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%\documentclass[handout]{beamer}
%\usepackage{pgfpages}
%\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm]
\mode{\setbeamercolor{background canvas}{bg=black!3}}
\usepackage{epstopdf}
\usepackage[absolute,overlay]{textpos}
% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% % since he customized it, it needs to be changed (linked to
% % /usr/share/texmf/tex/latex/misc)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}
\usepackage{threeparttable}
%\usepackage{MnSymbol}%
% for smileys
\usepackage{wasysym}%
\usepackage{multirow}
% for subfloat figures:
\usepackage{subfig}
\usepackage{tabularx}
%used for truncated section title in headers
\usepackage[breakall]{truncate}
%\usepackage{caption}
\usepackage{multimedia}
% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}
%This is a macro to convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
% \usepackage{graphicx}
% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************
%% ovo je za cirilicu
\input vuk.def
\newfont{\cyr}{wncyr10 scaled 1000 }
\newfont{\cyb}{wncyb10 scaled 1000 }
\newfont{\cyi}{wncyi10 scaled 1000 }
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\newfont{\cyss}{wncyss10 scaled 1200 }
\newfont{\romjba}{cmss10 scaled 1000}
\newfont{\cyrjbnaslov}{wncyss10 scaled 1400 }
% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
% showonlyrefs
% }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FEI LOGO definition
\newcommand{\FEI}
{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % ovo je za cirilicu
% % \input vuk.def
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% % %\newfont{\cyrnaslov}{wncyb10 scaled 2600}
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%
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% \newfont{\cyrimena}{wncyss10 scaled 2000}
% \newfont{\cyrnaslov}{wncyss10 scaled 2800}
% \newfont{\cyrpodnaslov}{wncyss10 scaled 1400}
%
% \newfont{\cyn}{wncyss10 scaled 2200}
% %% JB sig
% \newfont{\cyrjb}{wncyr10 scaled 600}
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% {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode
{
% \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 sadrzxaj za desne strane
% \usetheme{Montpellier} % ima graf sadrzaj gore
% \usetheme{Warsaw}
% \usetheme{Warsaw}
\usetheme{Dresden}
\usecolortheme[RGB={20,0,128}]{structure}
% or ...
\setbeamercovered{transparent}
% \setbeamercovered{transparent}
% or whatever (possibly just delete it)
% \usecolortheme{albatross} % teget sa svetlim slovima
% \usecolortheme{beetle} % siva pozadina (vrh plav)
\usecolortheme{seagull} % sivo
%%%%%%%
% \usecolortheme{BorisJeremic}
%%%%%%%
% \usecolortheme{rose}
% \usefonttheme[onlylarge]{structuresmallcapsserif}
% \usefonttheme{structuresmallcapsserif}
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\usepackage[greek,english]{babel}
\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\newcommand{\ud}{{\rm d}}
\usepackage{array}
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
\definecolor{webgreen}{rgb}{0, 0.35, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
\definecolor{webred}{rgb}{0.35, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}
\usepackage{hyperref}
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pdfmenubar=true,
pdftoolbar=true,
pdfpagemode={None}
colorlinks=true,
linkcolor=webblue,
citecolor=webblue,
urlcolor=webblue,
}
% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
% urlcolor=webblue,
% linktocpage,
% pdftex]{hyperref}
\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}
\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% 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[Risk Analysis - SEPFEM]
{Seismic Risk Analysis: \\
Time Domain, Intrusive, \\
Stochastic Elastic Plastic \\
Finite Element Method}
% {Interface Between Earthquake Ground Motions and Structural
%Response: Numerical Modeling and Simulation of ESSI Behavior}
%\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} et al. Best PSHANI] % (optional, use only with lots of authors)
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Jeremi{\'c}, Wang, Wang, Yang}
%Fangbo Wang, David McCallen}
%Floriana Petrone, Francis McKenna, David McCallen}
%
%\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%%{Boris~Jeremi{\'c}}
%{Boris Jeremi{\'c}
%}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-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 CompDyn\\ Crete, June 2019}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.
%
%\date[] % (optional, should be abbreviation of conference name)
%{\small United States Society on Dams\\
% Chicago, April 2019}
%
%\subject{}
% This is only inserted into the PDF information catalog. Can be left
% 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}}
% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
\AtBeginSubsection[]
% \AtBeginSection[]
{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
\tableofcontents[currentsection,currentsubsection]
% \tableofcontents[currentsection]
\end{frame}
\end{scriptsize}
}
% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:
% - \documentclass[fleqn]{beamer}
% - %\documentclass[handout]{beamer}
% - %\usepackage{pgfpages}
% - %\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm]
% -
% - \mode{\setbeamercolor{background canvas}{bg=black!3}}
% -
% - % for extra, backup slides, see https://www.yesterdayscoffee.de/2013/03/20/backup-slides-in-latex-beamer/
% - % then in front of extra slides put
% - % \appendix
% - % start backup slides here
% - \usepackage{appendixnumberbeamer}
% -
% - \usepackage{epstopdf}
% -
% -
% - \usepackage[absolute,overlay]{textpos}
% -
% - \usepackage{multimedia}
% -
% - % for inclusion of other PDF pages, in this case Frank's presentation
% - \usepackage{pdfpages}
% -
% - %This is a macro to convert eps to pdf files on the fly.
