Conversion of one or several relevant driving cycles to stationary operating points is a fundamental step at the beginning of each test bench calibration. Compliance with certification limits while minimizing CO2-emission can be met if these stationary operating points are optimized. The substitute operating point can be placed in frequently occurring operating conditions of the driving cycle, such as sections with constant vehicle speed. A better approach is to place the substitute operating points automatically using an appropriate algorithm. In this article an algorithm for robust and automatic placement of stationary substitute operating points is presented. The algorithm is based on the k-means procedure for cluster detection. Modifications of this algorithm are proposed enabling boundary conditions during cluster detection. Basic engine physics of the combustion engine require adherence of these boundary conditions, such as conservation of energy of the certification cycle and its stationary substitute operating points. To demonstrate the algorithm's performance, fuel consumption forecasts using substitute operating points defined by different placement strategies are compared. Separation of the effects of placement from other influences is ensured throughout the comparison. A cluster is a set of points in some data space sharing some common attribute. This attribute is expressed either by a measure of similarity or dissimilarity. A measure for dissimilarity is the distance between two points: A small value indicates proximity, a large value spatial distance between them. Cluster analysis using the k-means algorithm optimizes a sum of distances. The distances between each individual point x and respective cluster point q are summed up. A cluster point q itself is the center point of all associated cycle points. From a mathematical point of view, two calculation steps are required: (1) Calculation of distance between individual cycle points and cluster center, or in general between 2 points. The distance is used for assigning the closest cluster center. (2) Calculation of a center of a set of individual cycle points. The center minimizes the sum of distances. This step will update the cluster center if associated cycle points have changed.The k-means process is a fast and robust algorithm for clustering. It is highly useful for substituting a transient test cycle with a limited number of stationary operating points. These stationary operating points are that calibrated using for example a cycle fuel consumption prediction based on DoE models. The placement of the substitute operating points must be performed using some measure of optimality and incorporating boundary conditions. The newly developed extended k-means process allows the definition of boundary conditions The article describes the calculation steps in detail. The algorithm for clustering with boundary conditions is formulated in a general way and presented using energy conservation as an example. The analysis of practical examples deepens the understanding and demonstrates the capability of the algorithm. The process was developed in close cooperation with the users. For deployment purposes a tool was developed which combines preparation steps such as data filtering and post processing steps such as detailed exports in one graphical user interface.


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    Titel :

    Cluster analysis using an extended k-means process


    Beteiligte:


    Erscheinungsdatum :

    2011


    Format / Umfang :

    22 Seiten, 20 Bilder, 6 Quellen



    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Print


    Sprache :

    Englisch