Mathematical Model for Prediction of Fuel Consumption During Drive Cycles - Research Paper Example

Table of Contents 4.Mathematical model for prediction of fuel consumption during drive cycles 3 3New European Drive Cycle – Phases in a drive cycle 34.3.1.Urban Driving Cycle 4 4.3.2.Extra Urban Driving Cycle 4 4.3.3.Soaking 5 4.3.4.Idling 6 4.3.5.Cycle Duration 7 4.3.6.Critique 8 4Mathematical Modelling 10 4.3.7.Mathematically classified phases in a drive cycle 10 4.3.8.Driving parameters processing 11 4.3.9.Mathematical relationships between fuel consumption and drive-cycle parameters 13 4.3.10.Least squares fitting 14 4.3.11.Constant speed 17 4.3.12.Acceleration 20 4.3.13.Deceleration 22 4.3.14.Gear change 24 5Functional representation of the complete drive cycle 25 4.3.15.Algorithm to divide drive cycles into short phases 26 5.Bibliography 28 List of Figures Figure 4.1 - The New European Drive Cycle sourced from (Berry, 2007, p.132) 5 Figure 4.2 - Theoretical Framework 9 Figure 4.3 - Time history of the drive-cycle parameters during a drive cycle, (a) city driving, (b) extra urban driving 12 Figure 4.4 - Fuel consumption in “constant speed” phases in the New European Drive Cycle 19 Figure 4.5 - Fuel consumption in “acceleration” phases in the New European Drive Cycle 21 Figure 4.6 - Fuel consumption in “deceleration due to gradient with throttle” phases in the New European Drive Cycle 23 Figure 4.7 - Fuel consumption in “gear change” phases in the New European Drive Cycle 25 Chapter 4 4. Mathematical model for prediction of fuel consumption during drive cycles Comment: revise equation numbering. A mathematical model has been developed to predict fuel consumption in passenger cars. The model estimates fuel consumption depending on drive cycle parameters that were measured during the simulation of the New European Drive Cycle (NEDC) under laboratory conditions as was described in Chapter 3. 3 New European Drive Cycle – Phases in a drive cycle When compared to other drive cycles, such as the EUDC and the Japan 15 cycles, the NEDC is a more aggressive drive cycle (Berry, 2007, p.93). This allows the use of the NEDC to model real world driving situations better but this does not suggest that the NEDC is truly representative of all factors required for real world driving. As noted earlier, the urban driving cycle is a driving cycle that is representative of urban setting. It is characterised by low vehicle speed, soft acceleration, and low engine loads. These are the typical driving conditions that are encountered in most European cities. On the other hand, the EUDC segments are added to account for highway, sub-urban, and motorway driveway. The NEDC is seen to override all previous engine testing directives issued by the European Commission such as 70/220/EC. NEDC testing methods are now the primary means of evaluation for approval of engines and are specified as the Type I testing methods in the original directive. The NEDC has been modified as gasoline engine technology has evolved over recent years. This has been done in an effort to make the testing method more reliable and valid, not merely for real world driving conditions but also to account for changes to gasoline engine technologies, which were previously being ignored. The test is composed largely around urban driving techniques such that two major testing sections are present that are: Urban driving cycle; Extra urban driving cycle. 4.3.1. Urban Driving Cycle The urban driving cycle is composed of consecutive accelerations, steady speed patches, decelerations as well as idling patches. The contention is to simulate average daily road conditions in any large European city. It needs to be kept in mind that this methodology has been implemented to simulate typical driving conditions based on traffic stops, low speed driving and frequent stops as is typical of any urban driving cycle. However, it would be unrealistic to expect that urban driving alone would suffice for testing purposes, especially for fuel consumption testing purposes, so an extra urban driving mode has also been incorporated for testing. The diagram provided below shows the NEDC graphically in terms of the speed against the testing time. 4.3.2. Extra Urban Driving Cycle The EUDC portion of the test, occurring at roughly after 800 seconds of testing is composed roughly half of steady speed driving. The steady speed for testing is maintained between 75 km/hr and 120 km/hr but the testing speed is not pushed any further to accommodate for legal speed restrictions. Moreover, the other half of the EUDC testing cycle is composed of accelerations, decelerations as well as some idling patches (DEFRA, 2013, p.12). Figure 4.1 - The New European Drive Cycle sourced from (Berry, 2007, p.132) 4.3.3. Soaking Initially, the vehicle is allowed to ‘soak’ before the test for at least six hours at a temperature between 20oC and 30 °C. The soaking process is allowed to continue until the engine oil temperature and the coolant temperatures are within ±2oC of the ambient temperature (DEFRA, 2013, p.12). The contention behind soaking is to allow engine lubricating oil to come to a steady state before testing is realised. Losses resulting from cold engine oil and the lack of engine oil recirculation to all parts of the engine cause an increase of fuel consumption figures that would tend to offset the balance of the overall test. In order to ensure that the engine would produce consistent results throughout the various phases of the test, it is essential to have a steady engine oil temperature before testing would begin. Moreover, if soaking were not allowed, there are large chances that the cold sections of the cold engine block would take up heat as the engine is being warmed up. A cold engine would allow for higher efficiencies to emerge during the start of the test while the performance efficiency would fall off as the engine block were to assume more temperature since engine efficiency depends on the engine’s lowest temperature directly. Engine soaking has been allowed for six hours in order to ensure that the entire engine compartment of the tested vehicle is at the same temperature level before testing begins. 