Determination of the Model Basis for Assessing the Vehicle Energy Efficiency in Urban Traffic

Abstract

The paper studies the problem of assessing the vehicle energy efficiency on the streets of urban road network. As a result of morphological analysis of the system “Vehicle—Traffic flow—Road—Traffic Environment” 18 significant morphological attributes of its functional elements, that affect the energy efficiency of vehicles, were identified. Each attribute is characterized by 3–6 implementation variants, which are evaluated by the relevant quantitative or qualitative parameters. The energy efficiency of vehicles is determined by the criteria of their energy consumption considering the vehicle category, type of energy unit, mode of vehicle movement and adjustment factors—road, climatic and others. The input parameters values of the system in the process of traffic flow on the linear fragments of streets and road networks of the cities of Ukraine and Poland were measured. The set of independent system parameters is determined by applying the Farrar-Glober method based on statistical estimates. The specified set is the basis of the studied system and is formed of 10 independent input parameters. The presence in the basis of parameters that correspond to the morphological features of all four functional elements, confirmed the importance of these elements of the system. The mathematical dependence of the impact of vehicle characteristics, traffic flow, road and environment on vehicle energy efficiency is built. The standard deviation of the model values from the tabular ones equals $\acute{\sigma }=0.0091$. Relative standard deviation equals ${\acute{S}}_r=1.5\%$. The results of the study could be used in the development of new and optimization of existing intelligent traffic control systems of urban transport.

1. Introduction

The development of the world economy and population growth inevitably led to an increase in freight and passenger traffic. The needs for population mobility are growing every year. Around 70% of the European Union population lives in urban areas (cities, towns and suburbs) and generate around 85% of European Union’s GDP [1]. At the same time, the level of motorization of large cities is growing rapidly. Urbanization coupled with motorization directly causes several issues, such as environmental pollution by harmful emissions and noise, congestion, and accidents. Urban transport is still mainly based on conventional private passenger vehicles equipped with internal combustion engines, which are the main sources of greenhouse gas emissions. Around 40% of all CO₂ emissions from transport and up to 70% of other pollutants generated by transport are emitted by urban traffic [2]. Inefficient traffic control and poorly designed urban road network causes unnecessary energy consumption while the vehicle is driving in heavy traffic or idling in traffic jams. Idling refers to engine working while vehicle is not moving. Idling fuel consumption of conventional vehicles can be as high as 15 mL per minute [3]. Conventional vehicles are still emitting exhaust gases while idling, hence they are polluting air under idling conditions. Reduction of emissions can be achieved by redesigning of intersections. Authors of [4] found that change of one specific roundabout layout can reduce up to 30% of emissions from this intersection.

City’s inhabitants should be encouraged to use public transport, as fuel consumption per passenger of city bus can be much lower than of private passenger vehicles what confirms high energy efficiency of public transport [5]. City’s authorities might take measures to encourage its inhabitants to use public transport instead of private vehicles, i.e., creation of proper urban infrastructure (bus lanes and parking lots), replacement of public transport fleet, development of Integrated Traffic and Public Transportation Management System [6]. Authors of [7] found that urban mobility planning can affect number of passengers of urban public transport.

The intensity of traffic has a great influence on the level of roadside pollution. Authors of [8] calculated that during pandemic, decrease of daily traffic intensity by 66% accounted for decrease of total daily emissions of: CO by factor of 2.25, CnHm by factor of 3.55, PM concentration by factor of 1.39–3.42, NOx, by factor of 2.64 and PM by factor of 1.96. In addition, there is a global trend of rising energy prices. These factors require the optimization of traffic management systems in large cities and identification of energy reserves during vehicle operation to ensure sufficient air quality in cities, as most of the cities in European Union do not meet the air quality requirements [9].

In developed countries, the transition of transport to alternative fuels and the creation of appropriate infrastructure is carried out, which requires significant financial investment. Therefore, it is important to identify and implement alternative ways to reduce energy consumption by ensuring energy-efficient traffic in urban mobility to reduce cost of urban transportation. One way of reducing energy consumption is to provide guidance of eco-driving to drivers [10,11].

Energy consumption and the harmful effects of the vehicle movement on the environment can be determined by real-time measurements while the vehicle is in motion or by computer simulation. In the case of measurements of harmful substances emitted into the atmosphere by vehicles, the applied test method requires appropriate equipment and is most often used to assess pollution in a limited area [8]. In the case of measurements performed over a large area, it is required to have an extensive measuring and monitoring system. A method that requires the use of a much smaller amount of specialized measuring equipment is the use of a computer simulation based on a mathematical model of fuel consumption, emissions or energy efficiency. The available literature describes 2 simulation methods. The first one consists in determining the quantities values, such as fuel consumption, energy efficiency and emissions, separately for each vehicle [12,13,14]. The input data for the simulation process may be the measured traffic profiles [15,16,17] or driving cycles characteristic for a given section of the route [18,19,20,21]. A driving cycle is defined as the speed over time profile of a representative vehicle that can be obtained by combining a series of micro journeys. A micro journey is defined as the journey between the starts of two periods of idling. Driving cycles may be divided into 2 types: standard and real-world. Usually, standard driving cycles are used to ensure emission norms and real-world driving cycles are used to test and evaluate field performance [22]. Authors of [23] developed a model to estimate diesel bus fuel consumption. Authors of [24] developed a model to estimate influence of changing traffic conditions on fuel consumption of public urban bus. The process of simulating selected quantities separately for each vehicle requires additional knowledge of the Brake-Specific Fuel Consumption (BSFC) characteristics [25,26]. But these characteristics are not always available.

