (t) (t ∈ [T i )) in interval i by the same process as step S102 in FIG. 3. s,i

[0064] As an example, FIG. 12 shows a method for generating the output feature quantity Y s,i in each interval i when I = 5. As shown in FIG. 12, for each interval i, the output time series y s (t) (t ∈ [T i-1 , T​i ) outputs the output feature amount Y s,i is generated. In the example shown in FIG. 12, the output time series y s (t) (t ∈ [T i-1 , T i )) of the initial value (that is, y s (T i-1 )) is represented by y s,0,i .

[0065] Step S306: The model learning unit 201 uses the input feature amount U s and the output feature amount Y s,i to create the feature model F i . That is, the model learning unit 201 uses the input feature amount U s and each output feature amount Y s,i to input the input feature amount U s into the feature model F i so that the output feature amount Y s,i can be accurately predicted. The feature model F i is created by an existing prediction model creation method.

[0066] As each feature model F i , for example, a linear model shown in the following example (Part 1) or a non-linear model shown in the example (Part 2) can be used. Each input feature amount U s is an m-dimensional vector, and each output feature amount Y s,i is an n-dimensional vector.

[0067] · Example of the feature model (Part 1) F1: Y s,1 = A1 · U s + b1 (when i = 1) F i : Y s,i = A i · U s + C i · Y s,i-1 + b i (when i > 1) Here, for i ≥ 1, A i is an n × m matrix, C i is an n × n matrix, bi is an n-dimensional vector.

[0068] · Example of Feature Model (Part 2) F1: Y s,1 = NN1(U s ) (when i = 1) F i : Y s,i = NN i (U s , Y s,i-1 ) (when i > 1) Here, for i ≥ 1, NN i is a neural network. However, it is not limited to neural networks, and for example, known non-linear functions such as SVR or random forest may be used.

[0069] Note that in the above example (Part 1), the matrices A i , C i and the n-dimensional vector b i are the parameters to be learned. On the other hand, in the above example (Part 2), the learnable parameters of the neural network are the parameters to be learned.

[0070] Hereinafter, the feature model when i = 1 is represented as Y1 = F1(U), and the feature model when i > 1 is represented as Y i = F i (U, Y i-1 ) Here, U represents the input feature amount, and Y i represents the output feature amount.

[0071] Step S307: The model learning unit 201 determines whether the feature model F i has been created for all intervals i. That is, the model learning unit 201 determines whether I feature models F1, ···, F I have been created.

[0072] In step S307 above, for all intervals i, the feature model F iIf it is determined that [the model] has been created, the model learning unit 201 ends the operation. On the other hand, if it is not determined that the feature model F has been created for all intervals i in step S307 above, the model learning unit 201 proceeds to step S308. i If it is not determined that [the model] has been created, the model learning unit 201 proceeds to step S308.

[0073] Step S308: The model learning unit 201 adds 1 to the interval number i and returns to step S305. That is, the model learning unit 201 returns to step S305 with i←i + 1. As a result, steps S305 to S306 above are repeatedly executed until the feature model F is created for all intervals i. i Until the feature model F is created for all intervals i, steps S305 to S306 above are repeatedly executed.

[0074] <Operation example of the simple output prediction unit 202 according to the second embodiment> An operation example of the simple output prediction unit 202 according to the second embodiment will be described with reference to FIG. 13. FIG. 13 is a flowchart showing an operation example of the simple output prediction unit 202 according to the second embodiment.

[0075] Step S401: The simple output prediction unit 202 performs preprocessing on the input time series u k (t) by the same process as step S201 in FIG. 8. Hereinafter, it is assumed that the input time series u k (t) is the time series data after preprocessing.

[0076] Step S402: The simple output prediction unit 202 generates the input feature amount U k from the input time series u k by the same process as step S202 in FIG. 8.

[0077] Step S403: The simple output prediction unit 202 initializes the interval number i to 1. That is, the model learning unit 201 sets i←1.

