Analysis of Pollutant Emissions and Fuel Consumption in Chassis Dynamometer Testing of a Passenger Car Under United Nations Climate and Sustainability Frameworks

Abstract

This publication presents the results of studies on exhaust emissions and fuel consumption from spark-ignition engines in the NEDC test, which applies to the vast majority of passenger cars in use in the European Union. This emissions testing procedure was selected based on an analysis of the number of existing engines meeting specific emission standards. A statistical analysis of the studied processes was conducted. Additionally, the product of speed and acceleration modulus was examined as quantities characterizing the dynamic characteristics of the vehicle speed process during testing. Correlation studies of vehicle speed and exhaust emission rates, particle number rates, and mass fuel consumption rates were presented. Average distance-specific emissions, average distance-specific particulate number, and average distance-specific fuel consumption were determined in the NEDC test. The probability density distributions of the investigated processes in the NEDC test were analyzed. Based on an assessment of the conformity of the studied sets with the normal distribution using the Kolmogorov–Smirnov, Lilliefors, and Shapiro–Wilk hypotheses, it was concluded that there was no basis for accepting the hypotheses that the sets conform to the normal distribution. Moreover, the power spectral density of the investigated processes was evaluated. Significant variation in spectral characteristics, especially at high frequencies, was identified, revealing substantial dynamic differences between the processes. The average road emission values in the NEDC test were significantly lower than even the limits for Euro 7.

1. Introduction and Literature Review

Transport remains a significant source of greenhouse gas emissions and atmospheric pollutants, generating significant challenges for environmental protection efforts and human health [1,2]. In response to these challenges, the United Nations 2030 Agenda and its Sustainable Development Goals (SDGs) provide a comprehensive framework for mitigating the environmental impact of transport activities [3]. Specifically, DSG 13 (Climate Action) and DSG 7 (Affordable and Clean Energy) highlight the importance of emission reductions, improving energy efficiency, and the adoption of cleaner and more sustainable transportation technologies.

Passenger cars equipped with internal combustion engines, including spark-ignition engines, still constitute a significant portion of the vehicle fleet in Europe, despite the increasing electrification of transport. Therefore, detailed studies of exhaust emissions and fuel consumption under controlled and repeatable conditions are essential to assess their environmental impact and compliance with current and future emission regulations [4]. Chassis dynamometer tests, conducted in accordance with standardized driving tests such as the NEDC, enable precise analysis of emission intensity and fuel consumption patterns as a function of time and engine operating states.

From the perspective of achieving the SDGs, it is particularly important to reduce emissions of carbon dioxide, carbon monoxide, nitrogen oxides and hydrocarbons, which affect both climate change and air quality [5]. At the same time, reducing fuel consumption leads to improved energy efficiency, which is consistent with global efforts for rational energy management [6].

Building on previous research into exhaust emissions and fuel consumption in standardized driving tests, this study broadens the analysis to encompass issues related to global sustainability challenges. The findings can provide a basis for developing more effective emission reduction strategies and support the achievement of sustainable transport goals aligned with the United Nations.

Vehicle performance tests, particularly with respect to exhaust emissions, were conducted through research tests that characterize engine operating conditions and determine engine operating states, which are determined by the following parameters [7]:

• Engine rotational speed;
• Engine thermal state, determined by the temperature distribution within engine components and its operating conditions, and typically described by a representative thermal parameter, primarily the coolant or engine oil temperature;
• Engine load, typically expressed in terms of engine torque; it can also be measured by net power, fuel delivery and, in spark-ignition engines, intake system pressure.

