WO2024025385A1

WO2024025385A1 - Method for building reduced order model by using principal component vector based on simulation and principal component constant through machine learning based on measurement data

Info

Publication number: WO2024025385A1
Application number: PCT/KR2023/011039
Authority: WO
Inventors: 허강열; 한우주
Original assignee: 주식회사 페이스
Priority date: 2022-07-29
Filing date: 2023-07-28
Publication date: 2024-02-01
Also published as: KR102484587B1

Abstract

The present invention relates to a method for building a reduced order model through machine learning by using measurement data, the method comprising: a CAE analysis step of obtaining a CAE analysis result by selecting, as parameters, operating variables or conditions that determine operating conditions of a target product or facility, and performing CAE analysis on cases sampled in a given parameter space; a principal component analysis step of extracting a principal component for the CAE analysis result obtained in the CAE analysis step and obtaining a principal component constant value; a machine learning model building step of building a machine learning model for the correlation between field measurement data and the principal component constant value by using the principal component constant value obtained in the principal component analysis step and the CAE analysis result corresponding to the field measurement data; and a simulation result acquisition step of acquiring a simulation result matching the field measurement data by using the principal component constant value obtained by inputting the field measurement data into the machine learning model.

Description

Method of building a reduced-order model using simulation-based principal component vectors and principal component constants through machine learning based on measurement data.

The present invention relates to a method of building a reduced-order model, and in particular, to a method of building a reduced-order model through machine learning using measurement data.

3D simulation using Computer Aided Engineering (hereinafter referred to as 'CAE') has been widely used for design and problem solving in various industrial fields such as airplanes, vehicles, ships, semiconductors, steel, and power plants.

However, the following limitations exist in using CAE for industrial field problems.

① Skilled engineers required: In order to utilize CAE, engineering, physics, and mathematical understanding of the given problem and computer knowledge are required.

② Excessive analysis time: Depending on the shape and analysis conditions of the application object, excessive calculation time can take from several hours to several weeks per case, so it is difficult to understand the internal situation in real time according to changing operating conditions, such as in a large combustion furnace. impossible.

③ Cost issue: When large-scale calculations need to be performed, large-scale computing resources are required and corresponding software license costs are incurred.

④ Accuracy problem: Because CAE analysis inevitably involves various simplifying assumptions in the basic conservation equations, errors from actual phenomena may occur.

Recently, in order to overcome the above problems of CAE, a reduced order model (ROM) based on CAE analysis has been established, and a digital twin (real-world machine) is used to derive real-time results. Technology that implements equipment, objects, etc. into a virtual world within a computer is on the rise.

Reduced-order models are a technique for obtaining numerical analysis results in a short time by simplifying the solutions of physical and mathematical models used in CAE without directly obtaining solutions. Using reduced-order models enables real-time monitoring and response in the field.

However, due to the various simplifying assumptions involved in CAE analysis, there is bound to be a limit to its accuracy when building a reduced-order model using only CAE. Accordingly, a new method of building a reduced-order model that combines field measurement data and CAE analysis is needed. It is being attempted.

As part of this attempt, a reduced-order model construction method using gappy-POD or associated-POD techniques (see 'Patent Document 1' and 'Non-Patent Document 1' below) has been proposed, but this reduced-order model construction method is based on field data. If the number of sensors measuring is small, the accuracy can be greatly reduced, and there is a disadvantage that at least more sensors are required for the number of main components.

Therefore, there is a need to develop a new reduced-order model construction method that can maintain high accuracy with a small number of sensors so that it can be useful even in situations where it is difficult to obtain measurement data in the field.

(Patent Document 1) KR 10-2048243 B1 (2019.11.25)

(Non-patent Document 1) Woojin Lee, Kwonwoo Jang, Woojoo Han, Kang Y. Huh, “Model order reduction by proper orthogonal decomposition for a 500 MWe tangentially fired pulverized coal boiler”, case Studies in Thermal Engineering, 2021

The present invention was created to solve the above problems, and the purpose of the present invention is to construct a reduced-order model combining field measurement data and CAE analysis, based on POD-machine learning, to reduce the number of variables for a limited type. The goal is to provide a method of building a reduced-order model that has high accuracy with only field measurement data and allows anyone to easily obtain information on all variables of interest in real time.