4.3.4. Idling Initially, the engine is allowed to idle after the soaking period before being worked up. The engine is allowed to idle for 40 seconds of the test. After the year 2000, the idling period was eliminated for carbon dioxide sampling purposes, i.e., engine is cold started and the emission sampling process begins immediately. The New European Driving Cycle (NEDC) is used for CO2 emission measurement. Emissions are sampled during the cycle, using the constant volume sampling technique, analyzed, and expressed in grams per kilometre for each pollutant (Giakoumis & Lioutas, 2010). However, it needs to be kept in mind that such directives are not applicable for fuel consumption testing. The idling process is still included for fuel consumption testing as shown in the diagram above. A number of different idling cycles have been emulated for the urban driving mode of the NEDC testing regime to allow for countenance of traffic stops, routine pullovers etc. This is expected to make the overall testing regimen as realistic as practically possible but is not expected to account for all forms of driving situations such as long traffic stops etc. 4.3.5. Cycle Duration The “duration of the cycle is 19m 40s (1180 seconds) for Euro III and later certification, with the two phases being 13m and 6m 40s long, respectively. The Euro III test differs from the Euro II and earlier certification procedure (specified in directive 98/69/EC) in that the earlier test started with a 40-second idling period that preceded the start of gaseous emissions sampling (DEFRA, 2013, p.12). Consequently the earlier test: • was 40 seconds longer, i.e. 20m 20s, although emissions were only collected for the last 19m 40s and • Vehicles were idling for 51 seconds, rather than 11 seconds, before the start of the first acceleration. (DEFRA, 2013, p.13) These changes are implemented to quantify, and control, the high level of emissions (especially carbon monoxide) occurring during the first part of a journey before the three way catalyst of a gasoline fuelled car is fully operational, thus, it reduces polluting emissions to a very low level. In this context, New European Driving Cycle provides an image of real-world driving condition in most European cities. However, New European Driving Cycle has been criticised as not truly representative of real-world driving condition in Europe. This is based on the supposition that variables integral in New European Driving Cycle does not necessarily depict real-world conditions. These are (1) New European Driving Cycle consisted of slow accelerations and decelerations and that there are several steady states. (2) it does not take into account other factors such as air-conditioning, vehicle accessories, reduced tyre pressure have an impact in the reduction of CO2 in real world driving conditions (Fontaras & Dilara, 2012) (Yu et al., 2010). 4.3.6. Critique Nonetheless, these limitations do not deter the fact that New European Driving Cycle is the driving cycle that is used for certification of passenger cars in Europe. As such, as a tool for measuring CO2 emissions, it can be maintained that it is the standard procedure to be followed by passenger cars in Europe. In addition, it clearly manifest that existing driving cycles have limitations. As such, there is no one perfect driving cycle that can cover all of the real-world driving conditions. In case there is one, it will be the panacea for the issues of driving. Unfortunately, there is none. In this regard, this researcher holds as this study intends to know the greenhouse gas emission of Nissan Patrol in urban and extra-urban setting, New European Driving Cycle provides the most efficient procedure. Since, the two road routes and conditions under New European Driving Cycle are the primary focus of this study. Likewise, as the research seeks to understand the driving conditions of some cities in Europe and since, New European Driving Cycle is representative of it, and it is assumed that the New European Driving Cycle is the most appropriate driving cycle suitable in attaining the aims and objectives of this study. In this context, this research adopted New European Driving Cycle as the driving cycle to be used in the analysis of the Nissan Patrol engine, the identified vehicle. Figure 4.2 - Theoretical Framework This figure presents the framework that presents what the research intends to attain. By using New European Driving Cycle, fuel consumption and CO2 emission of Nissan Patrol engine can be measured. The information that will be gathered from this step will be used in three