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2
0,1 1
0,05
0
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35
Stroke [m]
0,08 t3 [s] 3
1
0,07
5
0,06
0,05 2
4
0,04
0,03
0,02 0
0,01
0,0
0,1 0,2 0,3
Stroke [m]
Fig. 5.a) Value of the opening time t1 and the piston stroke x, b) Value of time t3 and the piston stroke x, for different initial air pressure values (de-noted with values [bar] near the curves).
As an introduction for some effective conclusions a lot of experiments (over 800) have been performed. The relation form, between the piston stroke x and the valve opening time t1 for the different initial air pressure, was expectable and an approximation of corresponding function can be easy. However a corresponding relation of time t3, Fig. 5b, was hard to explain and to estimate by any reasonable determinis-tic function. After the testing of many approximation methods for a development of a compact rules for the times t1, t2, t3 an application of neural networks has been considered and a set of three multi-layer perceptrons was used. In the experiments were observed many cases, where the initial pressure values p10 and p20 had not satisfied equilibrium conditions (2). This effect was resulted by the adhesive friction force that was quite respectable up to 45N. Therefore initial pressure values were considered as different inputs for the nets. The single
parameter tk was determined as the output of one network with inputs being: the pressure p1 and p2, the initial position xp and the desired final piston position xk.
The resulting net structures (calculated with Statistica pack-age) were simple and composed of initial layer and two or three hidden neurons and output nod with application of see Fig. 6. The net quality value and the correlation factor for verification set in case of the t1 were quite good and equal respectively: 0.106 and 0.987 and for the t3 were even better: 0.0243 and 0.9997
p10 a. p10 b.
p20 p20
xp xp
xk xk
Fig.6 Structures of the neural nets for: a) time t1, b) time t3
Relative errors of time t1
0,25
0,2
0,15