JP2022011858A - Prediction model learning method, predication model learning system, and plant control system - Google Patents

Abstract

To learn a prediction model that is superb in reliability.SOLUTION: A prediction model for use in predicting an objective variable from at least one explanatory variable is updated based on a first evaluation value and second evaluation value. The first evaluation value is calculated as an index representing a prediction error of the prediction model. The second evaluation value is calculated as an index representing a degree of consistency between feature quantities concerning at least some sensitivity directions of the explanatory variables with respect to the objective variable and permissible ranges set for the feature quantities on the basis of known information.SELECTED DRAWING: Figure 1

Description

The present disclosure relates to a prediction model learning method, a prediction model learning device, and a plant control system.

In various fields, predictions of future events are being made using prediction models that represent the relationships between explanatory variables and objective variables that are causally related to each other. For example, in a thermal power plant that burns fuel, a prediction model is constructed with the control parameters that define the operating conditions of the plant as explanatory variables and the efficiency of the plant as the objective variable, and changes in operating conditions are used using the prediction model. Optimal operating conditions can be verified by predicting changes in efficiency with respect to.

Such a prediction model can be constructed by machine learning using teacher data that represents the relationship between the explanatory variables and the objective function based on past data. For example, when using a neural network, which is a method of machine learning, it is necessary to learn parameters such as the weight and bias of the neural network so that the output value of the prediction model when the training data is input approaches the value of the teacher data. Then, the prediction model is constructed.

Event prediction using predictive models built by machine learning has spread to a variety of applications in recent years and does not lead to inappropriate decisions except for extremely low-risk applications such as product recommendations. Therefore, it is necessary to ensure sufficient reliability. In particular, if the relationship between the explanatory variables and the objective variables learned by the predictive model is different from the existing knowledge, it may cause inappropriate decision making. For example, according to existing knowledge, if the temperature rises, the sales of ice cream will increase, but due to lack of data etc., the prediction model will learn the opposite relationship (the lower the temperature, the more ice cream will sell). If so, the prediction model recommendations are the opposite of what they really are and can lead to inappropriate decisions.

In order to prevent such inappropriate decision-making, it is necessary to have sufficient teacher data necessary for constructing a prediction model. In Patent Document 1, the data area defined by the explanatory variable and the objective variable is divided into a plurality of areas, and the index value indicating the data shortage is calculated for each area, so that the user can use the data shortage area. It has been proposed to help obtain the additional data needed to recognize and build reliable predictive models. In particular, in Patent Document 1, an area in which additional data acquisition is required in order to improve the prediction accuracy of the prediction model by calculating an index value indicating data shortage in consideration of the sensitivity of the objective variable to the explanatory variable in each area. Is presented to the user.

Japanese Unexamined Patent Publication No. 2019-197267

The above-mentioned Patent Document 1 presents to the user an area in which data necessary for constructing a predictive model having sufficient reliability is lacking. Therefore, even if the user can recognize the lacking data, the prediction model cannot be improved when the data acquisition itself is difficult, for example, when the data collection requires cost and time. Even if the prediction model is built on sufficient teacher data, it is not built as a prediction model with correct sensitivity due to the nature of the algorithm and the multicollinearity of the data, making inappropriate decisions. May bring.

At least one aspect of the present disclosure is made in view of the above circumstances, and provides a learning method of a predictive model capable of constructing a highly reliable predictive model, a learning device of the predictive model, and a plant control system. With the goal.

The method of learning the prediction model according to at least one aspect of the present disclosure is to solve the above-mentioned problems.
A method of learning a prediction model for predicting an objective variable from at least one explanatory variable.
The first evaluation value calculation process for calculating the first evaluation value indicating the prediction error of the prediction model, and
A second evaluation value indicating the degree of agreement between the feature amount related to the sensitivity direction of at least a part of the at least one explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information is calculated. Second evaluation value calculation process and
A predictive model update step in which learning is performed by updating the predictive model based on the first evaluation value and the second evaluation value.
To prepare for.

The learning device for the prediction model according to at least one aspect of the present disclosure is to solve the above-mentioned problems.
A prediction model learning device for predicting an objective variable from at least one explanatory variable.
The first evaluation value calculation unit that calculates the first evaluation value indicating the prediction error of the prediction model, and
A second evaluation value indicating the degree of agreement between the feature amount related to the sensitivity direction of at least a part of the at least one explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information is calculated. The second evaluation value calculation unit and
A prediction model update unit that performs learning by updating the prediction model based on the first evaluation value and the second evaluation value.
To prepare for.

The plant control system according to at least one aspect of the present disclosure is to solve the above problems.
The learning device for the prediction model according to at least one aspect of the present disclosure,
A prediction unit that predicts parameters corresponding to the objective variable by inputting input parameters corresponding to the at least one explanatory variable into the prediction model updated by the prediction model update unit.
An optimum value calculation unit that calculates the optimum value of the at least one explanatory variable based on the parameters predicted by the prediction unit.
A control unit that controls the plant based on the optimum value,
To prepare for.

According to at least one aspect of the present disclosure, it is possible to provide a predictive model learning method capable of constructing a highly reliable predictive model, a predictive model learning device, and a plant control system.

It is an overall block diagram of the plant control system which concerns on at least one Embodiment of this disclosure. It is a table which shows the classification example of a sensitivity direction type, and the feature amount and allowable range corresponding to each sensitivity direction type. It is a block diagram which shows the structure for calculating the sensitivity direction error with respect to the objective variable of the explanatory variable in the 2nd evaluation value calculation part of FIG. It is a flowchart which shows the learning method of the prediction model which concerns on at least one Embodiment of this disclosure for each process. It is a flowchart which shows the detailed process of step S20 of FIG. It is a scatter matrix of a data set used for constructing a prediction model M by a learning device. This is an example of selecting the sensitivity direction type for each explanatory variable. The PD plot and the ICE plot obtained for each explanatory variable. This is the verification result of the convergence of the prediction error and the sensitivity direction error with respect to the number of epochs. This is the verification result of the convergence of the prediction error and the sensitivity direction error with respect to the number of epochs. It is a CCPP data set showing the relationship between AT (horizontal axis) representing the outside air temperature and PE (vertical axis) representing the generated power. It is a prediction model M obtained from the CCPP data set of FIG. 10A. It is a bike sharing data set showing the relationship between atemp (horizontal axis) representing the sensible temperature and ct (vertical axis) representing the number of rental bicycles. It is a predictive model obtained from the bike sharing data set of FIG. 11A. It is a table which compares the evaluation result of the prediction model obtained by each method of FIG. 10B and FIG. 11B.

