Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

Bearing fault is the most likely to occur in mechanical fault, and stochastic resonance (SR), as a noise enhanced signal processing tool, can find mechanical faults as early as possible, so as to avoid larger problems. However, most of the existing research methods are based on the first-order Langevin equation. According to the previous studies of many scholars, the weak signal detection ability of the second-order system is better than that of the first-order system, and the coupled system also has better performance due to the addition of the control system. So, in order to detect the fault signal more easily, a second-order coupled tristable stochastic resonance system (SCTSR) based on the adaptive genetic algorithm (AGA) is proposed, it is an improvement on improving the first-order coupled tristable stochastic resonance system (FCTSR). First, based on the fourth-order Runge–Kutta algorithm (F-RK), the performances of monostable, bistable and tristable control systems to SCTSR are compared, it is verified that the monostable system has the best performance as SCTSR’s control system. Secondly, the equivalent potential function of SCTSR is derived, and the influences of each system parameters on it are researched. The output signal-to-noise ratio gain (SNRG) is chosen as a measure to verify that SCTSR’s performance is better than that of FCTSR, and the influences of parameters on SNRG are discussed. SCTSR and FCTSR are used to detect low-, high- and multi-frequency cosine signals combined with AGA. The simulation results are compared with the wavelet transform method, which proves the performance superiority of SR, and also prove that SCTSR is easier to detect weak signals and has a stronger de-noising ability. Finally, SCTSR and FCTSR are applied in bearing fault detection under Gaussian white noise and trichotomous noise. The results also prove that SCTSR can get larger peaks and SNRG, and it is easier to detect fault signals. This proves that SCTSR’s performance is superior that of other methods in bearing fault detection, and has better engineering application value.

     

Nonlinear analysis and effectiveness of weakly coupled microbeams for mass sensing applications

Nonlinear Dynamics - Kaplan turbines, also known as movable propeller turbines, are attractive for power generation from water currents. They are controlled by guide vanes and runner blades, whose...     

A block particle coupled model and its application to landslides

To simulate the progressive failure of slope, a block particle coupled model is introduced. Particle oriented cell mapping(POCM) algorithm is used to enhance the search efficiency, and particlepoint, particle-edge, particle-face contact detecting method is adopted to establish contact pair between particles and blocks precisely. Strain softening Mohr Coulomb model with tensile cutoff is adopted for blocks, and brittle Mohr Coulomb model is used for particles. The particle-block replacement approach is used to describe the fracture and fragmentation process of continuum media. Once the cohesion or tensile strength of one block reaches zero, the block will be deleted,and particles are generated at the same place with all information inherited from the deleted block. Some numerical cases related to landslides demonstrate the precision and rationality of the coupled model.     

一种FEM－EFGM耦合技术及其应用

利用面力耦合(traction matching)技术，导出了增量形式的一般固体力学问题的FEM—EFGM耦合求解格式。在相应的域内分别建立FE和EFG的离散方程，利用交界面上的连续条件，可方便地建立耦合求解方程，简明有效，易于编程计算。数值算例给出令人满意的结果。     

一种新型SPH-FEM耦合算法及其在冲击动力学问题中的应用

为了充分发挥光滑粒子流体动力学方法(smoothed particle hydrodynamics,SPH)在处理大变形和有限元(finite element method,FEM)问题时计算精度高的优势,提出了一种新型SPH-FEM耦合算法.该耦合算法在大变形区域使用SPH粒子离散,其余区域使用有限元离散.在耦合界面...     

基于极大似然估计的BP算法及其在深基坑开挖参数辨识中的应用

本文采用人工神经网络BP算法对深基坑开挖工程中的参数进行辨识,将某些现场实测值作为网络输入,土层物性参数作为网络的输出, 限元计算取得学习样本来训练网络,从而地深基坑开挖工程中的参数进行辨识的目的,同时,本文提出了将极大似然估计引入BP学习算法中,可以考虑学习样本和网络输入（现场产测值）的误差,可以求得所辨识参数的可靠度,本文还对动态调整BP学习算法的学习速度因子,冲量系数以加快网络学习速度的算法进行了研究,本文算例表明本文算法训练速率可比传统BP算法快10倍以上。     

参数概率灵敏度分析的神经网络方法及其应用

参数概率灵敏度分析是可靠性设计中非常重要的一项工作,它可以提供基本变量分布参数的变化引起可靠性的变化信息,为判断系统参数的重要性提供依据.本文将商用有限元计算.神经网络方法-Monte Carlo法相结合,基于这种快速响应模型的复杂结构可靠性分析方法,针对结构随机参数的概率灵敏度分析,提出一个考虑随机变量全局分散性的新...     