It is also essential to evaluate the time-dependent nature of engine operating states, distinguishing between predominantly stable (static) conditions and those characterized by significant temporal fluctuation (dynamic states) [8,9]. Static engine operating states are typical for heavy-duty vehicle engines, such as buses and trucks. Therefore, such engines can be tested on an engine dynamometer in tangential states described by the speed-torque coordinates with appropriate weighting factors [10]. Such testing is considerably more practical, given the limited availability and high operational complexity of chassis dynamometers for heavy vehicles. This allows for the determination of specific exhaust emissions, which are quantities characterizing the emissions for all pollutants. There are also procedures for testing exhaust emissions on an engine dynamometer in dynamic tests defined by the speed and torque functions over time, e.g., FTP—Federal Test Procedure, as well as on a chassis dynamometer, e.g., HD-UDDS (EPA Urban Dynamometer Driving Schedule) [11]. Specific exhaust emission values are derived from the measured exhaust emissions, specifically by adjusting for the power output relative to the effective work performed by the engine. These values are traditionally expressed in units of grams per kilowatt-hour [g/(kW·h)]. There are also methods for testing heavy-duty vehicles in driving tests conducted on roads, primarily to measure fuel consumption. Examples of such tests include the UITP (Union Internationale des Transports Publics) tests: SORT 1, SORT 2, and SORT 3 (SORT—Standardized On-Road Test Cycles) [12] and the MZA (Warsaw City Bus Company) [13].

In light vehicles (passenger cars, light trucks, and L-category vehicles—motorcycles, mopeds, quad bikes, and microcars), exhaust emissions are measured in driving tests, where specific road emissions along with particulate matter numbers are determined. Light vehicle tests are performed in most cases, particularly in type-approval procedures, due to the accuracy and repeatability of conditions on a chassis dynamometer. An extension of these procedures is the RDE (Real Driving Emissions) procedure [14] using PEMS (Portable Emissions Measurement Systems) and Semtech equipment to confirm the consistency of test results in driving conditions and in the WLTC (Worldwide Harmonized Light Vehicle Test Cycle) test, performed on a chassis dynamometer in the WLTP (Worldwide Harmonized Light Vehicle Test Procedure) [15].

Apart from the procedures required for vehicle type approval, numerous other test methods are used, including those developed under the ARTEMIS (Assessment and Reliability of Transport Emission Models and Inventory Systems) program [16]: AMDC 130 (Artemis Motorway Driving Cycle 130), AMDC 150 (Artemis Motorway Driving Cycle 150), ARDC (Artemis Rural Driving Cycle), and AUDC (Artemis Urban Driving Cycle). Special tests have also been developed: Autobahn—a test for testing light vehicles on highways and expressways and Stop&Go—a test for testing light vehicles in congestion [17].

Tests based on empirical research—driving speed measurements in typical traffic conditions—have also been developed, e.g., the Malta test [18]. Paper [8] presents the results of empirical studies enabling the development of stochastic driving tests in the form of sets of representations of vehicle speed processes [19]. The traffic models for which the stochastic driving tests were developed are consistent with the standards used in road transport emission inventories [20]:

• Driving in cities with significant traffic disruptions: in traffic jams or during hours of significant traffic disruptions;
• Driving in cities with minor traffic disruptions: without traffic jams or during hours of minor traffic disruptions;
• Outside urban areas;
• On expressways: on motorways and highways.

The quantities characterizing exhaust emissions in driving tests are the specific distance emissions and the particulate matter number. Specific distance emissions are defined as the amount of pollutants emitted per unit distance traveled by the vehicle and may be interpreted as the derivative of cumulative emissions with respect to the distance. Similarly, distance-specific particle number emissions are defined as the particle number emitted per distance traveled. Traditionally, road emissions are expressed in grams per kilometer (g/km), or the particle number per kilometer—1/km.

There are two basic methods for creating driving tests:

• Synthesis of tests with assumed characteristics of the speed process and identification of parameters of this process, such as the average value, extreme values, extreme accelerations, etc., based on experience from empirical research results (e.g., NEDC test, Japanese 10–15 Mode);
• Faithful simulation in the time domain (Malta test); sometimes, recorded fragments are used, and then, by using the Monte Carlo method, for example [21], tests are created, e.g., FTP-75.

In September 2017, the WLTP (Worldwide Harmonized Light Vehicle Test Procedure) procedure was introduced in the European Union for the approval of light vehicles, with the new WLTC (Worldwide Harmonized Light Vehicle Test Cycle) test specified in Commission Regulation (EU) 2017/1151 [4]. Between September 2017 and September 2018, the provisions of either the NEDC or WLTC tests could be applied to the approval tests of light vehicles. From September 2018 onwards, all new light vehicles placed on the market in the European Union must be tested and approved in accordance with the WLTP procedure. An exception is end-of-series vehicles (sale of a limited number of unsold vehicles that were approved under the old NEDC test for one more year). However, despite the new WLTC test being in force since September 2017, a significant proportion of vehicles meeting Euro 6 requirements have already been introduced since September 2014, when the NEDC test was mandatory in the type approval procedure. Therefore, testing vehicles for exhaust emissions in the NEDC test is justified.

