§ 1065.1139 Aging cycle generation.
Generation of the accelerated aging cycle for a given application involves analysis of the field data to determine a set of aging modes that will represent that field operation. There are two methods of cycle generation, each of which is described separately below. Method 1 involves the direct application of field data and is used when the recorded data includes sufficient exhaust flow and temperature data to allow for determination of aging conditions directly from the field data set and must be available for all of the key components. Method 2 is meant to be used when insufficient flow and temperature data is available from the field data. In Method 2, the field data is used to weight a set of modes derived from the laboratory certification cycles for a given application. These weighted modes are then combined with laboratory recorded flow and temperatures on the certification cycles to derive aging modes. There are two different cases to consider for aging cycle generation, depending on whether or not a given aftertreatment system incorporates the use of a periodic regeneration event. For the purposes of this section, a “regeneration” is any event where the operating temperature of some part of the aftertreatment system is raised beyond levels that are observed during normal (non-regeneration) operation. The analysis of regeneration data is considered separately from normal operating data.
(a) Cycle generation process overview. The process of cycle generation begins with the determination of the number of bench aging hours. The input into this calculation is the number of real or field hours that represent the useful life for the target application. This could be given as a number of hours or miles, and for miles, the manufacturer must use field data and good engineering judgment to translate this to an equivalent number of operating hours for the target application. The target for the accelerated aging protocol is a 10-time acceleration of the aging process, therefore the total number of aging hours is always set at useful life hours divided by 10. For example, if an on-highway heavy duty engine has a full useful life of 750,000 miles and this is determined to be represented by 24,150 field hours, the target duration for the DAAAC protocol for this application would be 2,415 bench-aging hours. The 2,415 hours will then be divided among different operating modes that will be arranged to result in repetitive temperature cycling over that period. For systems that incorporate periodic regeneration, the total duration will be split between regeneration and normal (non-regeneration) operation. The analysis of normal operation data is given in paragraph (b) of this section. The analysis of regeneration data is given in paragraph (c) of this section.
(b) Analysis of normal (non-regeneration) operating data. This analysis develops a reduced set of aging modes that represent normal operation. As noted earlier, there are two methods for conducting this analysis, based on the data available.
(1) Method 1—Direct clustering. Use Method 1 when sufficient exhaust flow and temperature data are available directly from the field data. The data requirements for Method 1 are described in § 1065.1133(b)(1). The method involves three steps: clustering analysis, mode consolidation, and cycle building.
(i) The primary method for determining modes from a field data set involves the use of k-means clustering. K-means clustering is a method where a series of observations is partitioned into set of clusters of “similar” data points, where every observation is a member of a cluster with the nearest mean, which is referred to as the centroid of that cluster. The number of clusters is a parameter of the analysis, and the k-means algorithm generally seeks an optimal number of clusters to minimize the least-squares distance of all points to their respective centroids. There are a number of different commercially available software programs to perform k-means clustering, as well as freely available algorithm codes. K-means clustering can arrive at many different solutions, and we are providing the following guidance to help select the optimal solution for use in accelerated aging cycle generation. The process involves analyzing the data multiple time using an increasing number of clusters for each analysis. Use at least 5 clusters, and we recommend developing solutions for the range between 5 and 8 clusters, although you may use more if desired. Each cluster is a potential aging mode with a temperature and flow rate defined by the centroid. More clusters result in more aging modes, although this number may be reduced later via model consolidation.
(ii) The cubic clustering criteria (CCC) is a metric calculated for each solution having a different number of clusters. The computation of CCC is complex and described in more detail in the following reference. The CCC computation is normally available as one of the metrics in commercially available software packages that can be used for k-means clustering. The optimal solution is typically the one with the number of clusters corresponding to the highest CCC.
(iii) Check each solution, starting with the one with the highest CCC to determine if it satisfies the following requirements:
(A) No more than one cluster contains fewer than 3% of the data points.
(B) The temperature ratio between the centroid with the maximum temperature and the centroid with the minimum temperature is at least 1.6 for clusters containing more than 3% of the data points.
(C) If that solution does not satisfy these requirements move to the solution with the next highest CCC.