Hereinafter, some embodiments of the present disclosure will be described with reference to the accompanying drawings. However, the dimensions, materials, shapes, relative arrangements, etc. of the components described as embodiments or shown in the drawings are not intended to limit the scope of the present disclosure to this, and are merely explanatory examples. do not have.
For example, expressions that represent relative or absolute arrangements such as "in one direction", "along a certain direction", "parallel", "orthogonal", "center", "concentric" or "coaxial" are exact. Not only does it represent such an arrangement, but it also represents a tolerance or a state of relative displacement at an angle or distance to the extent that the same function can be obtained.
For example, expressions such as "same", "equal", and "homogeneous" that indicate that things are in the same state not only represent exactly the same state, but also have tolerances or differences to the extent that the same function can be obtained. It shall also represent the existing state.
For example, the expression representing a shape such as a quadrangular shape or a cylindrical shape not only represents a shape such as a quadrangular shape or a cylindrical shape in a geometrically strict sense, but also an uneven portion or a chamfer within the range where the same effect can be obtained. It shall also represent the shape including the part and the like.
On the other hand, the expressions "equipped", "equipped", "equipped", "included", or "have" one component are not exclusive expressions excluding the existence of other components.

FIG. 1 is an overall configuration diagram of a plant control system 100 according to at least one embodiment of the present disclosure. The plant control system 100 controls the control end of the plant. The plant control system 100 has a hardware configuration including an electronic arithmetic unit such as a computer, and cooperates with the hardware configuration by installing a program for executing the control described below as software. It is configured to function as the plant control system 100 according to at least one embodiment of the present disclosure.

FIG. 1 shows a functional configuration of such a plant control system 100 as a block diagram. The plant control system 100 includes a prediction model storage unit 110, an explanatory variable acquisition unit 120, a prediction unit 130, an optimum value calculation unit 140, a control unit 145, and a learning device 150.

The prediction model storage unit 110 stores a prediction model M for predicting the objective variable y from at least one explanatory variable. In the following embodiment, as an example of the prediction model M, a prediction model for predicting the objective variable y from a plurality of explanatory variables X _k (= x ₁ , x ₂ , ...) Is handled, but the explanatory variable is singular. May be. The prediction model M stored in advance is stored in the prediction model storage unit 110, and the prediction model M is configured to be updatable by machine learning by the learning device 150. The predictive model M is constructed using an algorithm that learns the parameters of the model so as to optimize the evaluation index indicating the performance of the model, for example, a neural network. In the present embodiment, for example, a prediction model M for inputting a parameter related to the operating conditions of the plant as the explanatory variable X _k and predicting a parameter related to the performance of the plant (for example, efficiency) as the objective variable y will be described as an example.
In the following description, when the kth (k is an arbitrary natural number) of a plurality of explanatory variables X _k is indicated, it is indicated as "explanatory variable x _k ".

The explanatory variable acquisition unit 120 acquires at least one explanatory variable X _k to be input to the prediction model M. As described above, at least one explanatory variable X _k is a parameter relating to the operating conditions of the plant, and these parameters are, for example, actually measured values such as sensor detection values installed in the plant and each component of the plant. A control value for, etc. can be used.

The prediction unit 130 predicts the objective variable y from at least one explanatory variable X _k acquired by the explanatory variable acquisition unit 120 using the prediction model M. Specifically, the prediction unit 130 reads the prediction model M from the prediction model storage unit 110 by accessing the prediction model storage unit 110, and at least one explanation acquired by the explanatory variable acquisition unit 120 for the prediction model M. By inputting the variable X _k , the objective variable y is calculated. In the present embodiment, as described above, by inputting the parameters related to the operating conditions of the plant into the prediction model M, for example, the parameters related to the performance of the plant are predicted.

The optimum value calculation unit 140 calculates the optimum value for controlling the control end of the plant based on the prediction result of the prediction unit 130. The optimum value is calculated as an explanatory variable X _k when the objective variable y calculated by the prediction unit 130 is the best. For example, when the objective variable y predicted by the prediction model M is the plant efficiency, the parameter corresponding to the explanatory variable X _k when the plant efficiency is the best is calculated as the optimum value.

The control unit 145 controls the plant based on the optimum value of the explanatory variable _Xk calculated by the optimum value calculation unit 140. This enables plant control in which the objective variable y is the best.

The learning device 150 updates the prediction model M stored in the prediction model storage unit 110 by performing machine learning. By repeatedly performing machine learning by the learning device 150 at a predetermined timing, the reliability of the prediction model M is sequentially improved. In particular, the learning device 150 learns the prediction model M so as to have the following configuration, which is less likely to cause inappropriate decision making and has excellent reliability.

As shown in FIG. 1, the learning device 150 includes a data set creation unit 152, a first evaluation value calculation unit 156, a second evaluation value calculation unit 158, a knowledge table storage unit 159, and an analysis unit 160. A model update unit 162 is provided.

The data set creation unit 152 creates a data set DS including a plurality of explanatory variables X _k and an objective variable y by using the prediction model M stored in the prediction model storage unit 110. The creation of the data set DS is performed, for example, by inputting a plurality of explanatory variables X _k into the prediction model M, outputting the objective variable y, and associating these explanatory variables x and the objective variable y.

