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Новые принципы формирования режимов периодического технического обслуживания воздушных судов по критериям безопасности полетов..pdf

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2015
ɇȺɍɑɇɕɃ ȼȿɋɌɇɂɄ ɆȽɌɍ ȽȺ
ʋ 219
ɍȾɄ 629.7.083
ɇɈȼɕȿ ɉɊɂɇɐɂɉɕ ɎɈɊɆɂɊɈȼȺɇɂə ɊȿɀɂɆɈȼ
ɉȿɊɂɈȾɂɑȿɋɄɈȽɈ ɌȿɏɇɂɑȿɋɄɈȽɈ ɈȻɋɅɍɀɂȼȺɇɂə
ȼɈɁȾɍɒɇɕɏ ɋɍȾɈȼ ɉɈ ɄɊɂɌȿɊɂəɆ ȻȿɁɈɉȺɋɇɈɋɌɂ ɉɈɅȿɌɈȼ
ɋ.ȼ. ȾȺɅȿɐɄɂɃ, ɘ.Ɇ. ɑɂɇɘɑɂɇ, ɇ. ɈɃȾɈȼ
ɋ ɩɨɡɢɰɢɢ ɬɟɨɪɢɢ ɧɚɞɺɠɧɨɫɬɢ ɪɚɫɫɦɨɬɪɟɧɵ ɫɯɟɦɵ ɨɛɨɫɧɨɜɚɧɢɹ ɨɛɴɺɦɨɜ ɢ ɩɪɢɧɰɢɩɵ ɩɨɫɬɪɨɟɧɢɹ ɫɬɪɭɤɬɭɪɵ
ɮɨɪɦ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɬɟɯɧɢɱɟɫɤɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɪɟɦɨɧɬɚ) ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɝɪɚɠɞɚɧɫɤɨɣ ɚɜɢɚɰɢɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫ ɭɱɟɬɨɦ ɬɪɟɛɨɜɚɧɢɣ ɩɨ ɨɛɟɫɩɟɱɟɧɢɸ ɛɟɡɨɬɤɚɡɧɨɫɬɢ, ɞɨɥɝɨɜɟɱɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ
ɢ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɥɟɬɨɜ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɧɚɞɺɠɧɨɫɬɶ, ɜɨɡɞɭɲɧɨɟ ɫɭɞɧɨ, ɬɟɯɧɢɱɟɫɤɨɟ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɪɟɦɨɧɬ, ɛɟɡɨɬɤɚɡɧɨɫɬɶ, ɞɨɥɝɨɜɟɱɧɨɫɬɶ, ɭɫɥɨɜɢɹ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɮɨɪɦɚ ɨɛɫɥɭɠɢɜɚɧɢɹ.
Ɉɫɧɨɜɧɨɣ ɰɟɥɶɸ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ (ɪɟɦɨɧɬɚ) ȼɋ ɹɜɥɹɟɬɫɹ ɩɨɞɞɟɪɠɚɧɢɟ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ
ɧɚɞɺɠɧɨɫɬɢ ȼɋ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɛɟɡɨɬɤɚɡɧɨɫɬɶ ɢ ɞɨɥɝɨɜɟɱɧɨɫɬɶ ȼɋ ɨɛɟɫɩɟɱɢɜɚɥɢ ɛɟɡɨɩɚɫɧɨɫɬɶ ɩɨɥɺɬɨɜ ɢ ɷɤɨɥɨɝɢɱɟɫɤɭɸ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɷɤɫɩɥɭɚɬɚɰɢɢ.
ȼɵɞɟɥɹɹ ɞɨɥɸ ɌɈɢɊ ɜ ɨɛɟɫɩɟɱɟɧɢɢ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɥɟɬɨɜ ȼɋ, ɦɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɜ ɱɚɫɬɢ
ɛɟɡɨɬɤɚɡɧɨɫɬɢ ȼɋ ɜ ɰɟɥɨɦ ɩɥɚɧɨɜɨ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɢ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚ ɩɟɪɢɨɞɢɱɟɫɤɨɦ ɌɈ
ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɤɚɠɞɨɦɭ ɷɤɡɟɦɩɥɹɪɭ ɤɨɧɤɪɟɬɧɨɝɨ ɬɢɩɚ ȼɋ.
ɉɪɢ ɌɈ ȼɋ ɜɵɩɨɥɧɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɜɢɞɵ ɪɚɛɨɬ [1]: ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɟ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɤɨɧɬɪɨɥɶ ɫɨɫɬɨɹɧɢɹ, ɩɨɞɞɟɪɠɚɧɢɟ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɧɚɞɺɠɧɨɫɬɢ. ɉɟɪɢɨɞɢɱɟɫɤɨɟ ɌɈ ɜ ɩɨɥɧɨɣ ɦɟɪɟ
ɫɜɨɣɫɬɜɟɧɧɨ ɪɚɛɨɬɚɦ ɩɨ ɩɨɞɞɟɪɠɚɧɢɸ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɧɚɞɺɠɧɨɫɬɢ.
ȼ ɫɜɹɡɢ ɫ ɬɟɦ, ɱɬɨ ɧɨɪɦɚɬɢɜɧɵɟ ɞɨɤɭɦɟɧɬɵ (ɇɅȽɋ) ɪɟɝɥɚɦɟɧɬɢɪɭɸɬ ɬɪɟɛɨɜɚɧɢɹ ɤ ɛɟɡɨɬɤɚɡɧɨɫɬɢ ɪɚɡɞɟɥɶɧɨ ɩɨ ɮɭɧɤɰɢɨɧɚɥɶɧɵɦ ɫɢɫɬɟɦɚɦ (Ɏɋ) ȼɋ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɦ «ɫɨɜɨɤɭɩɧɨɫɬɶ
ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢ ɚɝɪɟɝɚɬɨɜ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɵɯ ɮɭɧɤɰɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɨɥɟɬɨɦ», ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɛɟɡɨɬɤɚɡɧɨɫɬɶ ȼɋ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɫɢɫɬɟɦ ȼɋ.
