Effects of Error, Variability, Testing and Safety Factors on Aircraft Safety

1
Effects of Error, Variability, Testing and Safety
Factors on Aircraft Safety

• Erdem Acar, Amit Kale and Raphael T. Haftka
• eacar_at_ufl.edu akale_at_ufl.edu
  haftka_at_ufl.edu

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
2
Motivation

• The FAA makes a distinction between error and
  variability through use of A-basis and B-basis
  properties.
• A-Basis property is the value exceeded by 99 of
  population with 95 confidence.
• Problems in acceptance of probabilistic design.
  We are interested to see whether the
  differentiating errors and variability may help.
• We are interested to see how epistemic and
  alleatory uncertainty interact in determining the
  safety factor of aircraft.

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
3
Outline

• Definition of uncertainties and safety measures
  considered
• The error model
• Simulation process for certification testing
• Certification test effectiveness in terms of
  error, variability and average safety factor
• Uncertainty in probability of failure
• Concluding remarks

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
4
Error and Variability
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
5
Safety measures

• FAA requirements
• Safety factor (SF) 1.5
• Certification tests Testing the structural
  design for failure
• to compensate for ERROR (our interpretation!)
• A-basis and B-basis material properties
• to account for VARIABILITY

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
6
Approach to the problem

• Structural failure due to stress failure without
  damage propagation ?P/A??f
• (? is the point stress in any structural
  component)
• A single test, which is a pass-fail certification
  test
• Simulation of variability and error requires
  simulating the design of multiple aircraft and
  multiple models.
• Monte Carlo simulation and analytical
  approximation used.

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
7
Error model

• The deviation of actual load and stress values
  (fleet-average value) from the values calculated
  by the designer

Error in load calculation
(1)
(2)
Error in point stress analysis
The designer uses Eq. (2) to calculate design
thickness
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
8
Error in implementation

• Deviation of average actual geometry and material
  properties from design specification

Error in geometric parameters
Error in material properties
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
9
Fleet-Average safety factor
Fleet average of stress in a panel under correct
design loads
Fleet-average safety factor
where
cumulative error in safety factor for the average
airplane (fleet-average) built by a company
is safety margin for variability
(brings 1.27 additional safety factor)
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
10
Error factor distributions
Uniform distribution with zero mean
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
11
Variability

• Variation from one aircraft to another in the
  fleet.

For example,
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
12
Monte Carlo simulation
N different aircraft models (Boeing 777, Airbus
320A)
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
13
Effect of certification on SF fleet
The model is certified if

• Mean initial 1.9071.5 x 1.27
• Mean updated 1.932
• SAFETY IS IMPROVED !
• Since some unsafe designs fail in certification
  test.

The use of A-basis properties gives and
additional safety factor of 1.27.
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
14
Comparison of Monte Carlo and analytical
approximation

• Bayes Theorem is used to compute analytical
  approximation
• Variability in geometric variables are
  approximated as lognormal
• Certification testing does not affect error term
  ep

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
15
For low variability errors lead to safer design
When the variability is very small!

• SAFETY
• IS IMPROVED !

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
16
Effect of certification on Pf
Introduce a new parameter k,

• With variability, increase of k leads to increase
  of probability of failure
• As error grows, Pf ratio becomes smaller
  indicating that the certification tests become
  more effective

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
17
Effect of variability

• Increase of variability leads to
• Increase in probability of failure (A-basis not
  sufficient?!)
• Increase in Pf ratio indicating that
  certification testing loses
• its efficiency

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
18
Effect of different safety measures (simpler
error model)
The usefulness of certification tests increases
with - low safety factor - low variability -
high error
Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
19
Coefficient of Variation of Pf

• Coefficient of variation of probability of
  failure is huge.
• It may be difficult for an individual company to
  use the
• computed probability of failure.
• However, for FAA it is O.K. since they are judged
  based on
• national average.

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
20
Small changes in SF may be sufficient for
reliability based design

• Deterministic and probabilistic design
  optimization of a simplified wing model.
• For deterministic optimization, SF1.5 and
  A-basis properties used. The use of both safety
  measure translates into an effective safety
  factor of 1.907.
• The probabilistic optimization for fixed weight
  corresponding to deterministic optimum.

• Aircraft companies may be given freedom to select
  conservative material properties
• to account for variability.

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu
21
Concluding Remarks

• Safety is determined by error and variability.
• for error SF and Cert. test --- for
  variability A-basis
• Hence, certification tests are most effective
  for
• low safety factors
• high errors
• low variability
• Large coefficient of variation in probability of
  failure is found.
• Safety factor may be useful for FAA to manage
  error.
• Aircraft companies may be given freedom to
  select conservative material properties to
  account for variability to improve safety.

Structural and Multidisciplinary Optimization
Group Dept. of Mechanical and Aerospace
Engineering University of Florida
eacar_at_ufl.edu