PLAT: An Automated Fault and Behavioural Anomaly Detection Tool for PLC Controlled Manufacturing Systems

Algorithm 2

Function ⁢_Means_Algorithm().

  % all function parameters are passed by reference (⁢c++ style⁢) %

  % prm implies Function Parameter %

  % Apply (traditional) ⁢-means Algorithm on the transition time data-set

  (the initial cluster centers are stored in Clus_Avg⁢) %

() var repeat_ _means = true;    % repeat until a condition is met %

() do     % classify the samples according to the nearest mean

  (the sorted mean values are stored in Clus_Avg⁢) %

  % in other words, split the array into partitions based on the distance from

  nearest mean (note: Time_Array⁢ is also a sorted array) %

()   var temp = 0;

()   for   to   do   % calculate the distances from the centres %

()     var dist1 = Time_Array⁢  −  Clus_Avg⁢temp⁢;

()     var dist2 = Time_Array⁢  −  Clus_Avg⁢temp + 1;

()     if  dist1 > dist2  then  % determine the new splitting positions %

()      Pos⁢temp⁢ = ; temp = temp + 1;

()     if  temp == ()  then  break;  % exit the loop %

     end for

()   declare Old_Clus_Avg⁢  % stores the means of the previous iteration %

()   for   to   do  % shift the mean values to Old_Clus_Avg  %

()     Old_Clus_Avg⁢] = Clus_Avg⁢]; Clus_Avg⁢ = 0

    end for

  % calculate the means of the (new) clusters and store them in Clus_Avg⁢  %

()   for   to   do

()     var temp1 = −1; var temp2 = −1;

()     if    then

()      temp1 = 0; temp2 = Pos⁢;

()     else if    then

()      temp1 = Pos⁢; temp2 = Pos⁢;

()     else

()      temp1 = Pos⁢; temp2 = ;

()     for   = temp1 to temp2  do

()       Clus_Avg⁢ = Clus_Avg⁢ + Time_Array⁢;

      end for

()     if  Clus_Avg⁢  then

()      Clus_Avg⁢ = Clus_Avg⁢/(temp2 − temp1 + 1);

    end for

()   repeat_⁢_means = false;

()   for   to   do

()     if  Clus_Avg⁢ − Old_Clus_Avg⁢ > (very small) threshold value

  then     % refers that the cluster means are significantly different %

()       repeat_⁢_means = true; break;   % another iteration %

     end for

() while  repeat_⁢_means ≠ false   % termination condition %

  % note: ⁢_Means_Algorithm⁢() only updates the mean values

  (stored in Clus_Avg⁢) and the array splitting positions (stored in Pos⁢) %