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Background, Aim and Scope:
In 1995, with funding from the U.S. Department of Energy (DOE), the Center for Transportation Research (CTR) of Argonne National Laboratory (ANL) began to develop a model for estimating the full fuel-cycle energy and emissions impacts of alternative transportation fuels and advanced vehicle technologies. The model, called GREET (Greenhouse gases, Regulated Emissions, and Energy use in Transportation), calculates fuel-cycle energy use in Btu/mi and emissions in g/mi for various transportation fuels and vehicle technologies. The parametric assumptions used in the GREET model involve uncertainties. In situations involving uncertainties, a deterministic approach to solve the problem would produce results which might not be a true reflection of reality and in such cases stochastic simulations incorporating uncertainties need to be performed in the model. A new stochastic simulation tool, developed by Vishwamitra Research Institute (VRI), is built in the GREET model to address uncertainties. This paper presents the methodology and feature of this new stochastic simulation tool and evaluates the performance of the sampling techniques in the tool.
Materials and Methods:
The new tool is interfaced through the graphical user interface (GUI) to perform the stochastic simulation. In general, totally five steps need to be followed to run a complete simulation: 1) Specify probability distribution functions to the input variables; 2) Indicate the number of samples required and the sampling technique to be used; 3) Define the forecast variables; 4) Delete distribution functions defined previously; and 5) Propagate the uncertainties and statistically analyze the outputs. The GREET model contains more than 700 default distribution functions for a wide variety of key parameters and as many as ~3000 forecast variables. For such a large database, the stochastic simulation tool has been developed to incorporate an inbuilt bank of as many as 11 probability distribution function types for representing uncertain parameters and four sampling techniques (Monte Carlo sampling [MCS], Hammersley Sequence sampling [HSS], Latin Hypercube sampling [LHS] and Latin Hypercube Hammersley sampling [LHHS]) for stochastic simulation. To evaluate the performance of the four sampling techniques, 16 independent stochastic simulation runs were conducted in GREET and the output results were analyzed and compared.
Results:
With the same number of samples, the output distribution curve simulated by HSS is the smoothest corresponding to the highest level of uniformity, followed by LHHS and while MCS and LHS are almost the same with respect to smoothness factor. To achieve the similar level of smoothness as HSS with 1000 samples, LHHS needs to be simulated with ~1500 samples and LHS and MCS with ~3000 samples. As a result, HSS can achieve more than 200% reduction in running time without compromising on the accuracy and quality of the prediction curves while LHHS can achieve a 150% reduction compared to LHS or MCS. The simulated mean values are close to the actual mean value enough (within ±1%) no matter the selection of sampling technique and the number of samples (between 1000 and 4000).
Discussion:
The standard deviation values from each other are close enough as well (within ±5%). It shows the trend that the increasing number of samples makes the simulated mean value marginally closer to the actual mean value; however, the improvement effect is negligible. On the other hand, the simulation time is strictly positive-correlated with the number of samples. Therefore, the trade-off of extending simulation time and improving the outputs (e.g., smoothness of the distribution curve) needs to be carefully assessed by the user.
Conclusions:
A new stochastic simulation tool has been developed to be built in the Argonne’s GREET model to enhance the capability for addressing the uncertainties incorporated in a wide variety of input parameters. This tool has been designed as a Microsoft® Excel add-in file with Visual Basic macros which can be loaded whenever the user needs to perform a stochastic simulation within the model. This new tool automates the process of setting up a stochastic simulation to a great extent and guides the user in each step of the process through the user-friendly GUI windows. According to the performance comparison among these four sampling techniques, HSS was found to be the highest efficient technique. Therefore, we applied HSS as the default technique with 1000 as the default sampling number in GREET.
Recommendations and
Perspectives:
A new stochastic simulation tool has been developed to be built in the Argonne’s GREET model to enhance the capability for addressing the uncertainties incorporated in a wide variety of input parameters. This tool has been designed as a Microsoft® Excel add-in file with Visual Basic macros which can be loaded whenever the user needs to perform a stochastic simulation within the model. This new tool automates the process of setting up a stochastic simulation to a great extent and guides the user in each step of the process through the user-friendly GUI windows. According to the performance comparison among these four sampling techniques, HSS was found to be the highest efficient technique. Therefore, we applied HSS as the default technique with 1000 as the default sampling number in GREET.
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