One of those methods, that do not require such knowledge, is estimation based on VSP (Vehicle Specific Power) model [24,27,28]. VSP is defined as the required engine power to offset vehicle acceleration, wind, rolling and road slope resistances. VSP model is a function of a vehicle velocity, acceleration, deceleration and road slope. VSP model connects instantaneous driving state, required engine power and fuel consumption. VSP model could be used for comparisons of fuel consumption characteristics between different vehicles [29].

The second method does not consider individual vehicles but takes a comprehensive approach to the entire traffic flow in the entire area. In this method, vehicles are divided into categories [30] and for each category, assuming specific traffic conditions, fuel consumption, emission and energy efficiency are determined. With a comprehensive approach to the issue, the most advanced is the method of morphological analysis. Morphological analysis is defined as a method for structuring and evaluation of the total set of relationships contained in complex, multidimensional, non-quantifiable problem [31]. The morphological analysis begins by identifying and defining dimensions of the investigated complex problem, that are the most important for this problem. Then, each of these dimensions is given a range values or conditions, that are relevant. These together make up the structure of variables or parameters of the problem. Then, a morphological field is created by making the table of the parameters placed in parallel columns, representing an n-dimensional configuration space. The last step is to examine each configuration (created by selecting a single value from each of the variables) or to reduce number of configurations by a process of cross-consistency assessment before examination (by applying logical, empirical and normative constrains) [32].

To assess the efficiency of vehicle motion on the urban road network in the paper [33] a morphological analysis of the system “Vehicle-Traffic flow-Road-Means of traffic flow control” was performed. For each functional element the variants of realization of its morphological attributes and ranges of their values are given. However, the methods of calculating the values of individual parameters are not described in detail and the criteria for assessing the energy efficiency of vehicles moving on the urban road network are not defined. The authors of [34] provide regression equations describing the dependence of energy consumption of vehicles on their speed. When choosing the parameters values of these equations, the category, energy unit type and operation mode of the vehicle are considered significant. For hybrid and electric vehicles, these mathematical dependencies are not defined. The parameters of the road and the flow of traffic, in which the vehicle is moving, are not considered. In the article [35], in assessment of the vehicle’s energy efficiency, the following functional elements of the transport system are considered: the driver, the vehicle, the environment. The functional element “Driver” is characterized by the following functional characteristics: aggressiveness of driving, psychological and behavioral traits. The parameters of the element “Vehicle” are determined by the type of engine and type of gearbox (for vehicles with internal combustion engine), battery efficiency and regenerative braking (for hybrid and electric vehicles), vehicle body type, geometric parameters, weight and age of the vehicle, tire pressure. Environmental factors include traffic (e.g., heaviness, time of day, day of the year, exceptional situations), type of roads (small public or private roads with city’s traffic, city’s highways and highways), weather conditions. The total energy consumption of a vehicle is defined as the sum of the energy consumption of the vehicle and the standby energy consumption. In [36] the comparative analysis of dependencies of energy efficiency of vehicles on their technical parameters for vehicles with internal combustion engines and with electric energy units is carried out. It is determined that for vehicles with an internal combustion engine, fuel consumption depends significantly on the rated engine power. In electric vehicles, increasing the battery capacity by 10 kWh increases energy consumption by 0.7–1.0 kWh/100 km. Modern mass-produced electric passenger vehicles are 2.1 ± 0.8 kWh/100 km more efficient than first-generation cars. Vehicles with gas-balloon energy units are not considered. The authors [37] study the energy consumption of vehicles with a hybrid engine. The value of the total energy consumption depends on the energy consumption of the internal combustion engine (1.25–2.95 (J/(kg·m)) and the electric drive (0.27–1.1 (J/(kg·m)). The power consumption of an internal combustion engine is 3.4 times higher than the power consumption of an electric drive. Ref. [38] proposes a methodology for estimating the energy consumption of vehicles for different traffic models, what takes into account the parameters that characterize the vehicle, the environment and the driver’s behavior when moving along a given route. It was found that among the considered parameters the greatest influence on energy consumption has the speed and acceleration of the vehicle. Regeneration of energy from braking gave significant energy savings and weakened the correlation between most of the source and the resulting parameters. The authors [39] consider that movement energy consumption is largely determined by driving behavior, terrain information and the situation on the road, which is difficult to predict. The paper develops a model for estimating the energy consumption of electric vehicles. The number of passengers, weather conditions, road category, parameters that characterize the traffic flow, driver and route were determined as the significant parameters. Two algorithms for estimating energy consumption are presented: under the condition of maximum speed and to achieve maximum efficiency.

Despite the large number of scientific studies on the energy efficiency of vehicles, the development of a mathematical apparatus for comprehensive assessment and forecasting of energy consumption of a wider range of vehicles, considering the characteristics of all functional elements of the transport system remains relevant.