[0078] Step S404: The simple output prediction unit 202 uses the feature model F i created by the model learning unit 201 to obtain the output feature amount Y from the input feature amount U k ​k,i Predict. That is, when i = 1, the simple output prediction unit 202 outputs Y k,1 = F1(U k ) to predict the output feature amount Y k,1 , and when i> 1, Y k,i = F i (U k , Y k,i-1 ) to predict the output feature amount Y k,i .

[0079] Step S405: The simple output prediction unit 202 predicts the simple output time series v in the interval i from the output feature amount Y by the same process as step S204 in FIG. 8 k,i (t) (t ∈ [T k (t) (t ∈ [T i-1 , T i )) That is, the simple output prediction unit 202, for example, sets t = 0 to t = T i-1 , t = t end to t = T i and applies the above number 7 or number 8 to predict the simple output time series v from the output feature amount Y k,i (t) (t ∈ [T k (t) (t ∈ [T i-1 , T i )) However, at this time, the simple output prediction unit 202 uses y0 as the output reference value in the interval i when i = 1, while using v instead of y0 as the output reference value in the interval i when i> 1 k (T i-1 ) are used respectively.

[0080] As an example, FIG. 14 shows a method for predicting the simple output time series v in each interval i when I = 5 k (t) (t ∈ [T i-1 , T i )) As shown in FIG. 14, for each interval i, the simple output time series v in that interval i k (t) (t ∈ [T i-1 , T i )) is predicted from the output feature amount Y k,i . In the example shown in FIG. 14, the simple output time series v when i = 1 kThe initial value of (t) (t ∈ [0, T1)) is y0, and for the case where i > 1, the simplified output time series v k (t) (t ∈ [T i-1 , T i )) is represented by y k (T i-1 )) k,0,i .

[0081] Step S406: The simplified output prediction unit 202 determines whether the simplified output time series v k (t) (t ∈ [T i-1 , T i )) has been predicted for all intervals i. That is, the simplified output prediction unit 202 determines whether the I simplified output time series v k (t) (t ∈ [0, T1)), ···, v k (t) (t ∈ [T I-1 , T I )) have been predicted

[0082] If it is determined in step S406 above that the simplified output time series v k (t) (t ∈ [T i-1 , T i )) has been predicted for all intervals i, the simplified output prediction unit 202 proceeds to step S408. On the other hand, if it is not determined in step S406 above that the simplified output time series v k (t) (t ∈ [T i-1 , T i )) has been predicted for all intervals i, the simplified output prediction unit 202 proceeds to step S407

[0083] Step S407: The simplified output prediction unit 202 adds 1 to the interval number i and returns to step S404. That is, the simplified output prediction unit 202 sets i ← i + 1 and returns to step S404. As a result, steps S404 to S405 are repeatedly executed until the simplified output time series v k (t) (t ∈ [T i-1 , T i )) is predicted

[0084] Step S408: The simple output prediction unit 202 concatenates the simple output time series v k (t) (where t ∈ [T i-1 , T i )) for all intervals i. That is, the simple output prediction unit 202 concatenates the simple output time series v I-1 , t end ) in each interval [0, T1), ···, [T k (t) to create the simple output time series v k (t) (where t ∈ [0, t end ). As a result, the simple output time series v end (t) represented by a continuous trajectory in the time interval [0, t k ) is obtained.

[0085] [Third Embodiment] Next, the third embodiment will be described. In addition to the output time series, a case where the input time series is also divided into a plurality of intervals and input feature amounts are generated for each interval will be described.

[0086] Note that in the third embodiment, mainly, the differences from the second embodiment will be described, and the description of the components that may be the same as those in the second embodiment will be omitted or simplified.

[0087] <Operation Example of the Model Learning Unit 201 According to the Third Embodiment> An operation example of the model learning unit 201 according to the third embodiment will be described with reference to FIG. 15. FIG. 15 is a flowchart showing the operation example of the model learning unit 201 according to the third embodiment.

[0088] Step S501: The model learning unit 201 performs preprocessing on the given input time series u s (t) and output time series y s (t) by the same processing as in step S301 of FIG. 11.

