Home > wafo > wdemos > itmkurs > itmkurs_lab1.m

itmkurs_lab1

PURPOSE Script to computer exercises 1

SYNOPSIS This is a script file.

DESCRIPTION ``` ITMKURS_LAB1 Script to computer exercises 1

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Measured data```

CROSS-REFERENCE INFORMATION This function calls:
 alevel Slice virkler.mat at a given crack length. cc2amp Calculates the amplitudes from a cycle count. cc2dam Calculates the total Palmgren-Miner damage of a cycle count. ccplot Plots a cycle count as a point process in the plane. dat2spec Estimate one-sided spectral density from data. dat2tp Extracts turning points from data, democc A program for visualization of cycle counts in random ftf Calculates the fatigue failure time distribution. nlevel Slice virkler.mat at a given number of cycles. sn Fatigue experiment, constant-amplitude loading. snplot Plots SN-data and estimates parameters spec2mom Calculates spectral moments from spectrum tp2lc Calculates the number of upcrossings from the turning points. tp2mm Calculates min2Max and Max2min cycles from a sequence of turning points tp2rfc Finds the rainflow cycles from the sequence of turning points. wnormplot Plots data on a Normal distribution paper wspecplot Plot a spectral density
This function is called by:

SOURCE CODE ```001 %ITMKURS_LAB1 Script to computer exercises 1
002 %
003 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
004 %
006 %
007 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
008 % A Stochastic Load Process
009 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
010 %
011 %%Measured data
012 %
013
015 x = deep;
016 plot(x(:,1),x(:,2))
017 plot(x(1:1000,1),x(1:1000,2))
018
019
020 T=x(end,1)-x(1,1);
021
022 whos
023
024
025 tp = dat2tp(x);
026 plot(x(:,1),x(:,2),tp(:,1),tp(:,2),'.-')
027 axis([0 100 -20 20])
028
029 tp1 = dat2tp(x,1);
030 plot(x(:,1),x(:,2),tp(:,1),tp(:,2),tp1(:,1),tp1(:,2))
031 axis([0 100 -20 20])
032
033
034 lc = tp2lc(tp);
035 lc(:,2)=lc(:,2)/T;
036 plot(lc(:,1),lc(:,2))
037 semilogx(lc(:,2),lc(:,1))
038
039
040 m=mean(x(:,2));
041 f0 = interp1(lc(:,1),lc(:,2),m,'linear');
042 f0
043
044
045
046 extr0=length(tp)/2/T;
047 alfa=f0/extr0
048
049 %
050 %%Gaussian process as a model for the deep water data
051 %
052
053
054 wnormplot(x(:,2))
055
056
057
058 S = dat2spec(deep);
059 wspecplot(S);
060
061 S
062 plot(S.w,S.S)
063
064
065
066 lam = spec2mom(S,4); L0=lam(1); L2=lam(2); L4=lam(3);
067
068
069 f0=1/(2*pi)*sqrt(L2/L0)
070 ux = -20:0.1:20;
071 ricex = f0*exp(-ux.*ux./(2*L0));
072 plot(lc(:,1),lc(:,2),'-',ux,ricex,'--')
073 semilogx(lc(:,2),lc(:,1),'-',ricex,ux,'--')
074
075
076
077
078 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
079 % Cycle counts
080 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
081 %---------------------
082 %Cycle Counts
083 %---------------------
084
085 proc = x(1:500,:);
086 democc
087
088 RFC = tp2rfc(tp);
089 mM = tp2mm(tp);
090
091
092 subplot(1,2,1), ccplot(RFC)
093 subplot(1,2,2), ccplot(mM)
094
095
096 ampRFC = cc2amp(RFC);
097 ampmM = cc2amp(mM);
098 subplot(1,2,1), hist(ampRFC)
099 subplot(1,2,2), hist(ampmM)
100
101
102 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
103 % SN-data
104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105 %
106 %%Calculation of damage intensity}
107 %
108
109 beta=3.2; gam=5.5E-10;
110 d_beta=cc2dam(RFC,beta)/T;
111 time_fail=1/gam/d_beta/3600 %in hours of the specific storm
112
113
114 %
116 %
117
119
120 plot(N,s,'o')
121 axis([0 14e5 5 35 ])
122 loglog(N,s,'o')
123
124
125 wnormplot(reshape(log(N),8,5))
126
127
128 [e0,beta0,s20] = snplot(s,N,12)
129 [e0,beta0,s20] = snplot(s,N,14)
130 e0    = 5.5361e-10
131 beta0 = 3.2286
132 s20   = 0.0604
133
134 %
135 %%Calculation of the 95\% quantile for the fatigue life time
136 %
137 %%Fatigue life distribution under variable random load
138 %
139
140 D0 = e0*cumsum((RFC(:,2)-RFC(:,1)).^beta0);
141 plot(D0)
142
143
144 beta = 3:0.1:8;
145 DRFC = cc2dam(RFC,beta);
146 dRFC = DRFC/T
147 plot(beta,dRFC)
148
149
150 help ftf
151 [t0,F0] = ftf(e0,cc2dam(RFC,beta0)/T,s20,0.5,1);
152
153 [t1,F1] = ftf(e0,cc2dam(RFC,beta0)/T,s20,0,1);
154 [t2,F2] = ftf(e0,cc2dam(RFC,beta0)/T,s20,5,1);
155 plot(t0,F0,t1,F1,t2,F2)
156
157
158 taRFC = exp(-1.96*sqrt(0.06))/e0./dRFC;
159 DmM = cc2dam(mM,beta);
160 dmM = DmM/T
161 tamM = exp(-1.96*sqrt(0.06))/e0./dmM;
162 plot(beta,taRFC,beta,tamM,'r')
163
164 %
165 %%Crack growth data}  %%%%%%%%%%%%%
166 %
167
168
169
170
171 clear
173
174 plot(v(:,2),v(:,1))
175
176
177 plot(v(:,2:69),v(:,1),'b-')
178
179
180
181 N = alevel(v,15);
182
183 plot(N,ones(1,length(N)),'o')
184
185 a = nlevel(v,2e5);
186 plot(a,ones(1,length(a)),'o')
187
188
189```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

Generated on Thu 06-Oct-2005 02:21:16 for WAFO by m2html © 2003