Connective Complexity Methods for Analysis and Prediction in

Connective Complexity Methods for Analysis and Prediction in Engineering Design Master of Science Thesis Defense James Louis Mathieson Research Assistant Mechanical Engineering Clemson University jmathie@clemson. edu

MS Defense Complexity Methods Motivation jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 2/39 11/29/2020

MS Defense Complexity Methods Motivation jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 3/39 11/29/2020

Systems MS Defense Complexity Methods 4/39 11/29/2020 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Complex MS Defense Complexity Methods Abstraction & System Boundary Designer 5/39 11/29/2020 User Simple jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Existing Approaches Computational Complexity l l Used for processes Requires directionality Example: big-O notation Information Theory l l Used for sets of data Ignores directionality Example: entropy jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 6/39 11/29/2020

MS Defense Complexity Methods Connectivity Graph (Undirected) Representations Function Structure (Directed) 7/39 11/29/2020 Design Structure Matrix (Mixed) A A C D C D B jmathie@clemson. edu http: //www. clemson. edu/ces/cedar B

MS Defense Complexity Methods RQ 1 RQ 2 Research Questions 8/39 11/29/2020 How can complexity be measured? What can these measures be used for? jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Hypergraph Conceptualization MS Defense Complexity Methods Legend: Source Sink E 1 E 3 9/39 11/29/2020 -t 1 E 1 -t 2 Time E 2 -t 3 R 1 (t 1, t 3) E 2 R 1 R 2(t 1, t 5) R 3 E 1 E 3 R 3(t 2, t 4) -t 4 E 4 -t 5 R 2 (a) (b) jmathie@clemson. edu http: //www. clemson. edu/ces/cedar (c)

MS Defense Complexity Methods Measurement Interconnection 10/39 11/29/2020 Centrality Size Decomposition Complexity jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Size MS Defense Complexity Methods 11/39 11/29/2020 E 1 R 1 (t 1, t 3) E 2 R 2(t 1, t 5) E 3 R 3(t 2, t 4) E 4 Connective Dimensional l How many elements? l 4 How many bipartite edges? 8 l How many relationships? 3 l How many degrees of freedom? 6 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Interconnection MS Defense Complexity Methods 12/39 11/29/2020 E 1 R 1 (t 1, t 3) E 2 R 2(t 1, t 5) E 3 R 3(t 2, t 4) E 4 Flow Capacity Shortest Path Length l Maximum distance between elements? l 2 Mean distance between elements? 0. 75 Maximum paths between elements? l Mean paths between elements? 0. 5625 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Centrality MS Defense Complexity Methods 13/39 11/29/2020 E 1 R 1 (t 1, t 3) E 2 R 2(t 1, t 5) E 3 R 3(t 2, t 4) E 4 Clustering Coefficient Betweenness l Most shortest paths through one element? 1 l Mean shortest paths through any element? l Proportion of elements’ neighbors which connect to each other? 0 0. 5 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Decomposition MS Defense Complexity Methods 14/39 11/29/2020 E 1 R 1 (t 1, t 3) E 2 R 2(t 1, t 5) E 3 R 3(t 2, t 4) E 4 Core Number Ameri-Summers l First removal? l R 2 l l 1 Second removal? R 1, R 3 Score? 5 What is the degeneracy of the graph? l Mean k-core for any element? 0. 75 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Application jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 15/39 11/29/2020

MS Defense Complexity Methods Assembly Time Estimation jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 16/39 11/29/2020

MS Defense Complexity Methods Graph Translation 17/39 11/29/2020 1) Part 1 2) Part 2 3) Bolting Instance 4) Nut 1) Part 1 2) Part 2 Surface Contact Snap Fit Instance 3) Bolt 4) Nut Bolting Instance 1) Part 1 Snap Fit Instance 2) Part 2 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Relationship Identification MS Defense Complexity Methods 18/39 11/29/2020 Assembly Time (ta) [sec] 100000 10000 Rel. 1000 Elem. Conn. 100 DOF 10 10 1000 Metric Value jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 10000

