Fatigue in WAFO (Wave Analysis for Fatigue and Oceanography). Version 2.1.1 28-Sep-2005 Routines for Markov models, cycle counting, damage, and fatigue. Cycle counting (Rainflow, min-max cycles) & Crossings. [WAFO/cycles] dat2tp - The turning points from data, optionally rainflowfiltered. [onedim] dat2rfm - Calculates the rainflow matrix from a time signal. rfcfilter - Rainflow filter turning points. tp2lc - Level crossings from turning points. tp2mm - min2Max (and Max2min) cycles from turning points. tp2rfc - Rainflow cycles from turning points. tp2arfc - Asymmetric rainflow cycles from TP. tp2arfc4p - Asymmetric RFC and residual from TP (used by tp2arfc). res2arfc - Asymmetric rainflow cycles for a residual. cc2lc - Level crossings from a cycle count. cc2amp - Amplitude histogram from a cycle count. findrfc - Finds indices to rainflow cycles of a sequence of TP. [onedim] findcross - Finds the indices of level v up- and down- crossings of a vector. [onedim] Discrete loads & Cycle matrices (Rainflow matrix). [WAFO/cycles] dat2dtp - Discrete TP from load. cc2dcc - Discretization of a cycle count. dtp2rfm - Rainflow matrix from discrete TP. dtp2arfm - Asymmetric rainflow matrix from discrete TP. dtp2arfm4p - Asymmetric RFM and residual from discrete TP (used by dtp2arfm). dtp2rfm_sid - RFM from discrete turning points with side information. dtp2arfm_sid- Asymmetric RFM from discrete TP with side information. cc2cmat - Estimates cycle matrix from a cycle count. dcc2cmat - Histogram matrix from discrete class indices. cmat2nt - Counting distribution from cycle matrix. nt2cmat - Cycle matrix from counting distribution. cmat2lc - Level crossings from cycle matrix. nt2lc - Level crossings from counting distribution. cmat2amp - Amplitude histogram from cycle matrix. cmat2rmcmat - Convert cycle matrix from min-max to range-mean. rmcmat2cmat - Convert cycle matrix from range-mean to min-max. cmatresamp - Resamples a cycle matrix, random resampling. cmatcombine - Combines two cycle matrices. Extrapolation & Smoothing of RFM/CMAT/LC. [WAFO/cycles] rfmextrapolate - Extrapolates a rainflow matrix. tpextrapolate - Extrapolates a sequence of turning points. cmat2extralc - Extrapolate level crossing spectrum from cycle matrix. wgpdfit_mld - Routine for ML estimation of GPD with discrete data. lc2rfmextreme - Compute extreme RFM from level crossings. extralc - Extrapolate a level crossing spectrum. smoothcmat - Smooth a cycle matrix. Plotting. [WAFO/cycles] ccplot - Plot cycle count. cmatplot - Plot cycle matrix. cocc - Plot a cycle count with cycle matrix isolines. lcplot - Plot level crossing intensity/spectrum. [onedim] lsplot - Plot load spectra. Markov model. [WAFO/markov] mat2tmat - Convert matrix to transition matrix. mc2stat - Stationary distribution for a Markov chain. mc2rfm - RFM for a Markov chain. mctp2stat - Stationary distribution for a MCTP. mctp2reverse- Calculate time-reversed MCTP. mctp2rfm - RFM for a Markov chain of turning points. mctp2arfm - Asymmetric rainflow matrix for a MCTP. arfm2mctp - Markov matrix given an asymmetric rainflow matrix. mktestmat - Makes test matrices for min-Max (and Max-min) matrices. Switching Markov model. [WAFO/markov] smc2rfm - RFM for a Switching Markov chain. smctp2stat - Stationary distribution for a SMCTP. smctp2joint - Calculate joint Markov chain for a SMCTP. smctp2rfm - RFM for a Switching Markov chain of turning points. smctp2arfm - Asymmetric rainflow matrix for a SMCTP. hmmplot - Plot Hidden Markov Model (HMM). Estimate a Switching Markov model. [WAFO/markov] estsmctp - Estimate SMCTP model from an observed RFM. f_smctp - Help routine to estsmtp. estmc - Estimate Transition matrix of MC from signal. loglcmat - log-Likelihood of cycle matrix. chi2cmat - Chi-square distance of cycle matrix. hdcmat - Hellinger distance of cycle matrix. klcmat - Kullback-Leibler distance of cycle matrix. tr_p2x - Transform P-matrix to X-vector (Used by 'estsmctp') tr_x2p - Transform X-vector to P-matrix. (Used by 'estsmctp') tr_m2x - Transform Model-structure to X-vector. (Used by 'estsmctp') tr_x2m - Transform X-vector to Model-structure. (Used by 'estsmctp') scalemat - Scale and translate a cycle matrix. (Used by 'estsmctp') f_funm - Calculate min-max matrix for Model-structure. (Used by 'estsmctp') Fatigue & damage. [WAFO/damage] cc2dam - Calculate total damage from a cycle count. cmat2dam - Calculate total damage from a cycle matrix. cmat2dmat - Calculate damage matrix from cycle matrix. lc2dplus - Upper bound for total damage from level crossings. snplot - Plots S-N data and estimates parameters. sphdam - Calculates spherical damage for a 3-D load. ftf - Calculates fatigue failure time distribution. damint - Calculates damage intensity from counting distribution. down2cc - Calculates the most damaging cycle count given crossings. roadspec - Road spectrum. Simulation of random loads [WAFO/wsim] lc2sdat - Simulates a process with given irregularity factor and crossing spectrum. rfm2dtp - Reconstructs a sequence of turning points from a rainflow matrix. mcsim - Simulates a discrete Markov chain mctpsim - Simulates a discrete Markov chain of turning points smcsim - Simulates a switching Markov chain smctpsim - Simulates a switching Markov chain of turning points sarmasim - Simulates a switching AR- or ARMA-process Demos. [WAFO/wdemos] rfcdemo1 - Demo for switching AR(1)-processes. rfcdemo2 - Demo for calculation of the RFM for a switching MCTP model. itmkurs - Initiate paths for Demo Load and Fatigue Analysis. democc - Demo of rainflow and min-max cycle definitions. democc_markmax - plots load and marks a maximum. (Used by democc) democc_rfcdef - illustrates the definition of rainflow cycles. (Used by democc) democc_mmdef - illustrates the definition of min-max cycles. (Used by democc) democc_tpdef - illustrates the definition of turning points. (Used by democc) democc_plotmat - plots RFC and min-max counts. (Used by democc)

