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A Getz-Masden dynamic system 2 (GMDS2) is investigated in this paper. For the purpose of solving time-varying complex matrix inverse, we propose a TZ-type (i.e., Taylor-Zhang type) discrete Getz-Masden dynamic system 2; i.e., the proposed TZ-type discrete Getz-Masden dynamic system 2 is discretized by Taylor-Zhang discretization formula. The results of numerical experiments not only show the efficacy...
Quadratic minimization (QM) has been investigated for many years, which is generally supposed to be time-invariant and at the same level. Nevertheless, the QM which arises in practical applications, is usually time-varying and may be at the different levels. Different from general QM, a novel different-level time-varying QM (DLTVQM) is proposed and investigated in this paper. Firstly, the DLTVQM solving...
Time-varying problems are widely encountered in various engineering fields, such as signal processing, construction monitoring, and automation. However, traditional arithmetics intrinsically aim at time-invariant problems solving. When running on relatively low-speed processing units, traditional arithmetics may generate quite large and unacceptable lagging errors. In this paper, the problems of discrete...
Time-varying reciprocal and inverse computation are considered as fundamental problems in scientific and engineering fields, which are more complicated than static computation. Continuous-time Zhang dynamics (CTZD) model is a powerful method for such complicated situations. To obtain a discrete-time Zhang dynamics (DTZD) model, a new formula of 4-instant g-square finite difference (4IgSFD_L) is proposed...
In this paper, we propose and investigate a new Euler-precision 3-node g-proportional finite difference formula [also named Zhang finite difference (ZFD) formula 3NgPFD_G], which achieves an error pattern of O(g), where g denotes the sampling gap. Moreover, the proposed formula is extended to future minimization (FM). Specifically, the ZFD formula 3NffPFD_G and its extension to discretize continuous-time...
Static Euclid division has been studied for many decades. In this paper, we focus on time-varying division (or termed, Zhang division). As Zhang dynamics (ZD) and gradient dynamics (GD) have shown powerful abilities to solve a great variety of time-varying problems, we present a ZD model and a GD model for time-varying division by defining a Zhang function and an energy function, respectively. Through...
Mistuned blades are inevitable in compressor, and modal parameters of mistuned blades will change significantly compare with tuned blades. In this paper, mistuning stiffness is introduced and a lumped parameter model of coupled multi-blades is established. Mode localization of mistuned blades is analyzed by this model. When a crack appears in mistuned blades, local flexibility method is used to analyze...
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