Spectral Unmixing of Hyperspectral Remote Sensing Imagery via Preserving the Intrinsic Structure Invariant

Hyperspectral unmixing, which decomposes mixed pixels into endmembers and corresponding abundance maps of endmembers, has obtained much attention in recent decades. Most spectral unmixing algorithms based on non-negative matrix factorization (NMF) do not explore the intrinsic manifold structure of hyperspectral data space. Studies have proven image data is smooth along the intrinsic manifold structure. Thus, this paper explores the intrinsic manifold structure of hyperspectral data space and introduces manifold learning into NMF for spectral unmixing. Firstly, a novel projection equation is employed to model the intrinsic structure of hyperspectral image preserving spectral information and spatial information of hyperspectral image. Then, a graph regularizer which establishes a close link between hyperspectral image and abundance matrix is introduced in the proposed method to keep intrinsic structure invariant in spectral unmixing. In this way, decomposed abundance matrix is able to preserve the true abundance intrinsic structure, which leads to a more desired spectral unmixing performance. At last, the experimental results including the spectral angle distance and the root mean square error on synthetic and real hyperspectral data prove the superiority of the proposed method over the previous methods.

A Projection Neural Network for Circular Cone Programming

A projection neural network method for circular cone programming is proposed. In the KKT condition for the circular cone programming, the complementary slack equation is transformed into an equivalent projection equation. The energy function is constructed by the distance function and the dynamic differential equation is given by the descent direction of the energy function. Since the projection on the circular cone is simple and costs less computation time, the proposed neural network requires less state variables and leads to low complexity. We prove that the proposed neural network is stable in the sense of Lyapunov and globally convergent. The simulation experiments show our method is efficient and effective.

A Posterior Model Reduction Method Based on Weighted Residue for Linear Partial Differential Equations

This paper is concerned with a new model reduced method based on optimal large truncated low-dimensional dynamical system, by which the solution of linear partial differential equation (PDE) is able to be approximate with highly accuracy. The method proposed is based on the weighted residue of PDE under consideration, and the weighted residue is used as an alternative optimal control condition (POT-WR) while solving the PDE. A set of bases is constructed to describe a dynamical system required in case. The Lagrangian multiplier is introduced to eliminate the constraints of the Galerkin projection equation, and the penalty function is used to remove the orthogonal constraint. According to the extreme principle, a set of the ordinary differential equations is obtained by taking the variational operation on generalized optimal function. A conjugate gradients algorithm on FORTRAN code is developed to solve these ordinary differential equations with Fourier polynomials as the initial bases for iterations. The heat transfer equation under a potential initial condition is used to verify the method proposed. Good agreement between the simulations and the analytical solutions of example was obtained, indicating that the POT-WR method presented in this paper provides the most effective posterior way of capturing the dominant characteristics of an infinite-dimensional dynamical system with only finitely few bases.

A persistent method for parameter identification of a seven-axes manipulator

SUMMARYThis paper presents a persistent method for the identification problem of open-chained robotic systems. Based on the Projection Equation, a new, direct method to collect the dynamic and friction parameters in linear form is worked out. However, in this form, linear dependencies in the parameters occur and they are canceled out with the help of the QR algorithm. The obtained linear independent parameters are the base parameters of the system. To ensure a good excitation, the identification is improved by using optimized trajectories defined by Fourier-series, taking also physical constraints into account. The evaluation of the dynamic robot parameters is realized with a least squares error optimization. Furthermore, the result strongly depends on a special choice of weighting matrices for the error. Experimental results for a seven-axes robotic system (standard six-axes industrial manipulator mounted on a linear axis) are presented in detail. Additionally, the influence of temperature effects to base parameter changes is discussed.

Neural Network to Solve Concave Games

The issue on neural network method to solve concave games is concerned. Combined with variational inequality, Ky Fan inequality, and projection equation, concave games are transformed into a neural network model. On the basis of the Lyapunov stable theory, some stability results are also given. Finally, two classic games’ simulation results are given to illustrate the theoretical results.

On the Choice of Shape Functions of Unsymmetrical Elastic Rotors

In this paper the effects of rotordynamics under the aspect of the choice of shape functions are discussed. For this purpose a rotor system which consists of a slim shaft and two rigid disks is modeled using the Projection Equation. The shaft is assumed as an elastic Euler-Bernoulli beam, supported by two bearings modeled as radial spring systems. The rotor is driven by a permanent-magnet synchronous motor whose torque is transmitted with a spur gear pair next to one of the bearings. A Ritz approach is used to separate the elastic displacements in position and time, thereby different shape functions are evaluated. Approximated eigenfunctions are computed and used as shape functions as well. For validation, the eigenfrequencies are compared with semi-analytical ones, calculated with the Transfer-Matrix-Method and experimental results. The insights obtained from this work should make it easier to choose the appropriate shape functions for such problems.

Dynamical Modeling of Flexible Linear Robots

The production sector aims towards increasing capacity and energy efficiency. A possibility to achieve this is the usage of manipulators built of lightweight structures in order to raise the maximum velocity, acceleration and payload. This leads to an elastic robot that tends to vibrate. The main focus of this paper is the modeling of a fast moving, elastic robot with three linear axes. These axes are connected by four flexible links driven by synchronous motors with elastic gear racks and bearing elasticities. The Projection Equation in subsystem form is used to calculate the dynamic model. This equation in combination with a Ritz approximation for the flexible links, which are modeled as Rayleigh beams, leads to a set of highly nonlinear ordinary differential equations. The usage of the Projection Equation in subsystem form simplifies the modeling of this system and offers the possibility of a fast numerical integration supported by the Maple® packages SimCode2, SimSubs and SimRecursive. The subsystems of the elastic bodies are assembled by the kinematical chain. This leads to the possibility to evaluate the minimal accelerations of the system by a recursive scheme with O(n) efficiency. These results for the endpoint (position and acceleration) of the complete elastically modeled robot are compared to experimental measurements.