1. Mining Sequence Patterns from Wind Tunnel Experimental Data Zhenyu Liu †, Wesley W. Chu †, Adam Huang ‡, Chris Folk ‡, Chih-Ming Ho ‡ {wwc,vicliu}@cs.ucla.edu, {pohao,chrisf,chihming}@ucla.edu † Computer Science Department ‡ Mechanical and Aerospace Engineering Department University of California Los Angeles, California

2. Outline Problem statement Scientific experimental data characteristics Conventional mining methods Decision tree Association rules Mining of sequence patterns Conclusion

3. Delta Wing Aircraft Control via MEMS Actuators Vortices symmetry is broken by the actuation of MEMS actuators, resulting in desirable aerodynamics loadings Werle, 1958

4. Problem Statement Inputs: angle of attack, stream velocity, actuation angle Output: rolling moment Problem: discover knowledge on input-output relationship

5. Scientific Experimental Data Characteristics The output is highly dependent on all inputs. A subset of inputs is inadequate to predict the output. Sequences of input-output relationships contained (e.g. the rolling moment w.r.t. the actuation angle)

6. Conventional Methods: Decision Tree Generation High coverage but low accuracy (an error rate of 46.35% in predicting the original dataset using the decision tree) Reason: The decision tree generation algorithm uses univariate-split strategy to induce the input-output relationship Each single input has low prediction power over the output. Angle of Attack Actuation Angle MZ in [-0.00024,0.00028] 0,5,1015,20,25,30,35 60,10040,80,120,140 MZ in [-0.0124,0.00537] Angle of Attack 15,2025,30,35 MZ in [-0.00024,0.00028] MZ in [-0.01179,-0.0038]

7. Conventional Methods: Rule Induction Acceptable accuracy Low input state space coverage (which is 25%) and insufficient for flight control applications

8. Conventional Methods: The Cause of The Low Coverage The output variable in scientific dataset cannot be summarized using a subset of the inputs Rules induced from the sensitive input regions (large angle of attack in this case) cannot have both high confidence and high support

9. Mining of Sequence Patterns Extract sequences from the dataset Bottom-up sequence clustering (binary hierarchy) based on Euclidean distance measure Sequence pattern extraction from the binary cluster hierarchy based on the variance measure Rule induction from sequence patterns

10. Mining of Sequence Patterns: 1. Sequence Extraction Merging the output with one of the input to form a composite output variable. More specifically: A dataset D with inputs X 1, …, X n and an output Y A predicate p defined on the inputs A sequence of Y w.r.t. X i (1  i  n) characterized by p is a set of 2- item tuples: {, …, } calculated by  Y, Xi (  p (D)) a sequence characterized by p =“aoa=20, vel=10”

11. Mining of Sequence Patterns: 2. Bottom-up Sequence Clustering Using the Euclidean distance measure to generate a binary cluster hierarchy

12. Mining of Sequence Patterns: 3. Sequence Pattern Extraction From the hierarchy, merge branches with variances below a user-specified threshold (0.35 in this example)

13. cluster #8 wvar 0.243029 aoa 35 vel 10 aoa 35 vel 15 aoa 35 vel 20 Mining of Sequence Patterns: 4. Rule Induction from Sequence Patterns Cluster #8 as an example: Sample rules generated IF angle of attack = 35  THEN the rolling moment curve with actuation angle follows mean(cluster #8), confidence 100%, variance 0.243029 Rules have higher coverage and confidence, and the accuracy (of the mean) is controllable through the variance measure All sequences in cluster #8 The average of sequences in cluster #8, or, mean(cluster #8)

14. Conclusion Developed a mining technique to discover relationship for highly correlated input-output pairs Conventional methods (decision tree or rule induction) fail to generate knowledge with both high coverage and accuracy Developed a new technique for mining sequence patterns from the wind tunnel experimental data Sequence extraction Sequence clustering (binary hierarchy) based on the Euclidean distance measure Sequence patterns extracted from the binary cluster hierarchy using variance measure Rule induction from sequence patterns Rules generated Nontrivial to experimenters Useful for flight control

15. Directly Applying Conventional Mining Methods Conventional methods works with categorical variables. The first step will be a discretization of the output variable 6 partitions generated: [-0.01179, -0.00380], [- 0.00380, -0.00138], [-0.00138, -0.00024], [-0.00024, 0.00028], [0.00028, 0.00124], [0.00124, 0.00537] Then apply decision tree or rule induction to the discretized dataset