Global Sensitivity Analysis for Vehicle–Track Interactions: Special Attention on Track Irregularities

The dynamic vehicle–track interactions are complex processes due to the highly nonlinear terms and spatially varying excitations in vehicle design, track maintenance, dynamic prediction, etc. Therefore, it is of importance to clarify the key factors affecting the dynamic behaviors of system components. In this paper, a comprehensive model is presented, which is capable of analyzing the global sensitivity of vehicle–track interactions. In this model, the vehicle–track interactions considering the nonlinear wheel–rail contact geometries are depicted in three-dimensional (3D) space, and then the approaches for global sensitivity analysis (GSA) and time–frequency analysis are combined with the dynamic model. In comparison to the local sensitivity analysis, the proposed model has accounted for the coupling contributions of various factors. Thus, it is far more accurate and reliable to evaluate the critical factors dominating the vehicle–track interactions. Based on the methods developed in the present study, numerical examples have been conducted to draw the following marks: track irregularities possess the dominant role in guiding the dynamic performance of vehicle–track systems, besides, the vertical stiffness of primary suspension and rail pads also shows significant influence on vertical acceleration of the car body and the wheel–rail vertical force, respectively. Finally, a method is developed to precisely extract the characteristic wavelengths and amplitude limits of track irregularities.

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Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

10.5194/egusphere-egu21-6131 ◽

2021 ◽

Author(s):

Sabine M. Spiessl ◽

Dirk-A. Becker ◽

Sergei Kucherenko

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Higher Order ◽

Model Parameters ◽

High Dimensional Model Representation ◽

Model Output ◽

Global Sensitivity ◽

Sparse Polynomial ◽

Sensitivity Indices ◽

Highly Nonlinear

Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.

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Global Sensitivity Analysis of Leaf-Canopy-Atmosphere RTMs: Implications for Biophysical Variables Retrieval from Top-of-Atmosphere Radiance Data

Remote Sensing ◽

10.3390/rs11161923 ◽

2019 ◽

Vol 11 (16) ◽

pp. 1923 ◽

Cited By ~ 6

Author(s):

Jochem Verrelst ◽

Jorge Vicent ◽

Juan Pablo Rivera-Caicedo ◽

Maria Lumbierres ◽

Pablo Morcillo-Pallarés ◽

...

Keyword(s):

Sensitivity Analysis ◽

Concept Maps ◽

Global Sensitivity Analysis ◽

Dominant Role ◽

Atmospheric Correction ◽

Total Contribution ◽

Area Index ◽

Global Sensitivity ◽

Radiance Data ◽

Leaf Canopy

Knowledge of key variables driving the top of the atmosphere (TOA) radiance over a vegetated surface is an important step to derive biophysical variables from TOA radiance data, e.g., as observed by an optical satellite. Coupled leaf-canopy-atmosphere Radiative Transfer Models (RTMs) allow linking vegetation variables directly to the at-sensor TOA radiance measured. Global Sensitivity Analysis (GSA) of RTMs enables the computation of the total contribution of each input variable to the output variance. We determined the impacts of the leaf-canopy-atmosphere variables into TOA radiance using the GSA to gain insights into retrievable variables. The leaf and canopy RTM PROSAIL was coupled with the atmospheric RTM MODTRAN5. Because of MODTRAN’s computational burden and GSA’s demand for many simulations, we first developed a surrogate statistical learning model, i.e., an emulator, that allows approximating RTM outputs through a machine learning algorithm with low computation time. A Gaussian process regression (GPR) emulator was used to reproduce lookup tables of TOA radiance as a function of 12 input variables with relative errors of 2.4%. GSA total sensitivity results quantified the driving variables of emulated TOA radiance along the 400–2500 nm spectral range at 15 cm − 1 (between 0.3–9 nm); overall, the vegetation variables play a more dominant role than atmospheric variables. This suggests the possibility to retrieve biophysical variables directly from at-sensor TOA radiance data. Particularly promising are leaf chlorophyll content, leaf water thickness and leaf area index, as these variables are the most important drivers in governing TOA radiance outside the water absorption regions. A software framework was developed to facilitate the development of retrieval models from at-sensor TOA radiance data. As a proof of concept, maps of these biophysical variables have been generated for both TOA (L1C) and bottom-of-atmosphere (L2A) Sentinel-2 data by means of a hybrid retrieval scheme, i.e., training GPR retrieval algorithms using the RTM simulations. Obtained maps from L1C vs L2A data are consistent, suggesting that vegetation properties can be directly retrieved from TOA radiance data given a cloud-free sky, thus without the need of an atmospheric correction.

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