ways. First, it will be used to compare the difference between urban driving cycle and extra-urban driving cycle with Nissan Patrol as the identified vehicle. This is significant as there limited information regarding this matter. Second, the data that will be gathered in the simulation can be used as the benchmark for the on–road test that will be conducted in order to cover some of the observable gaps in New European Driving Cycle. The on-road test is critical, as the information that will be gathered is the data that will be transferred to Google Map. The third step deals with the development of pathways that will allow for the gathering of data while the vehicle is on-road travel. This means developing mechanisms that will allow for the collection, storage, and transfer of CO2 emissions of Nissan Patrol to Google and thus, create a live feed of actual CO2 emission of Nissan Patrol when it is used, wherever it is used. In this context, this researcher holds that there are three essential phases in the methodology. This is to ensure that all the necessary data needed for the study will be gathered. Since, the information that will be gathered are critical in the attainment the aims of this research. 4 Mathematical Modelling The NEDC consists of four differentiated cycles of urban driving and one cycle of extra urban (EUDC) driving that have been discussed above and in Section 2.4.2. The total resultant drive cycle was simulated in laboratory conditions in order to extract quantifiable results for prediction of fuel consumption. Results from laboratory tests were measured and were further used to fit a mathematical function on drive cycle parameters as a means of predicting fuel consumption. 4.3.7. Mathematically classified phases in a drive cycle For the purposes of mathematical modelling the NEDC classifications of urban driving and extra urban driving were decomposed into smaller more quantifiable driving phases. A number of different phases were observed in NEDC components that are listed below: Constant speed driving; Acceleration; Deceleration due to gradient with throttle; Deceleration without gear engagement; Gear changes. These phases may be used to construct any random driving cycle that emulates the different kinds of driving conditions and driving behaviour experienced on both urban and extra urban roads. The fuel consumption of any vehicle driven in these phases depends on several different parameters that are used to describe the driving cycle. An examination of multiple factors was carried out to classify which factors made the greatest contributions to fuel consumption. Within the examined parameters, the following parameters were observed to exert a large influence: Vehicle speed (v); Acceleration (a); Throttle position (p); Gear (G). The parameters listed above have been used extensively throughout the analysis presented below to propose a mathematical model that can predict fuel consumption (c) in a variety of different driving conditions. 4.3.8. Driving parameters processing Laboratory test runs were used to capture parameter data that was then plotted against the time in order to create a mathematical model. Four different parameters were focused on namely vehicle speed (in kilometres per hour), acceleration (in kilometres per hour per second), throttle position (in percentage opening) and fuel consumption (in grams per second). The vehicle was sped up and decclerated along with idling stops in order to emulate the NEDC criterion as discussed in preceding sections. (a) (b) Figure 4.3 - Time history of the drive-cycle parameters during a drive cycle, (a) city driving, (b) extra urban driving The vehicle was soaked before testing was initated to ensure that the conditions of the NEDC were met as prescribed. Total running times of two hundred and four hundred seconds were used in order to emulate the driving test for urban driving and extra urban driving, respectively, including driving and idling patches. 4.3.9. Mathematical relationships between fuel consumption and drive-cycle parameters The total driving test run was divided into a number of different phases for simplification of the mathematical modelling. The various drive cycle parameters recorded during test runs were used in terms of their averaged values only. The nature of the driving cycle included constant speed, accelerating, decclerating and idle patches that were not defined by a fixed frequency that could classify each driving cycle as being related to the other. In order to circumvent processing difficulties such as constructing approximated driving cycles, it was chosen to average the captured values. The creation of entire cyclical patterns was seen as promoting errors in the final mathematical modelling relationship since close approximation for differing runs was not a distinct possibility. It could be argued that averaging would produce larger errors in the overall relationship but it cannot be denied that using a simple measure such as averages would provide for simpler processing. The tradeoff between accuracy using cyclical mathematical relationships and simple averaging to promote processing ease was seen to be in favour of using simple averaging techniques. Since the current research is interested in investigating the fuel consumption of the vehicle in relation to the parameters discussed above, so the fuel consumption was