JP5457879B2 - Polynomial generator for estimation, estimation apparatus, polynomial generation method for estimation, and estimation method - Google Patents

Description

  The present invention relates to an estimation polynomial generating apparatus that calculates an estimation polynomial for estimating an output parameter value such as a state quantity, and an estimation apparatus that estimates a state quantity using the estimation polynomial.

  In thermal processes and plasma processes in semiconductor manufacturing equipment, FPD (Flat Panel Display) manufacturing equipment, or solar cell manufacturing equipment, important state quantities such as wafer and glass surface temperatures (substance temperatures) are displayed online during processing. There is a demand to manage and control. However, it is difficult to perform processing with the temperature sensor mounted on the surface of the wafer or glass.

  Therefore, the relationship between the temperature at a location that can be measured during the processing process and the surface temperature (substance temperature) of the wafer or glass that cannot be measured during the processing process is examined offline in advance, and the processing process is executed. In some cases, important state quantities are managed and controlled on-line by estimating the surface temperature (substance temperature) of the wafer or glass based on the relationship between the measurable temperature and the preliminarily grasped relationship. In such a case, the measurement can be performed by applying the multivariate analysis method to the measurable temperature obtained by the offline survey and the measurement data (analytical data) of the surface temperature (substance temperature) of the wafer or glass. A method of obtaining a polynomial (approximate state quantity estimation using a polynomial) for approximating a numerical relationship between a possible temperature and the surface temperature of a wafer or glass is widely practiced (see, for example, Patent Document 1). When using a multivariate analysis approach, the temperature that can be measured during the execution of the processing process is positioned as a polynomial input parameter. On the other hand, the surface temperature (substance temperature) of the wafer or glass to be estimated is positioned as a polynomial output parameter.

JP-A-5-141999

  In many cases, the target of state quantity estimation does not have a simple linear relationship between input parameters and output parameters. Therefore, in order to improve the accuracy of state quantity estimation, the estimation polynomial obtained by multivariate analysis must be made higher order. At this time, data density may exist in the parameter space on the input parameter side of the analysis data unless the input conditions are experimentally set. When the estimation polynomial is made higher-order, the accuracy of the dense data area is easily improved, but the probability of becoming an unrealistic estimation value polynomial in the sparse data area is high. In particular, when an estimation function is implemented in a device such as a semiconductor manufacturing device and the device manufacturer ships to the device user and the device user collects data for analysis, the input parameter space assumed by the device manufacturer and the device user are conscious. The input parameter space to be matched does not always match. Therefore, in such a distribution form of the apparatus, a sufficient time is not necessarily used for data collection even though the problem of density of data collection for analysis tends to occur.

  For simplicity of explanation, it is assumed that there is one input parameter. The combination (X, Y) of the input parameter X and the output parameter Y is A (1.6, 20.024), B (2.0, 21.000), C (2.4, 23.304), D Six values of A to F, which are (2.8, 27.272), E (3.2, 33.288), and F (3.5, 39.375), are obtained as analytical data. It shall be. FIG. 6 shows the distribution of six sets of analysis data A to F at this time.

As a characteristic of the analysis data at this time, if the physical relationship between the input / output parameters (X, Y) is considered, it can be predicted that the relationship will increase monotonically in a common sense. That is, it is assumed that the input / output parameters (X, Y) can be imagined in a knowledgeable manner as shown in FIG. Even when there is such a relationship, the situation where data near X = 0 is not obtained due to the data collection time on the device user side, that is, the situation where there is a sparse data area is a semiconductor manufacturing It occurs frequently on the spot.
Here, when a cubic polynomial that reproduces the relationship between the input / output parameters (X, Y) with high accuracy is obtained by multivariate analysis using the data set of A to F, for example, the following mathematical formula is obtained. Will be.
Y = X ³ −2.0X ² +21.0 (1)

  A cubic curve 220 shown in FIG. 8 is obtained by the cubic polynomial of equation (1). On the other hand, reference numeral 221 denotes a curve showing the relationship between the input / output parameters (X, Y) obtained from the common sense assumption as described above. As shown in FIG. 8, the cubic polynomial of the equation (1) matches the data A to F with high accuracy. However, according to this cubic polynomial, S (0.0, 21.000) is obtained as a point near X = 0. That is, in the parameter space of the input parameter X, there are a region where data of 1.6 ≦ X ≦ 3.5 is dense and a region where data other than this is sparse, but the cubic polynomial of equation (1) is This means that it is a polynomial that calculates an unrealistic estimate in a sparse area.

