High Performance Data Mining Chapter 9: Case Studies in Scientific Simulation Data

1. High Performance Data MiningChapter 9: Case Studies in Scientific Simulation Data Vipin Kumar Army High Performance Computing Research Center Department of Computer Science University of Minnesota http://www.cs.umn.edu/~kumar

2. Case Studies: Scientific Simulation Data • Mesh Density • R. Kanapady, S. K. Bathina, K. K. Tamma, C. Kamath, V. Kumar, “Determination of an Initial Mesh Density for Finite Element Computations via Data Mining,” Workshop on Mining Scientific Data, KDD 2001, San Francisco, CA, 2001. • Modeling of Damage in Structure • S. S. Sandhu, R. Kanapady, K. K. Tamma, C. Kamath, V. Kumar, “Damage Prediction and Estimation in Structural Mechanics Based on Data Mining,” Workshop on Mining Scientific Data, KDD 2001, San Francisco, CA, 2001.

3. Mesh Density Estimation: Finite element computations Design phases Mesh generation Simulation Solid modeling Adaptive computations Intermediate refined mesh Initial mesh Final mesh

4. Motivation • Geometry • dimensions • sharp corners • curvatures • Physics • loads • boundary conditions • stress gradients, jumps • shocks • Geometric features • design features • ribs • slots Data mining • Errors • Data collection • Choice of methods A priori mesh optimization Providing refined mesh generation parameters prior to any FE analysis at low cost Automatic meshing or re-meshing Acceptable mesh First initial mesh Small geometric design changes or changes in material, load and boundary conditions Adaptive finite element computations • Advantages • Knowledge based system • No burden on finite element user • Mesh generation experts avoided • Reduced design iteration • Solution times reduced • Advantages • Faster convergence to ideal mesh • Solution times reduced • Improved accuracy

5. Mesh density: definition Quadrilateral family of elements Triangular family of elements

6. Data mining: problem definition Problem description Finite element model for test example Finite element models for training example

7. Goals and Objectives • Overall objective: • To predict the close to optimal mesh generation parameters for finite element model involving arbitrary material distribution, loads, boundary conditions and small geometric changes via data mining techniques • Specific objectives : focus of the work • Proof-of-concept application • simple geometry • known analytical response • Creation of training data set • Data mining via Artificial Neural Networks (ANN)

8. Problem description Structural mechanics: simply supported plate

9. Feature selection

10. Creation of training data Circular magnifier (radius of influence) and directions Typical sampling locations for a given loading Best fit curves

11. Modeling • Neural network • input layer – 7 processing units • hidden layer – 19 processing units • output layer – 1 processing units • Clementine version 5.0.1 • auto pruning option • Random selection • load co-ordinates • sampling points co-ordinates • number of sampling points for given load • load value (p) range – 100 to 10,000 units • plate thickness (t) range – 0.01 to 0.1 units Reported relative importance of features (sensitivity) to the developed neural network model Total data distribution Test data distribution Training data distribution

12. Predicted element size Actual element size Results

13. Results: experiments 1. Asymmetric scaling: W = number of records k = 2 Loading region 5 2. Modified loading region range: 0.5 5

14. Predicted element size Actual element size Results

15. Results: validation Mesh generation using actual and predicted finite element size Actual Predicted Finite element mesh for load location 1.5, 3.5 (MESH1)

16. Results: validation Mesh generation using actual and predicted finite element size Actual Predicted Finite element mesh for load location 3.25, 3.0 (MESH2)

17. Results: validation Mesh generation using actual and predicted finite element size Actual Predicted Finite element mesh for load location 3.3, 1.9 (MESH3)

18. Results: validation Mesh generation using actual and predicted finite element size Actual Predicted Finite element mesh for load location 2.4, 3.5 (MESH4)

19. Results Relative performance Predicted h-ideal greater than actual h-ideal (above the linear regression line) Actual and predicted number of elements in the finite element mesh generated

20. Summary • Considered a proof-of-concept application in structural mechanics • Training data sets are created without finite element mesh generation and simulations • Performance improvements via asymmetric scaling are demonstrated • Preliminary results employing ANN are encouraging

21. Future directions • Finite element realm • Work directly with CAD geometry files • Generate training data sets: • Known analytical response with complex geometric features • Cases without analytical results • Different element shapes for 2D and 3D cases Plate with hole problem

22. Future directions • Data mining realm • Consider more complex geometric, material and physical features • Alternatives to reduce training set size • Develop performance metric to directly incorporate into the models • Finite element solution accuracy ( predicted size > actual size ) • Number of elements ( predicted size < actual size ) • Other regression programs such MARS and CART for continuous target variable • Develop models based on Mean Field Theory (MFT) etc.

23. Modeling of Damage in Structure Damage in material, due to localized softening or cracks Reduction in stiffness of structure Simplistically modeled by Reduction in Young’s modulus (E) Hence, reduction in Young’s modulus is used to characterize damage in structure.

24. Potential Applications • Non-destructive evaluation of structure. • Continuous monitoring of damage in bridges, skyscrapers and structures deployed in space. • Testing the integrity of structures like vehicles and aircrafts.

25. Objective of the Study Predicting the Young’s modulus of each element in the Structure: • Recognition - whether the damage has taken place in the structure. • Location - where the damage has taken place in the structure. • Quantification - the severity of the damage in the structure. Young’s modulus is target variable.

26. Methodology Changes in structural responses Damage in Structure • Static Displacement • Dynamic properties, like natural frequencies and mode shapes. We build a model for Young’s modulus of the elements in the structure as a function of structural response using artificial neural networks (ANN) and decision trees.