Ɍɨɝɞɚ ɨɛɨɛɳɟɧɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ j-ɯ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ ɧɚ ɧɚɞɟɠɧɨɫɬɶ ɟɝɨ i-ɣ Ɏɋ
ɩɪɨɹɜɥɹɟɬɫɹ ɱɟɪɟɡ ɜɨɡɞɟɣɫɬɜɢɟ ɨɬɞɟɥɶɧɵɯ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɮɚɤɬɨɪɨɜ ɢ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɮɭɧɤɰɢɨɧɚɥɨɦ ɜɢɞɚ
n
Pi , j (t ) = Pi 0(t ) ∏ ϕi , j (Δxi , j ) ,
(1)
i =1
ɝɞɟ Pi,j(t) – ɮɭɧɤɰɢɹ ɧɚɞɟɠɧɨɫɬɢ i -ɣ Ɏɋ ɜ j-ɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ;
Pi0(t) – ɮɭɧɤɰɢɹ ɧɚɞɟɠɧɨɫɬɢ i -ɣ Ɏɋ ɜ ɬɢɩɨɜɵɯ ɭɫɥɨɜɢɹɯ;
ϕi , j(Δxi, j ) – ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɮɭɧɤɰɢɢ ɫɜɹɡɢ ɧɚɞɟɠɧɨɫɬɢ i-ɣ Ɏɋ ɫ j-ɦ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɦ
ɮɚɤɬɨɪɨɦ.
Ɋɟɚɥɶɧɵɟ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɟ ɮɚɤɬɨɪɵ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɧɚɞɟɠɧɨɫɬɶ Ɏɋ ɜ
ɷɤɫɩɥɭɚɬɚɰɢɢ, ɦɨɝɭɬ ɛɵɬɶ ɪɚɡɞɟɥɟɧɵ ɩɨ ɨɛɳɧɨɫɬɢ ɞɟɣɫɬɜɢɹ ɧɚ ɬɪɢ ɝɪɭɩɩɵ: ɮɭɧɤɰɢɨɧɚɥɶɧɵɟ,
ɪɟɝɢɨɧɚɥɶɧɵɟ ɢ ɬɟɯɧɢɱɟɫɤɢɟ. Ɏɭɧɤɰɢɨɧɚɥɶɧɵɟ ɮɚɤɬɨɪɵ ɫɜɹɡɚɧɵ ɫ ɜɵɩɨɥɧɟɧɢɟɦ ɮɭɧɤɰɢɣ ɫɢɫɬɟɦ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ȼɋ ɩɨ ɧɚɡɧɚɱɟɧɢɸ. Ɋɟɝɢɨɧɚɥɶɧɵɟ ɮɚɤɬɨɪɵ ɫɜɹɡɚɧɵ ɫ ɜɨɡɞɟɣɫɬɜɢɟɦ ɧɚ
ȼɋ ɜɧɟɲɧɟɣ ɫɪɟɞɵ. Ɍɟɯɧɢɱɟɫɤɢɟ ɮɚɤɬɨɪɵ ɫɜɹɡɚɧɵ ɫ ɩɪɨɰɟɫɫɚɦɢ ɜ ɫɢɫɬɟɦɟ Ɍɗ.
Ɋɟɚɥɢɡɚɰɢɢ ɮɭɧɤɰɢɨɧɚɥɚ (1) ɜ ɪɚɡɥɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢɥɥɸɫɬɪɢɪɭɸɬɫɹ ɧɚ
ɪɢɫ. 1, 2.
21
ɇɨɜɵɟ ɩɪɢɧɰɢɩɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɪɟɠɢɦɨɜ…
ɇɚ ɪɢɫ. 1 ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɧɚɞɟɠɧɨɫɬɢ i-ɣ Ɏɋ ɨɬ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ.
Ɍɨɝɞɚ, ɟɫɥɢ tijɧ ɟɫɬɶ ɦɨɦɟɧɬ ɨɠɢɞɚɧɢɹ (ɦ.ɨ.) ɜɪɟɦɟɧɢ ɩɟɪɟɫɟɱɟɧɢɹ ɮɭɧɤɰɢɟɣ Pij ɩɪɟɞɟɥɶɧɨɞɨɩɭɫɬɢɦɨɝɨ ɭɪɨɜɧɹ Ɋiɧ, ɭɫɥɨɜɢɟ (1) ɛɭɞɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɫ ɡɚɞɚɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ, ɟɫɥɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ i-ɣ Ɏɋ ɜ j-ɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ ɜɵɩɨɥɧɢɬɶ ɩɪɢ ɧɚɪɚɛɨɬɤɟ
tij = tijɧ − ασ (tijɧ ) ,
(2)
ɝɞɟ α – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɜɢɞɚ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ tijɧ ɢ ɭɪɨɜɧɹ ɞɨɫɬɨɜɟɪɧɨɫɬɢ
1 ≤ ɚ ≤ 3;
ı – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɟ ɨɬɤɥɨɧɟɧɢɟ.
Ɋɢɫ. 1. Ɋɟɚɥɢɡɚɰɢɹ ɧɚɞɟɠɧɨɫɬɢ i-ɣ ɫɢɫɬɟɦɵ ȼɋ ɜ ɪɚɡɥɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ:
Di(Pi) - ɨɛɥɚɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɜɨɡɦɨɠɧɵɯ ɪɟɚɥɢɡɚɰɢɣ ɮɭɧɤɰɢɢ ɧɚɞɟɠɧɨɫɬɢ i-ɣ ɫɢɫɬɟɦɵ
ɜ ɞɨɩɭɫɤɚɟɦɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ;Pi1(t), Pin(t)- ɝɪɚɧɢɱɧɵɟ ɪɟɚɥɢɡɚɰɢɢ ɮɭɧɤɰɢɢ
ɧɚɞɟɠɧɨɫɬɢ i-ɣ ɫɢɫɬɟɦɵ ɜ ɧɚɢɛɨɥɟɟ ɢ ɧɚɢɦɟɧɟɟ ɛɥɚɝɨɩɪɢɹɬɧɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; Pio(t) - ɪɟɚɥɢɡɚɰɢɹ ɮɭɧɤɰɢɢ ɧɚɞɟɠɧɨɫɬɢ ɫɢɫɬɟɦɵ ɜ ɪɚɫɱɟɬɧɵɯ ɭɫɥɨɜɢɹɯ
ɷɤɫɩɥɭɚɬɚɰɢɢ; tin - ɧɚɪɚɛɨɬɤɚ, ɩɪɢ ɤɨɬɨɪɨɣ ɧɚɞɟɠɧɨɫɬɶ ɫɢɫɬɟɦɵ ɞɨɫɬɢɝɚɟɬ ɩɪɟɞɟɥɶɧɨ
ɞɨɩɭɫɬɢɦɨɝɨ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ; Piɧ - ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɭɪɨɜɟɧɶ ɧɚɞɟɠɧɨɫɬɢ
i-ɣ ɫɢɫɬɟɦɵ
ȿɫɥɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ i-ɣ Ɏɋ ȼɋ ɩɪɨɢɡɜɨɞɢɬɶ ɩɪɢ ɧɚɪɚɛɨɬɤɟ:
{
}
t i = min tijí − ασ(t ijí ) , j = 1, N ,
(3)
ɬɨ ɭɫɥɨɜɢɟ (3) ɛɭɞɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɫ ɩɪɢɧɹɬɨɣ ɞɨɫɬɨɜɟɪɧɨɫɬɶɸ ɞɥɹ ɥɸɛɨɝɨ ɢɡ N ȼɋ ɩɚɪɤɚ.
