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%  \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
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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[Real-ESSI]
      { Time Domain \\ 
        Seismic Risk Analysis Framework \\
        for Nuclear Installations}



%\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.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Hexiang Wang, Fangbo Wang, Han Yang, \\
Yuan Feng, Jeff Bayless,\\
\vspace*{2mm}
Norman A. Abrahamson and 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 SMiRT25\\
         Charlotte, NC, USA, August 2019}

\subject{}
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%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
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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
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% - 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.
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%   just say so once. Everybody will be happy with that.



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\section{Introduction}




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\subsection{\ }



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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[]  Improve  modeling  and  simulation  for  infrastructure objects
 

% \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*{2mm}
  \item[]  Control and reduction  of modeling uncertainty

\vspace*{2mm}
  \item[] Propagation of parametric uncertainty
       \begin{itemize}
         \item[-] uncertain seismic motions
         \item[-] uncertain material in soil and structure
       \end{itemize}



%\vspace*{1mm}
%  \item[] Goal: Predict and Inform rather than fit
%
%\vspace*{1mm}
%  \item[] Engineer needs to know!

\vspace*{2mm}
  \item[] Full risk calculations for earthquake, soil structure system



%
%  
%  
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy, 

 
\vspace*{2mm}
  \item[]  System  for {\bf Real}istic modeling and simulation of
  {\bf E}arthquakes,  {\bf S}oils,    {\bf S}tructures and  
  their {\bf I}nteraction: \\
\vspace*{1mm}
   {\bf Real-ESSI Simulator}  \hspace*{2mm}  
  {\bf \url{http://real-essi.info/}} 



\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Uncertain Motions and Uncertain Material}



\vspace*{-2mm}
\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{-7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/time_series_motionsn_06ug2019_SMIRT/Acc_realization_200.pdf}
%\hspace*{-3mm}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion70.pdf}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion100.pdf}
%% \includegraphics[width=0.31\textwidth]{Figures/Acc_time_series_realiztion350.pdf}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion367.pdf}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/SA_GMPE_verification_std_08_no_smooth.pdf}
%
\end{center}
\end{figure}


\vspace*{-7mm}
\begin{flushright}
{\tiny
(cf. Wang et al. (2019))\\
~}
\end{flushright}



%\vspace*{2mm}
\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.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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\section{Uncertain Modeling}




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\subsection{\ }








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\begin{frame}
 \frametitle{Performance Based Earthquake Engineering}


\begin{equation}
\lambda(EDP>z) = \int \underbrace{|\frac{d\lambda(IM>x)}{dx}|}_\text{PSHA} \underbrace{G(EDP>z|IM=x)}_{\text{fragility}} dx 
\nonumber
%\label{eq:seismic_risk_analysis}
\end{equation}



\begin{itemize}


  \item  $\lambda(EDP>z) \rightarrow$ annual rate of occurrence of engineering
  demand parameter (EDP) exceeding specified value $z$


  \item EDP  hazard $\leftarrow$ convolution of probabilistic seismic
hazard  analysis  (PSHA)  and  structural  fragility for intensity
measure (IM) of ground shaking
% 

  \item PSHA $\leftarrow$  exceedance
  rate of intensity measure $\lambda(IM>x)$ considering faults and
  scenarios near site
%

  \item Structural  fragility  $G(EDP>z|IM=x)$  is the   probability of exceeding
  of EDP for ground motion with IM level $x$
%

\end{itemize}



\end{frame}
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\begin{frame}
 \frametitle{Choice of Intensity Measure}


\begin{itemize}

  \item With defined damage measure (DM) as a function of EDP(s),
  seismic risk of damage state is calculated

%

  \item The  choice  of IM is important

\item IM is a proxy of damaging ground motions 

\item All the uncertainty in ground motions is represented by the variability of
      IM
%

\vspace*{3mm}
\item[----] However!

\item Single IM or multiple IMs cannot represent all uncertainty in ground
motions


\item Vector, multiple IMs require a large number  of simulations

\item No guaranty that all uncertainties in motions are addressed



%  \item Spectral   acceleration  $Sa(T_0)$  is  commonly  adopted  as  IM  for  building
%structures.
%%
%
%  \item Many  ground  motion predictions equations (GMPEs) are developed to
%  quantify the median and aleatory variability of $Sa(T_0)$

\end{itemize}



\end{frame}
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\begin{frame}
 \frametitle{Risk Analysis for Uncertain Nonlinear ESSI Systems}


\begin{itemize}


  \item Time domain, intrusive stochastic, inelastic seismic risk analysis

  \item Time histories of uncertain motions $\rightarrow$ a random proceess, 
        developed from stochastic Fourier spectra and stochastic Fourier phase
        spectra

% 
% %\vspace*{1mm}
%   \item The inter-frequency correlation structure of Fourier amplitude spectrum is captured.
% 
% 
%   \item  The non-stationarity of ground motion is quantified by statistical phase derivative model.