The method of constructing a reduced-order model according to the present invention to solve the above problems is performed by a program on a computer, and the operating variables or conditions that determine the operating conditions of the target product or facility are selected as parameters, and the given parameter space is A CAE analysis step of obtaining CAE analysis results by performing CAE analysis on the cases sampled in; A principal component analysis step of extracting principal components for the CAE analysis results obtained in the CAE analysis step and obtaining principal component constant values; The CAE analysis results corresponding to the field measurement data are extracted from the CAE analysis results obtained in the CAE analysis step, and the field measurement data and the CAE analysis results corresponding to the field measurement data are extracted using the principal component constant values obtained in the principal component analysis step and the CAE analysis results corresponding to the field measurement data. A machine learning model construction step of constructing a machine learning model for the correlation between principal component constant values; And a simulation result acquisition step of obtaining simulation results that match the field measurement data using the main component constant values obtained by inputting the field measurement data into a machine learning model.

In the present invention, the principal component analysis step is performed by an appropriate orthogonal decomposition method.

According to the reduced-order model construction method according to the present invention, by improving the reduced-order model that combines the measurement data of the conventional gappy-POD and associated-POD techniques, it is possible to build a reduced-order model with high accuracy with only a small number of measurement sensors. It becomes possible.

Figure 1 is a flow chart sequentially showing the steps of performing the reduced-order model construction method according to the present invention.

Figure 2 is a diagram showing the process of extracting CAE analysis results corresponding to field measurement data.

Figure 3 is a diagram showing the process of building a model for the correlation between measurement data and principal component constants by performing machine learning by matching CAE analysis results and principal component constants corresponding to field measurement data.

Figure 4 is a diagram showing the location of measurement data in a natural gas boiler as an example of applying the present invention.

Figures 5a to 5c are diagrams showing the results of comparing the prediction results for a natural gas boiler with the existing gappy-POD technique as an example of applying the present invention.

*Explanation of major symbols in the drawing*

S100: CAE analysis stage

S200: Principal component analysis step

S300: Machine learning model building stage

S400: Simulation result acquisition step

Below, the method of constructing a reduced order model according to the present invention will be described in detail with reference to the attached drawings. However, detailed descriptions of well-known functions and configurations that may unnecessarily obscure the gist of the present invention are omitted.

Referring to Figure 1, the reduced-order model building method according to the present invention includes a CAE analysis step (S100), a principal component analysis step (S200), a machine learning model building step (S300), and a simulation result acquisition step (S400).

Each step of the present invention can be performed by a program implementing the present invention on a computer, and field measurement data can be obtained in real time by various sensors installed in the field.

The CAE analysis step (S100) is a step in which operating variables or conditions that determine the operating conditions of the target product or facility are selected as parameters and CAE analysis is performed on cases sampled in a given parameter space.

Here, the parameters are operating variables or conditions that determine the internal state of the target equipment. For example, in the case of a burner, they may be fuel injection amount, air flow rate, air temperature, and rotation ratio.

In addition, sampling is a procedure for pre-determining the combination of parameters for an appropriate number of cases needed to build a reduced-order model, and is referred to as random sampling or Latin Hyper Cube Sampling (hereinafter referred to as 'LHS'). Methods such as ) may be used. LHS is a method of dividing each parameter into ranges with equal probability and then sampling variables within each range according to a specific correlation. It is known to reproduce the average value better than complete random sampling.

The principal component analysis step (S200) is a step of performing principal component analysis to extract principal components for the CAE analysis results performed in the CAE analysis step (S100).

Here, principal component analysis is an analysis method that finds a common denominator in data obtained by performing CAE analysis on the parameters extracted by sampling in the CAE analysis step (S100), and is a similar concept to finding the greatest common divisor. In other words, just as you can obtain the original number by finding the greatest common divisor and multiplying the value by an appropriate constant, you can reproduce the original data by multiplying each principal component by the corresponding constant and adding them all together.

In the present invention, principal component analysis is, for example, performed based on the Proper Orthogonal Decomposition (POD) method.

POD provides CAE analysis data for a random sample case (

) as the main component (

) is expressed as a combination of

here,

is the number of samples, and is the principal component vector

is a snapshot matrix that combines the CAE analysis results of all samples.

It can be obtained through Singular Value Decomposition.

snapshot matrix

The singular value decomposition for can be defined as the equation below.

here,

Is

An orthogonal matrix obtained by decomposing into eigenvalues,

Is

An orthogonal matrix obtained by eigenvalue decomposition,

Is

and

Each represents a diagonal matrix whose diagonal elements are the square roots of the eigenvalues resulting from eigenvalue decomposition. In this case, the POD main component is

can be selected as follows.

here,

is a matrix

of

It is the second column.

principal component constant

is a snapshot

main ingredient

can be obtained by taking the dot product as follows.

Using this, arbitrary CAE analysis data

can be expressed as follows.

Here, an appropriately small error (

) to have the number of samples (

)lesser

The main components are extracted and stored.

