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Workshop at Matforsk, Ås, Norway 13 th -14 th May 2004 Design of Experiments – Benefits to Industry. Advances in Robust Engineering Design. Henry Wynn and Ron Bates Department of Statistics. Background. 2 EU-Funded Projects:

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slide1

Workshop at Matforsk, Ås, Norway13th-14th May 2004Design of Experiments – Benefits to Industry

Advances in Robust Engineering Design

Henry Wynn and Ron Bates

Department of Statistics

background
Background
  • 2 EU-Funded Projects:
    • (CE)2 : Computer Experiments for Concurrent Engineering (1997-2000)
    • TITOSIM: Time to Market via Statistical Information Management (2001-2004)

Wynn & Bates, Dept. of Statistics, LSE

what is robustness
What is Robustness?
  • Many different definitions
  • Many different areas
    • Biological
    • Systems theory
    • Software design
    • Engineering design, Reliability ….
  • Quick Google web search : 176,000 entries
  • 16 different definitions on one website!

Wynn & Bates, Dept. of Statistics, LSE

working definitions santa fe inst
Working definitions (Santa Fe Inst.)
  • 1. Robustness is the persistence of specified system features in the face of a specified assembly of insults.
  • 2. Robustness is the ability of a system to maintain function even with changes in internal structure or external environment.
  • 3. Robustness is the ability of a system with a fixed structure to perform multiple functional tasks as needed in a changing environment.
  • 4. Robustness is the degree to which a system or component can function correctly in the presence of invalid or conflicting inputs.
  • 5. A model is robust if it is true under assumptions different from those used in construction of the model.
  • 6. Robustness is the degree to which a system is insensitive to effects that are not considered in the design.
  • 7. Robustness signifies insensitivity against small deviations in the assumptions.
  • 8. Robust methods of estimation are methods that work well not only under ideal conditions, but also under conditions representing a departure from an assumed distribution or model.
  • 9. Robust statistical procedures are designed to reduce the sensitivity of the parameter estimates to failures in the assumption of the model.

Wynn & Bates, Dept. of Statistics, LSE

continued
Continued…
  • 10. Robustness is the ability of software to react appropriately to abnormal circumstances. Software may be correct without being robust.
  • 11. Robustness of an analytical procedure is a measure of its ability to remain unaffected by small, but deliberate variations in method parameters, and provides an indication of its reliability during normal usage.
  • 12. Robustness is a design principle of natural, engineering, or social systems that have been designed or selected for stability.
  • 13. The robustness of an initial step is determined by the fraction of acceptable options with which it is compatible out of total number of options.
  • 14. A robust solution in an optimization problem is one that has the best performance under its worst case (max-min rule).
  • 15. "..instead of a nominal system, we study a family of systems and we say that a certain property (e.g., performance or stability) is robustly satisfied if it is satisfied for all members of the family."
  • 16. Robustness is a characteristic of systems with the ability to heal, self-repair, self-regulate, self-assemble, and/or self-replicate.
  • 17. The robustness of language (recognition, parsing, etc.) is a measure of the ability of human speakers to communicate despite incomplete information, ambiguity, and the constant element of surprise.

Wynn & Bates, Dept. of Statistics, LSE

slide6

Engineering design paradigms

  • Example: Clifton Suspension Bridge
  • Creative input vs. mathematical search

Wynn & Bates, Dept. of Statistics, LSE

a framework for redesign
A Framework for Redesign
  • Define the “Design Space”,
  • Write where,
  • Parameterisation is important

Wynn & Bates, Dept. of Statistics, LSE

robustness in engineering design
Robustness in Engineering Design
  • Based around the notion of “Design Space” and “Performance Space”

Wynn & Bates, Dept. of Statistics, LSE

adding noise
Adding Noise
  • No noise
  • Internal noise
  • External noise

Wynn & Bates, Dept. of Statistics, LSE

propagation of variation
Propagation of variation
  • Monte Carlo
    • Flexible
    • Expensive
  • Analytic
    • Need to know function
    • Mathematically more complex
    • (Usually) restricted to univariate distributions