001 % Fatigue in WAFO (Wave Analysis for Fatigue and Oceanography). 002 % Version 2.1.1 28-Sep-2005 003 % 004 % Routines for Markov models, cycle counting, damage, and fatigue. 005 % 006 % 007 % Cycle counting (Rainflow, min-max cycles) & Crossings. [WAFO/cycles] 008 % dat2tp - The turning points from data, optionally rainflowfiltered. [onedim] 009 % dat2rfm - Calculates the rainflow matrix from a time signal. 010 % rfcfilter - Rainflow filter turning points. 011 % tp2lc - Level crossings from turning points. 012 % tp2mm - min2Max (and Max2min) cycles from turning points. 013 % tp2rfc - Rainflow cycles from turning points. 014 % tp2arfc - Asymmetric rainflow cycles from TP. 015 % tp2arfc4p - Asymmetric RFC and residual from TP (used by tp2arfc). 016 % res2arfc - Asymmetric rainflow cycles for a residual. 017 % cc2lc - Level crossings from a cycle count. 018 % cc2amp - Amplitude histogram from a cycle count. 019 % findrfc - Finds indices to rainflow cycles of a sequence of TP. [onedim] 020 % findcross - Finds the indices of level v up- and down- crossings of a vector. [onedim] 021 % 022 % Discrete loads & Cycle matrices (Rainflow matrix). [WAFO/cycles] 023 % dat2dtp - Discrete TP from load. 024 % cc2dcc - Discretization of a cycle count. 025 % dtp2rfm - Rainflow matrix from discrete TP. 026 % dtp2arfm - Asymmetric rainflow matrix from discrete TP. 027 % dtp2arfm4p - Asymmetric RFM and residual from discrete TP (used by dtp2arfm). 028 % dtp2rfm_sid - RFM from discrete turning points with side information. 029 % dtp2arfm_sid- Asymmetric RFM from discrete TP with side information. 030 % cc2cmat - Estimates cycle matrix from a cycle count. 031 % dcc2cmat - Histogram matrix from discrete class indices. 032 % cmat2nt - Counting distribution from cycle matrix. 033 % nt2cmat - Cycle matrix from counting distribution. 034 % cmat2lc - Level crossings from cycle matrix. 035 % nt2lc - Level crossings from counting distribution. 036 % cmat2amp - Amplitude histogram from cycle matrix. 037 % cmat2rmcmat - Convert cycle matrix from min-max to range-mean. 038 % rmcmat2cmat - Convert cycle matrix from range-mean to min-max. 039 % cmatresamp - Resamples a cycle matrix, random resampling. 040 % cmatcombine - Combines two cycle matrices. 041 % 042 % Extrapolation & Smoothing of RFM/CMAT/LC. [WAFO/cycles] 043 % rfmextrapolate - Extrapolates a rainflow matrix. 044 % tpextrapolate - Extrapolates a sequence of turning points. 045 % cmat2extralc - Extrapolate level crossing spectrum from cycle matrix. 046 % wgpdfit_mld - Routine for ML estimation of GPD with discrete data. 047 % lc2rfmextreme - Compute extreme RFM from level crossings. 048 % extralc - Extrapolate a level crossing spectrum. 049 % smoothcmat - Smooth a cycle matrix. 050 % 051 % Plotting. [WAFO/cycles] 052 % ccplot - Plot cycle count. 053 % cmatplot - Plot cycle matrix. 054 % cocc - Plot a cycle count with cycle matrix isolines. 055 % lcplot - Plot level crossing intensity/spectrum. [onedim] 056 % lsplot - Plot load spectra. 057 % 058 % Markov model. [WAFO/markov] 059 % mat2tmat - Convert matrix to transition matrix. 060 % mc2stat - Stationary distribution for a Markov chain. 061 % mc2rfm - RFM for a Markov chain. 062 % mctp2stat - Stationary distribution for a MCTP. 063 % mctp2reverse- Calculate time-reversed MCTP. 064 % mctp2rfm - RFM for a Markov chain of turning points. 065 % mctp2arfm - Asymmetric rainflow matrix for a MCTP. 066 % arfm2mctp - Markov matrix given an asymmetric rainflow matrix. 