Characterization, stability and hyperstability of multi-quadratic–cubic mappings

Bodaghi, Abasalt; Fošner, Ajda

doi:10.1186/s13660-021-02580-4

Cited by 9 publications

(6 citation statements)

References 27 publications

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“…Using chaotic sequences for population initialization, selection, crossover and mutation will affect the whole process of the algorithm and usually achieve better results than pseudorandom numbers [52]. Chaotic mapping commonly used in the field of intelligent optimization includes Logistic-Sine mapping [53], Tent mapping [54], Chebyshev mapping [55], ICMIC mapping [56], and Cubic mapping [57], etc. To analyze the chaotic properties of the above six one-dimensional chaotic graphs, their bifurcation diagrams are plotted separately, as shown in figure 5.…”

Section: Chaotic Mapmentioning

confidence: 99%

Fault diagnosis in asynchronous motors based on an optimal deep bidirectional long short-term memory networks

Xu,

Li,

Liu

et al. 2023

Meas. Sci. Technol.

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Fault diagnosis of asynchronous motors has become a pressing need in the metallurgical industry. Due to the complex structure of asynchronous motors, fault types and fault characteristics are diverse, with strong nonlinear relationships between them, which leads to the difficulty of fault diagnosis. To efficiently and accurately diagnose various motor faults, we propose a fault diagnosis method based on an optimal deep bidirectional long short-term memory neural network. First, the three-phase current, multidimensional vibrational signal, and acoustic signal of the asynchronous motor are collected and construct diverse and robust data sample set to enhance the generalization ability of the model. Next, a modified 3D logistics-sine complex chaotic map (3D LSCCM) is constructed to improve the global and local search capabilities of the pigeon swarm optimization algorithm (PIO). Then, we construct a deep bidirectional long short-term memory network (Bid-LSTM) with attention mechanism to mine high-value fault characteristic information. Meanwhile, the optimal hyper-parameters of the deep ABid-LSTM are explored using the modified PIO to improve the training performance of the model. Finally, the fault data samples of asynchronous motor are induced to train and test the proposed framework. By fusing diverse data samples, the proposed method outperforms conventional deep Bid-LSTM and achieves fault diagnosis accuracy of 99.13%. It provides a novel diagnostic strategy for motor fault diagnosis.

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Section: Chaotic Mapmentioning

confidence: 99%

Fault diagnosis in asynchronous motors based on an optimal deep bidirectional long short-term memory networks

Xu,

Li,

Liu

et al. 2023

Meas. Sci. Technol.

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show abstract

“…In addition, the general system of cubic functional equations has been defined in [25] and characterized as a single equation in [23]. For the definitions and the structure of multiadditive-quadratic and multiquadraticcubic mappings, see [3] and [8].…”

Section: A(x + Y) = A(x) + A(y) (The Cauchy Equation)mentioning

confidence: 99%

“…In Definition 2.5, we suppose for simplicity that f is quadratic in each of the first k variables, but one can obtain analogous results without this assumption. It is obvious that for k = n (resp., k = 0), the above definition leads to the so-called multiquadratic (resp., multicubic) mappings; some basic facts on the mentioned mappings can be found, for instance, in [8,13] and [45].…”

Section: Proposition 24mentioning

confidence: 99%

Equalities and inequalities for several variables mappings

Bodaghi

2022

J Inequal Appl

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In this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.

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“…The stability results for n-monomial functional equations with n < 9 can be found in [6,[14][15][16][17][18][19][20][21][22][23][24]. In the papers [16,[25][26][27][28][29][30][31][32][33], one can find hyperstability results for various types of functional equation. Recent results regarding the stability of the functional equation described in Equation (1) with n < 9 can be found in [34][35][36][37][38][39], and hyperstability results for this functional equation with n < 9 can be found in [38,40].…”

Section: Introductionmentioning

confidence: 99%