The object of research is the system “Vehicle—Traffic flow—Road—Traffic Environment” (the TrEECS system).

The purpose of the article is to determine the character of influence exerted independent parameters of the TrEECS system on the energy efficiency of vehicles.

To achieve this goal the following tasks were solved:

• to identify significant morphological attributes of the TrEECS system;
• to investigate the state of functional elements of TrEECS in the traffic process on linear sections of street and urban road networks and to form an array of initial data;
• on the basis of statistical estimates to determine the basic parameters corresponding to the morphological attributes of the TrEECS system;
• build the analytical dependence of energy efficiency on system parameters and evaluate its accuracy.
• In order to achieve the assumed goals, the article includes the following sections:
• Section 1 introduces the subject of the article and provides an overview of the literature;
• Section 2 presents a description of the used methodology and includes a description of the model;
• Section 3 presents the input data and an example of the model application for the analysis of energy efficiency on a linear road section. In this section, the Farrar-Glober method was used to evaluate the significance of the model parameters;
• Section 4 summarizes the work and contains conclusions concerning further research directions.

2. Materials and Methods

The movement of traffic flows on the urban road network forms a complex system (hereinafter the TrEECS system), the internal processes of which occur according to certain laws, the mathematical representation of which is necessary to assess both individual processes and the efficiency of the system. This system is represented by four functional elements: “Vehicle” (V), “Traffic flow” (TF), “Road” (R) and “Traffic environment” (Env). Morphological analysis of the TrEECS system [33] allowed to determine 18 morphological attributes of its functional elements that are significant in terms of assessing the energy efficiency of a vehicle in urban traffic, namely: X₁—vehicle category, X₂—vehicle energy unit type, X₃—vehicle age, X₄—degree of use of load capacity and/or passenger capacity of the vehicle, X₅—vehicle motion mode, X₆—vehicle autonomy level, X₇—traffic intensity, X₈—traffic density, X₉—traffic flow complexity level, X₁₀—traffic flow phase, X₁₁—number of lanes on the road in both directions, X₁₂—road resistance degree, X₁₃—carriageway curvature degree, X₁₄—group of localities determined by the city population, X₁₅—population density, X₁₆—level of motorization, X₁₇—time interval, X₁₈—complexity of weather conditions. The results of morphological analysis of the TrEECS system presented in the form of a morphological matrix of the system (

Table 1. Results of the analysis of the functional elements “Vehicle” and “Traffic flow”.

Vehicle						Traffic Flow
1. Category	2. Energy Unit Type	3. Vehicle age	4. The Degree of Use of Load Capacity and/or Passenger Capacity	5. Movement Mode	6. Autonomy Level	7. Traffic Intensity, Reduced Units/Hour	8. Traffic Density, Reduced Units/km	9. Traffic Flow Complexity Level	10. Traffic Flow Phase
1.1. M1 1	2.1. Petrol 1	3.1. Up to 5 years 1	4.1. Low 0–0.4	5.1. Acceleration dV/dt > 0 1	6.1. Null 1	7.1. Very small 0–200	8.1. Small 0–12	9.1. Very low 0–0.25	10.1. Free 1
1.2. M2 2	2.2. Diesel 2	3.2. 5–10 years 2	4.2. Medium 0.41–0.5		6.2. First 2	7.2. Small 200–400	8.2. Medium 12–36	9.2. Low 0.25–0.5	10.2. Stable 2
1.3. M3 3	2.3. Gas 3	3.3. 10–15 years 3	4.3. High 0.051–0.7	5.2. Movement at a constant speed V = const 2	6.3. Second 3	7.3. Medium 400–600	8.3. Large 36–60	9.3. Medium 0.5–0.75	10.3. Unstable 3
1.4. N1 4		3.4. 15–20 years 4				7.4. Large 600–800
1.5. N2 5	2.4. Hybrid and electric 4	3.5. More than 20 years 5	4.4. Very high 0.71–1	5.3. Idle mode V = 0 3	6.4. Third 4	7.5. Very large >800	8.4. The largest >60	9.4. High 0.75–1	10.4. Intense 4
1.6. N3 6

and

Table 2. Results of the analysis of the functional elements “Road” and “Traffic environment”.

Road			Traffic Environment
11. Number of Lanes on the Road in Both Directions	12. Road Resistance Degree, f + i	13. Carriageway Curvature Degree	14. Group of Localities Determined by the City Population, Thousand People	15. Population Density, People/km2	16. Level of Motorization, Cars/1000 Inhabitants	17. Time Interval	18. Complexity of Weather Conditions
11.1 2	12.1. Low 0.007–0.05	13.1. Low 2maxR/3-maxR 1	14.1. Small <50 1	15.1. Low <500 1	16.1. Low <200 1	17.1. Night hours 1	18.1. Low 0–0.2
11.2 3			14.2. Medium 50–250 2	15.2. Medium 500–1000 2		17.2. Hours of decreasing traffic intensity 2	18.2. Medium 0.21–0.4
11.3 4	12.2. Medium 0.05–0.1	13.2. Medium maxR/3-2maxR/3 2	14.3. Large 250–500 3	15.3. High 1000–4000 3	16.2. Medium 200–300 2	17.3. Hours of steady intensity during the day 3	18.3. High 0.41–0.7
11.4 6			14.4. Significant 500–1000 4
11.5 8	12.3. High 0.1–0.15	13.3. High 0-maxR/3 3		15.4. Very high >4000 4	16.3. High >300 3	17.4. Hours of increasing traffic intensity 4	18.4. Very high 0.71–1
			14.5. Most important >1000 5			17.5. Rush hours 5

).

