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Нейросетевая система выбора трасс захода на посадку воздушных судов при изменении направления ветра..pdf

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2015
ɇȺɍɑɇɕɃ ȼȿɋɌɇɂɄ ɆȽɌɍ ȽȺ
ʋ 221
ɍȾɄ 629.7.351
ɇȿɃɊɈɋȿɌȿȼȺə ɋɂɋɌȿɆȺ ȼɕȻɈɊȺ ɌɊȺɋɋ
ɁȺɏɈȾȺ ɇȺ ɉɈɋȺȾɄɍ ȼɈɁȾɍɒɇɕɏ ɋɍȾɈȼ
ɉɊɂ ɂɁɆȿɇȿɇɂɂ ɇȺɉɊȺȼɅȿɇɂə ȼȿɌɊȺ1
Ƚ.ɇ. ɅȿȻȿȾȿȼ, ȼ.Ȼ. ɆȺɅɕȽɂɇ
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɪɟɲɟɧɢɟ ɜɚɠɧɨɣ ɩɪɚɤɬɢɱɟɫɤɨɣ ɡɚɞɚɱɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɩɪɢ ɢɯ ɡɚɯɨɞɟ
ɧɚ ɩɨɫɚɞɤɭ ɧɚ ɪɚɡɧɵɟ ɬɪɚɫɫɵ Ɇɨɫɤɨɜɫɤɨɝɨ ɚɷɪɨɭɡɥɚ ɜ ɫɥɭɱɚɟ ɜɧɟɡɚɩɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɦɟɬɟɨɭɫɥɨɜɢɣ. ɇɚ ɨɫɧɨɜɟ
ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɩɪɟɞɥɨɠɟɧɚ ɧɟɣɪɨɫɟɬɟɜɚɹ ɩɪɨɰɟɞɭɪɚ ɧɚɡɧɚɱɟɧɢɹ ɩɪɢɨɪɢɬɟɬɨɜ ɞɥɹ ɤɚɠɞɨɝɨ
ɜɨɡɞɭɲɧɨɝɨ ɫɭɞɧɚ ɜ ɪɟɚɥɶɧɨɦ ɦɚɫɲɬɚɛɟ ɜɪɟɦɟɧɢ, ɱɬɨ ɩɨɡɜɨɥɢɥɨ ɮɨɪɦɢɪɨɜɚɬɶ ɫɩɢɫɤɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɞɥɹ ɤɚɠɞɨɣ
ɬɪɚɫɫɵ ɩɨɫɚɞɤɢ ɢ ɨɩɪɟɞɟɥɹɬɶ ɩɟɪɜɨɨɱɟɪɟɞɧɨɫɬɶ ɢɯ ɩɨɫɚɞɤɢ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɩɪɢɨɪɢɬɟɬɧɨɟ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɧɟɣɪɨɧɧɵɟ ɫɟɬɢ, ɨɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ,
ɜɨɡɞɭɲɧɵɟ ɫɭɞɚ, ɞɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ, ɡɚɯɨɞ ɧɚ ɩɨɫɚɞɤɭ.
ɉɪɢ ɜɧɟɡɚɩɧɨɦ ɢɡɦɟɧɟɧɢɢ ɭɫɥɨɜɢɣ ɩɨɫɚɞɤɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ (ȼɋ) ɜ Ɇɨɫɤɨɜɫɤɨɦ
ɚɷɪɨɭɡɥɟ ɧɟɨɛɯɨɞɢɦɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɨɩɟɪɚɬɢɜɧɨɟ ɩɟɪɟɩɥɚɧɢɪɨɜɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɡɚɯɨɞɚ ɧɚ
ɩɨɫɚɞɤɭ ɢ ɫɚɦɨɣ ɩɨɫɚɞɤɢ ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɱɚɫɬɶ ɩɨɫɚɞɨɱɧɵɯ ɤɭɪɫɨɜ ɫɬɚɧɨɜɢɬɫɹ ɢɫɤɥɸɱɟɧɧɨɣ
ɢɡ ɨɛɫɥɭɠɢɜɚɧɢɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨ ɡɚɧɨɜɨ ɮɨɪɦɢɪɨɜɚɬɶ ɫɩɢɫɤɢ ɫɭɞɨɜ ɩɪɢ ɞɜɢɠɟɧɢɢ ɤ
Ɇɨɫɤɜɟ ɩɨ ɤɚɠɞɨɣ ɬɪɚɫɫɟ, ɨɩɪɟɞɟɥɹɬɶ ɩɪɢɨɪɢɬɟɬɵ ɢɯ ɩɨɩɚɞɚɧɢɣ ɷɲɟɥɨɧ ɢ ɭɫɬɚɧɨɜɢɬɶ
ɩɟɪɜɨɨɱɟɪɟɞɧɨɫɬɶ ɢɯ ɩɪɢɡɟɦɥɟɧɢɹ. Ɉɞɧɢɦ ɢɡ ɢɡɜɟɫɬɧɵɯ ɩɨɞɯɨɞɨɜ ɞɥɹ ɪɟɲɟɧɢɹ ɭɤɚɡɚɧɧɨɣ
ɡɚɞɚɱɢ ɹɜɥɹɟɬɫɹ ɜɵɱɢɫɥɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɢɨɪɢɬɟɬɨɜ ɞɥɹ ɤɚɠɞɨɝɨ ȼɋ ɩɨ ɫɩɟɰɢɚɥɶɧɵɦ
ɮɨɪɦɭɥɚɦ, ɩɨɡɜɨɥɹɸɳɢɦ ɚɥɝɟɛɪɚɢɱɟɫɤɢɦ ɩɭɬɟɦ ɭɱɢɬɵɜɚɬɶ ɟɝɨ ɛɥɢɡɨɫɬɶ ɤ ɡɚɞɚɧɧɨɣ ɬɪɚɫɫɟ, ɟɝɨ
ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɤɭɪɫ, ɨɫɬɚɜɲɢɣɫɹ ɡɚɩɚɫ ɬɨɩɥɢɜɚ ɢ ɟɝɨ ɬɟɯɧɢɱɟɫɤɨɟ ɫɨɫɬɨɹɧɢɟ [1], [2]. Ɉɞɧɚɤɨ
ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨ ɨɫɭɳɟɫɬɜɢɬɶ ɪɹɞ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɧɚɞ
ɬɟɤɭɳɢɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ ɦɟɫɬɨɩɨɥɨɠɟɧɢɹ ȼɋ, ɱɬɨ ɜ ɰɟɥɨɦ ɨɩɪɟɞɟɥɹɟɬ ɜɵɫɨɤɭɸ ɬɪɭɞɨɟɦɤɨɫɬɶ
ɜɵɱɢɫɥɟɧɢɣ ɩɪɢ ɩɨɹɜɥɟɧɢɢ ɜ ɜɨɡɞɭɲɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ȼɋ.
