A new gear fault feature extraction method based on hybrid time–frequency analysis

Gear is one of the popular and important components in the rotary machinery transmission. Vibration monitoring is the common way to take gear feature extraction and fault diagnosis. The gear vibration signal collected in the running time often reflects the characteristics such as non-Gaussian and nonlinear, which is difficult in time domain or frequency domain analysis. This paper proposed a novel gear fault feature extraction method based on hybrid time–frequency analysis. This method combined the Mexican hat wavelet filter de-noise method and the auto term window method at the first time. This method can not only de-noise noise jamming in raw vibration signal, but also extract gear fault features effectively. The final experimental analysis proved the feasibility and the availability of this new method.     

A new arc detection method based on fuzzy logic using S-transform for pantograph–catenary systems

pantograph–catenary system is one of the critical components used in electrical trains. It ensures the transmission of the electrical energy to the train taken from the substation that is required for electrical trains. The condition monitoring and early diagnosis for pantograph–catenary systems are very important in terms of rail transport disruption. In this study, a new method is proposed for arc detection in the pantograph–catenary system based signal processing and S-transform. Arc detection and condition monitoring were achieved by using current signals received from a real pantograph–catenary system. Firstly, model based current data for pantograph–catenary system is obtained from Mayr arc model. The method with S-transform is developed by using this current data. Noises on the current signal are eliminated by applying a low pass filter to the current signal. The peak values of the noiseless signals are determined by taking absolute values of these signals in a certain frequency range. After the data of the peak points has been normalized, a new signal will be obtained by combining these points via a linear interpolation method. The frequency-time analysis was realized by applying S-transform on the signal obtained from peak values. Feature extraction that obtained by S-matrix was used in the fuzzy system. The current signal is detected the contdition as healthy or faulty by using the outputs of the fuzzy system. Furthermore the real-time processing of the proposed method is examined by applying to the current signal received from a locomotive.     

A new graph representation for cable–membrane structures

In this paper, a new graph representation is proposed which is applicable to cable–membrane structures modelled using both one- and two-dimensional elements. The proposed graph representation is an engineering design approach and not based on a mathematically derived representation. The proposed graphs are partitioned using state-of-the-art tools, including METIS [METIS, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices (1997); J Parallel Distribut Comput (1997)], and JOSTLE [Advances in computational mechanics with parallel and distributed processing (1997); Parallel dynamic graph-partitioning for unstructured meshes (1997); Int J High Perform Comput Appl 13 (1999) 334; Appl Math Model 25 (2000) 123]. The graph representation performs better than standard graph representations for those cases when the rules of geometric locality and uniform element distribution around nodes are violated. The relation of the proposed graph representation to the most advanced hyper-graph representation [IEEE Trans Parallel Distribut Syst 10 (1999) 673; Parallel Comput 26 (2000) 673] is also discussed.     

A new numerical method on American option pricing

Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.     

Spectral–spatial co-clustering of hyperspectral image data based on bipartite graph

The high dimensionality of hyperspectral images are usually coupled with limited data available, which degenerates the performances of clustering techniques based only on pixel spectral. To improve the performances of clustering, incorporation of spectral and spatial is needed. As an attempt in this direction, in this paper, we propose an unsupervised co-clustering framework to address both the pixel spectral and spatial constraints, in which the relationship among pixels is formulated using an undirected bipartite graph. The optimal partitions are obtained by spectral clustering on the bipartite graph. Experiments on four hyperspectral data sets are performed to evaluate the effectiveness of the proposed framework. Results also show our method achieves similar or better performance when compared to the other clustering methods.     

A solving method based on neural network for a class of multi-leader–follower games

In this paper, we present a new solving approach for a class of multi-leader–follower games. For the problem studied, we firstly propose a neural network model. Then, based on Lyapunov and LaSalle theories, we prove that the trajectory of the neural network model can converge to the equilibrium point, which corresponds to the Nash equilibrium of the problem studied. The numerical results show that the proposed neural network approach is feasible to the problem studied.

     

Structural descriptors in organic chemistry—new topological parameter based on electrotopological state of graph vertices

The new topological parameter TI^E is proposed for encoding the organic structure into numerical value. The discriminating power of the E-state topological parameter TI^E is discussed for the group of isoquinoline derivatives.     

A robust direct modeling method for quadric B-rep models based on geometry–topology inconsistency tracking

Engineering with Computers - Boundary representation (B-rep) model editing plays an essential role in computer-aided design, and has motivated the very recent direct modeling paradigm, which...     

A new high-accuracy method based on off-step cubic polynomial approximations for the solution of coupled Burgers’ equations and Burgers–Huxley equation

Engineering with Computers - Using two off-step points and a central point, we discuss a new two-time-level implicit method of order three based on polynomial cubic spline approximations for the...     

The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method

The purpose of this paper is to investigate the discrete collocation method based on moving least squares (MLS) approximation for Fredholm–Hammerstein integral equations. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. Error analysis of this method is also investigated. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.     

A RBF partition of unity collocation method based on finite difference for initial–boundary value problems

Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can also provide high order convergence. Since one of the main disadvantages of global RBF-based methods is generally the computational cost associated with the solution of large linear systems, in this paper we focus on a localizing RBF partition of unity method (RBF-PUM) based on a finite difference (FD) scheme. Specifically, we propose a new RBF-PUM-FD collocation method, which can successfully be applied to solve time-dependent PDEs. This approach allows to significantly decrease ill-conditioning of traditional RBF-based methods. Moreover, the RBF-PUM-FD scheme results in a sparse matrix system, reducing the computational effort but maintaining at the same time a high level of accuracy. Numerical experiments show performances of our collocation scheme on two benchmark problems, involving unsteady convection–diffusion and pseudo-parabolic equations.     