% - % make sure figure syntax uses graphicx syntax NOT epsfig syntax
% - %from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
% - %
% - % \ifx\pdfoutput\undefined
% - % % we are running LaTeX, not pdflatex
% - % \usepackage{graphicx}
% - % \else
% - % % we are running pdflatex, so convert .pdf files to .pdf
% - % \usepackage[pdftex]{graphicx}
% - % \usepackage{epstopdf}
% - % \fi
% - % %*****************************************
% -
% -
% - %% ovo je za cirilicu
% - \input vuk.def
% - \newfont{\cyr}{wncyr10 scaled 1000 }
% - \newfont{\cyb}{wncyb10 scaled 1000 }
% - \newfont{\cyi}{wncyi10 scaled 1000 }
% - \newfont{\cysc}{wncysc10 scaled 1000 }
% - \newfont{\cyss}{wncyss10 scaled 1200 }
% - \newfont{\romjba}{cmss10 scaled 1000}
% - \newfont{\cyrjbnaslov}{wncyss10 scaled 1400 }
% -
% -
% -
% - % % for not showing eq numbers unless eq is references
% - % \usepackage[fleqn,tbtags]{mathtools}
% - % \mathtoolsset{
% - % showonlyrefs
% - % }
% -
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - % FEI LOGO definition
% - \newcommand{\FEI}
% - {{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}
% -
% - % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - % % % ovo je za cirilicu
% - % % \input vuk.def
% - % % %\newfont{\cyr}{wncyr10 scaled 1200}
% - % % %\newfont{\cyrimena}{wncyb10 scaled 1800}
% - % % %\newfont{\cyrnaslov}{wncyb10 scaled 2600}
% - % % %\newfont{\cyrpodnaslov}{wncyr10 scaled 1400}
% - %
% - % \newfont{\cyr}{wncyss10 scaled 1200}
% - % \newfont{\cyrimena}{wncyss10 scaled 2000}
% - % \newfont{\cyrnaslov}{wncyss10 scaled 2800}
% - % \newfont{\cyrpodnaslov}{wncyss10 scaled 1400}
% - %
% - % \newfont{\cyn}{wncyss10 scaled 2200}
% - % %% JB sig
% - % \newfont{\cyrjb}{wncyr10 scaled 600}
% - % \newcommand{\JB}
% - % {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
% - % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -
% -
% - \setbeamertemplate{navigation symbols}{}
% - \mode
% - {
% - % \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 sadrzxaj za desne strane
% - % \usetheme{Montpellier} % ima graf sadrzaj gore
% - % \usetheme{Warsaw}
% - % \usetheme{Warsaw}
% - \usetheme{Dresden}
% - \usecolortheme[RGB={20,0,128}]{structure}
% -
% - % or ...
% -
% - \setbeamercovered{transparent}
% -
% -
% - % \setbeamercovered{transparent}
% - % or whatever (possibly just delete it)
% - % \usecolortheme{albatross} % teget sa svetlim slovima
% - % \usecolortheme{beetle} % siva pozadina (vrh plav)
% - \usecolortheme{seagull} % sivo
% - %%%%%%%
% - % \usecolortheme{BorisJeremic}
% - %%%%%%%
% - % \usecolortheme{rose}
% - % \usefonttheme[onlylarge]{structuresmallcapsserif}
% - % \usefonttheme{structuresmallcapsserif}
% - }
% -
% - \definecolor{mycolor}{rgb}{0,0.08,0.45}%
% -
% -
% - \usepackage[greek,english]{babel}
% -
% -
% -
% - \usepackage{amsmath}
% - \usepackage{mathrsfs}
% - \usepackage{amsfonts}
% -
% - \newcommand{\ud}{{\rm d}}
% -
% -
% - \usepackage{tikz}
% -
% - \usetikzlibrary{calc}
% -
% - \usepackage[export]{adjustbox}
% -
% -
% - \usepackage{array}
% -
% -
% -
% - %%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
% - %%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
% - \definecolor{webgreen}{rgb}{0, 0.15, 0} % less intense green
% - \definecolor{webblue}{rgb}{0, 0, 0.45} % less intense blue
% - \definecolor{webred}{rgb}{0.15, 0, 0} % less intense red
% - \definecolor{gray}{rgb}{0.6, 0.6, 0.6} % gray
% - %\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}
% -
% - \usepackage{hyperref}
% - \hypersetup{
% - pdfmenubar=true,
% - pdftoolbar=true,
% - pdfpagemode={None}
% - % Commenting this out fixes Windows acrobat problem (?!)
% - colorlinks=true,
% - linkcolor=webblue,
% - citecolor=webblue,
% - urlcolor=webblue,
% - }
% - % \usepackage[pdfauthor={Boris Jeremic},
% - % colorlinks=true,
% - % linkcolor=webblue,
% - % citecolor=webblue,
% - % urlcolor=webblue,
% - % linktocpage,
% - % pdftex]{hyperref}
% -
% -
% - \usepackage{pause}
% - % or whatever
% - %\usepackage{html}
% - %\usepackage{url}
% -
% - \usepackage[latin1]{inputenc}
% - % or whatever
% - \usepackage{times}
% - \usepackage[T1]{fontenc}
% - % Or whatever. Note that the encoding and the font should match. If T1
% - % 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[Risk Analysis - SEPFEM]
% - {Seismic Risk Analysis: \\
% - Time Domain, Intrusive, \\
% - Stochastic Elastic Plastic \\
% - Finite Element Method}
% - % {Interface Between Earthquake Ground Motions and Structural
% - %Response: Numerical Modeling and Simulation of ESSI Behavior}
% -
% -
% - %\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=0.15cm]{UCD-logo}{/home/jeremic/BG/amblemi/UCD/ucdavis_logo_blue_sm}
% - \pgfdeclareimage[height=0.18cm]{lbnl-logo}{/home/jeremic/BG/amblemi/LBNL/BerkeleyLab_Masterbrand_logo}
% - % \pgfdeclareimage[height=0.15cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
% - % \pgfdeclareimage[height=0.17cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_white_01}
% -
% - % \pgfdeclareimage[height=0.20cm]{UCD-logo}{/home/jeremic/BG/amblemi/UCD/UCD_white_01}
% - % \pgfdeclareimage[height=0.20cm]{LBNL-logo}{/home/jeremic/BG/amblemi/LBNL/LBNL_white_01}
% - % % \pgfdeclareimage[height=0.15cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
% - % \pgfdeclareimage[height=0.20cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI-C_white_01}
% -
% -
% -
% - % \pgfdeclareimage[height=0.40cm]{Best_PSHANI_2018_logo}{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/Best_PSHANI_2018_logo}
% -
% - %\author[Jeremi{\'c} et al. Best PSHANI] % (optional, use only with lots of authors)
% - \author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
% - %{Boris~Jeremi{\'c}}
% - {Jeremi{\'c}, Wang, Wang, Yang}
% - %Fangbo Wang, David McCallen}
% - %Floriana Petrone, Francis McKenna, David McCallen}
% -
% - %\institute[Computational Geomechanics Group \hspace*{0.3truecm}
% - \institute[\pgfuseimage{UCD-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-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.