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɪɚɫɫɦɨɬɪɟɧ ɞɪɭɝɨɣ ɫɩɨɫɨɛ ɚɥɶɬɟɪɧɚɬɢɜɧɨɝɨ ɜɵɛɨɪɚ ɧɭɠɧɵɯ ɪɟɲɟɧɢɣ
ɧɚ ɨɫɧɨɜɟ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ (ɇɋ) ɞɥɹ ɪɟɲɟɧɢɹ ɞɜɭɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ
ɜɵɩɨɥɧɹɟɦɵɯ ɡɚɞɚɱ:
- ɜɵɛɨɪ ɞɥɹ ɤɚɠɞɨɝɨ ȼɋ ɧɚɢɛɨɥɟɟ ɩɨɞɯɨɞɹɳɟɣ ɬɪɚɫɫɵ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɢ ɫɩɢɫɤɨɜ ɫɭɞɨɜ
ɞɥɹ ɤɚɠɞɨɣ ɬɪɚɫɫɵ ɜ ɨɬɞɟɥɶɧɨɫɬɢ;
- ɨɩɪɟɞɟɥɟɧɢɟ ɩɟɪɜɨɨɱɟɪɟɞɧɨɫɬɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ȼɋ ɜɧɭɬɪɢ ɤɚɠɞɨɝɨ ɫɩɢɫɤɚ ɫ ɰɟɥɶɸ
ɧɚɡɧɚɱɟɧɢɹ ɩɪɢɨɪɢɬɟɬɧɵɯ ɫɭɞɨɜ ɞɥɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ «ɬɪɨɦɛɨɧɟ». ɂɥɥɸɫɬɪɚɰɢɹ ɪɟɲɟɧɢɹ ɷɬɢɯ
ɡɚɞɚɱ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 1.
Ɉɫɧɨɜɧɨɣ ɫɦɵɫɥ ɧɟɣɪɨɫɟɬɟɜɨɣ ɬɟɯɧɨɥɨɝɢɢ ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ [3]. ɂɫɤɭɫɫɬɜɟɧɧɵɟ
ɧɟɣɪɨɧɧɵɟ ɫɟɬɢ ɫɬɪɨɹɬɫɹ ɩɨ ɩɪɢɧɰɢɩɚɦ ɨɪɝɚɧɢɡɚɰɢɢ ɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɢɯ ɛɢɨɥɨɝɢɱɟɫɤɢɯ
ɚɧɚɥɨɝɨɜ. Ɉɧɢ ɫɩɨɫɨɛɧɵ ɪɟɲɚɬɶ ɲɢɪɨɤɢɣ ɤɪɭɝ ɡɚɞɚɱ ɪɚɫɩɨɡɧɚɜɚɧɢɹ ɨɛɪɚɡɨɜ, ɢɞɟɧɬɢɮɢɤɚɰɢɢ,
ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ, ɨɩɬɢɦɢɡɚɰɢɢ, ɭɩɪɚɜɥɟɧɢɹ ɫɥɨɠɧɵɦɢ ɨɛɴɟɤɬɚɦɢ.
ɇɟɣɪɨɧ ɹɜɥɹɟɬɫɹ ɫɨɫɬɚɜɧɨɣ ɱɚɫɬɶɸ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ. ɇɚ ɪɢɫ. 2 ɩɨɤɚɡɚɧɚ ɟɝɨ ɫɬɪɭɤɬɭɪɚ, ɨɧ
ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɦɟɧɬɨɜ: ɭɦɧɨɠɢɬɟɥɟɣ (ɫɢɧɚɩɫɨɜ), ɫɭɦɦɚɬɨɪɚ ɢ ɧɟɥɢɧɟɣɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ.
ɋɢɧɚɩɫɵ ɨɫɭɳɟɫɬɜɥɹɸɬ ɫɜɹɡɶ ɦɟɠɞɭ ɧɟɣɪɨɧɚɦɢ, ɭɦɧɨɠɚɸɬ ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ ɧɚ ɱɢɫɥɨ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ ɫɢɥɭ ɫɜɹɡɢ (ɜɟɫ ɫɢɧɚɩɫɚ). ɋɭɦɦɚɬɨɪ ɜɵɩɨɥɧɹɟɬ ɫɥɨɠɟɧɢɟ ɫɢɝɧɚɥɨɜ,
ɩɨɫɬɭɩɚɸɳɢɯ ɩɨ ɫɢɧɨɩɬɢɱɟɫɤɢɦ ɫɜɹɡɹɦ ɨɬ ɞɪɭɝɢɯ ɧɟɣɪɨɧɨɜ ɢ ɜɧɟɲɧɢɯ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ.
ɇɟɥɢɧɟɣɧɵɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɪɟɚɥɢɡɭɟɬ ɧɟɥɢɧɟɣɧɭɸ ɮɭɧɤɰɢɸ ɨɞɧɨɝɨ ɚɪɝɭɦɟɧɬɚ –
ɜɵɯɨɞɚ ɫɭɦɦɚɬɨɪɚ. ɗɬɚ ɮɭɧɤɰɢɹ ɧɚɡɵɜɚɟɬɫɹ ɮɭɧɤɰɢɟɣ ɚɤɬɢɜɚɰɢɢ ɢɥɢ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɟɣ
ɧɟɣɪɨɧɚ.
1
Ɋɚɛɨɬɚ ɜɵɩɨɥɧɟɧɚ ɩɪɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɩɨɞɞɟɪɠɤɟ ɝɪɚɧɬɚ ɊɎɎɂ 13-08-00182.
ɇɟɣɪɨɫɟɬɟɜɚɹ ɫɢɫɬɟɦɚ ɜɵɛɨɪɚ…
139
Ɋɢɫ. 1. Ɋɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɩɨ ɬɪɚɫɫɚɦ
Ɋɢɫ. 2. ɋɬɪɭɤɬɭɪɚ ɢɫɤɭɫɫɬɜɟɧɧɨɝɨ ɧɟɣɪɨɧɚ
ɇɟɣɪɨɧ ɜ ɰɟɥɨɦ ɪɟɚɥɢɡɭɟɬ ɫɤɚɥɹɪɧɭɸ ɮɭɧɤɰɢɸ ɜɟɤɬɨɪɧɨɝɨ ɚɪɝɭɦɟɧɬɚ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ
ɦɨɞɟɥɶ ɧɟɣɪɨɧɚ:
S = ¦ i =1 wi xi + b,
n
(1)
y = f (s),
ɝɞɟ wi - ɜɟɫ (weight) ɫɢɧɚɩɫɚ, i = 1…n; b – ɡɧɚɱɟɧɢɟ ɫɦɟɳɟɧɢɹ (bias); s – ɪɟɡɭɥɶɬɚɬ
ɫɭɦɦɢɪɨɜɚɧɢɹ (sum); xi – ɤɨɦɩɨɧɟɧɬ ɜɯɨɞɧɨɝɨ ɜɟɤɬɨɪɚ (ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ), i = 1…n; y - ɜɵɯɨɞɧɨɣ
ɫɢɝɧɚɥ ɧɟɣɪɨɧɚ; n – ɱɢɫɥɨ ɜɯɨɞɨɜ ɧɟɣɪɨɧɚ; f – ɧɟɥɢɧɟɣɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ (ɮɭɧɤɰɢɹ ɚɤɬɢɜɚɰɢɢ).
Ɉɞɧɨɣ ɢɡ ɫɚɦɵɯ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɯ ɹɜɥɹɟɬɫɹ ɧɟɥɢɧɟɣɧɚɹ ɮɭɧɤɰɢɹ ɚɤɬɢɜɚɰɢɢ ɫ
ɧɚɫɵɳɟɧɢɟɦ, ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɥɨɝɢɫɬɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ ɢɥɢ ɫɢɝɦɨɢɞ (ɮɭɧɤɰɢɹ S-ɨɛɪɚɡɧɨɝɨ ɜɢɞɚ)
1
f (s) =
. ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ a ɫɢɝɦɨɢɞ ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɟɟ ɩɨɥɨɝɢɦ, ɜ ɩɪɟɞɟɥɟ ɩɪɢ a = 0
1 + e − as
ɜɵɪɨɠɞɚɹɫɶ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɥɢɧɢɸ ɧɚ ɭɪɨɜɧɟ 0,5, ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ a ɫɢɝɦɨɢɞ ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ
ɜɢɞɭ ɟɞɢɧɢɱɧɨɝɨ ɫɤɚɱɤɚ ɫ ɩɨɪɨɝɨɦ ࣝ. ɂɡ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɫɢɝɦɨɢɞɚ ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜɵɯɨɞɧɨɟ
ɡɧɚɱɟɧɢɟ ɧɟɣɪɨɧɚ ɧɚɯɨɞɢɬɫɹ ɜ ɞɢɚɩɚɡɨɧɟ (0,1).
