Parsimonious statistical learning models for low-flow estimation

Statistical learning methods offer a promising approach for low-flow regionalization. We examine seven statistical learning models (Lasso, linear, and nonlinear-model-based boosting, sparse partial least squares, principal component regression, random forest, and support vector regression) for the prediction of winter and summer low flow based on a hydrologically diverse dataset of 260 catchments in Austria. In order to produce sparse models, we adapt the recursive feature elimination for variable preselection and propose using three different variable ranking methods (conditional forest, Lasso, and linear model-based boosting) for each of the prediction models. Results are evaluated for the low-flow characteristic Q95 (Pr(Q>Q95)=0.95) standardized by catchment area using a repeated nested cross-validation scheme. We found a generally high prediction accuracy for winter (RCV2 of 0.66 to 0.7) and summer (RCV2 of 0.83 to 0.86). The models perform similarly to or slightly better than a top-kriging model that constitutes the current benchmark for the study area. The best-performing models are support vector regression (winter) and nonlinear model-based boosting (summer), but linear models exhibit similar prediction accuracy. The use of variable preselection can significantly reduce the complexity of all the models with only a small loss of performance. The so-obtained learning models are more parsimonious and thus easier to interpret and more robust when predicting at ungauged sites. A direct comparison of linear and nonlinear models reveals that nonlinear processes can be sufficiently captured by linear learning models, so there is no need to use more complex models or to add nonlinear effects. When performing low-flow regionalization in a seasonal climate, the temporal stratification into summer and winter low flows was shown to increase the predictive performance of all learning models, offering an alternative to catchment grouping that is recommended otherwise.

Development of a Simplified PWR Fuel Assembly Nonlinear Model

This paper proposes a computation technique to develop a simplified nonlinear model for a typical nuclear fuel assembly. Because more than a hundred fuel assemblies are packed in the reactor, simplistic model generation is critical to evaluate the motion during an anticipated event such as earthquake. Two straight beams are introduced to simplify the fuel assembly, and the beam properties are moderately defined to represent the skeleton structure and a bundle of slender fuel rods. Because nonlinearity is caused by the interaction between the rods and the spacer grids in the skeleton structure, the two beams are connected with multilinear joints that characterize the mechanical interaction between them. An equation of motion for the model is provided, and the degree of the freedom of the model can be reduced by using a few major modes of the beams. Significant mechanical parameters must be defined reasonably, so a method is proposed to identify unknown parameters through a deterministic calculation and an optimization process. All the information, including the identified parameters, are utilized to develop a nonlinear finite element model with a commercial code. The performance of the model is compared with the test results.

Analytical Solving a Nonlinear Model of the Glow Discharge

A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.