KR102048243B1 - Method for Building Reduced Order Model by Combining CAE Simulation and Measurement Data through Coupled-POD - Google Patents

Abstract

When constructing an order reduction model combining field measurement data and CAE analysis, the present invention provides a method for constructing an order reduction model, which enables anyone to accurately and easily check information on all variables of interest in real time, only with field measurement data on limited types of variables through coupled-POD.

Description

Method for Building Reduced Order Model by Combining CAE Simulation and Measurement Data through Coupled-POD}

The present invention relates to an order reduction model construction method, and more particularly, to an order reduction model construction method combining field measurement data and CAE analysis.

Three-dimensional simulation using computer aided engineering (CAE) has been widely used for design and problem solving in various industries such as airplanes, vehicles, ships, semiconductors, steel, and power plants.

However, there are limitations in applying CAE to industrial site problems.

① Skilled Engineers Needed: To use CAE, you need engineering, physical, mathematical understanding and computer knowledge of a given problem.

② Excessive analysis time: Depending on the shape and analysis conditions of the application, excessive calculation time from several hours to several weeks per case may be required. Therefore, it is necessary to grasp the internal situation in real time according to changing operating conditions such as a large combustion furnace. impossible.

3. The cost problem: If you need to perform large calculations, you need a large amount of computational resources, which incurs software license costs.

4. Accuracy problem: Since CAE interpretation inevitably involves many simplifications in basic preservation equations, actual phenomena and errors can occur.

Recently, in order to overcome the problems of CAE, Digital Twin (Reduced Order Model) based on CAE analysis and using it to generate real-time results, digital twin (real world machine or equipment) Technology in the virtual world of computers.

The order reduction model is a technique to obtain numerical results in a short time by simplifying and not directly solving physical mathematical models used in CAE. The order reduction model enables real-time monitoring and response in the field.

However, due to the various simplifications that accompany CAE analysis, the accuracy of the reduction model can only be limited when building the CAE model using only CAE. New attempts are being made.

US 2016-0275234 A1 (2016.09.22) US 2018-0210436 A1 (2018.07.26) US 2019-0122416 A1 (2019.04.25)

 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  Asal Kaveh, Wagdi G. Habashi, Zhao Zhan, `` Combining CFD, EFD and FFD Data via Gappy Proper Orthogonal Decomposition ", AIAA, 2018

The present invention has been made to solve the above problems, and an object of the present invention is the accuracy of the field measurement data for a limited type of variable through the association-POD in constructing an order reduction model combining field measurement data and CAE analysis. It is to provide a method for constructing an order reduction model so that anyone with a high level can easily grasp information on all variables of interest in real time.

In order to solve the above problems, the method for constructing an order reduction model according to the present invention selects an operating variable or condition that determines an operating condition of a target product or a facility as a parameter, and analyzes CAE of cases sampled in a given parameter space. CAE analysis step of performing; A principal component analysis step of extracting a principal component for a CAE analysis result performed in the CAE analysis step; And field measurement data combining step of introducing field measurement data into the principal component extracted in the principal component analysis step to obtain a principal component constant value, wherein the principal component analysis step and the field measurement data combining step are related to the interest through the association-POD. It is characterized by obtaining the principal component extraction and principal component constant values by simultaneously correlating all the 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, the main component analysis step may perform a procedure for normalizing the absolute size of the data value between different variables in advance.

According to the method for constructing an order reduction model according to the present invention, it is possible to construct an order reduction model that can quickly and easily obtain CAE results for all types of variables associated with only field measurement data for limited types of variables without degrading accuracy and reliability. It becomes possible.

1 is a flow chart sequentially showing the steps of performing a method for constructing an order reduction model according to the present invention.
2 is a view showing an example of reconstructing the temperature distribution by the gapp-POD method using only cell data corresponding to 0.1% of the original temperature distribution in the pulverized coal burner.
FIG. 3 shows a combination of principal components linked to temperature and oxygen mass fraction data for associative-POD.
4 is a view showing the results of predicting the temperature and oxygen mass fraction distribution in the pulverized coal burner using the order reduction model constructed by the present invention.

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

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

Referring to FIG. 1, the method for constructing an order reduction 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 may be performed by a program in which the present invention is implemented on a computer, and field measurement data may be obtained in real time by various sensors provided in the field.