140
Ƚ.ɇ. Ʌɟɛɟɞɟɜ, ȼ.Ȼ. Ɇɚɥɵɝɢɧ
ɇɟɣɪɨɧɧɚɹ ɫɟɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɟɣɪɨɩɨɞɨɛɧɵɯ ɷɥɟɦɟɧɬɨɜ,
ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɫɨɟɞɢɧɟɧɧɵɯ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɢ ɫ ɜɧɟɲɧɟɣ ɫɪɟɞɨɣ ɫ ɩɨɦɨɳɶɸ ɫɜɹɡɟɣ,
ɨɩɪɟɞɟɥɹɟɦɵɯ ɜɟɫɨɜɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɮɭɧɤɰɢɣ, ɜɵɩɨɥɧɹɟɦɵɯ
ɧɟɣɪɨɧɚɦɢ ɜ ɫɟɬɢ, ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɬɪɢ ɬɢɩɚ:
• ɜɯɨɞɧɵɟ ɧɟɣɪɨɧɵ, ɧɚ ɤɨɬɨɪɵɟ ɩɨɞɚɟɬɫɹ ɜɟɤɬɨɪ, ɤɨɞɢɪɭɸɳɢɣ ɜɯɨɞɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɢɥɢ
ɨɛɪɚɡ ɜɧɟɲɧɟɣ ɫɪɟɞɵ; ɜ ɧɢɯ ɨɛɵɱɧɨ ɧɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɩɪɨɰɟɞɭɪ, ɚ
ɢɧɮɨɪɦɚɰɢɹ ɩɟɪɟɞɚɟɬɫɹ ɫ ɜɯɨɞɚ ɧɚ ɜɵɯɨɞ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɢɯ ɚɤɬɢɜɚɰɢɢ;
• ɜɵɯɨɞɧɵɟ ɧɟɣɪɨɧɵ, ɜɵɯɨɞɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɵɯ ɩɪɟɞɫɬɚɜɥɹɸɬ ɜɵɯɨɞɵ ɧɟɣɪɨɧɧɨɣ
ɫɟɬɢ; ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɜ ɧɢɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɜɵɪɚɠɟɧɢɹɦ (1);
• ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɧɟɣɪɨɧɵ, ɫɨɫɬɚɜɥɹɸɳɢɟ ɨɫɧɨɜɭ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ, ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜ
ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɹɟɬɫɹ ɬɚɤɠɟ ɩɨ ɜɵɪɚɠɟɧɢɹɦ (1).
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɬɨɩɨɥɨɝɢɢ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɬɪɢ ɨɫɧɨɜɧɵɯ ɬɢɩɚ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ:
• ɩɨɥɧɨɫɜɹɡɧɵɟ;
• ɦɧɨɝɨɫɥɨɣɧɵɟ;
• ɫɥɚɛɨɫɜɹɡɧɵɟ.
ȼ ɦɧɨɝɨɫɥɨɣɧɵɯ ɧɟɣɪɨɧɧɵɯ ɫɟɬɹɯ ɧɟɣɪɨɧɵ ɨɛɴɟɞɢɧɹɸɬɫɹ ɜ ɫɥɨɢ. ɋɥɨɣ ɫɨɞɟɪɠɢɬ
ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɟɣɪɨɧɨɜ ɫ ɟɞɢɧɵɦɢ ɜɯɨɞɧɵɦɢ ɫɢɝɧɚɥɚɦɢ. ɑɢɫɥɨ ɧɟɣɪɨɧɨɜ ɜ ɫɥɨɟ ɦɨɠɟɬ ɛɵɬɶ
ɥɸɛɵɦ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɧɟɣɪɨɧɨɜ ɜ ɞɪɭɝɢɯ ɫɥɨɹɯ.
Ʉɥɚɫɫɢɱɟɫɤɢɦ ɜɚɪɢɚɧɬɨɦ ɫɥɨɢɫɬɵɯ ɫɟɬɟɣ ɹɜɥɹɸɬɫɹ ɩɨɥɧɨɫɜɹɡɧɵɟ ɫɟɬɢ ɩɪɹɦɨɝɨ
ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ (ɪɢɫ. 3).
Ɋɢɫ. 3. Ɇɧɨɝɨɫɥɨɣɧɚɹ ɫɟɬɶ ɩɪɹɦɨɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɨɰɟɫɫ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ, ɫɭɳɧɨɫɬɶ ɞɟɣɫɬɜɢɣ, ɤɨɬɨɪɵɟ
ɨɧɚ ɫɩɨɫɨɛɧɚ ɜɵɩɨɥɧɹɬɶ, ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧ ɫɢɧɨɩɬɢɱɟɫɤɢɯ ɫɜɹɡɟɣ. ɉɨɷɬɨɦɭ, ɡɚɞɚɜɲɢɫɶ
ɨɩɪɟɞɟɥɟɧɧɨɣ ɫɬɪɭɤɬɭɪɨɣ ɫɟɬɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɚɤɨɣ-ɥɢɛɨ ɡɚɞɚɱɟ, ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ
ɨɩɬɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɜɫɟɯ ɩɟɪɟɦɟɧɧɵɯ ɜɟɫɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ (ɧɟɤɨɬɨɪɵɟ ɫɢɧɨɩɬɢɱɟɫɤɢɟ
ɫɜɹɡɢ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɨɹɧɧɵɦɢ). ɗɬɨɬ ɷɬɚɩ ɧɚɡɵɜɚɟɬɫɹ ɨɛɭɱɟɧɢɟɦ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ, ɢ ɨɬ ɬɨɝɨ,
ɧɚɫɤɨɥɶɤɨ ɤɚɱɟɫɬɜɟɧɧɨ ɨɧ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧ, ɡɚɜɢɫɢɬ ɫɩɨɫɨɛɧɨɫɬɶ ɫɟɬɢ ɪɟɲɚɬɶ ɩɨɫɬɚɜɥɟɧɧɵɟ
ɩɟɪɟɞ ɧɟɣ ɩɪɨɛɥɟɦɵ ɜɨ ɜɪɟɦɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ.
Ⱦɥɹ ɪɚɡɪɚɛɨɬɤɢ ɧɟɣɪɨɫɟɬɟɜɨɝɨ ɪɟɝɭɥɹɬɨɪɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɪɚɬɶ ɫɬɪɭɤɬɭɪɭ ɧɟɣɪɨɧɧɨɣ
ɫɟɬɢ (ɬɨɩɨɥɨɝɢɸ), ɫɮɨɪɦɢɪɨɜɚɬɶ ɨɛɭɱɚɸɳɭɸ ɜɵɛɨɪɤɭ ɢ ɜɵɛɪɚɬɶ ɚɥɝɨɪɢɬɦ ɨɛɭɱɟɧɢɹ ɫ
ɡɚɞɚɧɧɵɦ ɤɪɢɬɟɪɢɟɦ.
