Vychislitelny_praktikum

							1
(δ3M				0 )
					i0.867
(δ3M				1 )
					i0.733
(δ3M				2 )		0.6
					i
(δ3M 3 )
(δ3M				4 )i0.467
					i
					0.333
						0.2 0									2				4	6	8	10
																				i 0.1+0.01
(			0 )			= 0.519
min δ3M
	(			(			0 )					0 )							3.41
match					δ3M					,δ3M				0.1		+ 0.01 =
		min																	3.51
																			3.61
χminM				:= match				(		(	δ3M		0 )		,	δ3M	0 )		0.1	+ 0.01
		0							min									1
(			1 )			= 0.439
min δ3M
match	(			(	δ3M		1 )			,δ3M		1 )		0.1 + 0.01 = ( 1.81)
		min
χminM				:= match				(		(	δ3M		1 )		,	δ3M	1 )		0.1	+ 0.01
		1							min									0
(			2 )			= 0.375
min δ3M
match	(			(	δ3M		2 )			,δ3M		2 )		0.1 + 0.01 = ( 2.21)
		min
χminM				:= match				(		(	δ3M		2 )		,	δ3M	2 )	0 0.1		+ 0.01
		2							min

223

min(δ3M 3 ) = 0.316

match(min(δ3M 3 ),δ3M 3 ) 0.1 + 0.01 = ( 1.41)

χminM3 := match(min(δ3M 3 ),δ3M 3 )0 0.1 + 0.01

min(δ3M 4 ) = 0.273

match(min(δ3M 4 ),δ3M 4 ) 0.1 + 0.01 = ( 1.61)

χminM		:= match		( (	δ3M	4 )	,δ3M	4 )	0 0.1	+ 0.01
	4			min
			1.81
			3.51
χminM = 2.21
			1.41
			1.61

j := 0.. 4 min(δ3M j )

0.519

0.439

0.375

0.316

0.273

4. Построить графические зависимости от параметра , m; = 0 - 5 m = 2 - 6, opt.

ω1 := 0.. 5

δ4V0ω1	:= δ1(χminM0,2,ω1)	δ4V2ω1	:= δ1(χminM2,4,ω1)	δ4V4ω1 := δ1(χ ,6,ω1)
δ4V1ω1	:= δ1(χminM1,3,ω1)	δ4V3ω1	:= δ1(χminM3,5,ω1)

224

δ4M 0 := δ4V0				δ4M 2 := δ4V2			δ4M 4 := δ4V4
δ4M 1 := δ4V1				δ4M 3	:= δ4V3
		0.6
(δ4M 0 )		ω10.5
(δ4M	1 )
		ω2
(δ4M	2 )	0.4
		ω1
(δ4M	3 )	0.3
		ω1
(δ4M	4 )	ω10.2
(δ4M	5 )	ω10.1
		0	1	2	3	4	5
				ω1
m2 := 2.. 6
δ5V0m2 := δ1(χminMm2−2,m2,0)				δ5V2m2 := δ1(χminMm2−2,m2,2)			δ5V4m2 := δ1(χminMm2−2,m2,4)
δ5V1m2 := δ1(χminMm2−2,m2,1)				δ5V3m2 := δ1(χminMm2−2,m2,3)			δ5V5m2 := δ1(χminMm2−2,m2,5)

δ5M 0	:= δ5V0	δ5M 2	:= δ5V2	δ5M 4	:= δ5V4
δ5M 1	:= δ5V1	δ5M 3	:= δ5V3	δ5M 5	:= δ5V5

225

	0.6
(δ5M 0 )
(δ5M	1 )m20.5
	m2
(δ5M	2 ) 0.4
	m2
(δ5M	3 ) 0.3
	m2
(δ5M	4 )
	m20.2
(δ5M	5 )
	m20.1
		2	2.8	3.6	4.4	5.2	6
				m2
5. Построить графические зависимости					от параметра , m;		= 0 - 5 m = 2 - 6, .
t := 1		8 0.02
	λ	ω	2
		λ	− 1

	χ1m2	:=		0.4			χ1m2 =		0.4
			(m2	+ 1)	t			χ1c(mx) :=
									(mx + 1) t
							1.633
							1.225
							0.98
							0.816
							0.7

δ6V0ω1 := δ1(χ12,2,ω1)		δ6V2ω1 := δ1(χ14,4,ω1)		δ6V4ω1 := δ1(χ16,6,ω1)
δ6V1ω1 := δ1(χ13,3,ω1)		δ6V3ω1 := δ1(χ15,5,ω1)
δ6M 0	:= δ6V0	δ6M 2	:= δ6V2	δ6M 4 := δ6V4
δ6M 1	:= δ6V1	δ6M 3	:= δ6V3

226

			0.8
(δ6M 0 )		ω10.667
(δ6M 1 )		ω10.533
(δ6M 2 )
		ω1	0.4
(δ6M 3 )
		ω10.267
(δ6M 4 )
		ω1
		0.133
				0	1	2	3	4	5
						ω1
δ7V0m2 := δ1(χ1m2,m2,0)						δ7V2m2 := δ1(χ1m2,m2,2)			δ7V4m2 := δ1(χ1m2,m2,4)
δ7V1m2 := δ1(χ1m2,m2,1)						δ7V3m2 := δ1(χ1m2,m2,3)			δ7V5m2 := δ1(χ1m2,m2,5)
δ7M 0		:= δ7V0				δ7M 2 := δ7V2			δ7M 4 := δ7V4
δ7M 1		:= δ7V1				δ7M 3	:= δ7V3		δ7M 5 := δ7V5
				0.8
(δ7M 0 )
(δ7M	1 )m20.667
			m2
(δ7M	2 )			0.533
			m2
(δ7M	3 )			0.4
			m2
(δ7M	4 )		m20.267
(δ7M	5 )		m20.133
				2	2.8	3.6	4.4	5.2	6
							m2
									227

