Biblio: array methods

biblio/chapters/literature.tex

@@ -17,38 +17,87 @@ reflected waves, while PUV methods use colocated pressure and velocity
 measurements to separate incident and reflected components of the signal.
 
 \subsection{Array methods}
-\begin{itemize}
-	\item \cite{mansard1980measurement}: Presentation of least-square method to separate
-incident and reflected spectra. Requires simultaneous measurement at 3
-positions, on a line parallel to the direction of wave propagation.
-\parencite{gaillard1980}
+\subsubsection{2-point methods}
+Array methods were developped as a way to isolate incident and reflected wave
+components using multiple wave records.
+\textcite{goda1977estimation,morden1977decomposition} used two wave gauges
+located along the wave direction, along with spectral analysis, in order to
+extract the incident and reflected wave spectra. Their work is based on the
+earlier work of \textcite{thornton1972spectral}. \textcite{goda1977estimation}
+analyzed the wave spectrum components using the Fast Fourier Transform, and
+suggests that this method is adequate for studies in wave flumes. They noted
+that this method provides diverging results for gauge spacings that are
+multiples of half of the wave length. \textcite{morden1977decomposition}
+applies this technique to a field study, where the sea state is wind generated.
+\textcite{morden1977decomposition} showed that, using appropriate spectral
+analysis methods along with linear wave theory, the decomposition of the sea
+state into incident and reflected waves is accurate. A relation between the
+maximum obtainable frequency and the distance between the sensors is provided.
+According to \textcite{morden1977decomposition}, the only needed knowledge on
+the wave environment is that wave frequencies are not modified by the
+reflection process.
 
-	\item \cite{frigaard1995time}: Separate 2D wave field into waves propagating towards
-and away from a structure, using 2 gauges. Method quite efficient, even with
-small filters. SIRW Method, realtime.
+\subsubsection{3-point methods}
+In order to alleviate the limitations from the 2-point methods,
+\textcite{mansard1980measurement} introduced a 3-point method. The addition of
+a supplementary measurement point along with the use of a least-squares method
+most importantly provided less sensitivity to
+noise, non-linear interactions, and probe spacing. The admissible frequency
+range could also be widened. A similar method was proposed by
+\textcite{gaillard1980}. The accuracy of the method for the estimation of
+incident and reflected wave components was once again highlighted, while the
+importance of adequate positioning of the gauges was still noted.
 
-	\item \cite{baldock1999separation}: Starting from \textcite{frigaard1995time},
-arbitrary 2D bathymetry using linear shoaling. Small error for large reflection
-coefficients, larger for low reflection.
+\subsubsection{Time-domain method}
+\textcite{frigaard1995time} presented a time-domain method for reflected and
+incident wave separation. This method, called SIRW method, used discrete
+filters to extract the incident component of an irregular wave field. The
+results were as accurate as with the method proposed by
+\cite{goda1977estimation}, while singularity points are better accounted for.
+The main advantage of the SIRW method is that it works in the time-domain,
+meaning that real time computations can be performed.
+\textcite{frigaard1995time} also mentions the possibility of replacing one of
+the wave gauges by a velocity meters to prevent singularities.
 
-	\item \cite{suh2001separation}: Technique to separate incident and reflected waves on
-a known current.
+This method was improved by \textcite{baldock1999separation} in order to
+account for arbitrary bathymetry. Linear theory is used to compute shoaling on
+the varying bathymetry. Resulting errors in the computed reflection coefficient
+are low for large reflection coefficients, but increase with lower
+coefficients. The neglect of shoaling can lead to important error in many
+cases. The presented method could also be extended to three-dimensionnal waves
+and bathymetry by considering the influence of refraction.
 
-	\item \cite{inch2016accurate}: creation of a lookup table to correct noise-induced
-bias in array methods.
+\subsubsection{Further improvements}
+Further additions were made to array methods. \textcite{suh2001separation}
+developped a method taking constant current into account to separate incident
+and reflected waves. This method relies on two or more gauges, using a least
+squares method. Results are very accurate in the absence of noise, but a small
+amount of error appears when noise is added.
 
