Random vibration analysis of vibro-impact systems: RBF neural network method

Qian, Jiamin; Chen, Lincong; Sun, Jian‐Qiao

doi:10.1016/j.ijnonlinmec.2022.104261

Cited by 19 publications

(5 citation statements)

References 27 publications

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“…However, the links from the hidden layer to the output layer are trained. This is a simpler training process than that of standard neural network models [23].…”

Section: Rbf Neural Networkmentioning

confidence: 99%

Improved Bootstrap Method Based on RBF Neural Network for Reliability Assessment

Wang,

Liu,

Shao

2024

Applied Sciences

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The investigation of the reliability of long-life equipment is typically hindered by the lack of experimental data, which makes accurate assessments challenging. To address this problem, a bootstrap method based on the improved RBF (radial basis function) neural network is proposed. This method utilizes the exponential function to modify the conventional empirical distribution function and fit right-tailed data. In addition, it employs the RBF radial basis neural network to obtain the distribution characteristics of the original samples and then constructs the neighborhood function to generate the input network. The expanded sample is used to estimate the scale and shape parameters of the Weibull distribution and obtain the estimated value of the MTBF (mean time between failures). The bias correction method is then used to obtain the interval estimate for the MTBF. Subsequently, a simulation experiment is conducted based on the failure data of a CNC (computer numerical control) machine tool to verify the effect of this method. The results show that the accuracy of the MTBF point estimation and interval estimation obtained using the proposed method is superior to those of the original and conventional bootstrap methods, which is of major significance to engineering applications.

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“…However, the links from the hidden layer to the output layer are trained. This is a simpler training process than that of standard neural network models [23].…”

Section: Rbf Neural Networkmentioning

confidence: 99%

Improved Bootstrap Method Based on RBF Neural Network for Reliability Assessment

Wang,

Liu,

Shao

2024

Applied Sciences

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“…Based on the above Chebyshev polynomial approximation, the introduced average constraint conditions, Equation (19), and the average jump, Equation (20), the stochastic three-degree-of-freedom vibroimpact system is transformed into an equivalent deterministic system. When N → ∞ , the solution…”

Section: Equivalent Deterministic Systemmentioning

confidence: 99%

“…Liu [ 19 ] studied the crises in the Duffing vibroimpact oscillator with non-viscously damping via the composite cell coordinate system method. Qian [ 20 ] utilized the radial basis function neural networks method to analyze typical randomly excited vibroimpact systems. Ding [ 21 ] established a six-dimensional Poincaré map to explore the double Neimark–Sacker bifurcation, torus T2 of a three-degree-of-freedom vibro-impact system.…”

Section: Introductionmentioning

confidence: 99%

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

Yang,

Deng,

et al. 2023

Entropy

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The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

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“…By using the traditional theoretical analysis, the stochastic dynamical property of a nonlinear vibroimpact system with Coulomb friction under stochastic noise has been researched by Su et al [27]. Besides investigating the stochastic response of SDOF vibro-impact oscillators under wide-band noise excitations, Qian et al [28] have also studied the response of vibro-impact systems by the RBF neural network method [29]. Although numerous papers have been published, some stochastic non-smooth systems cannot be investigated by these theoretical methods due to the limited application.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

Huang,

Hong,

et al. 2024

Computer Modeling in Engineering &Amp; Sciences

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In this paper, the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated. Firstly, by means of the orthogonal polynomial approximation (OPA) method, the nonlinear damping and stiffness are expanded into the linear combination of the state variable. The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of the mean value. Afterwards, the stochastic vibro-impact system can be turned into an equivalent high-dimensional deterministic non-smooth system. Two different Poincaré sections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response. Consequently, the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system. Furthermore, the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system. It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation. Increasing the random intensity may result in a diffusion-based trajectory and the impact with the constraint plane, which induces the topological behavior of the non-smooth system to change drastically. It is also found that grazing bifurcation appears in advance with increasing of the random intensity. The stronger impulse force can result in the appearance of the diffusion phenomenon.

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Random vibration analysis of vibro-impact systems: RBF neural network method

Cited by 19 publications

References 27 publications

Improved Bootstrap Method Based on RBF Neural Network for Reliability Assessment

Improved Bootstrap Method Based on RBF Neural Network for Reliability Assessment

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

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