The choice of morphological features is based on the results of a survey conducted within the studied transport networks with the involvement of experts—employees in the field of organization and provision of road safety, including specialists of the civil service “Ukrtransbezpeka”. For the functional elements, the features that, according to experts, have an impact on the energy efficiency of vehicles, and the value of which can be determined based on current statistical information within the information space, are selected. When choosing features that are quantitative in nature, the possibility of studying their structure and obtaining calculation algorithms is considered. The characteristics of the element “Traffic environment” are unmanageable within transport systems but must be taken into account in the process of finding strategies to improve the vehicle energy efficiency.

Each morphological attribute is characterized by 3 to 6 implementation variants. A numeric value or range of values is defined for each implementation (Table 1 and Table 2). The combination of specific values of all implementation variants forms a certain structure of the system, which determines the degree of energy consumption of the vehicle under given conditions. To choose the rational structure of the system it is necessary to comprehensively assess the impact of morphological attributes of its functional elements on the energy consumption of vehicles based on developed mathematical models.

Morphological attributes of the TrEECS system are estimated by quantitative or qualitative parameters of the corresponding model. The parameters x₄, x₇–x₉, x₁₁–x₁₂, x₁₈ are quantitative. The degree of use of the load capacity and/or passenger capacity of the vehicle x₄ is the ratio of the actual weight of cargo and passengers carried to the nominal load capacity of the vehicle. By analogy with the distribution of the values of the coefficient of utilization of load capacity by load classes for trucks in this study, we take the following ranges of values x₄:

• low—from 0 to 0.4;
• middle—from 0.41 to 0.5;
• high—from 0.51 to 0.7;
• very high—from 0.71 to 1.

Parameters x₇ and x₈ are standard traffic flow meters. The traffic flow complexity level x₉ is defined as the share of freight and public vehicles in the flow. Parameter x₁₂—road resistance degree ψ = f + i, where f is the coefficient of rolling resistance; i—the slope of the road.

The complexity of weather conditions x₁₈ is an integral indicator, calculated as the sum of the evaluations of the four components:

• strong wind—from 0 to 0.2;
• ice—from 0 to 0.3;
• atmospheric precipitation—from 0 to 0.2;
• fog—from 0 to 0.3.

Qualitative parameters x₁–x₃, x₅–x₆, x₁₀, x₁₃–x₁₇ are described in detail in the paper [33].

The ranges of values of the parameters x₁–x₃ and x₅ correspond to the ranges of values of the corresponding morphological features, which are exhaustively presented in Table 1.

The area of definition of the parameter x₆ is a set containing four options for implementing the levels of autonomy of the car:

• zero level—lack of automation of operational tasks;
• the first level—automation of only certain functions, but acceleration, braking and monitoring of the situation around the car is not automated;
• second level—partial automation of control functions;
• third level—an autonomous system can monitor the situation on the road with the help of leaders, under safe conditions to perform braking functions.

Four phases of the transport flow x₁₀ are selected in accordance with the values of the congestion coefficient K: free flow, stable, unstable and tense. The congestion coefficient is determined by expression (1) [40]:

$$\mathrm{K}=\frac{H_x-H_{opt}}{H_{max}-H_{opt}}$$

(1)

where $H_x$, $H_{opt}$, $H_{max}$—the density of the transport flow to its stop at point x and the optimal and maximum density of the transport flow, vehicle/km. $H_{opt}$ is achieved provided that the maximum intensity is reached at the optimal speed of the traffic flow.

Carriageway curvature degree x₁₃ has the following implementations:

• low—from 2maxR/3 to maxR (maxR is maximum radius of the road on fragments of the studied system);
• medium—from maxR/3 to 2maxR/3;
• high—from 0 to maxR/3.

The larger the turning radius of the road, the lower the level of curvature of the carriageway x₁₃.

The ranges of values of the variants of the implementation of the features corresponding to the parameters x₁₄–x₁₆ are given in the corresponding cells of Table 2.

The same implementations of the parameter x₁₇ may have different ranges of values depending on the settlement. In the process of further modeling, the reduced value of this qualitative parameter to the number of the variant of realization of the corresponding feature is used.

When reduced to quantitative values, these parameters are equated to the number of the implementation variant of the corresponding morphological attribute. Quantitative values (ranges of values) of system parameters are given in the corresponding cells Table 1 and Table 2.

The resulting parameter of the system is the level of energy efficiency of vehicle LEE in the process of traffic on the road network of the city, which is calculated as follows:

$$\mathrm{LEE}=\frac{E_{\mathrm{reason}}}{E_{\mathrm{fact}}}$$

(2)

where $E_{\mathrm{reason}}$—energy needed for a movement at a given mode of movement of the vehicle on a horizontal road in moderate weather conditions, MJ;

$E_{\mathrm{fact}}$—energy in fact consumed by the engine, MJ.

