+

2 + +

+

ˆ ˆ

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ

ˆ ˆ ˆ ˆ 2

ˆ

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ

ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ = 2 1 1 2 1 1

ˆ ˆ ˆ ˆ ˆ

+ +

+

+

ˆ ˆ ˆ

+

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ ˆ

+

+

+ +

<, > = <, >

(, )

-------------[INITIALIZATION COMPONENT] 1 -------------[DETECTION COMPONENT] <= == > == <= { } + -------------[FILTERING COMPONENT]

< { } { } >> >> { }

( ) = { < < 0 = 1 1 1, 1, < < 1, ( ) = 2 2, 2, < < 2,, 0, < <,

A A = {, ( ), ( ), ( )} ( ) : = 0, 1,... ( ) : = 0,..., 1440 ( ) : = 0, 1,...

( ) ( ) ( ) ( ) ( ) ( ) = N ( µ, σ ) = ( ) ( ), = 1,..., N ( µ, σ ), = 1,..., µ σ A R R R = {<, A,θ >: = 1,..., },θ A,θ

θ θ θ {1,..., 1440} (( = ) ( = 1)) (( = 1) ( > 1)) (( = 2) ( > 2))... ( ) τ ( ) = ( ) ( τ) ( > τ) (τ) =0 τ=0 τ ( ) ( ) ( ) R 1440 R = ( ) =1

ˆ ˆ ˆ

= 1 1 υ υ 100 υ = 1 1 σ υ 100 σ

= 1 =1 + 100 5.98 ± 4.29 8.16 ± 7.31 8.74 ± 6.44 14.24 ± 7.78 11.08 ± 9.66 10.51 1.28

± ± ± ± ± ± ± ± R

= =1 (υ ) 2 υ = =1 υ υ 100 υ ( ) = 1 2 ( ) + 1 2 ( ) = 1 2 ( + ) ( ) ( ) = ( ( ) ( ) ) ( )

+ 8.52 2.78 7.61 ± 5

16 6.03 ± 3.85 0.59 ± 0.48

+ + 3 + +

+ + +

2

+

ˆ ˆ

ˆ 2 A = {, ( ), ( ), ( )}

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = ( ) ( )

( ) ( ) = 1440 =1 ( ) ( ) 1440 =1 ( ) ( )

( ) (, ) ( ) (, ) ( ) ( ) ( )

(, ) ( ) = ( ) (1 + ( (, ), ( ))) ( (, ), ( )) ˆ ˆ

( (, ), ( )) 2 (, ) ( ) < 1 ( (, ), ( )) = 2 1 1 ( ( ) 1) (, ) 1 ( ) < 1 4 3 1 ( ( ) 1) (, ) 1 ( ) < 3 4 (, ) ( ) > 3 1, 2, 3, 4 R 1, 3 1 ( ) ˆ ( ) = ( ) 1440 =1 ( ) ( )

1 = 0 2 = 10 3 = 3 4 = 5 (, ) =, {0, 1440} ( ) < 1

( ) > 1 {, } N (, 2 ) 0 < < (, ) = 0 < N (, 2 ) > N (µ, σ) µ σ

(, ) = ( ), {0, 1440} ( ) ( ) = ( ( ) 1) ( ) ( ) ( ) ( ) > 1 ( ) = 0, : >

{ ( ) ( ) = ( ) = ( ) (1 + ( )) 1 ( ) = 1 ( ) ( 1 ) 1 ( ) < 1 { ( ) ( ) = 0 ( ) = ( ) (1 + ( )) 1 (0) = 0 = 1 (0) (1) = 0 = 1

(, ) = ( ) ( ) ( ) ( ( )) {0, 1440} (, ) (, ) ( ( )) 2 ( ) < 1 ( ( )) = 2 1 1 ( ( ) 1) 1 ( ) < 1 4 3 1 ( ( ) 1) 1 ( ) < 3 4 ( ) > 3 (, )

ˆ ˆ ˆ

= 42 ±8 29 ± 12 15 ± 4 29 ± 12 25 400 ±80

31 ± 8 100

> 1

= E ( ) E ( ) E 100 ( ) {0, 1440} E E = E ( ) E ( ) E 100 ( ) {0, 1440} = 1440 =1 E ( ) 1440 1440 =1 E ( ) =1 E ( ) 100

10.97 ± 5.14 3.66 ± 3.94

9.83 ± 5.00 0.59 ± 0.48

+ 6.86±2.58 3.26±2.90

+ + + +

ˆ ˆ

= ( 1, 2,...,,..., ) X = : = 1,...,,, ˆ = (, )/(,, ) = ( 1, 2,..., ) C = : = 1,..., Ω N

-------------[INITIALIZATION COMPONENT] ϵ 10 5 -------------[PEAK DETECTION COMPONENT] < > ϵ ϵ -------------[POST PROCESSING PEAK LIST] <

-------------[INITIALIZATION COMPONENT] ϵ 10 5 -------------[PEAK DETECTION COMPONENT] <= > ϵ ϵ -------------[POST PROCESSING VALLEY LIST] <

