The Application of Advanced Signal Processing Techniques to Induction Motor Bearing Condition Diagnosis

Four approaches based on bispectral and wavelet analysis of vibration signals are investigated as signal processing techniques for application in the diagnosis of a number of induction motor rolling element bearing faults. The bearing conditions considered are a normal bearing and bearings with cage and inner and outer race faults. The vibration analysis methods investigated are based on the bispectrum, the bispectrum diagonal slice, the summed bispectrum and wavelets. Singular value decomposition (SVD) is used to extract the most significant features from the vibration signatures and the features are used as inputs to an artificial neural network trained to identify the bearing faults. The results obtained show that the diagnostic system using a supervised multi-layer perceptron type neural network is capable of classifying bearing condition with high success rate, particularly when applied to summed bispectrum signatures.     

The trispectrum for Gaussian driven, multiple degree-of-freedom, non-linear structures

Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and type of system non-linearity. Two such spectra that have figured prominently in signal processing are the bispectrum and trispectrum. In a previous work, the authors developed an analytical solution for the bispectrum for multi-degree-of-freedom systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for the trispectrum of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary location. The analytical expression is compared to those obtained via estimation using the direct method.     

Parameter estimation of chaotic systems by an oppositional seeker optimization algorithm

The parameter estimation can be formulated as a multi-dimensional optimization problem. By combining the seeker optimization algorithm with the opposition-based learning method, an oppositional seeker optimization algorithm is proposed in this work, and is applied to the parameter estimation of chaotic systems. The seeker optimization algorithm provides a new alternative for population-based heuristic search. By considering an estimate and its opposite of current solutions at the same time, the opposition-based learning method is employed for population initialization and also for generation jumping in seeker optimization algorithm. Numerical simulations on two typical chaotic systems are conducted to show the effectiveness and robustness of the proposed scheme.     

Parallel implementation of data assimilation

Kalman filter is a sequential estimation scheme that combines predicted and observed data to reduce the uncertainty of the next prediction. Because of its sequential nature, the algorithm cannot be efficiently implemented on modern parallel compute hardware nor can it be practically implemented on large‐scale dynamical systems because of memory issues. In this paper, we attempt to address pitfalls of the earlier low‐memory approach described in and extend it for parallel implementation. First, we describe a low‐memory method that enables one to pack covariance matrix data employed by the Kalman filter into a low‐memory form by means of certain quasi‐Newton approximation. Second, we derive parallel formulation of the filtering task, which allows to compute several filter iterations independently. Furthermore, this leads to an improvement of estimation quality as the method takes into account the cross‐correlations between consequent system states. We experimentally demonstrate this improvement by comparing the suggested algorithm with the other data assimilation methods that can benefit from parallel implementation. Copyright © 2016 John Wiley & Sons, Ltd.     

The back and forth nudging algorithm applied to a shallow water model,comparison and hybridization with the 4D‐VAR

We study in this paper a new data assimilation algorithm, called the back and forth nudging (BFN). This scheme has been very recently introduced for simplicity reasons, as it does not require any linearization, or adjoint equation, or minimization process in comparison with variational schemes, but nevertheless it provides a new estimation of the initial condition at each iteration. We study its convergence properties as well as efficiency on a 2D shallow water model. All along the numerical experiments, comparisons with the standard variational algorithm (called 4D‐VAR) are performed. Finally, a hybrid method is introduced, by considering a few iterations of the BFN algorithm as a preprocessing tool for the 4D‐VAR algorithm. We show that the BFN algorithm is extremely powerful in the very first iterations and also that the hybrid method can both improve notably the quality of the identified initial condition by the 4D‐VAR scheme and reduce the number of iterations needed to achieve convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义,本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式,此方法将Roe型熵稳定格式与自适应移动网格算法结合,空间方向采用熵稳定格式对磁流体动力学方程进行离散,利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布,在此基础上采用守恒型插值公式实现新旧节点上的量值传递,利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明,该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高,通用性好,具有强鲁棒性。     

Fault Detection of DC Electric Motors Using the Bispectral Analysis

The two major advantages of bispectral analysis are: resistance to noise and the ability to detect nonlinearities, like quadratic phase coupling. The first aim was to study some of the theoretical aspects of bispectral estimation. A lot of attention was paid to the influence of noise, the number of segments, the influence of one or several harmonic deterministic components and aliasing. These aspects are typical of rotating machinery. An example of successful fault identification in DC electric motors is presented. The identification proved to be capable to identify quadratically coupled mechanical system when the power-spectra analysis failed. Further it proved to be quite resistant to noise.     

