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%3. From internet
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% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
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% % since he customized it, it needs to be changed (linked to
% % /usr/share/texmf/tex/latex/misc)
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% \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
% \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzaj za desne strane
% \usetheme{Montpellier} % ima graf sadrzaj gore
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%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
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% linktocpage,
% pdftex]{hyperref}
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% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[3Deconvolution]
{3D-Deconvolution}
% {Three Dimensional, Three Component \\
% Seismic Wave Field Reconstruction from \\
% Limited Surface Measurements}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}
\author[Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}, Han Yang
}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
\institute[\pgfuseimage{university-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA}
% \\
% % and\\
% % Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
% Lawrence Berkeley National Laboratory, Berkeley, CA}
% % - Use the \inst command only if there are several affiliations.
% % - Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small CompDyn2023}
\subject{}
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% out.
% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:
%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}
% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}
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% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
\AtBeginSubsection[]
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{
\begin{scriptsize}
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\frametitle{Outline}
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% You might wish to add the option [pausesections]
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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
% 15 and 30 frames, all told.
% - A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
% - If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
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\section{Introduction}
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% \begin{frame}
% \frametitle{OVERVIEW}
%
%
%
% Lecture 1 - Advanced numerical analysis of dams - Modeling:
%
%
% ** Seismic wave fields:
%
% - Influence of realistic seismic wave fields on dynamic Soil Structure Interacting (SSI) behavior
%
% - Realistic three component (3C) seismic wave fields, including 3 translations and 3 rotations, free
% field observations,
%
% - Differences between 1C and 3C wave propagations
%
% ** Inelastic/nonlinear behavior of:
%
% - Rock and soil
%
% - Concrete dams: interfaces/joints/contacts, concrete materials,
%
% - Earth dams: soil material, large deformations
%
%
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% \end{frame}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[-] Improve analysis and design for infrastructure
%\vspace*{1mm}
% \item[] Expert numerical modeling and simulation tool
%%
%% \vspace*{1mm}
%% \item[] Use of numerical models to
%% analyze statics and dynamics of soil/rock-structure systems
%%
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%% %% \vspace*{1mm}
%% \item[-] Reduction of modeling, epistemic uncertainty
%%
%% %\vspace*{1mm}
%% % \item[] Choice of analysis level of sophistication
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%% \item[-] Propagation of parametric, aleatory uncertainty
%%
\vspace*{4mm}
\item[-] Control modeling, epistemic uncertainty
%\vspace*{3mm}
% \item[] Choice of analysis level of sophistication
\vspace*{4mm}
\item[-] Propagate parametric, aleatory uncertainty
%\vspace*{1mm}
% \item[] Goal: predict and inform
\vspace*{4mm}
\item[-] Predict and inform, Engineer needs to know!
%
%\vspace*{2mm}
% \item[-] Credible numerical analysis
%%
% %% \vspace*{1mm}
% \vspace*{2mm}
% \item[-] Design, build and maintain sustainable objects
\end{itemize}
% %\vspace*{6mm}
% %
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-4mm}
% %\includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Kuca_Bajina_Basta-Drina.jpg}
% %%\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Ctesiphon_arch_Iraq.jpg}
% %%\hspace*{2mm}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Brooklyn_bridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Hoover_dam.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Diablo_Canyon_NPP.jpg}
% \hspace*{-10mm}
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\section{Seismic Motions}
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\subsection{Realistic Wave Propagation}
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\begin{frame}
\frametitle{Seismic Motions}
\begin{itemize}
%\vspace*{0.3cm}
\item[-] Knowledge about seismic motions (?)
\vspace*{4mm}
\item[-] Uncertainty in seismic motions (!)
\vspace*{4mm}
\item[-] Simplifying assumptions, 1D/2D/3D; 1C, 2C, 3C, 3$\times$1C, 6C
\vspace*{4mm}
\item[-] Seismic energy input and dissipation within ESSI systems
\vspace*{4mm}
\item[-] Seismic motions have critical importance for ESSI analysis
% \vspace*{4mm}
% \item[-]
%
% \vspace*{4mm}
% \item[-]
%
\end{itemize}
% %\vspace*{6mm}
% %
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-4mm}
% %\includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Kuca_Bajina_Basta-Drina.jpg}
% %%\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Ctesiphon_arch_Iraq.jpg}
% %%\hspace*{2mm}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Brooklyn_bridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Hoover_dam.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Diablo_Canyon_NPP.jpg}
% \hspace*{-10mm}
% %
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% \end{center}
% \end{figure}
% %\vspace*{3mm
% %
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\end{frame}
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\begin{frame}
\frametitle{ESSI Analysis}
\begin{itemize}
%\vspace*{0.3cm}
\item[-] Earthquake Soil Structure Interaction (ESSI)
\vspace*{4mm}
\item[-] Developments in last 50+ years
\vspace*{4mm}
\item[-] ESSI: Nuclear Power Plants, Dams, Bridges, Buildings
\vspace*{4mm}
\item[-] Domain Reduction Method, DRM (J.Bielak et al.) !
