Automated Design of an FDI System for the Wind Turbine Benchmark

Algorithm 2

Find a computation sequence.

(1):    function FINDCOMPUTATIONSEQUENCE(𝐸^,𝑋^)

(2):  𝒞∶=∅

(3):  𝑆∶=FINDALLSCCS(𝐸^,𝑋^)

(4):     for 𝑖=1,2,…,|𝑆|  do

(5):     (𝐸_𝑖,𝑋_𝑖)∶=𝑆(𝑖)

(6):    𝐷_𝑖∶=DIFF(𝑋_𝑖)

(7):    𝑍_𝑖∶=var_𝐷(𝐸_𝑖)∩𝐷_𝑖

(8):    𝑊_𝑖∶=𝑋_𝑖⧵UNDIFF(𝑍_𝑖)

(9):    if not ISINITCONDKNOWN(𝑍_𝑖)  then

(10):   return  ∅

(11):  end If

(12):  𝐸_𝑍𝑖∶=GETDIFFERENTIALEQUATIONS(𝐸_𝑖,𝑍_𝑖)

(13):  𝐸_𝑊𝑖∶=𝐸_𝑖⧵𝐸_𝑍𝑖

(14):  𝑆_𝑍𝑖∶=FINDALLSCCS(𝐸_𝑍𝑖,𝑍_𝑖)

(15):  for 𝑗=1,2,…,|𝑆_𝑍𝑖|  do

(16):   (𝐸^𝑗𝑍_𝑖,𝑍^𝑗𝑖)∶=𝑆_𝑍𝑖(𝑗)

(17):   if ISTOOLSOLVABLE(𝑍^𝑗𝑖,𝐸^𝑗𝑍_𝑖)  then

(18):     APPEND(𝒞,(𝑍^𝑗𝑖,𝐸^𝑗𝑍_𝑖))

(19):   else

(20):    return  ∅

(21):   end if

(22):  end for

(23):  if ISJUSTDETERMINED(𝐸_𝑊𝑖,𝑊_𝑖)  then

(24):   𝑆_𝑊𝑖∶=FINDALLSCCS(𝐸_𝑊𝑖,𝑊_𝑖)

(25):   for 𝑗=1,2,…,|𝑆_𝑊𝑖|  do

(26):    (𝐸^𝑗𝑊_𝑖,𝑊^𝑗𝑖)∶=𝑆_𝑊𝑖(𝑗)

(27):    if ISTOOLSOLVABLE(𝑊^𝑗𝑖,𝐸^𝑗𝑊_𝑖)  then

(28):     APPEND(𝒞,(𝑊^𝑗𝑖,𝐸^𝑗𝑊_𝑖))

(29):    else

(30):       return  ∅

(31):     end if

(32):    end for

(33):   else

(34):    return  ∅

(35):   end if

(36):   end for

(37):   return  𝒞

(38):   end function