From e95fdfcb10b21e93180a28020de5d6db70bcdeb7 Mon Sep 17 00:00:00 2001 From: wactbprot <thsteinbock@web.de> Date: Fri, 28 Feb 2014 14:48:31 +0100 Subject: [PATCH] rnm --- cal.Rtex | 2 +- figure/latex-unnamed-chunk-11.pdf | Bin 4841 -> 4872 bytes figure/latex-unnamed-chunk-13.pdf | Bin 4841 -> 4841 bytes figure/latex-unnamed-chunk-15.pdf | Bin 4860 -> 4841 bytes figure/latex-unnamed-chunk-17.pdf | Bin 4860 -> 4860 bytes figure/latex-unnamed-chunk-19.pdf | Bin 4836 -> 4860 bytes figure/latex-unnamed-chunk-21.pdf | Bin 4836 -> 4836 bytes figure/latex-unnamed-chunk-23.pdf | Bin 4858 -> 4836 bytes figure/latex-unnamed-chunk-25.pdf | Bin 4858 -> 4858 bytes figure/latex-unnamed-chunk-9.pdf | Bin 4872 -> 4872 bytes cal.tex => qse-se2-14-1.Rtex | 778 +++++++++++++++++------------- cal.pdf => qse-se2-14-1.pdf | Bin 339862 -> 409655 bytes ufprime.max | 32 ++ 13 files changed, 469 insertions(+), 343 deletions(-) rename cal.tex => qse-se2-14-1.Rtex (50%) rename cal.pdf => qse-se2-14-1.pdf (51%) 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ecmeBB>rk6u!ES13Vq|D!Jkeeh#@raaRtNxb%?GCd diff --git a/cal.tex b/qse-se2-14-1.Rtex similarity index 50% rename from cal.tex rename to qse-se2-14-1.Rtex index b53bb6d..4b50f1f 100644 --- a/cal.tex +++ b/qse-se2-14-1.Rtex @@ -5,56 +5,7 @@ ,abstracton ,titlepage ,pagesize -]{scrartcl}\usepackage[]{graphicx}\usepackage[]{color} -%% maxwidth is the original width if it is less than linewidth -%% otherwise use linewidth (to make sure the graphics do not exceed the margin) -\makeatletter -\def\maxwidth{ % - \ifdim\Gin@nat@width>\linewidth - \linewidth - \else - \Gin@nat@width - \fi -} -\makeatother - -\definecolor{fgcolor}{rgb}{0.345, 0.345, 0.345} -\newcommand{\hlnum}[1]{\textcolor[rgb]{0.686,0.059,0.569}{#1}}% -\newcommand{\hlstr}[1]{\textcolor[rgb]{0.192,0.494,0.8}{#1}}% -\newcommand{\hlcom}[1]{\textcolor[rgb]{0.678,0.584,0.686}{\textit{#1}}}% -\newcommand{\hlopt}[1]{\textcolor[rgb]{0,0,0}{#1}}% -\newcommand{\hlstd}[1]{\textcolor[rgb]{0.345,0.345,0.345}{#1}}% -\newcommand{\hlkwa}[1]{\textcolor[rgb]{0.161,0.373,0.58}{\textbf{#1}}}% -\newcommand{\hlkwb}[1]{\textcolor[rgb]{0.69,0.353,0.396}{#1}}% -\newcommand{\hlkwc}[1]{\textcolor[rgb]{0.333,0.667,0.333}{#1}}% -\newcommand{\hlkwd}[1]{\textcolor[rgb]{0.737,0.353,0.396}{\textbf{#1}}}% - -\usepackage{framed} -\makeatletter -\newenvironment{kframe}{% - \def\at@end@of@kframe{}% - \ifinner\ifhmode% - \def\at@end@of@kframe{\end{minipage}}% - \begin{minipage}{\columnwidth}% - \fi\fi% - \def\FrameCommand##1{\hskip\@totalleftmargin \hskip-\fboxsep - \colorbox{shadecolor}{##1}\hskip-\fboxsep - % There is no \\@totalrightmargin, so: - \hskip-\linewidth \hskip-\@totalleftmargin \hskip\columnwidth}% - \MakeFramed {\advance\hsize-\width - \@totalleftmargin\z@ \linewidth\hsize - \@setminipage}}% - {\par\unskip\endMakeFramed% - \at@end@of@kframe} -\makeatother - -\definecolor{shadecolor}{rgb}{.97, .97, .97} -\definecolor{messagecolor}{rgb}{0, 0, 0} -\definecolor{warningcolor}{rgb}{1, 0, 1} -\definecolor{errorcolor}{rgb}{1, 0, 0} -\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX - -\usepackage{alltt} +]{scrartcl} \usepackage{Sweavel} \usepackage{graphicx} @@ -69,6 +20,7 @@ \usepackage{longtable} \usepackage{hyperref} \usepackage{url} +\usepackage{shortvrb} \usepackage{tikz,pgflibraryarrows,pgflibraryshapes,pgflibrarysnakes} \setlength\unitlength{0.01\textwidth} @@ -129,6 +81,8 @@ } \makeatother +\MakeShortVerb{\|} + \usepackage{listings} \lstset{% basicstyle=\ttfamily\small, @@ -165,23 +119,28 @@ \publishers{ \begin{quote} \normalsize - Im den vergangenen Monaten fiel eine Abweichung von ca. 0,2\% zwischen den - Expansionen mit der Bezeichnung D und C auf. Dies soll mit den hier + Im den vergangenen Monaten fiel eine Abweichung von $\approx 0,2$\,\% zwischen den + Expansionen mit der Bezeichnung C und B auf. Dies soll mit den hier dargestellten Messungen untersucht werden. Durch einen erhöhten Aufwand bei der Bestimmung der Gastemperatur soll die Unsicherheit der - Expansionsverhältnisse gegenüber den bisherigen Werten veringert