Are Chebyshev-based stability analysis and Urabe’s error bound useful features for Harmonic Balance?
نویسندگان
چکیده
Harmonic Balance is one of the most popular methods for computing periodic solutions nonlinear dynamical systems. In this work, we address two its major shortcomings: First, investigate to what extent computational burden stability analysis can be reduced by consistent use Chebyshev polynomials. Second, problem a rigorous error bound, which, authors' knowledge, has been ignored in all engineering applications so far. Here, rely on Urabe's bound and, again, polynomials computationally involved operations. We estimate automatically adjust harmonic truncation order during numerical continuation, and confront algorithm with state-of-the-art adaptive implementation. Further, rigorously prove, first time, existence some isolated forced-damped Duffing oscillator softening characteristic. find that effort obtaining present form, may too high useful many problems. Based results obtained sequence examples, conclude Chebyshev-based indeed permits substantial speedup. Like itself, however, method becomes inefficient when an extremely needed as, e.g., presence (sharply regularized) discontinuities.
منابع مشابه
Are Word Embedding-based Features Useful for Sarcasm Detection?
This paper makes a simple increment to state-ofthe-art in sarcasm detection research. Existing approaches are unable to capture subtle forms of context incongruity which lies at the heart of sarcasm. We explore if prior work can be enhanced using semantic similarity/discordance between word embeddings. We augment word embedding-based features to four feature sets reported in the past. We also e...
متن کاملCoupled Harmonic Equations , SOR , and Chebyshev Acceleration
A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely imaginary (or zero) eigenvalues. Comparison is made with a block SOR method used to solve the same problem. Introduction. In [4], we proposed a general block SOR method for solving the biharmonic equa...
متن کاملAnalysis of Stability and Bifurcations of Limit Cycles in Chua’s Circuit Through the Harmonic-Balance Approach
This paper presents a spectral approach, based on the harmonic-balance technique, for detecting limit-cycle bifurcations in complex nonlinear circuits. The key step of the proposed approach is a method for a simple and effective computation of the Floquet multipliers (FM’s) that yield stability and bifurcation conditions. As a case-study, a quite complex system, Chua’s circuit, is considered. I...
متن کاملWhat Kinds of Relational Features Are Useful for Statistical Learning?
A workmanlike, but nevertheless very effective combination of statistical and relational learning uses a statistical learner to construct models with features identified (quite often, separately) by a relational learner. This form of model-building has a long history in Inductive Logic Programming (ILP), with roots in the early 1990s with the LINUS system. Additional work has also been done in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mechanical Systems and Signal Processing
سال: 2023
ISSN: ['1096-1216', '0888-3270']
DOI: https://doi.org/10.1016/j.ymssp.2023.110265