[Objectives] [Members] [A Case Study] [Methodical Approach]

Methodical Approach

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Design Of Experiments

Design of Experiments (DOE) is used to select a suitable set of trials on the simulator to facilitate the identification of the emulators. As for real experiments the choice of the set of points to be used to identify emulators is very important. Latin Hypercube Sampling (LHS) designs are good for filling space in high dimensions. They are also fast to compute because of their pseudo-random nature. These facts make them highly suited for use as experimental design plans for computer experiments in high dimensions, involving many input factors.

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Latin Hypercube Sampling (LHS)

Latin Hypercube Sampling (LHS) designs are good for filling space in high dimensions. They are also fast to compute because of their pseudo-random nature. These facts make them highly suited for use as experimental design plans for computer experiments in high dimensions, involving many input factors.

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Simulators

• The use of simulators that are able to simulate very complex systems has increased the interest in emulators as a tool to optimise product designs.
• Simulation codes are in general cheaper than real experiments and can often provide very accurate approximations of the physical system.
• However their high complexity means high computational effort to compute even a single trial.
• It follows that optimisation using simulation codes directly is inefficient and unlikely to lead to globally optimal design solutions in a competitive timeframe.

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Emulators Definition

Statistical methods for empirical model building used to describe the relationship between one or more output responses y and a number of predictor variables, or factors x=(x1,...,xn).

The substitution of the simulator by an emulator represents a trade-off between accuracy and speed of analysis as shown in the following table:

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Emulator’s Usage

Once a sufficiently accurate emulator is identified, it can be used in the following ways:

	Predicting the response at untried inputs. The emulator can be evaluated at particular factor settings instead of performing often very expensive and time consuming physical tests. Physical tests are limited to the validation stage to confirm predictions corresponding to optimal configurations .
	Studying how a given factor affects the response globally over the design space and in specific regions of interest (for sensitivity analysis).
	Optimization AND Robustness.

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Common Emulator Types

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Cross Validation

Cross validation is used to check the accuracy of emulators. This involves predicting at each design point in turn when that point is left out of the set used to identify the emulator.

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Multi Objective Optimization

Except in very rare situations, it is impossible to minimize all the responses at the same time, and multi-objective optimization can be considered as the process of obtaining reasonable compromises from previously defined preferences.

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Multi Domain Optimization

The use of emulator models in optimization naturally leads one to consider multi-domain optimization . A common design scenario is where several different type of response are considered from a single design of a product or process, for example in the design of a turbine blade, one needs to conduct stress analysis and thermal analysis of the turbine blades. The advantage of the emulator approach is that each design response is modeled in the same statistical environment. This provides, perhaps for the first time, global optimal robust solutions to complex multi-domain engineering design problems.

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Validating Results

After getting results of the Multi Objective optimizations these results should be verified in one of the following:

• Real Tests

• Full simulations

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