Further, the data set creation unit 152 outputs the teacher data TD used for machine learning of the prediction model M. The teacher data TD is prepared, for example, in a database (not shown) in which plant operation data is stored in advance, and the database creation unit 152 outputs the teacher data TD acquired by accessing the database. The teacher data TD is prepared to include a plurality of explanatory variables X _k and an objective variable y, as in the data set DS created by the data set creation unit 152.

The first evaluation value calculation unit 156 calculates the first evaluation value R1. The first evaluation value R1 is an index showing a prediction error with respect to the teacher data of the prediction model M. In the present embodiment, the first evaluation value calculation unit 156 has a prediction error e calculated based on the data set DS created by the data set creation unit 152 and the teacher data TD acquired by the teacher data acquisition unit 154. Calculated as _p .

The second evaluation value calculation unit 158 calculates the second evaluation value R2. The second evaluation value R2 is an index relating to the sensitivity direction of the plurality of explanatory variables X _k in the prediction model M with respect to the objective variable y, and more specifically, the feature quantity relating to the sensitivity direction of the plurality of X _k objective variables y. , Indicates the degree of agreement with the allowable range set for the feature amount.

The calculation of the second evaluation value R2 is performed based on the knowledge table KT stored in the knowledge table storage unit 159. The knowledge table KT defines a sensitivity direction type t _sd for classifying the sensitivity direction. The sensitivity direction of the plurality of explanatory variables X _k with respect to the objective variable y can be classified into any of the sensitivity direction types t _sd specified in the knowledge table KT.

Here, FIG. 2 is a table showing a classification example of the sensitivity direction type t _sd , and a feature amount and an allowable range corresponding to each sensitivity direction type t _sd . Various patterns can be considered for the classification of the sensitivity direction type t _sd , but in this embodiment, "increase", "decrease", "convex downward", "convex upward", "negligible" and "unknown". The case where it can be classified into the 6 patterns of the above will be described by way of example.

When the sensitivity direction type t _sd is classified as "increase", the explanatory variable x _k increases when the other explanatory variables X _c excluding the explanatory variable x _k among the plurality of explanatory variables X _k are set as fixed values. Accordingly, the objective variable y also has an increasing sensitivity direction (at this time, among the plurality of explanatory variables X _k , the other explanatory variables X _c excluding the explanatory variable x _k are constants). For example, when the relationship between the explanatory variable x _k and the objective variable y is represented by the approximation line y = a · x _k , the features corresponding to the sensitivity direction type tsd are _{Ak (= a k (} ⁰⁾ , a). _k ⁽¹⁾ , ..., a _k ⁽ⁿ⁾ ), and the upper limit value a _max (> 0) and the lower limit value a _min (> 0) of the slope a are defined as the allowable range of the feature amount. Will be done.

When the sensitivity direction type t _sd is "decrease", when the explanatory variables X _c other than the explanatory variables x _k among the plurality of explanatory variables X _k are set as fixed values, as the explanatory variables x _k increase. , The objective variable y has a sensitivity direction in which it decreases (at this time, among the plurality of explanatory variables X _k , the other explanatory variables X _c excluding the explanatory variable x _k are constants). For example, when the relationship between the explanatory variable x _k and the objective variable y is represented by the approximation line y = a · x _k , the features corresponding to the sensitivity direction type t _sd are _{Ak (= a k (} ⁰⁾ , a). _k ⁽¹⁾ , ..., _Ak ⁽ⁿ⁾ ), and the upper limit value a _max (<0) and the lower limit value a _min (<0) of the slope a are defined as the allowable range of the feature amount. Will be done.

When the sensitivity direction type t _sd is "convex downward", when the explanatory variables X _c other than the explanatory variables x _k among the plurality of explanatory variables X _k are set as fixed values, the explanatory variables x at the initial stage. The objective function y decreases as _k increases, and the objective function y has a sensitivity direction in which the objective function y turns to increase from the middle (at this time, among the plurality of explanatory variables X _k , the other explanatory variables X _c excluding the explanatory variables x _k are Let it be a constant). For example, when the relationship between the explanatory variable x _k and the objective variable y is represented by the approximation line dy / dx = a'· x _k , the feature quantity corresponding to the sensitivity direction type t _sd is _A'k (= _a'k ). ⁽⁰⁾ , _a'k ( ¹⁾ , ..., a'k (n)), and X _ipk (= x _ipk ⁽⁰⁾ , x _ipk ⁽¹⁾ , ..., x _ipk ⁽ⁿ⁾ ), As the permissible range of the feature amount, the upper limit value _a'max (> 0) of the slope a', the lower limit value _a'min (> 0), and the inflection point coordinates X _ipk of the explanatory variable x _k . An upper limit value x _ipmax and a lower limit value x _ipmin are specified.

When the sensitivity direction type t _sd is "convex upward", when the explanatory variables X _c other than the explanatory variables x _k among the plurality of explanatory variables X _k are set as fixed values, the explanatory variables x at the initial stage. The objective function y increases as _k increases, and the objective function y starts to decrease from the middle. (At this time, among the plurality of explanatory variables X _k , the other explanatory variables X _c excluding the explanatory variables x _k are Let it be a constant). For example, when the relationship between the explanatory variable x _k and the objective variable y is represented by the approximation line dy / dx = a'x, the feature quantity corresponding to the sensitivity direction type tsd is _A'k (= _a'k ^(0)). , _A'k ⁽¹⁾ , ..., a'k (n)), and X _ipk (= x _ipk ⁽⁰⁾ , x _ipk ⁽¹⁾ , ..., x _ipk ⁽ⁿ⁾ ). As the permissible range of the feature amount, the upper limit value _a'max (<0) of the slope a', the lower limit value _a'min (<0), and the inflection point coordinate X _ipk of the explanatory variable x _k are the upper limit value x. _ipmax and lower limit x _ipmin are specified.

