Policonsumo

Numerical methods have been preferred for the development of this model, as they are more appropriate to the nature of the engine-operating patterns, rather than differential calculus and other curve fitting techniques. The engine-operating patterns, as defined in Section 3.3.4, are made up of discrete values for engine speed and engine load intervals.

This makes them suitable for advanced database techniques, which are ideal for filtering and matching large sets of numerical data.

The basic principle behind the model is that similar engine-operating patterns for the same fuel type and emissions regulation compliance have similar fuel consumption and emission factors. From this, fuel consumption and emission factors for a newly measured engine-operating pattern can be derived by matching it to engine-engine-operating patterns of known fuel consumption and emission factors. This is mathematically executed by finding the maximum matching index (defined in Equation 8, Section 3.3.4) of the new engine-operating pattern and a combination of engine-engine-operating patterns of known fuel

consumption and emission factors. The base engine-operating patterns, developed in Section 3.3, provide a set of reference engine-operating patterns and corresponding fuel consumption and emission factors. Individual base engine-operating patterns represent specific driving conditions that on their own may not closely match measured engine-operating patterns. However, by adding several base patterns together in various combinations to produce an aggregated pattern, it is possible to build an artificial pattern which closely matches any measured pattern.

Practical implications of this method require that the number of base patterns and interval step sizes for the proportion of each base pattern contributing towards an aggregate pattern be limited. For the purposes of this study the maximum number of base patterns involved in any linear combination is limited to three and the proportion that each base pattern that may contribute towards the aggregate pattern is in intervals of 1%. The procedure involves numerically maximising Equation 9 :

(9) where Pi is the pattern being evaluated; PA, PB, and PC are base patterns with the unique

identifiers A, B and C respectively and are of the same fuel type and emissions regulation as pattern i; A ≠ B ≠ C; Pi, PA,PB and PC are two dimensional vectors; X, Y and Z are the scalar proportions of patterns PA, PB, and PC respectively in 1% intervals; and X+Y+Z = 1.

The structure and operation of the model is shown in Figure 4.1. Inputs into the model are fuel type, emissions regulation, an engine-operating pattern to be evaluated, average engine speed and average engine load of the pattern. Outputs from the model include the linear combination of base engine-operating patterns that best match the new pattern, the resulting matching index (MI), the emissions rates per litre engine capacity (in g s^-1 ℓ^-1 ) of CO, HC, NOx, CO2 and fuel consumption.

Within the software implementation of the simulation model an optimisation strategy was used to maximise the speed of the calculation process. The procedure in Figure 4.1 illustrates the optimisation strategy for the calculation of fuel consumption and emission factors for a measured engine-operating pattern.

Figure 4.1: Structure and optimisation process within the fuel consumption and emissions simulation model.

An initial part of the optimisation involved pre-calculating average engine speed, average engine load and specific power (average engine speed × average engine load) for all combinations of any three base engine-operating patterns of the same fuel type and emissions regulation pair (Euro-0 petrol, Euro-2 petrol, Euro-3 petrol and Euro-2 diesel). A total of 4.5 million combinations are possible. These were inserted into a database table which was then indexed for rapid searches. Three steps were used to optimise the process of evaluating the fuel consumption and emission factors for a new engine-operating pattern:

(i) The closest matching base engine-operating pattern for the specified fuel type, emissions regulation and pattern being evaluated is found i.e. the base pattern that has the highest MI when compared to the new pattern;

(ii) All linear combinations of base patterns that include this closest matching base pattern and two other patterns are compared to the new pattern using the average specific power calculated for the new pattern and extracted from the pre-calculated table of values for the base patterns; and

(iii) A single engine-operating pattern is calculated for each of the 1 000 closest matching combinations (by specific power) of base patterns and compared to the new pattern by calculating the matching index. The linear combination of base patterns which results in the maximum matching index is then used to calculate the fuel consumption and emission factors for the new pattern.

Evaluating all possible combinations of base patterns would not add any accuracy to the model and would increase processing time considerably. The closest single matching base pattern from point (i) ensures that the individual base patterns, which deviate considerably from the average power of the new pattern, are excluded from the analysis, to avoid unnecessary calculations. The average specific power calculation point (ii) ensures that only the most relevant (1 000 closest) combinations of base patterns are compared to the new pattern using the matching index (MI) calculation.

The MI calculation is processor intensive so reducing the number of times this calculation is executed improves the speed of the overall process. The optimisation strategy reduced the time to evaluate a single pattern from an average of 1 minute to 10 seconds, effectively reducing the time it took to calculate the emissions factors for all the measured engine operating patterns from the survey from six hours to just over one hour.

The software implementation of the model relies on six tables in a database: (i) definitions of the new operating patterns to be evaluated; (ii) definitions of base engine-operating patterns; (iii) fuel consumption and emission factors for the base patterns;

(iv) average engine speeds and average engine loads for all possible combinations of any three base patterns; (v) best matching combination of base patterns for the new pattern as a result of the simulations; and (vi) emissions factors resulting from the simulations.

The fuel consumption and emissions simulation model was implemented as a set of stored procedures and user defined functions (both are software components to be called by other processes within the context of a relational database management system) within Microsoft SQL Server^®. The components were written in Transact SQL, which is a mixture of procedural and set based progamming languages used in SQL Server^®.

The definitions of the relevant tables in the database are provided in APPENDIX G:

Emissions simulation model table definitions and the computer code for the stored procedures and user defined functions are provided in APPENDIX H: Transact SQL code for emissions simulation.