WO2021049858A1

WO2021049858A1 - Method for building reduced order model combining field measurement data and cae analysis through coupled-pod

Info

Publication number: WO2021049858A1
Application number: PCT/KR2020/012136
Authority: WO
Inventors: 허강열; 한우주
Original assignee: 포항공과대학교 산학협력단; 주식회사 페이스
Priority date: 2019-09-09
Filing date: 2020-09-09
Publication date: 2021-03-18
Also published as: KR102048243B1

Abstract

The present invention provides, in building a reduced order model combining field measurement data and CAE analysis, a method for building a reduced order model, the reduced order model, through coupled-POD, being highly accurate and enabling anyone to easily identify information on all variables of interest in real time, even by means of only field measurement data for limited types of variables.

Description

A method of constructing a reduced-order model that combines field measurement data and CAE analysis through association-POD

The present invention relates to a method for constructing an order reduction model, and more particularly, to a method for constructing an order reduction model that combines field measurement data and CAE analysis.

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 applying CAE to industrial field problems.

① Requires skilled engineer: To use CAE, engineering, physics, and mathematical understanding of a given problem and computer knowledge are required.

② Excessive analysis time: Depending on the shape and analysis conditions of the application, it may take an excessive calculation time from several hours to several weeks per case. impossible.

③ Cost problem: When large-scale calculations have to be performed, large-scale computational resources are required, and software license fees are incurred.

④ Accuracy problem: Because the basic conservation equations inevitably involve various simplification assumptions in CAE analysis, actual phenomena and errors may occur.

Recently, in order to overcome the above problems of CAE, a Reduced Order Model based on CAE analysis is built, and a digital twin that derives real-time results by using it is a real-world machine or equipment. , Objects, etc. implemented in a virtual world in a computer) technology is emerging.

The order reduction model is a technique for obtaining numerical analysis results in a short time by simplifying the solution of the physical and mathematical models used in CAE without directly obtaining the solution. If the order reduction model is used, real-time monitoring and response in the field becomes possible.

However, due to the various simplification assumptions that accompany CAE analysis, when constructing the order reduction model using only CAE, the accuracy is bound to be limited, and accordingly, the method of constructing the order reduction model combining field measurement data and CAE analysis A new attempt is being made.

(Patent Document 1) US 2016-0275234 A1 (2016.09.22)

(Patent Document 2) US 2018-0210436 A1 (2018.07.26)

(Patent Document 3) US 2019-0122416 A1 (2019.04.25)

(Non-Patent Document 1) T. Braconniera, M. Ferriera, J-C. Jouhauda, M. Montagnaca, P. Sagautb, "Towards an adaptive POD/SVD surrogate model for aeronautic design", Computers and Fluids, 2010

(Non-Patent Document 2) Asal Kaveh, Wagdi G. Habashi, Zhao Zhan, "Combining CFD, EFD and FFD Data via Gappy Proper Orthogonal Decomposition", AIAA, 2018

The present invention was conceived to solve the above problems, and an object of the present invention is to construct an order reduction model that combines on-site measurement data and CAE analysis. The goal is to provide a method of building a reduction-order model so that anyone can easily grasp information on all variables of interest in real time.

In order to solve the above problems, the method of constructing a reduction-order model according to the present invention selects an operating variable or condition that determines the operating condition of a target product or facility as a parameter, and analyzes CAE for cases sampled in a given parameter space. CAE analysis step of performing; A principal component analysis step of extracting a principal component of the CAE analysis result performed in the CAE analysis step; And combining field measurement data to obtain a principal component constant value by introducing field measurement data to the principal component extracted in the principal component analysis step; wherein the principal component analysis step and the field measurement data combination step include: It is characterized in that the principal component extraction and principal component constant values are obtained by simultaneously relating all variables.

In the present invention, the number of variables of the field measurement data is less than or equal to the number of variables of interest.

In addition, in the principal component analysis step, a procedure of normalizing the absolute size of data values between different variables may be performed in advance.

According to the method of constructing the order reduction model according to the present invention, it is possible to construct an order reduction model in which CAE results for all types of related variables can be obtained quickly and easily without deteriorating accuracy and reliability with only field measurement data for limited types of variables. You will be able to.

1 is a flowchart sequentially showing steps of performing a method for constructing an order reduction model according to the present invention.