  \item The random process motions characterized by Polynomial Chaos
        Karhunen-Lo{\`e}ve expansion

\item Propagation through  uncertain soil-structural system using Stochastic Elastic
      Plastic Finite Element Method (SEPFEM)

  \item Time-evolving probabilistic structural response is used for calculating
        full-spectrum seismic risk




\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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% 


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\begin{frame} 

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}



\item Incremental el--pl constitutive equation
%  
    \begin{eqnarray}
    \nonumber
  \Delta \sigma_{ij} 
  = 
%  E^{EP}_{ijkl} 
     E^{EP}_{ijkl} \; \Delta \epsilon_{kl}  
     =  
     \left[
     E^{el}_{ijkl}
       -
       \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
           {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
           \right]
    \Delta \epsilon_{kl}
    \end{eqnarray}

 
  

\vspace*{2mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
    \nonumber
\end{equation}


\vspace*{2mm}
\item Material and load parameters are uncertain



\end{itemize}



\end{frame}






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% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
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% 
% \begin{frame}
% \frametitle{Probabilistic Elastic-Plastic Modeling}
% 
% 
% % % \vspace*{-5mm}
% % \begin{center}
% % % \hspace*{-15mm}
% % \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% % {\includegraphics[width=7cm]
% % {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% % %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% % {NPP_without_Contact_vonMises.mp4}
% % \end{center}
% 
% %\vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% {\includegraphics[width=9cm]
% {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
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%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Time Domain Stochastic Galerkin Method}

\begin{itemize}
\item Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}
 \begin{itemize}
 \item[] Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
 \end{itemize}
\vspace{0.05in}
\item Output response process
 \begin{itemize}
 \item[] Multi-dimensional Hermite PC with {unknown coefficients}
 \end{itemize}
 \vspace{0.05in}
 \item Galerkin projection: minimize the error to compute unknown coefficients
 of response process, displacements
% \vspace{0.05in}
%   \item Time integration using Newmark's method
%   \begin{itemize}
%    \item[] Update coefficients following an elastic-plastic constitutive law at each time step
%   \end{itemize}
 
\end{itemize}

%\scriptsize 
%Note: PC = Polynomial Chaos

\end{frame}

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\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method}



\begin{itemize}

\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$

\vspace*{1mm} 
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$

%\item 
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item  Time domain integration  using Newmark and/or HHT, in probabilistic spaces


\end{itemize}


\begin{tiny}
\[
%$
\begin{bmatrix}
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\  \\
    \vdots & \vdots & \vdots & \vdots\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)}     & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
    \Delta u_{10} \\
    \vdots \\
    \Delta u_{N0}\\
    \vdots \\
    \Delta u_{1P_u}\\
    \vdots \\
    \Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
     \sum_{i=0}^{P_f} f_i  <\Psi_0\zeta_i> \\
    \sum_{i=0}^{P_f} f_i   <\Psi_1\zeta_i> \\
   \sum_{i=0}^{P_f} f_i    <\Psi_2\zeta_i> \\
    \vdots \\
     \sum_{i=0}^{P_f} f_i  <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}





\end{frame}






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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 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{Cyclic Inelastic Uncertain Response}


%\vspace*{-5mm}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=7cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/constitutive_relation_MC_verification.pdf}
\end{center}
\end{figure}



\end{frame}
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\begin{frame} 

\frametitle{Time History of Inelastic Uncertain Response}


%\vspace*{-5mm}
\begin{figure}[htb]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=5.9cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/mean_disp.pdf}
\includegraphics[width=5.9cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/std_disp.pdf}
\hspace*{-15mm}
\end{center}
\end{figure}



\end{frame}
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\begin{frame} 

\frametitle{Time History  of PDF of MIDR}


\noindent
Maximum Interstory Drift Ratio (MIDR)

%\vspace*{-5mm}
\begin{figure}[htb]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=5.9cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/MIDR_PDF_evolution.pdf}
\includegraphics[width=5.9cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Contour_PDF_evolution_MIDR.pdf}
\hspace*{-15mm}
\end{center}
\end{figure}



\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Select PDFs of MIDR}
% 
% 
% %\vspace*{-5mm}
% \begin{figure}[htb]
% \begin{center}
% \hspace*{-15mm}
% \includegraphics[width=5.9cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/PDF_MIDR_combine.pdf}
% \hspace*{-15mm}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% 
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\begin{frame} 