expressed in terms of these parameters. To make the mathematical model more realistic, the fuel consumption was expressed as being functionally related to the various parameters in each driving cycle being tested in laboratory conditions. Since the data obtained from the tests was not linear, quadratic or otherwise simply relatable, so instead ordinary least squares regression was utilised to create mathematical relationships. This required the determination of constants in such mathematical relationships. Reference values of each recorded parameter; velocity, acceleration, throttle position and fuel consumption (v0, a0, p0, and c0) were determined before hand and these were then used for relating to the overall relationship. This allowed the creation of mathematical relationships that could be used independently in a number of situations no matter what units were used to express these parameters. It needs to be kept in mind that the created mathematical relationship would require the insertion of reference values in the same units as the units in which the answer is desirable. 4.3.10. Least squares fitting The least squares method (also known as ordinary least squares method) is extensively employed to fit distributed data along a function that can broadly describe the behaviour being studied. Ideally all data from experimentation should lie by default on a mathematically discernable relationship but practicality demands otherwise. The inclusion of various errors, beyond feasible levels of control, causes data to be scattered. This in turn requires the implementation of ordinary least squares, or some other form of regression, to ensure that a discernable mathematical relationship is developed between the independent and dependant variable(s). The method of least squares fits a function on a data set that is, in the present case, available from experiments. Assume that the data set includes n points (xi; yi), i = 1,…,n, where xi is the independent variable, i.e. a drive-cycle parameter, and yi is the dependent parameter, i.e. the fuel consumption. The dependence of parameter y on parameter x is approximated by the model function f(x; k), where k is a constant. In a more general case, the function f may include more than one independent parameter and more than one constant. The method will be presented here as it is applied to obtain a relationship for the constant speed phase, and the relationships for the other phases can be derived in a similar fashion. In the constant speed phase (see Section 4.4.5), there is one independent parameter, the vehicle speed v, and three constants k10, k11 and k12. The reason for using more than one constant is the nature of the assumed relationship itself. The application of a quadratic relationship mandates that one constant be assumed for the squared term, one variable for the linear term and finally one variable as a constant of the overall equation. Thus, the aim is to express consumption by a function that best fits the measured data at measurement points i = 1,…,n as follows: (4.1) The relationship in the constant speed phase is assumed in the form expressed below: (4.2) Note that if reference values v0 and c0 are used, then v and c should be replaced by v/v0 and c/c0, respectively, in Eq. (4.2); for this discussion, however, the above form will be kept for the sake of simplicity. Since the system is overdetermined, a residual ri can be defined at each measurement point as the difference between the measured and predicted values of fuel consumption: (4.3) The residual discussed above could be either positively or negatively related to the speculated mathematical relationship. This occurs since the data points scattered around the speculated quadratic curve could be either above or below the curve. The constants k10, k11 and k12 are determined by using the condition that the sum of squared residuals R2 is a minimum. The expression for R2 is as expressed in the equation presented below: (4.4) The minimization of R2 can only occur if the constants declared above can be minimised as much as possible. This contention occurs since the curve should be as close as possible to the scattered data points without compromising the residual. R2 needs to be differentiated in order to discover its rate of change with respect to the constant under consideration so that its minimum limits can be fathomed and utilised further. The lowest possible difference between the curve and the available data points would occur if the residual would approach zero or alternatively when R2 is as close to zero as possible or is zero. This condition is satisfied by making the derivatives of R2 with respect to the constants k10, k11 and k12 equal to 0: (4.5a) (4.5b) (4.5c) The equations listed above can be solved using linear methods such as simultaneous equations. One simple method of doing this can happen if the system of equations can be expressed in matrix form. The system of equations (4.5) can be organized in matrix form as follows: (4.6) This is a linear system of equations that can be solved for the vector including the constants k10, k11 and k12 through the application of matrix handling methods. 