FIG. 2 is a diagram showing an example of reconstructing a temperature distribution by a gappy-POD method using only cell data corresponding to 0.1% of an original temperature distribution in a pulverized coal burner.

3 is a diagram showing a combination of principal components to which temperature and oxygen mass fraction data are connected for a related-POD.

4 is a diagram showing a result of predicting a temperature and oxygen mass fraction distribution in a pulverized coal burner using the order reduction model constructed according to the present invention.

*Explanation of the main symbols in the drawings*

S100: CAE analysis stage

S200: principal component analysis step

S300: Steps to combine field measurement data

Hereinafter, a method of constructing an order reduction model according to the present invention will be described in detail with reference to the accompanying drawings. However, detailed descriptions of known functions and configurations that may unnecessarily obscure the subject matter of the present invention will be omitted.

Referring to FIG. 1, a method for constructing a reduced-order model according to the present invention includes a CAE analysis step (S100), a principal component analysis step (S200), and a field measurement data combining step (S300).

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

In the CAE analysis step S100, an operation variable or condition that determines the operation condition of a target product or facility is selected as a parameter, and CAE analysis is performed on cases sampled in a given parameter space.

Here, the parameter is an operation variable or condition that determines the internal state of the target facility. For example, in the case of a burner, it may be a fuel injection amount, an air flow rate, an air temperature, a turning ratio, and the like.

In addition, sampling is a procedure for pre-determining a combination of parameters for an appropriate number of cases required to build a degree reduction model, such as Random Sampling or Latin Hyper Cube Sampling (hereinafter'LHS'). (Referred to as "referred to as" LHS is a method of dividing each parameter into a range with the same probability and then sampling variables within each range according to a specific correlation, and is known to reproduce the mean value better than complete randomization.

Principal component analysis step (S200) is a step of performing a principal component analysis (Principal Component Analysis) to extract a principal component of the CAE analysis result performed in the CAE analysis step (S100).

Here, principal component analysis is an analysis method that finds a common denominator of data obtained by performing CAE analysis on a parameter extracted by sampling in the CAE analysis step (S100), and is a concept similar to obtaining a maximum common divisor. That is, just as the original number can be obtained by multiplying the value by an appropriate constant when the greatest common divisor is found, the original data can be reproduced by multiplying and adding all the constants corresponding to each principal component.

In the present invention, the principal component analysis is preferably performed based on a Proper Orthogonal Decomposition (hereinafter referred to as'POD') method.

POD is the CAE analysis data (

) As the main component (

) In combination.

here,

Is the number of samples, 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 following equation.

here,

Is

Orthogonal matrix obtained by decomposing Eigenvalue,

Is

Orthogonal matrix obtained by decomposing the eigenvalues,

Is

Wow

Each represents a diagonal matrix using the square root of the eigenvalues resulting from decomposing the eigenvalues as the diagonal element, where the POD main component

Can be selected as follows.

here,

Is a matrix

of

It is the second row.

Using this, arbitrary CAE analysis data

Can be expressed as

Here, an appropriately small error (

The number of samples (

)lesser

The main components of the dog are extracted and stored.

Next, in the field measurement data combining step (S300), the field measurement data is introduced into the principal component extracted in the principal component analysis step (S200), and the principal component constant value (

).

At this time, since the field measurement data corresponds to only a small part of the CAE analysis data, the principal component constant value can be obtained by performing a gappy-POD. Gappy-POD is a concept first introduced in the field of facial recognition (Emerson and Sirovich, "Karhunen-Loeve procedure for gappy data" 1996), and is a technique for inferring original data using only some lost data or measured values. For example, if temperature measurement data is given near a wall through an actual experiment, the principal component constant value can be calculated so that the measured data at the temperature measurement location and the predicted value coincide. In other words, the temperature measurement data at a specific location

And the main component constructed using the temperature distribution result by CAE analysis

If you say,

To minimize

When is obtained, the distribution reflecting the original data or measured data can be inferred.

FIG. 2 shows an example of reconstructing the temperature distribution by the gappy-POD method using only cell data corresponding to 0.1% of the original temperature distribution in the pulverized coal burner.

Meanwhile, in the present invention, in performing the principal component analysis step (S200) and the field measurement data combining step (S300), all variables of interest are simultaneously associated to perform principal component analysis and gappy-POD procedures. do.

