Minimum Norm Method Research Articles

Deformation mechanics of generalized missing rib chiral lattice structures

The planar missing rib lattice topology is generalized to construct a family of regular and irregular tetra-chiral periodic lattices. The geometry of a lattice in the family is completely defined by a set of six parameters. Using a unified energy based approach, the constitutive model and all effective elastic properties of the resulting lattice structures are determined from the unit periodic element of the lattice. Straightforward analytical expressions of the effective properties are obtained for some special geometries, which for the general case may be lengthy. In the latter case, the compliance tensor can easily be obtained numerically. The proposed approach involves accurate determination of the strain tensor and the compliance tensor for which a minimum error norm method is used. The results from the analytical expressions are compared with those obtained from Finite Element Analysis (FEA), and a very good match is observed. To draw a parity with experimental determination of the elastic properties and address the observation of auxeticity (negative Poisson’s ratio) in such lattice structures, the concept of empirical Young’s modulus and Poisson’s ratio is introduced. Using this idea, for the conventional chiral lattice, some disagreement in the existing literature is resolved.

Image parallel block compressive sensing scheme using DFT measurement matrix

Compressive sensing (CS)-based image coding has been widely studied in the field of image processing. However, the CS-based image encoder has a significant gap in image reconstruction performance compared with the conventional image compression methods. In order to improve the reconstruction quality of CS-based image encoder, we proposed an image parallel block compressive sensing (BCS) coding scheme, which is based on discrete Cosine transform (DCT) sparse basis matrix and partial discrete Fourier transform (DFT) measurement matrix. In the proposed parallel BCS scheme, each column of an image block is sampled by the same DFT measurement matrix. Due to the complex property of DFT measurement matrix, the compressed image data is complex. Then, the real part and imaginary part of the resulting BCS data are quantized and transformed into two bit streams, respectively. At the reconstruction stage, the resulting two bit streams are transformed back into two real signals using inverse quantization operation. The resulting two real signals are combined into one complex signal, which is served as the input data of the CS reconstructed algorithm. The theoretical analysis based on minimum Frobenius norm method demonstrates that the proposed DFT measurement matrix outperforms the other conventional measurement matrices. The simulation results show that the reconstructed performance of the proposed DFT measurement matrix is better than that of the other conventional measurement matrices for the proposed parallel BCS. Specifically, we analyzed the impact of quantization on the reconstruction performance of CS. The experiment results show that the effect of the quantization on reconstruction performance in BCS framework can nearly be ignored.

Simple phase unwrapping method with continuous convex minimization.

Phase unwrapping is a problem to reconstruct true phase values from modulo 2π phase values measured using various phase imaging techniques. This procedure is essentially formulated as a discrete optimization problem. However, most energy minimization methods using continuous optimization techniques have ignored the discrete nature and solved it as a continuous minimization problem directly, leading to losing exactness of the algorithms. We propose a new minimum norm method that can yield the optimal solution of the discrete problem by minimizing a continuous energy function. In contrast to the graph-cuts method, which is state of the art in this field, the proposed method requires much less memory space and a very simple implementation. Therefore, it can be simply extended to 3D or 4D phase unwrapping problems.

Performance analysis of beamforming algorithm based on compressed sensing

The beamforming (BF) algorithm is widely used in sound source recognition due to its superior performance, but its main lobe is wide, side lobes are high, and its running speed is slow. Therefore, a method based on the compressed sensing beamforming method is proposed. The sound source measurement model is established, the compressed sensing reconstruction matrix is applied to the beamforming method, and propose a compressed sensing beamforming sound source recognition method. The sound source recognition performance of orthogonal matching pursuit (OMP), generalized orthogonal matching pursuit (gOMP), and regularized orthogonal matching pursuit (ROMP) is compared and analyzed through MATLAB simulation, and the OMP algorithm is selected to combine with the beamforming method. Further study the OMP-BF way and compare and analyze the recognition accuracy and running time of OMP-BF with functional beamforming (F-BF) and L1 minimum norm method beamforming (L1-BF). The results show that the OMP-BF method can accurately identify the sound source location, and the running time is much lower than L1-BF and F-BF. Finally, through experiments, the effectiveness of the algorithm is verified.