werden. + Expansionsverhältnisse gegenüber den bisherigen Werten verringert werden. \end{quote} } \pagestyle{headings} -\IfFileExists{upquote.sty}{\usepackage{upquote}}{} \begin{document} \maketitle \tableofcontents - - +%% begin.rcode setup, include=FALSE +% opts_chunk$set(fig.width=6, fig.height=4,fig.path='figure/latex-', +% cache.path='cache/latex-', +% tidy.opts=list(keep.blank.line=FALSE, width.cutoff=60) ) +% options(digits=7) +% options(replace.assign = TRUE) +% #render_listings() +%% end.rcode \section{Vorab} \label{sec:vorab} @@ -193,20 +152,19 @@ Erfahrung zurückgegriffen werden. Das hier angewandte Modell wurde in Bei den vorliegenden Messungen wurde ein erhöhter Aufwand bei der Bestimmung der Gastemperatur betrieben. -Die im Dokument sichtbaren Quelltextausschnitte werden zur +Die im Dokument sichtbaren Quelltextausschnitte werden zum Übersetzungszeitpunkt (compile time) dieses -Dokumentes ausgeführt und erzeugen die Ergebnisse. Die Messdaten werden -mittels \emph{R4CouchDB} aus der Labordatenbank bezogen. +Dokumentes ausgeführt und erzeugen so die Ergebnisse. Die Messdaten werden +mittels |R4CouchDB|\footnote{\url{https://github.com/wactbprot/R4CouchDB}, + \url{http://cran.r-project.org/web/packages/R4CouchDB/index.html}} direkt +aus der Labordatenbank +|vaclab_db|\footnote{\url{http://a73434.berlin.ptb.de:5984/_utils/database.html?vaclab_db}} +bezogen. %% a chunk with default options -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{library}\hlstd{(R4CouchDB)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% library(R4CouchDB) +%% end.rcode \section{Rechnung} \subsection{Modell} @@ -220,7 +178,7 @@ Wie in den unter \ref{sec:vorab} erwähnten Dokumenten wird zum Zeitpunkt des Druckgleichgewichts angenommen. Hier bezeichnet $p_{FRS}$ den mit der FRS gemessenen Druck, $p_{ND}$ den Druck -am Nullindikator und $p_{SE2}$ den in SE2 generieren Druck. Es ist: +am Nullindikator (ND) und $p_{SE2}$ den in SE2 generieren Druck. Es ist: \begin{equation} \label{eq:pse2} @@ -230,6 +188,7 @@ am Nullindikator und $p_{SE2}$ den in SE2 generieren Druck. Es ist: wobei $p_{fill}$ den Fülldruck, $f_i$ das Expansionsverhältnis, $K_{RG}$ die Realgaskorrektur und $T_{before}$ und $T_{after}$ die Temperatur vor und nach der Expansion bezeichnet. + Das Expansionsverhältnis: \begin{equation} @@ -245,50 +204,38 @@ beinhaltet noch das Zusatzvolumen. Dies kann über: \end{equation} herausgerechnet werden. In den Datenbankdokumenten sind die so berechneten -$f_i$ unter dem Pfad: -\begin{verbatim} -doc$Calibration$Analysis$Values$Expansion -\end{verbatim} -gespeichert. Der Typ -\begin{verbatim} -f_pure -\end{verbatim} -entspricht $f_i$ -\begin{verbatim} -f\_prime -\end{verbatim} -ist $f_i'$. +$f_i$ unter dem Pfad |doc$Calibration$Analysis$Values$Expansion| gespeichert. Der Typ +|f_pure| entspricht $f_i$ |f_prime| ist $f_i'$. \subsection{Systematische Unsicherheit} \label{ssec:sysUns} -Die Unsicherheit der Expansionsverhältnisse wird bir auf $u(T)$ wie in +Die Unsicherheit der Expansionsverhältnisse wird bis auf $u(T)$ und $u(p_{ND})$ wie in \emph{QSE-SE2-09-1} berechnet. Die Unsicherheit der Temperatur wird durch die größere Anzahl der Temperatursensoren in zweifacher Weise beeinflußt: \begin{itemize} -\item Die in \emph{QSE-SE2-05-1} mit $u_2^m = 0.3$\,K (Gleichung 13) +\item Die in \emph{QSE-SE2-05-1} mit $u_2^m = 0,3$\,K (Gleichung 13) abgeschätzten nichterfassbaren Wärmequellen können durch die 6 zusätzlichen - Sensoren auf $0.1$\,K reduziert werden. -\item Die in \emph{QSE-SE2-05-1} mit $u_0 = 0.05$\,K angegebene Unsicherheit - durch Temperaturgradienten an den Ausgangsvolumen kann durch die 4 - zusätzlichen Sensoren ebenfalls veringert werden $u_0 = 0.03$\,K. + Sensoren auf $0,1$\,K reduziert werden. +\item Die in \emph{QSE-SE2-05-1} mit $u_0 = 0,05$\,K (Gleichung 19) angegebene + Unsicherheit durch Temperaturgradienten an den Ausgangsvolumen kann durch + die 4 zusätzlichen Sensoren ebenfalls veringert werden $u_0 = 0.03$\,K. \end{itemize} Da bei der vorliegenden Messung ein anderes CDG als Nullindikator als in \emph{QSE-SE2-09-1} benutzt wurde, wird $u(p_{ND})$ neu aufgestellt. Als obere Abschätzung soll hier ein Vergleichsdruck von $1$\,mbar als Bezugsgröße dienen. -\begin{itemize} - -\item Die Nullpunktsstabilität $u_1(p_{ND})$ wird mit $0,1$\,mV abgeschätzt. Durch -die Verwendung der X.01-Range ergibt sich ein Umrechnungsfaktor von -$1,33/10$\,mbar/V so dass dies mit $u_1(p_{ND}) = 1,3\cdot10^{-5}$ zu einem -Vergleichsdruck von $1$\,mbar beiträgt. +\begin{itemize} +\item Die Nullpunktsstabilität während eines Messpunkts $u_1(p_{ND})$ wird mit + $0,1$\,mV abgeschätzt. Durch die Verwendung der X.1-Rangeeinstellung ergibt + sich ein Umrechnungsfaktor von $\approx 1,33/10$\,mbar/V so dass dies mit + $u_1(p_{ND}) = 1,3\cdot10^{-5}$ zu einem Vergleichsdruck von $1$\,mbar beiträgt. \item Die Unsicherheit durch Digitalisierung ergibt sich zu $0,29 \cdot -1,0\cdot10^{-5} \cdot 1,3/10$\,mbar. Bezogen auf einen Vergleichsdruck von +0,00001 \cdot 1,3/10$\,mbar. Bezogen auf einen Vergleichsdruck von $1$\,mbar sind das relative $u_2(p_{ND}) = 3,8\cdot10^{-7}$ \item Bei einer Temperaturabhängigkeit von typisch $5\cdot10^{-5}$\,1/K kann dieser @@ -297,51 +244,73 @@ nur um ca. $0,5$\,K anwächst $u_3(p_{ND}) = 0$. \item Die Unsymmetrie links und rechts von $p_{ND} = 0$\,mbar beträgt sicher nicht mehr als $u_4(p_{ND}) = 1\cdot10^{-5}$ da sonst eine Abhängigkeit -$f_i(p_{ND})$ zu erkennen wäre. +$f_i(p_{ND})$ zu erkennen wäre. Dies wurde kontrolliert. \item Die Nichtlinearität der Anzeige von $p_{ND}$ wird mit $u_5(p_{ND}) = -1\cdot10^{-5}$ abgeschätzt. + 1\cdot10^{-5}$ abgeschätzt. \end{itemize} Das Skript zur Berechnung der Unsichertheit ist in Anhang -\ref{ssec:unsicherheit} dargestellt. Es ergibt sich für die Expansionen $f_1$, -$f_3$ und $f_5$ eine relative Unsicherheit von +\ref{ssec:unsicherheitfip} dargestellt. Es ergibt sich für die Expansionen $f'_1$, +$f'_3$ und $f'_5$ eine relative systematische Unsicherheit von \begin{equation} - \label{eq:uf135} - u_{sys}(f_{1,3,5}) = 2.9\cdot 10^{-4} + \label{eq:ufp135} + u_{sys}(f'_{1,3,5}) = 2.9\cdot 10^{-4} \end{equation} -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{u.sys.f135} \hlkwb{<-} \hlnum{0.00029} -\end{alltt} -\end{kframe} -\end{knitrout} +für die Expansionen $f'_2$ und $f'_4$ erhält man +\begin{equation} + \label{eq:ufp24} + u_{sys}(f'_{2,4}) = 3.6\cdot 10^{-4} +\end{equation} +Einen weiteren Unsicherheitsbeitrag liefetr die Umrechnung von $f'_i$ in +$f_i$. Im Anhang unter Abschnitt \ref{ssec:unsicherheitfi} ist diese Rechnung +dargestellt. Für |ufp| können die ermittelten, jedoch hier absoluten +Unsicherheiten eingesetzt werden (es wird $f_{1,3,5} \approx 9,2\cdot10^{-3}$ +und $f_{2,4} \approx 7,4\cdot10^{-4}$ angenommen): -für die Expansionen $f_2$ und $f_4$ erhält man +%[1346.8*(1.0*ufp^2+5.7E-16)^0.5, +% 108.3*(1.0*ufp^2+9.4E-14)^0.5] \begin{equation} \label{eq:uf135} - u_{sys}(f_{2,4}) = 3.6\cdot 10^{-4} + u_{sys}(f_{1,3,5}) = 108,3 \sqrt{(3,6\cdot 10^{-4} \cdot 9,2\cdot10^{-3})^2 + 9,4\cdot10^{-14}} \end{equation} +%% begin.rcode +% u.sys.f135 <- 108.3 * sqrt((3.6e-4 * 9.2e-3)^2 + 9.4e-14) +% u.sys.f135 +%% end.rcode + +für die Expansionen $f'_2$ und $f'_4$ erhält man +\begin{equation} + \label{eq:uf24} + u_{sys}(f'_{2,4}) = 1346,8 \sqrt{(2.9\cdot 10^{-4} \cdot 7,4\cdot10^{-4})^2 + 5.7\cdot10^{-16}} +\end{equation} +%% begin.rcode +% u.sys.f24 <- 1346.8 * sqrt((2.9e-4 * 7.4e-4)^2 + 5.7E-16) +% u.sys.f24 +%% end.rcode + +Die eigentlichen Unsicherheitsbeiträge durch die Zusatzvolumina sind also nur: +%% begin.rcode +% sqrt( 9.4e-14) +%% end.rcode +bzw. +%% begin.rcode +% sqrt( 5.7E-16) +%% end.rcode + + -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{u.sys.f24} \hlkwb{<-} \hlnum{0.00036} -\end{alltt} -\end{kframe} -\end{knitrout} \section{Messung} \subsection{Messmittel} Die benutzten Messmittel sind in Tabelle \ref{tab:messmittel} -zusammengefasst. Über die Datenbank-Id (DB-Id) können weitere Einzelheiten +zusammengefasst. Über die Datenbank-Id (Spalte DB-Id) können weitere Einzelheiten zu den Geräten erfragt werden. \begin{table} @@ -377,7 +346,7 @@ zu den Geräten erfragt werden. \end{tabular} \end{table} -\subsection{Messablauf und Messaufbau } +\subsection{ Messaufbau und Messablauf } \begin{figure} \centering @@ -431,39 +400,61 @@ verweist auf Temperatursensor an Kannal 101) wurden wie folgt verteilt: \subsubsection{Nullindikator} -Für den Nullindikator wurden folgende Einstallungen gewählt: +Für den Nullindikator wurden folgende Einstellungen gewählt: \begin{itemize} -\item Refseite war an $V_6$ bzw $V_4$ angeschlossen -\item Druckseite an FRS -\item X0.1 Range -\item Unit mbar -\item Heater off +\item Referenzseite war an $V_6$ bzw. an $V_4$ angeschlossen +\item Druckseite war stets mit der FRS verbunden +\item es wurde grundsätzlich mit der Rangeeinstellung X.1 gemessen +\item das Steuergerät war auf die Einheit mbar gestellt +\item die Heizung des CDG-Kopfes war aus \end{itemize} -Der Unsicherheitsbeitrag des Nullindikators wird wie im Folgenden -dargestellt. -\section{Ergebnisse} +Der Unsicherheitsbeitrag des Nullindikators wurde unter Abschnitt +\ref{ssec:sysUns} besprochen. + +\subsubsection{Zusatzvolumen} -Die Daten werden wie erwähnt über den bereits im Abschnitt \ref{sec:vorab} -geladenen Treiber bezogen: +Das Zusatzvolumen bestand bei den Messungen zu $f_1$, $f_2$ und $f_5$ aus der +Umwegleitung $V_{UL}$ und dem Volumen des Nullindikators $V_{ND}$. Bei den Messungen zu $f_3$ +und $f_4$ war der ND direkt mit dem unteren Kessel $V_4$ verbunden. Als Wert +$V_{UL}$ wurde der in \emph{QSE-SE2-09-1} bestimmte Wert benuzt +$327.3$\,cm$^3$\footnote{Der in Wert \emph{QSE-SE2-09-1} aufgeführte Wert ist +bezüglich SRG-Messung (Viskosität) unkorrigiert}. +Das Volumen des ND wurde vor den Messreihen zu $f_i$ in üblicher Weise +ermittelt: $V_{ND} = 142.9$\,cm$^3$. -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb} \hlkwb{<-} \hlkwd{cdbIni}\hlstd{()} -\hlstd{cdb}\hlopt{$}\hlstd{DBName} \hlkwb{<-} \hlstr{"vaclab_db"} -\end{alltt} -\end{kframe} -\end{knitrout} +\section{Ergebnisse} + +Die Daten werden über den bereits im Abschnitt \ref{sec:vorab} +geladenen Treiber (\emph{R4CouchDB} bezogen. +%% begin.rcode +% cdb <- cdbIni() +% cdb$DBName <- "vaclab_db" +%% end.rcode Im Abschnitt zum Expansionsverhältniss $f_1$ sind die Quelltexte eingeblendet; es lassen sich daraus die Bedeutung der Spalten der Ergebnisstabellen ablesen. - - +%% begin.rcode include=FALSE +% +% ## ---------------- +% setwd("/home/bock04/eig/r4vl/devel/") +% srcPath <- "../utils/" +% fn <- list.files(srcPath, pattern=".R$") +% for (k in 1:length(fn)) source(paste(srcPath,fn[k],sep="")) +% +% srcPath <- "../cal/" +% fn <- list.files(srcPath, pattern=".R$") +% for (k in 1:length(fn)) source(paste(srcPath,fn[k],sep="")) +% +% srcPath <- "../uncert/" +% fn <- list.files(srcPath, pattern=".R$") +% for (k in 1:length(fn)) source(paste(srcPath,fn[k],sep="")) +% ## ---------------- +%% end.rcode \subsection{Expansionsverhältnis $f_1$} \label{ssec:exf1} @@ -472,236 +463,297 @@ Das Expansionsverhältniss $f_1$ wurde am 12. und 13. Februar vermessen. Es existieren zwei Kalibrierdokumente: -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f03ed200"} \hlcom{# 12.2.14} -\hlstd{doc.1} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f.1} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc.1}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f05355c2"} \hlcom{# 13.2.14} -\hlstd{doc.2} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f.2} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc.2}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\hlstd{f} \hlkwb{<-} \hlkwd{c}\hlstd{(f.1, f.2)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% cdb$id <- "7f696c493207f8d813f3b4e1f03ed200" # 12.2.14 +% doc.1 <- cdbGetDoc(cdb)$res +% f.1 <- getConstVal(doc.1$Calibration$Analysis$Values, "f_pure") +% +% cdb$id <- "7f696c493207f8d813f3b4e1f05355c2" # 13.2.14 +% doc.2 <- cdbGetDoc(cdb)$res +% f.2 <- getConstVal(doc.2$Calibration$Analysis$Values, "f_pure") +% +% f <- c(f.1,f.2) +%% end.rcode Vor der Berechnung des Mittelwerts und der Standardabweichung wird der größte und der