Air-Gap Flux Oriented Vector Control Based on Reduced-Order Flux Observer for EESM

Electrically excited synchronous motor (EESM) has the characteristics of high order, nonlinear and strong coupling, so it is difficult to be controlled. However, it has the advantages of adjustable power factor, high efficiency, and high precision torque control, so it is widely used in high-power applications. The accuracy of a flux observer influences the speed control system of EESM. Based on state observer in modern control theory and electrical excitation synchronous machine state equation, a reduced-order flux observer is designed. Using the first-order difference method and forward bilinear transformation method, the reduced-order flux observer is discrete, and the stability of the motor system is analyzed. The analysis shows that the stability of the system using the bilinear transformation method is better than that using the first order forward difference method. In motor operation, motor parameters will be affected by the factors of temperature, magnetic saturation, and motor frequency. In this paper, the influence of parameter variation on the motor system is studied by using the variation of the pole distribution. Finally, the speed regulation system using the reduced-order observer is simulated, which verifies the accuracy of the reduced-order flux observer observation.

D’Alembert wave and soliton molecule of the generalized Nizhnik–Novikov–Veselov equation

Traveling wave solution is one of the effective methods for solving nonlinear partial differential equations. D’Alembert solution is a special kind of traveling wave solution. There have been many studies about D’Alembert solution. In this paper, we will solve D’Alembert-type wave solutions for (2+1)-dimensional generalized Nizhnik–Novikov–Veselov equation. Based on the Hirota bilinear transformation and velocity resonance mechanism, the states of soliton molecules composed of two solitons, three solitons and four solitons are studied. It is concluded that D’Alembert-type wave is closely related to soliton molecules.

Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold. To get over the problems caused by the high data dimensionality, dimensionality reduction (DR) is a key subject for SPD data, where bilinear transformation plays a vital role. Because linear operations are not supported in nonlinear spaces such as Riemannian manifolds, directly performing Euclidean DR methods on SPD matrices is inadequate and difficult in complex models and optimization. An SPD data DR method based on Riemannian manifold tangent spaces and global isometry (RMTSISOM-SPDDR) is proposed in this research. The main contributions are listed: (1) Any Riemannian manifold tangent space is a Hilbert space isomorphic to a Euclidean space. Particularly for SPD manifolds, tangent spaces consist of symmetric matrices, which can greatly preserve the form and attributes of original SPD data. For this reason, RMTSISOM-SPDDR transfers the bilinear transformation from manifolds to tangent spaces. (2) By log transformation, original SPD data are mapped to the tangent space at the identity matrix under the affine invariant Riemannian metric (AIRM). In this way, the geodesic distance between original data and the identity matrix is equal to the Euclidean distance between corresponding tangent vector and the origin. (3) The bilinear transformation is further determined by the isometric criterion guaranteeing the geodesic distance on high-dimensional SPD manifold as close as possible to the Euclidean distance in the tangent space of low-dimensional SPD manifold. Then, we use it for the DR of original SPD data. Experiments on five commonly used datasets show that RMTSISOM-SPDDR is superior to five advanced SPD data DR algorithms.

Theory of the Design, and Operation of Digital Filters

Chapter 16 present the theoretical basis for digital filters, including issues related to their design. The basic characteristics and structures of finite impulse response and infinite impulse response filters are presented and discussed. In addition, the ideal and practical transfer characteristics of the digital filters are defined. The basic advantage of finite impulse response filters is that they can be designed to have an exact linear phase. However, infinite impulse response filters are generally more efficient computationally. The methods for filters design and related algorithms, which are based on the bilinear transformation method, windowed Fourier series, and algorithms based on iterative optimization, are also presented.

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

Transformations for FIR and IIR Filters’ Design

In this paper, the transfer functions related to one-dimensional (1-D) and two-dimensional (2-D) filters have been theoretically and numerically investigated. The finite impulse response (FIR), as well as the infinite impulse response (IIR) are the main 2-D filters which have been investigated. More specifically, methods like the Windows method, the bilinear transformation method, the design of 2-D filters from appropriate 1-D functions and the design of 2-D filters using optimization techniques have been presented.

Learning temporal attention in dynamic graphs with bilinear interactions

Reasoning about graphs evolving over time is a challenging concept in many domains, such as bioinformatics, physics, and social networks. We consider a common case in which edges can be short term interactions (e.g., messaging) or long term structural connections (e.g., friendship). In practice, long term edges are often specified by humans. Human-specified edges can be both expensive to produce and suboptimal for the downstream task. To alleviate these issues, we propose a model based on temporal point processes and variational autoencoders that learns to infer temporal attention between nodes by observing node communication. As temporal attention drives between-node feature propagation, using the dynamics of node interactions to learn this key component provides more flexibility while simultaneously avoiding issues associated with human-specified edges. We also propose a bilinear transformation layer for pairs of node features instead of concatenation, typically used in prior work, and demonstrate its superior performance in all cases. In experiments on two datasets in the dynamic link prediction task, our model often outperforms the baseline model that requires a human-specified graph. Moreover, our learned attention is semantically interpretable and infers connections similar to actual graphs.

Localized interaction solutions of the (2+1)-dimensional Ito Equation

Localized interaction solutions of the (2+1)-dimensional Ito equation with free parameters are obtained by using a Hirota bilinear transformation. Various plots with particular choices of the involved parameters are made to show energy distributions and dynamical properties of the special exact solutions. This phenomenon may provide us with interesting information on dynamics in the higher-dimensional nonlinear world.

A step edge detector based on bilinear transformation

Nowadays, Canny edge detector is considered to be one of the best edge detection approaches for the images with step form. Various overgeneralized versions of these edge detectors have been offered up to now, e.g. Saryazdi edge detector. This paper proposes a new discrete version of edge detection which is obtained from Shen-Castan and Saryazdi filters by using bilinear transformation. Different experimentations are conducted to decide the suitable parameters of the proposed edge detector and to examine its validity. To evaluate the strength of the proposed model, the results are compared to Canny, Sobel, Prewitt, LOG and Saryazdi methods. Finally, by calculation of mean square error (MSE) and peak signal-to-noise ratio (PSNR), the value of PSNR is always equal to or greater than the PSNR value of suggested methods. Moreover, by calculation of Baddeley’s error metric (BEM) on ten test images from the Berkeley Segmentation DataSet (BSDS), we show that the proposed method outperforms the other methods. Therefore, visual and quantitative comparison shows the efficiency and strength of proposed method.