[0089] Step S502: The model learning unit 201 divides the time interval [0, t end ) into two or more intervals by the same processing as in step S303 of FIG. 11.

[0090] Step S503: The model learning unit 201 initializes the section number i to 1 by the same process as step S304 in FIG. 11.

[0091] Step S504: The model learning unit 201 generates the output time series y s (t) (t ∈ [T i-1 , T i )) into the output feature amount Y s,i .

[0092] Step S505: The model learning unit 201 generates the input feature amount U s,i . That is, the model learning unit 201 generates the input time series u s (t) (t ∈ [T i-1 , T i )) into the input feature amount U s,i by the same process as step S103 in FIG. 3.

[0093] Step S506: The model learning unit 201 creates the feature model F s,i from the input feature amount U s,i and the output feature amount Y i . That is, the model learning unit 201 uses the input feature amount U s,i and the output feature amount Y s,i for s = 1, ···, S, and uses the input feature amount U s,i as the input to the feature model F i to accurately predict the output feature amount Y s,i , and creates the feature model F i by an existing prediction model creation method.

[0094] As each feature model F i , for example, a linear model shown in the following example (Part 1) or a non-linear model shown in example (Part 2) can be used. Note that each input feature amount U s,i is represented as an m-dimensional vector, and each output feature amount Y s,i is represented as an n-dimensional vector.

[0095] · Example of Feature Quantity Model (Part 1) F1: Y s,1 = A1 · U s,1 + b1 (when i = 1) F i : Y s,i = A i · U s,i + C i · Y s,i-1 + b i (when i > 1) Here, for i ≥ 1, A i is an n × m matrix, C i is an n × n matrix, and b i is an n - dimensional vector.

[0096] · Example of Feature Quantity Model (Part 2) F1: Y s,1 = NN1(U s,1 ) (when i = 1) F i : Y s,i = NN i (U s,i , Y s,i-1 ) (when i > 1) Here, for i ≥ 1, NN i is a neural network. However, it is not limited to neural networks, and for example, known non - linear functions such as SVR or random forest may be used.

[0097] Note that in the above example (Part 1), the matrix A i , C i and the n - dimensional vector b i are the parameters to be learned. On the other hand, in the above example (Part 2), the learnable parameters of the neural network are the parameters to be learned.

[0098] Hereinafter, the feature quantity model when i = 1 is expressed as Y1 = F1(U1), and the feature quantity model when i > 1 is expressed as Y i = F i (U i , Y i-1 ) and U iis the input feature amount, Y i represents the output feature amount.

[0099] Steps S507 to S508 in FIG. 15 may be the same as steps S307 to S308 in FIG. 11 respectively, so the description thereof is omitted.

[0100] <Operation example of the simple output prediction unit 202 according to the third embodiment> The operation example of the simple output prediction unit 202 according to the third embodiment will be described with reference to FIG. 16. FIG. 16 is a flowchart showing the operation example of the simple output prediction unit 202 according to the third embodiment.

[0101] Step S601: The simple output prediction unit 202 performs preprocessing on the input time series u k (t) in the same manner as in step S401 of FIG. 13. Hereinafter, it is assumed that the input time series u k (t) is the time series data after preprocessing.

[0102] Step S602: The simple output prediction unit 202 initializes the section number i to 1 in the same manner as in step S403 of FIG. 13.

[0103] Step S603: The simple output prediction unit 202 generates the input feature amount U k (t) (t ∈ [T i-1 , T i )) from the input time series u k,i in the same manner as in step S505 of FIG. 15.

[0104] Step S604: The simple output prediction unit 202 uses the feature amount model F i created by the model learning unit 201 to predict the output feature amount Y k,i from the input feature amount U k,i . That is, when i = 1, the simple output prediction unit 202 predicts the output feature amount Y k,1 = F1(U k,i ) and predicts the output feature amount Y k,i , and when i>1, Y k,i = Fi (U k,i ,Y k,i-1 ) predicts the output feature quantity Y k,i .

