JP2013168020A - State prediction method for process - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide the state prediction method of a process of structuring an appropriate local model by optimizing the number of explanatory variables and the number of past events.SOLUTION: A state prediction method of a process for creating a database in which input vectors and output vectors consisting of observation data representing the operation states of processes are accumulated as pairs, and for acquiring a proximity data vector which is similar to a request point vector consisting of the input vector corresponding to the output vector at a desired point of time of prediction from the database, and for structuring a local model from the proximity data vector to search the output vectors at the desired point of time of prediction includes: structuring a plurality of local models by using the number M of explanatory variables constituting the input vector and the maximum number NNof the proximity data vector as parameters; and selecting the local model in which an error between the predicted value and measured value of the local model is minimized.

Description

  The present invention relates to a process state prediction method in a plant facility.

  When it is necessary to grasp the state of a process, it may take time to analyze with a normal measuring instrument, and the process state may not be grasped in real time. Also, depending on the measurement environment and measurement target, installation of the measurement device itself may be difficult. When a clear physical model showing the process state can be obtained, a highly accurate predicted value can be obtained by calculation, but the process in the plant equipment is often expressed in a complex form of complex physicochemical phenomena. In many cases, it cannot be represented by a physical model.

  Therefore, a local modeling method called “Just-In-Time (JIT) modeling” against the backdrop of recent advances in computer hardware and database system technology, which enabled the storage of large amounts of data and high-speed retrieval. Is attracting attention. In JIT modeling, observed data is stored in a database, and whenever a system prediction or the like becomes necessary, a data vector highly related to the input “request point vector” is searched as a neighborhood data vector from the database. Then, a local model that interpolates the output of the searched neighborhood data vector is constructed, and the output of the “request point vector” is predicted. In this method, whenever there is further accumulation of observation data, the existing local model is discarded and a new local model is constructed again.

  In JIT modeling, every time a prediction is made, a data vector similar to a request point vector is searched from the database. Therefore, when the database becomes large, the calculation load becomes too large. For this reason, a technique called large-scale database online modeling (LOM) has been developed in which a stepwise method is applied to JIT modeling to reduce variables. For example, in Patent Documents 1 and 2, for a large-scale database composed of operation data of a thermal reactor, a variable having a high contribution rate to the furnace top gas temperature is selected using a stepwise method, and a new database composed of the variable is created. The top gas temperature is predicted using a local model that is created and constructed based on the neighborhood data vector obtained from a new database.

  In this specification, in order to clarify that “request point” and “neighbor data” are vector quantities, “request point” is “request point vector” and “neighbor data” is “neighbor data vector”. It describes. Also, a “data vector set” that is a set of data vectors may be referred to as a “data set”.

JP 2009-076036 A JP 2009-076037 A

In the process state prediction methods disclosed in Patent Documents 1 and 2, an explanatory variable having a high contribution rate to the objective variable is selected using a stepwise method. Specifically, a limit value for the F value that is an index of the contribution rate is set in advance, and the explanatory variable is selected so that the F value is equal to or greater than the limit value. Therefore, in the stepwise method, setting of the limit value is important, but there is no method for theoretically determining the limit value, and there is a problem that the limit value is determined empirically.
In addition, regarding the number of past cases that make up the database, if the number of explanatory variables to be adopted changes, the optimum number of past cases also changes accordingly, so in order to build an appropriate local model, the number of explanatory variables And the number of past cases need to be optimized.

  The present invention has been made in view of such circumstances, and provides a process state prediction method capable of constructing an appropriate local model by optimizing the number of explanatory variables and the number of past cases together. Objective.

In order to achieve the above-mentioned object, the present invention creates a database in which a data vector in which an input vector and an output vector composed of observation data indicating the operation state of a process in a plant facility are paired is accumulated and is to be predicted At least one of the data vectors similar to the request point vector consisting of input vectors corresponding to the output vector in FIG. 5 is obtained as a neighborhood data vector from the database, a local model is constructed from the neighborhood data vector, and the prediction time point In the process state prediction method for predicting the output vector at
Using the number M of explanatory variables constituting the input vector and the maximum number NN _MAX of the neighborhood data vectors as parameters, a plurality of neighborhood data vector sets in which the neighborhood data vectors are stored are created, and each neighborhood data vector set is Performing component analysis, constructing the local model having a minimum Q statistic for the request point vector for each set of neighboring data vectors, and calculating an error between a predicted value and an actual measurement value of the local model When,
Selecting the local model that minimizes the error among a plurality of the local models constructed using the number M of the explanatory variables and the maximum number NN _MAX of the neighboring data vectors as parameters. It is said.