When the sensitivity direction type t _sd is "negligible", when the other explanatory variables X _c excluding the explanatory variables x _k among the plurality of explanatory variables X _k are set as fixed values, the change of the explanatory variables x _k is satisfied. The sensitivity direction is so small that the change in the objective variable y is negligible (at this time, among the plurality of explanatory variables X _k , the other explanatory variables X _c excluding the explanatory variable x _k are constants). In this case, it corresponds to the case where the inclination a is sufficiently small when the above-mentioned sensitivity direction type tsd is "increase" or "decrease". Therefore, the feature amount corresponding to the sensitivity direction type tsd is Ak (= _ak ⁽⁰⁾ , _ak ⁽¹⁾ , ..., _Ak ( _n ⁾ ), and the sensitivity is allowed as the allowable range of the feature amount. As in the case where the direction type tsd is "increase" or "decrease", the upper limit value a _max and the lower limit value a _min of the slope a are specified.

When the sensitivity direction type t _sd is "unknown", the explanatory variable x _k and the objective variable y when the other explanatory variables X _c excluding the explanatory variable x _k among the plurality of explanatory variables X _k are set as fixed values. Since the relationship with the feature amount is unknown, the feature amount and the permissible range corresponding to the feature amount are not defined, and the sensitivity direction error is always regarded as 0.

The second evaluation value calculation unit 158 calculates the sensitivity direction error e _sd of the prediction model by calculating the sensitivity direction error e _sdk with respect to the objective variable y of at least one explanatory variable X _k . Here, FIG. 3 is a block diagram showing a configuration for calculating the sensitivity direction error e _sdk with respect to the objective variable y of a certain explanatory variable x _k in the second evaluation value calculation unit 158 of FIG. 1. The second evaluation value calculation unit 158 includes a feature amount calculation unit 158a and a sensitivity direction error calculation unit 158b.

The feature amount calculation unit 158a calculates the feature amount based on the sensitivity direction type t _sd selected for the explanatory variable x _k and the data set DS created by the data set creation unit 152. The feature amount calculated here is calculated as follows based on the type of the sensitivity direction type _tsd input to the feature amount calculation unit 158a.

ここでｘ_ｋ、ｊは、ＩＣＥプロットにおける説明変数ｘ_ｋのｍ個の成分のうちｊ番目を示す。またＸ_ｋは、各ｘ_ｋ、ｊ（＝［ｘ_ｋ、０、ｘ_ｋ、１、・・・ｘ_ｋ、ｍ］）のベクトルである。またＦ（Ｘ_ｋ，Ｘ_ｃ ^（ｉ））は各ｆ（ｘ_ｋ、ｊ、Ｘ_ｃ ^（ｉ））のベクトルであり、Ｆ’（Ｘ_ｋ，Ｘ_ｃ ^（ｉ））は各ｆ’（ｘ_ｋ、ｊ、Ｘ_ｃ ^（ｉ））のベクトルである。尚、ｆ’はｆのｘ_ｋによる微分である。 When the sensitivity direction type t _sd is "increase", "decrease", or "negligible", the feature amount calculation unit 158a determines that the feature amount is _{Ak (= a k (0), a k (} ¹ ₎ ^, ..., Ak ⁽ⁿ⁾ ₎ is calculated from the following equation.

Here, x _{k and j} indicate the jth of the m components of the explanatory variable x _k in the ICE plot. Further, X _k is a vector of each x _{k, j} (= [x _{k, 0} , x _{k, 1} , ... x _{k, m} ]). Further, F (X _k , X _c ⁽ⁱ⁾ ) is a vector of each f (x _{k, j} , X _c ⁽ⁱ⁾ ), and F'(X _k , X _c ⁽ⁱ⁾ ) is each f'(x). It is a vector of _{k, j} , X _c ⁽ⁱ⁾ ). In addition, f'is a derivative of f by x _k .

When the sensitivity direction type t _sd is "convex upward" and "convex downward", the feature amount calculation unit 158a is used as a feature amount of _A'k (= _a'k ⁽⁰⁾ , a'. _k ⁽¹⁾ , ..., a'k (n)) and X _ipk (= x _ipk ⁽⁰⁾ , x _ipk ⁽¹⁾ , ..., x _ipk ⁽ⁿ⁾ ) are calculated from the following equations. do.

Subsequently, the sensitivity direction error calculation unit 158b calculates the sensitivity direction error e _sdk based on the feature amount calculated by the feature amount calculation unit 158a and the allowable range corresponding to the feature amount.
For example, when the sensitivity direction type t _sd is "increase", "decrease", or "negligible", the sensitivity direction error e _sdk is the feature amount Ak corresponding to the sensitivity direction type _tsd and the feature amount. It is obtained by the following equation using the permissible range (a _max , a _min ) corresponding to _Ak .
e _sdk = _calDev (Ak, a _max , a _min ) (4)

Here, _calDev is a function that outputs the root mean square of the amount of deviation from the permissible range (a _max , a _min ) of the feature amount Ak. To give a specific example, for example, when the feature amount Ak = [ _-0.3,0.0,1.1 ] and a _max = 0.5 and a _min = 0.0 are set, the sensitivity direction error e _sdk is. It is calculated as follows.
e _sdk = (0.3) ² + (0.0) ² + (0.6) ² = 0.15

When the sensitivity direction type t _sd is "convex upward" and "convex downward", the sensitivity direction error e _sdk is the feature quantities _A'k , X _ipk , and corresponding to the sensitivity direction type t _sd . , The permissible range corresponding to the feature quantities _A'k and X _ipk ( _a'max , _a'min , _xipmax , _xipmin ) is used and is obtained by the following equation.
e _sdk = calDev ( _A'k , _a'max , _a'min ) + calDev (X _ipk , x _ipmax , x _ipmin ) (5)
Here, calDev is a function that outputs the root mean square of the deviation amount from the allowable range of the feature quantities _A'k and X _ipk ( _{a'max, a'min, x ipmax , x ipmin} ).

