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% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[RealESSI]
{ 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}}
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\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{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (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.
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{\small SMiRT25\\
Charlotte, NC, USA, August 2019}
\subject{}
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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/rockstructure 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 RealESSI Simulator} \hspace*{2mm}
{\bf \url{http://realessi.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/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
\hspace*{3mm}
% \hfill
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{5mm}
%\vspace*{1.8cm}
%\hspace*{3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
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\section{Uncertain Modeling}
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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>zIM=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 $G(EDP>zIM=x)$ 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 interfrequency correlation structure of Fourier amplitude spectrum is captured.
%
%
% \item The nonstationarity of ground motion is quantified by statistical phase derivative model.
\item The random process motions characterized by Polynomial Chaos
KarhunenLo{\`e}ve expansion
\item Propagation through uncertain soilstructural system using Stochastic Elastic
Plastic Finite Element Method (SEPFEM)
\item Timeevolving probabilistic structural response is used for calculating
fullspectrum 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}oisMarie Arouet, Voltaire)
\end{frame}
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\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl 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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%
% \frametitle{Probabilistic ElasticPlastic Response}
%
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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_PDFedited.pdf}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDFedited.pdf}
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% \begin{frame}
% \frametitle{Probabilistic ElasticPlastic Modeling}
%
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% % % \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]}
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\begin{frame}{Time Domain Stochastic Galerkin Method}
\begin{itemize}
\item Input random field/process{\normalsize{(nonGaussian, heterogeneous/ nonstationary)}}
\begin{itemize}
\item[] Multidimensional Hermite Polynomial Chaos (PC) with {known coefficients}
\end{itemize}
\vspace{0.05in}
\item Output response process
\begin{itemize}
\item[] Multidimensional 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 elasticplastic 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 ElasticPlastic 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}
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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}
%
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% \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 deaggregation 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}
%
%
% \end{frame}
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\section{Summary}
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\subsection{\ }
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{RealESSI Simulator System}
%
% The RealESSI, 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 soilstructure systems, and
% \vspace*{1mm}
% \item dynamics of earthquakesoilstructure system interaction
% \end{itemize}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{RealESSI Simulator System}
%
%
% \begin{itemize}
%
%
% \item RealESSI System Components
% \begin{itemize}
% \item RealESSI Preprocessor (gmsh/gmESSI, X2ESSI)
% \item RealESSI Program (local, remote, cloud)
% \item RealESSI PostProcessor (Paraview, Python, Matlab)
%
% \end{itemize}
%
% \vspace*{1mm}
% \item RealESSI 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, ASMENQA1, ISO90032018, Certification in progress
%
%
% \vspace*{1mm}
% \item RealESSI 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://realessi.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}oisMarie 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 USDOE, USNRC, USNSF,
% USBR, USFEMA CNSCCCSN, UNIAEA, and Shimizu Corp. is greatly appreciated,
\vspace*{4mm}
\item {\bf \url{http://realessi.info/}}
\end{itemize}
\end{frame}
%
\end{document}
%
%