1#. • Basis Weight Control System
selected as their dynamic coefficients. A mutation rule with strange nonchaotic characteristics is applied for each particle. If r 3 >0.9, then n =[ N·r 4 ], x jn = x min +( x max ϖ x min ) ŷ j , and r 3 and r 4 are random values in the range of [0, 1]. ŷ j is the normalized strange nonchaotic sequence. The process of the proposed SNPSO algorithm is illustrated in Fig. 5.
higher quality initialization particles, the strange nonchaotic sequence is employed to generate particles instead of random generation. Because the random distribution is not affected by external forces, the distribution of strange nonchaotic sequences can be altered according to the change of parameters. Therefore, we can determine a group of strange nonchaotic particles uniformly distributed in the target space, which can overcome the uncertainty of the particle mass of the random sequence. It is also adopted to replace the linear attenuation weight to improve the convergence speed of the algorithm. From Fig. 4(b), we observe that the randomness of strange nonchaotic sequences is different from that of linear decay sequences. The strange nonchaotic sequences will quickly determine a valid value of w v , and the non-repetition strange nonchaotic sequences will continue to search for a better value of w near the valid value ( w v ). Eq. (6) and Eq. (7) are 'JH Ȟ (a) phase diagram and (b) time sequence diagram of a strange nonchaotic attractor for a =0.5965 and č =0.1
'JH Ȟ Flow chart of SNPSO algorithm
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