215Optimization techniques in diesel engine system design
© Woodhead Publishing Limited, 2011
are optimized to bring the mean to the target, and the levels of some other
control factors that affect f
S/N
are optimized in order to maximize f
S/N
and
equivalently to minimize variance.
Standard ANOVA techniques are often applied on the mean response and
the signal-to-noise ratio in order to identify the control factors that affect
them. ANOVA can also quantify the effects and relative contribution of each
factor to the total variation of the responses.
The summary statistics of the responses of each DoE run include mean,
variance, and signal-to-noise ratio. Depending on optimization criteria, the
output responses can be separated into three categories: smaller-the-better,
larger-the-better, and nominal-the-best. Variable screening can be conducted
using the main effect plot or linear regression. The response in the main
effect plot of an independent factor is the average of all the responses over
all the levels of other factors. It should be noted that the unit or the range
is usually very different from one factor to the next. The main effect plot
allows an intuitive visualization of the trends between the inputs and the
outputs and identies strong and weak factors as well as the optimal factor
levels (Fig. 3.5). The greater the departure of the points from the global
mean of all the response data, the more important the factor is. The optimal
levels are chosen for each control factor from the main effect plot. In the
interaction plot, parallel lines (strictly speaking, non-crossing lines within the
factor range) indicate no interaction. It should be noted that the main effect
plot can be highly misleading when there are strong interactions between the
factors such as in many engine applications. Also note that the main effect
plot can be biased if the experimental design is not properly balanced. The
linear regression method computes the correlation coefcients for the factors
and also outputs the p-values that indicate the statistical signicance between
the factors and the response. Although the linear regression method does not
provide a visualization of the plot, it does not produce biased conclusions.
After the optimum combination of the control factor level is selected from
the main effects plot, the optimum signal-to-noise ratio and mean can be
predicted. At the end, a conrmation run is conducted as a nal check to
conrm the predicted optimum outcome.
As summarized in Fig. 3.4, the Taguchi method consists of the following
nine steps:
1. dening the goal or target;
2. brainstorming for possible factors;
3. designing a DoE (selecting factors, levels, ranges and orthogonal
arrays);
4. conducting DoE runs to collect data;
5. analyzing and plotting the results with statistical analysis (e.g., ANOVA,
regression analysis, main effect plot, and interaction plot);
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