The reproducibility of facial approximation accuracy results generated from photo-spread tests

<p>1D-3D methods are used to describe root water and nutrient uptake in complex root networks. Root systems are described as networks of line segments embedded in a three-dimensional soil domain. Particularly for dry soils, local water pressure and nutrient concentration gradients can be become very large in the vicinity of roots. Commonly used discretization lengths (for example 1cm) in root-soil interaction models do not allow to capture these gradients accurately. We present a new numerical scheme for approximating root-soil interface fluxes. The scheme is formulated in the continuous PDE setting so that is it formally independent of the spatial discretization scheme (e.g. FVM, FD, FEM). The interface flux approximation is based on a reconstruction of interface quantities using local analytical solutions of the steady-rate Richards equation. The local mass exchange is numerically distributed in the vicinity of the root. The distribution results in a regularization of the soil pressure solution which is easier to approximate numerically. This technique allows for coarser grid resolutions while maintaining approximation accuracy. The new scheme is verified numerically against analytical solutions for simplified cases. We also explore limitations and possible errors in the flux approximation with numerical test cases. Finally, we present the results of a recently published benchmark case using this new method.</p>

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Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

Journal of Circuits System and Computers ◽

10.1142/s0218126619500683 ◽

2019 ◽

Vol 28 (04) ◽

pp. 1950068 ◽

Cited By ~ 2

Author(s):

Tian-Bo Deng

Keyword(s):

Stability Margin ◽

Transformation Method ◽

Second Order ◽

Approximation Accuracy ◽

Parameter Transformation ◽

Practical Applications ◽

Compensator Design ◽

Novel Method ◽

Design Idea ◽

The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

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A Robust AdaBoost.RT Based Ensemble Extreme Learning Machine

Mathematical Problems in Engineering ◽

10.1155/2015/260970 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Pengbo Zhang ◽

Zhixin Yang

Keyword(s):

Extreme Learning Machine ◽

Learning Algorithm ◽

Approximation Accuracy ◽

Weak Learner ◽

Fast Learning ◽

Learning Speed ◽

Regression Problems ◽

Learning Machine ◽

The Stability ◽

Stability And Accuracy

Extreme learning machine (ELM) has been well recognized as an effective learning algorithm with extremely fast learning speed and high generalization performance. However, to deal with the regression applications involving big data, the stability and accuracy of ELM shall be further enhanced. In this paper, a new hybrid machine learning method called robust AdaBoost.RT based ensemble ELM (RAE-ELM) for regression problems is proposed, which combined ELM with the novel robust AdaBoost.RT algorithm to achieve better approximation accuracy than using only single ELM network. The robust threshold for each weak learner will be adaptive according to the weak learner’s performance on the corresponding problem dataset. Therefore, RAE-ELM could output the final hypotheses in optimally weighted ensemble of weak learners. On the other hand, ELM is a quick learner with high regression performance, which makes it a good candidate of “weak” learners. We prove that the empirical error of the RAE-ELM is within a significantly superior bound. The experimental verification has shown that the proposed RAE-ELM outperforms other state-of-the-art algorithms on many real-world regression problems.

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