2. Methodology

The research method used in this paper involved empirical testing of a passenger car on a chassis dynamometer using the NEDC test, consisting of a quadruple repetition of the ECE 15—Economic Commission for Europe (or UDC—Urban Driving Cycle) test and the EUDC—Extra-Urban Driving Cycle test [4] (Figure 1). The NEDC test characteristics were presented in

Table 1. NEDC test characteristics.

Characteristic	Unit	UDC 1	EUDC	NEDC
Distance	km	0.994	6.955	10.931
Time	s	195	400	1180
Idle time (stationary)	s	57	39	267
Average speed (including stops)	km/h	18.35	62.59	33.35
Average speed (excluding stops)	km/h	25.93	69.36	43.1
Maximum speed	km/h	50	120	120
Average acceleration	m/s2	0.599	0.354	0.506
Maximum acceleration	m/s2	1.042	0.833	1.042

¹ Four UDC test repetitions followed by single EUDC test.

[10,11].

In the type approval procedure, the criteria for the NEDC test results are the average specific distance emissions of carbon monoxide (b_CO [mg/km]), hydrocarbons (b_HC [mg/km]), nitrogen oxides (b_NOx [mg/km]), particulate matter (b_PM [mg/km]) and the particulate number (b_PN [1/km]). The empirical test results performed in the NEDC test on a chassis dynamometer yielded the following values:

• Vehicle speed—v;
• Exhaust emission intensity of: carbon monoxide—E_CO, hydrocarbons—E_HC, nitrogen oxides—E_NOx and carbon dioxide—E_CO2;
• Particulate matter number intensity—E_PN;
• Fuel mass consumption intensity—q_f.

Exhaust emission intensity is the derivative of exhaust emission with respect to time, and particulate matter emission intensity is the derivative of particulate matter intensity with respect to time. The product of velocity and acceleration modulus—v·|a| was determined. This quantity characterizes the dynamic properties of the vehicle speed process.

The studies included:

• Statistical characteristics of the processes [22,23];
• Pearson’s linear correlation coefficients between the processes tested in the NEDC test; determining the average specific distance emissions, average specific distance particulate matter numbers, and average specific distance fuel consumption in the NEDC test;
• Determining the product of speed and acceleration modulus and the average value of the test;
• Standardization of the recorded drive tests [24], which is necessary when comparing the results of analyses of various physical quantities;
• Probability density of the processes in the NEDC test: vehicle speed, exhaust emission intensity, particulate matter number intensity, and fuel mass consumption intensity;
• Zero-padding of the analyzed test drives to the number of points 2^N, where N is a natural number, which enables the use of the Fast Fourier Transform (FFT) algorithm [25] to determine the power spectral density of the tested processes;
• Power spectral density of processes in the NEDC test: vehicle speed, exhaust emission intensity, particulate matter number intensity, and fuel mass consumption intensity;
• Formulation of research conclusions.

Pollutant-specific distance—b—is defined as the ratio of the pollution emission rate—E—and the vehicle speed—v (for a vehicle speed different from 0 km/h), taking into account the appropriate units of measurement:

$$\mathrm{b}={\displaystyle \frac{\mathrm{E}}{\mathrm{v}}}$$

Particulate number-specific distance—b_PN—is defined as the ratio of pollutant emissions intensity—PN—to vehicle speed—v (for vehicle speeds other than 0 km/h), taking into account the appropriate units of measurement:

$${\mathrm{b}}_{\mathrm{P}\mathrm{N}}={\displaystyle \frac{{\mathrm{E}}_{\mathrm{P}\mathrm{N}}}{\mathrm{v}}}$$

Statistical characteristics of the studied velocity processes are determined [8,23]:

• Average value—AV,
• Minimum value—Min,
• Maximum value—Max,
• Range—R,
• Standard deviation—D,
• First quartile—Q1,
• Median (second quartile)—M,
• Third quartile—Q3,
• Interquartile range—RQ,
• Interquartile deviation—DQ,
• Coefficient of variation—W,
• Interquartile coefficient of variation—WQ,
• Kurtosis—K,
• Skewness—S.

