Advances in Acoustics and Vibration

Research Article

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

Table 2

Formulation for normative knowledge updating.
𝑙 𝑡 + 1 𝑗 = ⎧ ⎪ ⎨ ⎪ ⎩ 𝑥 𝑖 , 𝑗 i f 𝑥 𝑖 , 𝑗 ≤ 𝑙 𝑡 𝑗 o r 𝑓 ( 𝑋 𝑖 ) < 𝐿 𝑡 𝑗 𝑙 𝑡 𝑗 , o t h e r w i s e 𝐿 𝑡 + 1 𝑗 = ⎧ ⎪ ⎨ ⎪ ⎩ 𝑓 ( 𝑋 𝑖 ) i f 𝑥 𝑖 , 𝑗 ≤ 𝑙 𝑡 𝑗 o r 𝑓 ( 𝑋 𝑖 ) < 𝐿 𝑡 𝑗 𝐿 𝑡 𝑗 , o t h e r w i s e
𝑢 𝑡 + 1 𝑗 = ⎧ ⎪ ⎨ ⎪ ⎩ 𝑥 𝑘 , 𝑗 i f 𝑥 𝑘 , 𝑗 ≥ 𝑢 𝑡 𝑗 o r 𝑓 ( 𝑋 𝑘 ) < 𝑈 𝑡 𝑗 𝑢 𝑡 𝑗 , o t h e r w i s e 𝑈 𝑡 + 1 𝑗 = ⎧ ⎪ ⎨ ⎪ ⎩ 𝑓 ( 𝑋 𝑘 ) i f 𝑥 𝑘 , 𝑗 ≥ 𝑢 𝑡 𝑗 o r 𝑓 ( 𝑋 𝑘 ) < 𝑈 𝑡 𝑗 𝑈 𝑡 𝑗 , o t h e r w i s e
where the 𝑖 th individual affects the lower bound for variable 𝑗 , and the 𝑘 th individual affects the upper bound for variable 𝑗 . Note that 𝑡 denotes the current generation of the belief space.