[0105] Step S605: The simple output prediction unit 202 predicts the simple output time series v k,i in section i from the output feature quantity Y k (t) (t ∈ [T i-1 , T i ). That is, the simple output prediction unit 202 applies, for example, t = 0 as t = T i-1 , t = t end as t = T i and applies the above formula 7 or formula 8 to predict the simple output time series v k,i from the output feature quantity Y k (t) (t ∈ [T i-1 , T i ). However, at this time, when i = 1, the simple output prediction unit 202 uses y0 as the output reference value in section i, while when i > 1, it uses v k (T i-1 ) instead of y0 as the output reference value in section i, respectively.

[0106] As an example, the prediction method of the simple output time series v k (t) (t ∈ [T i-1 , T i ) in each section i when I = 5 is shown in Fig. 17. As shown in Fig. 17, for each section i, the simple output time series v k (t) (t ∈ [T i-1 , T i ) in that section i is predicted from the output feature quantity Y k,i . In the example shown in Fig. 17, the initial value of the simple output time series v k (t) (t ∈ [0, T1)) when i = 1 is y0, and the initial value of the simple output time series v k (t) (t ∈ [T i-1 , T i ) when i > 1 (that is, v k (T i-1 )) is represented by y k,0,i .

[0107] Steps S606 to S608 in FIG. 16 may be the same as steps S406 to S606 in FIG. 13 respectively, so the description thereof is omitted.

[0108] As described above, in the third embodiment, for each section i, the input feature amount U k,i is also used to predict the output feature amount Y k,i Thus, compared with the second embodiment, an improvement in the prediction accuracy of the feature amount model F i can be expected. This is because input feature amounts that are closer in section are more likely to affect the output feature amount, and the future input feature amount does not affect the past output feature amount to ensure the causality law.

[0109] [Application Example] An application example when the time series prediction device 10 according to the first to third embodiments described above is incorporated into the plant monitoring device 20 will be described with reference to FIG. 18. FIG. 18 is a diagram for explaining an application example to the plant monitoring device 20.

[0110] As shown in FIG. 18, in this application example, it is assumed that the conventional control device 40 outputs the actual operation amount u to the controlled plant 30 for control. At this time, the plant monitoring device 20 in this application example performs model learning using the control amount u output from the controlled plant 30 and the operation amount u output from the conventional control device 40, and predicts a simple time series of the control amount for the virtual operation amount series that is a virtual input time series.

[0111] The plant monitoring device 20 in this application example includes a model learning unit 201, a simple output prediction unit 202, a measurement unit 203, a display control unit 204, and a timer 205. Each of these units is realized, for example, by a process executed by a processor such as a CPU for one or more programs installed in the plant monitoring device 20. Further, the plant monitoring device 20 in this application example includes a learning data storage unit 206, a feature model storage unit 207, a prediction input data storage unit 208, and a prediction output data storage unit 209. Each of these storage units is realized, for example, by a storage area such as an auxiliary storage device provided in the plant monitoring device 20.

[0112] The model learning unit 201 creates a feature model from the input time series u s (t) and the output time series y s (t) stored in the learning data storage unit 206 during model learning.

[0113] The simple output prediction unit 202 uses the feature model stored in the feature model storage unit 207 to predict the simple output time series v k (t) from the input time series u k (t) and the output reference value y0 stored in the prediction input data storage unit 208 during time series prediction.

[0114] The measurement unit 203 measures the control amount y output from the controlled plant 30 and the operation amount u output from the conventional control device 40 every sampling period T c . Hereinafter, the control amount y and the operation amount u measured at time t will also be represented as y(t) and u(t), respectively.

[0115] The display control unit 204 outputs the simple output time series v k (t) stored in the prediction output data storage unit 209 to a display device such as a display.

[0116] The timer 205 operates the measurement unit 203 every given sampling period T c .

[0117] The learning data storage unit 206 stores the time-series data of the control amount y(t) in a time interval with a predetermined time width, measured by the measurement unit 203, as the output time series y s (t). Also, the learning data storage unit 206 stores the time-series data of the operation amount u(t) in the time interval of the time width, measured by the measurement unit 203, as the input time series u s (t).