基于不等式约束卡尔曼滤波的双MIMU导航位置校正方法

为了实现GPS信号缺失下的单兵自主导航,提出一种基于微惯性测量技术(MIMU)的单兵导航方案。由于惯性导航时误差随着时间而积累,提出了基于双MIMU的单兵导航位置校正方法,通过将两个MIMU分别固联在单兵的双脚上,根据行走时候的步态特性,利用基于假设检验和极大似然估计的零速检测器,进行零速检测修正。结合单兵行走时最大步长约束,设计一种最大步长分解约束下的卡尔曼滤波椭球约束算法,进一步校正单兵导航位置估计。研究结果表明,采用最大步长分解约束不等式卡尔曼滤波的双MIMU单兵导航方案,与未加约束时相比双脚位置均方根误差下降了41.46%。     

A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—Part II. Numerical algorithm and example applications

In the present study, an algorithm is presented for the dual-porosity model formulated in Part I of this series. The resultant flow equation with the dual-porosity formulation is of an integro-(partial) differential equation involving differential terms for the Darcy flow in large fractures and integrals in time for diffusion within matrix blocks. The algorithm developed here to solve this equation involves a step-by-step finite difference procedure combined with a quadrature scheme. The quadrature scheme, used for the integral terms, is based on the trapezoidal method which is of second-order precision. This order of accuracy is consistent with the first- and second-order finite difference approximations used here to solve the differential terms in the derived flow equation. In an approach consistent with many petroleum reservoir and groundwater numerical flow models, the example formulation presented uses a first-order implicit algorithm. A two-dimensional example is also demonstrated, with the proposed model and numerical scheme being directly incorporated into the commercial gas reservoir simulator SIMED II that is based on a fully implicit finite difference approach. The solution procedure is applied to several problems to demonstrate its performance. Results from the derived dual-porosity formulation are also compared to the classic Warren–Root model. Whilst some of this work confirmed previous findings regarding Warren–Root inaccuracies at early times, it was also found that inaccuracy can re-enter the Warren–Root results whenever there are changes in boundary conditions leading to transient variation within the domain.     

Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media

Environmental studies are commonly carried out through numerical simulations, which have to be accurate, reliable and efficient. When transient problems are considered, the validity of the solutions requires the calculation and management of the temporal discretization errors. This article describes an adaptive time stepping strategy based on the estimation of the local truncation error via the Richardson extrapolation technique. The time-marching scheme is mathematically based on this a posteriori error estimation that has to be gauged. General optimizations are also suggested making the control of both the temporal error and the evolution of the time step size very efficient. Furthermore, the algorithm connecting these methods is all the more interesting as it could be implemented in many computational codes using different numerical schemes. In the hydrogeochemical domain, this algorithm represents an interesting alternative to a fixed time step as shown by the various numerical tests involving reactive transport and unsaturated flow.     

干涉型光纤陀螺仪零漂建模方法

光纤陀螺仪零漂是衡量光纤陀螺仪精度的重要指标。文中对某光纤陀螺仪的零偏数据进行分析和预处理,采用时间序列分析法建立了AR（2）模型,同时基于BP神经网络建立了预测模型。建模结果分析表明：AR建模方法简单易行,但适用性不如BP网络模型,BP网络模型建模精度高,但算法复杂且收敛速度慢,容易陷入局部极小,因此采用了改进训练方法,改善了BP网络性能。     

Adaptive delaunay triangulation with multidimensional dissipation scheme for high-speed compressible flow analysis

IntroductionHigh-speed compressible flows normally involve many complex flow phenomena,suchas shock waves,flow expansions,and shock-shock interactions[1].Effects of thesephenomena are critical in the design of high-speed structures.These flows are charact…     

Multi-symplectic Runge-Kutta methods for Landau-Ginzburg-Higgs equation

Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the Landau-Ginzburg-Higgs equation. The numerical re- sults for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.     

Investigation of use of reach-back characteristics method for 2D dispersion equation

The use of the Holly-Preissmann two-point scheme has been very popular for the calculation of the dispersion equation. The key to this scheme is to use the characteristics method incorporating the Hermite cubic interpolation technique to approximate the trajectory foot of the characteristics. This method can avoid the excessive numerical damping and oscillation associated with most finite difference schemes for advection computation. On the basis of the fundamental idea of the Holly-Preissmann two-point scheme, a new technique is introduced herein for the computation of the two-dimensional dispersion equation. This new scheme allows the characteristics projecting back several time steps to fall on the spatial or temporal axis, while the characteristics foot is still solved by the Holly-Preissmann two-point method. The diffusion portion of the dispersion equation is solved by the commonly used Crank-Nicholson method. The calculation for these two processes consisting of advection and diffusion is carried out separately but consecutively in one time step, a method known as the split operator algorithm. A hypothetical model was constructed to demonstrate the applicability of this new technique for the calculation of the pure advection and dispersion equation in two dimensions.     