% \vspace*{4mm}
% \item[-]
%
% \vspace*{4mm}
% \item[-]
%
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{DRM}
\vspace*{-5mm}
\begin{flushleft}
\begin{eqnarray*}
\hspace*{-10mm}
\left[\begin{array}{ccc}M^{\Omega}_{ii} & M^{\Omega}_{ib} & 0 \\
M^\Omega_{bi} & M^\Omega_{bb}+M^{\Omega+}_{bb} & M^{\Omega+}_{be}
\\ 0 & M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\ \ddot{w}_e\end{array}\right\}
+\\
\left[ \begin{array}{ccc}K^\Omega_{ii} & K^{\Omega}_{ib} & 0 \\
K^{\Omega}_{bi} & K^{\Omega}_{bb}+K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
0 & K^{\Omega+}_{eb} & K^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c} u_i \\ u_b \\ w_e \end{array} \right\}
= \nonumber \\ \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
\\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\label{DRMeq08}
\end{eqnarray*}
\end{flushleft}
\vspace*{-5mm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=40mm]{/home/jeremic/tex/works/psfigures/DRM_NPP_idea01.pdf}
\end{flushright}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{DRM}
%DRM features:
\vspace*{2mm}
\begin{itemize}
%\vspace*{-0.2cm}
\item[-] Seismic forces $P_e$ replaced by $P^{eff}$
%\vspace*{-0.2cm}
\item[-] $P^{eff}$ applied only to a single layer of elements next to $\Gamma$
%\vspace*{-0.2cm}
\item[-] Only outgoing waves from structural oscillations
%\vspace*{-0.2cm}
\item[-] Material inside $\Omega$ can be elastic-plastic
\item[-] Any wave field can be input/imposed
\item[-] Neglect the outside ($\Omega^+$) problems
% \item[-] The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}
\vspace*{-3mm}
\begin{figure}[!h]
\begin{flushright}
%\vspace*{-0.50cm}
%\begin{center}
%\hspace*{1cm}
%\vspace*{-3.50cm}
%{\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
%
{\includegraphics[width=8.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea03_with_element.pdf}}
%\vspace*{-5.50cm}
%\hspace*{1cm}
%\vspace*{-2.50cm}
%\end{center}
%\vspace*{-0.3cm}
\end{flushright}
\end{figure}
\end{frame}
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%
%
%
% \end{frame}
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\begin{frame}
\frametitle{Realistic Seismic Motions}
% \begin{itemize}
%
% \item[-] Free field seismic motion models
%
% \end{itemize}
% local
% local
% local
\vspace*{-2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
\hspace*{-12mm}
% %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% \movie[label=show3,width=6.0cm,poster]
% {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% \hspace*{-2mm}
% %\hfill
\hspace*{5mm}
\movie[label=show3,width=100mm,poster,showcontrols]
%\movie[label=show3,width=90mm,poster]
% {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
{\includegraphics[width=90mm]{movie_input_mp4_icon.jpeg}}
%{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
{movie_input.mp4}
\hspace*{-12mm}
\end{center}
% local
% local
% local
%
% online
% online
% online
\vspace*{-10mm}
\hspace*{-7mm}
\begin{flushleft}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01Apr2015/movie_input.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
% online
% online
%
\end{frame}
% ln -s /home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4 .
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\begin{frame}
\frametitle{Development of Realistic Seismic Motions}
\begin{itemize}
\item[-] Sources will send both P and S waves
\end{itemize}
% online
% online \begin{center}
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
% online {\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
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\movie[label=show3,width=80mm,poster, showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.jpg}}
{movie_input_closeup.mp4}
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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}
\begin{itemize}
\item[-] One component of motions, 1C from 6C
% or 3$\times$1D (it is done all the time!)