Ɋɚɫɫɦɚɬɪɢɜɚɹ ȼɋ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ n ɫɨɫɬɚɜɥɹɸɳɢɯ ɟɝɨ i-ɯ Ɏɋ (ɢɥɢ Ɏɋ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ k
ɫɨɫɬɚɜɥɹɸɳɢɯ ɟɟ ɷɥɟɦɟɧɬɨɜ) ɢ ɭɱɢɬɵɜɚɹ ɫɭɳɟɫɬɜɟɧɧɵɟ ɪɚɡɥɢɱɢɹ ɜ ɮɚɤɬɢɱɟɫɤɢɯ ɭɪɨɜɧɹɯ
ɧɚɞɟɠɧɨɫɬɢ ɤɚɠɞɨɣ i-ɣ Ɏɋ ɢ ɜ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɡɧɚɱɢɦɨɫɬɢ ɤɚɠɞɨɣ ɫɢɫɬɟɦɵ ɫ ɩɨɡɢɰɢɣ ɨɛɟɫɩɟɱɟɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɢ ɪɟɝɭɥɹɪɧɨɫɬɢ ɩɨɥɟɬɨɜ, ɩɟɪɢɨɞɢɱɧɨɫɬɶ IJ ɩɪɨɜɟɞɟɧɢɹ ɩɨɥɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɜɫɟɯ Ɏɋ ɥɸɛɨɝɨ ȼɋ ɩɚɪɤɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɯɭɞɲɢɦ ɭɫɥɨɜɢɹɦ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ
22
ɋ.ȼ. Ⱦɚɥɟɰɤɢɣ, ɘ.Ɇ. ɑɢɧɸɱɢɧ, ɇ. Ɉɣɞɨɜ
{
}
τ = min tijí −ασ(tijí )
i = 1, n; j = 1, N .
(4)
ɉɨɫɤɨɥɶɤɭ ɜɥɢɹɧɢɟ ɧɟɫɥɭɱɚɣɧɵɯ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɮɚɤɬɨɪɨɜ ɩɪɢɜɨɞɢɬ ɤ ɜɧɭɬɪɟɧɧɟɣ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɪɨɰɟɫɫɨɜ ɢɡɦɟɧɟɧɢɹ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ Ɏɋ ɢ ɢɯ ɷɥɟɦɟɧɬɨɜ, ɱɬɨ ɜɵɡɵɜɚɟɬ
ɧɟɷɪɝɨɞɢɱɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɢɡɦɟɧɟɧɢɹ ɧɚɞɟɠɧɨɫɬɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ȼɋ ɩɚɪɤɚ, ɡɚɞɚɱɭ ɪɟɚɥɢɡɚɰɢɢ
ɭɫɥɨɜɢɣ (1) ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ: ɞɥɹ ɜɫɟɝɨ ɩɚɪɤɚ ȼɋ; ɞɥɹ ɝɪɭɩɩɵ ȼɋ, ɷɤɫɩɥɭɚɬɢɪɭɸɳɢɯɫɹ ɜ
ɨɞɢɧɚɤɨɜɵɯ ɭɫɥɨɜɢɹɯ; ɞɥɹ ɨɞɢɧɨɱɧɨɝɨ ȼɋ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɧɟ ɦɟɧɹɹ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ
ɩɪɢ ɡɚɞɚɧɧɨɣ ɨɪɝɚɧɢɡɚɰɢɢ ɢ ɬɟɯɧɨɥɨɝɢɢ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɰɟɫɫɨɜ ɌɈɢɊ, ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɧɚɞɟɠɧɨɫɬɶ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɬɨɥɶɤɨ ɢɡɦɟɧɟɧɢɟɦ ɪɟɠɢɦɨɜ ɩɥɚɧɨɜɨɝɨ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈɢɊ, ɬ.ɟ. ɢɡɦɟɧɟɧɢɟɦ ɨɛɴɟɦɨɜ ɪɚɛɨɬ ɢ ɩɟɪɢɨɞɢɱɧɨɫɬɢ ɜɵɩɨɥɧɟɧɢɹ ɮɨɪɦ ɌɈɢɊ.
Ɋɢɫ. 2. ɇɚɞɟɠɧɨɫɬɶ j-ɝɨ ȼɋ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɢ ɫɨɫɬɚɜɥɹɜɲɢɯ ɟɝɨ ɫɢɫɬɟɦ ɜ ɞɚɧɧɵɯ
ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ: Dj(Pj) - ɨɛɥɚɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɪɟɚɥɢɡɚɰɢɣ ɮɭɧɤɰɢɣ
ɧɚɞɟɠɧɨɫɬɢ i–ɯ ɫɢɫɬɟɦ j-ɝɨ ɫɚɦɨɥɟɬɚ; Pij(t), Pnj(t) - ɪɟɚɥɢɡɚɰɢɢ ɧɚɞɟɠɧɨɫɬɢ ɧɚɢɦɟɧɟɟ
ɢ ɧɚɢɛɨɥɟɟ ɧɚɞɟɠɧɵɯ ɫɢɫɬɟɦ ȼɋ ɜ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɹɯ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɢ;
−
t ij ɧ - ɧɚɪɚɛɨɬɤɚ i-ɣ ɫɢɫɬɟɦɵ ɜ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ j-ɝɨ ȼɋ, ɩɪɢ ɤɨɬɨɪɨɣ
ɞɨɫɬɢɝɚɟɬɫɹ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɭɪɨɜɟɧɶ ɧɚɞɟɠɧɨɫɬɢ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ;
Ɋiɧ - ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɭɪɨɜɟɧɶ ɧɚɞɟɠɧɨɫɬɢ i-ɣ ɫɢɫɬɟɦɵ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ ɚɜɢɚɰɢɨɧɧɨɣ ɬɟɯɧɢɤɢ ɩɪɢɜɟɥɨ ɤ ɬɨɦɭ, ɱɬɨ ɛɟɡɨɩɚɫɧɨɫɬɶ ɩɨɥɟɬɨɜ ɜ ɛɨɥɶɲɟɣ ɫɬɟɩɟɧɢ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɤɨɧɫɬɪɭɤɬɢɜɧɵɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ ȼɋ, ɱɟɦ
ɪɟɝɥɚɦɟɧɬɨɦ ɌɈ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ ɢɡɦɟɧɹɬɶ ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɢ ɨɛɴɟɦɵ ɪɚɛɨɬ
ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɤɨɧɤɪɟɬɧɵɦ ɭɫɥɨɜɢɹɦ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɩɨɬɪɟɛɧɨɫɬɹɦ ɚɜɢɚɤɨɦɩɚɧɢɣ.
