A new dynamic mode decomposition (DMD) method is introduced for simultaneous
system identification and denoising in conjunction with the adoption of an extended
Kalman filter algorithm. The present paper explains the
extended-Kalman-filter-based DMD (EKFDMD) algorithm which is an online
algorithm for dataset for a small number of degree of freedom (DoF). It also
illustrates that EKFDMD requires significant numerical resources for manydegreeof-
freedom (many-DoF) problems and that the combination with truncated proper
orthogonal decomposition (trPOD) helps us to apply the EKFDMD algorithm to
many-DoF problems, though it prevents the algorithm from being fully online. The
numerical experiments of a noisy dataset with a small number of DoFs illustrate
that EKFDMD can estimate eigenvalues better than or as well as the existing
algorithms, whereas EKFDMD can also denoise the original dataset online. In
particular, EKFDMD performs better than existing algorithms for the case in which
system noise is present. The EKFDMD with trPOD, which unfortunately is not fully
online, can be successfully applied to many-DoF problems, including a
fluid-problem example, and the results reveal the superior performance of system
identification and denoising.

제 1편 : MATLAB 기본편
1. MATLAB 기본사용편 ···················· 003
1.1 MATLAB 시작하기 ·························· 003
명령창(command Window)에서의 입력 005
도움말(Help)의 이용 ······························· 007
1.2 입력 오류의 수정 ····························· 008
계산의 중지 ·············································· 009
MATLAB 종료하기 ································· 009
1.3 연산과 변수의 할당 ·························· 009
연산자 우선순위 ······································· 011
내장함수 ···················································· 012
1.4 데이터의 표현 ··································· 013
1.5 변수의 처리 ······································· 015
변수 이름 ·················································· 015
clear 명령어 ············································· 016
특수변수와 정수 ······································· 017
whos 명령어 ············································ 017
1.6 벡터와 행렬 ······································· 018
벡터 ··························································· 018
행렬 ·························································· 023
스크린 출력과 억제 ································· 024
1.7 랜덤(Random)수와 복소수 ·············· 025
랜덤 수 ····················································· 025
복소수 ······················································· 027
1.8 기호를 이용한 연산 ·························· 028
기호식에서의 치환 ··································· 029
1.9 코드 파일 ·········································· 030
스크립트 코드 파일 ································· 030
코멘트의 추가 ·········································· 032
함수 코드 파일 ···································· 033
사용자 정의함수 ······································ 036
1.10 간단한 그래프의 생성 ····················· 037
ezplot을 이용한 그래프 ·························· 037
plot을 이용한 그래프 ·························· 039
3차원 그래프 ··········································· 042
1.11 MATLAB과 엑셀(Excel)의 접속 043 엑셀 데이터 불러오기 ····························· 043
데이터 가져오기 옵션 ························· 046
스크립트 생성 옵션 ································· 049
함수 생성 옵션 ········································ 049
생성된 데이터를 엑셀파일로 저장하기 ·· 050

제 2편 : 연구논문
Extended-Kalman-filter-based dynamic mode decomposition for
simultaneous system identification and denoising

1. Introduction 51
2. Previous methods compared in the present study 53
3. Extended Kalman filter DMD 57
4. Numerical Experiments and discussion 61
5. Complexity and computational cost 87
7. References 95