JP5510642B2 - Prediction / diagnosis model construction device - Google Patents

Description

  The present invention relates to a prediction / diagnostic model construction apparatus using a partial least squares method.

  Conventionally, data, quality / state prediction, and normal / abnormal diagnosis have been performed in various fields. For example, in production lines such as factories and various plants, product quality and production volume are predicted from current operation data, and the apparatus is adjusted in a direction in which these improve. In addition, the equipment is constantly monitored for normality and abnormalities, and the occurrence of abnormalities is detected quickly to make efforts to restore normal production conditions.

  As a method for performing various predictions and normal / abnormal diagnosis using a computer system, for example, there is a method using a multiple regression model. While this method has an advantage that it is easy to intuitively understand the model formula, it is difficult to construct a stable model for data having so-called multicollinearity in which input variables are correlated with each other. In this case, in order to create an appropriate model, it is necessary to remove certain variables from the input variables, and there is a problem that much labor is required to perform this manually.

On the other hand, when building a model (PLS model) using the partial least squares method (PLS), even if there is a correlation between input variables, these are aggregated into intermediate variables called latent variables. Since the output variable is expressed, a stable model can be obtained even when there is multicollinearity. This is also described in Patent Document 1 relating to an energy demand prediction device.
On the other hand, Patent Document 2 is known as a conventional process abnormality analysis apparatus that performs process abnormality analysis using a PLS model. In this process abnormality analysis apparatus, a PLS model is used as a model for creating an abnormality analysis rule for abnormality determination based on a process feature amount extracted from process data.

JP 2009-169930 A (paragraphs [0014] to [0022], FIG. 1 etc.) JP 2007-250748 A (paragraphs [0026] to [0055], FIGS. 2 to 7 etc.)

When prediction / diagnosis is performed using a PLS model or the like, it is necessary to prepare learning data suitable for construction of a prediction / diagnosis model by determining in advance whether the measurement data is normal or abnormal. The reason is that the measurement data usually includes noise and abnormal data, and if these measurement data are used as they are for learning, an appropriate model cannot be constructed.
Conventionally, humans have manually performed learning data to be used for model construction by removing noise and abnormal data from raw measurement data.

  Since human judgment is extremely high, it is ideal that a few experts prepare learning data when building a prediction / diagnosis model. However, if this type of work is done manually, it takes a lot of time, so if a prediction / diagnostic model is required for each of many production lines, the models for all production lines in time May not be able to be built. Moreover, since the learning data selected by the unskilled person is not always appropriate, the accuracy of the prediction / diagnosis model may be low as a result.

  Note that the prior art related to Patent Document 2 has a problem of simultaneously determining whether there is an abnormality in a manufacturing apparatus and whether there is an abnormality in a product, and uses a PLS model as a prediction / diagnosis model for creating an abnormality analysis rule. It is assumed that a modeling device using data mining or a model obtained by manual analysis exists (see paragraph [0033] in Patent Document 2), and appropriate learning data is used. No specific means for constructing a predictive / diagnostic model is mentioned.

  Therefore, a problem to be solved by the present invention is to provide a prediction / diagnosis model construction apparatus that can easily construct a highly accurate prediction / diagnosis model by using appropriate learning data.

In order to solve the above problems, the invention according to claim 1 is a prediction / diagnostic model construction apparatus that constructs a model for performing prediction or normality / abnormality diagnosis using a partial least square method by a computer system.
Data storage means for storing a data set composed of input data of N items (N is a positive integer) and output data of M items (M is a positive integer) as learning data for model construction;
First learning data creating means for generating first learning data by deleting abnormal data not suitable for learning from the data set;
Model construction means for constructing a partial least squares model from the first learning data;
Prediction or normality / abnormality diagnosis is performed on the first learning data using the partial least squares model, and abnormal data whose numerical index deviates from a predetermined criterion is deleted from the first learning data Second learning data creating means for generating second learning data,
Model construction means for constructing a partial least square method model again using the second learning data.

The invention according to claim 2 is the predictive / diagnostic model construction apparatus according to claim 1, wherein the first learning data creating means is configured to arbitrarily set at least one item of data among (N + M) items. The first learning data is deleted from the data set accumulated in the data accumulating means by deleting the data set including the data when deviating from the upper and lower limit values or when deviating from the average value ± ( integer multiple of standard deviation ). Is generated .

