Artificial intelligence to aid in designing electromagnetic devices

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23 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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1

A
rtificial intelligence to aid in designing electromagnetic devices

b
y Jilu Mathew, ALSTOM SA


Abstract


We are at the break of a new dawn where we can now make use of artificial intelligence to design products
in industry to meet all the requirements of
the clients. As part of my design thesis at the university of Natal a fully
automatic system was developed to find the best shape of electromagnetic devices.

The performance of electromagnetic devices such as electrical machines and electromagnetic actua
tors is greatly dependant on
the shape of its core as the flux patterns are affected with the change in shape. To the design engineer finding the optimal
or
best shape is a time consuming and difficult process which is greatly determined by design constrai
nts and own experience.
However the right search methods or optimisation algorithms can be adapted to solve particular engineering probelms with
little computaional effort and at a reasonable time.

The optimisation algorithms used

Genetic Algorithm (GA) i
s a search method rooted in the mechanisms of evolution and natural genetics. GA combines the
principles of survival of the fittest with randomized information exchange. It generates a sequence of populations by using a

selection search mechanism (Tourname
nt Selection is used in this design) and uses crossover and mutation as the search
mechanisms to guide search towards the optimal solution [1].

Steepest descent moves in the direction of negative gradient for minimization and positive gradient for maximiza
tion [2]. In
order to terminate the algorithm we must find the position where gradient equals zero or is very close to it.

The objective function

The professional edition of Quickfield 5.0 was used to re
-
evaluate the objective function each time. The

GA module



.




Fig. 1. The three variable solenoid actuator model.

used in the design was integrated with Quickfield to solve for

the shape of the electromagnetic devices. The entire coding for
the system integration was done in the Vis
ual basic environment. The completed software system would thus rebuild, re
-
mesh
and solve the problem continuously until the termination criteria are met.



Fig. 2. The six variable 4

pole dc brushless machine.


The objective function is the only connec
tion between the physical problem being optimized and the genetic algorithm. The
objective function is also known as the fitness function as it is used to assign a fitness value to each of the individuals i
n the
GA population. In the automated system we ar
e designing the finite element analysis or FEA software tool will be used to

2

build the objective function that will produce the goal value or optimal solution we are trying to reach.


For the axisymmetric (cylindrical) actuator problem in fig.1 the object
ive function is:


F (X1, X2, X3) =


(Force on Plunger)






(1)


(Total Volume of Actuator)


For the miniature DC brushless machine shown in
F
ig.

2 the objective function is:


F (X1, X2, X3, X4, X5, X6) =


(Torque
on Rotor)



(2)





(Total Volume of Machine)


Results

In the actuator problem the results produced using the GA after 120 generations in one population run is shown in fig. 3. Usi
ng
a crossover probability of

0
,
8 and mutation probability of 0
,
05 with each generation consisting of 25 individuals or children
showed convergence at around the 20
th

generation as seen in the fig. 3. The estimated simulation time here is 10 hours. The
most optimal fitness value was f
ound in the 87
th

generation with X1 = 27 cm, X2 = 22 cm, X3 = 20 cm and

the force to
volume ratio is 0.2366 N/cm
3
.



Fig. 3: Plot of fitness of objective function value versus generation number for the 3 variable actuator problem.


The result is qu
ite noisy however this is expected as we are dealing with a nonlinear problem with no clearly defined bounds. If
we fine
-
tune the genetic algorithm further, perhaps varying the mutation and crossover operators we may obtain an improved
plot. It should be a
lso noted that once we pass the 40
th

generation there was no real significant improvement in the solution.


For the six variable dc brushless machine model the results were as follows:


Fig. 4:

Objective function fitness value versus generation number for

the six variable
DC

brushless machine model.


The population run was for 100 generations, again each generation consisting of 25 individuals and the time taken to complete

the simulation was approximately 20 hours. The probability of crossover was 0
,
8 and

probability of mutation was 0
,
08. Again
the output is quite noisy but this could be due to the high mutation probability used which was necessary the convergence
would have taken longer if a smaller mutation probability value was used.



3

At the 93
rd

gener
ation the optimum values for the dc brushless machine were X1= 2 mm, X2= 0.15625 mm, X3= 7

mm, X4=4 mm, X5=13 mm, X6=11 mm and torque to volume ratio is 2
,
72e
-
005 Nm/mm
3
.




Fig. 5: Quickfield plot of flux density distribution for the GA optimized full mo
del of DC brushless machine
.


The flux density distribution shows (
F
ig. 5) on average the flux density is around 2.1 Tesla on the stator back iron. The max
flux values are found in certain hotspots at the edges of the slot teeth. Although this yields a goo
d torque to volume ratio
practically we may want to increase the back iron of both the stator and rotor a little more to prevent overheating.

When employing the gradient method or steepest descent method after the GA run was completed it was observed that

for the
3 variable actuator problem an improvement of 0
,
42% was observed. With X1=27
,
36 cm, X2=21
,
62 cm, X3= 19
,
65 cm and
force to volume ratio at 0.237 N/cm
3
. For the six variable dc brushless machine a 7
,
4% improvement was obtained with X1 = 1
mm, X2 =
0
,
15625 mm, X3 = 8 mm, X4 = 4 mm, X5 = 19 degrees, X6 = 11 degrees and torque to volume ratio at 2.927E
-
05
Nm/mm
3
.

Conclusion

The genetic algorithm method arrived at the near optimal solution well before the 100 generation mark. Thus the design
engineer ca
n terminate the GA search much earlier if there is no significant improvement in the solution. A simplistic local
search technique such as the steepest descent method can be then employed to improve on the near optimal solution. Thus it
can be seen that o
ne can use artificial intelligence to aid in the design of electrical machines and actuators.
Other applications
also include the use of A.I. in cost optimization, in control systems and in stock market forecasting. Next time one should n
ot
be surprised to

hear that the design engineer is playing a round of golf whilst his A.I. is working for him.

References

[1]

Y

R Samii and E. Michielssen, “Electromagnetic Optimization by Genetic Algorithms”, Wiley.

[2]

Singiresu S Rao, “Engineering optimization, Theory and p
ractice”, Third edition, Wiley publication.