45 Identification of Acoustic Emission Signals …
519
follows:
δ = δ 0
x
t
i − x best
(45.2)
where δ 0 is a constant and generally takes the value δ 0 = 0.01. x best is the current
optimal value. levy(β) is a step size of Lévy flight, a Lévy flight is performed as
follows:
levy(β) ∼ μ = t
−β
, 1 < β ≤ 3
(45.3)
However, in order to make the calculation simple in practice, levy(β) is also
expressed as follows:
levy(β) =
φ ∗ μ
|ν|
−β
(45.4)
where μ, ν obey the normal distribution of the standard vertebra, such as μ ∼ N (0, 1)
and ν ∼ N (0, 1); β is a Lévy flight parameter (β = 1.5). φ is usually expressed as
follows:
φ =
⎛
⎝
(1 + β) ∗ sin
π ∗
1
2
β
1+β
2
∗ β ∗ 2
β−1
2
⎞
⎠
−β
(45.5)
In summary, the expression of the new position in the cuckoo algorithm as follows:
x
t+1
i
= x
t
i + δ 0
φ ∗ μ
|ν|
−β
x
t
i − x best
(45.6)
In addition, a fraction of the solution are abandoned and build a biased random
walk shown as follows:
x
t+1
i
= x
t
i + γ
x
t
g − x
t
k
(45.7)
where γ ∈ [0, 1] denotes scaling factor; x
t
g , x
t
k are the locations of two nests randomly
selected in the tth generation. The pseudocode of cuckoo search (CS) is illustrated
in Fig. 45.1.
45.2.2 Cuckoo Search Algorithm Optimization BP Neural
Network
The BP network structure is initially determined based on the data sample dimension,
and the total number of weights and thresholds is determined, then the code length
519
follows:
δ = δ 0
x
t
i − x best
(45.2)
where δ 0 is a constant and generally takes the value δ 0 = 0.01. x best is the current
optimal value. levy(β) is a step size of Lévy flight, a Lévy flight is performed as
follows:
levy(β) ∼ μ = t
−β
, 1 < β ≤ 3
(45.3)
However, in order to make the calculation simple in practice, levy(β) is also
expressed as follows:
levy(β) =
φ ∗ μ
|ν|
−β
(45.4)
where μ, ν obey the normal distribution of the standard vertebra, such as μ ∼ N (0, 1)
and ν ∼ N (0, 1); β is a Lévy flight parameter (β = 1.5). φ is usually expressed as
follows:
φ =
⎛
⎝
(1 + β) ∗ sin
π ∗
1
2
β
1+β
2
∗ β ∗ 2
β−1
2
⎞
⎠
−β
(45.5)
In summary, the expression of the new position in the cuckoo algorithm as follows:
x
t+1
i
= x
t
i + δ 0
φ ∗ μ
|ν|
−β
x
t
i − x best
(45.6)
In addition, a fraction of the solution are abandoned and build a biased random
walk shown as follows:
x
t+1
i
= x
t
i + γ
x
t
g − x
t
k
(45.7)
where γ ∈ [0, 1] denotes scaling factor; x
t
g , x
t
k are the locations of two nests randomly
selected in the tth generation. The pseudocode of cuckoo search (CS) is illustrated
in Fig. 45.1.
45.2.2 Cuckoo Search Algorithm Optimization BP Neural
Network
The BP network structure is initially determined based on the data sample dimension,
and the total number of weights and thresholds is determined, then the code length