1. LECTURE 27. Course: “Design of Systems: Structural Approach” Dept. “Communication Networks &Systems”, Faculty of Radioengineering & Cybernetics Moscow Institute of Physics and Technology (University) Email: mslevin@acm.org / mslevin@iitp.ru Mark Sh. Levin Inst. for Information Transmission Problems, RAS Nov. 12, 2004 PLAN: 1.Hierarchical approach to diagnosis of complex systems 2.Hierarchical evaluation of composable system: example for building: *models of building and corresponding evaluation scales for building parts *method of integration tables *usage of hierarchical combinatorial synthesis *change operations and planning an upgrade process

2. Multi-level diagnosis of complex systems PROCESS CONTROL INPUTOUTPUT DIAGNOSIS

3. Multi-level diagnosis of complex systems F1F1 F6F6 F3F3 F2F2 F1F1 F5F5 F4F4 P R O C E S S F6F6 F 2&3 F2F2 F3F3 F4F4 F5F5 F 4&5

4. Multi-level diagnosis of complex systems SCALE DAMAGE 1 234 BADNORMALOK F1F1 F2F2 F3F3 F4F4 F5F5 F6F6

5. Multi-level diagnosis of complex systems F 2&3 F2F2 F3F3 F 4&5 F4F4 F5F5 F 1 and F 2&3 and F 4&5 and F 6 TOTAL ESTIMATE

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

7. Generalized ordinal scale for damage 1.Distriction (global) 2.Distriction (local) 3.Chinks 4.Small chinks (hair like) 5.Without damage 1234512345

8. 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 1.2.1.1 Bearing structures 1.2.1 Nonbearing structures 1.2.2 Staircase 1.2.1.3 Rigity core 1.2.1.2 Partitioning walls 1.2.2.2 Filler walls 1.2.2.1 X X X X X X XXX X X X X XX X Example 1 Example 2

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

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

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

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

13. 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 1.2.1.1 Bearing structures 1.2.1 Nonbearing structures 1.2.2 Staircase 1.2.1.3 Rigity core 1.2.1.2 Partitioning walls 1.2.2.2 Filler walls 1.2.2.1 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

14. 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)

15. Method 2: Hierarchical morphological design (combinatorial synthesis) E1E2G1G2E1E2G1G2 G 1 G 2 H 1 H 2 H 3 3 2 3 1 2 2 1 2 1 2 3 2 1 2 1 1 NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility J1J2J3J1J2J3 I 1 I 2 I 3 I 4 1 2 3 3 1 1 1 2 3 3 Compatibility

16. 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 12 3 3 3 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 1 1 1 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility Compatibility

17. Method 2: Hierarchical morphological design (combinatorial synthesis) A1A2A3C1C2C3A1A2A3C1C2C3 C 1 C 2 C 3 B 1 B 3 B 4 B 13 2 2 2 2 2 2 1 3 2 2 3 3 3 2 2 2 2 2 2 2 1 3 3 3 2 2 2 2 3 NOTE: 3 corresponds to the best level of compatibility 0 corresponds to incompatibility Compatibility

18. 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

19. 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

20. 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

21. 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

22. 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