Could be a good idea to just try and word vomit maths over the weekend.
Research
The MC methods don’t really make sense for one pertubation. It’s used in modelling a process with multiple random variables, along the chain to the output. Just changing one is a function of a singular random variable.
The use case for monte carlo is when there is mult variation. If we think of a model (could be unit process or whole fuel production) and along the X we have each input paramter along the way to calculation of the output. On the y would be the value that RV on the x takes on (which is random), the MC method goes through like a pinball to get some output.
If we just have 1 variable on the X, its not really something that requires MC. Its not a dramatic stochastic process.
So if we think of each input along the change as an iid, then where t is ‘toward’ the output which is also an RV.
To use MC your treating the model as a stochastic process. This makes sense when it makes sense to model computation stochastically, with one input it doesn’t really make sense.
Sketch of poster
A lifecycle assessment (LCA) is a decision support tool that evaluates the inputs, outputs and the potential environmental impacts of a product system throughout its life cycle (ISO 14044). The following research concerns an LCA done by Liam Mannion and Aron Bell under Stephen Dooleys Carbon technologies research group. The LCA focuses on the emissions generated from production, transportation, and combustion of Sustainable Aviation Fuels, considered a key support for the transistion to clean energy in the aviation industry.
There are many components to carrying out an LCA, of particular interest in this research is the Lifecycle Inventory analysis phase. This phase of the life cycle assessment involves the compilation and quantification of inputs and outputs for a product throughout its life cycle (ISO 14044).
An uncertainty analysis is an important component the modern Scientific method. With regards to an LCA it quantifies the uncertainty introduced in the results of a life cycle inventory analysis due to the cumulative effects of model imprecision, input uncertainty and data variability.
Methodology
A unit process is the smallest element considered in the life cycle inventory analysis for which input and output data are quantified. A unit process is defined in Python and works just like a function. It takes a set of inputs, or parameters and returns an output that represents energy in kJ for that unit process. The goal is to develop a template of analysis for a singular unit process and use that to define the whole LCA (as an aggregation of these processes).
The unit process shown here is the ‘filtration’ process of the ‘Fuel production’ stage defined by Liam Mannion (cite?). This process defines the heating of an input feedstock mass from an initial to a final temperature. To equate it to a function, this unit process takes feedstock composition, initial and final temperature as inputs and produces energy in kJ to heat the input mass up from the initial to a final temperature.
Basic uncertainty
Uncertainty classified for different stages of the LCA, the following considers quantity uncertainty (Igos), that is uncertainty in the inputs to the function representing the unit process.
An input parameter to this process is the mass of triolen, a number representing the mass in kilograms of the triglyceride, triolein, present in the initial feedstock. The range of values we feel that this input could plausibly take on is called the input domain.
The following plot is the Cumulative Distribution Function (CDF) of the output energy of the ‘filtration’ process when an input domain for the ‘mass of triolein’ is an interval from .
Sensitivity Analysis
The first results show changing each function paramter one at a time while keeping all other parameters constant (their default values). The input parameter is the ‘mass of triolein’ which is the mass in kilograms of triolein, a triglyceride, present in the feedstock to be converted to Sustainable Aviation Fuel (SAF).
Intro about uncertainty
Start with sensitivity analysis (variance of output rv)
If you want to perturb multiple input parameters. View the unit process as a stochaistic process, where a path functions maps to output energy.
A Life cycle inventory analysis (LCI) is the phase of life cycle assessment involving the compilation and quantification of inputs and outputs for a product throughout its life cycle (ISO 14044).
Results
- Basic CDF for one input paramter with two input distributions
- A sensitivity analysis for all inputs individually.
- One large view of all input paramters and path function as output.