Sensitivity analysis

A sensitivity analysis was performed to study how simulated fuel consumption and emission factors change in response to changes in the input parameters (average engine speed, average engine load, fuel type and emissions regulation). A two-step process was used. The first step finds the partial functional forms of the qualitative input parameters (average engine speed and average engine load) using a simple regression analysis of the individual parameters against the output fuel consumption and emission factors. The second step combines the functional forms of the quantitative input parameters and the qualitative input parameters (fuel type and emissions regulation) into a single multi-parameter equation. The coefficients for the multi-parameters, which indicate the sensitivity of the model to the input parameters are solved using the engine speeds, engine loads, fuel types, emissions regulations and the fuel consumption and emission factors from the 48 base engine-operating patterns.

The results of the simple regression analysis of the engine speed and engine load are represented as curve fits in APPENDIX J: Sensitivity Analysis of Emissions Simulation Model: Curve fits. From experimenting with different forms of curve fits, it was found that a second-order polynomial gave adequate fits for fuel consumption and emissions for both engine speed and engine load. The quality of the fit was best (typical R² value of 0.95) for CO2 and fuel consumption vs. engine speed and engine load respectively. A second order polynomial fit also provided a suitable correlation for CO, HC and NOx emissions.

However, the relationship weakened with the most recent (Euro-3) emissions regulations considered. HC, followed by CO emissions, had the poorest correlation (R² between 0.004 and 0.66) to engine speed and engine load. The relationships between engine operation and emission factors (excluding CO2 and fuel consumption) weaken because the improved efficiency of catalytic converters under the newer (Euro-3) emissions regulations are more influential on the overall vehicle emissions than emission controls which determine the exhaust gases entering the exhaust system (de Haan and Keller, 2004a).

As examples of the curve fits Figure 4.2 shows the relationships between CO2 emissions and engine speed and Figure 4.3 shows the relationship between CO and engine load for the various types of vehicles.

Figure 4.2: CO2 emissions per litre engine capacity vs. engine speed for different fuels and emissions regulations.

Figure 4.3: CO emissions per litre engine capacity vs. engine load for different fuels and emissions regulations.

Having determined the appropriate functional relationships between fuel consumption and emission factors for the input parameters, a multiple linear regression method, as defined by Stephens (2004), was used to determine which of the parameters has the most significant impact on the fuel consumption and emissions. The following relationship, Equation 11, was assumed based on the curve fits:

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where y is the fuel consumption or emissions factor; x1 is average engine speed; x2 is average engine speed squared; x3 is average engine load; x4 is average engine load squared;

x5 is a dummy variable for fuel type (0 for diesel and 1 for petrol); x6 and x7 are dummy variables for the emissions regulation (x6=1 and x7=0 for Euro-0; x6=0 and x7=1 for Euro-2; and x6=0 and x7=0 for Euro-3 respectively); and β1 to β7 are coefficients to be fitted.

The analysis was performed using the regression analysis tool in Microsoft Excel. The summary outputs from the analysis, including the coefficients for Equation 11, their significance (P-values) and their 95% confidence intervals are given in APPENDIX J:

Sensitivity Analysis of Emissions Simulation Model: Regression analysis. The coefficients

are summarised in Table 4.4 below. Significant values (P-value <0.05) are in bold and power refers to the product of x1 and x3.

Table 4.4: Coefficients from regression analysis to determine the sensitivity of the simulation model. Significant values (P-value <0.05) are in bold.

From Table 4.4 and Appendix J all the output parameters are significantly influenced by, in order of sensitivity, average engine speed, average engine speed squared, average engine load, average specific power and average engine load squared with respect to the other input parameters. The squared terms (i.e. engine speed squared and engine load squared) in and multi-linear regression are a result of the assumption that fuel consumption and emissions are second order functions of the engine speed and engine load. The inclusion of the term power indicates that the interaction between engine speed and engine load is significant in terms of the other input parameters.

The fuel type (difference between petrol and diesel) has the most significant impact on CO2 and fuel consumption but no significant impact on the other output parameters. The shift from Euro-0 to Euro-2 (petrol vehicles only) emissions regulation has a significant impact on CO2, CO, HC and NOx emissions after engine speed; however, there is no significant change in emissions with respect to the other input parameters with a change from Euro-2 to Euro-3.

4.2.4. Conclusions

In this section, a fuel consumption and emissions simulation model was developed and presented. The software implementation of the model was discussed, the model was validated and a sensitivity analysis was performed.

The model was validated using a cross validation i.e. the base engine-operating patterns were used to simulate each other. The validation showed that the method used in the model provides good results for engine operation when compared to a similar statistical method using vehicle kinematics to produce the HBEFA. The HBEFA is used to develop national emissions inventories in Europe. The engine-operating patterns at each end of the engine operating envelope i.e. low speed - low load and high speed - high load, were predicted with less accurately.

The output of the simulation model was analysed with respect to the input parameters using a sensitivity analysis. The analysis showed that CO2 and fuel consumption are most sensitive to fuel type, followed by engine speed, engine speed squared, a switch from Euro-0 to Euro-2 emissions regulation, engine load, engine power and engine load squared.

The analysis also showed that pollutant emissions are most sensitive to engine speed followed by engine speed squared, a switch from Euro-0 to Euro-2 emissions regulation, engine load, engine power and engine load squared. A shift from Euro-2 to Euro-3 emissions regulation had no significant effect on the output parameters with respect to the other input parameters. Implementation of the Euro-2 regulation required use of catalytic converters to meet the emissions limits. This had a significant impact on emissions from previous emissions regulations. Improvements in emissions with the change from Euro-2 to Euro-3 regulation vehicles are not as great because there was only an incremental improvement in catalytic converter technologies and not a technology change. The changes to the specified emissions limits between Euro-0 and Euro-2 are also greater than the changes in the specified emissions limits from Euro-2 and Euro-3.

From the analysis, driving conditions, driving behaviour and driving styles have a significant impact on emission factors within the set of fuel types, emissions regulations and engine-operating patterns considered, because they determine engine speed and engine load. The sensitivity analysis suggests that the most effective way to reduce pollutant emissions is by managing driving behaviour and driving styles to encourage less aggressive driving with earlier gear changes. This would require modification to road infrastructure to promote smoother traffic flow, such as traffic light synchronisation and driver education and training. While it is generally understood that fuel consumption increases with increasing acceleration and speed, the relationship between emissions rates and fuel consumption is not proportional. Less aggressive driving styles would result in a

significantly larger reduction in exhaust emissions compared to the reduction in fuel consumption.

Further development of the model should include validation of the model by using on-board measurement of emissions and engine operation from vehicles being used in the City of Johannesburg.