The invention according to claim 3 is the predictive / diagnostic model construction apparatus according to claim 1 or 2, wherein the second learning data creating means has a constant T ² statistic or Q statistic as the numerical index. a data set of greater than, and generates a second training data deleted from the first learning data.

According to the present invention, it is possible to create learning data with a constant quality at high speed regardless of the level of human skill, and use the learning data for model construction to perform prediction or normal / abnormal diagnosis with high accuracy. A large number of prediction / diagnosis models can be created.
In particular, in a factory equipped with a large number of production lines, labor and cost can be greatly reduced as compared with a method of building models one by one manually.

It is explanatory drawing of the object which performs prediction and diagnosis with the prediction and diagnosis model constructed | assembled by this embodiment. It is a functional block diagram of a prediction / diagnosis apparatus using a prediction / diagnosis model according to an embodiment of the present invention. It is a flowchart which shows the function of the prediction / diagnosis model construction means in FIG. It is a flowchart which shows the processing content of step S2 in FIG. It is a flowchart which shows the processing content of step S23 in FIG. It is a conceptual diagram which shows the abnormal data deleted by step S3 of FIG. T ² is a conceptual diagram of a statistic and Q statistic. It is a diagram illustrating an example of a frequency distribution of T ² statistic and Q statistic. It is a figure which shows the usage data (gas amount data) at the time of performing abnormality diagnosis using the partial least square method model which concerns on embodiment of this invention. It is a figure which shows the usage data (pressure data) at the time of performing an abnormality diagnosis using the partial least square method model which concerns on embodiment of this invention. It is a figure which shows the usage data (temperature data) at the time of performing abnormality diagnosis using the partial least square method model which concerns on embodiment of this invention. It is a figure which shows the relationship between gas amount and temperature. It is a figure which shows the abnormality diagnosis result by Q statistic.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, FIG. 1 shows an example of the object of prediction / diagnosis in this embodiment. For example, in a production line of a factory, the amount of gas such as steam discharged from the pipe 10, at a predetermined position inside the pipe 10. It is assumed that prediction and diagnosis are performed using temperature, pressure, etc. as measurement data.
When a prediction / diagnosis model is constructed by a partial least square method model, the model is a kind of regression equation, and therefore input data and output data are required. Here, in order to simplify the explanation, there are three types of input / output data, of which temperature and pressure are input data and gas amount is output data.

FIG. 2 is a functional block diagram of a prediction / diagnosis apparatus 500 including a prediction / diagnosis model construction unit 300, which is a main part of the present embodiment. The prediction / diagnosis device 500 is configured by a computer system such as a personal computer, and the prediction / diagnosis model construction unit 300 and the prediction / diagnosis unit 400 are realized by hardware and software of an arithmetic processing unit including a CPU and the like. Is.
The prediction / diagnostic model construction unit 300 creates learning data for prediction / diagnosis and performs a process of constructing a partial least square method model. The prediction / diagnosis unit 400 uses the constructed partial least square method model. Use to predict gas quantity and perform normal / abnormal diagnosis of the target.
An output unit 600 outputs a prediction / diagnosis result by a display device, a printing device, a transmission device, or the like.

The input unit 100 includes a keyboard and a measurement / transmission device, and the temperature, pressure, and gas amount of the pipe 10 described above are input to the database 200 as measurement data.
The database 200 constitutes data storage means for storing measurement data from the past to the present. For example, as shown in Table 1, for each date from the past to the present, the gas amount, pressure, and temperature are the hour. Accumulated in series.

  The database 200 also stores a partial least square method model constructed by the partial least square method model construction unit 302. Specific data stored in the database 200 regarding the partial least square method model is a coefficient matrix of the partial least square method as described later.

Hereinafter, the function of the prediction / diagnosis model construction unit 300 will be described with reference to the flowcharts of FIGS.
[Step S1]
First, the learning data creation means 301 in the prediction / diagnosis model construction means 300 checks whether or not the temperature, pressure, and gas amount deviate from the upper and lower limit values, and the measurement deviates from the upper and lower limit values. The first learning data 701 shown in FIG. 3 is created by performing processing for deleting the data as abnormal data that is not suitable for learning (simple abnormal data deletion processing by the first learning data creating means in claim 1 ). To do.
For example, if a transmission error or a power failure occurs in the process in which measurement data is stored in the database 200, a physically impossible value is measured. The first learning data 701 is obtained by deleting the data set in the time zone in which the measurement data is mixed. In Table 1 described above, for example, data indicating values of “999” and “0” in February 2007 correspond to abnormal data that is not suitable for learning. Therefore, a data set including these abnormal data (February 2007 Data sets dated 26th, 27th February, 28th February).