kleinste Wert sowie eventuelle Fehlmessungen verworfen. -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} - \hlstd{mi} \hlkwb{<-} \hlkwd{which.min}\hlstd{(f)} - \hlstd{ma} \hlkwb{<-} \hlkwd{which.max}\hlstd{(f)} - \hlstd{rn} \hlkwb{<-} \hlkwd{which}\hlstd{(}\hlkwd{is.na}\hlstd{(f))} - \hlstd{f} \hlkwb{<-} \hlstd{f[}\hlopt{-}\hlkwd{c}\hlstd{(mi,ma,rn)]} - \hlstd{N} \hlkwb{<-} \hlkwd{length}\hlstd{(f)} - \hlstd{mv} \hlkwb{<-} \hlkwd{mean}\hlstd{(f)} - \hlstd{sd.s} \hlkwb{<-} \hlkwd{sd}\hlstd{(f)} - \hlstd{sd.rel} \hlkwb{<-} \hlkwd{sd}\hlstd{(f)}\hlopt{/}\hlkwd{sqrt}\hlstd{(N)}\hlopt{/}\hlstd{mv} - \hlstd{f.old} \hlkwb{<-} \hlnum{9.185402e-3} - \hlstd{u.f} \hlkwb{<-} \hlstd{u.sys.f135} - \hlstd{d.hist} \hlkwb{<-} \hlstd{mv}\hlopt{/}\hlstd{f.old} \hlopt{-} \hlnum{1} - - \hlstd{f1} \hlkwb{<-} \hlstd{mv} - - \hlstd{dafr} \hlkwb{<-} \hlkwd{data.frame}\hlstd{(} - \hlkwc{mv} \hlstd{= mv,} \hlcom{# Mittelwert} - \hlkwc{u.f} \hlstd{= u.f,} \hlcom{# systematische Unsicherheit } - \hlkwc{N} \hlstd{= N,} \hlcom{# Anzahl der Messpunkte} - \hlkwc{sd.s} \hlstd{= sd.s,} \hlcom{# Standardabw. der Einzelwerte} - \hlkwc{sd.rel} \hlstd{= sd.rel ,} \hlcom{# rel. Standardabw. des Mittelwerts} - \hlkwc{d.hist} \hlstd{= d.hist,} \hlcom{# Differenz zum alten Wert} - \hlkwc{u.ges} \hlstd{= sd.rel} \hlopt{+} \hlstd{u.f)} \hlcom{# Gesamtunsicherheit} - \hlstd{uf1} \hlkwb{<-} \hlstd{sd.rel} \hlopt{+} \hlstd{u.f} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% mi <- which.min(f) +% ma <- which.max(f) +% rn <- which(is.na(f)) +% f <- f[-c(mi,ma,rn)] +% N <- length(f) # Anzahl der Messpunkte +% mv <- mean(f) # Mittelwert +% sd.s <- sd(f) # Standardabw. der Einzelwerte +% sd.rel <- sd(f)/sqrt(N)/mv # rel. Standardabw. des Mittelwerts +% f.old <- 9.185402e-3 # +% u.f <- u.sys.f135 # systematische Unsicherheit +% d.hist <- mv/f.old - 1 # Differenz zum alten Wert +% uf1 <- sd.rel + u.f # Gesamtunsicherheit +% +% dafr <- data.frame( +% mv = mv, +% u.f = u.f, +% N = N, +% sd.s = sd.s, +% sd.rel = sd.rel , +% d.hist = d.hist, +% u.ges = uf1) +% f1 <- mv +% +%% end.rcode In folgender Tabelle und in folgendem Diagramm werden die Ergebnisse der Messung zusammengefasst. Die im Abschnitt \ref{ssec:sysUns} abgeleitete systematische Unsicherheit wird benutzt, um zusammen mit der Standardabweichung des Mittelwerts die Gesamtunsicherheit zu berechnen. -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## | mv| u.f| N| sd.s| sd.rel| d.hist| u.ges| -## |-----------:|--------:|---:|--------:|----------:|----------:|-----------:| -## | 0.00918083| 0.00029| 17| 8.6e-07| 2.264e-05| -0.000498| 0.00031264| -\end{verbatim} -\end{kframe} -\end{knitrout} - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor} -\includegraphics[width=\maxwidth]{figure/latex-unnamed-chunk-9} - -\end{knitrout} - +%% begin.rcode echo=FALSE +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +%% begin.rcode echo=FALSE +% plot(f, +% main=expression(f[1]), +% sub="Spannweite der y-Achse: 0.05%", +% xlab="Messpunkt", +% ylab="", +% pch=15, +% ylim=c(mv*(1 - 2.5e-4),mv*(1 + 2.5e-4))) +% abline(h=mv, col="green") +% abline(h=mv + sd.s, col="red") +% abline(h=mv - sd.s, col="red") +% grid(col=1) +% text(5,mv, paste("f =", round(mv, 8))) +%% end.rcode \subsection{Expansionsverhältnis $f_2$} Das Expansionsverhältniss $f_2$ wurde am 13. und 14. Februar vermessen. -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f06073a7"} \hlcom{# 13. & 14. 2.14} -\hlstd{doc} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% cdb$id <- "7f696c493207f8d813f3b4e1f06073a7" # 13. & 14. 