Regression MS Defense Complexity Methods 19/39 11/29/2020 Assembly Time (ta) [sec] 100000 10000 R 2 = 0. 9932 1000 10 10 1000 Elements (n) jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 10000

rg i na r R l ed es Tw ig ee n l O Tw rig in ee al l R ed es Kn ig ife n O rig Kn in ife al R ed es M ig ix n er O rig M ix in er al R ed C ho es pp ig n e r O C ho rig pp in er al R ed es ig n ift e Sh fte r O Sh i Assembly Time (ta) [seconds] MS Defense Complexity Methods Refined Model 10000 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 20/39 11/29/2020 100000 Boothroyd DFA Complexity Model 1000 10

Validation MS Defense Complexity Methods Clicker Pen Electric Can Opener Cordless Drill Clicker Pen Mean [s] 42. 5 Gear Shifter CD Changer Fuel Tank 141. 82 54. 3 126. 98 21/39 11/29/2020 B&D Time [sec] Model Time [sec. ] % Error 34. 66 292. 22 128. 06 37. 42 286. 15 101. 19 8% -21% St. Dev. Δ [s] %E 8. 07 19% Maximum Val [s] %E 57. 15 34% Minimum Val [s] %E 23. 3 45% 37. 12 11. 4 25. 29 204. 94 74. 68 171. 99 104. 19 45. 92 106. 97 Mean %E: 26% 21% 20% 45% 38% 35% 27% 15% 16% 22% Mean %E: 38% Mean %E: 26% jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Application jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 22/39 11/29/2020

MS Defense Complexity Methods What if. . 23/39 11/29/2020 l $$$$ jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Market Values jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 24/39 11/29/2020

Graph Translation MS Defense Complexity Methods F 7 Element (Function) Transfer EE T 2 F 1 Transfer EE T 1 F 2 D 1 F 3 Transfer EE T 4 F 9 F 4 Transfer EE T 5 Transfer EE F 5 Distribute EE 25/39 11/29/2020 F 8 Relationship (Flow) D 1 F 6 T 3 Transfer EE F 11 T 6 F 10 Rel. F 6 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar Source D 1 Sink T 3, T 6

Graph Translation MS Defense Complexity Methods 26/39 11/29/2020 Element (Function) F 7 T 1 Transfer EE T 2 F 1 Transfer EE T 1 F 2 D 1 F 3 Transfer EE T 4 F 9 F 4 Transfer EE T 5 F 1 Transfer EE F 5 Distribute EE Relationship (Flow) T 2 F 7 F 8 T 3 F 6 F 8 Transfer EE F 11 E T 6 Rel. F 10 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar Source Sink F 1 E T 3 F 7 T 2 E F 8 T 3 E

MS Defense Complexity Methods l 27/39 11/29/2020 Architecture – l Neural Network: Properties Cascade-forward Backpropagation Networks Validation internal to training algorithm. – – – Repetition of inputs requires Training and Validation sets to interleave. Interleaved Training and Validation requires external validation. Products 15 -18 withheld for external validation. jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods l Output Layer – – l Layer Parameters Single, Pure-Linear Neuron Scales function Hidden Layers – 1 – 3 Layers, Maximum 15 Neurons l l l – 1 Layer: (1 – 15 Neurons) 2 Layer: (1 – 7 Neurons in each) 3 Layer: (1 – 5 Neurons in each) 189 Permutations l l 100 networks permutation Output evaluated on Kernel smoothing probability density estimate. jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 28/39 11/29/2020

Network Structure Evaluation 3. 5 7 3 6 2. 5 5 Probability Density MS Defense Complexity Methods 2 1. 5 1 0. 5 29/39 11/29/2020 4 3 2 1 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1 Minimum Normalized Probability Density 90% probability that all expected validation values will be in upper 50% 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1 Mean Normalized Probability Density 95% probability that mean expected validation values will be in upper 75% jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Validation Results MS Defense Complexity Methods Jigsaw 30/39 11/29/2020 Sewing Machine 0. 0080 0. 0250 Probability Density 0. 0070 0. 0200 0. 0150 0. 0100 0. 0050 0. 0060 0. 0050 0. 0040 0. 0030 0. 0020 0. 0010 0. 0000 $0 $20 35 mm Camera $40 $60 $80 Value [USD] $100 $120 $50 $100 $150 $200 $250 $300 $350 Value [USD] $0 $100 $200 $300 $400 $500 $600 $700 Value [USD] VCR 0. 0080 0. 0030 0. 0070 0. 0025 0. 0060 Probability Density $0 0. 0050 0. 0040 0. 0030 0. 0020 0. 0015 0. 0010 0. 0000 $0 $50 $100 $150 $200 Value [USD] $250 $300 0. 0000 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Application jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 31/39 11/29/2020