The second evaluation value calculation unit 158 calculates the sensitivity direction error e _sdk for each explanatory variable x _k in this way, and by synthesizing these, the second evaluation value R2 indicating the sensitivity direction type t _sd of the prediction model M. Is calculated.

Returning to FIG. 1, the analysis unit 160 predicts based on the first evaluation value R1 calculated by the first evaluation value calculation unit 156 and the second evaluation value R2 calculated by the second evaluation value calculation unit 158. The total error e of the model M is calculated. For example, the total error e is calculated as the linear sum of the prediction error e _p calculated as the first evaluation value R1 and the sensitivity direction error e _sd calculated as the second evaluation value R2.

The prediction model update unit 162 updates the prediction model M stored in the prediction model storage unit 110 based on the total error e calculated by the analysis unit 160. For example, the prediction model update unit 162 updates the prediction model M so that the total error e is minimized. For example, when the prediction model M is constructed as a neural network, each coefficient set between each hidden layer existing between the input layer and the output layer of the neural network minimizes the total error e. Will be updated. The prediction model M is learned by executing such an update operation of the prediction model M a predetermined number of times.

In the conventional machine learning with teacher data, the prediction model M is updated based only on the first evaluation value R1 so that the prediction error _ep is minimized. In this case, if the teacher data TD is insufficient, only the prediction error _ep with respect to the teacher data may be reduced, and a prediction model M having a large sensitivity direction error may be obtained. Since such a prediction model M does not have the correct sensitivity, it may lead to inappropriate decision making as described above.

In the present embodiment, such a problem can be effectively solved by updating the prediction model M based on both the first evaluation value R1 and the second evaluation value R2. Since the second evaluation value R2 is calculated in consideration of the sensitivity direction error e _sd of the prediction model M as described above, by considering it together with the first evaluation value R1 indicating the prediction error e _p , for example, the teacher data TD Even when it is difficult to learn the correct sensitivity, such as when there is a shortage, the prediction accuracy by the prediction model M can be improved. For example, when the data set DS used for learning is close to the teacher data TD, overfitting may occur in the learning considering only the first evaluation value R1, but the second evaluation value R2 should be considered. Therefore, it is possible to avoid such a possibility and learn a highly reliable prediction model M. Further, even when the teacher data TD is not insufficient, the learning accuracy can be improved as compared with the conventional case. As a result, the possibility that the prediction model M leads to inappropriate decision making can be reduced, and more reliable machine learning can be performed.

Subsequently, a learning method of the prediction model M carried out by the learning device 150 having the above configuration will be described. FIG. 4 is a flowchart showing the learning method of the prediction model M according to at least one embodiment of the present disclosure for each process.

First, the first evaluation value calculation unit 156 calculates the first evaluation value R1 (step S10). First, in the calculation of the first evaluation value R1, as described above, the prediction error _ep based on the data set DS created by the data set creation unit 152 and the teacher data TD acquired by the teacher data acquisition unit 154 is obtained. It is done by.

The data set DS created by the data set creation unit 152 may be treated as batch data. The batch data includes at least one dataset DS and may include a plurality of dataset DSs. By using the batch data as the data set DS in this way, it is possible to reduce the number of repeated operations described later and effectively reduce the processing load of the learning device 150.

Subsequently, the second evaluation value calculation unit 158 calculates the second evaluation value R2 (step S20). Here, the calculation method of the second evaluation value R2 will be described in more detail with reference to FIG. FIG. 5 is a flowchart showing the detailed process of step S20 of FIG.

In FIG. 5, first, the constant k for designating an arbitrary one from the plurality of explanatory variables X _k is set to the initial value “1” (step S21). Then, the sensitivity direction type t _sd is selected for the explanatory variable X _k (step S22). The selection of the sensitivity direction type t _sd is based on the knowledge of the user, for example, when the explanatory variables X _c other than the explanatory variable X _k are set as constants, which of the explanatory variables X _k is relative to the objective variable y. It is done by determining if it has the sensitivity direction type t _sd . Subsequently, the feature amount calculation unit 158a calculates the feature amounts _Ak , _A'k , and X _ipk corresponding to the sensitivity direction type tsd selected in step S22 (step S23). In the calculation of the feature quantities Ak, _A'k , and X _ipk in step S23, the explanatory variables X _k , are expressed in the above equations ₍ 1) to (3) so as to correspond to the sensitivity direction type t _sd selected in step S22. This is done by inputting X _c .

Subsequently, the sensitivity direction error calculation unit 158b calculates the sensitivity direction error e _sdk corresponding to the explanatory variable X _k using the feature quantities Ak, _A'k , and X _ipk calculated in step S23 ₍ step S24). ). The calculation of the sensitivity direction error e _sdk in step S24 is performed according to the above equation (4) or (5) so as to correspond to the sensitivity direction type t _sd selected in step S22.

Subsequently, the constant k is incremented (step S25), and then it is determined whether or not the constant k is equal to or greater than the upper limit value k _max (step S26). In the above description, since k = 1 is set in step S21, k = 1 + 1 = 2 in the first step S25. Therefore, assuming that the constant k is less than the upper limit value k _max (step S26: NO), the process is returned to step S22, so that the same sensitivity direction error e _sdk is calculated for the next explanatory variable X _k . The calculation loop of the sensitivity direction error e _sdk is repeated until the sensitivity direction error e _sdk is calculated for all the explanatory variables.

When the calculation of the sensitivity direction error e _sdk for all the explanatory variables is completed (step S26: YES), the analysis unit 160 synthesizes the sensitivity direction error e _sdk calculated for each explanatory variable to obtain the sensitivity of the prediction model M. The direction error e _sd is calculated (step S27). In the present embodiment, the sensitivity direction error e _sd is obtained by the following equation as a linear sum of the sensitivity direction error e _sdk calculated for each explanatory variable.
e _sd = e _sd 1 + e _sd 2 + ... (6)
In the equation (6), a predetermined weighting coefficient may be set for the sensitivity direction error e _sdk corresponding to each explanatory variable.