% -
% -
% - %\institute[Computational Geomechanics Group \hspace*{0.3truecm}
% - %\institute[] % (optional, but mostly needed)
% - %\institute[\pgfuseimage{UCD-logo}\hspace*{0.15truecm}\pgfuseimage{LBNL-logo}] % (optional, but mostly needed)
% - %\institute[\pgfuseimage{UCD-logo}\hspace*{0.15truecm}\pgfuseimage{LBNL-logo}\hspace*{0.15truecm}\pgfuseimage{ESSI-C-logo}] % (optional, but mostly needed)
% - %\institute[\pgfuseimage{UCD-logo}\mbox{;}\pgfuseimage{LBNL-logo}\mbox{;}\pgfuseimage{ESSI-C-logo}] % (optional, but mostly needed)
% - %{ Professor, University of California, Davis\\
% - % { University of California, Davis, CA, USA}
% - %{ University of California, Davis, CA\\
% - % and\\
% - % Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
% - % Lawrence Berkeley National Laboratory, Berkeley, CA}
% - % ESSI Consultants, Davis, 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 CompDyn 2019 \\ Crete, June 2019}
% -
% - \subject{}
% - % This is only inserted into the PDF information catalog. Can be left
% - % 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}}
% -
% -
% -
% -
% - % Delete this, if you do not want the table of contents to pop up at
% - % the beginning of each subsection:
% - % \AtBeginSubsection[]
% - \setcounter{tocdepth}{3}
% - \AtBeginSubsection[]
% - % \AtBeginSection[]
% - {
% - \begin{scriptsize}
% - \begin{frame}
% - \frametitle{Outline}
% - \tableofcontents[currentsection,currentsubsection]
% - % \tableofcontents[currentsection]
% - \end{frame}
% - \end{scriptsize}
% - }
% -
% -
% - % If you wish to uncover everything in a step-wise fashion, uncomment
% - % the following command:
% -
% -
% -
% -
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
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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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\subsection{\ }
%\subsection{Motivation}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Improve modeling and simulation for infrastructure objects
\vspace*{5mm}
\item[] Use of numerical modeling for design and assessment
% \vspace*{2mm}
% \item[] Expert numerical modeling and simulation tool
%
% \vspace*{1mm}
% \item[] Use of numerical models to
% analyze statics and dynamics of soil/rock-structure systems
%
\vspace*{5mm}
\item[] Analysis uncertainties
\begin{itemize}
\vspace*{2mm}
\item[] Modeling uncertainty
%
\vspace*{2mm}
\item[] Parametric uncertainty
%
\end{itemize}
% %
% %\vspace*{2mm}
% % \item[] Choice of analysis level of sophistication
%
%
% \vspace*{3mm}
% \item[] Goal: Predict and Inform rather than fit
%
%
%
% %\vspace*{2mm}
% % \item[] Follow the flow, input and dissipation, of seismic energy,
% %
%
% \vspace*{3wmm}
% \item[] System for modeling and simulation of
% Earthquakes and/or Soils and/or Structures and their Interaction
% % Real-ESSI/MS-ESSI:
% \\
% \vspace*{2mm}
% \hspace*{25mm}
% \href{http://real-essi.info/}{http://real-essi.info/}
% % \url{http://ms-essi.info/}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Personal Risk}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Personal exposure to natural and man made hazard
\vspace*{5mm}
\item[] Decision making under uncertainty
\vspace*{5mm}
\item[] Importance of education: engineering with uncertainty
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Motivation: Seismic Hazard}
\begin{figure}[!hbpt]
\begin{center}
% %
%\hspace*{-3mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Conferences/2018/GeoMEast2018/Short_Course/present/Global_Seismic_Hazard_Map_1999.jpg}
\end{center}
\end{figure}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Global Seismic Hazard Map}
%
%
% 10\% probability of exceedance in 50 years (Giardini et al.)
% %, 475 year return-period
%
%
%
% %\vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% %\hspace*{-3mm}
% \includegraphics[width=11.5truecm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/World_earthquake_hazard.jpg}
% \end{center}
% \end{figure}
%
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Mediterranean Seismic Hazard}
10\% probability of exceedance in 50 years (Giardini et al.)
%, 475 year return-period
%\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
% %
%\hspace*{-3mm}
\includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/Mediteranean_Earthquake_Hazard.jpg}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Crete Seismic Hazard}
10\% probability of exceedance in 50 years (Giardini et al.)
%, 475 year return-period
%\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
% %
%\hspace*{-3mm}
\includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/Crete_Seismic_Hazard.jpg}
\end{center}
\end{figure}
\end{frame}
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Predictive Capabilities}
% % \frametitle{High Fidelity Modeling of SFS System:
% % Verification, Validation and Prediction}
%
%
% \end{frame}
%
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\section{Modeling}
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\subsection{Prediction of Behavior}
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\begin{frame}
\frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
\item[] { Prediction under Uncertainty}: use of computational model
to predict the state of SSI system under
conditions for which the computational model has not been validated.
