Overview

The three design exploration modules are complementary, but their objectives sometimes coincide, depending on the complexity of the design.

Design of Experiments

This module makes it possible to compare the influence of different control parameters on one or several objective (or "response") functions. In the examples of this manual, those objective functions are tire compression and body acceleration. The aim of the DOE model is to develop a greater understanding and deeper physical analysis of the model, establishing a list of influential parameters of 1st, 2nd, 3rd order etc. This allows us to simplify the model or to perform a hierarchical optimization to reduce calculation times: optimizing only the influential 1st order parameters, and then if necessary, the 2nd order parameters (keeping the others static). in this way, we can avoid a costly optimization of all parameters simultaneously when some of them may not have any significant effect on performance.

Finally, DOE can be used to obtain a surrogate mathematical model, a polynomial Response Surface Model (RSM) of a costly objective function. If the response surface is a polynomial function, the effects of the parameters are reflected in the values of its coefficients.

Optimization

The objective of optimization is to obtain the best possible values of parameters in the design space with regard to one or more objective functions while respecting certain constraints. The NLPQL algorithm should be sufficient for most common situations. In more complex cases (with a large number of parameters and/or objectives and/or non-smooth functions), the state-of-the-art consists in performing a global optimization (Genetic algorithm) first, in order to explore the design space and to avoid local minima, and then to extend the study with a local algorithm (NLPQL) to refine the convergence. If there are several objective functions to minimize, they are aggregated into a single sum that we then try to minimize (see Optimization).

Using a Genetic algorithm can prove costly if the initial objective functions are also costly. This is why optimization can be carried out (at least partially) on a Response Surface Model, rather than on the model itself (see Optimization). This can be called a surrogate model. In this manual, we give the example of a Monte-Carlo analysis for a costly optimization problem, we opt for a Latin Hypercube or Optimized Latin Hypercube distribution (which are in fact random experiment planes whose number of experimental runs is fixed in advance independently of the number of parameters which is very practical for engineers). Such distributions optimize the sampling of experimental runs (representing a compromise between cost and model verisimilitude). Please see Latin Hypercubes for more information.

Monte Carlo

In Monte Carlo techniques you assign a statistical distribution associated with a standard deviation (or amplitude) to each parameter. Simcenter Amesim will randomly choose a set of parameter values for each run: Simcenter Amesim makes this choice respecting the statistical settings of parameters.

Simcenter Amesim provides tools to do the statistical analysis of the responses (statistic moments and histograms).