For example, for cars and buses with internal combustion engines at steady motion and in acceleration mode, the energy in fact consumed by the engine, E_fact, is equal to the quantity of heat released by fuel combustion, and is calculated by the Formula (3):

$$E_{\mathrm{fact}}=\mathrm{LHV}\cdot m=\mathrm{LHV}\cdot 0.001\cdot H_S\cdot S\cdot \left(1+0.01\cdot K_e\right)$$

(3)

where $\mathrm{LHV}$—lower heating value of combustion of fuel, MJ/kg;

$m$—fuel consumption for cars and buses, kg;

$H_S$—the basic rate of fuel consumption, g/km, the regression equation for the calculation of which and the values of the corresponding regression coefficients are given in [22];

$S$—distance travelled by the car, km;

$K_e$—total adjustment coefficient, %.

$$K_e={\displaystyle \sum }_{i=1}^n{K}_i-{\displaystyle \sum }_{j=n+1}^{n+m}{K}_j$$

(4)

where $K_i$, $K_j$—the i-th increasing and j-th lowering coefficients to fuel consumption rates [41], respectively, %;

n, m—the number of increasing and decreasing coefficients accordingly.

Correction coefficients that are significant in accordance with the purpose of the study are systematized and presented in

Table 3. List of significant adjustment coefficients to fuel consumption rates.

Marking	Title	Maximum Value, %	Condition of Application
$K_1$	increase depending on the ambient temperature	2	$T\in \left[-5,0\right]$
		4	$T\in \left[-10,-5\right)$
		6	$T\in \left[-15,-10\right)$
		8	$T\in \left[-20,-15\right)$
		10	$T\in \left[-25,-20\right)$
		12	$T<-25$
$K_2$	increase depending on movement up the slope or alternating climbing/descent	5	$i\in \left[0.04, 0.08\right)$
		10	$i\ge 0.08$
$K_3$	increase depending on a movement of vehicles on roads with a complex plan	10	the average presence of more than 5 curves with a radius of less than 40 m per 1 km of road
$K_4$	increase within the city	5	$\mathrm{at}k<250$ in the presence of adjustable controlled intersections
		10	$k\in \left[250, 500\right)$
		15	$k\ge 500$
$K_5$	increase in heavy road conditions of cities	10	at frequent traffic stops (in particular, in the central parts of cities)
$K_6$	increase in satisfactory road conditions of cities	10	$\mathrm{when}\mathrm{driving}\mathrm{in}\mathrm{traffic}\mathrm{jams},\mathrm{including}\mathrm{during}\mathrm{peak}\mathrm{hours},V<20$ km/h.
$K_7$	increase for new cars	10	in the case of the first thousand kilometers
$K_8$	increase depending on the age and mileage of the vehicle	3	$\mathrm{age}\in \left(5, 8\right]$$,L\in$(100, 150]
		5	$\mathrm{age}\in \left(8, 11\right]$$,L\in$(150, 250]
		7	$\mathrm{age}\in \left(11,14\right]$$,L\in$(250, 400]
		9	$\mathrm{age}>14$$,L>400$
$K_9$	increase for cooling the interior of the vehicle	5	$T\in \left[+20,+25\right]$
		7	$T\in \left(+25,+30\right]$
		10	$T \text{>}+30$
$K_{10}$	increase depending on increased aerodynamic resistance	5	for vans, trucks during the transportation of bulky goods
$K_{11}$	reduction for city buses not on regular routes	5–10	including in the mode “on demand”

. The parameter $H_S$ takes into account the category, type of energy unit, the mode of movement and speed of the vehicle. If the necessary information is available, this parameter can be replaced by a basic linear fuel consumption.

For the above vehicles when running at idle energy consumed by the engine E_fact is determined by expression (5):

$$E_{\mathrm{fact}}=\mathrm{LHV}\cdot m=\mathrm{LHV}\cdot 0.001\cdot H_i\cdot t\cdot \left(1+0.01\cdot K_e\right)$$

(5)

where $H_i$—the basic rate of fuel consumption at idle running, g/s; tabular values are presented in [34];

$t$—time interval, seconds.

In the Table 3 the following notation is adopted: T—ambient air temperature, °C; i—the slope of the road; k—population, thousand people; V—vehicle speed, km/h; age—vehicle age, years; L—mileage of the vehicle, thousand km, ∈—“is element of”.

3. Results

Energy efficiency assessment was implemented on the example of vehicles of categories M1–M3, N1–N3 with energy units of different types (petrol, diesel, gas, hybrid and electric) with the air conditioning turned off, constant speed and idling. Measurements of TrEECS system parameters were performed for road networks of cities: Boryspil, Zolotonosha, Kaniv, Kyiv, Lviv, Odesa, Smila, Cherkasy (Ukraine) and Rzeszow (Poland).

Numerical values of road parameters x₁₁, x₁₂ and x₁₃ are obtained using the Internet service Google Earth Pro version 7.3.

The results of measuring parameters of linear fragments of road networks considering Table 1 and Table 2 are given in

Table 4. Observation results for the functional elements “Vehicle” and “Traffic flow”.

