JP5707230B2 - Process state prediction method - Google Patents

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. If a clear physical model showing the state of the process can be obtained, a highly accurate estimate can be obtained by calculation, but the process in the plant equipment is often manifested 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 estimated. 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

Since JIT modeling and LOM construct a local model based on the neighborhood data vector of the request point, the number of neighborhood data to be used is important. Conventionally, in JIT modeling and LOM, the number of neighboring data vectors that are considered optimal by trial and error is determined depending on the object. However, it is considered that the optimum number of neighboring data vectors differs for each request point vector even for the same target. That is, when a frequently occurring case is used as a request point vector, the stability of prediction is increased by collecting many neighboring data vectors.
On the other hand, in the case where the request point vector is a case that occurs only infrequently, if the number of neighboring data vectors increases too much, a local model is constructed using even less relevant data vectors. For example, in the process state prediction methods described in Patent Documents 1 and 2, as for the variables selected by the stepwise method, as many pre-set numbers (6 in Patent Document 2) as the neighborhood data vectors of the request points are acquired. Therefore, the prediction accuracy was unstable.

The present invention has been made in view of such circumstances, and provides a process state prediction method in which the optimum number of neighboring data vectors is automatically determined for each request point vector and the prediction accuracy is stabilized. 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 estimating the output vector at
Creating a plurality of neighborhood data vector sets in which the neighborhood data vectors are stored by changing the number of the neighborhood data vectors; and performing principal component analysis on the plurality of neighborhood data vector sets for each neighborhood data vector set. And calculating a Q statistic for the request point vector, and selecting the neighborhood data vector set that minimizes the Q statistic to construct the local model.

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. 12 shows the correlation between the request point vector and the neighborhood data vector. FIG. 12A shows the case of JIT modeling or LOM. Since neighboring data vectors are selected based on the distance between vectors, there is a possibility that neighboring data vectors having different correlations may be selected. On the other hand, FIG. 12B shows the case of the process state prediction method according to the present invention. In order to measure the correlation between the request point vector and the data vector set (data set) using the Q statistic, Only a set of data vectors marked with a circle with a high correlation is selected.

Further, in the process state prediction method according to the present invention, when generating the plurality of neighboring data vector sets having different numbers of neighboring data vectors, the neighboring data vectors having the closest inter-vector distance to the request point vector are sequentially ordered. It is preferable to store and create the neighborhood data vector set, and in this way, it is possible to select a neighborhood data vector set with a higher degree of similarity.

In the process state prediction method according to the present invention, from among a plurality of neighborhood data vector sets having different numbers of neighborhood data vectors created for each request point vector, neighborhood data that minimizes the Q statistic for the request point vector. Since the local model is constructed by selecting the vector set, the optimum number of neighboring data vectors is automatically determined for each request point vector, and the prediction accuracy can be stabilized.

It is a flowchart for demonstrating the process state prediction method which concerns on one embodiment of this invention. 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 a graph which shows the correlation degree of the predicted value obtained by the process state prediction method which concerns on the same embodiment, and an actual value. It is a graph which shows the correlation degree of the predicted value and actual value which were obtained by the conventional LOM which made 1200 neighborhood data number. It is a time history graph which shows the result of having continuously predicted the temperature after 1 hour by the process state prediction method according to the embodiment. It is a time history graph which shows the result of having continuously estimated the temperature of 1 hour after by the conventional LOM which made 1200 neighborhood data number. It is a graph of the number of neighboring data used when the temperature after 1 hour is continuously predicted by the process state prediction method according to the embodiment. 4A and 4B are schematic diagrams showing correlations between request point vectors and neighboring data vectors, where FIG. 5A shows the case of JIT modeling and LOM, and FIG. 4B shows the case of the process state prediction method according to the present invention. .

