Local Sensivity Analysis

Hello!

I'm using Local Sensitivity Analysis in order to observe which parameter of the model is more sensitive. I’m using the model ASM1 AN in order to observe the nitrite profile in alternating cycles of nitrification and denitrification using intermittent aeration in the same process tank.

I would like to make some plots with the perturbation of the parameter on x-axis and the function of sensitivity on y-axis.

I would like also to plot the perturbed trajectories and the nominal trajectory for each parameter.

Then I would also like to define a ranking of sensitivity by the various parameters, so I can choose which ones I must calibrate.
Someone know how can I act?

Thank you for your attention and your help
Iacopo Totaro

[quote author=I.Totaro link=topic=1471.msg3612#msg3612 date=1370682008]
I would like to make some plots with the perturbation of the parameter on x-axis and the function of sensitivity on y-axis.
[/quote]

I am afraid this is not directly possible. You have the following options when creating a plot (AddSeries button):
- [b]Sens[/b]: typically, you would plot the "RunNo" (x-axis) vs. one of the sensitivity quantities (e.g. CRS, Central Relative Sensitivity; y-axis)
- [b]SensFunc(ParName)([VarName])[/b]: typicall, "t" vs. one of the sensitivity quantities (y-axis)
- [b]Simul(Ref)[/b]: same as the plain Simul, i.e. "t" vs. one of the data series
- [b]Simul([Backward OR Forward])([ParName])[/b]: same as Simul(Ref)

What you may have in mind is some sort of Scenario Analysis where you compare the use of different perturbation factors?

[quote author=I.Totaro link=topic=1471.msg3612#msg3612 date=1370682008]
I would like also to plot the perturbed trajectories and the nominal trajectory for each parameter.
[/quote]

This should be possible: one data series being Simul(Ref), the other one(s) Simul([Backward OR Forward])([ParName])

[quote author=I.Totaro link=topic=1471.msg3612#msg3612 date=1370682008]
Then I would also like to define a ranking of sensitivity by the various parameters, so I can choose which ones I must calibrate.
[/quote]

Is this not what one would typically do in a [b]Global[/b] Sensitivity Analysis rather? In GSA, you have what we termed "Tornado" plots which compare the sensitivities of a variables to a set of parameters. There you could establish a threshold: anything beyond that is worth calibrating.

[quote]
Quote from: I.Totaro on June 08, 2013, 10:00:08 AM
Then I would also like to define a ranking of sensitivity by the various parameters, so I can choose which ones I must calibrate.

Is this not what one would typically do in a Global Sensitivity Analysis rather? In GSA, you have what we termed "Tornado" plots which compare the sensitivities of a variables to a set of parameters. There you could establish a threshold: anything beyond that is worth calibrating.
[/quote]

Of course this is something that is typically done with Global Sensitivity Analysis. But you can do that with Local sensitivity analysis as well. But then you have to reduce your time series to one value, which is not done yet in the LSA (opposed to GSA), right?

I read your answers and I thank you, but then I would understand the main differences in WEST between local and global sensitivity analysis.

Enrico Remigi what do you mean for "Tornado plots"? Because in GSA I only have done plots which are explaned in the GettingStarted Tutorial.

[quote author=Youri Amerlinck link=topic=1471.msg3632#msg3632 date=1371044591]
[quote]
Quote from: I.Totaro on June 08, 2013, 10:00:08 AM
Then I would also like to define a ranking of sensitivity by the various parameters, so I can choose which ones I must calibrate.

Is this not what one would typically do in a Global Sensitivity Analysis rather? In GSA, you have what we termed "Tornado" plots which compare the sensitivities of a variables to a set of parameters. There you could establish a threshold: anything beyond that is worth calibrating.
[/quote]

Of course this is something that is typically done with Global Sensitivity Analysis. But you can do that with Local sensitivity analysis as well. But then you have to reduce your time series to one value, which is not done yet in the LSA (opposed to GSA), right?
[/quote]

I would say it is. LSA aggregates the differences between the reference time series and the perturbed time series (backward and forward), at the selected time points, into a number of values (MAE - Mean Absolute Error, MRE - Mean Relative Error, RMSE - Root Mean Squared Error, ...) that are presented in a table at the end the LSA experiment's execution (Analysis/Runs). This table can be used for ranking. Note that there is only one perturbation factor for each parameter / variable combination. Each such combination therefore only has one set (backward and forward) of perturbed time series.

In case a GSA experiment is set up in such a way that the difference between a reference time series (i.e. the "non-perturbed" series) and a number of perturbed series is used as an objective function, it could be considered similar to an LSA experiment, provided the perturbations are as small as the ones normally used in LSA. However, in GSA there is much more freedom & flexibility in the definition of objective functions.

[quote]I would say it is. LSA aggregates the differences between the reference time series and the perturbed time series (backward and forward), at the selected time points, into a number of values (MAE - Mean Absolute Error, MRE - Mean Relative Error, RMSE - Root Mean Squared Error, ...) that are presented in a table at the end the LSA experiment's execution (Analysis/Runs). This table can be used for ranking. [/quote]

Great, I didn't know that it was available already.

[quote author=Youri Amerlinck link=topic=1471.msg3644#msg3644 date=1371214035]
[quote]I would say it is. LSA aggregates the differences between the reference time series and the perturbed time series (backward and forward), at the selected time points, into a number of values (MAE - Mean Absolute Error, MRE - Mean Relative Error, RMSE - Root Mean Squared Error, ...) that are presented in a table at the end the LSA experiment's execution (Analysis/Runs). This table can be used for ranking. [/quote]

[/quote]

From what types of values in the table would you start to make a ranking of sensitivity by?

I would perform a GSA because you have rather large value ranges for parameters in such models, plus the models are highly non-linear, so you should not use LSA. You can rank then you parameters according to any regression coefficient from your GSA.