3D Imaging With Moving Fringe Structured Illumination Microscopy

Structured Light Illumination Microscopy (SIM) has proved itself as a very effective method to improve the resolution of a widefield (WF) fluorescent microscope. In this paper, we demonstrate a new approach to three-dimensional (3D) imaging with the SIM, using a moving fringe (MF) illumination pattern. Instead of the standard three-beam standing wave illumination pattern, our method requires a two-beam one, varying along the optical axis. Each axial layer of the MF illumination pattern contains single-spatial-frequency interference fringes, traversing the space with its own speed (temporal frequency), proportional to the axial offset of such layer from the excitation plane. The different axial layers of a fluorescent object, excited with the MF illumination, will emit a continuous amplitude modulated fluorescent signal with the frequency of modulation proportional to the temporal frequency of the moving fringe pattern. The fine 3D image reconstruction is achieved via extracting the spatial location of the fluorescent object from the temporal frequency of amplitude modulated signal emitted by it. Since in our approach the problem of 3D image reconstruction is reduced to the problem of accurate temporal frequency estimation, any of the well-known spectrum estimation techniques can be applied to the problem, allowing the axial resolution improvement far beyond the limits of the classical 3D SIM. In this research, we suggest using the Minimum-norm method for the proposed MF SIM system, which gives a superior resolving power in spectrum estimation. Simulation results show that such a simple and rapid hardware implementation in combination with a straightforward signal processing method can, however, deliver an improvement in axial resolution far beyond the classical 3D SIM approach.

Global energy efficiency improvement of redundant hydraulic manipulator with dynamic programming

Open-loop controlled hydraulic manipulators are still dominating in construction sites and forest fields thanks to little reliance on the expertise of human operators in manipulator control, which however exist large inlet/outlet and other energy losses during working cycles. And the situation further deteriorates with the increasing number of joints. This paper discusses the problem of global energy optimization of three-degrees-of-freedom (3-DOF) hydraulic manipulator in case of plane motion where exists an exceeding DOF for motion redundancy. Different from conventional energy optimization methods applied to electric driven manipulators, the proposed global energy-optimized dynamic programming (DP) algorithm models the whole system at the hydraulic level, which contains the dynamic characteristics of pressure-flow coupling between cylinders. The energy consumption models of constant pressure (CP), load-sensing (LS) and electrohydraulic load-sensing (ELS) systems are built in terms of cost functions formulated in the proposed algorithm together with penalty function containing physical actuator constraints at position, velocity and acceleration level. The DP algorithm is tested in various cases, and the convergence is proved consistent. To highlight the effectiveness of the proposed algorithm, the gradient projection (GP) method and the actuator velocity minimum norm (MA) method are introduced as a contrast. The results of the numerical examples of end-effector paths using the mechanical-hydraulic coupling AMESim model demonstrate that the DP algorithm saves around 10.49% hydraulic energy consumption in the CP system while saving around 76.55% in the LS system. Experiments performed on a typical-structured hydraulic manipulator further validate the effectiveness of the proposed algorithm, with approximately 4.61% energy saving in the CP system and 29.89% in the LS system. The energy-saving ratio is even larger in the ELS system, with around 80.03% comparing the max value. These contribute to the energy optimization resolution of redundant hydraulic manipulators to a degree.

Direction of Arrival Estimation by Matching Pursuit Algorithm With Subspace Information

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

Impulsive orbit correction using second-order Gauss’s variational equations

Based on Gauss’s variational equations (GVEs), the impulsive orbital-element corrections are investigated in orbit transfer problems. Both single impulse and multiple impulses are considered for the first-order and second-order GVEs. For the single impulse, a nonlinear least-squares iteration method for the minimum orbit error is provided to simultaneously solve for the impulse vector and the impulse position. For multiple impulses, a minimum-norm method for the energy cost is proposed to solve the three-impulse and two-impulse corrections for the in-plane and out-of-plane orbital elements, respectively. The impulse positions are analytically derived, and the impulse vectors are obtained by the minimum-norm method. Numerical examples are provided to verify the proposed single-impulse least-squares and multiple-impulse minimum-norm methods. The results show that the nonlinear solutions using the second-order GVEs are more accurate than those using the first-order GVEs.

Comparative Study of Accuracy of Direction of Arrival (DOA) Estimation using Genetic Algorithm and Multiple Signal Classification (MUSIC)