  Since this situation is likely to occur, it is necessary to use sufficient time for data collection. However, in a semiconductor manufacturing process, for example, even in an experiment for data collection, the wafer and the reaction gas must be consumed. When online temperature estimation is performed in such a situation, there are areas where high-precision estimation can be expected (area where data is dense) and areas where unrealistic estimation is performed (area where data is sparse). It will be. In the region where unrealistic temperature estimation is performed, there is a possibility that the manufacturing process may be greatly adversely affected.

  The present invention was made in order to solve the above-mentioned problem, and when an estimation polynomial is obtained using analysis data for a manufacturing apparatus or the like, and when estimating an amount of state using the estimation polynomial, It is an object of the present invention to provide an estimation polynomial generation device, an estimation device, an estimation polynomial generation method, and an estimation method that can supplement a situation where sufficient time cannot be taken for data collection.

  The estimation polynomial generating apparatus of the present invention includes a database for preliminarily storing reference data for supplementation consisting of a set of input parameter data and output parameter data corresponding thereto, for each type of estimation polynomial to be created; Analytical data storage means for preliminarily storing analytical data consisting of a set of input parameter data and corresponding output parameter data for the estimation polynomial creation target, input space dividing method, and input space dividing Input space division information storage means for storing the required number of data for each small area in advance, and whether the analysis data has reached the required number of data stored in the input space division information storage means Insufficient data judgment means for judging each area, and reference data used for supplementing the analysis data is a target for creating the estimation polynomial The output parameter value is estimated from the input parameter value using the data search means for replenishing the deficient data of the analysis data from the identified reference data and the replenished analysis data. An estimation polynomial calculating means for calculating an estimation polynomial is provided.

Further, in one configuration example of the estimation polynomial generating apparatus of the present invention, the data search means stores a plurality of sets of reference data corresponding to the type of the estimation polynomial to be created in the database. Each of the plurality of sets of reference data is used to cause the estimation polynomial calculation means to calculate an estimation polynomial, and the reference data that minimizes the error between the calculated estimation polynomial and the analysis data is It is characterized in that it is selected as reference data to be used for supplementing analysis data.
Further, in one configuration example of the estimation polynomial generating apparatus of the present invention, the creation object of the estimation polynomial is a manufacturing apparatus, and the reference data in the database is organized by model type of the manufacturing apparatus. It is what.
Also, in one configuration example of the estimation polynomial generating apparatus of the present invention, the creation object of the estimation polynomial is an air conditioning system, and the reference data in the database is organized by air conditioning instrumentation type, To do.
Further, the estimation apparatus of the present invention uses the input parameter value acquisition means for acquiring the input parameter value and the estimation polynomial calculated by the estimation polynomial calculation means of the estimation polynomial generation apparatus from the analysis data, and uses the input parameter value Polynomial estimation calculation means for estimating the output parameter value from the input parameter value acquired by the acquisition means.

  Further, the estimation polynomial generating method of the present invention comprises an analysis data storage means for preliminarily storing analysis data consisting of a set of input parameter data and output parameter data corresponding to the creation object of the estimation polynomial, And the input space division information storage means for preliminarily storing the input space division method and the required number of data for each small area obtained by dividing the input space, and the analysis data is stored in the input space division information storage means Estimating supplementary reference data consisting of a set of insufficient data judgment step for each small area of the input space to determine whether the required number of data has been reached, and input parameter data and corresponding output parameter data Refer to a database that is stored in advance for each type of polynomial to be created, and the reference data used to supplement the analysis data is From the input parameter value using the data search step for identifying the deficient polynomial of the analysis data and replenishing the deficient data of the analysis data from the identified reference data, and using the supplemented analysis data An estimation polynomial calculating step for calculating an estimation polynomial for estimating the output parameter value.