ȼ ɤɚɱɟɫɬɜɟ ɫɬɪɭɤɬɭɪɵ ɇɋ ɛɵɥɚ ɜɵɛɪɚɧɚ ɫɟɬɶ ɩɪɹɦɨɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫ ɞɟɜɹɬɶɸ
ɜɯɨɞɚɦɢ, ɞɟɫɹɬɶɸ ɧɟɣɪɨɧɚɦɢ ɫ ɝɢɩɟɪɛɨɥɢɱɟɫɤɨɣ ɬɚɧɝɟɧɰɢɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ ɚɤɬɢɜɚɰɢɢ ɜ
ɫɤɪɵɬɨɦ ɫɥɨɟ ɢ ɨɞɧɢɦ ɧɟɣɪɨɧɨɦ ɫ ɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɟɣ ɚɤɬɢɜɚɰɢɢ ɜ ɜɵɯɨɞɧɨɦ ɫɥɨɟ.
Ⱦɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɛɭɱɚɸɳɟɣ ɜɵɛɨɪɤɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɦɚɫɫɢɜɵ ɞɚɧɧɵɯ ɨ ɤɨɨɪɞɢɧɚɬɚɯ
X0, Z0, Xj, Yj, ࣛj, ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɮɨɪɦɢɪɨɜɚɧɢɢ ɡɚɤɨɧɨɜ ɭɩɪɚɜɥɟɧɢɹ.
ɋ ɩɨɦɨɳɶɸ ɩɚɤɟɬɚ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ Matlab ɛɵɥɚ ɧɚɩɢɫɚɧɚ ɩɪɨɝɪɚɦɦɚ
ɮɨɪɦɢɪɨɜɚɧɢɹ, ɨɛɭɱɟɧɢɹ ɢ ɬɟɫɬɢɪɨɜɚɧɢɹ ɪɚɛɨɬɵ ɇɋ. ɇɚɛɨɪ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɛɵɥ ɪɚɡɞɟɥɟɧ ɧɚ
ɇɟɣɪɨɫɟɬɟɜɚɹ ɫɢɫɬɟɦɚ ɜɵɛɨɪɚ…
141
ɞɜɟ ɱɚɫɬɢ – ɨɛɭɱɚɸɳɭɸ ɜɵɛɨɪɤɭ ɢ ɬɟɫɬɨɜɵɟ ɞɚɧɧɵɟ. Ɉɛɭɱɚɸɳɢɟ ɞɚɧɧɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ
ɨɛɭɱɟɧɢɹ ɇɋ, ɚ ɩɪɨɜɟɪɨɱɧɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɪɚɫɱɟɬɚ ɨɲɢɛɤɢ ɫɟɬɢ (ɪɢɫ. 4).
Ɋɢɫ. 4. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ, ɨɛɭɱɟɧɢɹ ɢ ɬɟɫɬɢɪɨɜɚɧɢɹ ɪɚɛɨɬɵ ɇɋ
Ɉɫɧɨɜɧɨɟ ɩɪɟɢɦɭɳɟɫɬɜɨ ɇɋ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɧɭɠɧɨɟ ɪɟɲɟɧɢɟ ɜ ɜɢɞɟ ɫɢɝɧɚɥɨɜ ɧɚ ɟɝɨ
ɜɯɨɞɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɜ ɚɥɝɟɛɪɚɢɱɟɫɤɨɣ ɮɨɪɦɟ, ɢ ɷɬɢɦ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɨɟ ɛɵɫɬɪɨɞɟɣɫɬɜɢɟ ɫɢɫɬɟɦɵ. ɇɟɞɨɫɬɚɬɤɨɦ ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɫɬɶ
ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɥɹ ɨɛɭɱɟɧɢɹ ɇɋ ɡɧɚɱɢɬɟɥɶɧɨɝɨ ɱɢɫɥɚ ɩɪɢɦɟɪɨɜ, ɟɫɥɢ ɤɨɥɢɱɟɫɬɜɨ ɜɯɨɞɧɵɯ
ɫɢɝɧɚɥɨɜ ɢ ɜɵɯɨɞɧɵɯ ɤɥɚɫɫɨɜ ɜɟɥɢɤɨ. ɉɨɷɬɨɦɭ ɢɦɟɟɬ ɫɦɵɫɥ ɨɝɪɚɧɢɱɢɬɶ ɪɚɡɦɟɪɧɨɫɬɶ ɪɟɲɚɟɦɵɯ
ɡɚɞɚɱ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɫɥɟɞɭɸɳɢɦ ɧɟɣɪɨɫɟɬɟɜɵɦ ɫɬɪɭɤɬɭɪɚɦ.
