Topic
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.
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58 citations
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TL;DR: In this article, the authors presented an alternative approach to evaluate the frequency coupling matrix (FCM) based on a time-domain derivation, which avoids truncation of the harmonic representation of signals.
Abstract: When a power-electronic converter is introduced into a linear network, voltage and current harmonics of differing orders become coupled (through the modulation effect of the converter). The interharmonic coupling introduced by the modulation effect of a converter may be mathematically represented through a frequency coupling matrix (FCM). Given that the source of the coupling is a modulation process, researchers have, in the past, focused on deriving the FCM in the frequency domain - a process that requires the truncation of the harmonic representation of signals. This paper presents an alternate approach to evaluate the FCM based on a time-domain derivation. In contrast to frequency-domain-based methods, it is shown that the time-domain approach avoids truncation. Furthermore, the time-domain approach does not require system linearization about an operating point; thus, the FCM is not limited by small-signal assumptions.
58 citations
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TL;DR: The piecewise-linear simplex algorithm is observed to run 2–6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program.
Abstract: The first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise-linear functions subject to linear constraints. This concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program. The advantages are shown to be implicit in relationships between the linear and piecewise-linear algorithms, and to be independent of many details of implementation. Two sets of computational results serve to illustarate these arguments; the piecewise-linear simplex algorithm is observed to run 2–6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program. Further support for the practical value of a good piecewise-linear programming algorithm is provided by a survey of many varied applications.
58 citations
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TL;DR: In this paper, the authors studied limit cycle bifurcations for a kind of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop around the origin.
Abstract: In this paper, we study limit cycle bifurcations for a kind of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop around the origin. By using the first Melnikov function of piecewise near-Hamiltonian systems, we give lower bounds of the maximal number of limit cycles in Hopf and homoclnic bifurcations, and derive an upper bound of the number of limit cycles that bifurcate from the periodic annulus between the center and the homoclinic loop up to the first order in. In the case when the degree of perturbing terms is low, we obtain a precise result on the number of zeros of the first Melnikov function.
58 citations
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TL;DR: In this article, a piecewise linear approximation of realistic force-deformation capacity curves is investigated for structural systems incorporating generalized plastic, hard-ening, and negative stiffness behaviors, and the error is quantified by studyin g it at the single-degree-of-freedom level.
Abstract: analysis. Abstract. The piecewise linear ("multilinear") approximation of realistic force-deformation capacity curves is investigated for structural syst ems incorporating generalized plastic, hard- ening, and negative stiffness behaviors. This fitti ng process factually links capacity and de- mand and lies at the core of nonlinear static asses sment procedures. Despite codification, the various fitting rules used can produce highly heter ogeneous results for the same capacity curve, especially for the highly-curved backbones rfrom the gradual plasticization or the progressive failures of structural elements. To achieve an improved fit, the error intro- duced by the approximation is quantified by studyin g it at the single-degree-of-freedom level, thus avoiding any issues related to multi- versus s ingle-degree-of-freedom realizations. In- cremental Dynamic Analysis is employed to enable a direct comparison of the actual back- bones versus their candidate piecewise linear appro ximations in terms of the spectral acceleration capacity for a continuum of limit-stat es. In all cases, current code-based proce- dures are found to be highly biased wherever widesp read significant stiffness changes occur, generally leading to very conservative estimates of performance. The practical rules deter- mined allow, instead, the definition of standardize d low-bias bilinear, trilinear, or quadrilin- ear approximations, regardless of the details of th e capacity curve shape.
58 citations