In the conventional gappy-POD method, principal component analysis is performed separately for each result value such as temperature distribution and oxygen concentration distribution. For example, by using temperature measurement data, only temperature data can be inferred. Information on the distribution of exhaust gas concentration, pressure, etc. cannot be obtained

In order to overcome this limitation, the present invention introduces a method of extending the principal component analysis called a coupled-POD. In association-POD, results of variables of interest are combined into one data during principal component analysis, and then principal component analysis is performed on the combined data. For example, if temperature data, carbon monoxide data, and oxygen concentration data are combined into one to perform a principal component analysis, and then go through the gappy-POD procedure using only the temperature measurement data, not only the temperature distribution, but also the distribution of carbon monoxide and oxygen concentration is obtained. You will be able to. Furthermore, when the measurement data includes not only temperature but also carbon monoxide data, a more accurate result value can be inferred by performing the gappy-POD procedure using both data for these two variables.

In this case, if the absolute size of the data value is different between the data of different variables, the data information of the variable having a relatively small size may be lost. It is desirable to perform the normalization procedure in advance.

This normalization procedure can be performed by dividing different variables by the reference value of the variable. For example, when performing a correlation-POD by combining the temperature and oxygen data values as they are, the value of the temperature data is larger than the value of the oxygen data. Therefore, since information on the oxygen data may be lost, a procedure such as dividing the temperature data and the oxygen data by the maximum value of each value to have a similar size and adding them can be performed in advance.

(Application example)

As an application example of the present invention, an order reduction model for analysis of pulverized coal combustion in a steady state was constructed.

Subject is a laboratory-scale pulverized coal burner with two parameters: oxygen (or air) flow rate and turn ratio, and 10 sample cases were determined via LHS for a given parameter operating range.

OpenFOAM was used as a CAE analysis tool, and a specialized simpleCoalCombustionFoam solver was used for the steady-state pulverized coal combustion analysis provided by OpenFOAM.

After obtaining information on all distributions such as temperature, flow rate, and concentration of various species in each sample case through CAE analysis, principal component analysis was performed on three-dimensional distributions such as temperature, flow rate, and chemical species.

In this application example, the main component was extracted by relating the distribution of the mass fraction of oxygen to the temperature so that both the temperature and the distribution of the mass fraction of oxygen can be obtained using only real-time temperature measurement data.

For this, temperature data

Oxygen mass fraction in

A new vector constructed by concatenating values

Was used, and principal component analysis was performed on this vector, and the temperature and oxygen mass fraction data were connected.

Was obtained. FIG. 3 shows a combination of principal components to which temperature and oxygen mass fraction data are linked for association-POD.

Next, the main component obtained in this way

By using the associated-POD procedure in which real-time temperature measurement data is combined, the order reduction model was constructed to obtain the temperature and oxygen mass fraction distribution reflecting the real-time field temperature data. 4 shows the results of predicting the temperature and oxygen mass fraction distribution in the pulverized coal burner using the order reduction model constructed according to this application example.

As in this application example, through the association-POD, the main component

When constructing a vector that connects the oxygen mass fraction as well as the temperature

By using, it is possible to obtain a distribution reflecting the real-time field measurement data at the same time as the oxygen mass fraction using only the temperature measurement data.

The embodiments disclosed in the present specification and the accompanying drawings are only used for the purpose of easily describing the technical idea of the present invention, and are not used to limit the scope of the present invention described in the claims. Therefore, those of ordinary skill in the art will understand that various modifications and equivalent other embodiments are possible therefrom.

Claims

A CAE analysis step of selecting an operation variable or condition that determines an operation condition of a target product or facility as a parameter, and performing CAE analysis on cases sampled in a given parameter space;

A principal component analysis step of extracting a principal component of the CAE analysis result performed in the CAE analysis step; And

Including; field measurement data combining step of obtaining a principal component constant value by introducing field measurement data to the principal component extracted in the principal component analysis step;

The principal component analysis step and the in-situ measurement data combining step include extracting principal components and obtaining principal component constant values by simultaneously relating all variables of interest through association-POD.
The method according to claim 1,

The number of variables of the field measurement data is less than or equal to the number of variables of interest.
The method according to claim 1,

In the principal component analysis step, a procedure for normalizing the absolute size of data values between different variables is performed in advance.