\vspace*{4mm}
\item[] {{ Verification:} provides evidence that the model is solved
correctly.} Mathematics issue.
\vspace*{4mm}
\item[] {{ Validation:} provides evidence that the correct model is
solved.} Physics issue.
%
\end{itemize}
\end{frame}
%
%
% \vspace*{1mm}
% \item Modeling and parametric uncertainties are always present, need to be
% addressed
% \vspace*{1mm}
% \item Predictive capabilities with {low Kolmogorov Complexity}
%
%
% \vspace*{1mm}
% \item Goal: Predict and Inform rather than (force) Fit
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Prediction under Uncertainty}
\begin{itemize}
%\vspace*{1mm}
\item[] \underline{Modeling Uncertainty}, simplifying assumptions
\begin{itemize}
\vspace*{2mm}
\item[] Low, medium, high sophistication modeling and simulation
\vspace*{2mm}
\item[] Choice of sophistication level for confidence in results
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
\item[] \underline{Parametric Uncertainty}, ${M} \ddot{u_i} + {C} \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,
\begin{itemize}
\vspace*{2mm}
\item[] Uncertain LHS: $M$, $C$ and $K^{ep}$
\vspace*{2mm}
\item[] Uncertain RHS $F(t)$
\vspace*{2mm}
\item[] Results are PDFs and CDFs for $\sigma_{ij}$, $\epsilon_{ij}$, $u_i$, $\dot{u}_i$, $\ddot{u}_i$
\end{itemize}
\end{itemize}
%
%
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\
% mais l'assurance est un {\'e}tat ridicule. (Fran{\c c}ois-Marie Arouet, Voltaire)
\end{frame}
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\subsection{Uncertainties}
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\begin{frame}
\frametitle{Modeling Uncertainty}
\begin{itemize}
\item[] Important (?!) features are simplified
\begin{itemize}
\vspace*{2mm}
\item[] Seismic motions, 1C vs 3C,
\vspace*{2mm}
\item[] Inelastic response
\end{itemize}
%\vspace*{4mm}
% \item Unrealistic and unnecessary modeling simplifications
\vspace*{6mm}
\item[] Modeling simplifications are justifiable if one or two
level higher sophistication model demonstrates that features being
simplified out are not important
\end{itemize}
%
% % local
% %\vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% %\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% \movie[label=show3,width=5.5cm,poster,autostart, showcontrols]
% {\includegraphics[width=50mm]
% {/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}
% %
% %\hfill
% \hspace*{-5mm}
% %
% \movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
% {\includegraphics[width=50mm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% \hspace*{-7mm}
% %\end{flushleft}
% %%
% \end{center}
% % local
% %
% % % \vspace*{-5mm}
% % \begin{center}
% % %\begin{flushleft}
% % % \hspace*{-15mm}
% % \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% % {\includegraphics[width=5cm]
% % {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% % {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% % %\end{flushleft}
% % %%
% % \hfill
% % %%
% % %\begin{flushright}
% % % \hspace*{-15mm}
% % \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% % {\includegraphics[width=5cm]
% % {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% % {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% % %\end{flushright}
% % \end{center}
% %
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling Uncertainty: Free Field Motions}
\begin{itemize}
\item One component of motions, 1C, from 3C
% or 3$\times$1D (it is done all the time!)
\item Excellent fit
% (goal is to predict and inform and not (force) fit)
\end{itemize}
% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
\hspace*{-16mm}
\end{center}
% local
% online
\begin{center}
\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}
{\tiny (MP4)}
%
\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}
{\tiny (MP4)}
\end{center}
% online
% out
% out % local
% out %\vspace*{-2mm}
% out \begin{center}
% out \hspace*{-16mm}
% out %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% out \movie[label=show3,width=61mm,poster, showcontrols]
% out {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% out % \hspace*{-16mm}
% out % \end{center}
% out % %
% out % %
% out % %
% out % \begin{center}
% out % \hspace*{-16mm}
% out \movie[label=show3,width=61mm,poster, showcontrols]
% out {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
% out \hspace*{-16mm}
% out \end{center}
% out %
% out
% out \begin{flushleft}
% out %\vspace*{-15mm}
% out \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}
% out % \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out {\tiny (MP4)}
% out %
% out \hspace*{55mm}
% out \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}
% out % \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out {\tiny (MP4)}
% out \end{flushleft}
% out %
% out
% out
% out
% out % online
% out % online \begin{center}
% out % online \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}
% out % online {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% out % online %
% out % online \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}
% out % online {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% out % online \end{center}
% out % online
% out
% out
% out
% out %
% out
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\end{frame}
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\begin{frame}
\frametitle{Modeling Uncertainty: 6C vs 1C}
% local
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
{\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}
% local
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% \end{center}
% online
\vspace*{-12mm}
\begin{flushleft}
%\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}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling Uncertainty: Input Frequency}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
% online
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
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\begin{frame}
\frametitle{Modeling Uncertainty: SMR ESSI}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
% online
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
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\begin{frame}
%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{Modeling Uncertainty: 3C vs 3$\times$1C}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\end{center}
% online
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
{\tiny (OGV)}
\end{flushleft}
% online
\end{frame}
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\begin{frame}
\frametitle{Modeling Uncertainty: Elastic vs Inelastic}
\vspace*{5mm}
Accelerations
\hspace*{-35mm}
\begin{figure}[!h]
\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{-20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{-25mm}
\end{center}
\end{figure}
\hspace*{-45mm}
\vspace*{-10mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
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\begin{frame}
\frametitle{Modeling Uncertainty: Elastic vs Inelastic}
\vspace*{5mm}
Displacements
\hspace*{-35mm}
\begin{figure}[!h]
\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{-20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{-25mm}