ɉɨɷɬɨɦɭ ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɜɵɩɨɥɧɟɧɢɹ ɛɚɡɨɜɨɣ ɮɨɪɦɵ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ ɨɛɵɱɧɨ ɡɚɞɚɟɬɫɹ
ɞɢɪɟɤɬɢɜɧɨ ɢ ɦɨɠɟɬ ɢɡɦɟɧɹɬɶɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ ɩɨ ɦɟɪɟ ɧɚɤɨɩɥɟɧɢɹ ɨɩɵɬɚ ɷɤɫɩɥɭɚɬɚɰɢɢ
ɬɢɩɚ ȼɋ ɢ ɚɞɚɩɬɚɰɢɢ ɪɟɠɢɦɨɜ ɤ ɨɪɝɚɧɢɡɚɰɢɨɧɧɵɦ ɫɬɪɭɤɬɭɪɚɦ ɚɜɢɚɩɪɟɞɩɪɢɹɬɢɣ.
Ɏɨɪɦɢɪɨɜɚɧɢɟ ɨɛɴɟɦɨɜ ɪɚɛɨɬ ɌɈɢɊ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ (ɪɟɦɨɧɬɚ) ȼɋ ɦɨɠɟɬ ɛɚɡɢɪɨɜɚɬɶɫɹ
ɧɚ 4-ɯ ɨɫɧɨɜɧɵɯ ɩɪɢɧɰɢɩɚɯ:
ɚ) ɩɨɥɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ;
ɛ) ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ;
23
ɇɨɜɵɟ ɩɪɢɧɰɢɩɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɪɟɠɢɦɨɜ…
ɜ) ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɩɨ ɫɨɫɬɨɹɧɢɸ;
ɝ) ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ, ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɧɨɟ ɩɨ ɧɚɪɚɛɨɬɤɟ.
Ɏɨɪɦɢɪɨɜɚɧɢɟ ɨɛɴɟɦɨɜ ɪɚɛɨɬ ɩɨ ɩɪɢɧɰɢɩɭ ɩɨɥɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɧɚ ɤɚɠɞɨɣ ɮɨɪɦɟ
ɌɈɢɊ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɫɥɟɞɭɸɳɢɯ ɩɨɥɨɠɟɧɢɹɯ:
- ɩɨɬɨɤ ɫɨɛɵɬɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɩɨɬɪɟɛɧɨɫɬɶ ɜ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬ ɩɨ ɌɈɢɊ ɷɥɟɦɟɧɬɨɜ
ȼɋ, ɹɜɥɹɟɬɫɹ ɫɬɚɰɢɨɧɚɪɧɵɦ;
- ɤɨɥɢɱɟɫɬɜɨ ɫɨɛɵɬɢɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɜɟɥɢɱɢɧɨɣ ɢɧɬɟɪɜɚɥɚ ɧɚɪɚɛɨɬɤɢ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ
ɷɬɚɩɚ ɧɚɪɚɛɨɬɤɢ ȼɋ ɫ ɧɚɱɚɥɚ ɷɤɫɩɥɭɚɬɚɰɢɢ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ ɩɨɹɜɥɟɧɢɹ ɩɨɬɪɟɛɧɨɫɬɢ ɜ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬ ɩɨ ɌɈɢɊ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɫɬɚɰɢɨɧɚɪɧɵɣ ɩɨɬɨɤ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɛɟɡ ɩɨɫɥɟɞɟɣɫɬɜɢɹ.
ɉɪɢ ɩɨɥɧɨɦ ɜɨɫɫɬɚɧɨɜɥɟɧɢɢ ɧɚ ɤɚɠɞɨɣ ɩɟɪɢɨɞɢɱɟɫɤɨɣ ɮɨɪɦɟ ɌɈ ɢ ɩɪɢ ɪɟɦɨɧɬɟ ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɝɥɚɫɧɨ (4) (ɪɢɫ. 1, 2).
ɂɡɭɱɟɧɢɟ ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɢɡɦɟɧɟɧɢɹ ɧɚɞɟɠɧɨɫɬɢ i-ɣ Ɏɋ ɢ ɟɟ ɷɥɟɦɟɧɬɨɜ ɜ ɧɚɢɯɭɞɲɢɯ
ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɪɚɛɨɬ ɩɨ ɌɈɢɊ ɢ ɢɯ ɨɛɴɟɦɵ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɫɥɨɜɢɸ (1) ɞɥɹ ɧɚɢɦɟɧɟɟ ɧɚɞɟɠɧɨɣ Ɏɋ ȼɋ, ɷɤɫɩɥɭɚɬɢɪɭɸɳɢɯɫɹ ɜ ɧɚɢɛɨɥɟɟ ɬɹɠɟɥɵɯ ɭɫɥɨɜɢɹɯ. Ɉɬɫɸɞɚ ɨɛɴɟɦ ɪɚɛɨɬ ɩɥɚɧɨɜɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɞɥɹ ɥɸɛɨɣ ɮɨɪɦɵ ɨɩɪɟɞɟɥɹɸɬ ɢɡ
ɭɫɥɨɜɢɹ
Ni
qi
Ɏi = ¦¦ Bɇ ijν ;
j =1 ν =1
ν = 1, qi ;
j = 1, N i ,
(5)
ɝɞɟ Ȟ – ɜɢɞ ɨɬɤɚɡɚ;
j – ɷɥɟɦɟɧɬ i-ɣ Ɏɋ;
ɤ – ɮɨɪɦɚ ɌɈ.
ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɢɡ ɝɢɩɨɬɟɡɵ ɨ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ ɩɨɬɨɤɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɢ ɭɫɥɨɜɢɹ ɩɨɥɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɧɚ ɤɚɠɞɨɣ ɮɨɪɦɟ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɦɨɦɟɧɬɵ t = τ ɩɪɨɢɫɯɨɞɢɬ ɩɨɥɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɜɫɟɯ Ɏɋ ɢ ɞɚɥɟɟ ɨɬɫɱɟɬ ɧɚɪɚɛɨɬɤɢ ɧɚɱɢɧɚɟɬɫɹ ɫ ɧɭɥɹ.