[0118] The feature quantity model storage unit 207 stores the feature quantity model created by the model learning unit 201.

[0119] The prediction input data storage unit 208 stores the given virtual operation amount time series as the input time series u k (t). Also, the prediction input data storage unit 208 stores the output reference value y0.

[0120] The prediction output data storage unit 209 stores the simple output time series v k (t) predicted by the simple output prediction unit 202.

[0121] Note that the model learning unit 201 may create a feature quantity model batchwise using a plurality of output time series y s (t) and input time series u s (t) stored in the learning data storage unit 206, or may create and update the feature quantity model sequentially using the output time series y s (t) and input time series u s (t). Also, the output reference value y0 may be given as an input, or the current value of the control amount y measured by the measurement unit 203 may be used.

[0122] For example, by using the current value of the control amount y as the output reference value y0, the plant monitoring device 20 having the above configuration can determine how the control amount y from the present to the future changes (that is, how the plant response changes) when the virtual operation amount time series is given to the controlled plant 30, which is represented by the simple output time series v k(t) can be displayed. Therefore, an operator or the like of the plant 30 to be controlled can know, for example, an appropriate operation for the plant 30 to be controlled with reference to the simple output time series v k (t).

[0123] [Embodiment] Hereinafter, examples of each embodiment described above will be described.

[0124] · Embodiment 1 First, Example 1 will be described as an example of the first embodiment.

[0125] In Example 1, the output time series y s (t) is time series data of one-dimensional scalar values, and the input time series u s (t) is time series data of two-dimensional vectors. The input time series u s (t) changes randomly, and the number of samples is assumed to be 100. That is, s ∈ {1, ···, 100}

[0126] Also, in Example 1, a virtual output time series is generated by the following generation formula and is used as the output time series y s (t). [Equation] Here, u s,1 (t) is the first element of the two-dimensional vector representing u s (t), and u s,2 (t) is the second element of the two-dimensional vector representing u s (t). Also, T is a predetermined value, and in this example, T = 1

[0127] Since the above generation formula includes the product and absolute value of a trigonometric function and an exponential function and also includes a trend term, it has characteristics that are not suitable for Fourier transform or linear models. Therefore, it can be said that it is difficult to perform prediction with existing linear methods. Furthermore, since the number of samples is only 100, it can be said that it is insufficient for learning a complex neural network such as a Transformer, for example.

[0128] In Example 1, the output feature quantity Y s was the following five-dimensional vector. [Number] Also, the input feature quantity U s was the following four-dimensional vector obtained by simplifying the input feature quantity shown in Equation 2 above. [Number] Furthermore, the feature quantity model was a linear model represented by F:Y s = A·U s + b. Here, A is a 5×4 matrix and b is a five-dimensional vector.

[0129] At this time, the model learning unit 201 created the above feature quantity model F using the PLS (Partial Least Squares) method, which is one of the linear model creation methods. Note that instead of the PLS method, the above feature quantity model F may be created using a method such as principal component regression (PCR).

[0130] Hereinafter, the first to fifth elements of the five-dimensional vector representing the output feature quantity Y s are respectively denoted as Y s,1 , Y s,2 , Y s,3 , Y s,4 , Y s,5 . At this time, the prediction accuracy of the feature quantity model F will be described with reference to FIG. 19. FIG. 19 is a diagram for explaining the prediction accuracy of the feature quantity model F in Example 1. In the example shown in FIG. 19, the vertical axis represents the predicted value by the feature quantity model F, and the horizontal axis represents the true value.

[0131] As shown in FIG. 19, Y s,1 can be predicted with relatively good accuracy, and since there is only one point for Y s,5 , it can be correctly predicted. On the other hand, for the other elements, the accuracies are scattered.

