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Design with uncertainty. Prof. Dr. Vasilios Spitas. What is uncertainty?. The deviation (u) of an anticipated result ( ) within a margin of confidence (p). How familiar are we with uncertainty?. Hesitation Chance Luck Ambiguity Expectation. Error Probability Risk Reliability - PowerPoint PPT Presentation

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Introduction

Design with uncertaintyProf. Dr. Vasilios SpitasAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsWhat is uncertainty?The deviation (u) of an anticipated result () within a margin of confidence (p)

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsHow familiar are we with uncertainty?HesitationChanceLuckAmbiguityExpectationErrorProbabilityRiskReliabilityToleranceQUALITATIVEQUANTITATIVEAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsQuantitative assessment requires Knowledge of the real problemBOUNDARY CONDITIONSKnowledge of the physical laws / interactionsCONSTITUTIVE EQUATIONS & CONSTANTSSolvable / treatable formulationMODELSolutionMATHEMATICSAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsDiscreteContinuousMean valueStandard deviationDiscrete and continuous probability distribution functionsMetrics:

Basic mathematical background

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, Netherlands

Normal distribution

Basic mathematical backgroundAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsWeibull distribution

Basic mathematical background

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsThe sample / measurement set

Follows the statistical distribution

If and only if the likelihood function

Satisfies the equation

From data sets to distribution functions

Maximum Likelihood MethodAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsState a null hypothesis

And an alternative hypothesis

Such that either Ho or H1 are true. Then verify the null hypothesis using

Z tests

Students tests

F tests (ANOVA)

Chi square tests

Statistical hypothesis testing

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsA random sample of size n

Coming from a population of unknown distribution function with mean value () and standard deviation (), has an average which follows the normal distribution with mean value:

And standard deviation:

Central limit theorem

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsLinking uncertainty with standard deviationLess strictMore strictConfidence level68.3%95.4%99.7%99.99966%Uncertainty1236AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsThe uncertainty of a function

With arguments xi and uncertainty ui each, is calculated as:

Combined uncertainty

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsDimensional toleranceThe acceptable uncertainty of a dimension

Tolerancing in Embodiment Design

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsGeometrical toleranceThe acceptable uncertainty of a feature form - location

Tolerancing in Embodiment Design

FormFormFormFormFormOrientationOrientationOrientationOrientationPositionPositionPositionRunoutRunoutAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsUnderstanding tolerancing

Tolerancing in Embodiment Design

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsCommunicating a function through tolerancing

Tolerancing in Embodiment Design

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsCommunicating functions through tolerancing

Tolerancing in Embodiment Design

AMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsA 50mm long 50 piezostack is formed by assembling 50 identical PZT disks, each 1mm in thickness and with a parallelism tolerance of 0.02mm. What is the resulting parallelism of the assembled stacks?Example of combined tolerance calculationAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsLet ti be the deviation in parallelism of part i (i=1-50)The piezostack length is the sum of the individual thicknesses of the parts ti The requested uncertainty would then be:

Example of combined tolerance calculationAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsIf we are sure that none of the parts exceeds the tolerance then where is the uncertainty ?Tolerance zoneAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsAnalysisbreak the complex part into two or more simpler partsSynthesiscombine two or more parts into one monolithic partInversionfemale geometries to male geometriescompression to tensioninternal features to external featuresConstraint control

Methods for reducing uncertainty in engineering designAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, NetherlandsThank you for your attention

Good luck with the workshop assignmentsAMP-EMBODYERASMUS Intensive ProgrammeDelft 8-24 July 2013, Netherlands