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ANALYSIS AND VISUALIZATION OF TIME-VARYING DATA USING ‘ACTIVITY MODELING’ By Salil R. Akerkar Advisor Dr Bernard P. Zeigler ACIMS LAB (University of Arizona) Presentation Outline Introduction Activity – A DEVS Concept Activity Modeler System Stage1 - Preprocessing Stage2 - Activity Engine Stage3 - Visualization Results Implications for Discrete Event Simulation Future Work Introduction Data Source and Problem under study Current trends Unexplored area Motivation – Discrete Events vs. Discrete Time Activity – A DEVS Concept Definition of Activity mn m1 mi q t t 1 i 0 T Activity (T ) | mi 1 mi | AvgActivity (T ) Activity / T NumberOfThresholdCross (T , q) Activity(T ) / q Activity – A DEVS Concept Coherency (Space and Time) Instantaneous Activity Instantaneous Activity(IA(t)) Value(t ) Value(t 1) Accumulated Activity (same as DEVS Activity) t Accum ulatedActivity( AA(t )) Value(t ) Value(t 1) i Activity Domain Activity Modeler System Stage-1 Stage-2 Stage-3 Raw Data RESULT S GNUPLOT MODULES PERL FORMATTER RESULT S ACTIVITY ENGINE ACTIVITY DATA AVSEXPRESS MODULES FORMATTED DATA GNUPLOT MODULES (OPTIONAL) PERL FORMATTER Stage 1 – Pre Processing Why do we need pre-processing? Regular Structure format PERL formatter Functions Extract Information Format Correction Logic Analyze part of information 2D formatter decrease IO operations standardization Stage 2 – Activity Engine DATA-FILE THE ACTIVITY ENGINE PATTERN INFORMATION ------------------- ACTIVITY GENERATOR PATTERN PREDICTOR ------------------- GNUPLOT SCRIPTS PERL Formatter DATA ENGINE STATISTIC ANALYZER ------------------------------------STATISTICAL INFORMATION ------------------- ACTIVITY TIMESERVICES AVS-EXPRESS MODULES ACTIVITY LOG ACTIVITY DATA Stage 2 – Data Engine Functions File handling Sequential / Random access Standardization of filenames for automation Memory Allocation Transformation Cellular and Temporal Transformation between domains between dimensions Val2D[i][j] = Val1D[i*Cols+j] Independent of spatial dimension Stage 2 - Activity Generator Instantaneous Activity Accumulated Activity Time Advances Activity Factor (AF) nTim eSteps( IA(t ) threshold) t[0, T ] TotalTim eSteps Cellular domain Threshold (AF) Activity factor IA( x, t ) t x NT Cells Stage 2 – Statistic Analyzer Extract Statistics in terms of groups Group1: Maximum, Minimum, Range, Average Group2: Standard deviation, Mean Group3: Living Factor (Temporal domain) Group4: Histogram of Time Advances Static in nature Provides meaningful threshold to Activity Factor Living Factor Stage 2 – Statistic Analyzer Group 3: Living Factor (LF) Temporal domain nCells ( IA(t ) threshold ) t[0, T ] TotalCells Group 4: Histogram of Time Advances Temporal domain Logarithmic in scale Maxtadv Min(tadv) 109 Time Stage 3 – Pattern Predictor Spatial and Temporal Coherency Peaks and Max Analyze activity pattern Predict activity pattern Stage 3 – Pattern Predictor •Max Locator •Peak Locator Difference in Peak and Max •False Peak problem •Eliminated by ROI (Region of Imminence) Stage 3 – Region Of Imminence (ROI) Definition Steps Peak Detection in IA Scanning algorithm Boundary conditions Threshold conditions () Significance Imminence Factor Cells Stage 3 – Pattern Predictor 1D scanning algorithm 2 neighbors Binary visualization 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Peak Under consideration: 2 Location of cell: 10 Initial Values: Left-neighbor = right- neighbor = 10 Final Values: Left-neighbor = 7 Right-neighbor = 13 Boundary condition Threshold condition Cells Stage 3 – Sphere Of Imminence 2D scanning algorithm 3 types of tuning Coarse Normal Fine Stage 3 – Sphere Of Imminence Fine Tuning Coarse Tuning Normal Tuning Type Of Tuning Computation time (ms) Imminence Factor (t= 5) Imminence Factor (t=10) Coarse 5393 0.0709 0.0974 Normal 6224 0.0985 0.1395 Fine 6456 0.1505 0.3327 