\item[-] Excellent fit, wrong physics
% (goal is to predict and inform and not (force) fit)
\end{itemize}
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%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}
{movie_ff_3d.mp4}
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\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}
{movie_ff_1d.mp4}
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% {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
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\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}
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\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
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{\includegraphics[width=92mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
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%\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
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\subsection{3Deconvolution}
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\begin{frame}
\frametitle{3-Deconvolution}
\begin{itemize}
\vspace*{2mm}
\item[-] 1D/1C deconvolution developed long time ago
\vspace*{3mm}
\item[-] Develop 3D/3C seismic waves from limited number of motion measurements, surface, depth
\vspace*{3mm}
\item[-] 3D/3C deconvolution provides many analysis opportunities
\vspace*{3mm}
\item[-] Utilize DRM features and the PDE-constrained optimization to develop DRM forces $P_{eff}$
\vspace*{3mm}
\item[-] C.Jeong et al. recent work on inverse modeling
%\item[-]
%
%\item[-]
%
\end{itemize}
\end{frame}
%
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%
% \begin{frame}
% \frametitle{3Deconvolution Methodology}
%
% The PDE-constrained optimization scheme analytically evaluates the gradient of
% a misfit between measured responses at sensors induced by a targeted {physical}
% profile {(e.g., material properties or dynamic forces)} and computed wave
% solutions induced by an estimated profile with respect to control parameters{,
% which parameterize the estimated profile}. Because of such an analytical nature,
% its computational efficiency of computing the gradient of a misfit with respect
% to control parameters does not depend on the number of {control parameters}.
% Thus, it can update a large set of control parameters very efficiently. Such
% robustness has led to a wide range of studies on elastodynamic inverse
% problems---e.g., full-waveform material inversion
%
% % \citep{kallivokas2013site,fathi2015full,fathi2016three,KUCUKCOBAN_2019_IJSS_Lame},
% % inverse material design \citep{Goh_JEM_2019_Group_Velocity}, full-waveform
% % inverse-scattering \citep{guzina2003stress,jeong2009near}, and full-waveform
% % source inversion \citep{Aquino_2013_Sandia_report,binder_defect_2015}---based on
% % the PDE-constrained optimization.
% %
%
%
%
%
% \end{frame}
%
%
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\begin{frame}
\frametitle{3Deconvolution Methodology}
\begin{itemize}
% \vspace*{2mm}
% \item[-]
% PDE-constrained optimization for inverse problems
\vspace*{2mm}
\item[-]
Full-waveform inversion
\vspace*{3mm}
\item[-]
Inversion modeling is a minimization process
\vspace*{3mm}
\item[-]
Minimize misfits between motions at sensors/nodes
\begin{itemize}
\vspace*{2mm}
\item[-]
Measured, real motions and
\vspace*{2mm}
\item[-]
Motions induced by developed effective forces $P_{eff}$
\end{itemize}
\end{itemize}
%
%%Lagrangian function $\mathcal{A}$
%
% To tackle the minimization problem, the following Lagrangian function
% $\mathcal{A}$ is built by imposing the discrete form of the forward wave
% problem, using a discrete Lagrange multiplier $\hat{\boldsymbol{\lambda}}$, onto
% a misfit function $\mathcal{L}$:
% %-----------------------------------------
% \begin{equation}
% \mathcal{A} =
% \underbrace{(\hat{\mathbf{s}}_{\text{m}}-\hat{\mathbf{s}})^\text{T}
% \,\overline{\textbf{B}}\,
% (\hat{\mathbf{s}}_{\text{m}}-\hat{\mathbf{s}})}_{\text{Misfit: } \mathcal{L} }
% + \hat{\boldsymbol{\lambda}}^T
% \underbrace{(\textbf{Q}\hat{\mathbf{s}}-\hat{\mathbf{F}}_{\text{estm}})}_{\text{0
% per \red{Eq.} (\ref{eq:forward_proposed})}},
% \label{disc_lagrangian_functional_again}
% \end{equation}
% %
% where vectors are defined as:
% \blue{
% \setcounter{MaxMatrixCols}{1}
% \begin{align}
% %
% \hspace{-5pt}
% \hat{\mathbf{s}} =
% \begin{bmatrix}
% \mathbf{s}_0^T,
% \dot{\mathbf{s}}_0^T,
% \ddot{\mathbf{s}}_0^T,
% ..,
% \mathbf{s}_N^T,
% \dot{\mathbf{s}}_N^T,
% \ddot{\mathbf{s}}_N^T
% \end{bmatrix}^T\hspace{-5pt},
% %\hspace{-5pt}
% %
% %\quad
% \hat{\boldsymbol{\lambda}} =
% \begin{bmatrix}
% \boldsymbol{\lambda}_0^T,
% \dot{\boldsymbol{\lambda}}_0^T,
% \ddot{\boldsymbol{\lambda}}_0^T,
% ..,
% \boldsymbol{\lambda}_N^T,
% \dot{\boldsymbol{\lambda}}_N^T,
% \ddot{\boldsymbol{\lambda}}_N^T,
% \end{bmatrix}^T\hspace{-5pt},
% %\quad
% \hat{\mathbf{F}} =
% \begin{bmatrix}
% 0,
% 0,
% \mathbf{F}_0^T,
% ..,
% \mathbf{F}_N^T,
% 0,
% 0
% \end{bmatrix}^T.
