Research on motor rotation anomaly detection based on improved VMD algorithm

Purpose–The electromechanical brake system is leading the latest development trend in railway braking technology.The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder.The tolerance leads to imprecise brake control,so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system.This paper aims to present improved variational mode decomposition(VMD)algorithm,which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.Design/methodology/approach–The VMD algorithm plays a pivotal role in the preliminary phase,employing mode decomposition techniques to decompose the motor speed signals.Afterward,the error energy algorithm precision is utilized to extract abnormal features,leveraging the practical intrinsic mode functions,eliminating extraneous noise and enhancing the signal’s fidelity.This refined signal then becomes the basis for fault analysis.In the analytical step,the cepstrum is employed to calculate the formant and envelope of the reconstructed signal.By scrutinizing the formant and envelope,the fault point within the electromechanical brake system is precisely identified,contributing to a sophisticated and accurate fault diagnosis.Findings–This paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake(EMB)motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction.The signal is reconstructed according to the effective intrinsic mode functions(IMFS)component of removing noise,and the formant and envelope are calculated by cepstrum to locate the fault point.Experiments show that the empirical mode decomposition(EMD)algorithm can effectively decompose the original speed signal.After feature extraction,signal enhancement and fault identification,the motor mechanical fault point can be accurately located.This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.Originality/value–By using this improved VMD algorithm,the electromechanical brake system can precisely identify the rotational anomaly of the motor.This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled.Compared with the conventional motor diagnosis method,this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs.Moreover,the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.

THE INSTABILITY OF TRAJECTORY AND ERROR GROWTH

The purpose of this paper is to study the dynamical mechanism of error growth in the numerical weather prediction. The error is defined in the sense of generalized energy,simply called energy error.From the spectral form of the primi- tive equations,we have derived the evolution equations of error in detail.The analyses of these equations have shown that the error growth rate is determined by the tangent linear equations.The nonlinear advection caused by the error perturbation itself contributes nothing to the error growth rate,and only redistributes the error.Furthermore,an ap- proach to calculation of the error growth rate has been developed,which can also be used to study the local instability of time-independent basic state as well as time-dependence basic state.This approach is applied to well-known Lorenz's system,and the results are indicative of the correctness and significance of the theoretical analyses.

Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation

This paper is devoted to the error estimate for the iterative discontinuous Galerkin(IDG)method introduced in[P.Yin,Y.Huang and H.Liu.Commun.Comput.Phys.16:491-515,2014]to the nonlinear Poisson-Boltzmann equation.The total error includes both the iteration error and the discretization error of the direct DG method to linear elliptic equations.For the DDG method,the energy error is obtained by a constructive approach through an explicit global projection satisfying interface conditions dictated by the choice of numerical fluxes.The L^(2) error of order O(h^(m+1))for polynomials of degree m is further recovered.The bounding constant is also shown to be independent of the iteration times.Numerical tests are given to validate the established convergence theory.

THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM

In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？

Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions.

THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION

The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.