  According to the present invention, whether or not the analysis data has reached the required number of data is determined for each small area of the input space, and the reference data used for supplementing the analysis data is determined from the type for which the estimation polynomial is to be created. Since the data for the shortage of analysis data is identified and supplemented from the identified reference data and the estimation polynomial is calculated using the supplemented analysis data, sufficient time is not collected for data collection. For this reason, it is possible to supplement the situation in which the analysis data for which the estimation polynomial is created is insufficient.

It is a block diagram which shows the structure of the polynomial generator for estimation which concerns on the 1st Embodiment of this invention. It is a flowchart which shows operation | movement of the polynomial generator for estimation which concerns on the 1st Embodiment of this invention. It is a figure which shows the relationship of the input / output parameter of the data for analysis obtained from the cubic polynomial by having supplemented the data for analysis in the 1st Embodiment of this invention. It is a block diagram which shows the structure of the estimation apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows operation | movement of the estimation apparatus which concerns on the 2nd Embodiment of this invention. It is a figure which shows one example of distribution of the data for analysis. It is a figure which shows the relationship of the input / output parameter of the data for analysis of FIG. 6 obtained from a common sense assumption. It is a figure which shows the relationship of the input / output parameter of the data for analysis of FIG. 6 obtained from the cubic polynomial calculated | required by multivariate analysis.

[Principle of the Invention]
In many cases, there are many cases where the same type of model or a similar type of model is used on the manufacturing line. In other words, it is not necessary to collect sufficient analysis data for all manufacturing apparatuses. However, if the estimation polynomial is completely shared (recycled), the difference between models (called machine difference) cannot be absorbed. Since such a situation is the actual state of data collection of the estimation polynomial in the manufacturing apparatus, the inventor has focused on separating the data sharing and the response to the machine difference as the estimation polynomial creation step.

  Therefore, it is configured so that data can be shared by creating a database for the same type of model or a model of a similar type, and if the newly installed device is the same as or close to the model already in the database, insufficient data is stored from the database. I thought of replenishing them as appropriate. As a result, even if there is not enough time for data collection, only the deficiency is replenished, so reliability is less than when creating a low-reliability estimation polynomial with insufficient data. A high estimation polynomial can be obtained.

  Specifically, the input space (X-axis in the example of FIG. 6) is divided into an appropriate number of small areas, and the same number from the database when there is no specified number of data in a specific small area Search and replenish data present in the same small area of the input space. As a search method, for example, data of another model that can be estimated as the closest characteristic based on the obtained data may be used as much as possible.

[First Embodiment]
Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing a configuration of an estimation polynomial generating apparatus according to the first embodiment of the present invention. The estimation polynomial generator includes a database unit 1, an analysis data storage unit 2, an input space division information storage unit 3, an insufficient data determination unit 4, a data search unit 5, and an estimation polynomial calculation unit 6. Prepare.

  The operation of the estimation polynomial generating apparatus of this embodiment will be described with reference to the flowchart of FIG. In the database unit 1, model type information indicating the model type of the manufacturing apparatus, and reference data including a set of input parameter data and corresponding output parameter data are stored in advance for each manufacturing apparatus. . In order to simplify the description, an example is shown in accordance with the example of FIG. That is, the reference data includes a set of an input parameter X value and an output parameter Y value.

  For example, for the manufacturing apparatus I, model type information indicating the model type α is stored in the database unit 1, and the combination (X, Y) of the input parameter X and the output parameter Y is 1A (0.0, 0.041). 1B (0.5, 10.488), 1C (1.6, 20.504), 1D (2.0, 21.030), 1E (2.4, 23.334), 1F (3.2 , 33.318), 7 sets of values 1A to 1G, which are 1G (3.5, 39.405), are stored as reference data.