In the present invention, a local model is constructed for each M value and each NN _MAX value while changing the number M of explanatory variables constituting the input vector and the maximum number NN _MAX (number of past cases) of neighboring data vectors. Since the local model that minimizes the error between the predicted value and the actual measurement value of each local model is selected, the number of explanatory variables and the number of past cases are optimized together, and an appropriate local model can be constructed. .

The principal component analysis and Q statistic used when constructing the local model have the following characteristics.
In principal component analysis, in order to capture the correlation between variables, a new synthetic variable called a principal component is created by linear combination of variables. With this principal component, it is possible to obtain a partial space that best represents the characteristics of the target data vector set. The Q statistic represents a portion that cannot be expressed in the subspace spanned by the principal components. That is, the Q statistic represents the degree of dissimilarity between the target data vector set and the requested point vector, and it can be determined that the smaller the Q statistic, the more similar the data vector set is to the requested point vector.

  FIG. 1 is a schematic diagram showing a correlation between a request point vector and a neighborhood data vector. FIG. 1A shows the case of JIT modeling or LOM. Since neighboring data vectors are selected based on the distance between vectors, neighboring data vectors having different correlations may be selected. On the other hand, FIG. 1 (B) shows the case of the state prediction method using principal component analysis and Q statistics, and the correlation between request point vectors and data vector sets (data sets) using Q statistics. Therefore, only a set of data vectors marked with ○ having a high correlation is selected.

  In the process state prediction method according to the present invention, the error between the predicted value and the actual measurement value by the local model may be calculated by a root mean square error, and the error over the entire evaluation interval is a single numerical value. Indicated.

In the process state prediction method according to the present invention, the principal component for each of a plurality of neighborhood data vector sets created using the number M of explanatory variables constituting the input vector and the maximum number of neighborhood data vectors NN _MAX (the number of past cases) as parameters. Analysis is performed, and a local model that minimizes the Q statistic for the requested point vector is constructed for each set of neighboring data vectors, and a local model that minimizes the error between the predicted value and the actual measurement value of the local model is selected. The number of explanatory variables and the number of past cases are optimized together, and an appropriate local model can be constructed.

FIG. 4 is a schematic diagram showing the correlation between a request point vector and a neighborhood data vector, where (A) shows the case of JIT modeling and LOM, and (B) shows the case of a state prediction method using principal component analysis and Q statistics. Each is shown. It is a flowchart for demonstrating the process state prediction method which concerns on one embodiment of this invention. It is a flowchart for demonstrating the state prediction method of the process. It is a table which shows the structure of a data set. It is a table which shows the structure of a request point vector. It is a table which shows the composition of neighborhood data set A where the number of neighborhood data is NN _MAX . Number of neighbors data is a table showing the structure of a neighboring data set _{B 0} is _{NN MIN.} It is a Q value table in which Q statistics are stored. It is the table which showed the list of RMSE _TOTAL when the number of explanatory variables and the number of past cases are used as parameters. It is the time history graph which contrasted the predicted value by the local model constructed | assembled with the state prediction method of the process with the measured value. It is the time history graph which contrasted the predicted value by the local model built by the conventional prediction method with the actual measurement value. It is the time history graph which contrasted the predicted value by the local model built by the conventional prediction method with the actual measurement value.

  Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention.

[Outline of process status prediction method]
First, a schematic procedure of a process state prediction method according to an embodiment of the present invention will be described below.
(A1) Regarding a database in which a data vector in which an input vector and an output vector composed of observation data indicating the operation state of a process in a plant facility are paired is stored, a range of the number M of explanatory variables constituting the input vector; Then, the range of the maximum number NN _MAX (the number of past cases) of the neighborhood data vectors similar to the request point vector composed of the input vector corresponding to the output vector at the time of the prediction is set.