The CAE analysis step S100 is a step of selecting an operating variable or condition that determines an operating condition of a target product or a facility as a parameter, and performing CAE analysis on cases sampled in a given parameter space.

Here, the parameter is an operating variable or condition that determines the internal state of the target equipment, and may be, for example, a fuel injection amount, an air flow rate, an air temperature, a turn ratio, and the like in the case of a burner.

In addition, sampling is a procedure for pre-determining a combination of parameters for an appropriate number of cases needed to build an order reduction model, such as random sampling or Latin hyper cube sampling (LHS). May be used. LHS divides each parameter into ranges with equal probability and then samples the variables within each range according to a specific correlation. It is known that LHS reproduces the mean value better than full random sampling.

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

Here, the principal component analysis is an analysis method for finding a common denominator of data obtained by performing CAE analysis on a parameter extracted by sampling in the CAE analysis step (S100), and has a concept similar to finding a maximum common divisor. In other words, if you find the greatest common divisor, you can multiply the value by an appropriate constant to get the original number. By multiplying the constant corresponding to each principal component and adding them together, you can reproduce the original data.

Principal component analysis in the present invention is preferably performed based on a suitable Orthogonal Decomposition (hereinafter referred to as 'POD') method.

)를 아래와 같이 주성분(

)들의 조합으로 나타낸다.The POD is the CAE interpretation data (for any sample case)

) The main component (

) As a combination.

는 샘플의 수이며, 주성분 벡터

는 모든 샘플들의 CAE 해석 결과를 합쳐놓은 스냅샷 행렬(Snapshot Matrix)

의 특이값 분해(Singular Value Decomposition)를 통해 얻을 수 있다.here,

Is the number of samples and the principal component vector

Is a snapshot matrix of the CAE analysis results of all the samples.

This can be obtained through Singular Value Decomposition.

에 대한 특이값 분해는 아래 식과 같이 정의될 수 있다.Snapshot matrix

The singular value decomposition for can be defined as

는

를 고유값(Eigenvalue) 분해해서 얻어진 직교행렬,

는

를 고유값 분해해서 얻어진 직교행렬,

는

와

를 고유값 분해해서 나오는 고유값들의 제곱근을 대각원소로 하는 대각행렬을 각각 나타내며, 이때 POD 주성분

은 아래와 같이 선택될 수 있다.here,

Is

An orthogonal matrix obtained by decomposing eigenvalues,

Is

An orthogonal matrix obtained by eigenvalue decomposition,

Is

Wow

Represents a diagonal matrix whose diagonal root is the square root of the eigenvalues resulting from the eigenvalue decomposition.

May be selected as follows.

는 행렬

의

번째 열이다.here,

Is a matrix

of

Second column.

는 다음과 같이 나타낼 수 있다.Use this to generate arbitrary CAE interpretation data

Can be expressed as:

)를 갖도록 샘플수(

)보다 작은

개의 주성분을 추출하여 저장하게 된다.Where an appropriately small error (

Samples to have)

)lesser

Dog's main components are extracted and stored.

)을 얻는 단계이다.Next, the field measurement data combining step (S300) is to introduce the field measurement data to the principal component extracted in the principal component analysis step (S200) to the principal component constant value (

) Step.

라고 하고, CAE 해석에 의한 온도 분포 결과를 이용하여 구축한 주성분을

라고 하면,In this case, since the field measurement data corresponds to only a part of the CAE analysis data, the principal component constant value may be obtained by performing a gap-POD (Gappy-POD). Gappy-POD is a concept first introduced in the field of face recognition (Emerson and Sirovich, "Karhunen-Loeve procedure for gappy data" 1996), and is a technique for inferring original data using only some missing data or measurements. For example, given the temperature measurement data near the wall through actual experiments, the principal component constant value can be obtained so that the measured data at the temperature measurement position and the predicted value coincide. That is, temperature measurement data at a specific position

The principal component constructed using the temperature distribution result by CAE analysis

Speaking of

을 구하게 되면 원본 데이터 혹은 측정 데이터를 반영한 분포를 유추할 수 있게 된다.To minimize

If we obtain, we can infer distribution reflecting original data or measured data.