Returning to FIG. 4, the prediction model update unit 162 updates the prediction model M based on the first evaluation value R1 calculated in step S10 and the second evaluation value R2 calculated in step S20 (step). S30). The update of the prediction model M in step S30 is performed so that the total error e obtained by the following equation is minimized.
e = e _p + r _sde x e _sd (7)
The coefficient r _sde is an arbitrary constant.

By updating the prediction model M based on the first evaluation value R1 and the second evaluation value R2 in this way, good learning accuracy can be obtained even when the teacher data TD is insufficient. Reliability can be improved. Then, in the plant control system 100, the control end of the plant can be appropriately controlled by predicting the control parameters using the prediction model M.

<Verification 1>
Subsequently, the verification result regarding the reliability of the prediction model M updated by the learning device 150 described above will be described. FIG. 6 is a scatter matrix of the data set DS used for constructing the prediction model M by the learning device 150. This scatter matrix is composed of 10 sets of data set DS including 9 explanatory variables x1 to x9 and an objective variable y. Each component of the scatter matrix is defined at intervals of 0.01 steps between 0.0 and 1.0 so as to satisfy the following equation, and is formed by adding a small amount of noise component to the interval. .. In this data set, since each explanatory variable x1 to x9 and the objective variable y have a linear relationship, the prediction model M learns the sensitivity direction of "upward convex" or "downward convex" without learning the sensitivity direction. It's hard to think of.
y = x1 = x2 = ... = x9 (8)

Subsequently, in order to confirm the effect of the sensitivity report learning, the sensitivity direction type t _sd is selected for each of the nine explanatory variables x1 to x9 defined in the scatter matrix prepared in this way. FIG. 7 is an example of selecting the sensitivity direction type t _sd for each explanatory variable x1 to x9. In this example, the "upwardly convex" sensitivity direction type tsd is selected for the explanatory variables x1 and x6, and the "downwardly convex" sensitivity direction type _tsd is selected for the explanatory variables x2 and x7. The "decrease" sensitivity direction type t sd is selected for the variables x3 and x8, the "increase" sensitivity direction type t _sd is selected for the explanatory variables x4 and _x9 , and "negligible" for the explanatory variables x5. ”Sensitivity direction type t _sd is selected.
In addition, in FIG. 7, the permissible range corresponding to the sensitivity direction type t _sd selected for each explanatory variable x1 to x9 is shown.

In this verification, PD plots and ICE plots were performed on the prediction model M constructed by the learning device 150 based on the data set DS and the sensitivity direction type t _sd included in the scatter matrix prepared in this way. .. FIG. 8 is a PD plot and an ICE plot obtained for each explanatory variable x1 to x9. (A) and (f) show the sensitivity directions of the explanatory variables x1 and x6 with respect to the objective variable y, and both the PD plot and the ICE plot are the sensitivity direction types t selected for the explanatory variables x1 and x6 in FIG. It was confirmed that the sensitivity direction of "convex upward" which is _sd is reflected. Further, (b) and (g) indicate the sensitivity directions of the explanatory variables x2 and x7 with respect to the objective variable y, and both the PD plot and the ICE plot are the sensitivity direction types selected for the explanatory variables x2 and x7 in FIG. It was confirmed that the sensitivity direction of "downward convex", which is t _sd , was reflected. Further, (c) and (h) indicate the sensitivity directions of the explanatory variables x3 and x8 with respect to the objective variable y, and both the PD plot and the ICE plot are the sensitivity direction types selected for the explanatory variables x3 and x8 in FIG. It was confirmed that the sensitivity direction of "decrease", which is t _sd , was reflected. Further, (d) and (i) show the sensitivity directions of the explanatory variables x4 and x9 with respect to the objective variable y, and both the PD plot and the ICE plot are the sensitivity direction types selected for the explanatory variables x4 and x9 in FIG. It was confirmed that the sensitivity direction of "increase", which is t _sd , was reflected. (E) shows the sensitivity direction of the explanatory variable x5 with respect to the objective variable y, and both the PD plot and the ICE plot of "negligible", which is the sensitivity direction type t _sd selected for the explanatory variable x5 in FIG. It was confirmed that the sensitivity direction was reflected.

Further, FIG. 9 shows the verification results of the convergence of the prediction error e _p and the sensitivity direction error e _sd with respect to the number of epochs. In (a), the sensitivity direction errors e _sdk corresponding to the explanatory variables x1 to x9 are shown, respectively, and the sensitivity direction error e _sdk converges when the number of epochs is about 20. Further, in (b), the prediction error e _p of the prediction model M and the sensitivity direction error e _sd (the linear sum of the sensitivity direction error e _sdk corresponding to the explanatory variables x1 to x9) are shown, respectively. Similar to (a), e _sd converges when the number of epochs is about 20. On the other hand, the prediction error e _p converges when the number of epochs is about 10, and shows the behavior of converging faster than the sensitivity direction error e _sd .

In the above-described embodiment, the case where the calculation frequency of the prediction error e _p and the calculation frequency of the sensitivity direction error e _sd are equal has been described. However, the calculation frequency of the prediction error e _p and the calculation frequency of the sensitivity direction error e _sd are described. It may be different. For example, in the verification result shown in FIG. 9, since the prediction error e _p converges with a smaller number of epochs than the sensitivity direction error e _sd , the calculation frequency of the prediction error e _p is within a range in which the convergence of the prediction error e _p does not become too slow. May be less than the calculation frequency of the sensitivity direction error. As a result, the number of operations can be reduced within the range in which the calculation accuracy of the prediction error e _p can be ensured.

<Verification 2>
Next, based on the data set existing in the real world, the prediction model M obtained by the above-mentioned learning device 150 is verified by comparing with the learning model obtained by the machine learning of another method. FIG. 10A is a CCPP data set showing the relationship between AT (horizontal axis) representing the outside air temperature and PE (vertical axis) representing the generated power, and FIG. 10B is a prediction model M obtained from the CCPP data set of FIG. 10A. .. Further, FIG. 11A is a bike sharing data set showing the relationship between atemp (horizontal axis) representing the sensible temperature and ct (vertical axis) representing the number of rental bicycles, and FIG. 11B is obtained from the bike sharing data set of FIG. 11A. It is a prediction model M to be obtained.

