Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

A Simplified Model-Based State-of-Charge Estimation Approach for Lithium-Ion Battery With Dynamic Linear Model

Abstract: The performance of model-based state-of-charge (SOC) estimation method relies on an accurate battery model. Nonlinear models are thus proposed to accurately describe the external characteristics of the lithium-ion battery. The nonlinear estimation algorithms and online parameter identification methods are needed to guarantee the accuracy of the model-based SOC estimation with nonlinear battery models. A new approach forming a dynamic linear battery model is proposed in this paper, which enables the application of the linear Kalman filter for SOC estimation and also avoids the usage of online parameter identification methods. With a moving window technology, partial least squares regression is able to establish a series of piecewise linear battery models automatically. One element state-space equation is then obtained to estimate the SOC from the linear Kalman filter. The experiments on a LiFePO4 battery prove the effectiveness of the proposed method compared with the extended Kalman filter with two resistance and capacitance equivalent circuit model and the adaptive unscented Kalman filter with least squares support vector machines.

A greedy Delaunay-based surface reconstruction algorithm

Abstract: In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.

Adaptive multilevel methods for obstacle problems

Abstract: The authors consider the discretization of obstacle problems for second-order elliptic differential operators by piecewise linear finite elements. Assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies, the linear problems are solved iteratively by preconditioned conjugate gradient iterations. The proposed preconditioners are treated theoretically as abstract additive Schwarz methods and are implemented as truncated hierarchical basis preconditioners. To allow for local mesh refinement semilocal and local a posteriors error estimates are derived, providing lower and upper estimates for the discretization error. The theoretical results are illustrated by numerical computations.

Computational Comparison of Piecewise−Linear Relaxations for Pooling Problems

Abstract: This work discusses alternative relaxation schemes for the pooling problem, a theoretically and practically interesting optimization problem. The problem nonconvexities appear in the form of bilinear terms and can be addressed with the relaxation technique based on the bilinear convex and concave envelopes. We explore ways to improve the relaxation tightness, and thus the efficiency of a global optimization algorithm, by employing a piecewise linearization scheme that partitions the original domain of the variables involved and applies the principles of bilinear relaxation for each one of the resulting subdomains. We employ 15 different piecewise relaxation schemes with mixed-integer representations and conduct a comprehensive computational comparison study over a collection of benchmark pooling problems. For each case, various partitioning variants can be envisioned, cumulatively accounting for a total of 56 700 relaxations. The results demonstrate that some of the schemes are clearly superior to their c...

The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications

Abstract: This paper studies applications of envelopes of piecewise linear functions to problems in computational geometry. Among these applications we find problems involving hidden line/surface elimination, motion planning, transversals of polytopes, and a new type of Voronoi diagram for clusters of points. All results are either combinatorial or computational in nature. They are based on the combinatorial analysis in two companion papers [PS] and [E2] and a divide-and-conquer algorithm for computing envelopes described in this paper.