2.14 +% doc <- cdbGetDoc(cdb)$res +% f <- getConstVal(doc$Calibration$Analysis$Values, "f_pure") +%% end.rcode Folgende Tabelle und folgendes Diagramm wurden analog Abschnitt \ref{ssec:exf1} erstellt. - - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## | mv| u.f| N| sd.s| sd.rel| d.hist| u.ges| -## |-----------:|--------:|---:|--------:|----------:|------------:|-----------:| -## | 0.00074455| 0.00036| 16| 1.1e-07| 3.698e-05| -0.00057984| 0.00039698| -\end{verbatim} -\end{kframe} -\end{knitrout} - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor} -\includegraphics[width=\maxwidth]{figure/latex-unnamed-chunk-13} - -\end{knitrout} - +%% begin.rcode echo=FALSE +% mi <- which.min(f) +% ma <- which.max(f) +% rn <- which(is.na(f)) +% f <- f[-c(mi,ma,rn)] +% N <- length(f) +% mv <- mean(f) +% sd.s <- sd(f) +% sd.rel <- sd(f)/sqrt(N)/mv +% f.old <- 7.449848e-4 +% u.f <- u.sys.f24 +% d.hist <- mv/f.old - 1 +% f2 <- mv +% dafr <- data.frame( +% mv = mv, # Mittelwert +% u.f = u.f, # systematische Unsicherheit +% N = N, # Anzahl der Messpunkte +% sd.s = sd.s, # Standardabw. der Einzelwerte +% sd.rel = sd.rel , # Standardabw. des Mittelwerts +% d.hist = d.hist, # Differenz zum alten Wert +% u.ges = sd.rel + u.f) # Gesamtunsicherheit +% uf2 <- sd.rel + u.f +%% end.rcode + +%% begin.rcode echo=FALSE +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +%% begin.rcode echo=FALSE +% plot(f, +% main=expression(f[2]), +% sub="Spannweite der y-Achse: 0.05%", +% xlab="Messpunkt", +% ylab="", +% pch=15, +% ylim=c(mv*(1 - 2.5e-4),mv*(1 + 2.5e-4))) +% abline(h=mv, col="green") +% abline(h=mv + sd.s, col="red") +% abline(h=mv - sd.s, col="red") +% grid(col=1) +% text(5,mv, paste("f =", round(mv, 8))) +%% end.rcode \subsection{Expansionsverhältnis $f_3$} Das Expansionsverhältniss $f_3$ wurde am 20. Februar vermessen: %% a chunk with default options -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f0bd4231"} \hlcom{# 20. 2.14} -\hlstd{doc} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% cdb$id <- "7f696c493207f8d813f3b4e1f0bd4231" # 20. 2.14 +% doc <- cdbGetDoc(cdb)$res +% f <- getConstVal(doc$Calibration$Analysis$Values, "f_pure") +%% end.rcode Folgende Tabelle und folgendes Diagramm wurden analog Abschnitt \ref{ssec:exf1} erstellt. - - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## | mv| u.f| N| sd.s| sd.rel| d.hist| u.ges| -## |-----------:|--------:|---:|--------:|----------:|------------:|-----------:| -## | 0.00919325| 0.00029| 16| 4.3e-07| 1.169e-05| -0.00045669| 0.00030169| -\end{verbatim} -\end{kframe} -\end{knitrout} - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor} -\includegraphics[width=\maxwidth]{figure/latex-unnamed-chunk-17} - -\end{knitrout} - +%% begin.rcode echo=FALSE +% mi <- which.min(f) +% ma <- which.max(f) +% rn <- which(is.na(f)) +% f <- f[-c(mi,ma,rn)] +% N <- length(f) +% mv <- mean(f) +% sd.s <- sd(f) +% sd.rel <- sd(f)/sqrt(N)/mv +% f.old <- 9.19745e-3 +% u.f <- u.sys.f135 +% d.hist <- mv/f.old - 1 +% f3 <- mv +% dafr <- data.frame( +% mv = mv, # Mittelwert +% u.f = u.f, # systematische Unsicherheit +% N = N, # Anzahl der Messpunkte +% sd.s = sd.s, # Standardabw. der Einzelwerte +% sd.rel = sd.rel , # Standardabw. des Mittelwerts +% d.hist = d.hist, # Differenz zum alten Wert +% u.ges = sd.rel + u.f) # Gesamtunsicherheit +% uf3 <- sd.rel + u.f +%% end.rcode + +%% begin.rcode echo=FALSE +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +%% begin.rcode echo=FALSE +% plot(f, +% main=expression(f[3]), +% sub="Spannweite der y-Achse: 0.05%", +% xlab="Messpunkt", +% ylab="", +% pch=15, +% ylim=c(mv*(1 - 2.5e-4),mv*(1 + 2.5e-4))) +% abline(h=mv, col="green") +% abline(h=mv + sd.s, col="red") +% abline(h=mv - sd.s, col="red") +% grid(col=1) +% text(5,mv, paste("f =", round(mv, 8))) +%% end.rcode \subsection{Expansionsverhältnis $f_4$} Das Expansionsverhältniss $f_4$ wurde am 19. Februar vermessen: %% a chunk with default options -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f09daa33"} \hlcom{# 19. 2.14} -\hlstd{doc} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% cdb$id <- "7f696c493207f8d813f3b4e1f09daa33" # 19. 