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 t1t1 0 titi m1m1 mimi mnmn T

Activity – A DEVS Concept Coherency (Space and Time) Instantaneous Activity Accumulated Activity (same as DEVS Activity) Activity Domain

Activity Modeler System Raw Data Raw Data FORMATTED DATA RESULT S Stage-1 RESULT S ACTIVITY DATA ACTIVITY DATA Stage-2Stage-3 PERL FORMATTER ACTIVITY ENGINE (OPTIONAL) PERL FORMATTER GNUPLOT MODULES GNUPLOT MODULES AVS- EXPRESS MODULES

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 ACTIVITY GENERATOR PATTERN PREDICTOR STATISTIC ANALYZER ACTIVITY TIME- SERVICES ACTIVITY LOG THE ACTIVITY ENGINE PERL Formatter GNUPLOT SCRIPTS AVS-EXPRESS MODULES DATA-FILE PATTERN INFORMATION STATISTICAL INFORMATION ACTIVITY DATA DATA ENGINE

Stage 2 – Data Engine Functions  File handling Sequential / Random access Standardization of filenames for automation  Memory Allocation  Transformation between domains Cellular and Temporal  Transformation 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)  Cellular domain Threshold (AF) Cells  Activity factor

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 Group 4: Histogram of Time Advances  Temporal domain  Logarithmic in scale 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 Cells Threshold condition Boundary condition Peak Under consideration: 2 Location of cell: 10 Initial Values: Left-neighbor = right- neighbor = 10 Final Values: Left-neighbor = 7 Right-neighbor = 13

Stage 3 – Sphere Of Imminence 2D scanning algorithm 3 types of tuning  Coarse  Normal  Fine

Stage 3 – Sphere Of Imminence Type Of Tuning Computation time (ms) Imminence Factor (t= 5) Imminence Factor (t=10) Coarse Normal Fine Coarse Tuning Normal Tuning Fine Tuning

Stage 3 – Region Of Imminence ROI: Overcome the False Peak problem

Stage 3 – Predict Pattern 1D space Linear Span Module  [0.9 – 0.95] Order of Pattern Pattern attributes  Offset  Direction  Difference Steps  Recognizing pattern t[n,n+1] 5 1 st order pattern 2 2 nd order  Predicting pattern t[n+2,T] t = ta t = tb t = ta t = tb ROI Linear span 2 nd Order 1 st

Stage 3 - Visualization Softwares  GNUPLOT  AVS-Express Visualization Stages  Reader (Import data)  Visualization modules  Writing stage Reader 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 DomainTypes Of ResultVisualization Techniques 1D 2D Spatio-Temporal 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)

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 Cells  Time 

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 Robots  Time 

Results – Robot Activity Living Factor Activity Factor Imminent groups

Results – 2D diffusion 2D space (100 x 100 cells) T = 50 Cellular domain results (2D)  Activity Factor  Statistics  Surface plot images IA surface characterized by  concentric circles  t adv histogram lower end Activity Factor Histogram of Time Advances

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 MODELCELLSTIMEMAX(IA)TOTAL AADEVS DTSS 1D diffusion (N=10) D diffusion (N=100) D diffusion (N=200) D diffusion Fire Front 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 ?