Plot the effects of input variables on output responses in hierarchical order
(highest to lowest).
Plot the Effects of Variables on Responses in Hierarchical Order
Rank the effects of input variables on output responses in hierarchical order
(highest to lowest) in the Pareto Plot post processing tab.
From the Post Processing step, click the Pareto Plot
tab.
Using the Channel selector, select the response to plot.
Tip: Analyze multiple responses simultaneously by switching the Multiplot
option to (multiple
plots) and selecting the responses to plot using the Channel Selector.
Analyze the pareto plot.
The effect of input variables on output responses
is indicated by bars. Hashed lines with a positive slope indicates a
positive effect. If an input variable increases, the output response
will also increase. Hashed lines with a negative slope indicates a
negative effect. Increasing the input variable lowers the output
response.
A line represents the cumulative effect.
From the Channel Selector,
review the Ranked Inputs.
Configure the pareto plot's display settings by clicking (located in the top, right corner of the work
area). For more information about these settings, refer to Pareto Plot Tab Settings.
Pareto Plot Tab Settings
Settings to configure the plots displayed in the Pareto Plot post processing
tab.
Access settings from the menu that displays when you click (located above the Channel selector).
Effect curve
Show line to represent the cumulative effect.
# Top factors displayed
Specify the number of input variables (bars) displayed in the
plot.
Note: This setting does not change the calculated
effects.
Multivariate Effects
Calculate the effect using all input variables simultaneously.
Linear Effects
Calculate the effect using each input variable independently.
Include first order, two way interactions along with first order
effects, and calculate interactions consistently with the choice of
linear or multi-variate effects.
Calculate the effect using all input variables simultaneously.
Multivariate effect of an input variable is the difference between the output
response values when the variable is at its lower and upper values while the
remaining variables are held constant. All calculations are based on a single linear
regression model including all variables.
Example
A system with two variables, X and Y and the output response, F (X,Y).
Table 1. Design Matrix
Run
X
Y
F (X, Y)
1
42.0
108.0
1385.4
2
54.0
156.0
2290.2
3
66.0
84.0
3421.2
4
78.0
132.0
4778.3
5
32.4
165.6
824.4
6
44.4
93.6
1548.3
is the reference regression model and
intercept. A and coefficients, B and C, are calculated using the data set above.
A = - 2609.8
B = 88.6
C = 2.5
Regression equation:
Effect of X (lower = 32.4, upper = 78.0)
Since we are investigating the
effect of X only, Y is held constant. For this example, use the mean
value ( = 123.2).
X = 32.4, Y = 123.2
X = 78, Y = 123.2
Effect of Y (lower = 84, upper = 165.6)
Since we are investigating the
effect of Y only, X is held constant. For this example, use the mean
value ( = 52.8).
X = 52.8, Y = 84
X = 52.8, Y = 165.6
Input Variable
Multivariate Effect
X
4040.4161
Y
202.7087
Global Sensitivity Analysis (GSA)
This sensitivity method is based upon probabilistic analysis framework, Sobol
Indices. It decomposes the variance of each response into fractions which are later
distributed to inputs. Final sensitivity values are a normalized version of Total
Sobol Index, including both main and all order interaction effects across the whole
input space. This sensitivity method is highly recommended for studies with
nonlinearity.
Steps in GSA:
A fit model via FAST based on the original DOE data.
Large number of sample points are generated using the fit model.
Decomposition of variance based on sample points and derivation of Total
Sobol Indices.
(multiple
plots) and selecting the responses to plot using the Channel Selector.
(located in the top, right corner of the work
area). For more information about these settings, refer to Pareto Plot Tab Settings.
Figure 2.