\frametitle{PDF and CDF of  MIDR}

% 
\begin{figure}[htb]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=60mm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/MIDR_distribution_different_floors.pdf}
\includegraphics[width=60mm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Risk_MIDR.pdf}
\hspace*{-15mm}
\end{center}
\end{figure}

\end{frame}
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\begin{frame} 

\frametitle{PDF and CDF of Peak Floor Acceleration}

% 
\begin{figure}[htb]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=60mm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/PFA_distribution.pdf}
\includegraphics[width=60mm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Risk_PFA.pdf}
\hspace*{-15mm}
\end{center}
\end{figure}

\end{frame}
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{MIDR: 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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Sensitivity Study}
% 
% \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}
% 
% \begin{textblock}{15}(0.3, 8.7)
% \scriptsize Source $\Delta \sigma$:
% \end{textblock}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \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}
% \end{textblock}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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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% \end{frame}
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\section{Summary}



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    \subsection{\ }





 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Real-ESSI Simulator System}
% 
% The  Real-ESSI, Realistic  
% {\underline {\bf M}}odeling  and  
% {\underline {\bf S}}imulation  of  
% {\underline {\bf E}}arthquakes,  
% {\underline {\bf S}}oils,
% {\underline {\bf S}}tructures  and  their  
% {\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
% documentation   system   for  high  fidelity,  high  performance,  time  domain,
% nonlinear/inelastic, deterministic or probabilistic, 3D, finite element modeling
% and simulation of:
% 
%     \begin{itemize}
% %\vspace*{1mm}
%       \item statics and dynamics of soil,
% \vspace*{1mm}
%       \item    statics and dynamics of rock,
% \vspace*{1mm}
%       \item    statics and dynamics of structures,
% \vspace*{1mm}
%       \item    statics of soil-structure systems, and
% \vspace*{1mm}
%       \item    dynamics of earthquake-soil-structure system interaction
%     \end{itemize}
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Real-ESSI Simulator System}
% 
%  
% \begin{itemize}
% 
% 
%   \item Real-ESSI System Components
%     \begin{itemize} 
%      \item Real-ESSI Pre-processor (gmsh/gmESSI, X2ESSI) 
%      \item Real-ESSI Program (local, remote, cloud)
%      \item Real-ESSI Post-Processor (Paraview, Python, Matlab)
% 
%     \end{itemize} 
% 
% \vspace*{1mm}
%   \item Real-ESSI System availability:                   
%     \begin{itemize}
% %\vspace*{1mm}
%      \item Educational  Institutions: Amazon Web Services (AWS), free 
%      \item Government Agencies, National Labs: AWS GovCloud
%      \item Professional  Practice: AWS, commercial
% %\vspace*{1mm}
% %%\vspace*{1mm}
% %      \item Sources available to collaborators
%     \end{itemize}
% 
% 
% 
% \vspace*{1mm}
% \item Quality Management System, ASME-NQA-1, ISO9003-2018, Certification in progress
% 
% 
% \vspace*{1mm}
%   \item Real-ESSI Short Courses (online, this Fall)
% 
% 
% 
% \vspace*{1mm}
%   \item System description and documentation at  
%     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% %
% %\url{http://real-essi.info/}
% %
% 
% 
% % \vspace*{2mm}
% %   \item
% % 
% 
% 
% \end{itemize}
% 
% 
% \end{frame}
% 




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%\subsection*{Summary}


% 
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% 
% 
% \begin{frame} 
% 
% \frametitle{Science Quotes}
% 
% \begin{itemize}
% 
% 
% \item Max  Planck: 
% "A    new    scientific  truth does not triumph by convincing  its opponents and
% making  them see the light, but rather because its opponents eventually die, and
% a  new  generation  grows  up  that  is familiar with it." (Science advances one
% funeral at a time)
% 
% 
%  \vspace*{3mm}
% 
% \item  Fran{\c c}ois-Marie Arouet,  Voltaire: 
% "Le doute n'est pas une condition agr{\'e}able, mais la certitude est absurde."
% 
%  \vspace*{3mm}
% 
% \item  Niklaus  Wirth:   
% "Software is getting slower more rapidly than hardware becomes faster."
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

\vspace*{2mm}
    \item Numerical modeling to predict and inform, rather than fit

\vspace*{4mm}
    \item Engineers need to know (probably)

\vspace*{4mm}
    \item Importance of modeling and propagating uncertainties

\vspace*{4mm}
    \item Full probabilistic modeling and simulation, full risk results


% \vspace*{4mm}
%     \item  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
%     US-BR, US-FEMA CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,

\vspace*{4mm}
    \item  {\bf \url{http://real-essi.info/}}
      
\end{itemize}

\end{frame}
%





\end{document}

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