Estimation of Contact Conductance Between Two Dissimilar Metal …
317
where n = number of measurement locations; tn = total time interval under
consideration.
T a (t) = Temperatures obtained from the direct problem (chosen measured temperature on rods).
T e (t) = Estimated temperatures.
The Jaya algorithm starts with random selection of ‘P’ number of candidate
solutions (i.e., population size, p = 1, 2, …, P) with ‘n’ measurement locations
(j = 1, 2, …, n). Let best candidate obtains the best value of objective function
J(h(t)) (i.e., J(h(t)) best), and worst candidate obtains the worst value of objective
function J(h(t)) (i.e., J(h(t)) worst) in the whole set of solutions. If h j,p,G is the value
of jth variable for pth candidate during Gth iteration, then this value is modified
according to following equation:
h(t)
j, p,G = h(t) j, p,G + r 1 j , G
h(t) j,best,G − |h(t) j, p,G |
− r 2 j , G
h(t) j,worst,G − |h(t) j, p,G |
(4)
where h(t)
j, p,G is updated value of variable h(t) j,p,G , and h(t) j,best,G and h(t) j,worst,G
are best and worse solutions of jth candidate. The r 1j,G and r 2j,G are random numbers
for jth variable during Gth iteration, and their range is [0, 1]. With Eq. (4), the inverse
solution will approach toward best and move far from the worst solutions. At the end
of current iteration, if h(t)
j, p,G gives better result than the previous, it is stored and
will go for the next iteration; otherwise, it is discarded, and old solution (h(t) j,p,G )
will be repeated for the next iteration. The computational algorithm of Jaya is shown
in Fig. 3.
The termination criteria involved in this work consists of two models. Firstly,
maximum error should be less than 10
–8 , or secondly, the algorithm terminates when
the number of iterations satisfied. When measurement errors are present in measured
data, the discrepancy principle is used for stopping criteria which is given by Ozisik
and Orlande [4],
J (h(t)) < Mσ
2 t f
(5)
where σ is standard deviation of measurement errors, M is number of measurement
locations, and t f is final time.
3 Results
Using MATLAB 2016b, experiments are carried out for 10, 30, and 50 populations.
Root mean square error is calculated for each case for the possible comparison.
317
where n = number of measurement locations; tn = total time interval under
consideration.
T a (t) = Temperatures obtained from the direct problem (chosen measured temperature on rods).
T e (t) = Estimated temperatures.
The Jaya algorithm starts with random selection of ‘P’ number of candidate
solutions (i.e., population size, p = 1, 2, …, P) with ‘n’ measurement locations
(j = 1, 2, …, n). Let best candidate obtains the best value of objective function
J(h(t)) (i.e., J(h(t)) best), and worst candidate obtains the worst value of objective
function J(h(t)) (i.e., J(h(t)) worst) in the whole set of solutions. If h j,p,G is the value
of jth variable for pth candidate during Gth iteration, then this value is modified
according to following equation:
h(t)
j, p,G = h(t) j, p,G + r 1 j , G
h(t) j,best,G − |h(t) j, p,G |
− r 2 j , G
h(t) j,worst,G − |h(t) j, p,G |
(4)
where h(t)
j, p,G is updated value of variable h(t) j,p,G , and h(t) j,best,G and h(t) j,worst,G
are best and worse solutions of jth candidate. The r 1j,G and r 2j,G are random numbers
for jth variable during Gth iteration, and their range is [0, 1]. With Eq. (4), the inverse
solution will approach toward best and move far from the worst solutions. At the end
of current iteration, if h(t)
j, p,G gives better result than the previous, it is stored and
will go for the next iteration; otherwise, it is discarded, and old solution (h(t) j,p,G )
will be repeated for the next iteration. The computational algorithm of Jaya is shown
in Fig. 3.
The termination criteria involved in this work consists of two models. Firstly,
maximum error should be less than 10
–8 , or secondly, the algorithm terminates when
the number of iterations satisfied. When measurement errors are present in measured
data, the discrepancy principle is used for stopping criteria which is given by Ozisik
and Orlande [4],
J (h(t)) < Mσ
2 t f
(5)
where σ is standard deviation of measurement errors, M is number of measurement
locations, and t f is final time.
3 Results
Using MATLAB 2016b, experiments are carried out for 10, 30, and 50 populations.
Root mean square error is calculated for each case for the possible comparison.