ȼ ɩɟɪɜɨɣ ɡɚɞɚɱɟ ɫ ɭɱɟɬɨɦ ɬɨɝɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚ, ɱɬɨ ɜ Ɇɨɫɤɨɜɫɤɨɦ ɚɷɪɨɭɡɥɟ ɢɦɟɟɬɫɹ
4 ɬɪɚɫɫɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɟɬɪɚ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ 4 ɩɨɫɚɞɨɱɧɵɦ ɤɭɪɫɚɦ ࣛi,
i = 1..4. ȿɫɥɢ ɩɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɫɟ ɬɪɚɫɫɵ ɩɟɪɟɫɟɤɚɸɬɫɹ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ
X0, Z0, ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɭɱɟɫɬɶ ɤɨɨɪɞɢɧɚɬɵ Xj, Yj, ࣛj ɦɟɫɬɨɩɨɥɨɠɟɧɢɹ ɢ ɤɭɪɫɚ j-ɝɨ ȼɋ, ɬɨ ɧɭɠɧɨ
ɢɦɟɬɶ 9 ɫɢɝɧɚɥɨɜ ɧɚ ɜɯɨɞɟ ɩɟɪɜɨɣ ɇɋ-1. ɇɚ ɟɟ ɜɵɯɨɞɟ ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɪɚɬɶ ɨɞɧɭ ɢɡ
4 ɚɥɶɬɟɪɧɚɬɢɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɦɟɟɦ n1 = 9, N = 4.
ȼɨ ɜɬɨɪɨɣ ɡɚɞɚɱɟ ɨɬɞɟɥɶɧɵɟ ɫɩɢɫɤɢ ȼɋ ɞɥɹ ɤɚɠɞɨɣ ɬɪɚɫɫɵ ɢɦɟɸɬ ɧɟɛɨɥɶɲɭɸ ɞɥɢɧɭ, ɧɨ
ɬɟɦ ɧɟ ɦɟɧɟɟ, ɟɫɥɢ ɜɡɹɬɶ n2 = 10, ɬɨ ɫ ɭɱɟɬɨɦ ɬɪɟɯ ɤɨɨɪɞɢɧɚɬ Xj, Yj, ࣛj ɞɥɹ ɤɚɠɞɨɝɨ ȼɋ ɭɠɟ
ɨɛɪɚɡɭɟɬɫɹ 30 ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ. ɑɬɨɛɵ ɫɨɨɬɧɟɫɬɢ ɨɞɧɭ ɡɚɞɚɱɭ ɫ ɞɪɭɝɨɣ, ɩɪɢɦɟɦ ɞɨɩɭɳɟɧɢɟ,
ɱɬɨ ɫɪɚɜɧɟɧɢɸ ɩɨɞɜɟɪɝɚɸɬɫɹ ɬɪɢ ȼɋ, ɚ ɜɵɛɢɪɚɟɬɫɹ ɨɞɧɨ ɢɡ ɧɢɯ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɪɚɡɭɟɬɫɹ ɇɋ-2
ɩɪɢ n2 = 9, N = 3. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢɫɩɨɥɶɡɭɹ ɇɋ-2 ɢ ɚɧɚɥɢɡɢɪɭɹ ɤɚɠɞɵɣ ɪɚɡ ɬɪɢ ȼɋ, ɦɨɠɧɨ
ɩɨɬɨɦ ɚɧɚɥɢɡɢɪɨɜɚɬɶ ɪɟɡɭɥɶɬɚɬɵ, ɨɛɴɟɞɢɧɹɹ ɢɯ ɧɚ ɜɯɨɞɟ ɧɨɜɨɣ ɇɋ-2 ɢ ɬ.ɞ. Ʌɟɝɤɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ
ɞɥɹ ɚɧɚɥɢɡɚ ɞɟɜɹɬɢ ȼɋ ɩɨɬɪɟɛɭɟɬɫɹ 17 ɩɨɩɵɬɨɤ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɇɋ-2, ɚ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɢɯ ɱɢɫɥɨ
ɩɪɢɦɟɪɧɨ ɪɚɜɧɨ n (0,1n + 1). Ⱦɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɷɬɢɯ ɩɨɩɵɬɨɤ ɜ ɰɢɤɥɟ ɞɨɫɬɚɬɨɱɧɨ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨɞɚɜɚɬɶ ɧɚ ɜɯɨɞ ɨɞɧɨɣ ɦɚɥɨɪɚɡɦɟɪɧɨɣ ɇɋ-2 ɧɭɠɧɵɣ ɫɨɫɬɚɜ ɫɢɝɧɚɥɨɜ.
ɊȿɁɍɅɖɌȺɌɕ ɈȻɍɑȿɇɂə ɇȿɃɊɈɇɇɕɏ ɋȿɌȿɃ
ȺɅɖɌȿɊɇȺɌɂȼɇɈȽɈ ɉɅȺɇɂɊɈȼȺɇɂə ɁȺɏɈȾȺ ɇȺ ɉɈɋȺȾɄɍ
Ɉɛɭɱɟɧɢɟ ɬɪɟɯɫɥɨɣɧɨɣ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ ɩɪɨɜɨɞɢɥɨɫɶ ɜ ɫɪɟɞɟ Matlab. ɉɪɢ ɷɬɨɦ ɜ ɡɚɞɚɱɟ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɭɞɨɜ ɦɟɠɞɭ ɬɪɚɫɫɚɦɢ ɱɢɫɥɨ ɚɥɶɬɟɪɧɚɬɢɜ ɛɵɥɨ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɬɪɚɫɫ ɩɨɫɚɞɤɢ
142
Ƚ.ɇ. Ʌɟɛɟɞɟɜ, ȼ.Ȼ. Ɇɚɥɵɝɢɧ
ɜ Ɇɨɫɤɨɜɫɤɨɦ ɚɷɪɨɭɡɥɟ (N = 4). ȼɨ ɜɬɨɪɨɣ ɡɚɞɚɱɟ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɢɨɪɢɬɟɬɧɨɫɬɢ ɫɭɞɨɜ ɞɥɹ ɨɞɧɨɣ
ɬɪɚɫɫɵ ɱɢɫɥɨ ɚɥɶɬɟɪɧɚɬɢɜ (N = 3). Ʉɚɤ ɛɵɥɨ ɫɤɚɡɚɧɨ ɜɵɲɟ, ɱɢɫɥɨ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ ɞɥɹ ɨɛɟɢɯ
ɡɚɞɚɱ ɛɵɥɨ ɪɚɜɧɨ 9. Ɋɟɡɭɥɶɬɚɬɵ ɨɛɭɱɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 5, ɝɞɟ ɫɥɟɜɚ ɩɨɤɚɡɚɧɚ ɫɬɪɭɤɬɭɪɚ
ɨɞɧɨɬɢɩɧɨɣ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ, ɫɩɪɚɜɚ ɝɪɚɮɢɤ ɫɧɢɠɟɧɢɹ ɱɢɫɥɚ ɨɲɢɛɨɤ ɪɚɫɩɨɡɧɚɜɚɧɢɹ ɨɬ
ɤɨɥɢɱɟɫɬɜɚ ɩɪɢɦɟɪɨɜ ɨɛɭɱɟɧɢɹ.