In addition, in FIGS. 10B and 11B, (f) the prediction model M obtained by the above-mentioned learning device 150 and the learning model obtained by the machine learning of another method are shown in (a) to (e), respectively. .. Note that (a) is a learning model obtained by machine learning using Random Forest (RF). (B) is a learning model obtained by machine learning using Lasso CV. (C) is a learning model obtained by machine learning using SVR (Support Vector Regression). (D) is a learning model obtained by machine learning using TPOT (The Tree-Based Pipeline Optimization Tool). (E) is a learning model obtained by machine learning using a neural network (NN).

FIG. 12 is a table comparing the evaluation results of the prediction model M obtained by each method of FIGS. 10B and 11B. FIG. 12 shows RMSE (Root Mean Square Errоr) and R2 (Root Mean of Determination) as evaluation items, and in the prediction model M obtained by the learning device 150 according to the present embodiment, it is obtained by another learning method. Good results were obtained in all the evaluation items compared to the predicted model. This indicates that the learning method of the present embodiment is used to learn the prediction model M, which is more reliable than the conventional one.

In addition, it is possible to replace the components in the above-described embodiment with well-known components as appropriate without departing from the spirit of the present disclosure, and the above-described embodiments may be combined as appropriate.

The contents described in each of the above embodiments are grasped as follows, for example.

(1) The learning method of the prediction model according to one aspect is
A method of learning a prediction model (for example, the prediction model M of the above embodiment) for predicting an objective variable (for example, the objective variable y of the above embodiment) from at least one explanatory variable (for example, the explanatory variable X _k of the above embodiment). There,
A first evaluation value calculation step (for example, the above embodiment) for calculating a first evaluation value (for example, the first evaluation value R1 of the above embodiment) indicating a prediction error of the prediction model (for example, a sensitivity direction error e _p of the above embodiment). Step S10) and
Feature quantities related to the sensitivity direction of at least a part of the at least one explanatory variable to the objective variable (for example, feature quantities _Ak , _{Ak, X ipk of} the above embodiment) and known information (for example, a knowledge table of the above embodiment). ), Which indicates the degree of agreement with the permissible range set for the feature amount (for example, the permissible range a _max , a _min , _{a'max, a'min, x ipmax , x ipmin} ) of the above embodiment. 2 A second evaluation value calculation step (for example, step S20 of the above embodiment) for calculating an evaluation value (for example, the second evaluation value R2 of the above embodiment) and
A predictive model updating step (for example, step S30 of the above embodiment) in which learning is performed by updating the predictive model based on the first evaluation value and the second evaluation value.
To prepare for.

According to the aspect (1) above, the prediction model is updated by machine learning based on the second evaluation value in addition to the first evaluation value indicating the prediction error of the prediction model. The second evaluation value is an index showing the degree of agreement between the feature amount related to the sensitivity direction of the explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information. By performing machine learning based on the first evaluation value and the second evaluation value in this way, it is possible to construct a highly reliable prediction model even when the teacher data when constructing the prediction model is small, for example. It becomes.

(2) In another aspect, in the above aspect (1),
In the second evaluation value calculation step, a sensitivity direction error (for example, the sensitivity direction error e _sd of the above embodiment) with respect to the allowable range of the feature amount is calculated as the second evaluation value.

According to the aspect (2) above, in the second evaluation value, the sensitivity direction of the prediction model deviates from the permissible range of the sensitivity direction based on known information such as knowledge possessed by the user. It is calculated as a so-called sensitivity direction error (or sensitivity direction accuracy), which is an index for quantitatively evaluating whether or not.

(3) In another aspect, in the above aspect (1) or (2),
The known information includes a plurality of preclassified sensitivity direction types (eg, the sensitivity direction type _tsd of the above embodiment) and the permissible range of the feature amount defined for each of the plurality of sensitivity direction types. include.

According to the aspect (3) above, a plurality of preclassified sensitivity direction types are set with respect to the sensitivity direction of the objective variable with respect to the explanatory variable. The known information used in the calculation of the second evaluation value includes such a plurality of sensitivity direction types and the allowable range of the feature amount specified for each sensitivity direction type.

(4) In another aspect, in any one of the above (1) to (3),
In the second evaluation value calculation step, the second evaluation value is calculated by synthesizing the degree of agreement for each explanatory variable using a preset weighting coefficient.

According to the aspect (4) above, the sensitivity of each explanatory variable to the objective variable is comprehensively evaluated by synthesizing the degree of agreement calculated for the permissible range for the feature value in the sensitivity direction for each explanatory variable. The second evaluation value is calculated as an index. By updating the prediction model based on such a second evaluation value, machine learning is performed so that the sensitivity direction of the objective variable for each explanatory variable approaches known information, and a prediction model with excellent reliability is constructed. can.

(5) In another aspect, in any one of the above (1) to (4),
In the prediction model update step, the prediction model is updated so that the linear sum of the first evaluation value and the second evaluation value is minimized.

According to the aspect (5) above, the prediction model is updated so that the linear sum of the first evaluation value and the second evaluation value is minimized. As a result, machine learning is performed so that the prediction error (conversely, the prediction accuracy) and the degree of agreement with the allowable range of the feature amount in the sensitivity direction are minimized, and a prediction model with excellent reliability can be constructed. ..

(6) In another aspect, in any one of the above (1) to (5),
In the first evaluation value calculation step and the second evaluation value calculation step, batch data including the plurality of data sets having at least one explanatory variable and the objective variable (for example, the data set DS of the above embodiment) is used. , The first evaluation value and the second evaluation value are calculated, respectively.

According to the aspect (6) above, the calculation load can be effectively reduced by performing the calculation of the first evaluation value and the second evaluation value using the batch data including a plurality of batch data.