% \label{eq_disc_vectors}
% \end{align}}
%
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\begin{frame}
\frametitle{3Deconvolution Methodology, Forward}
%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step;
%$\hat{\mathbf{s}}_{\text{m}}$ is the space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available;
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier;
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps.
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields) and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%
\begin{itemize}
\vspace*{3mm}
\item[-]
State problem: $\mathbf{Q} \hat{\mathbf{u}} = \hat{\mathbf{F}}$
\vspace*{5mm}
\item[-]
$\hat{\mathbf{u}}$ are DoFs in \underline{space and time}
\vspace*{5mm}
\item[-]
$\hat{\mathbf{F}}$ are loads in \underline{space and time}
%\vspace*{3mm}
% \item[-]
\end{itemize}
%
\end{frame}
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\begin{frame}
\frametitle{3Deconvolution, Discrete Forward Operator}
%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step;
%$\hat{\mathbf{s}}_{\text{m}}$ is the space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available;
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier;
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps.
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields) and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%
% Discrete forward operator
% $\mathbf{Q}$
%in {Eq.}
%({disc_lagrangian_functional_again})
%is defined as:
%
\setcounter{MaxMatrixCols}{15}
\begin{align}
\mathbf{Q} & =
\begin{bmatrix}
\mathbf{I} & 0 & 0 & 0 & 0 & 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & \mathbf{I} & 0 & 0 & 0 & 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
\mathbf{K}_{t_0} & \mathbf{C} & \mathbf{M} & 0 & 0 & 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
%----
\mathbf{L}_1 & \mathbf{L}_2 & \mathbf{L}_3 & \mathbf{Keff}_{t_1} & 0 & 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
a_1\mathbf{I} & \mathbf{I} & 0 & -a_1\mathbf{I} & \mathbf{I} & 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
a_0\mathbf{I} & a_2\mathbf{I} & \mathbf{I} & -a_0\mathbf{I} & 0 & \mathbf{I} & \dots & 0 & 0 & 0 & 0 & 0 & 0 \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
0 & 0 & 0 & 0 & 0 & 0 & \dots & \mathbf{L}_1 & \mathbf{L}_2 & \mathbf{L}_3 & \mathbf{Keff}_{t_{\text{N}}} & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & \dots & a_1\mathbf{I} & \mathbf{I} & 0 & -a_1\mathbf{I} & \mathbf{I} & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & \dots & a_0\mathbf{I} & a_2\mathbf{I} & \mathbf{I} & -a_0\mathbf{I} & 0 & \mathbf{I} \\
\end{bmatrix}
\label{eq:Q_proposed_plan},
\end{align}
%(\red{Boris: could check whether my argument is correct?})
%
\end{frame}
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\begin{frame}
\frametitle{3Deconvolution Methodology, Forward}
%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step;
%$\hat{\mathbf{s}}_{\text{m}}$ is the space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available;
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier;
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps.
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields) and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%
\begin{eqnarray*}
\mathbf{Keff}_{t_i} = a_0\textbf{M} + a_1\textbf{C} + \textbf{K}_{t_i}
\\
\mathbf{L}_1 = -a_0\textbf{M} - a_1\textbf{C}
\\
\mathbf{L}_2 = -a_2\textbf{M} - \textbf{C}
\\
\mathbf{L}_3 = -\textbf{M}
\\
a_0 = \frac{4}{(\Delta t)^2}
\\
a_1 = \frac{2}{\Delta t}
\\
a_2 = \frac{4}{\Delta t},
\nonumber\\
\end{eqnarray*}
% Here, $\textbf{K}_{t_i}$ and $\mathbf{Keff}_{t_i}$ are the stiffness and
% effective stiffness matrices, respectively, updated at the $i$-th time step in
% consideration of {mild}
% nonlinearity of {the stiffness of materials (i.e., either linear
% or secant, equivalent elastic stiffness)}.