	λ2 + ω2
χ2m2 := (m2 + 1)			χ2	m2	=		χ2c(mx) :=		λ2 + ω2
					1.7				(mx + 1)
				1.275
				1.02
				0.85
				0.728
δ8V0ω1 := δ1(χ22,2,ω1)						δ8V2ω1 := δ1(χ24,4,ω1)			δ8V4ω1 := δ1(χ26,6,ω1)
δ8V1ω1 := δ1(χ23,3,ω1)						δ8V3ω1 := δ1(χ25,5,ω1)
δ8M 0 := δ8V0						δ8M 2 := δ8V2			δ8M 4	:= δ8V4
δ8M 1 := δ8V1						δ8M 3	:= δ8V3
		0.8
(δ8M	0 )	ω10.667
(δ8M	1 )	ω10.533
(δ8M	2 )
		ω1 0.4
(δ8M 3 )
		ω10.267
(δ8M	4 )
		ω1
		0.133
		0	1			2	3	4	5
							ω1

228

δ9V0m2 := δ1(χ2m2,m2,0)		δ9V2m2 := δ1(χ2m2,m2,2)		δ9V4m2 := δ1(χ2m2,m2,4)
δ9V1m2 := δ1(χ2m2,m2,1)		δ9V3m2 := δ1(χ2m2,m2,3)		δ9V5m2 := δ1(χ2m2,m2,5)
δ9M 0	:= δ9V0	δ9M 2	:= δ9V2	δ9M 4	:= δ9V4
δ9M 1	:= δ9V1	δ9M 3	:= δ9V3	δ9M 5	:= δ9V5

		0.8
(δ9M 0 )
(δ9M	1 )m20.667
		m2
(δ9M	2 ) 0.533
		m2
(δ9M	3 )	0.4
		m2
(δ9M	4 )	m20.267
(δ9M	5 )	m20.133
		2	2.8	3.6	4.4	5.2	6
					m2

229

6. Построить модели корреляционной функции;				= 1,	= 5 m = 5/10,	opt.
	m
ρ(τ ,m,χ) :=	∑ (β5i(k ,χ ,ω) P7(k ,τ ,χ))
k = 0
Δτ := 0.081649		Nx := 37
τ := 0,0 + Δτ	.. (Nx − 1) Δτ
ρt(τ ) := e− λ τ cos (ω τ )
m_1 := 5
j := 0.. Nx − 1
ρ5χ1j := ρ(j Δτ ,m_1,χ1c(m_1))
ρ5χ2j := ρ(j Δτ ,m_1,χ2c(m_1))
ρ5χminj := ρ(j Δτ ,m_1,χminMm_1−2)
ρtj := ρt(j Δτ )
1
ρ5χ1 j
0.5
ρ5χ2 j
ρ5χmin j					0
0		1	2
ρtj
− 0.5
− 1
		j Δτ

230

δ3V8i := δ1(i 0.1 + 0.01,10,5)

δ3M 8 := δ3V8

min(δ3M 8 ) = 0.148

match(min(δ3M 8 ),δ3M 8 ) 0.1 + 0.01 = ( 1.11)

χminM8 := match(min(δ3M 8 ),δ3M 8 )0 0.1 + 0.01

m_2 := 10

ρ10χ1j := ρ(j Δτ ,m_2,χ1c(m_2))

ρ10χ2j := ρ(j Δτ ,m_2,χ2c(m_2))

ρ10χminj := ρ(j Δτ ,m_2,χminMm_2−2)

	1
	ρ10χ1 j
	0.5
	ρ10χ2 j
	ρ10χmin j		0
	0	1
			2
	ρtj
	− 0.5
	− 1
			j Δτ

231

Приложение 12

ВЫЧИСЛИТЕЛЬНЫЙ ПРАКТИКУМ 6. «АППРОКСИМАЦИЯ КОРРЕЛЯЦИОННЫХ ФУНКЦИЙ ОРТОГОНАЛЬНЫМИ ФУНКЦИЯМИ ПРИ ОГРАНИЧЕНИИ НА ЕЁ МОДЕЛЬ»

Цель работы: изучение метода и приобретение практических навыков при аппроксимации корреляционных функций случайных процессов ортогональными функциями при ограничении на её модель.

1. Определить коэффициенты разложения βκ и bκ. Построить графические зависимости βκ

иbκ от порядка κ; μ, m, γ.

λ:= 1

ω := 5

γ := 0.30619

m := 15

k := 0.. m

k

s

− (s+1) γ τ

P7(k ,τ ,γ ) := ∑

combin(k ,s) combin(k + s + 1,s + 1) (−1)

e

s = 0

⌠∞

− λ τ

β5Mk := 2γ (k + 1)

P7(k,τ ,γ ) e

cos (ω τ) dτ

⌡0

k

m

s

2 (−1)

(k + 1)

− ∑

1

(−1)

β5Ms

b5M k := β5Mk +

s = 0

(m + 1) (m + 2)

232