The publication defines the values:

• Coefficient of variation—W

  W = D/|AV|
• Quartile coefficient of variation

  WQ = DQ/|M|

The probability density of the processes was determined for standardized set values using the determined process histograms [8,24]. The power spectral density of the processes was determined using the fast Fourier transform [25]. Therefore, the set cardinality was padded with zeros up to a set cardinality of 2^N, where N is a natural number. The fast Fourier transform was performed for the standardized set values. The maximum frequency of the integral transform of the studied waveform is consistent with the Kotelnikov–Nyquist–Shannon theorem and results from the sampling interval of the time-domain waveform—in the case under consideration, this interval is 1 s. Estimates of the power spectral density were averaged using the simple moving average (SMA). Tests of the consistency of the distributions of the considered quantities with the normal distribution were performed for standardized quantities [8].

3. Research Results

An SUV test car with approximately 19,000 km mileage, serviced according to the manufacturer’s instructions, was used for the tests. The technical specifications of the tested passenger car are presented in

Table 2. Technical specifications of the tested vehicle.

Characteristic	Value
Engine	Gasoline, Turbo, R4, 16 V
Fuel system	Direct injection
Engine displacement	1984 cm3
Compression ratio	10.5
Max. power	195 kW at 5000 min−1
Max. torque	370 N·m/(1600–4200) min−1
Transmission	Automatic, 7 gears
Curb weight	1770 kg
Specific power output	9.1 kg/kW
Euro standard	Euro 6

.

The research was carried out at BOSMAL Automotive Research and Development Institute Ltd. The research laboratory meets the requirements of the PN-EN ISO/IEC 17025:2018-02 standard [26] and has an accreditation certificate issued by the Polish Centre for Accreditation (PCA) and foreign recommendations:

• Customers’ recommendations and accreditations,
• Fiat Chrysler Automobiles, conducting tests as part of qualifying the quality of parts and assemblies intended for assembly at FCA Poland SA,
• ITDC—Central Laboratories, Opel Rüsselsheim, testing parts and assemblies as part of the evaluation of OPEL suppliers,
• Laboratory approval from VW Group (VW 52000 [27] and VW 50180 Standard [28]),
• Laboratory approval from BMW,
• Laboratory approval from VOLVO (interior emission tests),
• FOEN Accreditation and List of Accredited Laboratories.

The empirical study was performed using a chassis dynamometer that complied with the requirements of the type approval procedures. The laboratory was air-conditioned to maintain a target temperature of ±2.0 °C and a target relative humidity of ±5% during testing. The tests were performed at 23 °C. Figure 2 presents the functional diagram and equipment of the BOSMAL laboratory.

The measuring equipment includes all necessary exhaust gas analyzers used during legislative emissions testing, as well as analyzers for continuous measurement of diluted exhaust gas component concentrations and for continuous measurement of raw exhaust gas component concentrations (

Table 3. Exhaust gas analyzers used in the Emissions Laboratory.

Measured Concentrations	Measurement from Bags		Continuous Measurement		Measurement Accuracy
Range	Least	Biggest	Least	Biggest
CO low (NDIR)	(0 ÷ 10) ppm	(0 ÷ 500) ppm	(0 ÷ 50) ppm	(0 ÷ 2500) ppm	±2% at the measuring point ±5% on a scale
CO high (NDIR)			(0 ÷ 0.5)%	(0 ÷ 12)%
CO2 (NDIR)	(0 ÷ 0.5)%	(0 ÷ 20)%	(0 ÷ 0.5)%	(0 ÷ 20)%
NOx low (CLD)	(0 ÷ 1) ppm	(0 ÷ 50) ppm	(0 ÷ 10) ppm	(0 ÷ 500) ppm
NOx high (CLD)	(0 ÷ 100) ppm	(0 ÷ 1000) ppm	(0 ÷ 1000) ppm	(0 ÷ 10,000) ppm
THC low (FID)	(0 ÷ 1) ppm	(0 ÷ 50) ppm	(0 ÷ 10) ppm	(0 ÷ 500) ppm
THC high (FID)			(0 ÷ 1000) ppm	(0 ÷ 50,000) ppm
CH4 (NMHC)	(0 ÷1) ppm	(0 ÷ 500) ppm
PN	(0 ÷ 10,000) 1/cm3				± 10%

). The measuring equipment is also equipped with a particulate matter counter.

