Adaptive Polynomial Approximation Research Articles

Multi‐objectives optimization of parameter design for LLC converter based on data‐driven surrogate model

AbstractDue to high computation complexity, traditional design methods for LLC converter usually consider limited kinds of performance, and the process for searching the optimal parameter scheme is discrete, which might cause the missing of real optimal solution. In order to solve these problems, a multi‐objectives optimization design method for the LLC converter is proposed in this paper. According to the numerical calculation method, a closed parameter space for resonant parameters is established under the constraints of operation mode, switching frequency, zero voltage switching (ZVS), and voltage stress of resonant capacitor. Besides, the root‐mean‐square (RMS) value of resonant current and secondary current, as well as the core loss of the transformer, are selected as the optimization objectives. Non‐dominated sorting genetic algorithm (NSGA‐II) is utilized to deal with these multi‐objective formulations. In order to reduce the computation complexity, a data‐driven method, called adaptive polynomial approximation (APA), is selected to obtain the explicit expressions of the parameter space and the optimization objectives. Then, by substituting this simplified surrogate model into the NSGA‐II algorithm, the optimal parameter scheme is obtained. The comprehensive comparison analysis is performed, and a 400 W/48 V experimental prototype was built to verify the theoretical analysis, which shows that the proposed method features the highest efficiency of 95%.

Numerical simulation acceleration of flat-chip solid oxide cell stacks by data-driven surrogate cell submodels

Three-dimensional (3D) multiphysics models are powerful tools for investigating the distributions of physical quantities such as temperature inside solid oxide cell (SOC) stacks, but their high computational cost remains an obstacle to their application in simulating industrial-scale stacks with tens of cells. To accelerate the simulation for the 3D model of a novel flat-chip SOC (FCSOC) stack, this study proposes a simplification method that replaces part of the governing equations with data-driven surrogate cell submodels. The submodels, built with the adaptive polynomial approximation (APA) method, take the form of polynomials and are easy to integrate into commercial CFD software such as COMSOL. Simulation shows that the simplified stack model can predict the temperatures and voltages accurately compared with the original stack model. At the same time, the time and memory required for computation are reduced by approximately 60% for a short stack model containing seven cells, owing to the simplified fuel-side mass transfer and charge transfer processes. For a large stack model with 21 cells, the reduction in computation time can even exceed 70%. The reduced computational cost makes it possible to simulate the models of industrial-scale FCSOC stacks with up to 61 cells.

A robust surrogate model of a solid oxide cell based on an adaptive polynomial approximation method

Surrogate models that predict the behaviors of solid oxide cells (SOCs) accurately at low computational cost are crucial to the control and optimization of SOC plants. Lumped physical models of SOCs, while widely used in such applications, lack accuracy because of neglected physical details. Data-driven models are the other options of surrogate models, which are proved to be more accurate because these models are identified directly from experiments or numerical simulations. However, due to the time cost of experiments and numerical simulations of SOCs, it is hoped that data-driven models can be constructed from a minimum amount of data. Also, the trained data-driven models should be robust, in other words, insensitive to the data set as well as the initial settings. These requirements are hard to be achieved by existing data-driven models of SOCs, such as lookup tables and artificial neural networks (ANNs). Aiming to preserve robustness and reduce the required amount of data, this paper introduces an adaptive polynomial approximation (APA) method, which is derived from the latest findings of numerical computation science, to the surrogate modeling of SOCs. The obtained models by the APA method are validated by both experiments and simulations. By analyzing the models, the coupling relationship among operating parameters of SOCs is revealed. The physical interpretability makes the APA method distinctive from common data-driven modeling methods. Performance comparison shows that the APA method is more accurate and robust than the existing ones with similar sampling costs. Additionally, the APA method can control the accuracy of the model by setting an error criterion in the algorithm iteration, endowing the APA method with an error control ability as per different accuracy requirements for SOC modeling.

Adaptive Polynomial Approximation to Circular Arcs

We present a new adaptive method for approximating circular arcs in polynomial form by using the s-power series. Circular arcs can be expressed in infinite series form, we obtain the order-k Hermite interpolant by truncating at the kth term. An upper bound on the error of the interpolant is available, so we can obtain the lowest degree polynomial curve that approximates a circular arc within any user-prescribed tolerance. And this degree can be further reduced through subdivision, which generates a spline approximation with Ck continuity at the joints.

Application of Lobatto polynomials in atomic physics

The approximation properties of Lobatto polynomials are analyzed and then applied to approximate the atomic Kohn–Sham eigenfunction. In the first part of this article the approximation algorithm based on the Galerkin finite element method is derived. To obtain the approximation of the function, based on the presented algorithm, the linear set of equations must be solved. The matrix of the equation set is very sparse and its elements can be evaluated analytically. In the second part of this article, the algorithm is applied to evaluate adaptive polynomial approximation of selected Kohn–Sham eigenstates of indium (In) atom. The proposed r-adaptive algorithm evaluates the minimum number of subintervals needed to represent the eigenfunction with required accuracy. Based on the r-adaptive algorithm, the approximations of 4d, 5s 5p In eigenfunctions were calculated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010