In this work we are involved in determining the direction of arrival estimation of the signals. For accomplishing this task, we are involved in using genetic algorithm method. Here are many methods of direction of arrival methods, such as MUSIC algorithm, Minimum Norm Method, ESPRIT. Among all the previously existing techniques, MUSIC algorithm is best method of direction arrival estimation method. But the MUSIC algorithm will take more time when compared to the genetic algorithm. If the signal is having more noise conditions, then MUSIC algorithm will not perform well when compared to the genetic algorithm. For 0db SNR, the DOA for the Genetic algorithm is 0.01 % varying but for the same SNR, in the case of MUSIC algorithm, DOS is 5% variation is observed. For a given SNR, the DOA estimated for 4 element antenna array in the case of Genetic algorithm is not observed for the MUSIC algorithm for the same signal SNR and number of antenna elements. Here a comparative study between the Genetic Algorithm and MUSIC algorithm performance is studied. The application can be included in the advanced system where a wireless device can detect the DOA very accurately without doing the more computations. The algorithms are implemented by using the MATLAB tool. Keywords: AWGN, Direction Of Arrival (DOA), ESPRIT Antenna Array, Genetic Algorithm (GA), MUSIC Algorithm, Minimum Norm Method

Two-dimensional Phase Unwrapping Method Using Cost Function of L0 Norm

Considering cost model and convergence speed of the minimum norm unwrapping, a highly efficient two-dimensional global phase unwrapping method optimized with L0 norm is proposed. As analysing features of cost model in phase unwrapping with minimum norm, a cost function definition is provided in line with the L0 norm, which impose a stronger constraint in the tangent direction of phase discontinuity boundary than that in normal direction, in order to preserve integrity of discontinuity during iterative unwrapping processing for continuous phase. For the sake of slow speed of low-frequency error convergence during linear solving, a data partitioning strategy is introduced into unwrapping processing. Due to independence of minimum norm method in blocks, linear solving only focus on high-frequency information and improve efficiency of iterative work, and the low-frequency processing part is transferred to offsetting-aligning between blocks. With experiments and analysis, reliability and efficiency of the novel phase unwrapping method are certified comparing to existing methods.

Inverse Kinematics Analysis of a 7-DOF Space Manipulator for Trajectory Design

To solve the inverse kinematics problem for redundant degrees of freedom (DOFs) manipulators has been and still continues to be quite challenging in the field of robotics. Aiming at trajectory planning for a 7-DOF space manipulator system, joint rotation trajectories are obtained from predetermined motion trajectories and poses of the end effector in Cartesian space based on the proposed generalized inverse kinematics method. A minimum norm method is employed to choose the best trajectory among available trajectories. Numerical simulations with the 7-DOF manipulator show that the proposed method can achieve the planned trajectory and pose under the circumstances of minimum angular velocities. Moreover, trajectory results from the proposed kinematics model and inverse kinematics method has the advantages of simple modelling, low computation cost, easy to solve and plan trajectory conveniently. The smooth and continuous joint rotation functions obtained from the proposed method are suitable for practical engineering applications.

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis

Mesh reflectors with large apertures have been used in many communication satellites. The performance of antenna reflectors crucially depends on the faceting error of the reflective surface, which is approximated by using meshes. The force density method (FDM) has been widely used for the form-finding analysis of mesh reflectors. However, after performing form-finding of some meshes, the effective reflective area will decrease. In addition, the form-finding of the auxiliary mesh has received little attention, and it cannot be achieved by using the FDM. Thus, in this study, an effective form-finding methodology that combines the iterative FDM and the minimum norm method (MNM) is proposed. To consider the flexibility of the reflector ring truss, a static analysis of the ring truss under the tension force actions is also performed in the form-finding processes. The reflector flexible parts are described by the absolute nodal coordinate formulation (ANCF). Finally, the form-finding analysis of the reflector with the standard configuration, the central hub configuration, and the circular configuration is performed to validate the proposed methodology. The influence of the mesh tension force on the reflector natural frequencies is also studied. After performing the form-finding analysis, the initial configuration of the reflector with tensioned meshes for the deployment dynamics study can be determined. Based on this paper, the deployment dynamics of a complex AstroMesh reflector will be studied in a successive paper “Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation.”

The MUSIC Minimum Norm Method for Linear Polarized Array Parameter Estimation

This paper used signal Cyclostationarity and MUSIC minimum norm method to estimate DOA and polarization parameters with linear polarization array. Cyclostationarity statistics have the advantage of limiting different frequencies of signal cycle stationary colored noise and inhibit both the minimum norm loop correlation function and estimation error. This paper also verifies the effectiveness of the method through simulation experiments.

Cyclic Relation Method for DOA and Polarization Parameters Estimation of Arbitrary Polarized Array

Focus on the estimation for DOA and polarization parameters of electromagnetic sensor array, this paper proposes the method that uses cyclic relation function to substitute for covariance matrix. Because cyclic statistic is less sensitive to stable noise and any cyclic stable noise with different cyclic frequency, the method proposed is immune to any stable color noise. This method use minimum norm method to solve the spectrum function. So this method can restrict the effect of the cyclic relation matrix estimating error. Computer simulation experiments prove the performance of this method.