\end{center}
\end{figure}
\hspace*{-35mm}
\vspace*{-10mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Modeling Uncertainty: Elastic and Inelastic Response}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% \end{center}
%
%
%
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% % \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Modeling Uncertainty: Energy Dissipation}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
% \href{./homo_50m-mesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness and Strength}
\vspace*{2mm}
%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}
%\vspace*{-5mm}
%\vspace*{-1.8cm}
%\hspace*{-3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{flushright}
%
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Material Properties}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
%\vspace*{-2mm}
\hspace*{-2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
\\
\vspace*{10mm}
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
%\vspace*{-8mm}
\hspace*{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Uncertain Results: Energy Dissipation}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/HanYang/Stocahstic_animations_14Jun2019/Blur_Videos/NPP_Blured_more_screeen_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Stocahstic_animations_14Jun2019/Blur_Videos/NPP_Blurred_More.mp4}
\end{center}
%\begin{flushleft}
%\vspace*{-15mm}
%\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%% \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
%\end{flushleft}
%%
\end{frame}
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\section{Time Domain Intrusive Seismic Risk Analysis}
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\subsection{Modeling Framework}
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\begin{frame}
\frametitle{Current State of Art Seismic Risk Analysis (SRA)}
\begin{itemize}
%\vspace{2mm}
\item[-] Intensity measure (IM) selected as a proxy for ground motions,
usually Spectral acceleration $Sa(T_0)$
\vspace{4mm}
\item[-] Ground Motion Prediction Equations (GMPEs) need development, ergodic or site specific
\vspace{4mm}
\item[-] Probabilistic seismic hazard analysis (PSHA)
% for ground motion $\lambda(Sa>z)$
% \begin{equation*}
% \resizebox{0.85\hsize}{!}{%
% $\lambda(Sa>z) = \sum_{i=1}^{NFL} \underbrace{N_i \int\int f_{mi}(M) f_{ri}(R|M)}_\text{seismic source characterization (SSC)} \underbrace{P(Sa>z|M, R)}_\text{GMPE} dM dR$}
% \end{equation*}
\vspace{4mm}
\item[-] Fragility analysis $P(EDP>x|IM=z)$, deterministic time domain FEM,
Monte Carlo (MC)
% \begin{itemize}
%
% \item[-] Records selection: Spectrum-matching technique UHS, etc
%
% \item[-] Incremental dynamic analysis: Monte Carlo
%
% \end{itemize}
\end{itemize}
% \begin{textblock}{15}(2.2, 9.2)
% \begin{figure}[H]
% \flushleft
% % \includegraphics[width=0.38\linewidth]{pic/hazard_curve.png}
% \includegraphics[width=0.38\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/hazard_curve.pdf}
% \enspace
% \includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/design_spectra.png}
% \end{figure}
% \end{textblock}
\end{frame}
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Issues in State-of-the-art SRA}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Risk Analysis Challenges}
\begin{itemize}
\vspace{4mm}
\item[-] Miscommunication between seismologists and structural engineers,
$Sa(T_0)$ not compatible with nonlinear FEM
\vspace{4mm}
\item[-] IMs difficult to choose, Spectral Acc, PGA, PGV...
\vspace{4mm}
\item[-] Single IM does not contain all/most uncertainty
\vspace{4mm}
\item[-] Monte Carlo, not accurate enough for tails
\vspace{4mm}
\item[-] Monte Carlo, computationally expensive, CyberShake for LA, 20,000
cases, 100y runtime, (Maechling et al. 2007)
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Time Domain Intrusive SRA Framework}
%
\begin{itemize}
\vspace*{2mm}
\item[-] Stochastic Elastic-Plastic Finite Element Method, SEPFEM,
${M} \ddot{u_i} + {C} \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,
\vspace*{2mm}
\item[-] Uncertain seismic loads, from uncertain seismic motions, using Domain
Reduction Method
\vspace*{2mm}
\item[-] Uncertain elastic-plastic material, stress and stiffness solution using
Forward Kolmogorov, Fokker-Planck equation
\vspace*{2mm}
\item[-] Results, probability distribution functions for $\sigma_{ij}$,
$\epsilon_{ij}$, $u_i$...
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Stochastic Elastic-Plastic Finite Element Method (SEPFEM)}
%
%
%
% \begin{itemize}
%
% \item[] Material uncertainty expanded along stochastic shape functions:
% $D(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
%
% \vspace*{4mm}
% \item[] Loading uncertainty expanded along stochastic shape functions:
% $f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
%
% \vspace*{4mm}
% \item[] Displacement expanded along stochastic shape functions:
% $u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
%
% \end{itemize}
%
%
%
% \end{frame}
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method (SEPFEM)}
%\frametitle{SEPFEM : Formulation}
Stochastic system of equations
\begin{tiny}
\[
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
u_{10} \\
\vdots \\
u_{N0}\\
\vdots \\
u_{1P_u}\\
\vdots \\
u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
\]
\end{tiny}
% \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
\scalebox{0.7}{
\begin{tabular}{ c c c c}
\# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
4 & 4 & 10 & 43758 \\
4 & 4 & 20 & 3 108 105 \\
4 & 4 & 30 & 48 903 492 \\
6 & 6 & 10 & 646 646 \\
6 & 6 & 20 & 225 792 840 \\
6 & 6 & 30 & 1.1058 $10^{10}$ \\
% 8 & 8 & 10 & 5 311 735 \\
% 8 & 8 & 20 & 7.3079 $10^{9}$ \\
% 8 & 8 & 30 & 9.9149 $10^{11}$\\
... & ... & ... & ...\\ \hline
\end{tabular}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic Seismic Motion Development}
\begin{itemize}
\item UCERF3 (Field et al. 2014)
\item Stochastic motions (Boore 2003)
\item Polynomial Chaos Karhunen-Lo{\`e}ve expansion
\item Domain Reduction Method for $P_{eff}$ (Bielak et al. 2003)
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/UCERF3.pdf}
\includegraphics[width=3.0cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SMSIM.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_dis_correlation_from_dis.pdf}
\end{center}
\end{figure}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/structural_uncertainty.pdf}
% \end{center}
% \end{figure}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/probabilsitc_evolution.png}
% \end{center}
% \end{figure}
%
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/seismic_risk_result_framework.png}
% \end{center}
% \end{figure}
%
%
\end{frame}
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\begin{frame}
\frametitle{Stochastic Ground Motion Modeling}
\begin{itemize}
%\vspace*{1mm}
\item[-] Modeling fundamental characteristics of uncertain ground motions,
Stochastic Fourier amplitude spectra (FAS). and Stochastic Fourier phase spectra
(FPS) and not specific IM
\vspace*{1mm}
\item[-] Mean behavior of stochastic FAS, $w^2$ source radiation spectrum by
Brune(1970), and Boore(1983, 2003, 2015).
