Systems, Man & Cybernetics - January 2016 - 31

101

100

HPSOM
HGAPSO
HPSOWM
CLPSO
OPSO
APSO
PICDPSO-M

0.44
0.42
Resistance (Ω)

Mean Fitness

HPSOM
HGAPSO
HPSOWM
CLPSO
OPSO
APSO
PICDPSO-M

0.4
0.38
0.36
0.34
0.32

10-1

0.3
0

50

100
150
200
Iteration Number

250

300

Figure 6. the convergence curve of PSOs on PmSm

100
150
200
Iteration Number
(a)

250

300

Flux Linkage (wb)

0.0795
0.079
0.0785
0.078
0.0775

HPSOM
HGAPSO
HPSOWM
CLPSO
OPSO
APSO
PICDPSO-M

0.077
0.0765
0.076
0

50

100
150
200
Iteration Number
(b)

250

300

250

300

d-Axis Inductance (H)

× 103
4
3.5
3
2.5

HPSOM
HGAPSO
HPSOWM
CLPSO
OPSO
APSO
PICDPSO-M

2
1.5
1
0.5
0

50

100
150
200
Iteration Number
(c)

× 10-3

4.1
q-Axis Inductance (H)

Experiment Results and Analysis
The convergence rates of different PSOs are shown in
Figure 6, as well as a comparison between PICDPSO-M
and other hybrid PSOs. It is obvious that PICDPSO-M
shows the best performance in terms of mean and standard deviations. In Figure 6, the convergence speed of
PICDPSO-M is faster than other hybrid PSOs. This
proves that the designed cost function based on reality
data-driven operations is a nonlinear multimodal with
local minima, and the poor performance of the identification method will progress from convergence to
localization. Therefore, an adaptive approach must be

50

0.08

parameter estimations.

algorithm (HGAPSO) [18], hybrid PSO with a wavelet
mutation (HPSOWM) [19], comprehensive learning PSO
(CLPSO) [20], adaptive PSO (APSO) [21], and oppositionbased learning PSO (OPSO) [22]. The setting of parameters for PICDPSO-M is as follows: The inertia weight
z in (5) is set to be z ! [0.4, 0.90] and linearly decreases as in [21], and the acceleration coefficients c1 and c2
are both set to be 1.49445. The maximum iteration is set
to be 300 and the runs number is 30 for the hybrid PSOs
using the same objective function. The software computing platform was Visual Studio 2010. All experiments
were implemented on one computer with an Intel i5
quad-core CPU. Parallel programming was developed
with OpenMP, standard, on a shared-memory computer
system with a multicore CPU. The OpenMP architecture
prov ided a fork-joi n prog r a m m i ng model for a
multithreaded standard, which did not require a large
amount of code restructuring for parallelization, and neither was it required to handle communication issues
[15], as is shown in Figure 5. The PICDPSO-M can be efficiently implemented in parallel with a multicore computing a rchitecture because the bioinspired swa r m
optimization method possesses natural parallelization.
The swarms are distributed among the threads and calculated by observing the OpenMP standard.

0

4
3.9
3.8

HPSOM
HGAPSO
HPSOWM
CLPSO
OPSO
APSO
PICDPSO-M

3.7
3.6
3.5

0

50

100
150
200
Iteration Number
(d)

250

300

Figure 7. Identified parameters under normal
temperature: (a) estimated winding resistance,
(b) estimated rotor flux linkage, (c) estimated d-axis
inductance, and (d) estimated q-axis inductance.

Ja nu a r y 2016

IEEE SyStEmS, man, & CybErnEtICS magazInE

31



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - January 2016

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