Observation Number	Vehicle						Traffic Flow
	Category	Energy Unit Type	Vehicle Age	The Degree of Use of Load Capacity and/or Passenger Capacity	The Movement Mode	The Autonomy Level	Traffic Intensity, Reduced Units/Hour	Traffic Density, Reduced Units/km	The Traffic Flow Complexity Level	The Traffic Flow Phase
	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10
1	1	1	3	0.75	1	4	655	22	0.03	2
2	1	3	5	0.49	1	1	655	20	0.03	2
3	5	2	2	0.64	2	1	770	31	0.24	3
4	3	2	4	0.72	2	1	770	33	0.24	3
5	1	1	4	0.57	1	1	710	42	0.52	4
6	3	4	2	0.8	3	3	864	216	0.04	4
7	1	3	5	0.3	2	1	828	207	0.06	4
8	1	1	1	0.36	2	4	577	46.27	0.35	3
9	1	1	3	0.13	1	2	10	2	0	1
10	2	2	3	0.77	3	1	550	11	0.06	1
11	6	2	3	0.71	2	2	710	27	0.22	4
12	4	2	4	0.69	3	1	376	125	0.31	4
13	4	2	2	0.86	2	1	534	13	0.25	2
14	3	2	5	0.5	1	1	279	5.58	0.17	2
15	5	2	4	0.91	2	1	592	22	0.33	2
16	1	3	5	0.2	1	1	417	18	0.21	2
17	1	2	5	0.15	2	1	535	12	0.49	2
18	1	1	3	0.42	2	2	133	5	0.21	1
19	4	3	5	0.37	1	1	26	1	0.038	1
20	4	2	4	0.73	2	1	875	25	0.58	3
21	3	2	3	0.82	2	2	775	31	0.76	4
22	1	1	3	0.27	1	3	956	90	0.01	4
23	1	1	1	0.31	2	4	1130	113	0.015	4
24	4	2	2	0.65	1	1	120	16	0.19	1
25	2	2	2	0.53	1	1	400	40	0.05	2

and

Table 5. Observation results for the functional elements “Road” and “Traffic environment”.

Observation Number	Road			Traffic environment
	Number of Lanes in Both Directions	Road Resistance Degree, f + i	Carriageway Curvature Degree	Group of Localities, Thousand People	Population Density, People/km2	Level of Motorization, Cars/1000 Inhabitants	Time Interval	Complexity of Weather Conditions
	x11	x12	x13	x14	x15	x16	x17	x18
1	2	0.09	2	3	4	2	2	0.4
2	2	0.068	2	3	4	2	2	0.2
3	4	0.023	1	3	4	2	3	0
4	4	0.023	1	3	4	2	3	0
5	4	0.023	1	3	4	2	4	0.5
6	8	0.015	1	5	3	3	5	0.2
7	8	0.017	1	5	3	3	4	0.2
8	4	0.065	1	4	4	1	3	0.1
9	4	0.02	2	3	4	2	1	0.7
10	4	0.02	2	3	4	2	3	0.2
11	4	0.023	1	3	4	2	4	0.5
12	4	0.018	1	2	3	1	5	0
13	4	0.03	1	1	3	1	5	0.4
14	4	0.03	1	1	3	1	2	0.4
15	2	0.077	1	2	3	1	3	0.2
16	2	0.077	1	2	3	1	2	0.2
17	2	0.049	1	3	4	2	5	0
18	2	0.049	1	3	4	2	2	0
19	2	0.049	1	3	4	2	1	0.1
20	6	0.025	1	3	4	2	3	0.2
21	6	0.025	1	3	4	2	4	0.1
22	2	0.029	3	3	4	2	3	0
23	2	0.037	1	5	4	3	5	0.2
24	2	0.13	3	1	3	2	3	0.7
25	2	0.08	3	1	3	2	4	0.3

.

The development of regression models of the system requires the independence of all input parameters. Estimation of the degree and elimination of multicollinearity in the array of data was performed by the Farrar-Glober method [42,43]. This algorithm is based on the consistent application of Pearson criterion χ²—to test for multicollinearity in the array, Fisher’s F—criterion to evaluate each TrEECS parameter by the degree of multicollinearity to others and Student’s t—criterion to assess the dependence of each variant for its implementation to others. At each stage of the algorithm, the input parameters, which are more correlated with others, are removed from further consideration. Generalized block diagram of algorithm for eliminating multicollinearity of input parameters of the TrEECS model based on the Farrar-Glober method is shown in Figure 1.

In block 1, a two-dimensional array of initial data $\mathrm{X}=\left\{x_{ij}\right\}$ is formed, $x_{ij}$ is the initial value of the j-th parameter of the i-th observation.

In block 2, a matrix X^N of normalized and centered values of input parameters is formed. The elements of the matrix X^N are calculated by the formula:

$$x_{ij}^N=\frac{x_{ij}-{\acute{x}}_j}{{\delta }_j},1\le i\le 25, 1\le j\le n,$$

(6)

where: $x_{ij}^N$ is the normalized value of the j-th parameter of the i-th observation, ${\acute{x}}_j$ is the average value of the j-th parameter, ${\delta }_j$ is the j-th parameter variance, n is the number of input parameters in this iteration.

In block 3, a sampling correlation matrix is formed:

$$\widehat{R}=\frac{1}{m}{\left(X^N\right)}^T{X}^N,$$

(7)

where: m is the number of observations, m = 25.