\vspace*{1mm}
\item[-] Variability models for stochastic FAS,
FAS GMPEs by Bora et al. (2015, 2018), Bayless \&
Abrahamson (2019),
% for marginal median \& variability,
%Inter-frequency correlation structure by
Stafford(2017) and Bayless \& Abrahamson (2018).
\vspace*{1mm}
\item[-] Stochastic FPS by phase derivative (Boore,2005), Logistic phase derivative
model by Baglio \& Abrahamson (2017)
%\item Upcoming: a major change from \textbf{ $\boldsymbol{Sa(T_0)}$ to FAS} in next five years as envisioned by Abrahamson (2018)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Stochastic Ground Motion Modeling}
%
% Boore (2003) approach for median of log-normal random FAS field:
%
% \[FAS(f) = \underbrace{S(M_0, f)}_\text{source}\underbrace{P(R, f)}_\text{path} \underbrace{A(f)D(f)}_\text{site}\]
%
% \vspace{-3mm}
%
% where:
% \begin{itemize}
% \small
%
% % \item $S(M_0,f) = \frac{CM_0(2\pi f)^2}{1+(f/f_0)^2}$
%
% \item $S(M_0,f) = CM_0(2\pi f)^2/[1+f^2/f_0^2]$
%
% \vspace{1mm}
%
% \item $P(R, f) = Z(R)exp(-\pi fR/Q\beta)$
%
% \vspace{1mm}
%
% \item $A(f)$: quarter wavelength approximation.
%
% \vspace{1mm}
%
% \item $D(f)= exp(-\pi \kappa_0f)$
%
% \end{itemize}
%
% Improvements:
%
% \begin{itemize}
% \small
%
% \item Inter-frequency correlation by \textit{Bayless \& Abrahamson (2018)}
%
% \vspace{1mm}
%
% \item Phase derivative model by \textit{Baglio \& Abrahamson (2017)}
%
% \end{itemize}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Stochastic Ground Motion Modeling}
%
% \begin{textblock}{15}(0.5, 4.2)
% Verification with GMPE for $M=7$, $R=15km$ scenario
% \end{textblock}
%
% \begin{textblock}{15}(0.0, 5.0)
% \includegraphics[width=0.4\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SA_GMPE_verification_std_08_no_smooth.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(5.3, 5.0)
% \includegraphics[width=0.4\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Goodness_fit_std_08_no_smooth.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(10.5, 5.0)
% \includegraphics[width=0.4\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Standard_deviation_std_08_no_smooth.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(0.5, 11.0)
% \begin{itemize}
% \item $\Delta \sigma= 84bar$, $\kappa=0.03s$ with total $\sigma=0.8ln$.
% \item Simulated median is not biased.
% \item Consistent total uncertainties with GMPE.
% \end{itemize}
% \end{textblock}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
% \begin{itemize}
% \vspace{-2mm}
% \item \small Unified uncertainty representation for forcing and media $D(\boldsymbol{x}, \theta)$.