[0132] Also, as an example, for the prediction accuracy when predicting the simple output time series v k (t) and u k' (t) using two input time series u k (t) and v k' (t), it will be described with reference to FIGS. 20 and 21. FIGS. 20 and 21 are diagrams for explaining the prediction accuracy of the simple output time series in Example 1. In the example shown in FIG. 20, y pred (t)=v k (t), and also y true (t) is the true value of y pred (t). Similarly, in the example shown in FIG. 21, y pred (t)=v k' (t), and also y true (t) is the true value of y pred (t).

[0133] As shown in FIGS. 20 and 21, it can be said that the general trend can be captured by the simple output time series v k (t) and u k' (t) for either of the input time series u k (t) and v k' (t).

[0134] ·Example 2 Next, Example 2 will be described as an example of the second embodiment.

[0135] In Example 2 as well, the same output time series y s (t) and input time series u s (t) are used. Also, in Example 2, as shown in FIG. 22, the output time series y end from time t = 0 to t = t s is divided into two intervals. Note that Interval 1 is from time 0 to 100, and Interval 2 is from time 100 to 400, and they are unequal intervals.

[0136] In Example 2, the output feature amount Y s,i is the following 5 - dimensional vector. [Number] Also, the input feature amount U s was set as the following 4-dimensional vector obtained by simplifying the input feature amount shown in the above formula 2, similar to Example 1.

[0137] Furthermore, the feature amount model was set as a linear model represented as follows.

[0138] F1: Y s,1 = A1·U s + b1 F2: Y s,2 = A2·U s + C2·Y s,1 + b2 Here, A1 and A2 are 5×4 matrices, C2 is a 5×5 matrix, and b1 and b2 are 5-dimensional vectors.

[0139] At this time, the model learning unit 201 created the above feature amount model F i (i = 1, 2) using the PLS method, which is one of the linear model creation methods.

[0140] Hereinafter, the first element to the fifth element of the 5-dimensional vector representing the output feature amount Y s,i are respectively denoted as Y s,i,1 , Y s,i,2 , Y s,i,3 , Y s,i,4 , Y s,i,5 . At this time, the prediction accuracy of the feature amount model F i will be described with reference to FIG. 23. FIG. 23 is a diagram for explaining the prediction accuracy of the feature amount model F i in Example 2. In the example shown in FIG. 23, the vertical axis represents the predicted value by the feature amount model F i , and the horizontal axis represents the true value.

[0141] As shown in FIG. 23, Y s,1,1 , Y s,1,3 , Y s,1,4 , Y s,2,2 , Y s,2,3 , Y s,2,4 , Y s,2,5It can be predicted with relatively good accuracy. On the other hand, for other elements, the accuracies are scattered. In Example 1, 2 / 5 of the output feature elements could be predicted with relatively good accuracy, while in Example 2, 7 / 10 could be predicted with relatively good accuracy. Therefore, it can be said that the prediction accuracy of the output features has been improved overall by interval division.

[0142] Also, as an example, regarding the prediction accuracy when predicting two simple output time series v k (t) and u k' (t) using the same two input time series u k (t) and v k' (t) as in Example 1, it will be described with reference to FIGS. 24 and 25. FIGS. 24 and 25 are diagrams for explaining the prediction accuracy of the simple output time series in Example 2. In the example shown in FIG. 24, y pred1 (t) is the simple output time series predicted in Example 1, y pred2 (t) is the simple output time series predicted in Example 2, and y true (t) is the true value of y pred2 (t). Similarly, in the example shown in FIG. 25, y pred1 (t) is the simple output time series predicted in Example 1, y pred2 (t) is the simple output time series predicted in Example 2, and y true (t) is the true value of y pred2 (t).

[0143] As shown in FIGS. 24 and 25, in Example 2, for waveforms with two peaks that could not be captured in Example 1, simple output time series capturing those peaks can be predicted, and it can be said that a more accurate prediction can be made than in Example 1.

[0144] [Summary] As described above, the time series prediction device 10 according to the first to third embodiments can perform accurate model learning with relatively little learning data even for a non-linear process that is difficult to model with a known linear method such as Fourier transform, etc., and can also predict the output time series with relatively high accuracy and at high speed.