MS Defense Complexity Methods Design Process Tracking jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 32/39 11/29/2020

Work Pattern MS Defense Complexity Methods 33/39 11/29/2020 Mean Shortest Path Length 2. 5 2 1. 5 1 0. 5 0 1/8/09 1/15/09 1/22/09 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 1/29/09 2/5/09

Design Phase MS Defense Complexity Methods 34/39 11/29/2020 2. 5 Project Organization Generative Design Betweenness Density 2. 0 1. 5 1. 0 0. 5 0. 0 1/8/09 1/13/09 1/18/09 1/23/09 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 1/28/09 2/2/09

Group Dynamics MS Defense Complexity Methods 'P 1. 1' 'P 1. 2' 35/39 11/29/2020 'P 1. 3' 'P 1. 4' 1000 Betweenness 750 500 250 0 1/8/09 1/13/09 1/18/09 1/23/09 1/28/09 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 2/2/09

MS Defense Complexity Methods What have we learned? ASSEMBLY TIME MARKET VALUE DESIGN PROCESS jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 36/39 11/29/2020

MS Defense Complexity Methods Where do we go from here? 37/39 11/29/2020 LENGTH, CAPACITY, WEIGHT MODELING, MAPPING, CONFIDENCE CAD, LINGUISTICS, IT, AI MANUFACTURING, RELIABILITY, SUSTAINABILITY, ETC. jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

MS Defense Complexity Methods Acknowledgements jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 38/39 11/29/2020

MS Defense Complexity Methods Thank you jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 39/39 11/29/2020

MS Defense Complexity Methods Training Set jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 40/39 11/29/2020

MS Defense Complexity Methods Validation Set jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 41/39 11/29/2020

MS Defense Complexity Methods Regression Error 42/39 11/29/2020 ta = 2. 8 n 1. 1912 B&D Time [sec] Reg. Time [sec. ] Shifter Original Shifter Redesign Mixer Original Mixer Redesign Chopper Original Chopper Redesign Knife Original Knife Redesign Tweel™ Original Tweel™ Redesign 104. 56 42. 60 136 74. 7 228. 5 201 13561. 35 4925. 00 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 146. 70 75. 29 170. 25 102. 33 256. 53 260. 23 338. 49 254. 34 13362. 01 6032. 32 % Error 40% 77% 25% 37% 12% 29% 4% 6% -1% 22%

MS Defense Complexity Methods l Refined Model 43/39 11/29/2020 Shifter Original Shifter Redesign Mixer Original Mixer Redesign Chopper Original Chopper Redesign Knife Original Knife Redesign Tweel™ Original Tweel™ Redesign B&D Time [sec] Model Time [sec. ] % Error 104. 56 42. 60 136 74. 7 228. 5 201 325. 00 240. 00 13561. 35 4925. 00 105. 37 46. 10 132. 28 83. 76 229. 20 232. 50 306. 26 217. 71 11430. 28 4919. 21 1% 8% -3% 12% 0% 16% -9% -16% 0% jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Graph Translation MS Defense Complexity Methods 44/39 11/29/2020 F 7 Transfer EE T 2 F 1 Transfer EE T 1 F 2 Distribute EE D 1 F 3 Transfer EE T 4 F 9 F 4 Transfer EE T 5 Transfer EE F 5 Element (Function) F 8 T 3 Relationship (Flow) T 1 F 6 Transfer EE D 1 F 11 T 6 F 10 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar Rel. Source Sink F 2 T 1 D 1

MS Defense Complexity Methods l Continuous output desired – l Neural Network: Architecture Back propagation network best suited Four types of backprop networks – – Feed-forward Cascade-forward Elman Dynamic jmathie@clemson. edu http: //www. clemson. edu/ces/cedar 45/39 11/29/2020