Figure 2 shows an example of reconstructing the temperature distribution by the gapp-POD method using only the 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), the principal component analysis and the gapp-POD procedure are performed in association with all variables of interest at the same time. do.

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

To overcome this limitation, the present invention introduces a method that extends principal component analysis called Coupled-POD (POD). In the association-POD, the result values of the variables of interest in the principal component analysis are combined into one data, and then principal component analysis is performed on the combined data. For example, after performing principal component analysis by combining temperature data, carbon monoxide data, and oxygen concentration data into one, and then performing gap gap-POD procedures using only temperature measurement data, not only temperature distribution but also carbon monoxide and oxygen concentration distributions are obtained. It becomes possible. Furthermore, if the measured data includes carbon monoxide data as well as temperature, the gapp-POD procedure can be used to infer more accurate results using the data for both variables.

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

This normalization procedure can be performed by dividing the different variables by the reference value of the variable. For example, when performing the association-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 the information about the oxygen data may be lost, a procedure such as dividing and combining the maximum value of each value so that the temperature data and the oxygen data have a similar size may be performed in advance.

(Application example)

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

Subject was 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 simpleCoalCombustionFoam solver specialized for the steady-state pulverized coal combustion analysis provided by OpenFOAM was used.

Through CAE analysis, information on all distributions such as temperature, flow rate, and various species concentrations in the burner was obtained in each sample case, and then principal component analysis was performed on these three-dimensional distributions such as temperature, flow rate, and species.

In this application example, the main components were extracted by correlating the mass fraction distribution of oxygen with the temperature so that the distribution of both the temperature and the oxygen mass fraction could be obtained using only real-time temperature measurement data.

에 산소 질량분률

값을 연결해서 구성한 새로운 벡터

를 이용하였으며, 이 벡터에 대하여 주성분 분석을 수행하여 온도와 산소 질량분률 데이터가 연결된 주성분

을 구하였다. 도 3은 연관-POD를 위해 온도와 산소 질량분률 데이터가 연결된 주성분들의 조합을 보여준다.To this end, temperature data

Oxygen mass fraction

New vector constructed of concatenated values

Principal component analysis is performed on this vector and the principal component is connected to temperature and oxygen mass fraction data.

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

을 이용하여 실시간 온도 측정 데이터가 결합된 연관-POD 절차를 수행하였고, 최종적으로 실시간 현장 온도 데이터를 반영한 온도 및 산소 질량분률 분포를 얻을 수 있는 차수 감축 모델을 구축하였다. 도 4는 본 적용예에 따라 구축된 차수 감축 모델을 이용하여 미분탄 버너에서의 온도 및 산소 질량분률 분포를 예측한 결과를 보여준다.Next, the principal component thus obtained

The correlation-POD procedure, which combines real-time temperature measurement data, was performed and finally, an order reduction model was developed to obtain temperature and oxygen mass fraction distribution reflecting real-time field temperature data. Figure 4 shows the results of predicting the temperature and oxygen mass fraction distribution in the pulverized coal burner using the order reduction model built in accordance with the present application.

를 구축할 때 온도뿐만이 아니라 산소 질량분률을 연결한 벡터

를 이용함으로써, 온도 측정 데이터만을 이용하여 산소 질량분률도 동시에 실시간 현장 측정 데이터를 반영한 분포를 얻을 수 있게 된다.As in this application, through association-POD, the principal component

Is a vector of oxygen mass fractions as well as 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.

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

S100: CAE Analysis Steps
S200: Principal Component Analysis Step
S300: Combined Site Measurement Data

Claims (3)

A CAE analysis step of selecting an operating variable or condition for determining an operating condition of a target product or a 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 for a CAE analysis result performed in the CAE analysis step; And
A field measurement data combining step of introducing field measurement data into the principal component extracted in the principal component analysis step to obtain a principal component constant value;
The principal component analysis step and the field measurement data combining step are associated with all the variables of interest through the association-POD at the same time to obtain a principal component extraction and a principal component constant value, characterized in that the method. The method according to claim 1,
And 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,
The principal component analyzing step of the step reduction model building method characterized in that for performing a procedure for normalizing the absolute size of the data value between different variables in advance.

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