ɉɪɢ ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɦ ɜɨɫɫɬɚɧɨɜɥɟɧɢɢ ɧɚ ɤɚɠɞɨɣ ɮɨɪɦɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɱɬɨ ɩɪɟɞɟɥɶɧɵɣ ɭɪɨɜɟɧɶ ɧɚɞɟɠɧɨɫɬɢ ɤɚɠɞɨɣ Ɏɋ ɞɨɫɬɢɝɚɟɬɫɹ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɧɚɪɚɛɨɬɤɟ
(ɪɢɫ. 2), ɩɨɷɬɨɦɭ ɫ ɩɟɪɢɨɞɢɱɧɨɫɬɶɸ τ ɧɚ ɤɚɠɞɨɣ ɮɨɪɦɟ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɹɬɶ ɪɚɛɨɬɵ ɩɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɬɨɥɶɤɨ ɬɟɯ ɎC, ɧɚɞɟɠɧɨɫɬɶ ɤɨɬɨɪɵɯ ɜ ɢɧɬɟɪɜɚɥɟ ɧɚɪɚɛɨɬɤɢ τ ⋅ ɤ ≤ t ≤ τ (ɤ + 1)
ɞɨɫɬɢɝɚɟɬ ɩɪɟɞɟɥɶɧɨɝɨ ɭɪɨɜɧɹ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬ
ɩɨɬɨɤ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɤɚɤ ɫɬɚɰɢɨɧɚɪɧɵɣ, ɩɟɪɢɨɞɢɱɟɫɤɢɣ, ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ ɫ ɩɟɪɢɨɞɨɦ
{
( )}
Ɍ = max t ijɧ − ασ t ijɧ ; i = 1, n ; j = 1, N .
Ɉɛɴɟɦ ɪɚɛɨɬ ɤ-ɣ ɮɨɪɦɵ ɜ ɩɪɟɞɟɥɚɯ ɰɢɤɥɚ ɮɨɪɦɢɪɭɟɬɫɹ ɤɚɤ
Ɏi ɤ = Ɏi ( ɤ −1) + ΔɎi ɤ .
(6)
(7)
Ɉɛɴɟɦ ɪɚɛɨɬ ɮɨɪɦɵ, ɡɚɦɵɤɚɸɳɟɣ ɰɢɤɥ, ɢɦɟɟɬ ɜɢɞ
ni
Ɏi n = Ɏi1 + ¦ Δ Ɏi ɤ .
(8)
ɤ =2
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɚɠɞɚɹ ɩɨɫɥɟɞɭɸɳɚɹ ɮɨɪɦɚ ɩɨɥɧɨɫɬɶɸ ɜɤɥɸɱɚɟɬ ɜɫɟ ɪɚɛɨɬɵ ɩɪɟɞɵɞɭɳɟɣ,
ɚ ɡɚɦɵɤɚɸɳɚɹ ɮɨɪɦɚ ɩɨ ɨɛɴɟɦɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɝɥɚɫɧɨ (4), ɩɪɢ ɷɬɨɦ ɩɪɨɢɫɯɨɞɢɬ ɩɨɥɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɜɫɟɯ Ɏɋ ɞɨ ɢɫɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɧɚɞɟɠɧɨɫɬɢ, ɢ ɞɚɥɟɟ ɨɬɫɱɟɬ ɧɚɪɚɛɨɬɤɢ ɧɚɱɢɧɚɟɬɫɹ ɫ
ɧɭɥɹ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɟɪɟɞ ɩɨɥɧɵɦ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ
ɤɚɠɞɚɹ μ -ɹ ɮɨɪɦɚ ɌɈ ɢɥɢ ɪɟɦɨɧɬɚ ɜ ɩɪɟɞɟɥɚɯ ɰɢɤɥɚ ɦɟɧɶɲɟ ɡɚɦɵɤɚɸɳɟɣ ɮɨɪɦɵ, ɪɚɜɧɨɣ ɩɨ
ɨɛɴɟɦɭ ɜɵɩɨɥɧɹɟɦɵɯ ɪɚɛɨɬ ɮɨɪɦɟ ɩɨɥɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ
ni
Δ = ¦ ΔɎiɤ .
i=μ
(9)
24
ɋ.ȼ. Ⱦɚɥɟɰɤɢɣ, ɘ.Ɇ. ɑɢɧɸɱɢɧ, ɇ. Ɉɣɞɨɜ
ɉɪɢɧɰɢɩ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɛɴɟɦɨɜ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɨ ɫɨɫɬɨɹɧɢɸ ɩɪɟɞɩɨɥɚɝɚɟɬ, ɱɬɨ ɨɛɴɟɦɵ ɢ
ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɪɚɛɨɬ ɩɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɞɨɥɠɧɵ ɨɩɪɟɞɟɥɹɬɶɫɹ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɦɢ ɢɡɦɟɧɟɧɢɹ
ɧɚɞɟɠɧɨɫɬɢ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ ɜ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɹɯ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɢ.
ɉɟɪɢɨɞɢɱɧɨɫɬɶ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɨɩɪɟɞɟɥɢɬɫɹ ɢɡ (2).
Ɉɛɴɟɦ ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɯ ɪɚɛɨɬ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɚɥɢɡɚɰɢɹ ɭɫɥɨɜɢɹ (1) ɧɚ ɤɚɠɞɨɦ ɷɬɚɩɟ
ɧɚɪɚɛɨɬɤɢ i-ɣ Ɏɋ ɜ ɥɸɛɵɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ɛɭɞɟɬ ɪɚɜɟɧ
Ni
qi
Ɏi ( t ) = ¦¦ ȼɇ f ª¬λiν j ( t ) ;τ
j =1 ν =1
iν j
iν j
º¼ ; j = 1, N ; ν = 1, q ,
(10)
ɚ ɞɥɹ ȼɋ ɜ ɰɟɥɨɦ ɜ j-ɯ ɭɫɥɨɜɢɹɯ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɢ
n
Ɏ j (t ) = ¦ Ɏi (t ) .