The measured values were recorded every 1 s. The recorded test results were filtered with a low-pass filter to reduce the contribution of high-frequency noise to the signal. A Savitzky–Golay filter with a 5-point averaging and second-order polynomial approximation parameters was used for filtering [29].

Figure 3 shows the vehicle speed during the NEDC test, recorded on the chassis dynamometer.

It is clearly visible that the recorded vehicle speed closely matches the reference (Figure 1). Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 present the exhaust emission intensity of: carbon monoxide—E_CO, hydrocarbons—E_HC, nitrogen oxides—E_NOx, carbon dioxide—E_CO2, particulate number intensity—E_PN and fuel mass consumption intensity—q_f.

Carbon monoxide emission intensity is characterized by significant variability and the occurrence of emission peaks, particularly during dynamic engine operation (Figure 4). In spark-ignition engines, carbon monoxide emissions result primarily from incomplete combustion of the mixture during momentary disruptions in the value of the air–fuel ratio. In compression-ignition engines, carbon monoxide emissions are typically lower because such engines operate with excess air. However, similarly, increased emissions of this compound are observed during transient states associated with delays in mixture formation and local oxygen deficiencies. Substantial differences in carbon monoxide emission intensity were observed depending on engine operating conditions, particularly rotational engine speed and load, and above all the occurrence of dynamic states.

Hydrocarbon emission intensity follows a similar pattern to carbon monoxide emissions, with significant increases during transition phases (Figure 5). In diesel engines, hydrocarbon emissions are typically lower than in SI engines, but they are caused by local areas of incomplete combustion, particularly in low-temperature zones and during engine start-up and load changes. Under dynamic conditions, increased hydrocarbon emissions are observed, resulting from insufficient mixture homogenization and delays in the injection and combustion processes. The dependence of hydrocarbon emission intensity on the engine operating states is similar to that observed for carbon monoxide emission intensity.

The nitrogen oxide emission intensity is dominated by engine load and maximum combustion temperature (Figure 6). Peak nitrogen oxide emissions occur at high engine speeds and high engine loads, which contribute to increased temperatures in the combustion chamber. In diesel engines, nitrogen oxide emissions are particularly significant due to the elevated temperatures and pressures in the combustion chamber, which intensify the formation of nitrogen oxides. Compared to SI engines, this relationship is more pronounced and represents one of the main environmental constraints of diesel engines. The dominant factor for nitrogen oxide emission intensity is the engine load, which is mainly related to the vehicle speed.

The particle number emission intensity is characterized by high dynamics and peaks during intense acceleration phases—showing only in the final phase of the NEDC test (Figure 7). Especially high particulate matter emission values were observed during rapid increases in fuel injection, leading to soot formation and agglomeration. In the case of particle number emissions intensity, the factor determining the value of this intensity is primarily the strong increase in rotational speed, which is accompanied by a rapid increase in the engine load.

Carbon dioxide emissions follow a relatively continuous pattern and are strongly correlated with engine load and fuel consumption (Figure 8 and Figure 9). The nature of the pattern indicates a close relationship between carbon dioxide emissions and the engine’s instantaneous effective power. Fuel injection increases with increasing power demand, particularly during acceleration and heavy-load driving.

4. Analysis of Research Results

Figure 10 shows the product function of the speed and acceleration modulus of the car in the NEDC test. This parameter strongly characterizes the dynamic properties of the vehicle speed process, and its strong dependence on vehicle speed is clearly evident. The statistical characteristics of the processes: speed—v—and the product of speed and acceleration modulus—v·|a—obtained in the NEDC test are presented in

Table 4. Statistical features of the product of velocity process—v—and acceleration modulus process—v·|a|—in the NEDC test.