In blocks 4, 7, 9, relevant statistical criteria are calculated.

In blocks condition check units 5, 10 and in block of call subprogram 13 Pearson criterion χ², Fisher’s F—criterion $F_j$, Student’s t–criterion $t_{ij}$ ($1\le i\le 25,1\le j\le n$) are compared with their tabular values ${\chi }_{tabl}^2$, $F_{tabl}$ and $t_{tabl}$, respectively. The significance level α = 0.05.

At each iteration of the algorithm, the dependent parameters of the system are deleted from the data array in accordance with the procedure of block 13. The algorithm terminates if condition 5 is not met.

In total, 4 iterations of the algorithm were performed. Intermediate results obtained at each iteration are given in

Table 6. The results of the step-by-step execution of the Farrar-Glober method.

Iteration No	Number of Parameters, n	Value of the Pearson Criterion, χ2		Presence of Multicollinearity in the Data Array	Parameters Deleted
		Calculated	Tabular
I	18	326.707	182.865	yes	x8, x14, x15
II	15	175.505	129.918	yes	x5, x11
III	13	120.091	99.617	yes	x6, x7, x10
IV	10	56.774	61.656	no	–

.

Based on the results of the evaluation of the states of the TrEECS system (Table 6), for its further modeling an input data array containing the values of the 10 remaining independent parameters is formed. Then the influence of the characteristics of the functional elements on the level of energy efficiency of the vehicle in general can be written by the following mathematical dependence:

$$\mathrm{LEE}=f\left(x_1,x_2,x_3,x_4,x_9,x_{12},x_{13},x_{16},x_{17},x_{18}\right)$$

(8)

where: x₁–x₄—basic parameters that correspond to the attributes of the functional element “Vehicle”, x₉—basic parameter of the functional element “Transport flow”, x₁₂–x₁₃—basic parameters that specify the state of the functional element “Road”, x₁₆–x₁₈—basic parameters that characterize the functional element “Traffic environment”:

• x₁—vehicle category;
• x₂—vehicle energy unit type;
• x₃—vehicle age;
• x₄—the degree of use of load capacity and/or passenger capacity;
• x₉—the traffic flow complexity level;
• x₁₂—road resistance degree;
• x₁₃—the carriageway curvature degree;
• x₁₆—level of motorization;
• x₁₇—time interval;
• x₁₈—complexity of weather conditions.

Thus, within this study, all functional elements of the TrEECS system are essential.

Table 7. Values of basic and resulting parameters of the TrEECS system.

Observation Number	x1	x2	x3	x4	x9	x12	x13	x16	x17	x18	LEE	Sampling Variance, Di
1	1	1	3	0.75	0.03	0.09	2	2	2	0.4	0.669	0.59478
2	1	3	5	0.49	0.03	0.068	2	2	2	0.2	0.746	0.90731
3	5	2	2	0.64	0.24	0.023	1	2	3	0	0.712	0.91001
4	3	2	4	0.72	0.24	0.023	1	2	3	0	0.784	0.11239
5	1	1	4	0.57	0.52	0.023	1	2	4	0.5	0.592	0.51240
6	3	4	2	0.8	0.04	0.015	1	3	5	0.2	0.676	1.19375
7	1	3	5	0.3	0.06	0.017	1	3	4	0.2	0.641	0.92145
8	1	1	1	0.36	0.35	0.065	1	1	3	0.1	0.813	1.07520
9	1	1	3	0.13	0	0.02	2	2	1	0.7	0.658	1.01842
10	2	2	3	0.77	0.06	0.02	2	2	3	0.2	0.803	0.09806
11	6	2	3	0.71	0.22	0.023	1	2	4	0.5	0.525	1.45173
12	4	2	4	0.69	0.31	0.018	1	1	5	0	0.707	0.75227
13	4	2	2	0.86	0.25	0.03	1	1	5	0.4	0.719	0.89939
14	3	2	5	0.5	0.17	0.03	1	1	2	0.4	0.806	0.61767
15	5	2	4	0.91	0.33	0.077	1	1	3	0.2	0.719	0.86156
16	1	3	5	0.2	0.21	0.077	1	1	2	0.2	0.840	0.97870
17	1	2	5	0.15	0.49	0.049	1	2	5	0	0.746	0.96579
18	1	1	3	0.42	0.21	0.049	1	2	2	0	0.787	0.56846
19	4	3	5	0.37	0.038	0.049	1	2	1	0.1	0.775	1.26295
20	4	2	4	0.73	0.58	0.025	1	2	3	0.2	0.760	0.33934
21	3	2	3	0.82	0.76	0.025	1	2	4	0.1	0.787	0.16389
22	1	1	3	0.27	0.01	0.029	3	2	3	0	0.730	0.68212
23	1	1	1	0.31	0.015	0.037	1	3	5	0.2	0.667	1.46929
24	4	2	2	0.65	0.19	0.13	3	2	3	0.7	0.548	0.75604
25	2	2	2	0.53	0.05	0.08	3	2	4	0.3	0.671	0.57780
${\acute{x}}_j$	2.52	1.96	3.32	0.546	0.2161	0.0437	1.4	1.88	3.24	0.232

shows the input and output data arrays used for further modeling of the dependence of the energy efficiency of the vehicle on the TrEECS parameters. The elements of the source array were obtained using (2) based on observations of the state of the system under different initial conditions.