4.3.11. Constant speed The primal method under consideration, that can be adapted for other parameters, is for constant speed results. Similar to above, the relationship between fuel consumption and vehicle speed is assumed to be of a quadratic nature. In this case, the independent variable is settled as the vehicle’s speed while the dependent variable is settled as the vehicle’s fuel consumption. Again, any set of units can be utilised as long as the reference parameter assumptions were using the same set of units. Reference values for constant vehicle speed and fuel consumption have been used to derive the mathematical regression relationship below. The reference values were not considered in the previous section for the sake of simplicity but to make the mathematical relationship between variables more realistic, these reference values are being considered in this case. The case of a constant speed vehicle has been assumed since this provides the simplification of not considering any acceleration terms in the final equation. When a passenger car moves with a constant speed, the acceleration is zero, and the throttle position is constant, although this constant depends on the vehicle speed. The fuel consumption in this case is a quadratic function of the vehicle speed. Thus, it can be assumed in the following form: (4.7) Figure 4.4 shows measured data in constant speed phases together with the quadratic curve that is fitted on those data. Using the relationship provided above along with the reference values, the corresponding constants can be determined as follows: k10 = 0.3037; k11 = 0.6650; k12 = 2.3814. Figure 4.4 - Fuel consumption in “constant speed” phases in the New European Drive Cycle As shown in the figure presented above, the plot of fuel consumption against vehicle speed can be approximated as a quadratic relationship. It is noticeable that there are data points in the slower speed regions (below 60 kilometers per hour) that are offset from the derived curve. The application of ordinary least squares allows the tabulation of a quadratic curve that is as close as possible to these data points without compromising either the data points or the final curve. The relationship discovered in this fashion can be expressed as: (4.8) 4.3.12. Acceleration The case of vehicle acceleration is far differentiated from constant vehicle speed. At constant vehicle speed, the acceleration is zero but in the case of considering acceleration, the vehicle speed itself becomes a transient under consideration. In the case of acceleration, the fuel consumption behaves proportional to the parameter a/v2. Unlike before, a power-law relationship between variables is assumed with two constants are considered since the relationship is not as complicated as before. Thus, the fuel consumption of the vehicle can be assumed to behave in the following form: (4.9) Figure 4.5 shows measured data in acceleration phases together with the curve that is fitted on those data. Again a number of plots are seen to arise on the diagram that can be approximated using the power-law relationship listed above. An investigation of the relationship along with the use of appropriate reference parameters reveals that the corresponding constants are as follows: k21 = 1.6323; k22 = –0.2514. Figure 4.5 - Fuel consumption in “acceleration” phases in the New European Drive Cycle The plot presented above makes it clear that the relationship between fuel consumption and the derived parameter of acceleration and velocity a/v2 emulates power-law like behaviour. The constant downslope of the curve presented in the figure above and its inflexion like behaviour at higher values of the parameter a/v2 provide ample evidence to classify the relationship as being polynomial in nature. It could be argued that plotting fuel consumption against acceleration would produce simpler data scatters. However, the presence of vehicle speed in acceleration (since acceleration is the rate of change of vehicle speed) tends to complicate matters further since it produces transients. A polynomial relationship between fuel consumption and acceleration alone could be produced but it would tend to be cumbersome and prone to errors so the parameter a/v2 has been chosen instead after careful consideration. The relationship between fuel consumption and the parameter a/v2 can be expressed mathematically with computed constants as follows: (4.10) 4.3.13. Deceleration The case of acceleration and deceleration may seem connected and simply antipodal to each other at first. However, the case of deceleration is far removed from acceleration on closer observation. Acceleration only occurs in vehicles when the driver depresses the pedal and causes an increase in the throttle position. In contrast, deceleration of the passenger car may happen under two very different circumstances. First, the vehicle may slow down due to a surface gradient even if the driver depresses the throttle pedal by some amount. The decrease in throttle opening reduces the air input to the engine and hence the engine power drops prompting a reduction in the vehicle speed. In the second scenario, the driver may choose to apply the vehicle’s brakes. The application of brakes would tend to decrease power output to the vehicle’s tyres and lead to deceleration. In the case of decreased throttle opening, the fuel consumption is proportional to the product of throttle position and vehicle speed vp. This indicates that the relationship would be linear in nature and can be expressed in the form of a simple linear equation. Thus, the relationship between throttle