Theory-Lesson 7 Flashcards
What is the sensitivity analysis?
Is a study of how the variation of the output of a model can be apportioned to different sources of variation.
What is the objective of a sensitivity analysis?
To determine the most contributing input variables to output behavior
Describe local sensitivity analysis and point out its main disadvantage
Local sensitivity analysis is valid only for a local area. Although it’s not computationally heavy, its unwarranted when the model input is uncertain and when the model is of unknown linearity.
So it’s always better to use global approximation.
Describe the global sensitivity analysis
In constrast to the local sensitivity analysis, a global sensitivity analysis considers the whole variation range of inputs. A handful of data points adequately selected in the space of the input factors is far more effective than estimating derivatives at a singel data point.
What is the One At a Time method?
OaT method refers to the process where one input at a time is evaluated with respect to the corresponding output.
Factor Prioritization
We must focus on the input variable which affects the output variance the most.
Factor fixing
Identify factors which make no significance difference to the output variance. They can be fixed an any given value within the acceptable range of variation without affecting the output variance.
Variance cutting
Reduction of the output variance to below a given tolerance.
Pearson Correlation Coefficient
Takes values between -1 and 1.
1->maximum correlation (slope 45 deg)
-1->maximum inverse correlation
0-> no correlation
Uses the covariance.
PCC=cov(x1,x2)/Σx1*Σx2
It’s advantage is that when we have a very high or very low PCC, its means that two OFs are similar and in this way we can reduce the number of the total OFs of the system and reduce the computational effort.
DRAWBACK:MOSTLY EFFICIENT FOR LINEAR PROBLEMS, while we mostly deal with non-linear ones.
Spearman correlation coefficient
The SCC is based on ranking principle. It ranks the inputs and the outputs and find the correlation based on those rankings.
Again values from -1 to 1.
The drawback of these are that if the function is non-monotonic, it can’t interpret it and the SCC would be 0.
It’s also possible to construct a matrix of correlations, which include the correlations coefficients between all OFs taken two by two.
rs.ij=rs.ji which is the correlation coefficient between the i-th and j-th OF.
It’s advantage is that when we have a very high or very low SCC, its means that two OFs are similar and in this way we can reduce the number of the total OFs of the system and reduce the computational effort.
Comparison between Spearman and Pearsons
-If not sure about the linearity and the monotonicity, its better to use Spearman.
-None of them are ideal for non-linear and non-monotonic functions.
Scatterplots
Allow the immediate visualization of the relative importance of factors.
-Sample each factor from its distribution and plot each factor against the output.
DRAWBACK:When there are a lot of factors, its different to rank the factors rapidly and automatically.
Linear Regression
Again used to identify the linear correlations between a generic design variable and a generic OF.
f.j=βο + Σ βi * xi
The accurace can be measured by R^2 ( coefficient of determination)
After a proper normalization of the DVs, βi can be used to rank the relative importance of each DV xi.