(11)
i =1
ɍɱɢɬɵɜɚɹ ɦɧɨɝɨɱɢɫɥɟɧɧɨɫɬɶ ɷɥɟɦɟɧɬɨɜ ɜ Ɏɋ ɢ ɪɚɡɥɢɱɧɵɯ Ɏɋ ɧɚ ȼɋ, ɚ ɬɚɤɠɟ ɦɧɨɠɟɫɬɜɨ
ɮɚɤɬɨɪɨɜ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɢɡɦɟɧɟɧɢɟ ɢɯ ɧɚɞɟɠɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ, ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɩɨɬɪɟɛɧɨɫɬɶ ɜ ɌɈ ɢɥɢ ɪɟɦɨɧɬɟ ɤɚɤɨɝɨ-ɥɢɛɨ ɷɥɟɦɟɧɬɚ. ɉɥɚɧɨɜɵɣ ɩɪɢɧɰɢɩ ɬɪɟɛɭɟɬ ɝɪɭɩɩɢɪɨɜɤɢ ɥɨɤɚɥɶɧɵɯ ɪɚɛɨɬ ɜ ɮɨɪɦɵ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɧɟɤɨɬɨɪɨɦɭ ɭɜɟɥɢɱɟɧɢɸ
ɨɛɴɟɦɨɜ ɜɵɩɨɥɧɹɟɦɵɯ ɪɚɛɨɬ, ɬɚɤ ɤɚɤ ɜ ɤɚɠɞɭɸ ɮɨɪɦɭ ɧɟɨɛɯɨɞɢɦɨ ɜɤɥɸɱɚɬɶ ɪɚɛɨɬɵ ɩɨ ɌɈɢɊ
ɷɥɟɦɟɧɬɨɜ, ɧɚɞɟɠɧɨɫɬɶ ɤɨɬɨɪɵɯ ɜ ɢɧɬɟɪɜɚɥɟ ɧɚɪɚɛɨɬɤɢ ɞɨ ɫɥɟɞɭɸɳɟɣ ɮɨɪɦɵ ɌɈ ɦɨɠɟɬ ɞɨɫɬɢɝɧɭɬɶ ɩɪɟɞɟɥɶɧɨɝɨ ɭɪɨɜɧɹ.
Ɉɩɬɢɦɢɡɚɰɢɹ ɞɨɫɬɢɝɚɟɬɫɹ ɡɚ ɫɱɟɬ ɦɢɧɢɦɢɡɚɰɢɢ ɡɚɬɪɚɬ ɬɪɭɞɚ ɢɥɢ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɤɫɢɦɭɦɚ
ɝɨɬɨɜɧɨɫɬɢ ȼɋ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɢɩɚ ɢ ɭɫɥɨɜɢɣ ɟɝɨ ɩɪɢɦɟɧɟɧɢɹ.
Ⱦɢɮɮɟɪɟɧɰɢɪɨɜɚɧɧɵɣ ɩɨ ɧɚɪɚɛɨɬɤɟ ɩɪɢɧɰɢɩ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ (ɪɟɦɨɧɬɚ)
ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɩɨɥɨɠɟɧɢɹ ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɨ ɫɨɫɬɨɹɧɢɸ, ɱɬɨ ɢ ɨɛɭɫɥɨɜɥɢɜɚɟɬ ɨɫɨɛɟɧɧɨɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɪɟɠɢɦɨɜ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ. ɉɟɪɢɨɞɢɱɧɨɫɬɶ ɮɨɪɦ ɌɈ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɩɪɢɧɰɢɩɚɦ ɪɟɝɥɚɦɟɧɬɢɪɨɜɚɧɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ. ȼ ɤɚɠɞɭɸ
ɮɨɪɦɭ ɌɈ ɜɤɥɸɱɚɸɬɫɹ ɪɚɛɨɬɵ ɫ ɛɚɡɨɜɨɣ ɩɟɪɢɨɞɢɱɧɨɫɬɶɸ, ɫɨɫɬɚɜɥɹɸɳɢɟ ɫɬɚɰɢɨɧɚɪɧɵɣ ɩɨɬɨɤ
ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɧɚɢɛɨɥɟɟ «ɫɥɚɛɵɯ» ɷɥɟɦɟɧɬɨɜ ɤɚɠɞɨɣ Ɏɋ, ɢ ɪɚɛɨɬɵ ɩɨ ɨɛɟɫɩɟɱɟɧɢɸ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ. ɋɨɜɨɤɭɩɧɨɫɬɶ ɷɬɢɯ ɪɚɛɨɬ ɫɨɫɬɚɜɥɹɟɬ ɨɛɴɟɦ ɩɟɪɜɨɣ, ɛɚɡɨɜɨɣ ɮɨɪɦɵ ɌɈ (Ɏ1i) ɞɥɹ
ɤɚɠɞɨɣ Ɏɋ. Ɉɛɴɟɦ ɪɚɛɨɬ ɤ-ɣ ɮɨɪɦɵ ɌɈ ɞɥɹ i -ɣ Ɏɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
ɤ
Ɏiɤ = Ɏ1i + ¦ ȼ( H )iɤ + ¦ ȼ( H )ɫɤ i .
i =1
(12)
ɫ =1
ɝɞɟ Â( H )iê – ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɪɚɛɨɬɵ, ɫɜɨɣɫɬɜɟɧɧɵɟ ɬɨɥɶɤɨ ɞɚɧɧɨɦɭ ɷɬɚɩɭ ɧɚɪɚɛɨɬɤɢ ȼɋ ɢ ɩɨɞ-
ɥɟɠɚɳɢɟ ɜɵɩɨɥɧɟɧɢɸ ɧɚ ɤ-ɣ ɮɨɪɦɟ, ɟɫɥɢ ɜ ɢɧɬɟɪɜɚɥɟ ɧɚɪɚɛɨɬɤɢ τ ⋅ ɤ ≤ t ≤ τ (ɤ + 1) ɧɚɞɟɠɧɨɫɬɶ
ɢɧɰɢɞɟɧɬɧɵɯ ɢɦ ɷɥɟɦɟɧɬɨɜ ɞɨɫɬɢɝɚɟɬ ɩɪɟɞɟɥɶɧɨɝɨ ɭɪɨɜɧɹ;
ȼ( H )ɫɤ i – ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɪɚɛɨɬɵ, ɫɜɨɣɫɬɜɟɧɧɵɟ ɨɞɧɨɣ ɢɡ ɩɪɟɞɵɞɭɳɢɯ ɮɨɪɦ, ɢ ɩɨɞɥɟɠɚɳɢɟ
ɜɵɩɨɥɧɟɧɢɸ, ɟɫɥɢ ɧɚɪɚɛɨɬɤɚ, ɩɪɢ ɤɨɬɨɪɨɣ ɜɵɩɨɥɧɹɟɬɫɹ ɤ-ɹ ɮɨɪɦɚ, ɤɪɚɬɧɚ ɩɨɬɪɟɛɧɨɣ ɩɟɪɢɨɞɢɱɧɨɫɬɢ ɢɯ ɜɵɩɨɥɧɟɧɢɹ.
Ⱦɥɹ ɪɟɚɥɢɡɚɰɢɢ ɭɪɚɜɧɟɧɢɹ (12) ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɩɟɪɢɨɞɢɱɧɨɫɬɶ ɛɚɡɨɜɨɣ ɮɨɪɦɵ.