opening and fuel consumption for decceleration can be assumed to be of the following form: (4.11) Fig. 4.6 shows measured data in deceleration due to gradient with throttle phases together with the curve that is fitted on those data. The corresponding constants are computed as follows: k30 = 0.4421; k31 = 14.0278. Figure 4.6 - Fuel consumption in “deceleration due to gradient with throttle” phases in the New European Drive Cycle Given the constraints presented above, the relationship between fuel consumption and throttle position can be expressed as a linear equation of the form: (4.12) Then, the vehicle may slow down while it is still in gear, but the driver released the throttle pedal. In this case, the fuel is not injected, thus, the fuel consumption drops to zero. Finally, the vehicle may slow down while the gear is in neutral. In this case, the fuel consumption is approximately the same as during idling, which is a special case of the constant speed phase, i.e. when the speed is zero. 4.3.14. Gear change The last phase that is discussed here is the gear change. During gear change, the consumption may vary considerably, but this variation occurs during quite short time intervals (1-3 s). Therefore, during this phase the consumption is approximated by a constant that is proportional to the vehicle speed. This relationship was assumed to be linear, although a significant scatter of data can be observed in this phase (see Fig. 4.7). The fuel consumption can be assumed in the following form: (4.13) Figure 4.7 shows measured data in gear change phases together with the curve that is fitted on those data. The corresponding constants are as follows: k40 = 0.4503; k41 = 1.4494. Figure 4.7 - Fuel consumption in “gear change” phases in the New European Drive Cycle The final linear equation can be expressed mathematically with computed constants as below: (4.14) 5 Functional representation of the complete drive cycle The functional relationships proposed in Section 4.2 can be applied for an arbitrary drive cycle. The drive cycle is divided into short phases, lasting 3-5 s each, and the consumption in each of those short phases is determined by the corresponding formula. Then, the total consumption during the whole cycle can be calculated. The application of the obtained relationships to the New European Drive Cycle provides a fuel consumption of 0.486 g/s. The consumption during the same cycle was measured 0.461 g/s in laboratory. Thus, the error in the prediction using the proposed formula is 5.4%. 4.3.15. Algorithm to divide drive cycles into short phases The NEDC drive cycle emulated under laboratory conditions for testing discussed above was sorted into an algorithm for generic processing of similar fuel consumption computations. The algorithm can be expressed as a series of different steps designed to simplify fuel consumption calculations for a number of different vehicles and situations. Software devised for these purposes depends on a number of different inputs. The program requires an input file including 6 columns: 1st column: time 2nd column: vehicle speed 3rd column: acceleration 4th column: gradient 5th column: throttle position 6th column: gear In simple terms, the algorithm derived for fuel consumption calculations based on several constraints and differing situations can be expressed as below: The program first examines if the gear changes from the first till last sample in a given short phase, and if so, then Eq. (4.4) is used to determine consumption in that phase. If the gear does not change (or it is changed from neutral), then velocity variation is investigated. If it is smaller than a prescribed limit (km/h), then Eq. (4.1) is applied to determine consumption. If the velocity variation is greater than the prescribed limit, then it is examined whether the acceleration is positive or negative. If it is positive, then Eq. (4.2) is used to determine consumption. If the acceleration is negative and the gear is in neutral, then Eq. (4.1) used to determine consumption. If the acceleration is negative, the gear is not in neutral, and throttle is not applied (or, throttle position is lower than a prescribed limit), then the consumption is zero. If the acceleration is negative, the gear is not in neutral, but throttle is applied (or, throttle position is greater than the prescribed limit), then the consumption is determined by Eq. (4.3). 5. Bibliography Berry, I. M. (2007). The Effects of Driving Style and Vehicle Performance on the Real-World Fuel Consumption of U.S. Light Duty Vehicles. Masters Thesis, Masachusetts Institute of Technology. DEFRA. (2013). Review of Test Procedures EMStec/02/027 Issue 3. Retrieved June 9, 2013, from DEFRA: http://uk-air.defra.gov.uk/reports/cat15/0408171324_Appendix2Issue3toPhase2report.pdf Fontaras, G., & Dilara, P. (2012). The evolution of European passenger car characteristics 2000–2010 and its effects on real-world CO2 emissions and CO2 reduction policy. Energy Policy , 49, 719-730. Giakoumis, E. G., & Lioutas, S. C. (2010). Diesel-engined vehicle nitric oxide and soot emissions during the European light-duty driving cycle using a transient mapping approach. Transportation Research Part D , 15, 134–143. Yu, L., Wang, Z., & Shi, Q. (2010). PEMS-Based Approach To Developing And Evaluating Driving Cycles For Air Quality Assessment. 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