MS Defense Complexity Methods l Neural Network: Training 46/39 11/29/2020 Validation internal to training algorithm. – – – Repetition of inputs requires Training and Validation sets to interleave. Interleaved Training and Validation requires external validation. Products 15 -18 withheld for external validation. jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Organization MS Defense Complexity Methods 47/39 11/29/2020 P 0. 0 - Sponsor Class P 0. 1 - Adviser A (Lead) P 0. 2 -Adviser B P 0. 3 - Adviser C P 1. 2 - Student B P 1. 3 - Student C P 1. 4 - Student D Stop Time Sources Sinks Org 1/8/09 4/27/09 P 0. 0 Org 1/8/09 4/27/09 P 0. 1 P 0. 2 P 0. 3 4/27/09 P 1. 1 P 1. 2 P 1. 3 P 1. 4 Org P 1. 1 - Student A Start Time Org 1/8/09 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar P 0. 1 P 0. 2 P 0. 3 P 1. 1 P 1. 2 P 1. 3 P 1. 4

MS Defense Complexity Methods Communication FROM: P 1. 1 – Student A TO: P 1. 2 – Student B, P 1. 3 – Student C SENT: 1/9/09 4: 52 PM SUBJECT: E 1. 1 – Email 1 ATTACHMENTS: D 1. 1 – Document 1 We need to discuss [T 1. 1 – Topic A], particularly with regards to [T 1. 2 – Topic B]. I’m also concerned that [T 1. 2 – Topic B] might have an impact on [T 1. 3 – Topic C]. What do you think? Class Start Time 48/39 11/29/2020 Stop Time Sources Sinks Comm 1/9/09 4: 52 PM P 1. 1 E 1. 1 P 1. 2 P 1. 3 T 1. 1 T 1. 2 T 1. 3 D 1. 1 E 1. 1 Comm 1/9/09 4: 52 PM D 1. 1 E 1. 1 Student A jmathie@clemson. edu http: //www. clemson. edu/ces/cedar

Document MS Defense Complexity Methods D 1. 2 D 1. 3 Class D 1. 1 P 1. 1 Doc Doc Start Time 1/9/09 1: 00 PM 1/9/09 5: 00 PM 1/9/09 1: 00 PM D 1. 1 Time 49/39 11/29/2020 P 1. 2 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar Stop Time 1/9/09 3: 30 PM 1/9/09 8: 30 PM Sources Sinks T 1. 1 T 1. 2 D 1. 1 T 1. 2 T 1. 3 P 1. 2 D 1. 1 P 1. 1 D 1. 2 D 1. 3 D 1. 1

Meeting MS Defense Complexity Methods MEETING MINUTES: M 1. 1 START: 1/15/09 3: 30 PM STOP: 1/15/09 4: 00 PM ATTENDEES: P 0. 1 – Adviser A, P 0. 2 – Adviser B, P 0. 3 – Adviser C, P 1. 1 – Student A, P 1. 2 – Student B, P 1. 3 – Student C, P 1. 4 – Student D Presentation (20 min): [T 1. 1 – Topic A], [T 1. 2 – Topic B], [T 1. 3 – Topic C] 50/39 11/29/2020 Start Time Class Meet 1/15/09 3: 30 PM Stop Time 1/15/09 3: 50 PM P 1. 1 P 1. 2 P 1. 3 P 1. 4 M 1. 1 1/15/09 4: 00 PM P 1. 1 P 1. 2 P 1. 3 P 1. 4 P 0. 1 P 0. 2 P 0. 3 M 1. 1 Discussion (10 min): [T 1. 2 – Topic B] Meet 1/15/09 3: 50 PM jmathie@clemson. edu http: //www. clemson. edu/ces/cedar Sources Sinks P 0. 1 P 0. 2 P 0. 3 T 1. 1 T 1. 2 T 1. 3 M 1. 1 P 1. 2 P 1. 3 P 1. 4 P 0. 1 P 0. 2 P 0. 3 T 1. 2 M 1. 1

Topic MS Defense Complexity Methods FROM: P 1. 1 – Student A TO: P 1. 2 – Student B, P 1. 3 – Student C SENT: 1/9/09 4: 52 PM SUBJECT: E 1. 1 – Email 1 ATTACHMENTS: D 1. 1 – Document 1 We need to discuss [T 1. 1 – Topic A], particularly with regards to [T 1. 2 – Topic B]. I’m also concerned that [T 1. 2 – Topic B] might have an impact on [T 1. 3 – Topic C]. What do you think? Student A Class 51/39 11/29/2020 Start Time Stop Time Sources Sinks Topic 1/9/09 4: 52 PM T 1. 1 T 1. 2 E 1. 1 Topic 1/9/09 4: 52 PM T 1. 2 T 1. 3 E 1. 1 jmathie@clemson. edu http: //www. clemson. edu/ces/cedar