  As for the manufacturing apparatus II, model type information indicating the model type α is stored in the database unit 1, and the combination (X, Y) of the input parameter X and the output parameter Y is 2A (0.0, 1.201). ), 2B (0.5, 11.688), 2C (1.6, 21.224), 2D (2.0, 22.200), 2E (2.4, 24.504), 2F (2. 8, 28.472) and 2G (3.2, 34.488), 7 sets of values 2A to 2G are stored as reference data.

  As for the manufacturing apparatus III, model type information indicating the model type β is stored in the database unit 1, and the combination (X, Y) of the input parameter X and the output parameter Y is 3A (0.0, 10.803). ), 3B (0.5, 15.733), 3C (1.6, 20.434), 3D (2.0, 22.234), 3E (2.4, 23.554), 3F (2. 8, 28.642) and 3G (3.2, 32.118), 7 sets of values 3A to 3G are stored as reference data.

  An example of the input parameter is a temperature that can be measured during execution of a process such as a thermal process or a plasma process of a semiconductor manufacturing apparatus. An example of the output parameter is the surface temperature (substance temperature) of the wafer or glass that cannot be measured during the process. The reference data can be obtained by an off-line survey performed before the processing process.

  The analysis data storage unit 2 includes an analysis comprising a set of model type information of the manufacturing apparatus IV for which an estimation polynomial is to be created, input parameter data of the manufacturing apparatus IV, and output parameter data corresponding thereto. Data is stored in advance. Here, for the manufacturing apparatus IV, model type information indicating the model type α is stored in the analysis data storage unit 2, and the combination (X, Y) of the input parameter X and the output parameter Y is 4A (1.6, 20.024), 4B (2.0, 21.000), 4C (2.4, 23.304), 4D (2.8, 27.272), 4E (3.2, 33.288), 4F Assume that six sets of values 4A to 4F (3.5, 39.375) are stored as analysis data. Similar to the reference data, the analytical data can be obtained by an offline survey.

  The input space division information storage unit 3 stores in advance the division method of the input space X-axis and the necessary number of data for each small area obtained by dividing the input space. As a method of defining the division of the input space, for example, there is a method of defining the range of each small region by a numerical value. Here, the range of the small area area1 is 0.0 ≦ X <1.0, the required number of data in the small area area1 is 2, the range of the small area area2 is 1.0 ≦ X <2.0, and the small area area2 is necessary. The number of data is 2, the range of the small area area3 is 2.0 ≦ X <3.0, the required number of data of the small area area3 is 2, the range of the small area area4 is 3.0 ≦ X <4.0, and the small area area4 It is assumed that the required number of data is defined as 1. Note that, for the manufacturing apparatus I, the manufacturing apparatus II, and the manufacturing apparatus III, the necessary number of data defined in all the small areas is obtained.

  The deficient data determination unit 4 determines, for each small area of the input space, whether the analysis data stored in the analysis data storage unit 2 has reached the required number of data stored in the input space division information storage unit 3. (Step S1 in FIG. 2). In the case of the above-described data for analysis of 4A to 4F, the data is insufficient due to the data collection time on the device user side, and the shortage data determination unit 4 has a small area of 0.0 ≦ X <1.0. It is determined that two pieces of data are lacking in area1.

  The data search unit 5 selects reference data to be used for supplementing analysis data (step S2). First, the data search unit 5 reads the model type information of the manufacturing apparatus IV for which the estimation polynomial is to be created from the analysis data storage unit 2 and refers to the database unit 1 to manufacture the same model type as the manufacturing apparatus IV. Search for devices. Since the model type of the manufacturing apparatus IV is α, the manufacturing apparatus to be selected is limited to the manufacturing apparatus I or the manufacturing apparatus II.