27. Building Training and Testing Set Each record in the data set corresponds to a failure state. The data mining model is build as follows: • Data for building the model is generated by failing either one or more elements in the structure in steps or randomly. Finite element analysis code Structural properties + Young’s modulus of elements Structural response

28. Static displacements as features 2-D Structure – plane frame: • The Plane frame has 5 elements. Nodes 1, 4, 5, 6 are fixed and Nodes 2 and 3 are loaded. • Absolute static displacement of node 2 and 3 are selected as features. • Data of 500 damaged states is generated by failing each element by varying its Young’s modulusfrom 0.99 E to 0.01 E is steps of 0.01 E. 60 %, of this data is selected for training and rest for testing.

29. Static displacements as features • The results of testing show that models generated by both ANN and decision tree prove to be accurate for predicting damage in this simple structure.

30. Static displacements as features 3-D Structure – electric transmission tower: • The electric transmission tower has 25 elements. Nodes 7, 8, 9 and 10 are fixed and, 3 and 4 are loaded. • Each node has six degrees of freedom • ( ) • Two sets of features are tried: • a. Absolute displacement of nodes. • (36 features). • b. Elemental displacement measure. • (100 features). • Data of 600 damaged states is generated by reducing the Young’s modulus of each element from E to 0.5 E in steps of 0.02 E. 70% of this data is used for training and rest for testing.

31. Static displacements as features • From the results of testing it is evident that model using elemental displacement measure is more accurate for both decision tree and ANN.

32. Static displacements as features • Decision tree generate interesting rules. • This rule implies that the failure of element 3 depends on the displacement of elements 7, 10 and 12. • Which can be useful to a structural engineer.

33. Static displacements as features • Failure of multiple elements • Plane frame structure is used to build model for predicting damage in multiple elements of structure. • Features are again the absolute static displacement of node 2 and 3. • The data of 7775 ( ) failure states is generated by simultaneously failing all the elements by reducing their Young’s moduli from E to 0.5 E in steps of 0.1 E. Only 5 % of this data is used for training.

34. Static displacements as features • Testing data of 1000 failure states is generated by failing multiple elements by a random amount. • The results of testing models, built by ANN and decision tree are accurate.

35. Static displacements as features Static displacement with varying load: • Plane frame structure subjected to varying load is used to generate data mining model for predicting damage. • The feature set consists of features corresponding to location and magnitude of loads in addition to static displacement. • Three loading conditions considered. First, node 2 and 6 are loaded. Next, node 3 and 5 are loaded. Finally, node 8 and 10 are loaded.

36. Static displacements as features • The training data is generated by reducing Young’s modulus from 1.0 E to 0.5 E in steps of 0.1 E and varying load from 500 N to 2500 N in steps of 500N. The testing data is generated by reducing Young’s modulus from 0.95 E to 0.45 E in steps of 0.1 E and varying load from 2250 N to 250 N in steps of 500N. • The results of testing generated models for both ANN and decision tree were not accurate enough. Because, two different loads corresponding to different failure states can produce same response.

37. Dynamic Properties as Features Advantage of using dynamic feature : • Dynamic features are load independent. • Dynamic properties such as natural frequencies are global in nature and hence selecting first ‘n’ natural frequency leads to considerable feature reduction. The natural frequencies and mode shapes of structure are obtained by solving the following eigenvalue problem: Where M and K are the mass and stiffness matrices of the structure respectively, and is the natural frequency corresponding to mode shape .

38. Dynamic Properties as Features Natural Frequency as Features 2-D Structure – three span bridge: • Three span bridge has 18 elements. Node 1 is fixed and node 7, 13, 19 are simply supported. Hence, it is unsymmetrical as regards to boundary conditions. • The lowest ‘n’ natural frequencies are chosen as features. • Training data of 181 records is generated by reducing the value of E from 1.0 E to 0.5 E in steps of 0.05 E. Testing data of 180 records is generated by reducing the value of E from 0.975 E to 0.525 E in steps of 0.05 E.

39. Dynamic Properties as Features • It is seen that first 9 natural frequencies are adequate to build a accurate model beyond which the performance of the model saturates.

40. Dynamic Properties as Features • If the structure is used with symmetric boundary conditions then it is seen that ANN predicts failure of both the symmetrical elements instead of predicting the failure of the correct element. This is due to the global nature of natural frequencies.

41. Dynamic Properties as Features 3-D Structure – electric transmission tower: • Data mining model is build to predict failure in electric transmission tower. • The first 12 natural frequencies are chosen as features. • Training data is generated by reducing the value of Young’s modulus from 1.0 E to 0.5 E in steps of 0.05 E, generating a total of 251 failure states. • Testing data of 500 failure states is generated by failing each element by an arbitrary amount. • The results of testing show that model created by ANN is accurate in predicting damage.

42. Dynamic Properties as Features

43. Summary • The prediction of the data mining techniques greatly depends on the features chosen. More meaningful features produce better results. • Performance results of developed ANN models are significantly better when compared to other relevant published results. • Models developed by decision trees have the added benefit of generating rules that can be manually interpreted. These rules, can potentially be helpful to structural engineers. • The development of predictive model that can correctly predict the location and severity of damage in large complex structures can be a considerable challenge.

44. Future Work • Preprocess static displacement so that better results in predicting damage when structure is subjected to variable loads can be achieved. • Complex structures have natural frequencies that are close to each other, and could be mistaken for one another. To distinguish between these frequencies modal assurance criteria (MAC) numbers can be used. • To reduce the set target variables (E) in complex structures, sub- structuring needs to be looked into.