http://swrc.ontoware.org/ontology#Thesis
Adjustment of Sampling Locations in Rail-Geometry Datasets with Dynamic Programming and Non-Linear Filtering
en
神山 雅子
カミヤマ マサコ
KAMIYAMA Masako
総研大甲第740号
The major purpose of this thesis is to adjust sampling locations in two rail-geometry datasets obtained by track-inspection cars. A special rolling stock called a track-inspection car periodically measures rail geometry in order to monitor rail geometry. This is because the railway track plays an important role in ensuring running safety of the trains and riding comfort of the passengers. Thus, railway companies must maintain the quality of their tracks against wear, tear, and so forth caused by the loads of the passing trains. <br /> A track-inspection car continuously measures various aspects of rail geometry while running on the rails. These geometric measurements are simultaneously discretized at fixed spatial intervals, and are recorded as digital datasets. The set of their discretized locations on the rail changes slightly with each measurement although it is desirable that these locations be fixed in order to observe variations in rail geometry. This location gaps are based on the fact that the wheel-rotation pulse that is used to select the discretized locations is linked to the rotation of the car wheel. Thus, identical spatial discretization cannot be reproduced. Moreover, it is difficult to adjust these location gaps after the discretization. If the spatial intervals(called sampling intervals) between the discretized locations stay constant in two measuring runs, these gaps could be easily adjusted by calculating the correlation coefficient distance between the two datasets, even if the locations themselves change. In reality, however, some sampling intervals shorten or lengthen locally due to slipping or sliding of the car wheel, respectively. In addition, the length and location of these locally irregular intervals cannot be detected unfortunately. This makes it difficult to adjust the location gaps. <br /> In this thesis a procedure is proposed to adjust the sampling locations in one spatially discretized dataset to the sampling locations in another when the differences between these sets are mainly caused by the sampling intervals that locally lengthen and shorten. This adjustment is formulated as an optimization problem that can be efficiently solved by dynamic programming. This formulation contains a few hyperparameters which are usually tuned by manual. Here these hyperparameters are identified automatically by using the Bayesian framework. <br /> The developed procedure is described in more detail as follows. First, the adjustment problem is formulated as an alignment problem between the reference dataset and the misregistered dataset. Then the alignment problem is reformulated as an optimization problem which can be solved efficiently with dynamic programming. <br /> Then, a Bayesian framework is introduced to determine the hyperparameters automatically. This idea is based on the observation that the optimal solution in dinamic programming is interpreted as the maximum a posteriori (MAP) estimate in a certain Bayesian model with the specific values of the hyperperparameters. With this framework, the hyperparameters are estimated with the maximum likelihood procedure for the associated Bayes model by employing the non-linear filtering procedure for a generalized state-space model. <br /> This approach appears to work reasonably well in detecting sliping and sliding of the wheels in view of the MAP estimate. But by taking a closer look, it turned out that the procedure gives unsatisfactory results in view of the smoothing (predictive)distribution of the adjusted data points. <br /> In order to resolve this problem, a refined Bayesian model is introduced. The hyperparameters in this model are classified into two categories: the one representing the state of the wheel rotation, and the other representing the noise from the measuring device which is formulated as AR model. When all parameters are simultaneously estimated with the maximum likelihood procedure, the results indicated that too many slippng or sliding occurred in the misregistered dataset than expected. To overcome this difficulty, a procedure is developed that estimates the noise parameters directly from the difference sequence between the reference and the roughly adjusted sets. This procedure alternatively identifies the wheel rotation and the noise parameters until the internal inconsistency incurred in the model is eliminated. Plausibility of the smoothing distribution of the adjusted data points obtained with this procedure is demonstrated through application to real datasets.