[0145] As also shown in the application example, the time series prediction device 10 according to the first to third embodiments can be applied, for example, to plant response prediction required in the field of plant monitoring, etc. In this case, as the output time series, for example, time series data such as temperature, pressure, flow rate, concentration, energy consumption, etc. can be used. On the other hand, as the input time series, for example, time series data such as current, voltage, rotational speed, valve opening degree, power storage amount, discharge amount, etc. can be used. However, these are all examples, and in addition to these, time series data of any input variable of a known plant can be used as the input time series, and time series data of any output variable can be used as the output time series. Also, in addition to plant response prediction, as long as it predicts the output time series from the input time series, it can be similarly applied when predicting the output time series of any object other than the plant.

[0146] The present invention is not limited to the specifically disclosed above embodiments, and various modifications, changes, combinations with known technologies, etc. are possible without departing from the description of the claims.

Explanation of Signs

[0147] 10 Time series prediction device 20 Plant monitoring device 30 Controlled plant 40 Conventional control device 101 Input device 102 Display device 103 External I / F 103a Recording medium 104 Communication I / F 105 RAM 106 ROM 107 Auxiliary storage device 108 Processor 109 Bus 201 Model learning unit 202 Simple output prediction unit 203 Measurement unit 204 Display control unit 205 Timer 206 Learning data storage unit 207 Feature model storage unit 208 Prediction input data storage unit 209 Prediction output data storage unit

Claims

1. A time series prediction device that predicts an output time series which is time series data of an output variable output from an object, using, as inputs, a first input time series which is time series data of an input variable input to the object, and a first output time series which is the output time series output from the object when the first input time series is input to the object, and creating a feature model that models the relationship between a first input feature amount representing the features of the first input time series and a first output feature amount representing the features of the first output time series, using, as inputs, a second input time series which is time series data of an input variable that is a prediction target of the output time series, and an output reference value which is a reference value of the output variable, predicting a second output feature amount from a second input feature amount representing the features of the second input time series by the feature model, and predicting, as a second output time series, time series data represented by a predetermined trajectory starting from the output reference value and having the features represented by the predicted second output feature amount, the time series data being predicted to be output from the object when the second input time series is input to the object, A time series prediction device having the above.

2. The model creation unit divides the first output time series into a plurality of sections, generates, for each of the plurality of sections, a first output feature amount in the section, creates a plurality of feature models that respectively model the relationships between the first input feature amount and each of the plurality of first output feature amounts for each section, The time series prediction unit predicts a plurality of second output feature amounts for each section from the second input feature amount and each of the plurality of feature models, The time series prediction device according to claim 1, predicting, as the second output time series, time series data represented by a predetermined trajectory starting from the output reference value and having the features represented by the plurality of second output feature amounts for each of the plurality of sections.

3. The model creation unit A feature model F that predicts the first output feature amount in the first section using the first input feature amount as an input １ and A feature model F that predicts the first output feature amount in the i-th section using, as inputs, the first input feature amount and the first output feature amount in the (i-1)-th section (where i > 1). ｉ Create each of them, The time series prediction unit the second input feature amount and the feature amount model F １ predict the second output feature amount in the first section from The second input feature amount, the second output feature amount in the i-1-th section, and the feature model F ｉ The time series prediction device according to claim 2, which predicts the second output feature amount in the i-th section from the above.

4. The model creation unit generates, for each of the plurality of sections, a first input feature amount in the section, creates a plurality of feature models that respectively model the relationships between the first input feature amount and the first output feature amount in the section for each section, The time series prediction unit The time series prediction device according to claim 2, which predicts a plurality of second output feature amounts for each interval from the plurality of second input feature amounts for each interval and each of the plurality of feature amount models.