If there is a large variation in measured data, etc., calculate the average value and standard deviation for each data item, and delete the data set that corresponds to abnormal data that exceeds the average value ± (integer multiple of standard deviation). May be.
Here, the above-mentioned two data deletion methods (a method of checking and deleting the deviation from the upper and lower limit values, and a method of deleting using the average value and the standard deviation) are not exclusive. Processing may be performed. These processes can be easily realized by arithmetic processing by the CPU and comparison processing by the comparator.

  In the present embodiment, a method for checking deviation from the upper and lower limit values is used, and a data set having a gas amount of “999” or more is deleted from Table 1 to show the first learning data 701 in Table 2. Get the data.

[Step S2]
Next, the partial least squares model construction means 302 in FIG. 2 uses the data in Table 2 (first learning data 701) created in step S1 to obtain the partial least squares model 801 in FIG. To construct. Note that the function of the same partial least squares model construction unit 302 is also used in step S4 described later.

Step S2 for constructing the partial least square method model 801 is composed of processing 1 to processing 3 (steps S21 to S23) shown in FIG.
First, in process 1 of FIG. 4 (step S21), the data in Table 2 is converted into a vector format as shown in Equation 1.

[Equation 1]
Pressure _i , Temperature _i , Gas amount _i
Pressure _i-1 , Temperature _i-1 , Gas amount _i-1
(Here, the subscript i indicates time (date in the example of Table 2).)

  Of course, not only the simple conversion to the array format as described above, but also variable conversion for squaring or squaring each data and other data processing processes may be included. Usually, these data are normalized by subtracting the average value of the data in the vertical column from the individual values so that the average value is 0 in the vertical column, and further dividing by the standard deviation of the data in the vertical column. Therefore, you may convert by such a method.

  In process 2 of FIG. 4 (step S22), data of N items (N = 2 in Table 2 because the input data is temperature and pressure) is converted into P types of components. When the above P (that is, the number of latent variables t) is 2, the final prediction model formula of X (temperature, pressure) and y (gas amount) is expressed by Formula 2. N and P are both positive integers.

  A coefficient matrix related to the first component is calculated by Equation 3.

In Equation 3, w ₁ is a vector of N rows × 1 column, and t ₁ is a vector of n rows (n is a positive integer) × 1 column. Since p ₁ is a vector of N rows × 1 column, p ₁ ^T (T indicates transposition) is a vector of 1 row × N columns. Q ₁ is a scalar.

  X in Equations 2 and 3 is a vector of n rows × N columns representing input variables (temperature, pressure), and is represented by Equation 4 in this embodiment.

  Further, y in Equations 2 and 3 is an n-row × M-column vector representing an output variable (gas amount), but here, n-row × 1 column (ie, M = 1) vector as in Equation 5. Will be described. Here, M is a positive integer.

Since the coefficient matrix related to the second component obtains a component not related to the first component, first, X and y are converted into X _new and y _new by Equation 6.

  Therefore, the coefficient matrix related to the second component is obtained from Equation 7.

  Although the above description relates to component conversion (coefficient matrix calculation) when the number of components is 2, even when the number of components is greater than 3, each coefficient matrix can be similarly obtained by Expression 8. In Equation 8, a indicates the number of components.

  In addition, the prediction model by the partial least square method, each coefficient matrix, the statistical index shown below, etc. are described in detail in Patent Document 1 described above.

In process 3 (step S23) of FIG. 4, the optimum number of components, that is, the number P (≦ N) of latent variables is determined. If the number of components is too large, a phenomenon called over-learning occurs, and learning is performed well, but the model has a large error in prediction.
Therefore, the number of components is sequentially increased from 1, and the number of components that minimizes the following formula 9 is set as the optimum number of components. Note that Equation 9 is a statistical index called AIC, but other statistical indexes such as a degree of freedom adjustment contribution rate may be used.

FIG. 5 shows details of step S23 in which the optimum number of components is determined by the above-described procedure.
In FIG. 5, first, each coefficient matrix is calculated with a = 1 (steps S231 and S232). Here, a has the same meaning as the number of components P described above. Next, a partial least square method model is constructed by the partial least square model construction means 302 using each coefficient obtained in step S232, and the prediction means 401 uses the constructed partial least square method model. The prediction result from one learning data 701 is obtained, a statistical index is calculated using Equation 9 or the like (step S233), and if the statistical index is smaller than the previous time and improved, a is incremented and step S232 is performed. (Steps S234 Yes, S235). If the statistical index has become larger than the previous time, the coefficient matrix of the number of components a-1 is saved, and the process of step S23 is terminated (steps S234 No, S236).