067 % mktestmat - Makes test matrices for min-Max (and Max-min) matrices. 068 % 069 % Switching Markov model. [WAFO/markov] 070 % smc2rfm - RFM for a Switching Markov chain. 071 % smctp2stat - Stationary distribution for a SMCTP. 072 % smctp2joint - Calculate joint Markov chain for a SMCTP. 073 % smctp2rfm - RFM for a Switching Markov chain of turning points. 074 % smctp2arfm - Asymmetric rainflow matrix for a SMCTP. 075 % hmmplot - Plot Hidden Markov Model (HMM). 076 % 077 % Estimate a Switching Markov model. [WAFO/markov] 078 % estsmctp - Estimate SMCTP model from an observed RFM. 079 % f_smctp - Help routine to estsmtp. 080 % estmc - Estimate Transition matrix of MC from signal. 081 % 082 % loglcmat - log-Likelihood of cycle matrix. 083 % chi2cmat - Chi-square distance of cycle matrix. 084 % hdcmat - Hellinger distance of cycle matrix. 085 % klcmat - Kullback-Leibler distance of cycle matrix. 086 % 087 % tr_p2x - Transform P-matrix to X-vector (Used by 'estsmctp') 088 % tr_x2p - Transform X-vector to P-matrix. (Used by 'estsmctp') 089 % tr_m2x - Transform Model-structure to X-vector. (Used by 'estsmctp') 090 % tr_x2m - Transform X-vector to Model-structure. (Used by 'estsmctp') 091 % scalemat - Scale and translate a cycle matrix. (Used by 'estsmctp') 092 % f_funm - Calculate min-max matrix for Model-structure. (Used by 'estsmctp') 093 % 094 % Fatigue & damage. [WAFO/damage] 095 % cc2dam - Calculate total damage from a cycle count. 096 % cmat2dam - Calculate total damage from a cycle matrix. 097 % cmat2dmat - Calculate damage matrix from cycle matrix. 098 % lc2dplus - Upper bound for total damage from level crossings. 099 % snplot - Plots S-N data and estimates parameters. 100 % sphdam - Calculates spherical damage for a 3-D load. 101 % ftf - Calculates fatigue failure time distribution. 102 % damint - Calculates damage intensity from counting distribution. 103 % down2cc - Calculates the most damaging cycle count given crossings. 104 % roadspec - Road spectrum. 105 % 106 % Simulation of random loads [WAFO/wsim] 107 % lc2sdat - Simulates a process with given irregularity factor and crossing spectrum. 108 % rfm2dtp - Reconstructs a sequence of turning points from a rainflow matrix. 109 % mcsim - Simulates a discrete Markov chain 110 % mctpsim - Simulates a discrete Markov chain of turning points 111 % smcsim - Simulates a switching Markov chain 112 % smctpsim - Simulates a switching Markov chain of turning points 113 % sarmasim - Simulates a switching AR- or ARMA-process 114 % 115 % Demos. [WAFO/wdemos] 116 % rfcdemo1 - Demo for switching AR(1)-processes. 117 % rfcdemo2 - Demo for calculation of the RFM for a switching MCTP model. 118 % itmkurs - Initiate paths for Demo Load and Fatigue Analysis. 119 % democc - Demo of rainflow and min-max cycle definitions. 120 % democc_markmax - plots load and marks a maximum. (Used by democc) 121 % democc_rfcdef - illustrates the definition of rainflow cycles. (Used by democc) 122 % democc_mmdef - illustrates the definition of min-max cycles. (Used by democc) 123 % democc_tpdef - illustrates the definition of turning points. (Used by democc) 124 % democc_plotmat - plots RFC and min-max counts. (Used by democc) 125 126

Mathematical Statistics

Centre for Mathematical Sciences

Lund University with Lund Institute of Technology

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