5. The model creation unit Using the first input feature amount in the first section as input, a feature amount model F that predicts the first output feature amount in the first section １ and A feature model F that predicts the first output feature amount in the i-th section by using, as inputs, the first input feature amount in the i-th section (where i > 1) and the first output feature amount in the (i - 1)-th section ｉ and create them respectively, The time series prediction unit The second input feature amount in the first section and the feature amount model F １ predict the second output feature amount in the first section from, The second input feature amount in the i-th section, the second output feature amount in the (i - 1)-th section, and the feature model F ｉ The time series prediction device according to claim 4, which predicts the second output feature amount in the i-th section from these.

6. The time series prediction unit The time series prediction device according to any one of claims 2 to 5, which predicts time series data represented by a predetermined trajectory that starts from the output reference value in the first interval and starts from the final value of the (i - 1)-th interval (where i > 1) in the i-th interval as the second output time series.

7. In the first output feature amount The difference d between the maximum value of the first output time series and the initial value of the first output time series １ and the elapsed time t when the maximum value is taken １ and the difference d between the minimum value of the first output time series and the initial value ２ and the elapsed time t when the minimum value is taken ２ and the difference d between the final value of the first output time series and the initial value ３ and, The time series prediction device according to claim 1, which includes.

8. The time series prediction unit When the output reference value is y ０ and the elapsed time is t １ after that, a first point where it becomes y ０ + d １ , a second point where it becomes y ２ + d ０ after the elapsed time t ２ , and a third point where it becomes y ０ + d ３ at the final time, and predicting a predetermined trajectory passing through these points as the second output time series, the time series prediction device according to claim 7.

9. The time series prediction unit the elapsed time t １ is the elapsed time t ２ when it is earlier than, a predetermined trajectory composed of a trajectory connecting the output reference value and the first point, a trajectory connecting the first point and the second point, and a trajectory connecting the second point and the third point is predicted as the second output time series, the elapsed time t １ is the elapsed time t ２ When it is later than, a predetermined trajectory composed of a trajectory connecting the output reference value and the second point, a trajectory connecting the second point and the first point, and a trajectory connecting the second point and the third point is predicted as the second output time series. The time series prediction device according to claim 8.

10. In the first input feature amount The elapsed time from the start time of the first input time series to the time when the change in the value of the first input time series starts, and The elapsed time from the start time to the time when the change in the value of the first input time series ends are included. The time series prediction device according to claim 1.

11. The feature amount model is a linear model or a non-linear model. The time series prediction device according to claim 1.

12. The object is a plant, The input variable is a variable representing the operation amount of the plant, and the output variable is a variable representing the control amount of the plant. The time series prediction device according to claim 1.

13. A time series prediction method for predicting an output time series that is time series data of an output variable output from an object, Using, as inputs, a first input time series that is time series data of an input variable input to the object and a first output time series that is the output time series output from the object when the first input time series is input to the object, a model creation procedure for creating a feature amount model that models the relationship between a first input feature amount representing the feature of the first input time series and a first output feature amount representing the feature of the first output time series A time series prediction procedure that takes as input a second input time series which is time series data of an input variable to be predicted for an output time series, and an output reference value which is a reference value of the output variable, predicts a second output feature amount from a second input feature amount representing features of the second input time series by means of the feature model, and predicts, as a second output time series which is a time series predicted to be output from the target when the second input time series is input to the target, time series data represented by a predetermined trajectory starting from the output reference value and having the features represented by the predicted second output feature amount. A time series prediction method executed by a computer.

14. A time series prediction device that predicts a time series of an output variable output from a target, A model creation unit that creates a feature model that models the relationship between a first input feature amount representing features of a first input time series and a first output feature amount representing features of a first output time series, taking as input the first input time series which is time series data of an input variable input to the target and the first output time series which is the time series output from the target when the first input time series is input to the target. A time series prediction unit that takes as input a second input time series which is time series data of an input variable to be predicted for an output time series, and an output reference value which is a reference value of the output variable, predicts a second output feature amount from a second input feature amount representing features of the second input time series by means of the feature model, and predicts, as a second output time series which is a time series predicted to be output from the target when the second input time series is input to the target, time series data represented by a predetermined trajectory starting from the output reference value and having the features represented by the predicted second output feature amount. A program for causing it to function as such.

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