Jacek Wawrzosek
Statistical modelling of fuel consumption and exhaust emissions in tractor engines supplied with biofuel
There have been worldwide initiatives which aim at limiting the emission of gases polluting natural environment and at satisfying the growing power consumption needs of people. One of these initiatives is introducing new types of biofuels for currently used drives. Moreover, for many years there has been research carried out on the use of RME higher fatty acids as engine fuel. In Polish agriculture there has been a large group of corn and rapeseed producers using compression-ignition engines, who are interested in producing biofuels for the needs of their farms. It is envisaged that significant changes to the tractors’ design and the provision of new generation power resources in Polish agriculture will start in the coming years after worn out tractors have been taken out of service.
The statistical methods designed for this work are to compare the properties of the biofuels used with the properties of the known standard fuels. They accomplish the basic research objectives of the work i.e. determination of simple dependencies which define the influence of various additives to biofuels on the fuel consumption and on the concentration of the basic components of exhaust gas emissions from the S-4002 tractor engines, because the models existing so far which describe the influence of biofuels additives on the changes of these values express them additionally depending on engine load and speed conditions. While designing traditional mathematical models it is not possible to achieve conclusions regarding power and ecological parameters characteristic for a given engine which are not based on the results of the engine random effective power measurements. Moreover, the problems determining the effective power probability distribution of an unmarked tractor engine were indicated.
The designed non-linear regression models describe the changes to the concentration of individual components of exhaust gases of tractor engines supplied with various biofuels at two engine speeds corresponding to the maximum torque nMomax (1600 rpm‑1) and maximum power nNemax (2000 rpm-1). The minimum and maximum changes to the fuel consumption caused by RME addition to diesel oil were described. The results obtained partly confirm the principles of these changes obtained in other research centres.
The models analyses include the additive error with the normal distribution or multiplicative error with the log-normal distribution. The starting point for the work is the nonlinear model containing proportion parameters designed using the Hadamard product. Compared to classical regression, in the designed nonlinear models for groups with polynominal internal function and with proportion parameters for groups in linear external functions, a significant decrease in the model parameters number is observed, which allows additionally an easy interpretation of the change to the concentration of the engine exhaust gases components caused by fuel additives.
Using the least squares method, the equivalence of conclusions achieved in this model as well as using four other alternative methods was shown:
  1. by hypotheses selection method in the linear model,
  2. by restriction selection method to  the linear model,
  3. by the method of selection of invariant linearly sufficient transformations,
  4. by the weight-selection method in the weighted variance analysis of the linear model.
The alternative methods are necessary when calculation problems occur in the nonlinear initial model.
Moreover, we catalogued a number of additional nonlinear models for groups in the form of composite function with one common internal function and several external functions. The determined diagrams of internal functions correspond to the changes of the exhaust gases emission or fuel consumption under the influence of the random effective power of the engine. On the other hand, the visualisation based in most cases on linear external functions allows to determine absolute and relative changes to the power and ecological parameters of the tractor engine which result exclusively from the use of biofuels. In this way the conclusions regarding the changes to the value of parameters and power and ecological indicators of the tractor engine resulting from the use of biofuels, formulated using new statistical procedures, are separated from the conclusions regarding the influence of the engine effective power on their values.
The procedures suggested in the work allow a wider interpretation of the results achieved by other authors and may be adopted on a wider scale not only in technology or agriculture. These new methods can be used both in the situations, when the measurements can be carried out both for determined and not determined values of the engine effective power, they can be also of use in the case of the lack of observation – based data and they add to reduction of the number of absolutely necessary measurements.
The results obtained indicate the low cost effectiveness of using low percentage mixtures of RME with diesel oil in case of persistent high purchase costs.
In this work the possibilities of use of available statistical packages SAS and Statistica as well as new Visual Basic calculation procedures for Applications in Microsoft Excel were presented for the needs of the analysis.