Next, the data search unit 5 passes the searched reference data of the manufacturing apparatus I to the estimation polynomial calculation unit 6 to calculate the estimation polynomial. The estimation polynomial calculation unit 6 performs multivariate analysis on the reference data received from the data search unit 5, and calculates an estimation polynomial for estimating the output parameter value from the input parameter value. The estimation polynomial calculation unit 6 executes, for example, SVR (Support Vector Regression) as multivariate analysis. Thereby, the estimation polynomial shown in Expression (2) is obtained. The estimation polynomial calculation unit 6 passes the calculated estimation polynomial to the data search unit 5.
Y = 2.11X ³ -11.55X ² + 25.65X + 0.05 (2)

Similarly, the data search unit 5 passes the searched reference data of the manufacturing apparatus II to the estimation polynomial calculation unit 6 to calculate an estimation polynomial. The estimation polynomial calculation unit 6 performs multivariate analysis on the reference data received from the data search unit 5, and calculates the estimation polynomial shown in Expression (3). The estimation polynomial calculation unit 6 passes the calculated estimation polynomial to the data search unit 5.
Y = 2.11X ³ -11.55X ² + 25.65X + 1.22 (3)

  The data search unit 5 calculates the output parameter Y by substituting the input parameter X of the analysis data into the estimation polynomial of the equation (2) received from the estimation polynomial calculation unit 6, and the analysis data used for the calculation The error between the output parameter Y and the calculated output parameter Y is obtained. The data search unit 5 calculates the average error of the output parameter Y by performing such error calculation for each analysis data. The data search unit 5 also calculates the average error of the output parameter Y using the analysis data for the estimation polynomial of Equation (3). Then, the data search unit 5 finally selects the reference data of the manufacturing apparatus corresponding to the estimation polynomial that minimizes the average error of the output parameter Y as reference data used for supplementing the analysis data. In the present embodiment, reference data for the manufacturing apparatus I is selected. This completes the selection of the reference data in step S2.

  When only one manufacturing apparatus of the same model type as the manufacturing apparatus IV is registered in the database unit 1, it is not necessary to calculate the estimation polynomial by the estimation polynomial calculation unit 6 to calculate the average error. It goes without saying that the reference data of only one manufacturing apparatus registered is selected.

  Next, the data search unit 5 selects the analysis data that the insufficient data determination unit 4 has determined to be insufficient in the small area area1 of 0.0 ≦ X <1.0 in the manufacturing apparatus I selected in step S2. It supplements from the reference data (step S3). The database unit 1 includes 1A (0.0, 0.041) and 1B (0.5, 10.488) as reference data in the range of 0.0 ≦ X <1.0 of the manufacturing apparatus I. It is remembered. Therefore, these two reference data are supplemented. As a result, the analysis data is 1A (0.0, 0.041), 1B (0.5, 10.488), 4A (1.6, 20.024), 4B (2.0, 21.000). ), 4C (2.4, 23.304), 4D (2.8, 27.272), 4E (3.2, 33.288), 4F (3.5, 39.375).

The estimation polynomial calculation unit 6 performs multivariate analysis such as SVR on the supplemented analysis data, and calculates the estimation polynomial shown in Expression (4) (step S4).
Y = 2.11X ³ -11.55X ² + 25.65X + 0.02 (4)

  A cubic curve 222 shown in FIG. 3 is obtained by the estimating polynomial of the equation (4). Reference numeral 220 denotes a cubic curve obtained from the cubic polynomial of equation (1), and 221 denotes a curve showing the relationship between input / output parameters (X, Y) obtained from common sense assumptions. According to the cubic curve 222, the estimated value in the region where the analysis data is sparse 0.0 ≦ X <1.0 is improved from an unrealistic value on the cubic curve 220 to a common sense value. I understand that.