(A2) in each range of the maximum number _{NN MAX} number M and the vicinity dataset explanatory variables, while changing the M and _{NN MAX,} carries out the following process for each selected M and _{NN MAX.}
(A2-1) A plurality of neighborhood data sets (neighboring data vector sets) storing neighborhood data vectors are created by changing the number of neighborhood data vectors (however, the maximum number NN _MAX is the upper limit).
(A2-2) Principal component analysis is performed on the plurality of generated neighborhood data sets, the Q statistic for the request point vector is calculated for each neighborhood data set, and the neighborhood data set that minimizes the Q statistic is selected. To build a local model.
(A2-3) Using the constructed local model, the predicted value of the output vector at the time point to be predicted is obtained, and the error is calculated by comparing with the actually measured value.

(A3) A local model that minimizes an error from an actual measurement value is selected from among a plurality of local models constructed within each range of the number M of explanatory variables and the maximum number NN _MAX of neighboring data sets.

Here, a basic description will be given of main methods constituting the process state prediction method according to the present embodiment.
[JIT modeling]
If a behavior that approximates the current behavior has been observed in the past, it can be considered that the progress of the current behavior will be an approximation of the past. One prediction method that reproduces this idea is Just-In-Time (JIT) modeling. JIT modeling does not have a fixed model, but retains past data vectors as a database. In this method, when a process needs to be predicted, a data vector having high similarity to a request point vector is searched from a database in which past data is accumulated, a local model is constructed, and an output is predicted.

  When the target process is a non-linear and dynamic process, the process can be represented by the following regression model.

Here, an input vector x ^k and an output vector y ^k of the process are defined as follows. That is, the output vector y ^k is an output at (k + p) with respect to the input vector x ^k at k, that is, a predicted value.

Over time, a large number of sets of data vectors of the input vector x ^k and the output vector y ^k can be obtained from the target process, such as (x ¹ , y ¹ ), (x ² , y ² ),. , Data vector set {(x ^k , y ^k )} (k = 1, 2,...) Is stored in the database. k is the discretization time.

An input vector x ^kq corresponding to the output vector y ^kq at the time point to be predicted is set as a request point vector, and a neighborhood data vector having high similarity to the request point vector is acquired from the database. As an index for selecting a neighborhood data vector having high similarity to the requested point vector, an intervector distance (Euclidean distance) as shown by the following equation can be used.

When the neighborhood data vector group {(x ^ki , y ^ki )} (i = 1, 2,..., M) is acquired, a local model is constructed using the neighborhood data vector group, and the output vector y ^kq Make a prediction. As the local model, a multiple regression model, an arithmetic average method or a weighted linear average method shown below, or the like is used.

[Principal component analysis]
Principal component analysis is a multivariate analysis method for the purpose of data feature extraction and reduction in dimensions, and uses synthetic variables called principal components obtained by linear combination of variables in order to capture correlations between variables. In the principal component analysis, the first principal component is set in the direction in which the data can be best expressed, and the variation in the data that cannot be expressed in the first principal component in the direction orthogonal to the first principal component is in the direction in which the first principal component can be expressed best. The principal components are set one after another by the procedure of setting two principal components. Here, the direction in which the data is best expressed means the direction in which the variance of the principal component scores is maximized. The principal component score is a value obtained by projecting data to a partial space spanned by the principal component.

[Q statistics]
The Q statistic represents a portion of the data vector that cannot be expressed in the subspace spanned by the principal components. The Q statistic is also called a square prediction error and is defined as follows.
Assume that there is a data matrix X of I rows × J columns. Here, J is the number of variables, I is the number of samples, and each variable is standardized.
When the singular value decomposition of the data matrix X is performed, the following equation is obtained.

U and V are orthogonal matrices, singular values s _r is the diagonal elements of the diagonal matrix S are arranged in descending order. When the number of employed principal component is R, the r principal component is given by the first r columns v _r loadings matrix V _R.
The r-th principal component score _tr is given by the equation (9), and when the R-th principal component score is collectively expressed, the equation (10) is obtained.

Expressing T _R with the coordinates on the original J-dimensional space, reconstructed data matrix X ^ is as follows.

  At this time, the Q statistic is given by the following equation.

