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Project Numina Project Numina II II Project Numina II UNCW UNCW UNCW Inverse Problems for Inverse Problems for Vibrating Beams Vibrating Beams ICTCM – 2002 ICTCM – 2002 Orlando, FL. Orlando, FL. Russ Herman, Mathematics and Statistics Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics and Gabriel G. Lugo, Mathematics and Statistics Statistics University of North Carolina at Wilmington University of North Carolina at Wilmington

Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

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Page 1: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Inverse Problems for Vibrating BeamsInverse Problems for Vibrating BeamsICTCM – 2002 Orlando, FL.ICTCM – 2002 Orlando, FL.

Russ Herman, Mathematics and StatisticsRuss Herman, Mathematics and StatisticsGabriel G. Lugo, Mathematics and StatisticsGabriel G. Lugo, Mathematics and Statistics

University of North Carolina at WilmingtonUniversity of North Carolina at Wilmington

Page 2: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Outline of PresentationOutline of Presentation

• The ProblemThe Problem• NC State ModelNC State Model

– Course PreparationCourse Preparation– Experimental SetupExperimental Setup– Experimental ResultsExperimental Results

• UNCW ModelUNCW Model– Course PreparationCourse Preparation– Experimental SetupExperimental Setup– Experimental ResultsExperimental Results

• Data AnalysisData Analysis– Matlab, MathCad, Maple, Excel, Matlab, MathCad, Maple, Excel,

Websites – Nonlinear RegressionWebsites – Nonlinear Regression

• Comparison of ModelsComparison of Models• SummarySummary

Page 3: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

The ProblemThe Problem

Will add problem statement .. Does it differ

between models?

Will add problem statement .. Does it differ

between models?

Page 4: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

NC State ModelNC State Model

• Course PreparationCourse Preparation

• Experimental SetupExperimental Setup

• Experimental ResultsExperimental Results

Need to add pics of NC State model and maybe Berkeley Model, info about students and type of model, results, …

Need to add pics of NC State model and maybe Berkeley Model, info about students and type of model, results, …

Page 5: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Course PreparationCourse Preparation

Page 6: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Experimental SetupExperimental Setup

Page 7: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Experimental ResultsExperimental Results

Page 8: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

UNCW ModelUNCW Model

• Course PreparationCourse Preparation

• Experimental SetupExperimental Setup

• Experimental ResultsExperimental Results

Page 9: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Course PreparationCourse Preparation

• Introduction to Harmonic OscillatorsIntroduction to Harmonic Oscillators

• Pre-project WorkPre-project Work

• Verify form of solutionsVerify form of solutions

• Graphing Typical SolutionsGraphing Typical Solutions

• Fitting Simulated SolutionsFitting Simulated Solutions

Page 10: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Experimental SetupExperimental Setup

• Handheld ComputersHandheld Computers

• Data Harvest DAQData Harvest DAQ

• Simple Springs and Meter StickSimple Springs and Meter Stick

Page 11: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

HP Jornada 720 Handheld ComputersHP Jornada 720 Handheld Computers• StrongArm CPU (206 MHz)StrongArm CPU (206 MHz)

• 32 MB RAM32 MB RAM

• 640 x 240 Color Display640 x 240 Color Display

• Compact Flash Type I & PC Card Type II SlotsCompact Flash Type I & PC Card Type II Slots

• RS232C serial & IrDA ports, 115KbpsRS232C serial & IrDA ports, 115Kbps

• 56k Modem56k Modem

• 9-Hour Li-ion Battery9-Hour Li-ion Battery

• MS HPC2000 v. 3 OSMS HPC2000 v. 3 OS

Page 12: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

• 12-bit DATAQ system12-bit DATAQ system

• Numerous probesNumerous probes

• Serial interface or CF+ unitSerial interface or CF+ unit

• Software runs on HPC, PPC, and Software runs on HPC, PPC, and desktop computersdesktop computers

Data Harvest DATAQ SystemData Harvest DATAQ System

Page 13: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Page 14: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Add sample spring data

Add sample spring data

Experimental ResultsExperimental Results

Page 15: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Data AnalysisData Analysis

Perhaps add only links to appropriate worksheets.

Perhaps add only links to appropriate worksheets.

• Nonlinear RegressionNonlinear Regression

• MatlabMatlab

• MathCadMathCad

• MapleMaple

• ExcelExcel

• Nonlinear Fitter WebsiteNonlinear Fitter Website

Page 16: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

Comparison of ModelsComparison of Models

• Student DemographicsStudent Demographics

• Common ProblemsCommon Problems

• Common SolutionsCommon Solutions

• Model DifferencesModel Differences

Page 17: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

SummarySummary

• The ProblemThe Problem• NC State ModelNC State Model• UNCW ModelUNCW Model• Data AnalysisData Analysis• Comparison of ModelsComparison of Models

Page 18: Project Numina II UNCW UNCW Inverse Problems for Vibrating Beams ICTCM – 2002 Orlando, FL. Russ Herman, Mathematics and Statistics Gabriel G. Lugo, Mathematics

Project Numina IIProject Numina IIProject Numina II

UNCWUNCWUNCW

http://aa.uncwil.edu/numinahttp://aa.uncwil.edu/numina

• Data HarvestData Harvest

• GraphDataGraphData

Thank you!Thank you!

Russ Herman, [email protected] G. Lugo, [email protected]