ɉɪɢ ɢɡɜɟɫɬɧɨɦ ɩɟɪɟɱɧɟ {ȼɄ,H} ɪɚɛɨɬ ɢ ɧɟɨɛɯɨɞɢɦɨɣ ɩɟɪɢɨɞɢɱɧɨɫɬɢ ɢɯ ɜɵɩɨɥɧɟɧɢɹ {tɄ,H}, ɩɪɢ
{ÂÊH } ∋ {t ÊH } ɜɵɛɨɪ ɩɟɪɢɨɞɢɱɧɨɫɬɢ τ ɛɚɡɨɜɨɣ ɮɨɪɦɵ ɦɨɠɟɬ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɩɨ ɤɪɢɬɟɪɢɸ ɦɢɧɢɦɚɥɶɧɵɯ ɩɨɬɟɪɶ ɨɬ ɧɟɞɨɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɟɪɢɨɞɢɱɧɨɫɬɢ ɜɵɩɨɥɧɟɧɢɹ τ i ɨɬɞɟɥɶɧɵɯ ɪɚɛɨɬ ɩɪɢ ɡɚɞɚɧɧɨɣ ɩɟɪɢɨɞɢɱɧɨɫɬɢ τ ɛɚɡɨɜɨɣ ɮɨɪɦɵ
wij = τ i − jτ , ɩɪɢ 0 ≤ ti − jτ < τ ,
(13)
ɝɞɟ τ i – ɩɟɪɢɨɞɢɱɧɨɫɬɶ i-ɣ ɪɚɛɨɬɵ;
j – ɧɨɦɟɪ ɛɚɡɨɜɨɣ ɮɨɪɦɵ ɨɬ ɧɚɱɚɥɚ ɰɢɤɥɚ.
ɉɨɬɟɪɢ ɨɬ ɝɪɭɩɩɢɪɨɜɤɢ m = {ȼɄ,ɉ} ɪɚɛɨɬ ɜ j-ɟ ɮɨɪɦɵ ɢ ɌɈ ɩɪɢ ɡɚɞɚɧɧɨɦ τ ɫɨɫɬɚɜɹɬ
25
ɇɨɜɵɟ ɩɪɢɧɰɢɩɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɪɟɠɢɦɨɜ…
m
n
ɉ = ¦¦ wij ⋅ xij ⋅ ri ,
(14)
i =1 j =1
ɝɞɟ xij – ɱɢɫɥɨ ɪɚɛɨɬ, ɫɝɪɭɩɩɢɪɨɜɚɧɧɵɯ ɜ j-ɣ ɮɨɪɦɟ;
ri – ɱɢɫɥɨ ɩɨɜɬɨɪɟɧɢɣ ɜɵɩɨɥɧɟɧɢɹ i-ɣ ɪɚɛɨɬɵ ɡɚ ɩɨɥɧɵɣ ɰɢɤɥ ɮɨɪɦ, ɪɚɜɧɵɣ τ ⋅ n .
ɇɚɤɨɧɟɰ, ɩɪɢɯɨɞɢɦ ɤ ɫɬɚɧɞɚɪɬɧɨɣ ɡɚɞɚɱɟ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɬɢɩɚ, ɩɥɚɧ ɝɪɭɩɩɢɪɨɜɨɤ xij ɤɨɬɨɪɨɣ ɦɢɧɢɦɢɡɢɪɭɟɬ wij.
Ɂɚɞɚɜɚɹɫɶ ɧɟɫɤɨɥɶɤɢɦɢ ɡɧɚɱɟɧɢɹɦɢ ɛɚɡɨɜɨɣ ɩɟɪɢɨɞɢɱɧɨɫɬɢ
τ 1 ,τ 2 ,...,τ ɤ
ɜ ɢɧɬɟɪɜɚɥɟ ɧɚɪɚ-
ɛɨɬɨɤ 100…1000 ɥɟɬɧɵɯ ɱ, ɧɚɯɨɞɹɬ ɨɩɬɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɦɢɧɢɦɭɦɭ ɮɭɧɤɰɢɢ
1
2
ɉ = ɉ (τ )
ɤ
ɩɪɢ τ = τ ,τ ,...,τ .
ɂɫɱɢɫɥɟɧɢɟ ɧɚɪɚɛɨɬɤɢ ȼɋ ɞɥɹ ɧɚɡɧɚɱɟɧɢɹ ɤɚɠɞɨɣ ɩɨɫɥɟɞɭɸɳɟɣ ɮɨɪɦɵ ɜɟɞɟɬɫɹ ɨɬ ɰɢɮɪ,
ɤɪɚɬɧɵɯ ɩɟɪɢɨɞɢɱɧɨɫɬɢ ɛɚɡɨɜɨɣ ɮɨɪɦɵ Ɏ1. ȿɫɥɢ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɞɨɩɭɫɤ ɧɚ ɜɵɩɨɥɧɟɧɢɟ ɮɨɪɦ,
ɜɟɥɢɱɢɧɚ ɞɨɩɭɫɤɚ ɜɤɥɸɱɚɟɬɫɹ ɜ ɭɫɥɨɜɢɟ ɝɪɭɩɩɢɪɨɜɤɢ. ɇɚɩɪɢɦɟɪ, ɩɪɢ (τ ± 0,1τ ) ɭɫɥɨɜɢɟɦ
ɝɪɭɩɩɢɪɨɜɤɢ ɛɭɞɟɬ 0,1τ ≤ ti − jτ < 0,9τ ɢ ɬ. ɞ. ȼɫɹ ɩɪɨɰɟɞɭɪɚ ɩɪɢɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɞɥɹ ɪɚɛɨɬ ɩɨ
ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɫɨɫɬɨɹɧɢɹ – ȼH ɢ ɤɨɧɬɪɨɥɸ – ȼɄ .