-	\item \cite{andersen2017estimation}: estimation of incident and reflected components
-for non-linear waves.
+\textcite{inch2016accurate} noticed that the presence of noise lead to
+overestimation of reflection coefficient. The creation of bias lookup tables is
+proposed in order to account for noise-induced error in reflection coefficient
+estimations.
 
-	\item \cite{roge2019estimation}: extension to irregular waves.
-\end{itemize}
+\textcite{andersen2017estimation,roge2019estimation} later proposed
+improvements to account for highly non-linear regular and irregular waves
+respectively. The improved method provides very accurate results for highly
+non-linear waves, but are expected to be unreliable in the case of steep
+seabeds, as shoaling is not part of the underlying model.
+
+\subsubsection{Conclusion}
+Array methods have been developped enough to provide accurate results in a wide
+range of situations. However, they require at least two wave gauges to be used.
+That means that in some situations such as the Saint-Jean-de-Luz event of 2017,
+other methods are needed since only one field measurement location is
+available.
 
 \subsection{PUV methods}
 
 \begin{itemize}
-	\item ?? \cite{guza1977resonant}: model of the surf zone as a standing wave combined
-with a progressive wave. Accurate results of surface elevation and runup for
-reflectivities over 0.3.
+	\item ?? \cite{guza1977resonant}: model of the surf zone as a standing wave
+		combined with a progressive wave. Accurate results of surface elevation and
+		runup for reflectivities over 0.3.
 
 	\item ?? \cite{guza1984}: 
 
@@ -63,8 +112,8 @@ reflectivities over 0.3.
 		reflected energy than incident energy.
 
 	\item \cite{hughes1993}: colocated horizontal and vertical velocities or
-	horizontal velocity and surface elevation. Validation for full reflection of
-	irregular non breaking waves.
+		horizontal velocity and surface elevation. Validation for full reflection
+		of irregular non breaking waves.
 
 	\item \cite{huntley1999use}: principal component analysis technique to avoid
 		noise-induced bias.

biblio/library.bib

@@ -694,3 +694,31 @@
 	publisher={École nationale des ponts et chaussées},
 	booktitle={Hydraulic Engineering Reports},
 }
+
+@incollection{goda1977estimation,
+  title={Estimation of incident and reflected waves in random wave experiments},
+  author={Goda, Yoshimi and Suzuki, Yasumasa},
+  booktitle={Coastal Engineering 1976},
+  pages={828--845},
+  year={1977}
+}
+
+@incollection{morden1977decomposition,
+  title={Decomposition of co-existing random wave energy},
+  author={Morden, Dennis B and Richey, Eugene P and Christensen, Derald R},
+  booktitle={Coastal Engineering 1976},
+  pages={846--865},
+  year={1977}
+}
+
+@article{thornton1972spectral,
+  title={Spectral resolution of breakwater reflected waves},
+  author={Thornton, Edward B and Calhoun, Ronald J},
+  journal={Journal of the Waterways, Harbors and Coastal Engineering Division},
+  volume={98},
+  number={4},
+  pages={443--460},
+  year={1972},
+  publisher={American Society of Civil Engineers}
+}
+

biblio/main.tex

@@ -1,4 +1,4 @@
-\documentclass[english, a4paper, 11pt]{book}
+\documentclass[english, a4paper]{book}
 \usepackage{cours}
 \setmainlanguage{english}
 
@@ -15,11 +15,6 @@
 	pdfauthor = {Edgar P. Burkhart},
 }
 
-\includeonly{
-	chapters/introduction,
-	chapters/literature,
-}
-
 \title{\interlight\huge M2 Internship\\{\Huge Bibliography review}\\
 \vspace{1em}
 Simulation
@@ -31,6 +26,8 @@ at the Artha breakwater on February 28, 2017}
 \affil{École Normale Supérieure Paris-Saclay}
 \date{February 2022}
 
+\setcounter{tocdepth}{3}
+
 \begin{document}
 \frontmatter
 \maketitle