Stage 3 – Region Of Imminence Valcell Valcell 1 & &Valcell Valcell 1 Valcell Valcell 1 & &Valcell Valcell 1 (Valcell Valcell 1) & &(Valcell Valcell 1) Valcell Valcell 1 & &Valcell Valcell 1 ROI: Overcome the False Peak problem Stage 3 – Predict Pattern 1D space Linear Span Module [0.9 – 0.95] Order of Pattern Pattern attributes ROI 1 1 1 0 1 0 0 0 t = ta 0 0 1 1 0 1 0 0 t = tb Offset Direction Difference Steps 3 Recognizing pattern t[n,n+1] 2nd Order 1st 1st 5 order pattern 2 2nd order Predicting pattern t[n+2,T] 0 0 0 0 0 1 0 0 0 t = ta 2 0 0 1 0 0 t = tb Linear span Stage 3 - Visualization Softwares GNUPLOT AVS-Express Reader Visualization Stages Reader (Import data) Visualization modules Writing stage VIZ modules Writer Stage 3 - Visualization Zero Padding Binary Visualization Advantages Eliminating unwanted data Reduction in file size Implementation set zrange [0.5:] Stage 3 - Visualization Domain Types Of Result Visualization Techniques 1D 2D Instantaneous Activity, Accumulated Activity, Time Advances Surface Plot Images (GNUPLOT) Surface Plot / Contour movies (GNUPLOT scripts/ AVS-Express) Region Of Imminence, Peak Locator, Max Locator Binary Visualization, Zero Padding (GNUPLOT) Binary Visualization, Zero Padding (GNUPLOT scripts) Cellular Statistics, Activity Factor 1D single / multi graphs (GNUPLOT) Surface Plot Images (GNUPLOT) Temporal Living Factor, Histogram of time advances 1D single / multi graphs (GNUPLOT) Surface Plot Images (GNUPLOT) Spatio-Temporal Results 1D space 1D heat diffusion process Robot Activity 2D space 2D heat diffusion process Fire-Front model Results – 1D Heat diffusion • 1D space ,T=100 • N=10, 100, 200 N 100 10 200 Results – Robot Activity 1D space Robots modeled as cells Simulation time steps – 2357 Data (Value domain) 1- Robot moving 0- Robot stopped Activity domain 1- State transition 0- Same state Results – Robot Activity Living Factor Activity Factor Imminent groups Results – 2D diffusion Histogram of Time Advances 2D space (100 x 100 cells) T = 50 Cellular domain results (2D) Activity Factor Statistics Surface plot images IA surface characterized by concentric circles tadv histogram lower end Activity Factor Results – 2D diffusion Movie of IA / AA (activity domain) and output values (value domain) Results – Fire Front model 2D space (100 x 100 cells) T = 297 Movie for Value domain Results – Fire Front model Living Factor 20% maximum t=180 boundary Imminence Factor = 0.7 t [50-150] Time Results – Fire Front model Instantaneous Activity Peak Bars Accumulated Activity Region Of Imminence Implications for Discrete Event Simulation DEVS transitions: DTSS transitions: Maximum Slope: DEVS v/s DTSS Implications for Discrete Event Simulation MODEL CELLS TIME MAX(IA) TOTAL AA DEVS DTSS 1D diffusion (N=10) 10 100 0.26318 2.4283 0.0093 1D diffusion (N=100) 100 100 0.9069 3.8296 0.00042 1D diffusion (N=200) 200 100 0.9635 3.9285 0.0002 2D diffusion 10000 50 0.2583 2048.77 0.819 Fire Front 10000 297 213.995 5321979 0.0083 DEVS v/s DTSS Results – Predict Pattern Test data - 3 1D diffusion (N=100) Results Results for 1D process Test data 1D diffusion Percentage Error decreases as N increases ROI characterized by linear curves Conclusion New perspective for data analysis – Activity domain ROI – Spatial Coherency in Temporal domain Analyze process behavior in terms of Activity Compute and Predict – activity pattern Results – process specific Predict Pattern - % Error decreases as N increases ROI curves are characterized by linear curves DEVS found to be more efficient than DTSS Future Work Extending system to data in 3D space Extending system to UNIX platform Enhancing the Pattern predictor module Efficiently Detecting the ‘new Imminent Cells’ in DEVS simulation ACKNOWLEDGEMENTS Dr. Bernard Zeigler Dr. Salim Hariri Dr. James Nutaro Dr. Xiaolin Hu, Alex Muzy Hans-Berhard Broeker Cristina Siegerist ACIMS LAB QUESTIONS ?