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# cmat2dam

## PURPOSE

Calculates the total Palmgren-Miner damage of a cycle matrix.

## SYNOPSIS

D = cmat2dmat(param,F,beta,K)

## DESCRIPTION

``` CMAT2DAM Calculates the total Palmgren-Miner damage of a cycle matrix.

CALL:  D = cmat2dam(param,F,beta,K);

Output:
D     = Damage.                                            [1xm]
Input:
param = Parameter vector, [a b n], defines discretization.
F     = Cycle matrix.                                      [nxn]
beta  = Beta-values, material parameter                    [1xm]
K     = K-value, material parameter (Optional, Default: 1) [1x1]

The damage is calculated as
D(i) = sum ( K * S^beta(i) ),  S = (max-min)/2

Example:
param = [-1 1 32]; F = mktestmat(param);
bv = 3:8; D = cmat2dam(param,F,bv); plot(bv,D,'x-')

## CROSS-REFERENCE INFORMATION

This function calls:
 cmat2amp Calculates a histogram of amplitudes from a cycle matrix. error Display message and abort function.
This function is called by:
 Chapter4 % CHAPTER4 contains the commands used in Chapter 4 of the tutorial itmkurs_lab2 Script to computer exercises 2 itmkurs_lab3 Script to computer exercises 3 itmkurs_lab4 Script to computer exercises 4 rfmextrapolate Extrapolates a rainflow matrix.

## SOURCE CODE

```001 function D = cmat2dmat(param,F,beta,K)
002 %CMAT2DAM Calculates the total Palmgren-Miner damage of a cycle matrix.
003 %
004 % CALL:  D = cmat2dam(param,F,beta,K);
005 %
006 % Output:
007 %   D     = Damage.                                            [1xm]
008 % Input:
009 %   param = Parameter vector, [a b n], defines discretization.
010 %   F     = Cycle matrix.                                      [nxn]
011 %   beta  = Beta-values, material parameter                    [1xm]
012 %   K     = K-value, material parameter (Optional, Default: 1) [1x1]
013 %
014 % The damage is calculated as
015 %     D(i) = sum ( K * S^beta(i) ),  S = (max-min)/2
016 %
017 % Example:
018 %   param = [-1 1 32]; F = mktestmat(param);
019 %   bv = 3:8; D = cmat2dam(param,F,bv); plot(bv,D,'x-')
020 %
022
023 % Tested on Matlab 6.0
024 %
025 % History:
026 % Revised by PJ 03-Nov-1999
027 % -  updated for WAFO
028 % Created by PJ (Pär Johannesson) 1997
029 %   from 'Toolbox: Rainflow Cycles for Switching Processes V.1.0'
030
031 % Check input and otput
032
033 ni = nargin;
034 no = nargout;
035 error(nargchk(3,4,ni));
036
037 if ni < 4
038   K=[];
039 end
040
041 % Set default values
042
043 if isempty(K)
044   K = 1;
045 end
046
047 % Calculate damage
048
049 n = length(F);
050 amp = cmat2amp(param,F);  % Histrogram of ranges
051
052 m=length(beta); D=zeros(1,m);
053
054 for i=1:m
055   D(i) = K*sum((amp(:,1).^beta(i)).*amp(:,2));
056 end
057
058
059```

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

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