Wynn & Bates, Dept. of Statistics, LSE

dual response methods
Dual Response Methods
  • Estimate both mean m and variance s2 of a response or key performance indicator (KPI)
  • This leads to either:
    • Multi-Objective problem e.g. min(m,s2)
    • Constrained optimisation e.g. min(s2) subject to: t1<m< t2

Wynn & Bates, Dept. of Statistics, LSE

slide12

Density

0%

5%

85 %

10%

Response

A

B

C

Stochastic Responses

  • Output distribution type is unknown
  • Possibilities:
    • Estimate Mean & Variance (Dual Response)
    • Select another criteria e.g. % mass

Wynn & Bates, Dept. of Statistics, LSE

slide13

Stochastic Simulation (Monte Carlo)

Wynn & Bates, Dept. of Statistics, LSE

piston simulator example
Piston Simulator Example

Wynn & Bates, Dept. of Statistics, LSE

noise added to design factors
Noise added to design factors

New bounds

for search

space

Wynn & Bates, Dept. of Statistics, LSE

experiment details
Experiment details
  • All 7 design factors are subject to noise
  • Minimize both mean and standard deviation of cycle time response
  • Perform 50 simulations in a sub-region of the design space:
  • For each simulation, compute mean and std of cycle time with 50 simulations

Wynn & Bates, Dept. of Statistics, LSE

visualisation of search strategy
Visualisation of search strategy

Wynn & Bates, Dept. of Statistics, LSE

searching for an improved design
Searching for an improved design

Wynn & Bates, Dept. of Statistics, LSE

features of stochastic simulation
Features of Stochastic Simulation
  • Large number of runs required (17500)
  • No errors introduced by modelling
  • Design improvement, but not optimisation.
  • Can accept any type of input noise (e.g. any distribution, multivariate)
  • Can be applied to highly nonlinear problems

Wynn & Bates, Dept. of Statistics, LSE

statistical modelling emulation
Statistical Modelling: Emulation
  • Perform computer experiment on simulator and replace with emulator…

Wynn & Bates, Dept. of Statistics, LSE

experimentation using the emulator
Experimentation using the Emulator
  • Perform a 2nd experiment on emulator and estimate output distribution using Monte Carlo

Wynn & Bates, Dept. of Statistics, LSE

stochastic emulation
Stochastic Emulation
  • Build 2ndstochastic emulator to estimate stochastic response…

Wynn & Bates, Dept. of Statistics, LSE

piston simulator example23
Piston Simulator Example
  • Initial experiment, 64-run LHS design
  • DACE Emulator of Cycle Time fitted

Wynn & Bates, Dept. of Statistics, LSE

stochastic emulators m and s
Stochastic Emulators (m and s)

Wynn & Bates, Dept. of Statistics, LSE

pareto optimal design points
Pareto-optimal design points

Wynn & Bates, Dept. of Statistics, LSE

satellite simulation data
Satellite simulation data
  • Historical data set
  • 999 simulation runs
  • Two responses: LOS and T
  • Data split into two sets of 96 and 903 points for modelling and prediction
  • Stochastic emulators built with reasonable accuracy

Wynn & Bates, Dept. of Statistics, LSE

response los vs factor 6
Response “LOS” vs. Factor 6

Wynn & Bates, Dept. of Statistics, LSE

dace emulator models
DACE emulator models

Wynn & Bates, Dept. of Statistics, LSE

dace emulator prediction
DACE Emulator Prediction

Wynn & Bates, Dept. of Statistics, LSE

satellite study pareto front
Satellite Study: Pareto Front

Wynn & Bates, Dept. of Statistics, LSE

conclusions
Conclusions
  • Need flexible methods to describe robustness in design
  • Simulations are expensive and therefore experiments need to be carefully designed
  • Stochastic Simulation can provide design improvement which may be useful in certain situations

Wynn & Bates, Dept. of Statistics, LSE

more specific conclusions
(more specific) Conclusions…
  • Two-level emulator approach provides a flexible way of achieving robust designs
  • Reduced number of simulations
  • Stochastic emulators used to estimate any feature of a response distribution
  • Method needs to be tested on more complex examples
  • Use of simulator gradient information may help when fitting emulators

Wynn & Bates, Dept. of Statistics, LSE