%
% \begin{itemize}
% \item [--] Hermite polynomial chaos (PC) for marginal distribution
% \item [--] Karhunen-Lo$\grave{e}$ve (KL) expansion for correlation structure
% \end{itemize}
%
% \item \small Hermite PCs: Non-Gaussian random field with underlying Gaussian random field
%
% \[D(\boldsymbol{x}, \theta) = \sum_{i=0}^{P} D_i(\boldsymbol{x}) \Omega_i(\gamma(\boldsymbol{x},\theta)) \]
%
% where: \[\Omega_i = 1, \gamma, \gamma^2-1, \gamma^3-3\gamma, ... \]
%
% \[<\Omega_i> =0; \ \ <\Omega_i\Omega_j> = 0 \ \ for \ \ i \neq j \]
%
% \end{itemize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
%
% \begin{textblock}{15}(0.5, 5.0)
% \includegraphics[width=0.4\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Hermite_PC_order.png}
% \end{textblock}
%
% \begin{textblock}{15}(7.5, 4.0)
% \includegraphics[width=0.5\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Gamma_distribution_hermite.png}
% \end{textblock}
%
% \begin{textblock}{15}(5.5, 12.0)
% \includegraphics[width=0.7\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Gamma_distribution.png}
% \end{textblock}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
%
% \vspace{0.1cm}
%
% \small Karhunen-Lo$\grave{e}$ve (KL) expansion: capture correlation structure
%
% \vspace{-0.3cm}
%
% \[Cov_D(x_1, x_2) = \sum_{i=1}^{P} D_i(x_1)D_i(x_2)i!Cov_{\gamma}(x_1, x_2)\]
%
% \vspace{-0.2cm}
%
% \small Eigen-decomposed Gaussian covariance kernel: $ \lambda_{i}$ eigenvalue, $f_i(\boldsymbol{x})$ eigen-function
%
% \vspace{-0.7cm}
%
% \[\gamma(\boldsymbol{x}, \theta)=\sum_{i=1}^{M}\sqrt{\lambda_i}f_i(\boldsymbol{x})\xi_i \]
%
% \vspace{-0.2cm}
%
% \small Fredholm's integral equation of the second kind:
%
% \[\int_V Cov_{\gamma}(x_1, x_2) f_i(x_1) \, dx_1 = \lambda_{i} f_i(x_2)\]
%
% \vspace{-0.1cm}
%
% \small \{$\xi_i$\} are zero mean, unit variance, mutually orthogonal Gaussian random variables
%
% \vspace{-0.2cm}
%
% \[<\xi_i> =0; \ \ <\xi_i\xi_j> = \delta_{ij}\]
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
% \begin{textblock}{15}(0.5, 6.0)
% \includegraphics[width=0.4\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/1D_KL_exp_illustration.png}
% \end{textblock}
% \begin{textblock}{15}(7.5, 4.0)
% \includegraphics[width=0.5\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_eigen_modes.png}
% \end{textblock}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
%
% \small Random field $D(\boldsymbol{x}, \theta)$ of arbitrary marginal distribution \& correlation structure can be represented as:
%
% \begin{textblock}{14}(-2.4, 6.0)
% \[D(\boldsymbol{x}, \theta) = \sum_{i=0}^{K} d_i(\boldsymbol{x}) \Psi_i(\{\xi_j(\theta)\})\]
% \[d_i(\boldsymbol{x}) = \frac{P!}{(\Psi_i^2)} D_P(\boldsymbol{x}) \prod_{j=1}^{P} \frac{\sqrt{\lambda_{k(j)}}f_{k(j)}(\boldsymbol{x})}{\sqrt{\sum_{m=1}^{M}(\sqrt{\lambda_m}f_m(\boldsymbol{x}))^2}}\]
% \end{textblock}
%
% \vspace{3.5cm}
% where: \\
% $\{\Psi_i\}$ are multi-dimensional Hermite \\
% PC bases of order $P$, dimension $M$.
%
% \begin{textblock}{15}(8.9, 5.5)
% \includegraphics[width=0.45\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Multidimensional_Hermite_PC.png}
% \end{textblock}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainty Representation \& Propagation}
%
% \small
%
% Galerkin stochastic finite element method (SFEM)
%
% \[M_{IacJ} \ddot{U}_{Jc} + \boldsymbol{K^{ep}_{IacJ}} U_{Jc} = \boldsymbol{F_{Ia}}\]
%
% Probabilistic discretization:
%
% \vspace{-0.2cm}
%
% \[K^{ep}_{IacJ}(\theta)= K^{ep}_{IacJi} \Psi_i (\theta)\]
%
% \vspace{-0.3cm}
%
% \[F_{Ia}(\theta)= F_{Iaj} \psi_j (\theta)\]
%
% \vspace{-0.3cm}
%
% \[U_{Jc}(\theta) = U_{Jck} \phi_k(\theta)\]
%
% \vspace{-0.3cm}
%
% Galerkin projection:
%
% \[M_{IacJ} (\phi_k \phi_m) \ddot{U}_{Jck} + K^{ep}_{IacJi} (\Psi_i\phi_k\phi_m) U_{Jck} = F_{Iaj} (\psi_j \phi_m) \]
%
% \vspace{0.2cm}
% \scriptsize where $(\Psi_i\phi_k\phi_m)$ is the triple product of multi-dimensional Hermite PCs
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Illustrative Example}
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\begin{frame}
\frametitle{Uncertain Model Description}
\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.70\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/example_illustration.png}
\end{textblock}
\begin{textblock}{15}(1.2, 11.6)
\scriptsize
\begin{itemize}
\item Fault 1: San Gregorio fault
\item Fault 2: Calaveras fault
\item Uncertainty: Segmentation, \\ slip rate, rupture geometry, etc.
\end{itemize}
\end{textblock}
\begin{textblock}{15}(7.2, 11.7)
\scriptsize
\begin{itemize}
\item $Vs_{30}=620m/s$
\item $m=100kips/g$
\item $\overline{k} = 168kip/in$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(9.7, 6.5)
\scriptsize
\[Cov_k =
\begin{bmatrix}
1.0 & 0.6 & 0.3 & 0.2\\
0.6 & 1.0 & 0.5 & 0.2\\
0.3 & 0.5 & 1.0 & 0.7\\
0.2 & 0.2 & 0.7 & 1.0
\end{bmatrix}
\]
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Seismic Source Characterization}
\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SSC_legend.pdf}
\end{textblock}
\begin{textblock}{15}(6.5, 12.1)
\scriptsize
\begin{itemize}
\item 371 total seismic scenarios
\item $M \ 5 \sim 5.5$ and $6.5 \sim 7.0$
\item $R_{jb} \ 20km \sim 40km$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(11.7, 3.3)
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series100.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series343.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series439.pdf}
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Stochastic Ground Representation}
{\begin{textblock}{15}(-0.1, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_acc_from_acc.pdf}
\quad \quad Acc. marginal mean
\end{textblock}
\begin{textblock}{15}(3.7, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_acc_from_acc.pdf}
\quad \quad Acc. marginal S.D.
\end{textblock}
\begin{textblock}{15}(7.6, 3.8)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_acc_correlation_from_acc.pdf}
\quad \quad \quad Acc. realization Cov.
\end{textblock}
\begin{textblock}{15}(11.8, 3.9)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_acc_correlation_from_acc.pdf}
\quad \quad Acc. synthesized Cov.