To build an adequate mathematical model, the input data set is divided into training and control samples. For this purpose, an algorithm based on the calculation of the values of the sampling variance Di [43] was used, calculated by the formulas:

$$D_i=\frac{1}{n-1}{\displaystyle \sum }_{j=1}^n{\left(x_{ij}-{\acute{x}}_j\right)}^2=\frac{1}{9}{\displaystyle \sum }_{j=1}^{10}{\left(x_{ij}-{\acute{x}}_j\right)}^2, i=\overline{1,25},$$

(9)

$${\acute{x}}_j=\frac{1}{25}{\displaystyle \sum }_{i=1}^{25}{x}_{ij},j=\overline{1,10},$$

(10)

where: n—number of independent system parameters.

The obtained values of the sampling variance for each observation and the average values of the basic parameters are presented in the Table 7.

The control sample included five arrays (20% of the initial sample), which have the lowest values of the sampling variance and correspond to the following numbers of observations: 4, 5, 10, 20, 21.

A mathematical model in the form of multiple linear regression is built on the educational sample. The coefficients of the regression equation a_j are determined by the Formula (11) [43]:

$${\left(a_0, a_1,a_2,a_3, a_4,a_9,a_{12}, a_{13},a_{16},a_{17}, a_{18}\right)}^T={\left(X^T\times X\right)}^{-1}\times X^T\times {\left(\overline{LEE}\right)}^T,$$

(11)

where: X—the matrix of dimension 20 × 11, the columns of which contain the values of the basic parameters at different states of the system (column $x_0$ contains units), ($\acute{LEE}$)—vector of statistical values of the resulting parameter.

Thus, the following analytical dependence is obtained, which reflects the influence of TrEECS parameters on the level of the vehicle energy efficiency:

$$\begin{array}{c}LEE=1.06414-0.02128·x_1+0.02675·x_2-0.01139·x_3-\\ -0.02787·x_4-0.07902·x_9-0.0187·x_{12}-0.02774·x_{13}-\\ -0.082·x_{16}-0.01742·x_{17}-0.18435·x_{18}.\end{array}$$

(12)

Mathematical modeling is an alternative to field experiment. The advantages of the model approach are determined by economic considerations. Experimental determination of the energy in fact consumed by the engine of vehicles, and accordingly the level of energy efficiency according to Formula (2), in some cases causes difficulties. Determining the input parameters of the model (12) is less complicated, and the calculation of the resulting parameter using the application software does not require much time. Therefore, model (12) is more productive than calculating the level of energy efficiency according to Formula (2).

Figure 2 and Figure 3 present a graphical representation of the simulation results of the states of the studied TrEECS system.

The largest error in the calculation of the resulting parameter is observed in the study of the movement of buses and trucks of category N1 aged more than 10 years with a high and very high degree of use of passenger capacity/load capacity.

The accuracy of the obtained model was evaluated for five TrEECS states of the control sample. The standard deviation of the model values from the tabular ones equals $\acute{\sigma }=0.0091$. Relative standard deviation equals ${\acute{S}}_r=1.5\%$.

4. Discussion

Based on the performed morphological analysis of the TrEECS system, 18 significant morphological attributes of its main functional elements have been identified. The input parameters of the corresponding system model take values from a set of implementation variants of each attribute. Each set has 3–6 variants. The degree of energy efficiency of the vehicle at a certain state of the system is chosen as the resulting parameter. A survey of the state of the system on the linear fragments of the road network of nine typical cities of Ukraine and Poland was performed. The basis of the system includes parameters that correspond to the following morphological attributes of its functional elements: vehicle category, vehicle energy unit type, vehicle age, the degree of use of load capacity and/or passenger capacity, traffic flow complexity level, road resistance degree, the carriageway curvature degree, level of motorization, time interval, complexity of weather conditions. It can be argued that all four functional elements are essential for this study and the basic parameters determine the most important attributes of these functional elements. Usage of the obtained model is more productive in terms of time and level of complexity than the calculation of the level of energy efficiency according to the statistical values of the energy in fact consumed by the vehicle engine. This mathematical model shows high accuracy of the resulting parameter and allows to quantify the impact of each of the basic parameters on the level of energy efficiency of vehicles. The developed mathematical model makes requirements for constructive properties of vehicles, their operating conditions, road infrastructure and can be used in the process of developing design solutions for planning and modernization of roads and buildings, taking into account the efficiency of transport and its impact on the environment. In addition, the results of the study can be applied in mathematical models of intelligent traffic control systems for urban traffic flows. This study is an intermediate stage in the development of a generalized methodology for improving the vehicle energy efficiency in terms of urban mobility. The integrated energy efficiency indicator is determined based on partial indicators for individual fragments of the road network. At this stage, an analytical dependence has been developed to calculate the level of the vehicle energy efficiency when driving on linear sections of the network. In the future it is planned to conduct a similar study for other structural elements of the network. In addition, further research will be aimed at solving problems of identification of nonlinear models of the system and determining the degree of impact of each morphological attribute on the vehicle energy efficiency.