<p>New emission legislations introduced in the European Union and the U.S. have made truck manufacturers face stricter requirements for low emissions and on-board diagnostic systems. The on-board diagnostic system typically consists of several tests that are run when the truck is driving. One way to construct such tests is to use so called consistency relations. A consistency relation is a relation with known variables that in the fault free case always holds. Calculation of a consistency relation typically involves eliminating unknown variables from a set of equations.</p><p>To eliminate variables from a differential polynomial system, methods from differential algebra can be used. In this thesis, the purely algebraic Gröbner basis algorithm and the differential Rosenfeld-Gröbner algorithm implemented in the Maple package Diffalg have been compared and evaluated. The conclusion drawn is that there are no significant differences between the methods. However, since using Gröbner basis requires differentiations to be made in advance, the recommendation is to use the Rosenfeld-Gröbner algorithm.</p><p>Further, attempts to calculate consistency relations using the Rosenfeld-Gröbner algorithm have been made to a real application, a model of a Scania diesel engine. These attempts did not yield any successful results. It was only possible to calculate one consistency relation. This can be explained by the high complexity of the model.</p>

New emission legislations introduced in the European Union and the U.S. have made truck manufacturers face stricter requirements for low emissions and on-board diagnostic systems. The on-board diagnostic system typically consists of several tests that are run when the truck is driving. One way to construct such tests is to use so called consistency relations. A consistency relation is a relation with known variables that in the fault free case always holds. Calculation of a consistency relation typically involves eliminating unknown variables from a set of equations. To eliminate variables from a differential polynomial system, methods from differential algebra can be used. In this thesis, the purely algebraic Gröbner basis algorithm and the differential Rosenfeld-Gröbner algorithm implemented in the Maple package Diffalg have been compared and evaluated. The conclusion drawn is that there are no significant differences between the methods. However, since using Gröbner basis requires differentiations to be made in advance, the recommendation is to use the Rosenfeld-Gröbner algorithm. Further, attempts to calculate consistency relations using the Rosenfeld-Gröbner algorithm have been made to a real application, a model of a Scania diesel engine. These attempts did not yield any successful results. It was only possible to calculate one consistency relation. This can be explained by the high complexity of the model.