ЛЕКЦИЯ 27. Курс: “Проектирование систем: Структурный подход” Каф. “Коммуникационных сетей и систем”, Факультет радиотехники и кибернетики Московский физико-технический институт (университет) / Марк Ш. ЛЕВИН Институт проблем передачи информации, РАН Ноябрь 12, 2004 ПЛАН: 1.Иерархический подход к диагностике сложных систем 2.Иерархическое оценивание составной системы: пример для здания: *модель здания и шкалы оценки для частей здания *метод интегрирующих таблиц *иерархический комбинаторный синтез *операции изменения и планирование процесса upgrade

Много-уровневая диагностика сложной (составной) системы ПРОЦЕСС УПРАВЛЕНИЕ ВХООДВЫХОД ДИАГНОСТИКА

F1F1 F6F6 F3F3 F2F2 F1F1 F5F5 F4F4 ПРОЦЕСС F6F6 F 2&3 F2F2 F3F3 F4F4 F5F5 F 4&5 Много-уровневая диагностика сложной (составной) системы

ШКАЛА РАЗРУШЕНИЕ ПЛОХОХОРОШО F1F1 F2F2 F3F3 F4F4 F5F5 F6F6 Много-уровневая диагностика сложной (составной) системы ОТЛИЧНО

F 2&3 F2F2 F3F3 F 4&5 F4F4 F5F5 F 1 и F 2&3 и F 4&5 и F 6 РЕЗУЛЬТИРУЮЩАЯ ОЦЕНКА Много-уровневая диагностика сложной (составной) системы

Example of building (evaluation from the viewpoint of earthquake engineering) Cantilever balcony Parapet wall

Generalized ordinal scale for damage 1.Distriction (global) 2.Distriction (local) 3.Chinks 4.Small chinks (hair like) 5.Without damage

Hierarchical model of building and corresponding scales Foundation 1.1 Basic structure 1.2 Floors 1.3 Building: S = A*B*C A C B F JI D HGE Frame Bearing structures Nonbearing structures Staircase Rigity core Partitioning walls Filler walls X X X X X X XXX X X X X XX X Example 1 Example 2

Method 1: integration tables E G H D Bearing structures D (1.2.1), scale [3,4,5]

Method 1: integration tables Nonbearing structures F (1.2.2), scale [2,3,4,5] J I

Method 1: integration tables Basic structure B (1.2), scale [2,3,4,5] F D

Method 1: integration tables A B C S Building S, scale [2,3,4,5] A B C S A B C S

Method 2: Hierarchical morphological design (combinatorial synthesis) Foundation 1.1 Basic structure 1.2 Floors 1.3 Building: S = A*B*C A C B F JI D HGE Frame Bearing structures Nonbearing structures Staircase Rigity core Partitioning walls Filler walls A 1 (2) A 2 (1) A 3 (2) C 1 (1) C 2 (3) C 3 (3) H 1 (1) H 2 (2) H 3 (3) J 1 (1) J 2 (3) J 3 (2) E 1 (1) E 2 (2) G 1 (1) G 2 (2) I 1 (2) I 2 (2) I 3 (1) I 4 (1) D 1 =E 1 *G 1 *H 1... D 12 =... F 1 =I 1 *J 1... F 12 =... B 1 =D 1 *F 7... B 16 =... S 1 =A 2 *B 1 *C 1 S 2 =A 2 *B 3 *C 1 S 3 =A 2 *B 4 *C 1 S 4 =A 2 *B 13 *C 1

Method 2: Hierarchical morphological design (combinatorial synthesis) Design Alternatives for Building Foundation A : A 1 (strip foundation), A 2 (bedplate foundation), A 3 (isolated parts) Frame E : E 1 (monolith frame), E 2 (precast frame) Rigidity core G : G 1 (monolith rigid core), G 2 (precast rigid core) Stair case H : H 1 (monolith staircase), H 2 (precast staircase), H 3 (composite staircase) Filler walls I : I 1 (small elements), I 2 (curtain panel walls), I 3 (precast enclose panel walls), I 4 (frame walls) Partitioning walls J : J 1 (precast panel walls), J 2 (small elements), J 3 (frame walls) Floors C : C 1 (monolith slabs), C 2 (composite slabs), C 3 (precast slabs)

Method 2: Hierarchical morphological design (combinatorial synthesis) E1E2G1G2E1E2G1G2 G 1 G 2 H 1 H 2 H NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility J1J2J3J1J2J3 I 1 I 2 I 3 I Compatibility

Method 2: Hierarchical morphological design (combinatorial synthesis) D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 D 12 F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility Compatibility

Method 2: Hierarchical morphological design (combinatorial synthesis) A1A2A3C1C2C3A1A2A3C1C2C3 C 1 C 2 C 3 B 1 B 3 B 4 B NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility Compatibility

Method 2: Hierarchical morphological design (combinatorial synthesis) Examples for building : S i = A 1 * (E 1 * G 1 * H 1 ) * (I 3 * J 1 ) * C 1 estimate 2 (Pareto-layer) S ii = A 2 * (E 2 * G 2 * H 2 ) * (I 3 * J 1 ) * C 1 estimate 2 (Pareto-layer) S iii = A 1 * (E 2 * G 2 * H 2 ) * (I 3 * J 1 ) * C 3 estimate 3 S iv = A 2 * (E 2 * G 2 * H 2 ) * (I 3 * J 1 ) * C 3 estimate 3 S v = A 1 * (E 2 * G 1 * H 1 ) * (I 3 * J 3 ) * C 3 estimate 4

Improvement (upgrade) of building Operation group I (frames): O 1 increasing a geometrical dimension and active reinforcement O 2 increasing of active reinforcement Operation group II (joints): O 3 increasing a level for fixing a longitudinal active reinforcement in zone of joints O 4 decreasing the step of reinforced cross rods in zone of joint Operation group III (cantilever and cantilever balcony): O 5 decreasing the projection cantilever O 6 supplementary supporting the cantilever Operation group IV (fronton and parapet wall): O 7 fixing a bottom part O 8 designing a 3D structure (special) Operation group V (connection between frame and filler walls): O 9 design of shear keys O 10 design of mesh reinforcement O 11 partition of filler walls by auxiliary frame

Improvement (upgrade) of building Binary relation “equivalence” and “nonequivalence” Binary relation “complementarity” and “noncomplementarity” Binary relation “precedence” BINARY RELATIONS OVER IMPROVEMENT OPERATIONS Group 1. Improvement of earthquake resistance Group 2. Quality of architecture and plan decisions Group 4. Utilization properties Group 4. Expenditure CRITERIA FOR IMPROVEMENT OPERATIONS

Improvement (upgrade) of building Model 1: Knapsack Model 2: Multiple choice problem Model 3: Multiple criteria ranking Model 4: Morphological clique problem Model 5: Scheduling ETC. COMBINATORIAL MODELS FOR PLANNING OF IMPROVEMENT

Combinatorial synthesis for planning of redesign (improvement, upgrade) Improvement : S = A*B*(C*D)*E A C B D E O 1 (3) O 2 (1) O 1 &O 2 (4) None O 3 (32) O 4 (1) O 3 &O 4 (2) None O 9 (3) O 10 (2) O 11 (3) None O 7 (3) O 8 (2) None O 5 (3) O 6 (4) None Strategy: O 2 => O 4 => O 5 &O 7 (4) => O 10