Statistical Features	v		v·|a|
	Unit	Value	Unit	Value
AV	km/h	33.15	km/h·m/s2	2.19
M		31.20		0.47
D		31.05		3.54
Rg		120.06		23.57
Min		0		0
Max		120.06		23.57
Q1		1.01		0.01
Q3		49.75		3.24
RQ		48.74		3.23
DQ		24.37		1.62
W	–	0.937	–	1.620
WQ		0.781		3.453
K		–0.077		9.707
S		0.813		2.768

.

The following statistical characteristics were examined: AV—mean value, M—median, D—standard deviation, Rg—range, Min—minimum value, Max—maximum value, Q1—first quartile, Q3—third quartile, RQ—interquartile range, DQ—interquartile deviation, W—coefficient of variation, WQ—quartile coefficient of variation, K—kurtosis and S—skewness.

The large difference between the maximum and average values of both vehicle speed and the product of vehicle speed and the acceleration modulus is characteristic of this type of measurement. The positive skewness observed in the distributions of the investigated processes further confirms these findings. The speed distribution is slightly platykurtic, the product of speed and acceleration modulus—strongly leptokurtic. The quarterly coefficient of variation of the product of speed and acceleration modulus was particularly large—this was consistent with the high value of the distribution’s kurtosis.

Table 5. Statistical features of exhaust emission intensity, particle number intensity and mass fuel consumption intensity in the NEDC test.

Statistical Features	Exhaust Emission Intensity
	Unit	ECO	EHC	ENOx	Unit	ECO2	Unit	EPN	Unit	qf
AV	mg/s	2.95	0.35	0.16	g/s	2.08	1/s	7.95 × 109	g/s	0.67
M		0.82	0.00	0.01		1.49		7.20 × 108		0.48
D		7.50	1.61	0.52		2.12		1.70 × 1010		0.68
Rg		80.30	18.54	4.68		11.92		1.03 × 1011		3.81
Min		0.035	0	0		0.0024		2.00 × 106		0.00
Max		80.33	18.54	4.68		11.92		1.03 × 1011		3.81
Q1		0.15	0.00	0.00		0.60		8.03 × 107		0.19
Q3		2.58	0.06	0.08		2.92		5.34 × 109		0.94
RQ		2.42	0.06	0.08		2.32		5.26 × 109		0.75
DQ		1.21	0.03	0.04		1.16		2.63 × 109		0.37
W	–	2.541	4.644	3.345	–	1.020	–	2.134	–	1.018
WQ		1.473	34.476	3.638		0.779		3.656		0.775
K		51.793	73.685	38.124		4.273		11.629		4.249
S		6.421	8.109	5.791		1.880		3.256		1.874

presents the statistical features of the exhaust emission rates of: carbon monoxide—E_CO, hydrocarbons—E_HC, nitrogen oxides—E_NOx, carbon dioxide—E_CO2, particle number emission intensity—E_PN and fuel mass consumption intensity—q_f.

Based on the determined statistical features of the studied processes, it can be concluded that there is a very large difference between the maximum and average values. The minimum values were very small. It is significant that the average value was higher than the median, which is confirmed by the high value of kurtosis, especially for the emission of carbon monoxide, hydrocarbons (mainly) and nitrogen oxides. In general, exhaust emission rates, particle number emission intensity and fuel mass consumption intensity have platykurtic and right-skewed distributions. The very large value of the quarterly coefficient of variation of the hydrocarbon emission rate is consistent with a large divergence from the normal distribution.

Table 6. Pearson’s linear correlation coefficient between the processes of speed—v—and exhaust emission intensities—E_CO, E_HC, E_NOx and E_CO2—and the emission intensity of particle number—E_PN—and the intensity of fuel mass consumption—q_f—in the NEDC test.

		v	ECO	EHC	ENOx	ECO2	EPN	qf
		km/h	mg/s	mg/s	mgs/s	g/s	1/s	g/s
v	km/h	1.000
ECO	mg/s	–0.040	1.000
EHC	mg/s	–0.089	0.672	1.000
ENOx	mg/s	0.311	0.139	0.374	1.000
ECO2	g/s	0.754	0.086	0.048	0.480	1.000
EPN	1/s	0.361	0.033	0.178	0.201	0.378	1.000
qf	g/s	0.754	0.093	0.054	0.481	1.000	0.378	1.000

shows Pearson’s linear correlation coefficients between the processes tested in the NEDC test: vehicle speed—v and the emission rates of: carbon monoxide—E_CO, hydrocarbons—E_HC, nitrogen oxides—E_NOx, carbon dioxide—E_CO2, particle number emission intensity—E_PN and fuel mass consumption intensity—q_f.