2.14 +% doc <- cdbGetDoc(cdb)$res +% f <- getConstVal(doc$Calibration$Analysis$Values, "f_pure") +%% end.rcode Folgende Tabelle und folgendes Diagramm wurden analog Abschnitt \ref{ssec:exf1} erstellt. - - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## | mv| u.f| N| sd.s| sd.rel| d.hist| u.ges| -## |-----------:|--------:|---:|------:|----------:|------------:|-----------:| -## | 0.00074564| 0.00036| 16| 8e-08| 2.725e-05| -0.00045621| 0.00038725| -\end{verbatim} -\end{kframe} -\end{knitrout} - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor} -\includegraphics[width=\maxwidth]{figure/latex-unnamed-chunk-21} - -\end{knitrout} - +%% begin.rcode echo=FALSE +% mi <- which.min(f) +% ma <- which.max(f) +% rn <- which(is.na(f)) +% f <- f[-c(mi,ma,rn)] +% N <- length(f) +% mv <- mean(f) +% sd.s <- sd(f) +% sd.rel <- sd(f)/sqrt(N)/mv +% f.old <- 7.459778e-4 +% u.f <- u.sys.f24 +% d.hist <- mv/f.old - 1 +% f4 <- mv +% dafr <- data.frame( +% mv = mv, # Mittelwert +% u.f = u.f, # systematische Unsicherheit +% N = N, # Anzahl der Messpunkte +% sd.s = sd.s, # Standardabw. der Einzelwerte +% sd.rel = sd.rel , # Standardabw. des Mittelwerts +% d.hist = d.hist, # Differenz zum alten Wert +% u.ges = sd.rel + u.f) # Gesamtunsicherheit +% uf4 <- sd.rel + u.f +%% end.rcode + +%% begin.rcode echo=FALSE +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +%% begin.rcode echo=FALSE +% plot(f, +% main=expression(f[4]), +% sub="Spannweite der y-Achse: 0.05%", +% xlab="Messpunkt", +% ylab="", +% pch=15, +% ylim=c(mv*(1 - 2.5e-4),mv*(1 + 2.5e-4))) +% abline(h=mv, col="green") +% abline(h=mv + sd.s, col="red") +% abline(h=mv - sd.s, col="red") +% grid(col=1) +% text(5,mv, paste("f =", round(mv, 8))) +%% end.rcode \subsection{Expansionsverhältnis $f_5$} Das Expansionsverhältniss $f_5$ wurde am 18. Februar vermessen: %% a chunk with default options -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{cdb}\hlopt{$}\hlstd{id} \hlkwb{<-} \hlstr{"7f696c493207f8d813f3b4e1f07ed445"} \hlcom{# 18.2.14} -\hlstd{doc} \hlkwb{<-} \hlkwd{cdbGetDoc}\hlstd{(cdb)}\hlopt{$}\hlstd{res} -\hlstd{f} \hlkwb{<-} \hlkwd{getConstVal}\hlstd{(doc}\hlopt{$}\hlstd{Calibration}\hlopt{$}\hlstd{Analysis}\hlopt{$}\hlstd{Values,} \hlstr{"f_pure"}\hlstd{)} -\end{alltt} -\end{kframe} -\end{knitrout} - +%% begin.rcode +% cdb$id <- "7f696c493207f8d813f3b4e1f07ed445" # 18.2.14 +% doc <- cdbGetDoc(cdb)$res +% f <- getConstVal(doc$Calibration$Analysis$Values, "f_pure") +%% end.rcode Folgende Tabelle und folgendes Diagramm wurden analog Abschnitt \ref{ssec:exf1} erstellt. - - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## | mv| u.f| N| sd.s| sd.rel| d.hist| u.ges| -## |-----------:|--------:|---:|--------:|---------:|------------:|----------:| -## | 0.00917322| 0.00029| 16| 5.4e-07| 1.46e-05| -0.00037079| 0.0003046| -\end{verbatim} -\end{kframe} -\end{knitrout} - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor} -\includegraphics[width=\maxwidth]{figure/latex-unnamed-chunk-25} - -\end{knitrout} - +%% begin.rcode echo=FALSE +% mi <- which.min(f) +% ma <- which.max(f) +% rn <- which(is.na(f)) +% f <- f[-c(mi,ma,rn)] +% N <- length(f) +% mv <- mean(f) +% sd.s <- sd(f) +% sd.rel <- sd(f)/sqrt(N)/mv +% f.old <- 9.176625e-3 +% u.f <- u.sys.f135 +% d.hist <- mv/f.old - 1 +% f5 <- mv +% dafr <- data.frame( +% mv = mv, # Mittelwert +% u.f = u.f, # systematische Unsicherheit +% N = N, # Anzahl der Messpunkte +% sd.s = sd.s, # Standardabw. der Einzelwerte +% sd.rel = sd.rel, # rel. Standardabw. des Mittelwerts +% d.hist = d.hist, # Differenz zum alten Wert +% u.ges = sd.rel + u.f) # Gesamtunsicherheit +% uf5 <- sd.rel + u.f +%% end.rcode + +%% begin.rcode echo=FALSE +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +%% begin.rcode echo=FALSE +% plot(f, +% main=expression(f[5]), +% sub="Spannweite der y-Achse: 0.05%", +% xlab="Messpunkt", +% ylab="", +% pch=15, +% ylim=c(mv*(1 - 2.5e-4),mv*(1 + 2.5e-4))) +% abline(h=mv, col="green") +% abline(h=mv + sd.s, col="red") +% abline(h=mv - sd.s, col="red") +% grid(col=1) +% text(5,mv, paste("f =", round(mv, 8))) +%% end.rcode \section{Zusammenfassung} @@ -711,39 +763,43 @@ Einzelmessungen neu bestimmt. Durch eine verbesserte Temperaturmessung konnten die Unsicherheit der $f_i$ um ca. 30\% (verglichen mit den 2009 bestimmten Werten) verringert werden. -Bei den Messungen zeigte sich, dass sich eine Isolierung der Anfangsvolumina -eher negativ auf die Wiederholbarkeit einer Messung auswirkt. Ein Abdecken der -Sensoren der Startvolumen vor allem