  Step S2 of FIG. 3 is executed by the processing of FIGS. 4 and 5 described above, and a partial least square method model 801 is constructed. In this way, the coefficient matrix is calculated by determining the optimal number of components, and the process of constructing the partial least squares model 801 is performed by the partial least squares model construction means 302 of FIG. 2 using the first learning data 701. The partial least squares model 801 constructed is stored in the database 200 while being executed by the arithmetic processing of the CPU.

  It should be noted that the partial least squares model equation (Equation 2, Equation 6, etc.) described above may be converted into a multiple regression equation as shown in Equation 10 below.

[Step S3]
In step S3 of FIG. 3, as in step S1, the process of deleting inappropriate learning data that cannot be deleted by simple processing such as determining whether or not there is a deviation from the upper and lower limit values for each variable ( second process in claim 1). Advanced abnormal data deletion processing by learning data creation means ) is performed, and second learning data 702 is created.
FIG. 6 shows the concept of abnormal data deleted in step S3. In FIG. 6, a large number of plots within the ellipse are normal data, and a plot outside the ellipse and surrounded by a square frame indicates abnormal data. These abnormal data are generated, for example, due to an abnormality of a measuring instrument, clogging or leakage of the pipe 10, and the like.

The abnormal data shown in FIG. 6 is within the range of the upper and lower limit values on the temperature axis (horizontal axis) (20 ° C. to 100 ° C.) and within the range of the upper and lower limit values on the pressure axis (vertical axis) ( (0.2 kPa to 0.5 kPa), it is not deleted in the above-described simple abnormal data deletion process in step S1. That is, the first learning data 701 in FIG. 3 includes the abnormal data shown in FIG.
Therefore, in step S3, the learning data creation unit 301 in FIG. 2 executes a process for deleting abnormal data that is not deleted by the simple abnormal data deletion process (high abnormal data deletion process) in FIG.

In the learning data creation means 301, first, the CPU calculates the T ² statistic and the Q statistic using the partial least square method model 801 and the first learning data 701 constructed in step S2. The function for calculating the T ² statistic and the Q statistic is implemented in the normal / abnormal diagnosis unit 402 in the prediction / diagnosis unit 400 in FIG. 2, and the function in this unit 402 is used as the learning data creation unit 301. Is implemented as a subroutine. Meaning it actually normal or abnormal diagnosis using the statistic calculation processing function to be used when performing, for calculating the T ² statistic and Q statistic for advanced abnormal data deletion process.

Here, the T ² statistic and the Q statistic are indices for applying principal component analysis (PCA) to abnormality diagnosis as is well known. The Q statistic is an index that evaluates deviations from the correlation between variables that the data used to create the model has, but the T ² statistic is obtained by compressing the original variable. In the component space, it corresponds to the distance from the average to each sample, and is an index for evaluating the degree of deviation from the average within the range of correlation. Therefore, as a result of the evaluation based on the Q statistic, even if it is determined that the correlation between the variables is maintained and normal, it is determined to be abnormal if the deviation from the average is large when the evaluation is performed based on the T ² statistic. .

Hereinafter, the calculation method of the T ² statistic and the Q statistic in step S3 will be described.
(1) T ² Statistics First, Equation 11 is used for the matrix t obtained in the learning of Step S2 (construction of the partial least squares model 801).

_{However, t 1, ~,} t _p is a vector of n lines × 1 column. Here, the standard deviation of each t is set as σ ₁ to σ _p .
Next, t ′ is calculated from the data set of the first learning data 701 as shown in Equation 12.

In Expression 12, t ₁ ′ to t _p ′ are scalar quantities. X is a vector of 1 row × N columns and is an input factor for prediction. w _{1 to} w _p are vectors of N rows × 1 column, and are coefficient matrices obtained by learning.
From the above, the T ² statistic is obtained by Equation 13.

(2) Q statistic The Q statistic is defined by Equation 14.

Each value in parentheses on the right side of Equation 14 is a scalar quantity, and the first term x _i in the parentheses indicates the i-th input. In addition, x _i ^ in the second term in parentheses (here, ^ is written after x for convenience) is a value converted inside the model. It is.