ɇɚ ɪɢɫ. 5 ɩɨɤɚɡɚɧɨ, ɱɬɨ ɡɚ 5 ɷɩɨɯ ɨɛɭɱɟɧɢɹ (1 ɷɩɨɯɚ = 1 ɰɢɤɥ ɨɛɭɱɟɧɢɹ) ɫɟɬɶ ɨɛɭɱɟɧɚ
ɜɵɞɚɜɚɬɶ ɫɢɝɧɚɥ ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ 1.68*10-11.
Pɢɫ. 5. ɉɪɨɰɟɫɫ ɨɛɭɱɟɧɢɹ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɰɟɫɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɧɚɫɬɪɨɣɤɢ ɨɞɧɨɬɢɩɧɨɣ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ ɧɚ
ɤɨɦɩɶɸɬɟɪɟ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɚɬɪɭɞɧɟɧɢɣ, ɚ ɩɪɨɰɟɫɫ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɬɨɣ ɫɟɬɢ ɩɪɢ ɷɤɫɩɥɭɚɬɚɰɢɢ
ɫɜɨɞɢɬɫɹ ɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɦɭ ɩɪɢɦɟɧɟɧɢɸ ɷɬɨɣ ɫɟɬɢ ɫɧɚɱɚɥɚ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɨɪɚ
ɬɪɚɫɫɵ ɞɥɹ ɤɚɠɞɨɝɨ ȼɋ, ɡɚɬɟɦ – ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɦɟɫɬɚ ɷɬɨɝɨ ȼɋ ɜ ɨɛɳɟɣ ɨɱɟɪɟɞɢ ɡɚɯɨɞɚ ɧɚ
ɩɨɫɚɞɤɭ.
ɁȺɄɅɘɑȿɇɂȿ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɩɪɨɜɟɞɟɧɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ:
1. ɉɪɟɞɥɨɠɟɧɨ ɞɜɭɯɷɬɚɩɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɨɩɪɟɞɟɥɟɧɢɹ ɞɥɹ ɤɚɠɞɨɝɨ ȼɋ ɧɨɦɟɪɚ ɬɪɚɫɫɵ
ɡɚɯɨɞɚ ɧɚ ɩɨɫɚɞɤɭ ɢ ɟɝɨ ɦɟɫɬɚ ɜ ɨɛɳɟɣ ɨɱɟɪɟɞɢ ɞɜɢɠɟɧɢɹ ɫɭɞɨɜ ɜ ɷɲɟɥɨɧɟ ɩɨɫɚɞɤɢ.
2. Ʉɚɠɞɵɣ ɷɬɚɩ ɪɟɲɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɨɞɧɨɬɢɩɧɨɣ ɬɪɟɯɫɥɨɣɧɨɣ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ, ɢɦɟɸɳɟɣ ɧɚ ɫɜɨɟɦ ɜɯɨɞɟ 9 ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ. ɗɬɨ
ɨɛɟɫɩɟɱɢɜɚɟɬ ɪɟɲɟɧɢɟ ɧɭɠɧɵɯ ɡɚɞɚɱ ɩɪɚɤɬɢɱɟɫɤɢ ɜ ɪɟɚɥɶɧɨɦ ɦɚɫɲɬɚɛɟ ɜɪɟɦɟɧɢ ɩɪɢ ɦɚɥɨɦ
ɱɢɫɥɟ ɚɥɶɬɟɪɧɚɬɢɜ.
3. Ɉɛɭɱɟɧɢɟ ɜɵɛɪɚɧɧɨɣ ɫɬɪɭɤɬɭɪɟ ɬɪɟɯɫɥɨɣɧɨɣ ɧɟɣɪɨɧɧɨɣ ɫɟɬɢ ɩɨɤɚɡɚɥɨ, ɱɬɨ ɦɚɥɚɹ
ɜɟɪɨɹɬɧɨɫɬɶ ɨɲɢɛɨɱɧɵɯ ɪɟɲɟɧɢɣ ɞɨɫɬɢɝɚɟɬɫɹ ɩɪɢ ɧɟɛɨɥɶɲɨɦ ɱɢɫɥɟ ɩɪɢɦɟɪɨɜ ɧɟ ɛɨɥɟɟ 100, ɚ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɩɪɢɦɟɧɟɧɢɟ ɷɬɨɣ ɫɟɬɢ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɚɬɪɭɞɧɟɧɢɣ ɩɪɢ ɬɟɯɧɢɱɟɫɤɨɣ
ɪɟɚɥɢɡɚɰɢɢ.