( ) = ( ) =1.. ( )

-------------[INITIALIZATION COMPONENT] -------------[ITERATION COMPONENT] < > >

,,

= { = (, ) > 0, 5 = (, + ) 0, 5

(, ) (, ) = (1 1 ( ) )

= 1 2( ), : Ω =1 + = 1 2 (, Ω ) =1 + = 1 =1 / ˆ 2 (Ω ) ˆ ( ) + = > {(1 1/ [ (, )]) 1 } :, = 1,...,

= 1 { (ˆ (Ω ) + ˆ (Ω ) )/ (, )} :, = 1,..., =1 = 2( / ), 2( ), =1 Ω 1 < (, Ω ˆ (Ω ) Ω (, ) Ω (, Ω ) = 2 (, )/N Ω Ω ˆ (Ω ) = 1 2N Ω 2 (, Ω )

,, = (,, ),,, = λ T λ λ [0, 1] λ = 0 λ

λ λ = 0.1 = (,,,,,,,, x ) x = E ( ) E ( ) E 100 ( ) {0, 1440} E

E = (( ) ( )) = 1,...,

ˆ ˆ = ( ) ( ) 100 ( ) {0, 1440}

+

+ + + +

ˆ ˆ ˆ

: 1 : P 1 : 1,,, : = {, } = { } = {, }

ˆ ˆ ˆ : 1 : P 1 : 1 1 : 1 1 : 1 P 1 {, } = {} = {, } = {,, } ˆ ˆ

: P 1 : 1 ( ) : ( ),, ::= {, } = {, } = { } = {, } ˆ ˆ ˆ : : 1 : (P 1 P 1 ) : 1 = {, } = {, } = {, }

ˆ ˆ : : 1 : 1 P : 1 P : (P P P ) : ( 1 ) 1 ::= {,, } = {, } = { } = {,,, }

ˆ ˆ ˆ ˆ : 1 : P 1 : P 1 P = {} = { } = {,, }

ˆ ˆ

ˆ ˆ ˆ ˆ

θ

ˆ ˆ

ˆ ˆ

ˆ ˆ

+ ˆ ˆ

E = =1 (, ) µ µ

µ = 1; 0 µ 1, =1 (, ) = µ (, ) =1 =1 / µ ( +1) = 1 =1 (, ( ) ) (, ( ) ) ( +1) = ( =1 ( µ ( +1) ) )/ =1 ( µ ( +1) (1, ) )

( ) ( ) : R R R R R ˆ

= [ 1 ( ), 2 ( ),..., ( )] ( ) 0 = 1, 2,..., ( ) = 0 = 1, 2,..., = [ 1, 2,..., ], = 1,...,, R = 1,..., X R X X F R F F P P = { F } PF PF = { R P }

F ˆ ˆ

ˆ ˆ

D D = + (0, ϕ 1 ) ( ) + (0, ϕ 2 ) ( ) = + (0, ϕ 1 ) ϕ 1

-------------[INITIALIZATION COMPONENT] -------------[ITERATION COMPONENT] > + ϕ 1 ϕ 2

+ ϕ 1 = ϕ 2 = 2 + = ω + (0, ϕ 1 ) ( ) + (0, ϕ 2 ) ( ) = + ω (0, ϕ 1 ) ( ) + (0, ϕ2 ) ( ) = (1 ω) (1 ω)

ϕ 1 ϕ 2

= 2

ˆ ˆ

ˆ ˆ

ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆ +1 = ( 1 + β ) + + 365 β β = 10 +1 = ) (1 + β + + 365

β = 5 ˆ ˆ

ˆ

ˆ ˆ ˆ ˆ [ + 1, + 2,..., + 24]

( ) = (1 )/ [0, ) ( ) = 1 (1 ) +1

ω 1440 ( > ) ω (1 ) +1 ω ω (1 ) 1 ( > ) ω 1 +1 ω 1 ω = 0.01 = 120 1 121 0.01 = 0.037 [ ω, 1] ω 0.01 = 0.037 ˆ

ˆ ˆ ˆ ˆ ˆ ˆ

= (,,,,,,,, x ),,,,

x,, = [0.. ] = =0 (,,, +, ),, = =0 (,,,, +, ) + (, +, +, ),, = (1.0, / ) = =0 (,,, +, ) η = 0 < η < 1

η < 0 η > 1 = η x x x [0..1] x [0..1] (/) η x > 1 = =1 =1,,, [0, 5]

= 4 3 5 T = 3 4 5 = 60 T P = λ T λ λ [0, 1] λ = 0 λ 1

< > <,, > <, > <, > <, > << 1, 1,, 1,, 1, >..., <,,,,,, >> <, > <,, > <, > < P 1, P 1 > <,,, > <, >

2

+

+

+ +

+

+ +

+

+ +

+

+

+ +

+ + +

+

+ +

+ 2 +

+

+

+ + + +