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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

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design with uncertainty

Design with uncertainty

Prof. Dr. Vasilios Spitas

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

QUANTITATIVE

QUALITATIVE

quantitative assessment requires
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
Basic mathematical background
  • Discrete and continuous probability distribution functions
  • Metrics:
basic mathematical background2
Basic mathematical background

Weibull distribution

from data sets to distribution functions
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
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
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
Combined uncertainty
  • The uncertainty of a function
  • With arguments xi and uncertainty ui each, is calculated as:
tolerancing in embodiment design
Tolerancing in Embodiment Design
  • Dimensional tolerance

The acceptable uncertainty of a dimension

tolerancing in embodiment design1
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 design2
Tolerancing in Embodiment Design
  • Understanding tolerancing
tolerancing in embodiment design3
Tolerancing in Embodiment Design
  • Communicating a function through tolerancing
tolerancing in embodiment design4
Tolerancing in Embodiment Design
  • Communicating functions through tolerancing
example of combined tolerance calculation
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 calculation1
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:
if we are sure that none of the parts exceeds the tolerance
If we are sure that none of the parts exceeds the tolerance

Tolerance zone

… then where is the uncertainty ?

methods for reducing uncertainty in engineering design
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