[Error evaluation method]
The error evaluation between the predicted value and the actual measurement value based on the local model is performed using a root mean square error (hereinafter, sometimes referred to as “RMSE”). The formula for defining RMSE is shown in equation (13).

In the present embodiment, the root mean square error RMSE _I (see equation (14)) from time t = t ₁ to t = t _MAX is calculated, and the bias due to the data group is averaged. RMSE _I is calculated for each data group and evaluated by the total amount RMSE _TOTAL (see equation (15)). For example, RMSE _I may be an error calculated over 24 hours, and RMSE _TOTAL may be an error calculated over H days.

[Detailed procedure for predicting process status]
Next, the procedure of the process state prediction method according to the present embodiment will be described in detail based on the flowcharts of FIGS.
(C1) A set of data vectors (x ^k , y ^k ) (k = 1, 2,...) Of the input vector x ^k and the output vector y ^k composed of observation data indicating the operation state of the process in the plant equipment is accumulated. The created large-scale database 10 is created.
(C2) Minimum value M _MIN , maximum value M _MAX , increment value M _INC of the number M of explanatory variables constituting the input vector, and minimum value N _MIN , maximum of the maximum number NN _MAX (number of past cases) of neighboring data vectors A value N _MAX and an increment value N _INC are set (ST10).

(C3) The initial value of the number M of explanatory variables is M _MIN , and the initial value of the maximum number NN _MAX of neighboring data sets is N _MIN (ST11).
(C4) The top M explanatory variables having a large single correlation coefficient with the objective variable constituting the output vector, that is, the contribution ratio with respect to the objective variable is selected (ST12), and the new database 11 composed of the variable is enlarged. Created from the scale database 10. If there is a possibility that a time delay exists between the objective variable and the explanatory variable, the maximum expected time delay variable is also added to the explanatory variable.
The configuration of the database 11 to be created is shown in FIG. In this database 11, the number of input variables is M, the number of output variables is L, and the number of samples of each variable is K. Each data is given an ID according to the date and time, and data belonging to the same ID is handled as one data vector.

(C5) sets the required point vector and an input vector ^{X q} corresponding to the output vector ^{Y q} at the time to be predicted (ST13). FIG. 5 shows the configuration of the request point vector.
(C6) The inter-vector distance between each data vector stored in the database 11 and the requested point vector is calculated using the formulas (4) and (5), and the NN _MAX pieces are calculated in order from the smallest vector distance. Collect all neighborhood data vectors. Then, the collected neighborhood data vectors are stored as the neighborhood data set A in order of increasing distance between vectors (ST14). FIG. 6 shows the configuration of the neighborhood data set A. In FIG. 6, “No.” represents the number of neighboring data.
(C7) number of neighbors data from neighboring data set A (No.) creates a neighboring data set _{B 0} Select neighborhood data vector to _{1~NN MIN} (ST15). That is, NN _MIN neighboring data vectors are selected in order from the shortest vector distance to the requested point vector. It shows the structure of a neighboring data set B ₀ in Fig.

(C8) The principal component analysis was performed on the proximate data sets _{B 0,} obtains the loading matrix _{V R} (ST16). Specifically, the singular value decomposition may be performed using the neighborhood data set B ₀ as the data matrix X.
(C9) the request point vector ^{x q} is to be expressed by equation (16), reconstructed vector x ^{^ q} to a reconstructed request point vector ^{x q} is the using load matrix _{V R} (17) below Calculated. Therefore, the Q statistic for the neighborhood data set B ₀ can be obtained from the equation (18) (ST17). The calculated Q statistic is stored in the Q value table shown in FIG.

(C10) It is determined whether or not the number of neighboring data in the neighboring data set B ₀ for which the Q statistic is calculated is greater than or equal to NN _MAX (ST18). When the number of neighboring data is less than NN _MAX , among the neighboring data sets that are not included in the neighboring data set B ₀ in the neighboring data set A, S neighboring data vectors are further converted into the number of neighboring data (No .) those from) selecting (close inter-vector distance between the request point vector from the smaller, in addition to the vicinity of the data set B ₀ to create a new neighborhood data set B ₁ (ST19). Then, the process returns to step ST16.
(C11) On the other hand, when the number of neighboring data becomes NN _MAX or more, the data set B _k having the minimum Q statistic is selected from the data set A based on the Q value table. Then, an output vector corresponding to the data set B _k, acquired from the database 11 based on the ID of the data set B _k, to construct a local model by using a multiple regression model and weighted linear average method (ST20) .

