The analysis of the noise of a system is often an effective way for obtaining information about its internal dynamics. In this article, an analysis of the variance of the noise on the power load curve of the Swiss railway system guides us towards the detection of a multimodality in the distribution of punctualities. This multimodality is regarded as a strong indicator for a dynamics with multiple, possibly self-organized, regimes. The presence of multiple regimes in the dynamics is of relevance for the design of control strategies. Based on information about the operation of the Swiss regular interval time table, we suggest and apply a simple way for identifying the part of the load signal that can be regarded as noise and we demonstrate the use of Hartigan's dip test for the identification of multimodalities in the distribution of random variables.

Safe transportation of hazardous materials by rail is an important issue in Switzerland. This study analyzes an existing model for the risk of transport of hazardous materials via Swiss railways, in collaboration with the Swiss Federal Office for the Environment. The model is the basis for the risk calculation of hazards for persons for all railway transports of hazardous materials in Switzerland and is published by the Swiss Federal Office of Transport. It includes 155 input variables estimated with different uncertainties. The objective of this study is to determine which input variables possess the strongest influence on the model output (the risk) and should therefore be determined with higher accuracy. To achieve this objective, different sensitivity analysis methods as suggested by Borgonovo are compared. The risk model is implemented in Maple and the Sobol decomposition is used for a global sensitivity analysis of the input variables. The Sobol method is a variance-based sensitivity analysis that decomposes the variance of the output of the model into contributions due to input variables or sets of input variables. The Sobol indices are calculated analytically by evaluating various integrals in the decomposition. In addition, the stability of the method is investigated by using different ranges of the input variables. As a first cross check, the partial derivatives of all input variables are calculated for the same model. As a second cross check, an independent analysis in Matlab is carried out, based on Monte Carlo simulation of the input variables within their uncertainty range. The results are stable and consistent among all methods and will be used by the Swiss Federal Office for the Environment to optimize the estimation of the input variables of this risk model.