Design with uncertainty

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# Design with uncertainty - PowerPoint PPT Presentation

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

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### Design with uncertainty

Prof. Dr. Vasilios Spitas

What is uncertainty?
• The deviation (u) of an anticipated result (μ) within a margin of confidence (p)
How familiar are we with uncertainty?
• Hesitation
• Chance
• Luck
• Ambiguity
• Expectation
• Error
• Probability
• Risk
• Reliability
• Tolerance

QUANTITATIVE

QUALITATIVE

Quantitative assessment requires …
• Knowledge of the real problem
• BOUNDARY CONDITIONS
• Knowledge of the physical laws / interactions
• CONSTITUTIVE EQUATIONS & CONSTANTS
• Solvable / treatable formulation
• MODEL
• Solution
• MATHEMATICS
Basic mathematical background
• Discrete and continuous probability distribution functions
• Metrics:
Basic mathematical background

Weibull distribution

From data sets to distribution functions
• The sample / measurement set
• Follows the statistical distribution
• If and only if the likelihood function
• Satisfies the equation

Maximum Likelihood Method

Statistical hypothesis testing
• State a null hypothesis
• And an alternative hypothesis
• Such that either Ho or H1 are true. Then verify the null hypothesis using
• Z – tests
• Student’s tests
• F – tests (ANOVA)
• Chi – square tests
Central limit theorem
• A random sample of size n
• Coming from a population of unknown distribution function with mean value (μ) and standard deviation (σ), has an average which follows the normal distribution with mean value:
• And standard deviation:
Combined uncertainty
• The uncertainty of a function
• With arguments xi and uncertainty ui each, is calculated as:
Tolerancing in Embodiment Design
• Dimensional tolerance

The acceptable uncertainty of a dimension

Tolerancing in Embodiment Design
• Geometrical tolerance

The acceptable uncertainty of a feature form - location

Orientation

Form

Orientation

Form

Orientation

Form

Position

Form

Orientation

Runout

Form

Runout

Position

Position

Tolerancing in Embodiment Design
• Understanding tolerancing
Tolerancing in Embodiment Design
• Communicating a function through tolerancing
Tolerancing in Embodiment Design
• Communicating functions through tolerancing
Example of combined tolerance calculation
• A 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 calculation
• Let Δti 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:

Tolerance zone

… then where is the uncertainty ?

Methods for reducing uncertainty in engineering design
• Analysis

break the complex part into two or more simpler parts

• Synthesis

combine two or more parts into one monolithic part

• Inversion

female geometries to male geometries

compression to tension

internal features to external features

• Constraint control