A note on “Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets”

In a recent paper in this journal, Ashtiani et al. [1] proposed a fuzzy TOPSIS method based on interval-valued fuzzy sets. They changed the information of example that expressed by Chen [2] for the purpose of adjustment with their method and applied their method for solving the changed example. When we investigated their method, we found that Although, Ashtiani et al.’s method is really interesting, but applying it for some fuzzy MCDM problems leads to the incorrect solution and results. In other words, Ashtiani et al.’s method is not applicable to some fuzzy MCDM problems. In this paper we try to eliminate this problem.     

Collegial verbalisation – a case study on a new method on information acquisition

The purpose of this paper is to propose and discuss a new method for information acquisition called collegial verbalisation. The method is explored in an empirical case study, and it consists of vehicle operators being videotaped while driving, followed by some of their colleagues making verbal reports while watching the video data. These colleagues have previously experienced exactly the same driving task as the operators, that is, they have travelled the same route, with the same craft, and used the same instrumentation. Thus, they are very familiar with the driving task and the driver environment. The empirical study is carried out on a high-speed ferry. The method is explored in relation to three rather open hypotheses: the amount of information provided in general; the reliability of the data; and how it contributes to the detection of ‘buggy mental models’ within the operators. The method is discussed in relation to the more traditional forms of verbal reports: concurrent and retrospective verbalisations, respectively. From the results of the empirical exploration, it is suggested that the method of collegial verbalisation may have combinatorial advantages that makes it more powerful as an analytical tool than the traditional forms of verbalisation, specifically if one wants to analyse work tasks that are dynamic and where the operators' behaviours are highly automated. However, more elaborate and systematic investigations must be conducted on the topic, and the paper therefore ends with a suggestion on an experimental design for this purpose.     

Three-dimensional beam propagation method based on the variable transformed Galerkin''''s method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.     

Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement

A numerical method for 2D LEFM crack propagation simulation is presented. This uses a Lepp–Delaunay based mesh refinement algorithm for triangular meshes which allows both the generation of the initial mesh and the local modification of the current mesh as the crack propagates. For any triangle t, Lepp(t) (Longest Edge Propagation Path of t) is a finite, ordered list of increasing longest edge neighbor triangles, that allows to find a pair of triangles over which mesh refinement operations are easily and locally performed. This is particularly useful for fracture mechanics analysis, where high gradients of element size are needed. The crack propagation is simulated by using a finite element model for each crack propagation step, then the mesh near the crack tip is modified to take into account the crack advance. Stress intensify factors are calculated using the displacement extrapolation technique while the crack propagation angle is calculated using the maximum circumferential stress method. Empirical testing shows that the behavior of the method is in complete agreement with experimental results reported in the literature. Good results are obtained in terms of accuracy and mesh element size across the geometry during the process.     

A new steric substituent constant Ωs based on molecular mechanics calculations

A new steric substituent constant Ωs was defined and the procedure for its calculation is given. It was calculated from the geometries and the relative free energies of the conformers of substituents from MM2.     

A new hybrid method for time series forecasting: AR–ANFIS

In this study, a new hybrid forecasting method is proposed. The proposed method is called autoregressive adaptive network fuzzy inference system (AR–ANFIS). AR–ANFIS can be shown in a network structure. The architecture of the network has two parts. The first part is an ANFIS structure and the second part is a linear AR model structure. In the literature, AR models and ANFIS are widely used in time series forecasting. Linear AR models are used according to model-based strategy. A nonlinear model is employed by using ANFIS. Moreover, ANFIS is a kind of data-based modeling system like artificial neural network. In this study, a linear and nonlinear forecasting model is proposed by creating a hybrid method of AR and ANFIS. The new method has advantages of data-based and model-based approaches. AR–ANFIS is trained by using particle swarm optimization, and fuzzification is done by using fuzzy C-Means method. AR–ANFIS method is examined on some real-life time series data, and it is compared with the other time series forecasting methods. As a consequence of applications, it is shown that the proposed method can produce accurate forecasts.

     

Parallel eigenvalue calculation based on multiple shift–invert Lanczos and contour integral based spectral projection method

We discuss the possibility of using multiple shift–invert Lanczos and contour integral based spectral projection method to compute a relatively large number of eigenvalues of a large sparse and symmetric matrix on distributed memory parallel computers. The key to achieving high parallel efficiency in this type of computation is to divide the spectrum into several intervals in a way that leads to optimal use of computational resources. We discuss strategies for dividing the spectrum. Our strategies make use of an eigenvalue distribution profile that can be estimated through inertial counts and cubic spline fitting. Parallel sparse direct methods are used in both approaches. We use a simple cost model that describes the cost of computing k eigenvalues within a single interval in terms of the asymptotic cost of sparse matrix factorization and triangular substitutions. Several computational experiments are performed to demonstrate the effect of different spectrum division strategies on the overall performance of both multiple shift–invert Lanczos and the contour integral based method. We also show the parallel scalability of both approaches in the strong and weak scaling sense. In addition, we compare the performance of multiple shift–invert Lanczos and the contour integral based spectral projection method on a set of problems from density functional theory (DFT).