\end{textblock}}
\begin{textblock}{15}(-0.1, 9.3)
\scriptsize
\includegraphics[width=0.31\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_dis_from_dis.pdf}
\end{textblock}
\begin{textblock}{15}(0.9, 13.75)
\scriptsize
Dis. marginal mean
\end{textblock}
\begin{textblock}{15}(4.2, 9.4)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_dis_from_dis.pdf}
\end{textblock}
\begin{textblock}{15}(5.1, 13.75)
\scriptsize
Dis. marginal S.D.
\end{textblock}
\begin{textblock}{15}(8.2, 9.5)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_dis_correlation_from_dis.pdf}
\quad \quad Dis. realization Cov.
\end{textblock}
\begin{textblock}{15}(12.2, 9.6)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_dis_correlation_from_dis.pdf}
\quad Dis. synthesized Cov.
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic Dynamic Response}
\begin{textblock}{15}(2.9, 4)
\scriptsize
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Probabilistic_Response_Node_1_new.pdf}
\end{textblock}
\begin{textblock}{15}(4.8, 3.8)
\scriptsize Probabilistic response of top floor from SFEM
\end{textblock}
\end{frame}
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% \begin{frame}
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% \frametitle{Probabilistic Dynamic Response}
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% \begin{textblock}{15}(0.9, 4.4)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/probability_evolution.jpg}
% \includegraphics[width=0.43\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Contour_PDF_evolution_top_floor_deformation.pdf}
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% \scriptsize Probabilistic density of displacements evolution of top floor
% \end{textblock}
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\begin{frame}
\frametitle{Maximum Inter-story Drift Ratio (MIDR)}
% \begin{textblock}{15}(0.7, 4.8)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/PDF_evolution.png}
% \end{textblock}
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\vspace*{-5mm}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/MIDR_distribution.pdf}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Seismic Risk Analysis}
\begin{textblock}{15}(0.7, 4.8)
\scriptsize
\includegraphics[width=0.45\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/combined_risk_curve.pdf}
\end{textblock}
\begin{textblock}{15}(7.9, 4.8)
\scriptsize
\includegraphics[width=0.48\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_deaggregation_MIDR1.pdf}
\end{textblock}
\begin{textblock}{15}(0.9, 11.9)
\begin{itemize}
\item[] \scriptsize $\lambda(MIDR >1 \%) = 9.7 \times 10^{-3}$
\item[] \scriptsize $\lambda(MIDR >2 \%) = 1.7 \times 10^{-3}$
\item[] \scriptsize $\lambda(MIDR >4 \%) = 5.9 \times 10^{-5}$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(9.3, 12.5)
\scriptsize Risk de-aggregation for $\lambda(MIDR >1 \%)$
\end{textblock}
\end{frame}
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% \frametitle{Sensitivity Study}
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% \begin{textblock}{15}(1.7, 3.0)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_stressdrop.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(9.1, 3.0)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_kappa.pdf}
% \end{textblock}
%
%
% \begin{textblock}{15}(1.7, 8.7)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_stressdrop_comparison.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(9.1, 8.7)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_kappa_comparison1.pdf}
% \end{textblock}
%
% \begin{textblock}{15}(7.9, 8.7)
% \scriptsize Site $\kappa_0$:
% \end{textblock}
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% \begin{textblock}{15}(0.3, 8.7)
% \scriptsize Source $\Delta \sigma$:
% \end{textblock}
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% \frametitle{Sensitivity Study}
%
% \begin{textblock}{15}(1.3, 4.2)
% Fundamental frequency $f$ increases from 1.6Hz to 8Hz:
% \end{textblock}
%
% \begin{textblock}{15}(4.7, 5)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_kappa_highfrequency.pdf}
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\begin{frame}
\frametitle{Seismic Risk, Uncertain Material}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/seismic_risk_compare.pdf}
\end{center}
\end{figure}
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\section{Summary}
%\subsection*{Summary}
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%\subsection{Summary}
\subsection{\ }
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\begin{frame}
\frametitle{Method Summary}
\begin{itemize}
\vspace*{1mm}
\item[-] Full probabilistic modeling and simulation of earthquake soil structure
interacting (ESSI) systems
\vspace*{2mm}
\item[-] Intrusive modeling using SEPFEM
\vspace*{2mm}
\item[-] Input: uncertain seismic ground motions
\vspace*{2mm}
\item[-] Input: uncertain material
\vspace*{2mm}
\item[-] Output: accurate probability density functions for
$\sigma_{ij}$,
$\epsilon_{ij}$,
$u_i$,
$\dot{u}_i$,
$\ddot{u}_i$,
and any of their combinations
\vspace*{2mm}
\item[-] Objective risk analysis, removing subjective choices
\vspace*{2mm}
\item[-] Requires data and is computationally intensive, however,
less demanding and more accurate than MC approach
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Conclusion}
\begin{itemize}
%\vspace*{1mm}
\item[-] Numerical modeling to predict and inform, rather than fit
\vspace*{2mm}
\item[-] Education and Training is the key!
\vspace*{2mm}
\item[-] Collaborators: Wang, Wang, Feng, Yang, Behbehani, Sinha,
Pisan{\'o}, Abell, Cheng, Jie, Luo, Tafazzoli, Preisig, Tasiopoulou, Watanabe
\vspace*{2mm}
\item[-] Funding from and collaboration with the US-DOE, US-NRC, US-NSF,
CNSC-CCSN, UN-IAEA, Shimizu Corp. and ILEE is greatly appreciated,
\vspace*{2mm}
\item[-] Real-ESSI Simulator System: \\
\hspace*{20mm} \textbf{\url{http://real-essi.info/}}
\end{itemize}
\end{frame}
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\end{document}
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