Primary resonance of coupled cantilevers subjected to magnetic interaction

Based on a distributed-parameter model, the forced vibration of a cantilever pair excited by a sinusoidal base movement is analyzed. Two cantilevers are coupled at their free ends by a linear spring. A nonlinear concentrated magnetic force acts on the tip of one cantilever, serving at the nonlinear boundary condition of the continuous model. The magnetic force is modeled as a fractional function, strongly dependent on the distance between two magnets. Via the method of multiple scales, the primary resonance is analyzed for all modes. A second-order approximate solution and its stability condition are analytically captured. It is revealed that the frequency–response curves are sensitive to the distance between the two magnets. The curve may exhibit the hardening-type, softening-type or linear behavior due to the existence of the quadratic nonlinearity. The outcomes are supported by the numerical simulations very well.     

Parameter sensitivity of cantilever beam with tip mass to parametric excitation

Nonlinear Dynamics - The sensitivity of the response of a parametrically excited cantilever beam with a tip mass to small variations in elasticity (stiffness) and the tip mass is performed. The...     

Constitutive computational modelling foundation of piezoelectronic microstructures and application to high-frequency microchip DSAW resonators

This paper establishes a piezoelectric constitutive computational approach based on generalized eigenvalue and multivariable finite element solutions with potential applications to accurate and effective analysis of layered piezoelectric microstructures of arbitrary geometries and different anisotropic materials, to ease the limitation of current computer capacity in analyzing large-scale high-frequency disturbed surface acoustic waves (DSAW) by mounted electrodes in piezoelectric devices such as microchip SAW resonators. A new incompatible generalized hybrid/mixed element GQM5 is also proposed for improving predictions of the piezoelectric surface mount thermal stresses that are shear-dominated. The (generalized) plane strain constitutive model is numerically verified for piezoelectric finite element computation. With the help of computational piezoelectricity (electro-mechanics) for general layered structures with metal electrodes and anisotropic piezoelectric substrates, some new interesting, reliable and fundamental constitutive finite element results are obtained for high-frequency piezoelectric and mechanical SAW propagations and can be used for further applications. The ST-cut FEA results agree quite well with available exact and lab solutions for free surface case. The project supported by SRF for ROCS, SEM of China, the past Rutgers Univer-Seiko Epson Joint Fund and Zhejiang Provincial NSF     

Lagrange-Maxwell equation and magnetic saturation parametric resonance of generator set

Lagrange-Maxwell's equation is extended firstly.With the theory of elec- tromechanical analytical dynamics,the magnetic complement energy in air gap of gener- ator is acquired.The torsional vibration differential equations with periodic coefficients of rotor shafting of generator which is in the state of magnetic saturation are established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment.By means of the averaging method,the first approximate solution and corre- sponding solution of the primary parametric resonance is obtained.The characteristics and laws of the primary parametric resonance excited by the electromagnetism are ana- lyzed and some of new phenomena are revealed.     

An adaptive vibrational resonance method based on cascaded varying stable-state nonlinear systems and its application in rotating machine fault detection

A weak character signal with low frequency can be detected based on the mechanism of vibrational resonance (VR). The detection performance of VR is determined by the synergy of a weak low-frequency input signal, an injected high-frequency sinusoidal interference and the nonlinear system(s). In engineering applications, there are many weak fault signals with high character frequencies. These fault signals are usually submerged in strong background noise. To detect these weak signals, an adaptive detection method for a weak high-frequency fault signal is proposed in this paper. This method is based on the mechanics of VR and cascaded varying stable-state nonlinear systems (VSSNSs). Partial background noise with high frequency is regarded as a special type of high-frequency interference and an energy source that protrudes a weak fault signal. In this way, high-frequency background noise is utilized in a VSSNS. To improve the detection ability, manually generated high-frequency interference is injected into another VSSNS. The VSSNS can be transformed into a monostable state, bistable state or tristable state by tuning the system parameters. The proposed method is validated by a simulation signal and industrial applications. The results show the effectiveness of the proposed method to detect a weak high-frequency character signal in engineering problems.

     

Solution of the incompressible mass and momentum equations by application of a coupled equation line solver

This paper describes an iterative technique for solving the coupled algebraic equations for mass and momentum conservation for an incompressible fluid flow. The technique is based on the simultaneous solution for pressure and velocity along lines. In a manner similar to ADI methods for a single variable, the solution domain is entirely swept line-by-line in each co-ordinate direction successively until a converged solution is obtained. The tight coupling between the equations that is guaranteed by the method results in an economical solution of the equation set.     