(C12) The root mean square error RMSE _I from time t = t ₁ to t = t _{MAX is} calculated by equation (14), and RMSE _TOTAL , which is the total amount for H days, is calculated by equation (15) (ST21). ).
_{(C13) NN MAX} is whether a check is made whether more than _{N MAX (ST22),} if _{NN MAX} is less than _{N MAX,} update the NN MAX _{+ N INC} to the new _{NN MAX} (ST25) to return to ST14 is.
(C14) On the other hand, if NN _MAX is greater than or equal to N _MAX , it is checked whether M is greater than or equal to M _MAX (ST23). If M is less than M _MAX , M + M _INC is updated to a new M (ST26). Return to ST12.
(C15) If M is greater than or equal to M _MAX , a local model with the smallest RMSE _TOTAL is selected from among the plurality of constructed local models (ST24).

  Although one embodiment of the present invention has been described above, the present invention is not limited to the configuration described in the above-described embodiment, and is within the scope of matters described in the claims. Other possible embodiments and modifications are also included. For example, in the above embodiment, the root mean square error is used for the error evaluation between the predicted value and the actual measurement value by the local model, but other evaluation methods such as the mean square error and the average absolute error are used. Also good.

  In order to verify the effect of the process state prediction method according to the present embodiment, the top gas temperature of the thermal reactor was predicted and compared with the actual measurement value.

  The data used for the verification is observation data measured in a waste disposal process over 2 years. The acquired data was smoothed by applying a moving average filter for 1 hour to remove noise. The sampling time is 20 minutes and the total number of data is 38809.

FIG. 9 shows a list of RMSE _TOTALs calculated for the number M of explanatory variables and the number of past cases NN _MAX set at the time of verification. In this verification, the minimum value of the number M of explanatory variables is 20, the maximum value is 46, the increment value is 2, the minimum value of the past case number NN _MAX is 100, the maximum value is 200, and the increment value is As 50, RMSE _TOTAL was calculated. As a result, when the number M of explanatory variables was 30 and the number of past cases NN _MAX was 150, the RMSE _TOTAL was minimized.
A multiple regression model was used to construct the local model.

FIG. 10 shows a time history graph in which a predicted value based on a local model (M = 30, NN _MAX = 150) constructed by the process state prediction method according to the present embodiment is compared with an actual measurement value, and is constructed by a conventional prediction method. FIG. 11 shows a time history graph in which the predicted value based on the local model (M = 20, NN _MAX = 150) is compared with the actual measurement value, and FIG. 11 shows the local model (M = 40, NN _MAX = 150) constructed by the conventional prediction method. FIG. 12 shows time history graphs in which the predicted values obtained by) are compared with the actually measured values.
From these figures, the prediction value by the local model constructed by the process state prediction method according to the present embodiment is the closest to the actual measurement value, and the error gradually increases in the case of the local model constructed by the conventional prediction method. I understand that it will become.

10: Large database, 11: Database

Claims (2)

A request that consists of an input vector corresponding to an output vector at the point in time when you want to create a database in which data vectors that consist of input vectors and output vectors consisting of observation data indicating the operational status of the process in the plant equipment are stored A process state prediction method for obtaining at least one or more data vectors similar to a point vector from the database as neighboring data vectors, constructing a local model from the neighboring data vectors, and predicting an output vector at the time point to be predicted In
Using the number M of explanatory variables constituting the input vector and the maximum number NN _MAX of the neighborhood data vectors as parameters, a plurality of neighborhood data vector sets in which the neighborhood data vectors are stored are created, and each neighborhood data vector set is Performing component analysis, constructing the local model having a minimum Q statistic for the request point vector for each set of neighboring data vectors, and calculating an error between a predicted value and an actual measurement value of the local model When,
Selecting the local model that minimizes the error among a plurality of the local models constructed using the number M of the explanatory variables and the maximum number NN _MAX of the neighboring data vectors as parameters. The process state prediction method.   2. The process state prediction method according to claim 1, wherein an error between the predicted value and the actual measurement value of the local model is calculated by a root mean square error.

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