1#. • Basis Weight Control System
k v k jn + c 1 r 1 ( p jn ϖ x jn ) + c 2 r 2 ( p gn ϖ
= w
v k + 1 jn x jn ) x
k + 1 jn (2) where r 1 and r 2 represent random numbers between 0 and 1, c 1 and c 2 are cognitive and social coefficients, w represents the inertia weight that decays linearly with the number of iterations and is expressed as w = w max ϖ ( w max ϖ w min ) iter / iter max , iter and iter max represent the current iteration number and maximum number of iterations, respectively, and w max and w min are 0.9 and 0.4, respectively. Fig. 3 illustrates a working principle of PSO, which helps to better understand its operation mode. = x jn + v k + 1 jn
` 2EVIEW`OF`THREE`03/`STRATEGIES Since the introduction of the PSO method, it has been applied in several applications, such as system identification [19] , odor source localization [30] , defense against synchronization (SYN) flooding attacks [31 32] , and other complex issues [33] . Here, several PSO algorithms are reviewed and become the performance measurement of SNPSO. 4.1 Ȟ PSO algorithm PSO is an intelligent search algorithm that mimics the social behavior of birds. Every particle in PSO is initialized at a random position within a given search space. These particles collect and exchange information with each other centered on their location. Furthermore, the positions of these particles are updated at a certain speed according to the effective information. Assuming that the dimension of the search space is N , for particle j , the position vector X j and velocity vector V j can be written as X j = ( x j 1 , ..., x jn ) and V j = ( v j 1 , ..., v jn ), respectively. The best position pbest j of the j -th particle is the best previous position that gives the best fitness value, and is expressed as pbest j =( p j 1 , ..., p jn ). The best one among all the positions of particles is the global optimal position gbest , it is expressed as gbest = pbest g = ( p g 1 , ..., p gN ). Each particle modifies its position according to a certain speed v jn ( n =1, ..., N ), and the distance forms the individual optimal and global solutions, pbest jn and gbest n , respectively. The new velocity and position updating equations of each particle in the next iteration are given by: Note: Ȟ n ( t ) is noise signal. 'JH Ȟ Block diagram of system identification based on PSO/ IPSO
4.2 Ȟ PSO-TVAC algorithm The time-varying inertia weight can make PSO algorithm converge to the solution with higher accuracy. However, the cognitive coefficient c 1 and social coefficient c 2 are 'JH Ȟ Flowchart of PSO working principle
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