  As specific examples of the model type, for example, “A company's 5-zone reflow furnace” is model type α, “A company's 7 zone reflow furnace” is model type β, and “B company's 5 zone reflow furnace” May be a model type γ, and “B company 7-zone reflow furnace” may be a model type ζ, or may be further subdivided. In any case, models may be classified as appropriate in consideration of the validity of data reuse.

  In the present embodiment, a manufacturing apparatus has been described as an example that is easily applied to the present invention. However, the present invention is not limited to the manufacturing apparatus in principle and can be applied. For example, even if it is the data regarding the characteristic of the air-conditioning control system in a building, this invention can be utilized. In this case, the information corresponding to the model type is, for example, an air conditioning instrumentation type that summarizes a heat source device, an air conditioning system, and the like.

  As a specific example of the air conditioning instrumentation type, for example, “500 square meter level space · 4 zone VAV” is defined as air conditioning instrumentation type α, “500 square meter level space · 6 zone VAV” as air conditioning instrumentation type β, “ “1000 square meter level space · 8 zone VAV” may be an air conditioning instrumentation type γ, and “1000 square meter level space · 12 zone VAV” may be an air conditioning instrumentation type ζ. In any case, models may be classified as appropriate in consideration of the validity of data reuse.

Further, the method for obtaining the estimation polynomial is not limited to SVR, and a similar method such as multiple regression analysis may be appropriately employed.
When there are a plurality of input parameters, each input parameter may be divided into an appropriate number of small regions by appropriately dividing the input parameters.

[Second Embodiment]
Next, a second embodiment of the present invention will be described. FIG. 4 is a block diagram showing the configuration of the estimation apparatus according to the second embodiment of the present invention. The estimation apparatus of FIG. 4 is used at an online stage in which an estimation value is calculated using the estimation polynomial calculated by the estimation polynomial generation apparatus of the first embodiment, and an estimation polynomial storage unit 10, an input parameter value acquisition unit 11, a polynomial estimation calculation unit 12, and an estimated value output unit 13. Note that the estimation device may include an estimation polynomial generation device.

FIG. 5 is a flowchart showing the operation of the estimation apparatus of the present embodiment. The estimation polynomial storage unit 10 stores the estimation polynomial calculated by the estimation polynomial calculation unit 6 described in the first embodiment in step S4.
The input parameter value acquisition unit 11 acquires an input parameter value such as a temperature input from a temperature sensor (not shown) during execution of a process such as a thermal process or a plasma process of the semiconductor manufacturing apparatus (step S10 in FIG. 5). .

  The polynomial estimation calculation unit 12 uses the estimation polynomial stored in the estimation polynomial storage unit 10 to estimate the output parameter value from the input parameter value acquired by the input parameter value acquisition unit 11 (step S11). The output parameter value estimated by the polynomial estimation calculation unit 12 is output to the outside through the estimated value output unit 13. The polynomial estimation calculation unit 12 performs such estimation processing at regular intervals, for example. Thus, in the present embodiment, it is possible to estimate an output parameter value such as a state quantity using the estimation polynomial calculated by the estimation polynomial generation apparatus of the first embodiment.

  Each of the estimation polynomial generator and the estimation device described in the first and second embodiments is realized by a computer having a CPU, a storage device, and an interface, and a program for controlling these hardware resources. Can do. The estimation polynomial generation device and the CPU of the estimation device execute the processing described in the first and second embodiments in accordance with a program stored in the storage device.

  The present invention can be applied to a technique for estimating a state quantity or the like using an estimation polynomial.

  DESCRIPTION OF SYMBOLS 1 ... Database part, 2 ... Analysis data storage part, 3 ... Input space division | segmentation information storage part, 4 ... Insufficient data judgment part, 5 ... Data search part, 6 ... Estimation polynomial calculation part, 10 ... Estimation polynomial storage part , 11 ... input parameter value acquisition unit, 12 ... polynomial estimation calculation unit, 13 ... estimated value output unit.