ɋɬɪɭɤɬɭɪɚ ɪɚɛɨɬ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶ ɧɟɡɚɜɢɫɢɦɵɣ ɩɟɪɟɧɨɫ ɪɚɛɨɬ ȼH ɢɡ ɨɞɧɨɣ ɮɨɪɦɵ ɜ ɞɪɭɝɭɸ, ɜɤɥɸɱɚɬɶ ɜ ɮɨɪɦɵ ɪɚɡɨɜɵɟ ɪɚɛɨɬɵ ɩɨ ɤɨɧɫɬɪɭɤɬɢɜɧɨɣ ɞɨɪɚɛɨɬɤɟ, ɡɚɦɟɧɟ ɢɥɢ ɰɟɥɟɜɨɦɭ ɤɨɧɬɪɨɥɸ ɫɨɫɬɨɹɧɢɹ, ɚ ɬɚɤɠɟ ɪɚɧɠɢɪɨɜɚɬɶ ɨɛɴɟɦɵ ɜɵɩɨɥɧɹɟɦɵɯ ɪɚɛɨɬ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɤɚɡɚɧɧɵɣ ɩɨɞɯɨɞ ɤ ɮɨɪɦɢɪɨɜɚɧɢɸ ɫɬɪɭɤɬɭɪɵ ɩɟɪɢɨɞɢɱɟɫɤɢɯ ɮɨɪɦ ɌɈ
ɜɨɡɦɨɠɟɧ ɤ ɩɪɢɦɟɧɟɧɢɸ ɧɟ ɬɨɥɶɤɨ ɞɥɹ ɪɚɛɨɬ ɩɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ {ȼH}
ȼɋ ɢ ɢɯ ɫɢɫɬɟɦ, ɧɨ ɢ ɞɥɹ ɪɚɛɨɬ ɩɨ ɤɨɧɬɪɨɥɸ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ {ȼɄ}, ɟɫɥɢ ɩɨɞ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟɦ ɩɨɧɢɦɚɬɶ ɧɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ ɢɡɞɟɥɢɹ, ɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɢɧɮɨɪɦɚɰɢɢ ɨ ɬɟɯɧɢɱɟɫɤɨɦ ɫɨɫɬɨɹɧɢɢ ɷɬɨɝɨ ɢɡɞɟɥɢɹ.
ɂɡɥɨɠɟɧɧɵɟ ɩɪɢɧɰɢɩɵ ɫɬɪɭɤɬɭɪɧɨɝɨ ɩɨɫɬɪɨɟɧɢɹ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ ɩɨɞɬɜɟɪɠɞɚɸɬɫɹ ɞɚɧɧɵɦɢ ɨɛɨɛɳɟɧɢɹ ɨɩɵɬɚ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ.
ɅɂɌȿɊȺɌɍɊȺ
1. Ⱦɚɥɟɰɤɢɣ ɋ.ȼ. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɝɪɚɠɞɚɧɫɤɨɣ
ɚɜɢɚɰɢɢ. Ɇ.: ȼɨɡɞɭɲɧɵɣ ɬɪɚɧɫɩɨɪɬ, 2005. 416 ɫ.
NEW PRINCIPLES OF PERIODIC AIRCRAFT MAINTENANCE
CONDITIONS DEFINITION IN ACCORDANCE
WITH AVIATION SAFETY CRITERIA
Daletskiy S.V., Chinyuchin Yu.M., Oidov N.
Based on the reliability theory schemes of justifying the volume and structural principles of periodic maintenance (repair) of civil aircraft depending on operational conditions meeting the requirements on the failure-free operation, aircraft
durability and flight safety are considered.
Keywords: reliability, aircraft, maintenance, repair, failure-free operation, durability, operating conditions, service
form.
26
ɋ.ȼ. Ⱦɚɥɟɰɤɢɣ, ɘ.Ɇ. ɑɢɧɸɱɢɧ, ɇ. Ɉɣɞɨɜ
REFERENCES
1. Daletskiy S.V. Formirovanie ekspluatatsionno-tekhnicheskikh kharakteristik vozdushnykh sudov grazhdanskoy
aviatsii. M.: Vozdushnyy transport, 2005. P. 416. (In Russian).
ɋɜɟɞɟɧɢɹ ɨɛ ɚɜɬɨɪɚɯ
Ⱦɚɥɟɰɤɢɣ ɋɬɚɧɢɫɥɚɜ ȼɥɚɞɢɦɢɪɨɜɢɱ, 1944 ɝ.ɪ., ɨɤɨɧɱɢɥ ɆȺɂ (1969), ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ,
ɧɚɱɚɥɶɧɢɤ ɨɬɞɟɥɚ Ƚɨɫɇɂɂ ȽȺ, ɚɤɚɞɟɦɢɤ Ɋɨɫɫɢɣɫɤɨɣ ɚɤɚɞɟɦɢɢ ɬɪɚɧɫɩɨɪɬɚ ɢ Ɋɨɫɫɢɣɫɤɨɣ ɚɤɚɞɟɦɢɢ ɩɪɨɛɥɟɦ ɤɚɱɟɫɬɜɚ, ɷɤɫɩɟɪɬ Ƚɨɫɫɬɚɧɞɚɪɬɚ ɊɎ ɢ Ɇɟɠɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɚɜɢɚɰɢɨɧɧɨɝɨ ɤɨɦɢɬɟɬɚ, ɚɜɬɨɪ ɛɨɥɟɟ
100 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɪɚɡɪɚɛɨɬɤɚ, ɢɫɩɵɬɚɧɢɹ ɢ ɬɟɯɧɢɱɟɫɤɚɹ ɷɤɫɩɥɭɚɬɚɰɢɹ
ɜɨɡɞɭɲɧɨɝɨ ɬɪɚɧɫɩɨɪɬɚ.
ɑɢɧɸɱɢɧ ɘɪɢɣ Ɇɢɯɚɣɥɨɜɢɱ, 1941 ɝ.ɪ., ɨɤɨɧɱɢɥ ɄɭȺɂ (1965), ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɡɚɜɟɞɭɸɳɢɣ ɤɚɮɟɞɪɨɣ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ ɢ ɚɜɢɚɞɜɢɝɚɬɟɥɟɣ ɆȽɌɍ
ȽȺ, ɚɜɬɨɪ ɛɨɥɟɟ 350 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɬɟɯɧɢɱɟɫɤɚɹ ɷɤɫɩɥɭɚɬɚɰɢɹ ɢ ɩɨɞɞɟɪɠɚɧɢɟ ɥɟɬɧɨɣ ɝɨɞɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ, ɚɧɚɥɢɡ ɢ ɫɢɧɬɟɡ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɫɜɨɣɫɬɜ
ɚɜɢɚɰɢɨɧɧɨɣ ɬɟɯɧɢɤɢ.
Ɉɣɞɨɜ ɇɚɦɛɚɬ, 1963 ɝ.ɪ., ɨɤɨɧɱɢɥ ɈɅȺȽȺ (2002), ɚɫɩɢɪɚɧɬ ɆȽɌɍ ȽȺ, ɚɜɬɨɪ 2 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɧɨɪɦɚɬɢɜɧɨ-ɩɪɚɜɨɜɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɩɨɞɞɟɪɠɚɧɢɹ ɥɟɬɧɨɣ ɝɨɞɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ
ɫɭɞɨɜ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɥɟɬɨɜ.
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