THSNLPDF2 Joint (Scf,Hd) PDF for nonlinear waves with Torsethaugen spectra. CALL: f = thsnlpdf2(Hd,Scf,Hm0,Tp) f = pdf struct evaluated at meshgrid(Scf,Hd) Hd = zero down crossing wave height (vector) Scf = crest front steepness (vector) Hm0 = significant wave height [m] Tp = Spectral peak period [s] THSNLPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, for 2nd order nonlinear waves with a Torsethaugen spectral density. The empirical parameters of the model is fitted by least squares to simulated (Scf,Hd) data for 600 classes of Hm0 and Tp. Between 40000 and 200000 zero-downcrossing waves were simulated for each class of Hm0 and Tp. THSNLPDF is restricted to the following range for Hm0 and Tp: 0.5 < Hm0 [m] < 12, 3.5 < Tp [s] < 20, and Hm0 < (Tp-2)*12/11. Example: Hm0 = 6;Tp = 8; h = linspace(0,4*Hm0/sqrt(2)); s = linspace(0,6*1.25*Hm0/Tp^2); f = thsnlpdf2(h,s,Hm0,Tp); w = linspace(0,40,5*1024+1).'; S = torsethaugen(w,[Hm0 Tp]); dt = 0.3; x = spec2nlsdat(S,80000,.2); rate = 8; [si,hi] = dat2steep(x,rate,2); fk = kdebin([si,hi],'epan',[],[],.5,128); fk.title = f.title; fk.labx = f.labx; plot(si,hi,'.'), hold on pdfplot(f),pdfplot(fk,'r'),hold off See also thsspdf
PDF class constructor | |
Calculates quantile levels which encloses P% of PDF | |
Joint (Scf,Hd) PDF for nonlinear waves with Torsethaugen spectra. | |
Display message and abort function. | |
X and Y arrays for 3-D plots. | |
Convert number to string. (Fast version) |
001 function [f,varargout] = thsnlpdf2(Hd,Scf,Hm0,Tp,normalizedInput) 002 %THSNLPDF2 Joint (Scf,Hd) PDF for nonlinear waves with Torsethaugen spectra. 003 % 004 % CALL: f = thsnlpdf2(Hd,Scf,Hm0,Tp) 005 % 006 % f = pdf struct evaluated at meshgrid(Scf,Hd) 007 % Hd = zero down crossing wave height (vector) 008 % Scf = crest front steepness (vector) 009 % Hm0 = significant wave height [m] 010 % Tp = Spectral peak period [s] 011 % 012 % THSNLPDF2 approximates the joint distribution of (Scf, Hd), i.e., crest 013 % steepness (2*pi*Ac/(g*Td*Tcf)) and wave height, for 2nd order 014 % nonlinear waves with a 015 % Torsethaugen spectral density. The empirical parameters of the model is 016 % fitted by least squares to simulated (Scf,Hd) data for 600 classes of 017 % Hm0 and Tp. Between 40000 and 200000 zero-downcrossing waves were 018 % simulated for each class of Hm0 and Tp. 019 % THSNLPDF is restricted to the following range for Hm0 and Tp: 020 % 0.5 < Hm0 [m] < 12, 3.5 < Tp [s] < 20, and Hm0 < (Tp-2)*12/11. 021 % 022 % Example: 023 % Hm0 = 6;Tp = 8; 024 % h = linspace(0,4*Hm0/sqrt(2)); 025 % s = linspace(0,6*1.25*Hm0/Tp^2); 026 % f = thsnlpdf2(h,s,Hm0,Tp); 027 % w = linspace(0,40,5*1024+1).'; 028 % S = torsethaugen(w,[Hm0 Tp]); 029 % dt = 0.3; 030 % x = spec2nlsdat(S,80000,.2); rate = 8; 031 % [si,hi] = dat2steep(x,rate,2); 032 % fk = kdebin([si,hi],'epan',[],[],.5,128); 033 % fk.title = f.title; fk.labx = f.labx; 034 % plot(si,hi,'.'), hold on 035 % pdfplot(f),pdfplot(fk,'r'),hold off 036 % 037 % See also thsspdf 038 039 040 % Reference 041 % P. A. Brodtkorb (2004), 042 % The Probability of Occurrence of Dangerous Wave Situations at Sea. 043 % Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, 044 % Trondheim, Norway. 045 046 % History 047 % revised pab 09.08.2003 048 % changed input 049 % validated 20.11.2002 050 % By pab 20.12.2000 051 052 error(nargchk(4,5,nargin)) 053 054 if (nargin < 5|isempty(normalizedInput)), normalizedInput = 0;end 055 if (nargin < 4|isempty(Tp)), Tp = 8;end 056 if (nargin < 3|isempty(Hm0)), Hm0 = 6;end 057 058 059 [V,H] = meshgrid(Scf,Hd); 060 061 f = createpdf(2); 062 [f.f,Hrms,Vrms,varargout{1:nargout-1}] = thsnlpdf(H,V,Hm0,Tp,normalizedInput); 063 064 f.x = {Scf(:),Hd(:)}; 065 066 if (normalizedInput) 067 f.labx={'Scf', 'Hd'}; 068 f.norm = 1; 069 else 070 f.norm=0; 071 f.labx={'Scf', 'Hd [m]'}; 072 end 073 f.title = 'Joint distribution of (Hd,Scf) in time (non-linear)'; 074 f.note = ['Torsethaugen Hm0=' num2str(Hm0) ' Tp = ' num2str(Tp)]; 075 [f.cl,f.pl] = qlevels(f.f); 076 077 return 078
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