Modeling fuel consumption in various external vehicle conditions for military vehicle using mixed linear models

Abstract


INTRODUCTION
Energy is an important factor in achieving goals and programs in a country.One of the energy that is always used is sourced from the fossil earth, namely petroleum or fuel oil.Fuel is used in almost every sector in the country to meet people's needs.Every year the need for fuel has increased higher and higher due to technological developments.The oil and gas industry is an important industry for national development, and to meet the energy and raw material needs of the country's industry, as well as generate foreign exchange for the country, its management must be managed as optimally as possible.Endeavor to realize an Saputra, et al.Modelling fuel consumption in various external vehicle… 68| International Journal of Applied Mathematics, Sciences, and Technology for National Defense oil and gas business that is independent, reliable, transparent, competitive, efficient by taking into account the preservation of environmental functions and the development of national potential and role that can support the sustainability of national development.
Indonesia is the country with the largest energy consumption in Southeast Asia and fifth in Asia Pacific in primary energy consumption, after China, India, Japan and South Korea with primary energy consumption of 185.5 MTOE in 2018.(Afriyanti Y et al., 2020) According to the Director General of New, Renewable Energy and Energy Conversion (EBTKE) of the Ministry of Energy and Mineral Resources (2018), fossil energy reserves are increasingly depleting.The data shows that the current coal reserves are around 7.3-8.3 billion tons which are predicted to be used up in 2026.Meanwhile, the current oil stocks of 3.7 billion barrels are predicted to be used up in 2028.
The transportation sector is the largest fuel consumption sector among other sectors.According to a study conducted by the Ministry of Transportation, the land transportation sub-sector consumes around 80% of all fuel consumed by the transportation sector.Meanwhile, the air transportation, sea transportation and ASDP sectors use international standard facilities, so consumption in this sub-sector is considered to have achieved reasonable efficiency.(Abdulkadir, 2000) Several factors affect the consumption of fuel oil energy in Indonesia, including economic growth, population growth, energy subsidies, and consumption of fossil energy.Consumers who use gasoline complain that gasoline-powered cars often experience knocking when using unleaded gasoline compared to unleaded gasoline.Engine knocking leads to unnecessary fuel consumption and increases exhaust emissions.One of the possible causes of knocking, especially at high loads, is that the engine octane number (MON) of the gasoline is much lower than the research octane number (RON).Usually, the RON value is larger than the MON, and the difference between the two values (RON -MON) is called sensitivity.It represents the sensitivity of the fuel to change under severe operating conditions from an anti-knock perspective (Djainuddin S., 2008).
In the field of defense, the presence of formidable military vehicles is indispensable.One form of toughness is not only about the strength of the structure, but can also talk about the effective use of fuel.Therefore, we need a way to regulate fuel consumption for vehicles, especially military vehicles.One of the factors that can be controlled in managing fuel oil is by choosing which fuel oil is right for consumption so as to reduce the occurrence of an energy deficit.This is one step for the government in an effort to reduce the use of fossil energy, especially fuel oil.The purpose of this research is to examine the fuel consumption pattern of vehicles in an area that experiences several weathers so that it can determine the level of efficiency of fuel used.

METHODS
This research method is qualitative, based on experimental data conducted by Andreas Wagener in the United States which began in November 2018.The experiment was conducted to determine the influence of several factors on fuel consumption in car vehicles, both from factors such as fuel type, distance, speed, and temperature, to weather.To determine the influence of these factors on car fuel consumption, a test was carried out using linear model techniques, the linear mixed effect model, and anova mathematical model (Pinherio & Bates, 2004;Aisyah et al, 2023).
Linear model commonly used to identify subclasses of models that allow substantial complexity of related statistical theories.Meanwhile, linear mixed model is the result of the development of a linear model where the response variable (Y) is influenced by fixed effects and random effects.A fixed effect is an explanatory variable while random effects can be explained using time, area, and other influences.Two-way anova is also called 2-way anova compares the mean differences between groups that have been divided into two independent variables (called factors).
In the study, the data used were secondary data such as speed, distance, temperature, and weather.In this case, the main reference is the gas type, both type E10 and SP98, which is a comparison in its effect on the effectiveness of car fuel consumption.Gas Type E10 is a type of fuel mixture between gasoline and ethanol as much as 10%.E10 is widely used in the United States, so the presence of this fuel is difficult to find in some countries.By and large, E10 gas is a fuel used in lawnmowers with a composition of 10% ethanol and 90% gasoline.(Wagener, 2018).Gas Type SP98 is a type of super plus gasoline that has a higher octane than E10 so the selling price is more expensive.Higher octane gasoline such as SP98 gasoline will have better crackling resistance and hence better combustion (controlled).In addition, the WHO says clean machines say optimization of consumption and, consequently, reduction of pollution (Gino, 2019).
In the experiment, data collection was carried out in certain weather, namely sunny, rainy, and snowy, thus affecting the outside temperature as well.When weathering, the temperature produced is greater than in rainy and snowy weather.In addition, data collection was carried out using a speed of about ≤90 km / h with mileage in each experiment from the range of 4.9 -28 km, but at a certain time the mileage taken was constant at ± 12 km.

Analysis of Models
In this study, several mathematical modeling was carried out to measure the level of significance of several types of variables that exist for an outcome, namely fuel consumption in vehicles.Several forms of models are used as shown in Table 1.