基于独立分量分析的多源动态载荷识别方法

提出了基于独立分量分析的多源动态载荷识别方法, 解决了在结构系统未知的情况下载荷波形的识别问题. 该方法基于结构在多源动态载荷作用下, 其响应是载荷与对应的结构脉冲响应卷积的原理, 并假设载荷源相互统计独立. 与既有的载荷识别方法相比,该识别方法特点表现在: 结构质量, 刚度及阻尼等信息可以完全未知, 但以实际载荷间的独立性为优化目标; 用互信息来度量识别载荷间的独立性, 通过梯度下降算法取消识别载荷间的各阶相关性, 使识别载荷间基本满足相互独立; 从波形的角度来进行载荷识别.通过数值仿真表明: 该方法对测点, 噪声, 不同载荷形式及不同结构有较好的鲁棒性; 识别载荷与实际载荷在归一化条件下, 识别载荷与实际载荷相关性系数约为1.      

船摇数据实时滤波与预报的时序法

作为船摇数据建立一个时序时域模型-长自回归模型,在此模型基础上给出了船摇数据的实时滤波和预报的方法,并从均方误差、预报误差、残差序列的相关性、拟合方差、仿真计算等多方面考察了滤波及预报效果。AR（p)模型的系数估计采用最小二乘递推方法,用较少的运算量和存贮量,得到了较高的估值精度。该方法是一种非常值得推荐的船摇数据实时处理方法。     

Improvements on the accuracy of derivative estimation from DPIV velocity measurements

Accuracy of out-of-plane vorticity estimation from in-plane experimental velocity measurements is investigated with particular application to digital particle image velocimetry (DPIV). Simulations of known flow fields are used to quantify errors associated with amplification of the velocity measurement noise and method bias error due to spatial sampling resolution. A novel, adaptable, hybrid estimation scheme combining implicit compact finite difference and Richardson extrapolation schemes is proposed for improved vorticity estimation. The scheme delivers higher-order truncation error with less noise amplification than an explicit second order finite difference scheme. Finally, a complete framework for predicting, a priori, the random, bias, and total error of the vorticity estimation on the basis of the error of the resolved velocities and the choice of differentiation scheme is developed and presented. A portion of this work was presented at ASME IMECE 2003 conference An erratum to this article is available at .     

A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures

A two-dimensional (2-D) continuous wavelet transform (CWT)-based damage detection algorithm using “Dergauss2d” wavelet for plate-type structures is presented. The 2-D CWT considered in this study is based on the formulation by Antoine et al. (2004). A concept of isosurface of 2-D wavelet coefficients is proposed, and it is generated to indicate the location and approximate shape or area of the damage. The proposed algorithm is a response-based damage detection technique which only requires the mode shapes of the damaged plates. This algorithm is applied to the numerical vibration mode shapes of a cantilever plate with different types of damage to illustrate its effectiveness and viability. A comparative study with other two 2-D damage detection algorithms, i.e., 2-D gapped smoothing method (GSM) and 2-D strain energy method (SEM), is performed, and it demonstrates that the proposed 2-D CWT-based algorithm is superior in noise immunity and robust with limited sensor data. The algorithm is further implemented in an experimental modal test to detect impact damage in an FRP composite plate using smart piezoelectric actuators and sensors, demonstrating its applicability to the experimental mode shapes. The present 2-D CWT-based algorithm is among a few limited studies in the literature to explore the application of 2-D wavelets in damage detection, and as demonstrated in this study, it can be used as a viable and effective technique for damage identification of plate- or shell-type structures.     

DAMAGE DETECTION BASED ON OPTIMIZED INCOMPLETE MODE SHAPE AND FREQUENCY

For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement(BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.     

A solution of steady-state fluid flow in multiply fractured isotropic porous media

Herein a plane, steady-state fluid flow solution for fractured porous media is first presented. The solution is based on the theory of complex potentials, the theory of Cauchy integrals, and of singular integral equations. Subsequently, a numerical method is illustrated that may be used for the accurate estimation of the pore pressure and pore pressure gradient fields due to specified hydraulic pressure or pore pressure gradient acting on the lips of one or multiple non-intersecting curvilinear cracks in a homogeneous and isotropic porous medium. It is shown that the numerical integration algorithm of the singular integral equations is fast and converges rapidly. After the successful validation of the numerical scheme several cases of multiple curvilinear cracks are illustrated.