ɇɟɣɪɨɫɟɬɟɜɚɹ ɫɢɫɬɟɦɚ ɜɵɛɨɪɚ…
143
ɅɂɌȿɊȺɌɍɊȺ
1. Ʌɟɛɟɞɟɜ Ƚ.ɇ., Ɇɚɥɵɝɢɧ ȼ.Ȼ., ɇɟɱɚɟɜ ȿ.ȿ., Ɍɢɧ ɉɯɨɧ ɑɠɨ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɫɢɫɬɟɦɵ
ɩɪɢɨɪɢɬɟɬɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɪɢ ɜɧɟɞɪɟɧɢɢ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɩɪɢɥɟɬɨɦɜɵɥɟɬɨɦ ɜ ɜɨɡɞɭɲɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ Ɇɨɫɤɨɜɫɤɨɝɨ ɚɷɪɨɭɡɥɚ // ɇɚɭɱɧɵɣ ɜɟɫɬɧɢɤ ɆȽɌɍ ȽȺ. 2012.
ʋ 180. ɋ. 254-259.
2. Ɍɢɧ ɉɯɨɧ ɑɠɨ. Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɨɩɟɪɚɬɢɜɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɦɟɠɞɭ
ɬɪɚɫɫɚɦɢ ɡɚɯɨɞɚ ɧɚ ɩɨɫɚɞɤɭ ɜ Ɇɨɫɤɨɜɫɤɨɦ ɚɷɪɨɭɥɟ ɩɪɢ ɜɧɟɡɚɩɧɨɦ ɢɡɦɟɧɟɧɢɢ ɦɟɬɟɨɭɫɥɨɜɢɣ //
ɇɚɭɱɧɵɣ ɜɟɫɬɧɢɤ ɆȺɂ. 2014. ʋ 3. ɋ. 128-140.
3. Ʉɭɡɢɧ Ⱥ.ɘ., Ʉɭɪɦɚɤɨɜ Ⱦ.ȼ., Ʌɭɤɶɹɧɨɜ Ⱥ.ȼ., Ɇɢɯɚɣɥɢɧ Ⱦ.Ⱥ. ɇɟɣɪɨɫɟɬɟɜɚɹ
ɪɟɚɥɢɡɚɰɢɹ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɛɟɡɨɩɚɫɧɨɣ ɩɨɫɚɞɤɨɣ ɛɟɫɩɢɥɨɬɧɨɝɨ ɥɟɬɚɬɟɥɶɧɨɝɨ
ɚɩɩɚɪɚɬɚ [ɷɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ] // Ɍɪɭɞɵ ɆȺɂ. 2013. ȼɵɩ. 70.
NEURAL NETWORK SYSTEM TRACKS LANDING AIRCRAFT WHEN
WIND DIRECTION CHANGES
Lebedev G.N., Malygin V.B.
The article describes the problem of solving important practical problems of redistribution of aircraft when landing
on a different route of the Moscow air hub in the event of a sudden change of weather conditions. The neural network
procedure to set priorities for each aircraft in real time based on dynamic programming is offered. This allowed us to
generate lists of vessels for each trace landing and to determine their priority for landing.
Keywords: priority service, artificial neural networks, optimal control, aircraft, dynamic programming, approach.
REFERENCES
1. Lebedev G.N., Malygin V.B., Nechayev E.E., Ting Phong Zhuo. Use of system of
priority service at introduction of automated management of an arrival departure in air space of the
Moscow airline hub // Nauchniy vestnik MGTU GA. 2012. No. 180. P. 254-259. (In Russian)
2. Ting Phong Zhuo. Automatization of expeditious distribution of aircrafts between routes of
landing approach in the Moscow airzone at sudden change of meteoconditions // Nauchniy vestnik
MAI. 2014. ʋ 3. P. 128-140. (In Russian)
3. Cousin A.Y., Kurmakov D.V., Lukyanov A.V., Mihailin D.A. Neural network realization
of automatic control of a safe landing of the pilotless aircraft [Electronic magazine] // Works MAI.
2013. Release 70. (In Russian)
ɋȼȿȾȿɇɂə ɈȻ ȺȼɌɈɊȺɏ
Ʌɟɛɟɞɟɜ Ƚɟɨɪɝɢɣ ɇɢɤɨɥɚɟɜɢɱ, 1936 ɝ.ɪ., ɨɤɨɧɱɢɥ ɆɂɎɂ (1959), ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ
ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ ɤɚɮɟɞɪɵ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɢ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ
Ɇɨɫɤɨɜɫɤɨɝɨ ɚɜɢɚɰɢɨɧɧɨɝɨ ɢɧɫɬɢɬɭɬɚ (ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ), ɚɜɬɨɪ
18 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɢ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ, ɦɟɬɨɞɵ ɨɩɬɢɦɢɡɚɰɢɢ ɢ ɞɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ.
Ɇɚɥɵɝɢɧ ȼɹɱɟɫɥɚɜ Ȼɨɪɢɫɨɜɢɱ, 1960 ɝ.ɪ., ɨɤɨɧɱɢɥ ɈɅȺȽȺ (1983), ɧɚɱɚɥɶɧɢɤ
ɭɱɟɛɧɨ-ɬɪɟɧɚɠɟɪɧɨɝɨ ɰɟɧɬɪɚ ɤɚɮɟɞɪɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ ɆȽɌɍ ȽȺ, ɚɜɬɨɪ
150 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɚɜɬɨɦɚɬɢɡɚɰɢɹ ɭɩɪɚɜɥɟɧɢɹ ɩɪɢɥɟɬɨɦ –
ɜɵɥɟɬɨɦ AMAN-DMAN.
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