% %\blue{We note that, because the strong nonlinearity is not considered in the proposed project, our forward wave solver does not need to employ Newton-Raphson method at each $i$-th time step.}
% %(\red{Boris: could check whether my argument is correct?})
%
\end{frame}
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\frametitle{3Deconvolution Methodology, Inverse}
\begin{itemize}
%
\vspace{2mm}
\item[-]
Objective functional
\begin{equation}
%{\cal L} = \frac{1}{2} (\hat{\bf{u}}_{esti}
% - \hat{\bf{u}}_{targ})^{T}
% \mathbf{B}
% (\hat{\bf{u}}_{esti}
% - \hat{\bf{u}}_{targ})
%\cal{L} = \frac{1}{2} (\bf{{u}}_{esti}
% - \bf{{u}}_{targ})^{T}
% \mathbf{B}
% (\bf{{u}}_{esti}
% - \bf{{u}}_{targ})
%{\cal L} = \frac{1}{2} (\hat{u}_{esti} - \hat{u}_{targ})^{T}
{\bf L} = \frac{1}{2} (\hat{\bf u}_{esti} - \hat{\bf u}_{targ})^{T}
{\bf B}
(\hat{\bf u}_{esti} - \hat{\bf u}_{targ})
\nonumber
\end{equation}
${\mathbf B}$ is a square matrix, pairing sensor locations
\vspace{4mm}
\item[-]
Lagrangian functional to solve minimization problem
\vspace{4mm}
\item[-]
Forward step, predictor
\vspace{4mm}
\item[-]
Backward step, checker, corrector
\end{itemize}
\end{frame}
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\frametitle{3Deconvolution Methodology, Benefits}
\begin{itemize}
%
\vspace{4mm}
\item[-]
Leveraging DRM features ($\mathbf{w}=0$) to improve accuracy
\vspace{4mm}
\item[-]
HPC/parallel implementation in the Real-ESSI Simulator
\vspace{4mm}
\item[-]
Still working on improving efficiency and accuracy
\vspace{4mm}
\item[-]
Large computational cost in 3D/3C
\vspace{4mm}
\item[-]
Wirth's law/observation and Moore's law/observation
\end{itemize}
\end{frame}
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\frametitle{3Deconvolution Methodology, Trials}
% local
% local
% local
\vspace*{-2mm}
\begin{center}
% %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% \hspace*{-12mm}
% % %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% % \movie[label=show3,width=6.0cm,poster]
% % {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% % \hspace*{-2mm}
% % %\hfill
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%\movie[label=show3,width=90mm,poster]
% {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
%{\includegraphics[width=100mm]{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare_inverse.jpg}}
{\includegraphics[width=120mm]{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare_inverse.jpg}}
%{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare.mpg}
% \hspace*{-12mm}
\end{center}
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\frametitle{Seismic Energy Input into ESSI System}
\begin{itemize}
%
\vspace{4mm}
\item[-]
Accurate seismic energy input into the ESSI system
\begin{itemize}
\vspace{2mm}
\item[] 3Deconvolution
\vspace{2mm}
\item[] DRM
\end{itemize}
\vspace{4mm}
\item[-]
Analysis of energy dissipation with ESSI system
\vspace{4mm}
\item[-]
Application: buildings, bridges, tunnels, dams, NPPs...
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Seismic Input Energy using DRM, Tunnel example}
%
%
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% \end{frame}
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% \begin{frame}
% \frametitle{Validation: Ventura Hotel, Northridge Eq.}
%
%
% % local
%
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\section{Summary}
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\frametitle{Summary}
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\item[-]
Improve analysis of ESSI systems
%for numerical analysis
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3D/3C deconvolution $\rightarrow$ 3Deconvolution
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Realistic dynamic motions, seismic, etc.
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Accurate energy input and dissipation analysis
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3Deconvolution available within
% the Real-ESSI Simulator \\
\href{http://real-essi.us}{http://real-essi.us}
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NSF project with Prof. Jeong CMichUniv.
% \item[-] Importance of using proper models correctly (verification, validation, level of sophistication)
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% \item[-] Collaborators: Feng, Yang, Behbehani, Sinha, Wang, Wang,
% Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Luo,
% Cheng, Yang.
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% \item[-] Funding from and collaboration with the ATC/US-FEMA, US-DOE, US-NRC, US-NSF,
% CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,
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% \url{http://sokocalo.engr.ucdavis.edu/~jeremic}
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