Fuel type
Weather Speed Distance Temp Outside In the first stage, we need to identify several variables that may have a high influence on the level of vehicle fuel consumption.We model this in the form of a mathematical equation which will be solved by a linear mixed model without random effects.In looking at the relationship of speed and distance to the effect of fuel consumption using the first model as follows, Where fuel consumption is expressed as   and   is the residue of the output variable for the fuel consumption of a vehicle.This model illustrates that there is no significant effect of the distance traveled by the car and the average speed driven on the fuel consumption of the car.This is evidenced by the p-value of speed and distance which is greater than the specified significance level (α = 0.05).Furthermore, a search for variables that affect fuel consumption is carried out by linking the type of fuel used to model 2.
Model 2 displays the effect of the type of fuel used on fuel consumption in the car used.The results of the p-value on the type of fuel show that the type of fuel has a significant effect on fuel consumption.This is indicated by the p-value which is close to 0, far from the established significance level.From the two models that have been tested using the linear mixed model, it is revealed that only the type of fuel has a significant effect on fuel consumption when compared to the average speed and distance traveled by the test car.The complete results of the linear mixed model significance model in model 1 and model 2 are presented in Table 2. To further prove the significance of the effect between variables on fuel consumption, the existing variables were re-modeled using an analysis of variance (anova) approach.With this approach, the condition of the distance traveled, the average speed of the car, and the ambient temperature will be modeled in a mathematical equation to determine the level of significance of the effect on fuel consumption.The ambient temperature variable is added to determine the relationship between high and low ambient temperatures around the car affecting engine performance which results in the level of fuel consumption also having an effect.This model 3 equation is described as From the results of the modeling carried out and presented in Table 3, it can be explained that in model 3 itself the type of fuel still has a very high level of significance in influencing the fuel consumption of the cars used.This is in contrast to the other variables included in model 3 such as distance traveled, average speed and ambient temperature which do not have a significant effect on high fuel consumption.This is in accordance with the modeling results of the 2 previous models using the linear mixed model.This means that the type of fuel has more influence when compared to mileage, average speed, ambient temperature using the ANOVA method.The next stage is to prove again that the variable type of fuel affects the fuel consumption of a vehicle using another method, namely the linear mixed model with random effects.We use weather condition variables as the effect of random variables in this form of modeling.This is expected to prove the effects of other variables such as mileage, speed and ambient temperature on fuel consumption with the influence of weather as an additional random variable.First, we re-model the effect of distance traveled and average speed on fuel consumption through model 4. Model 4 can be written into an equation as follows, From the results of the significance presented in table 4, the p-value of speed and distance is greater than the predetermined significance level.This indicates that by using the linear mixed model, speed and distance do not have a significant high level of influence on fuel consumption.Then re-modeled the significance of each fuel consumption to the influence of ambient temperature and the type of fuel used.This model is represented by model 5 and model 6 respectively.With this, we can see the effect of each independent variable on fuel consumption with the random effect of weather conditions when the data is collected.Further equations of these models are, The results of the significance of the two models show that the ambient temperature has a pvalue greater than the predetermined significance level.So that the ambient temperature does not have a significant enough effect on vehicle fuel consumption even though there is only one independent variable in one model and the influence of weather is added as a random variable.However, under the same conditions, the different types of fuel used have a significant effect on fuel consumption.This can be seen in the p-value of the type of fuel in Table 4, the results of model 6.The p-value is lower than the significance level.Thus, differences in fuel types consistently have a significant effect on fuel consumption.If previously only shown the results of the model where the type of fuel is the only independent variable in the mathematical model compiled, then the next model will be tried to combine the independent variable type of fuel with other independent variables on fuel consumption with a linear mixed model approach with random effects.Weather conditions are still a random variable used to generate random effects on the models used.In model 7, the effect of average speed, distance traveled and type of fuel is modeled on fuel consumption.Model 7 uses the following equation   ~(0,   2 ) ,   ~(0,   2 ) The results of the significance of the two models above are presented in Table 5.Both show almost similar results where only the type of fuel has a high significance in influencing fuel consumption.The p-value of the type of fuel in both models is close to 0, so it is far from the significance level.While other variables such as speed and mileage in model 7 and ambient temperature in model 8 have no significant effect on fuel consumption.In model 9, modeling with more complex conditions will be carried out.Fuel consumption will be modeled by being influenced by all the independent variables in this data, namely ambient temperature, average speed, distance traveled and the type of fuel used.The completion of this modeling still uses a linear mixed model with random effects.Weather conditions remain a random variable in this mathematical model.The model equation 9 as follows,   =  0 +  1   +  2  1 +  3  2 +  4  3 +  5  4 +   +   (8) ~(0,   2 ) ,   ~(0,   2 ) The results of the completion of model 9 are shown in Table 6.Similar to the results of the previous models, the difference in the type of fuel used has a high significance for fuel consumption.Other independent variables such as speed, distance traveled, and ambient temperature have a low significance for fuel consumption because the p-values of these three variables are above the significance level.The results of this model 9 strengthen the argument from the results of previous models where the type of fuel has a significant effect compared to the distance traveled, speed and ambient temperature on vehicle fuel consumption.

Table 2 .
The results of the Linear Mixed Model significance model ***significance at  = 1%

Table 3 .
The results of the ANOVA significance model International Journal of Applied Mathematics, Sciences, and Technology for National Defense | 71 ***significance at  = 1%

Table 4 .
The results of the Linear Mixed Model with random effect significance model International Journal of Applied Mathematics, Sciences, and Technology for National Defense Saputra, et al.Modelling fuel consumption in various external vehicle… 72| International Journal of Applied Mathematics, Sciences, and Technology for National Defense   =  0 +  1   +  2  1 +  3  2 +  4  3 +   +   Furthermore, in model 8, fuel consumption is modeled by being influenced by the type of fuel and ambient temperature.The modeling equation used is as follows,   =  0 +  1   +  2  1 +  3  2 +   +   (7)

Table 5 .
The results of the Linear Mixed Model with random effect significance model ***significance at  = 1%

Table 6 .
The results of the Linear Mixed Model with random effect significance model