Case Leastsquares noisefree

Table 5.2 summarizes the obtained results of the noise-free simulations performed on the DAWIDUM model Beamlsd using a least-squares method. The first column indicates the run number. The second till the fifth column specify the initial values of the tunable parameters. For example, Cz1 = 135% means that the initial value of the torsional spring constant between the first and the second rigid body is set to 135% of the real value (i.e. 6.5973 • 109). The sixth column shows the number of iterations it took to converge to to a local or to the global minimum. Again it is possible to make a distinction between a local and the global minimum since the real parameter vector is known.

It can be concluded that in this case the least-squares method greatly reduces the number of iterations. Consequently, the amount of time it takes to perform an optimization is decreased, since the majority of the optimization time is spent conducting simulations. Furthermore, the region of convergence is increased from —30% < A0O < +35% to —40% < A0O < +45%.

x 10

x 10

200 400 No. iterations Keq12

x 10

200 400 No. iterations Keq12

200 400 No. iterations

x 10

200 400 No. iterations

x 10

x 10

200 400 No. iterations Keq23

x 10

200 400 No. iterations Keq23

200 400 No. iterations

x 10

200 400 No. iterations

Figure 5.6: Convergence of the parameters for run NM6 (noise-free simulations performed on Beamlsd using Nelder-Mead simplex method; initial values of the tunable parameters: Czl = Cz3 = 8.9064 • 109; Keql2 = 4.995 • 107; and Keq23 = 4.3875 • 106).

Run

Noise-free simulations: "Beamlsd"

A CA

A*«,*

^

Minimum

LSO

55%

55%

55%

55%

62

local

LS 1

60%

60%

60%

60%

195

global

LS2

75%

75%

75%

75%

165

global

LS 3

90%

90%

90%

90%

106

global

LS 4

100%

100 %

100 %

100%

37

global

LS 5

110%

110%

110%

110%

128

global

LS 6

125%

125 %

125 %

125%

95

global

LS 7

145%

145 %

145 %

145%

186

global

LS 8

150%

150 %

150 %

150%

99

local

LS 9

135%

65%

65%

135%

122

global

Table 5.2: Model updating results for Beamlsd. Case 2: least-squares (noise-free).

Table 5.2: Model updating results for Beamlsd. Case 2: least-squares (noise-free).

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