Here, FIG. 7 is a conceptual diagram of a T ² statistic and Q statistic, T ² statistic measure the distance in the latent variable plane of the high P component correlated with the amount of gas _(t 1 _{~t p)} Statistics In contrast to the quantity, the Q statistic is a statistic of the distance from the latent variable plane. Q statistic likewise the T ² statistic, larger than the data value is a constant value indicates that it is distinguished from other normal data, likely to be abnormal data not suitable for learning Become. 7, a plot of a plurality of black circles normal data, one square plots were evaluated by T ² statistic conceptually shows an abnormal data as assessed by Q statistic.

The learning data creation unit 301 determines that a data set larger than a certain value for the T ² statistic and the Q statistic obtained by (1) and (2) for each data set is a data set including abnormal data. Then, the second learning data 702 is created.
In this case, an arbitrary value may be set as a constant value, or data having no superiority may be deleted by a chi-square test (for example, 1% confidence interval). Further, a certain value% (for example, 1%) may be deleted from the largest value. In any case, in the frequency distribution data as shown in FIG. 8, the data on the right side of a certain threshold is deleted. In the example of this data, there is no data that is extremely different from the data, so it was not deleted.

[Step S4]
In step S4 in FIG. 3, the same process as in step S2 is performed using the second learning data 702 created in step S3, and the partial least square method model 802 is constructed again.

  Using the partial least squares model 802 constructed as described above and the data in the database 200, the prediction by the prediction unit 401 in the prediction / diagnosis unit 400 of FIG. Diagnosis by is executed.

Next, the result of diagnosing data abnormality / normality using the partial least square method model 802 finally constructed by the processing of steps S1 to S4 is shown below.
As shown in FIGS. 9 to 11, gas amount data, pressure data, and temperature data from March 1, 2007 to June 10, 2007 were prepared as input / output data. A partial least squares model 802 was constructed by the processing of steps S1 to S4 using the data up to April 22, and the normality and abnormality of the data up to June 10 were diagnosed by Q statistics. In addition, temperature data that started to go out little by little from May 13 was prepared as abnormality data for testing.

Although the time measurement data of FIGS. 9 to 11 do not show temperature measurement abnormalities, as shown in FIG. 12, test data after May 13 (shown in light shading) is related to the gas amount. The temperature data is increasing little by little.
FIG. 13 is a diagram showing an abnormality / normal diagnosis result based on the Q statistic. A data set having a Q statistic larger than a certain value is determined to be abnormal and is deleted from the learning data. According to FIG. 13, as shown by the arrow, the Q statistic gradually increases from the second half of May, and it can be seen that abnormality can be diagnosed.

10: piping 100: input unit 200: database 300: prediction / diagnosis model construction means 301: learning data creation means 302: partial least squares model construction means 400: prediction / diagnosis means 401: prediction means 402: normal / abnormal diagnosis Means 500: Prediction / diagnosis device 600: Output unit 701, 702: Learning data 801, 802: Partial least squares model

Claims (3)

In a predictive / diagnostic model construction apparatus that constructs a model that performs prediction or normal / abnormal diagnosis by a computer system using a partial least squares method,
Data storage means for storing a data set composed of input data of N items (N is a positive integer) and output data of M items (M is a positive integer) as learning data for model construction;
First learning data creating means for generating first learning data by deleting abnormal data not suitable for learning from the data set;
Model construction means for constructing a partial least squares model from the first learning data;
Prediction or normality / abnormality diagnosis is performed on the first learning data using the partial least squares model, and abnormal data whose numerical index deviates from a predetermined criterion is deleted from the first learning data Second learning data creating means for generating second learning data,
Model building means for building a partial least squares model again using the second learning data;
An apparatus for constructing a prediction / diagnosis model characterized by comprising: In the prediction / diagnosis model construction apparatus according to claim 1,
The first learning data creation means includes
A data set including the data when the data of at least one item out of (N + M) items deviates from an arbitrarily set upper or lower limit value or deviates from an average value ± ( an integer multiple of standard deviation ) , An apparatus for constructing a prediction / diagnosis model, wherein the first learning data is generated by deleting from a data set stored in a data storage means . In the prediction / diagnosis model construction apparatus according to claim 1 or 2,
The second learning data creation means includes
Data sets T ² statistic or Q statistic as the numerical index exceeds a predetermined value, the prediction and diagnosis model and generates a second training data deleted from the first learning data Construction device.

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