DDA与FEM耦合法在分缝重力坝非线性分析中的应用

混凝土重力坝一般设有数条纵缝。纵缝使坝体的连续性遭到破坏,一般的有限单元法很难处理这样的不连续变形问题。本文首先阐述了DDA(Discontinuous Deformation Analysis)与FEM(Finite Element Method)耦合算法的原理,然后采用作者自行研制的DDA与FEM耦合法程序对一实际重力坝进行了详细的计算分析。重点讨论了纵缝的不同设置形式和缝宽大小对坝体变形和应力分布、坝底面接触应力分布以及坝基面应力分布的影响,为工程设计提供依据。     

Nonlinear responses of a cable-beam coupled system under parametric and external excitations

This paper analytically investigates the nonlinear responses of a cable-beam coupled system under the combined effects of internal and external resonance. The cable is considered a geometric nonlinearity, and the beam is considered as Euler–Bernoulli model, but it is coupled by fixing it at one end. The coupled nonlinear differential equations are formulated by using the Hamilton principle. The spatial problem is solved by using Galerkin’s method to simplify the governing equations to a set of ordinary differential equations. Applying the multiple time scales method to the ordinary differential equations, the first approximate solutions and solvability condition are derived. The effects of the cable sag to span ratio, mass ratio, and stiffness ratio on the nonlinear responses are investigated. The results show good agreement between the analytical and numerical solutions especially near the external resonance frequency.     

Principal resonance of a nonlinear system with two-frequency parametric and self-excitations

The principal resonance of a single-degree-of-freedom system with two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms with close frequencies is examined. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. Qualitative analyses are employed to study the behaviour of steady state responses, limit cycle responses and 2-torus responses, including their stability and bifurcation. The effects of damping, detuning, and magnitudes of self-excitation and parametric excitations are analyzed. The theoretical analyses are verified by numerical integration results of the governing equation and the modulation equations.     

微纳通道谐振器检测与表征中的动力学问题

微纳通道机械谐振器在液体环境中具有超高的谐振频率、品质因子和灵敏度,常用于液体环境中的高精度检测与表征,在生物、医药、化工等领域有着广阔的应用前景.微纳通道机械谐振器的检测与表征功能高度依赖其动力学特性,而此类器件是由谐振结构、内部流体、被检测物和外部激励等多因素组成的耦合系统,涉及的动力学问题较为复杂,已成为谐振器件研究中的前沿热点和瓶颈问题.本文综述了微纳通道机械谐振器的研究进展,总结了谐振器件实现高精度检测与表征功能时的动力学设计原理,详细讨论了谐振器件的稳定性、频响特性、能量耗散、频率波动等动态特性,阐明了不同动力学问题的物理机制及其对谐振器性能的影响规律,可为深入厘清微纳通道机械谐振器的动力学设计问题,提高器件动态性能提供理论参考和技术支撑,对超高频、超高灵敏度谐振器的设计、制造及应用发展具有重要意义.      

Dynamics problems of micro/nano channel resonators for detection and characterization

微纳通道机械谐振器在液体环境中具有超高的谐振频率、品质因子和灵敏度,常用于液体环境中的高精度检测与表征,在生物、医药、化工等领域有着广阔的应用前景.微纳通道机械谐振器的检测与表征功能高度依赖其动力学特性,而此类器件是由谐振结构、内部流体、被检测物和外部激励等多因素组成的耦合系统,涉及的动力学问题较为复杂,已成为谐振器件研究中的前沿热点和瓶颈问题.本文综述了微纳通道机械谐振器的研究进展,总结了谐振器件实现高精度检测与表征功能时的动力学设计原理,详细讨论了谐振器件的稳定性、频响特性、能量耗散、频率波动等动态特性,阐明了不同动力学问题的物理机制及其对谐振器性能的影响规律,可为深入厘清微纳通道机械谐振器的动力学设计问题,提高器件动态性能提供理论参考和技术支撑,对超高频、超高灵敏度谐振器的设计、制造及应用发展具有重要意义.     

Stochastic resonance in coupled weakly-damped bistable oscillators subjected to additive and multiplicative noises

With coupled weakly-damped periodically driven bistable oscillators subjected to additive and multiplicative noises under concern,the objective of this paper is to check to what extent the resonant point predicted by the Gaussian distribution assumption can approximate the simulated one.The investigation based on the dynamical mean-field approximation and the direct simulation demonstrates that the predicted resonant point and the simulated one are basically coincident for the case of pure additive noise,but for the case including multiplicative noise the situation becomes somewhat complex.Specifically speaking,when stochastic resonance(SR) is observed by changing the additive noise intensity,the predicted resonant point is lower than the simulated one;nevertheless,when SR is observed by changing the multiplicative noise intensity,the predicted resonant point is higher than the simulated one.Our observations imply that the Gaussian distribution assumption can not exactly describe the actual situation,but it is useful to some extent in predicting the low-frequency stochastic resonance of the coupled weakly-damped bistable oscillator.