(7) In another aspect, in any one of the above (1) to (6),
The calculation frequency of the first evaluation value in the first evaluation value calculation step and the calculation frequency of the second evaluation value in the second evaluation value calculation step are different.

According to the aspect (7) above, the calculation of the first evaluation value and the second evaluation value is performed at different frequencies from each other.

(8) The learning device for the prediction model according to one aspect is
A learning device (for example, a prediction model M of the above embodiment) for predicting an objective variable (for example, the objective variable y of the above embodiment) from at least one explanatory variable (for example, the explanatory variable X _k of the above embodiment). For example, in the learning device 150) of the above embodiment.
A first evaluation value calculation unit (for example, the embodiment) for calculating a first evaluation value (for example, the first evaluation value R1 of the embodiment) indicating a prediction error of the prediction model (for example, a sensitivity direction error e _p of the embodiment). 1st evaluation value calculation unit 156) and
Feature quantities related to the sensitivity direction of at least a part of the at least one explanatory variable to the objective variable (for example, feature quantities _Ak , _{Ak, X ipk of} the above embodiment) and known information (for example, a knowledge table of the above embodiment). ), Which indicates the degree of agreement with the permissible range set for the feature amount (for example, the permissible range a _max , a _min , _{a'max, a'min, x ipmax , x ipmin} ) of the above embodiment. 2 The second evaluation value calculation unit (for example, the second evaluation value calculation unit 158 of the above embodiment) for calculating the evaluation value (for example, the second evaluation value R2 of the above embodiment) and
A predictive model update unit (for example, the predictive model update unit 162 of the above embodiment) that performs learning by updating the predictive model based on the first evaluation value and the second evaluation value.
To prepare for.

According to the aspect (8) above, the prediction model is updated by machine learning based on the second evaluation value in addition to the first evaluation value indicating the prediction error of the prediction model. The second evaluation value is an index showing the degree of agreement between the feature amount related to the sensitivity direction of the explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information. By performing machine learning based on the first evaluation value and the second evaluation value in this way, it is possible to construct a highly reliable prediction model even when the teacher data when constructing the prediction model is small, for example. It becomes.

(9) The plant control system according to one aspect is
The learning device of the prediction model according to the aspect (8) above,
By inputting the at least one explanatory variable regarding the control parameters of the plant into the prediction model updated by the prediction model update unit, the prediction unit that predicts the objective variable regarding the performance of the plant (for example, in the above embodiment). Prediction unit 130) and
A control unit that controls the plant (for example, the control unit 145 of the above embodiment) based on the objective variable predicted by the prediction unit.
To prepare for.

According to the aspect (9) above, the objective variable, which is a parameter related to the performance of the plant, is predicted by using the prediction model updated by the above-mentioned learning method. The control unit can optimize the plant performance by performing plant control based on the objective variable predicted in this way.

100 Plant control system 110 Prediction model storage unit 120 Explanatory variable acquisition unit 130 Prediction unit 140 Optimal value calculation unit 145 Control unit 150 Learning device 152 Data set creation unit 156 First evaluation value calculation unit 158 Second evaluation value calculation unit 158a Feature quantity Calculation unit 158b Sensitivity direction error calculation unit 159 Knowledge table storage unit 160 Analysis unit 162 Prediction model update unit DS data set M Prediction model R1 First evaluation value R2 Second evaluation value TD Teacher data

Claims (9)

A method of learning a prediction model for predicting an objective variable from at least one explanatory variable.
The first evaluation value calculation process for calculating the first evaluation value indicating the prediction error of the prediction model, and
A second evaluation value indicating the degree of agreement between the feature amount related to the sensitivity direction of at least a part of the at least one explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information is calculated. Second evaluation value calculation process and
A predictive model update step in which learning is performed by updating the predictive model based on the first evaluation value and the second evaluation value.
A method of learning a predictive model. The method for learning a prediction model according to claim 1, wherein in the second evaluation value calculation step, the sensitivity direction error of the feature amount with respect to the permissible range is calculated as the second evaluation value. The predictive model according to claim 1 or 2, wherein the known information includes a plurality of preclassified sensitivity direction types and the permissible range of the feature amount defined for each of the plurality of sensitivity direction types. Learning method. In the second evaluation value calculation step, the second evaluation value is any one of claims 1 to 3, which is calculated by synthesizing the degree of agreement for each explanatory variable using a preset weighting coefficient. The method of learning the prediction model described in item 1. The prediction model according to any one of claims 1 to 4, wherein in the prediction model updating step, the prediction model is updated so that the linear sum of the first evaluation value and the second evaluation value is minimized. Learning method. In the first evaluation value calculation step and the second evaluation value calculation step, the first evaluation value and the second evaluation value are used by using batch data including a plurality of data sets having at least one explanatory variable and the objective variable. The method for learning a prediction model according to any one of claims 1 to 5, wherein evaluation values are calculated respectively. The item according to any one of claims 1 to 6, wherein the calculation frequency of the first evaluation value in the first evaluation value calculation step and the calculation frequency of the second evaluation value in the second evaluation value calculation step are different. How to learn a predictive model. A prediction model learning device for predicting an objective variable from at least one explanatory variable.
The first evaluation value calculation unit that calculates the first evaluation value indicating the prediction error of the prediction model, and
A second evaluation value indicating the degree of agreement between the feature amount related to the sensitivity direction of at least a part of the at least one explanatory variable with respect to the objective variable and the permissible range set for the feature amount based on known information is calculated. The second evaluation value calculation unit and
A prediction model update unit that performs learning by updating the prediction model based on the first evaluation value and the second evaluation value.
A learning device for predictive models. The learning device according to claim 8 and
A prediction unit that predicts the objective variable related to the performance of the plant by inputting the at least one explanatory variable related to the control parameters of the plant into the prediction model updated by the prediction model update unit.
A control unit that controls the plant based on the objective variable predicted by the prediction unit,
A plant control system.

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