The strongest positive correlation was found between vehicle speed and carbon dioxide emissions and fuel mass consumption intensity. Figure 11 shows the Pearson’s linear correlation coefficient between the vehicle speed process and the processes of exhaust emission rates of: carbon monoxide—E_CO, hydrocarbons—E_HC, nitrogen oxides—E_NOx, carbon dioxide—E_CO2, particle number emission intensity—E_PN and fuel mass consumption intensity—q_f.

The negative value of the linear correlation coefficient of vehicle speed is with the carbon monoxide emission intensity and stronger with the hydrocarbon emission intensity.

Table 7. Specific distance exhaust emission of: b_CO, b_HC, b_NOx and b_CO2, specific distance particle number–b_PN—and specific distance of mass fuel consumption—q_f—in the NEDC test and limits for Euro 7.

bCO	bHC	bNOx	bCO2	bPN	qf
mg/km			g/km	1/km	g/km
0.321	0.038	0.017	0.226	8.63 × 108	0.072
Euro 7
1.000	0.100	0.060	0.005	6.00 × 1011	-

shows specific distance exhaust emission of: b_CO, b_HC, b_NOx and b_CO2, specific distance particle number—b_PN—and specific distance of mass fuel consumption—q_f—in the NEDC test and limits for Euro 7.

The values of average specific distance emissions in the NEDC test were even much lower than the limits for Euro 7.

Figure 12 shows the probability density of standardized processes—PD in the NEDC test: exhaust emission intensity, particulate number emission intensity and fuel mass consumption intensity.

There is a strong asymmetry in the probability distributions of the studied processes, as measured by their strong right-skewness. A large variation in the probability density of the tested processes was observed. This may be associated with artificial vehicle operating conditions in the NEDC test cycle, which was developed through the synthesis of speed-profile requirements rather than by faithfully reproducing real-world driving conditions in the time domain. An assessment of the compliance of the investigated datasets with the normal distribution was carried out, which was verified by the Kolmogorov–Smirnov [30], Lilliefors [31] and Shapiro–Wilk [32] tests. The probability of not rejecting the Kolmogorov–Smirnov, Lilliefors and Shapiro–Wilk hypotheses about the compliance of the analyzed sets with a normal distribution was less than 0.01. Therefore, it was concluded that there are no grounds to adopt hypotheses about the compliance of the sets with a normal distribution.

Figure 13 illustrates the power spectral density of the vehicle speed processes—SPD, exhaust emission intensity, particulate number intensity and fuel mass consumption intensity.

There is significant variation in the power spectral density of the studied processes, especially for high frequencies, which indicates significant dynamic differences in the processes.

5. Summary

The main conclusions arising from the conducted research are as follows:

• It is typical for modern cars with high exhaust emission categories that in a significant part of the test the intensity of exhaust emissions is very low. This is the result of the use of advanced exhaust aftertreatment technologies. This also results in low exhaust emissions for the entire vehicle lifespan.
• Such a large difference between the maximum value and the average value of the examined processes is characteristic for this case. This is confirmed by the positive skewness of the distributions of the studied processes.
• In general, exhaust emission rates, particulate number emission intensity and fuel mass consumption intensity have platykurtic and right-skewed distributions.
• A large variation could be observed in the probability density of the tested processes, which may be influenced by unnatural vehicle movement conditions in the NEDC test.
• On the basis of an assessment of the compliance of the investigated datasets with the normal distribution using the Kolmogorov–Smirnov, Lilliefors and Shapiro–Wilk hypotheses, it was concluded that there are no grounds for adopting hypotheses about the compliance of the sets with normal distribution.
• There is a large variation in the power spectral density of the studied processes, especially for high frequencies, which indicates significant dynamic differences in the processes.
• The values of average road emissions recorded in the NEDC test were much lower than even the limits for Euro 7.