Meanwhile, in the present invention, in addition to the POD described above, various analysis methods such as Bayesian PCA, Dynamic Mode Decomposition (DMD), AutoEncoder, and kernel POD can be used for principal component analysis.

The machine learning model building step (S300) is a step of building a model through machine learning using the principal component constants obtained in the principal component analysis step (S200) and the CAE analysis results corresponding to the field measurement data. That is, in the machine learning model building step (S300), the result value corresponding to the field measurement data is extracted from the CAE analysis result obtained in the CAE analysis step (S100) (see Figure 2), and the principal component constant obtained in the principal component analysis step (S200) value(

), a model for the correlation between measurement data and principal component constants is built through machine learning (see Figure 3).

Machine learning can be applied to various methods, such as kriging and artificial neural networks.

Next, the simulation result acquisition step (S400) is a step of obtaining simulation results that match the current measurement data by inputting field measurement data into the machine learning model built in the machine learning model building step (S300). At this time, the simulation results (

) is the main component obtained in the previous main component analysis step (S200) (

) and the main component constant value (

) can be obtained in the form below.

The method of building a reduced-order model using field measurement data using the conventional gappy-POD or associated-POD technique may greatly reduce the accuracy if the number of measurement sensors is small and requires at least the number of sensors of the main component, but the method of the present invention In cases where the number of sensors is small, accuracy can be maintained at a high level, making it useful in situations where it is difficult to obtain measurement data in the field.

(Application example)

As an example of application of the present invention, a reduced-order model for a natural gas boiler was constructed.

The target was a boiler with 6 burners of the scale used in actual fields, and 20 samples were extracted using excess air ratio and swirl angle as operating conditions to determine the sample case.

OpenFOAM was used as a CAE analysis tool, and analysis was conducted using a self-developed solver using the SLFM (Steady Laminar Flamelet Model) model for turbulent diffusion combustion analysis.

After obtaining information on all distributions such as temperature, flow rate, and concentration of various chemical species inside the burner for each sample case through CAE analysis, temperature (

), principal component analysis was performed.

Afterwards, CAE analysis results corresponding to temperature results at 16 locations (see Figure 4) that can actually be measured near the boiler wall are extracted, and the extracted CAE analysis results and principal component constants (

) was used to perform machine learning.

As a machine learning method, Radial Basis Function Network (RBFN), a type of artificial neural network, was used.

Comparison of the simulation results obtained according to the method of the present invention and the simulation results according to the existing gappy-POD method based on the CAE analysis results that were not used to build the machine learning model is shown in Figures 5a to 5c.

Figure 5a is a CAE analysis result that was not used to build a machine learning model, Figure 5b is a simulation result obtained using the gappy-POD technique, and Figure 5c is a simulation result obtained using a technique according to the present invention. Temperature predicted by gappy-POD and the technique of the present invention (

) In the distribution, major errors occurred in the area where fuel and oxidizer are mixed and combustion reaction occurs. In Figures 5b and 5c, (b) is a picture showing the distribution of the error rate. The error rate of the present invention shows an overall lower numerical distribution compared to the conventional gappy-POD, visually demonstrating superior prediction performance. The average error rate for the entire area was 4.72% for gappy-POD, and 2.67% for the present invention, confirming quantitatively that the error rate is improved compared to the existing method.

The embodiments disclosed in this specification and the accompanying drawings are used only for the purpose of easily explaining the technical idea of the present invention, and are not used to limit the scope of the present invention as set forth in the patent claims. Accordingly, those skilled in the art will understand that various modifications and other equivalent embodiments are possible therefrom.

Claims

Executed by a program on a computer,

A CAE analysis step in which operating variables or conditions that determine the operating conditions of the target product or facility are selected as parameters, and CAE analysis is performed on cases sampled in a given parameter space to obtain CAE analysis results;

A principal component analysis step of extracting principal components for the CAE analysis results obtained in the CAE analysis step and obtaining principal component constant values;

The CAE analysis results corresponding to the field measurement data are extracted from the CAE analysis results obtained in the CAE analysis step, and the field measurement data and the CAE analysis results corresponding to the field measurement data are extracted using the principal component constant values obtained in the principal component analysis step and the CAE analysis results corresponding to the field measurement data. A machine learning model construction step of constructing a machine learning model for the correlation between principal component constant values; and

A method of building a reduced-order model that includes a simulation result acquisition step of obtaining simulation results that match the field measurement data using the principal component constant values obtained by inputting field measurement data into a machine learning model.
In claim 1,

A reduced-order model construction method, characterized in that the principal component analysis step is performed by a suitable orthogonal decomposition method.