Cortical graph smoothing: a novel method for exploiting DWI-derived anatomical brain connectivity to improve EEG source estimation.

The electroencephalography source estimation problem consists of inferring cortical activation from measurements of electrical potential taken on the scalp surface. This inverse problem is intrinsically ill-posed. In particular the dimensionality of cortical sources greatly exceeds the number of electrode measurements, and source estimation requires regularization to obtain a unique solution. In this work, we introduce a novel regularization function called cortical graph smoothing, which exploits knowledge of anatomical connectivity available from diffusion-weighted imaging. Given a weighted graph description of the anatomical connectivity of the brain, cortical graph smoothing penalizes the weighted sum of squares of differences of cortical activity across the graph edges, thus encouraging solutions with consistent activation across anatomically connected regions. We explore the performance of the cortical graph smoothing source estimates for analysis of the event related potential for simple motor tasks, and compare against the commonly used minimum norm, weighted minimum norm, LORETA and sLORETA source estimation methods. Evaluated over a series of 18 subjects, the proposed cortical graph smoothing method shows superior localization accuracy compared to the minimum norm method, and greater relative peak intensity than the other comparison methods.

Electromagnetic Vector Sensor array parameter estimation method

Joint estimation method for DOA and polarization parameters of single electromagnetic vector sensor is mostly concerned in radar signal processing now. This paper presents a new algorithm which uses the cyclostationary property of signal. It gets the estimation of DOA and polarization parameters from the noise subspace with minimum norm method. This method can reduce the estimate error of noise subspace vector. At the same time, it is immune to the additional stationary noise of any distribution and interference signals with different cyclic frequencies. Method has been tested by computer simulation and the test result is show in the paper. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2562 Full Text: PDF

Using Single-Cycle-Related Electromagnetic Vector Sensors to Estimation DOA and Polarization Parameters

This paper proposes a new algorithm for joint estimation of Directions-Of-Arrival (DOA’s) and polarization parameters of the single electromagnetic vector sensor. Based on the cyclostationary properties of the signal,the algorithm uses minimum norm method to strike the signal steering vector solution, and then gets the estimation of DOA and polarization parameters. Besides limiting the distribution of additional stationary noise and interference signals on various frequencies, this algorithm also restraints the estimation error of the noise subspace singular vector with outstanding results. Computer simulation verified the effectiveness of the algorithm.

Motion Planning of Underwater Vehicle-Manipulator System with Joint Limit

This paper studies motion planning of underwater vehicle-manipulator system (UVMS) based on weighted minimum norm method with joint limit. In response to the problem that joint motion is limited and cannot give full play to kinematical performance in the range of allowed orientation angle, existed in the traditional weighted minimum norm method for joint limit, an improved method about motion planning is proposed. By means of introducing threshold in the joint potential function to change the initial position where the joint velocity is limited, the method makes that joint is only limited between threshold and boundary when it moves from the middle position to bilateral boundaries. A simulation is carried out to verify the proposed motion planning method.

Optimal torque distribution method for a redundantly actuated 3-RRR parallel robot using a geometrical approach

SUMMARYIn this paper, a novel optimal torque distribution method for a redundantly actuated parallel robot is proposed. Geometric analysis based on screw theory is performed to calculate the stiffness matrix of a redundantly actuated 3-RRR parallel robot. The analysis is performed based on statics focusing on low-speed motions. The stiffness matrix consisting of passive and active stiffness is also derived by the differentiation of Jacobian matrix. Comparing two matrices, we found that null-space vector is related to link geometry. The optimal distribution torque is determined by adapting mean value of minimum and maximum angles as direction angles of null-space vector. The resulting algorithm is validated by comparing the new method with the minimum-norm method and the weighted pseudo-inverse method for two different paths and force conditions. The proposed torque distribution algorithm shows the characteristics of minimizing the maximum torque.

A comparison of minimum norm and MUSIC for a combined MEG/EEG sensor array

Abstract. Many different algorithms for imaging neuronal activity with magnetoencephalography (MEG) or electroencephalography (EEG) have been developed so far. We validate the result of other authors that a combined MEG/EEG sensor array provides smaller source localisation errors than a single MEG or single EEG sensor array for the same total number of sensors. We show that Multiple Signal Classification (MUSIC) provides smaller localisation errors than an unweighted minimum norm method for activity located in the cortical sulcus regions. This is important for many medical applications, e.g. the localisation of the origin of epileptic seizures (focal epilepsy) that can be located very deep in the cortical sulcus.