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Kalman filter의 개념 잡기Mathematics 2020. 9. 11. 20:20
아래의 링크 순서대로 공부하였다: 1. https://dynamic-positioning.com/proceedings/dp2003/design_cadet.pdf 2. https://arx.appi.keio.ac.jp/wp-content/uploads/2018/01/test.pdf 3. https://m.blog.naver.com/PostView.nhn?blogId=hms4913&logNo=30166486895&proxyReferer=https%3A%2F%2Fwww.google.com%2F 선형칼만필터 개념! - 5월 13일 수정 칼만필터를 공부하기 위해서 먼저 칼만필터의 전체적인 개념을 이해하고 보상필터를 공부한 뒤 보상필터를 ... blog.naver.com 5. https://pinkwink...
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Laplacian FilterMathematics 2020. 9. 11. 13:22
Laplacian of $f$ can be represented as follows, where 'div' denotes divergence and 'grad' denotes gradient. $\nabla{f}=\mathrm{div}(\mathrm{grad}(f)) = \frac{\partial^{2}f}{\partial{x^2}} + \frac{\partial^{2}f}{\partial{y^2}} + \frac{\partial^{2}f}{\partial{z^2}} $ The detailed explanation of the laplacian operation, divergence, and gradient are presented in the following urls: micropilot.tistor..
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FFT on an irregular wave from JONSWAP spectrumMathematics 2020. 9. 11. 12:26
Please refer to the following jupyter-notebook file: Result summary 1. JONSWAP spectrum 2. irregular wave generated by doing the IFT (inverse fourier transform) on the JONSWAP spectrum 3. Compare the reconstructed FFT graph and the normalized JONSWAP spectrum (the normalization is conducted according to Eq. (2.15) in my pf's thesis) ※ normalization of the JONSWAP spectrum The following figure sh..
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Implementation of DFT, IDFT, FFT, IFFTMathematics 2020. 9. 11. 12:17
Implementation of Discrete Fourier Transform (DFT) Inverse Discrete Fourier Transform (IDFT) Fast Fourier Transform (FFT) Inverse Fast Fourier Transform (IFFT) DFT, IDFT FFT, IFFT word documentation file1 simply considered as a fast version of DFT, IDFT jupyter-notebook files file2 file3 file1 (contains theory, equations, and code): file2: file3: results:
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This is why you're learning Taylor SeriesMathematics 2020. 9. 11. 10:57
To approximate a complex equation Taylor Series converts a complex (high-order) equation into an approximated linear or quadratic equation (usually) at a certain point $x$. For example, $y=e^{x}$ can be converted to $y=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\frac{x^{4}}{4!}+\cdots + (\mathrm{at} \: x=0)$ If we leave out the terms above 2nd-order, $y = 1 + x + \frac{x^2}{2!}$ ※ The above equation..
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AutocorrelationMathematics 2020. 9. 11. 10:50
autocorrelation은 "자기상관함수" 라고 불린다. 말 그대로, correlation을 자기 자신의 데이터에 대해서 한 것이다. 이때, 시간항에 대해서 shifted된 자기 자신에 대해서 correlation을 한것이라, auto correlation이라 불린다. 정말 간단하지 않은가? 다음은 예시를 보여준다. "shift=1"인 경우의 autocorrelation은 다음과 같이 나타내어진다. 여기서, 사용되는 데이터는 daily temperature 이다. 자세한 사항은 다음 Youtube tutorial을 참고하면 된다: https://youtu.be/ZjaBn93YPWo
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Load RAO, Froud-Kyrlov force, Diffraction forceMathematics 2020. 9. 11. 10:43
Froud-Krylov force a hydrodynamic force introduced by the unsteady pressure field generated by undisturbed waves (https://en.wikipedia.org/wiki/Froude%E2%80%93Krylov_force) Diffraction force: occurs due to a floating body disturbing the waves Load RAO (= Wave excitation force): Froud-Kyrlov force + Diffraction force
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Optimization Course [최민주 교수님 최적화 수업]Mathematics 2020. 9. 11. 09:57
1. Linear programming 2. Simplex 3. Mixed integer programming 4. Binary integer programming 5. Goal programming 6. Network models, Graph theory 7. Minimum spanning tree 8. Stenier tree problem 9. A* (A star) 10. Non-linear optimization problems and nonlinear programming 11. Meta-heuristics 12. Genetic algorithm (GA) 13. Particle swarm optimization Linear programming : to find optimal value(s) fo..