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) A database in which a data vector in which an input vector and an output vector composed of observation data indicating an operation state of a process in a plant facility are paired is created is created.
(A2) At least one data vector similar to a request point vector composed of an input vector corresponding to an output vector at a time point to be predicted is acquired as a neighborhood data vector from the database. Then, a plurality of neighborhood data sets (neighboring data vector sets) in which neighborhood data vectors are stored are created by changing the number of neighborhood data vectors (hereinafter simply referred to as “number of neighborhood data”).
(A3) Principal component analysis is performed on a plurality of neighboring data sets to calculate a Q statistic for the request point vector for each neighboring data set, and a local model is selected by selecting a neighboring data set that minimizes the Q statistic. To construct. Then, using the local model, an estimated value of the output vector at the time point to be predicted is obtained.

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. When a process needs to be predicted, a data vector having a 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 estimated.

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 an estimate. 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.

[Stepwise method]
The stepwise method excludes an explanatory variable having a small influence (contribution rate) to an objective variable, and includes a variable increasing step and a variable decreasing step. Hereinafter, the procedure of the stepwise method will be described.

(B1) The explanatory variable having the largest single contribution ratio to the objective variable is determined from the explanatory variables selected previously. Specifically, after creating a single regression model for each explanatory variable and obtaining a regression coefficient, the F value is calculated by equation (8), and the explanatory variable that maximizes the F value is selected.

(B2) Consider adding one explanatory variable to the current model determined in the previous procedure. That is, the partial regression coefficient is obtained for each case where one explanatory variable is added to the current model from among the explanatory variables not included in the current model, and the F value is calculated using equation (8). Then, an explanatory variable having the maximum F value is searched.
(B3) the maximum F value, if it is previously determined that F _in above, add the explanatory variable in the current model. Maximum F value is in the case of less than F _in, it terminates the selection procedure by the stepwise method.

(B4) If a new explanatory variable is added, it is checked whether the explanatory variable fetched so far is really a useful explanatory variable. That is, in order to find the explanatory variable with the lowest contribution rate among the explanatory variables constituting the current model, the explanatory variables imported so far are removed one by one in order, and the F value when there is no explanatory variable is obtained. Calculate and search for an explanatory variable that minimizes the F value.
(B5) If the minimum F value is less than the predetermined F _out (F _in ≧ F _out ), the explanatory variable is deleted from the current model. When the explanatory variable is deleted, (B4) and (B5) are repeated to search for further deletion of the explanatory variable. Minimum F value is equal to or larger than _{F out,} the flow returns to step (B2).

[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 N rows × M columns. Here, M is the number of variables, N 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 Equation (10), and when the R-th principal component score is expressed together, Equation (11) is obtained.

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

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

[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 flowchart of FIG.
(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) For the large-scale database 10, a variable having a high contribution rate to the target variable is selected using the stepwise method, and a new database 11 composed of the variable is created (ST1). If there is a possibility that a time delay exists between the objective variable and the explanatory variable, all the maximum time delay variables that can be expected are added to the selection target.
The configuration of the database 11 (data set) 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.

(C3) sets the required point vector and an input vector ^{X q} corresponding to the output vector ^{Y q} at the time to be predicted (ST2). FIG. 3 shows the configuration of the request point vector.
(C4) the inter-vector distances between the data vector stored in the database 11 and requests point vector (4) and (5) were calculated using the equation, in order of distance between vectors is small NN _MAX number of 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 (ST3). FIG. 4 shows the configuration of the neighborhood data set A. In FIG. 4, “No.” represents the number of neighboring data.
(C5) the number of neighboring data from neighboring data set A (No.) creates a neighboring data set _{B 0} Select neighborhood data vector to _{1~NN MIN} (ST4). 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.

(C6) performed principal component analysis on neighboring data sets _{B 0,} obtains the loading matrix _{V R} (ST5). Specifically, the singular value decomposition may be performed using the neighborhood data set B ₀ as the data matrix X.
(C7) when the request point vector ^{x q} is (14) and represented by the formula, reconstructed vector x ^{^ q} to a reconstructed request point vector ^{x q} is the using load matrix _{V R} (15) formula Calculated. Therefore, the Q statistic for the neighborhood data set B ₀ can be obtained from the equation (16) (ST6). The calculated Q statistic is stored in the Q value table shown in FIG.