Claims (10)

A database that pre-stores reference data for replenishment consisting of a set of input parameter data and corresponding output parameter data for each type of estimation polynomial to be created;
Analysis data storage means for preliminarily storing analysis data consisting of a set of input parameter data and output parameter data corresponding to the creation object of the estimation polynomial;
Input space division information storage means for preliminarily storing the input space division method and the required number of data for each small area obtained by dividing the input space;
Insufficient data judgment means for judging for each small area of the input space whether or not the analysis data has reached the required number of data stored in the input space division information storage means;
Data search means for identifying reference data to be used for replenishment of the analysis data from the type for which the estimation polynomial is to be created, and replenishing the deficient data of the analysis data from the identified reference data; ,
An estimation polynomial generating apparatus comprising: an estimation polynomial calculating means for calculating an estimation polynomial for estimating an output parameter value from an input parameter value using the supplemented analysis data. The estimation polynomial generator according to claim 1,
In the case where a plurality of sets of reference data corresponding to the type for which the estimation polynomial is to be created are stored in the database, the data search means uses each of the plurality of sets of reference data to store the estimation polynomial The calculation means calculates the estimation polynomial, and the reference data that minimizes the error between the calculated estimation polynomial and the analysis data is selected as reference data to be used for supplementing the analysis data. A characteristic polynomial generator for estimation. The estimation polynomial generator according to claim 1 or 2,
The creation object of the estimation polynomial is a manufacturing apparatus,
The estimation polynomial generating apparatus according to claim 1, wherein the reference data in the database is organized by model type of the manufacturing apparatus. The estimation polynomial generator according to claim 1 or 2,
The object of creation of the estimation polynomial is an air conditioning system,
Reference data in the database is arranged according to an air conditioning instrumentation type. An input parameter value acquisition means for acquiring an input parameter value;
The estimation polynomial calculation unit of the estimation polynomial generation device according to any one of claims 1 to 4 uses an estimation polynomial calculated from analysis data, and uses the input parameter value acquired by the input parameter value acquisition unit. An estimation apparatus comprising: a polynomial estimation calculation means for estimating an output parameter value. Analytical data storage means for preliminarily storing analytical data consisting of a set of input parameter data and corresponding output parameter data for the estimation polynomial creation target, and input space dividing method and input space divided With reference to the input space division information storage means for storing in advance the number of necessary data for each small area, whether or not the analysis data has reached the required number of data stored in the input space division information storage means An insufficient data determination step for determining each small area;
Reference data for replenishment consisting of a set of input parameter data and corresponding output parameter data is stored in advance for each type of estimation polynomial to be created, and used to replenish the analysis data. A data search step of identifying the reference data to be created from the type of the creation target of the estimation polynomial, and supplementing the deficient data of the analysis data from the identified reference data;
An estimation polynomial generation method comprising: an estimation polynomial calculation step for calculating an estimation polynomial for estimating an output parameter value from an input parameter value using the supplemented analysis data. The estimation polynomial generating method according to claim 6,
In the data search step, when a plurality of sets of reference data corresponding to the type for which the estimation polynomial is created is stored in the database, an estimation polynomial is obtained using each of the plurality of sets of reference data. An estimation polynomial generating method comprising: calculating reference data that minimizes an error between the calculated estimation polynomial and the analysis data as reference data used for supplementing the analysis data . The estimation polynomial generating method according to claim 6 or 7,
The creation object of the estimation polynomial is a manufacturing apparatus,
The estimation polynomial generating method characterized in that the reference data in the database is organized by model type of the manufacturing apparatus. The estimation polynomial generating method according to claim 6 or 7,
The object of creation of the estimation polynomial is an air conditioning system,
The estimation polynomial generating method, wherein the database reference data is organized by air conditioning instrumentation type. An input parameter value acquisition step for acquiring an input parameter value;
A polynomial estimation calculation step for estimating an output parameter value from an input parameter value acquired in the input parameter value acquisition step using the estimation polynomial calculated in the estimation polynomial calculation step according to any one of claims 6 to 9. An estimation method comprising:

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