# Simulation - identify the input parameters that impact the most the output

I am studying (via simulation) a system that has several input parameters. The output of the system is influenced by the input parameters. My goal is to identify the parameters that have the most impact on the output of the system. I ran a large amount of simulations and for each one of them I changed the value of each parameters using a random algorithm. To identify the parameters that have the most impact on the output I was planning on doing a basic multivariate linear regression including all the parameters, however, it turned out to have a low R2 and low F-stat.

I am working a little bit out of my element here so I am looking for suggestions regarding what I should investigate next to achieve my goal.

The context of the study is building energy efficiency and the main difficulty is that some input parameters have multiple effect on the system. For example: if I lower the total lighting power used in the simulation it will have for effect to decrease the cooling load of my building but if at the same time I was increasing the cooling efficiency of my cooling system the energy saved by increasing the efficiency would be less than if the lighting power was not decreased. In this example I would like to show which has more impact in regards to the energy consumption. However, in what I am trying to do I have a lot more input parameters.

With my background on Data Analysis and Nonlinear Regression, your question seems to be very general and blurry. I guess what you are looking for is called Sensitivity Analysis in some contexts.

You need to understand that parameters may have different orders of impact on different sub-spaces of variables (and Parameters) space.

You may also want to generate multiple sub-models based on this sub-spaces, so in each sub-model only a few of your parameters have the main effect and the rest could be neglected.

Again you need to make your question a little more detailed. for example tell us why you want to do this analysis. because your final goal totally impacts the solution.

• Yes, I am trying to do a Sensitivity Analysis. I want to do this analysis to identify which parameters have generally more impact on the output. I have updated my question. – Jeremy L. May 16 '16 at 17:53
• Following your recommendation I am exploring the possibility of using SALib to perform a Sobol Sensitivity Analysis. – Jeremy L. May 16 '16 at 19:27
• nice, if only you are looking for a sensitivity measure across the whole input space(Global). But in most applications you may want to divide your input space (Localized). Also as you have many parameters, it is a good idea to consider interaction of these parameters.For example maybe three of your parameters in interaction together make the most effect, while each of them individually have negligible effects. – eulerleibniz May 16 '16 at 23:32
• By divining my input space, do you mean to create group of parameters? For instance if I have 12 parameters, make two (or more) groups where I keep half constant and vary the others. – Jeremy L. May 17 '16 at 16:50
• No. assume you have 2 parameters ( x1 and x2 ) which can vary in (0, 1) interval (No loss of generality). then you scan have 4 sub-spaces as follow: sub1: 0<x1<0.5 and 0<x2<0.5 -- sub2: 0<x1<0.5 and 0.5<x2<1 -- sub3: 0.5<x1<1 and 0<x2<0.5, sub4: 0.5<x1<1 and 0.5<x2<1 – eulerleibniz May 18 '16 at 13:40

Sorry I can't comment yet - and this is not an answer: do you change all parameters at same time or do you have a strategy to change parameter per parameter (experiment)?

• Yes, I change all parameters at the same time since some have combined effects. I use a Monte Carlo approach where I randomly change the value of each parameter. I have updated my original question with an example. I hope it will help clarify the issue! – Jeremy L. May 16 '16 at 17:57