Advances in Acoustics and Vibration

Research Article

Hybrid Swarm Algorithms for Parameter Identification of an Actuator Model in an Electrical Machine

Table 3

Influence function for swarming.
Swarming
Ns 𝑥 𝑡 + 1 𝑖 𝑘 = 𝑥 𝑡 𝑖 𝑘 + s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖
Sd 𝑥 𝑡 + 1 𝑖 𝑘 = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 𝑥 𝑡 𝑖 𝑘 + | | | | r a n d ( 0 , 1 ) × 𝑠 × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 < 𝑠 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 − | | | | r a n d ( 0 , 1 ) × 𝑠 × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 > 𝑠 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 + r a n d ( 0 , 1 ) × 𝑠 × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ , o t h e r w i s e
NsSd 𝑥 𝑡 + 1 𝑖 𝑘 = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 𝑥 𝑡 𝑖 𝑘 + | | | | s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 < 𝑠 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 − | | | | s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 > 𝑠 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 + s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ , o t h e r w i s e
NsNd 𝑥 𝑡 + 1 𝑖 𝑘 = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 𝑥 𝑡 𝑖 𝑘 + | | | | s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 < 𝑙 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 − | | | | s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ | | | | i f 𝑥 𝑡 𝑖 𝑘 > 𝑢 𝑡 𝑘 𝑥 𝑡 𝑖 𝑘 + s i z e ( 𝐼 𝑘 ) × r a n d ( 0 , 1 ) × ( 𝑥 𝑡 𝑐 𝑘 − 𝑥 𝑡 𝑖 𝑘 ) ‖ 𝑋 𝑡 𝑐 − 𝑋 𝑡 𝑖 ‖ , o t h e r w i s e