aber auch der Kesselsensoren mit Al-Folie -scheint von Vorteil. Die sollte über einen längeren Zeitraum (im täglichen -Kalibrierbetrieb) verfolgt werden. +Bei den Messungen deutete sich an, dass sich eine sterke Temperaturisolierung +der Anfangsvolumina eher negativ auf die Wiederholbarkeit einer Messung +auswirkt. Ein Abdecken der Sensoren der Startvolumen vor allem aber auch der +Kesselsensoren mit Al-Folie scheint von Vorteil. Die sollte über einen +längeren Zeitraum (im täglichen Kalibrierbetrieb) verfolgt werden. Hinsichtlich der Expansionen A,B,C und D ergeben sich folgende Werte: -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{verbatim} -## |Exp.Name | Exp.Wert| Exp.Uns| Delta.rel| -## |:---------|-------------:|-------------:|--------------:| -## |A | 9.180828e-03| 0.0003126422| -0.0004979961| -## |B | 7.445528e-04| 0.0003969772| -0.0005798440| -## |C | 8.433172e-05| 0.0004287135| -0.0008273124| -## |D | 6.839898e-06| 0.0004926917| -0.0008268368| -\end{verbatim} -\end{kframe} -\end{knitrout} - +%% begin.rcode echo=FALSE +% f1.o <- 9.185402e-3 +% f2.o <- 7.449848e-4 +% f3.o <- 9.19745e-3 +% f4.o <- 7.459778e-4 +% f5.o <- 9.176625e-3 +% dafr <- data.frame( +% Exp.Name=c("A", "B", "C", "D"), +% Exp.Wert=c(f1,f2,f3*f5,f4*f5), +% Exp.Uns=c(uf1,uf2,sqrt(uf3^2 + uf5^2),sqrt(uf4^2 + uf5^2)), +% Delta.rel = c(f1,f2,f3*f5,f4*f5)/c(f1.o,f2.o,f3.o*f5.o,f4.o*f5.o) -1 +% ) +% kable(dafr,format = "markdown", digits = 8) +%% end.rcode + +Die in beobachteten $0,2$\,\% stammen demnach nicht von veränderten +Expansionsverhältnissen. \section{Anhang} -\subsection{Berechnung der Unsicherheit} -\label{ssec:unsicherheit} +\subsection{Berechnung der Unsicherheit von $f_i'$} +\label{ssec:unsicherheitfip} \begin{lstlisting} /* --*-- maxima --*-- Bestimmung der systematischen Unsicherheit -der Expansionsverh. +der Expansionsverh. f_i' QSE-SE2-14-1 @@ -776,7 +832,7 @@ up0: p0 * 0.000128242; /* absolut, k=1*/ /* Nullindikator*/ pnd: 0.0; -/* Umrechnung der Voltanzeige: 1.3mbar/10V (X0.1 Range) +/* Umrechnung der Voltanzeige: 1.3mbar/10V (X.1 Range) daraus abschaetzung der relativer Unsicherheit*/ upn1: 1.3e-5; /* nicht erfassb. Nullpkt.-schw. */ upn2: 3.77e-7; /*0.29*0.01e-3*1.3/10 Digit. */ @@ -817,4 +873,42 @@ ev(ufp/fp); */ \end{lstlisting} +\subsection{Berechnung der Unsicherheit von $f_i$} +\label{ssec:unsicherheitfi} + +\begin{lstlisting} +/* + +--*-- maxima --*-- + +Bestimmung der systematischen Unsicherheit +der Expansionsverh. + +QSE-SE2-14-1 + +*/ +remvalue(all); + +f : 1/(1/fp - Vz/Vs); +sVz : diff(f,Vz); +sVs : diff(f,Vs); +sfp : diff(f,fp); +uf: ((sVs*uVs)^2 + (sfp*ufp)^2 + (sVz*uVz)^2)^.5; +fp: [7.4e-4, 9.2e-3]; +Vs: [76.13, 920.0]; +Vz: 350.0; +/*ufp: f*4e-4;*/ +uV1: 0.343;/*Werte aus QSE-SE2-07-1*/ +uV2: 0.057;/*Werte aus QSE-SE2-07-1*/ +uVs: [uV2, uV1]; /* cm^3 */ +uVz: 3.3; /* cm^3 aus QSE-SE2-09-1 */ + +grind(ev(ev(uf)/f)); + +/* +[1346.8*(1.0*ufp^2+5.7E-16)^0.5, + 108.3*(1.0*ufp^2+9.4E-14)^0.5] +*/ +\end{lstlisting} + \end{document} diff --git a/cal.pdf b/qse-se2-14-1.pdf similarity index 51% rename from cal.pdf rename to qse-se2-14-1.pdf index 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zBJ){oXm{MNXN{}ErRQzEd(n7}*sF${>S^<5)FyrFgfTqp&Cb{v{yy?Xc(eZ*JHe@7 z#xL=tN1ci4ZF6T7C!OoGRR7EN_56`J!o_~c^R|AQm45gB&3gaHdy}T~Ik3s_8XH@f O8Ch_ts=E5SaRC6n&rfv# diff --git a/ufprime.max b/ufprime.max new file mode 100644 index 0000000..94453ba --- /dev/null +++ b/ufprime.max @@ -0,0 +1,32 @@ +/* + +--*-- maxima --*-- + +Bestimmung der systematischen Unsicherheit +der Expansionsverh. + +QSE-SE2-14-1 + +*/ +remvalue(all); + +f : 1/(1/fp - Vz/Vs); +sVz : diff(f,Vz); +sVs : diff(f,Vs); +sfp : diff(f,fp); +uf: ((sVs*uVs)^2 + (sfp*ufp)^2 + (sVz*uVz)^2)^.5; +fp: [7.4e-4, 9.2e-3]; +Vs: [76.13, 920.0]; +Vz: 350.0; +/*ufp: f*4e-4;*/ +uV1: 0.343;/* Werte aus QSE-SE2-07-1*/ +uV2: 0.057;/* Werte aus QSE-SE2-07-1*/ +uVs: [uV2, uV1]; /* cm^3 */ +uVz: 3.3; /* cm^3 aus QSE-SE2-09-1 */ + +grind(ev(ev(uf)/f)); + +/* +[1346.8*(1.0*ufp^2+5.7E-16)^0.5, + 108.3*(1.0*ufp^2+9.4E-14)^0.5]$ +*/ \ No newline at end of file -- GitLab