(C8) 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 (ST7). 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 (ST9). Then, the process returns to step ST5.
(C9) On the other hand, when the number of neighboring data is greater than or equal to NN _MAX , 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 averaging method, the request point An estimated output value for the vector is calculated (ST8).

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 Q statistic is obtained for all NN _MAX neighboring data sets, but when the Q statistic of a certain neighboring data set is determined to be a minimum value, the neighboring data set May be selected. In the above embodiment, the stepwise method is used to reduce the variables. However, the stepwise method may be omitted when the number of variables is small.

In order to verify the effect of the process state prediction method according to the present embodiment (hereinafter referred to as “neighboring data number sequential variable LOM”), prediction of the top gas temperature of the gasification melting furnace in the waste treatment process Went. In addition, in order to compare with the conventional prediction method, the top gas temperature prediction of the gasification melting furnace by the conventional LOM was also performed.

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.
When the stepwise method is applied to all the variables, enormous processing time and computer memory are required, and unnecessary variables cause a decrease in modeling accuracy. Therefore, after narrowing down to 37 explanatory variables that are considered to be related to the furnace top gas temperature in advance, variable selection was performed by the stepwise method with the delay time of each variable being 0 to 50 hours. As a result, 27 explanatory variables were selected, and the furnace top gas temperature after 1 hour was predicted.

The maximum neighborhood data number NN _MAX in the neighborhood data number sequential variable LOM is 1200, the minimum neighborhood data number NN _MIN is 100, and the increase width S of the neighborhood data number is 10. The number of principal components used in the principal component analysis was 10.
On the other hand, the number of neighboring data in the conventional LOM is a numerical value that gives the best result by trial and error.
In addition, the multiple regression model was used for the construction of the local model for both the LOM and the conventional LOM in which the number of neighboring data is sequentially variable.

200 required point vectors were randomly selected from the observation data, and the furnace gas temperature after 1 hour was predicted for each required point vector. FIG. 7 shows the degree of correlation between the predicted value and the actually measured value obtained by the LOM with the adjacent data number sequential variable LOM, and FIG. 8 shows the degree of correlation between the predicted value and the actually measured value obtained by the conventional LOM when the number of neighboring data is 1200. . From these figures, it can be seen that the LOM that is successively variable in the number of neighboring data has less variation between the predicted value and the actually measured value than the conventional LOM, and the correlation coefficient r is improved by about 0.08.
In FIG. 7 and subsequent figures, “T” displayed on the scale represents a reference temperature. That is, the amount of change from the reference temperature T is expressed.

Next, the result of continuous prediction for predicting the furnace top gas temperature after one hour every hour will be described. FIG. 9 shows a time history graph showing the continuous prediction result by the LOM with the sequential variable number sequential variable LOM, and FIG. 10 shows a time history graph showing the continuous prediction result by the conventional LOM when the number of neighboring data is 1200. Also, FIG. 11 shows a graph of the number of neighboring data used when continuously predicting by the neighboring data number sequential variable LOM.
From these figures, it can be seen that the rapid rise in temperature (refer to the fifth hour of the time history graph), which was difficult when the number of neighboring data is 1200, is captured by the LOM with the sequentially varying number of neighboring data. In addition, in the neighborhood data number sequential variable LOM, the overall error is smaller than when the number of neighborhood data is 1200.

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 estimating an output vector at the time point to be predicted In
Creating a plurality of neighborhood data vector sets in which the neighborhood data vectors are stored by changing the number of the neighborhood data vectors; and performing principal component analysis on the plurality of neighborhood data vector sets for each neighborhood data vector set. And calculating a Q statistic for the requested point vector; and selecting the neighborhood data vector set that minimizes the Q statistic to build the local model. Forecasting method 2. The process state prediction method according to claim 1, wherein when generating the plurality of neighborhood data vector sets having different numbers of the neighborhood data vectors, the neighboring data vectors are stored in order from the nearest vector distance with the request point vector. And generating the neighborhood data vector set.

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