Insufficient Degrees Of Freedom Research Articles

Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

AbstractThe density of a numerical mesh is a key component for the quality of the numerical solution. Common methods in groundwater simulations rely on meshes generated prior to simulation, which lead to unnecessary or insufficient degrees of freedom (dofs). In this study we use Adaptive Mesh Refinement (AMR) to substitute the subjective mesh generation process with a more rigorous approach where new dofs are iteratively added to the solution of an initial coarse mesh based on a solution error estimation. The simulation is solved on a succession of meshes through which the mesh density is increased in areas of steep gradients in the solution variable. Here, we apply the approach to unconfined aquifer flow which is a non‐linear problem commonly encountered in groundwater modeling. By taking advantage of the iterative nature of AMR we arrive at an efficient solver approach. We treat the position of the unconfined boundary as an additional unknown which is estimated iteratively. The first iterations are executed rapidly as the mesh is rather coarse, while the free boundary adapts to the computed water table position as close as the mesh density allows. In this study we demonstrate the viability of the proposed unconfined aquifer simulation method to a series of 2D hypothetical examples under several conditions and stresses as well as a 3D test case. In all cases the AMR was able to automatically resolve the solution in areas with steep hydraulic head gradient, using appropriately higher density to achieve high localized refinement and accuracy.

Analysis of the Unconstrained Frequency-Domain Block LMS for Second-Order Noncircular Inputs

The unconstrained frequency-domain block least mean square (UFBLMS) algorithm is a de facto standard in frequency-domain adaptive filtering, owing to its fast convergence for correlated input signals. However, although many complex-valued signals in real-world applications are second-order noncircular (improper), for computational convenience, existing mean square analyses of UFBLMS assume second-order circular (proper) input data. This, in turn, makes conventional mean square evaluations of UFBLMS inadequate. To address this issue, we propose a novel performance evaluation framework of UFBLMS, which makes it possible to investigate how the full second-order statistics of second-order noncircular correlated input signals, i.e., both their covariance and complementary covariance, influence the output error and the weight error of UFBLMS. A unified stability bound on the step-size of UFBLMS is next provided, enabling intuitive closed-form relations, in the steady-state stage, between the terms within full second-order error statistics, namely, the mean square error (MSE) and complementary MSE, and the input noncircularity. Furthermore, this proposed full second-order statistical framework is shown to enable more physical insight into the underlying physics of the contribution of the real and imaginary channels of UFBLMS, which cannot be achieved using the standard MSE analysis due to its insufficient degrees of freedom. Simulations and real-world experiments in the system identification setting support the analysis.

Direct Position Determination of Multiple Non-Circular Sources with a Moving Coprime Array.

Direct position determination (DPD) is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramer–Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.

Evaluation of quality of partial caging by a planar two-fingered hand

In partial caging, an object is partially constrained by robots and is able to escape from there. Although complete caging ensures the hand never releases the confined object, insufficient degrees of freedom of robots does not often satisfy the conditions for caging. Partial caging, however, can be accomplished even by robots having such mechanical restriction. We consider a case that an object moves in the semi-closed region formed by a planar robot hand with two fingers, as an example of partial caging in two-dimensional space. Then the parameters of fingers: joint angles interfere in the object motion to escape from the hand through the gap between the fingertips. Some simulation results show differences of difficulty of escaping according to arrangement of fingers, and factors interfering in the difficulty are analyzed. Additionally, we also evaluate ease of entering the hand through the gap and define an ability index of robot hand for partial caging with the above two evaluation scores. Then a high index score indicates that the hand assumed to be able to capture objects easily and confine it without any finger motion. It can be utilized for mechanical design and controlling strategies of robots in capturing objects.

Kinodynamically Consistent Motion Retargeting for Humanoids

Human-to-humanoid motion retargeting is an important tool to generate human-like humanoid motions. This retargeting problem is often formulated as a Cartesian control problem for the humanoid from a set of task points in the captured human data. Classically, Cartesian control has been developed for redundant systems. While redundancy fundamentally adds new sub-task capabilities, the degree to which secondary objectives can be faithfully executed cannot be determined in advance. In fact, a robot that exhibits redundancy with respect to an operational task may have insufficient degrees of freedom (DOFs) to satisfy more critical constraints. In this paper, we present a Cartesian space resolved acceleration control framework to handle execution of operational tasks and constraints for redundant and nonredundant task specifications. The approach is well suited for online control of humanoid robots from captured human motion data expressed by Cartesian variables. The current formulation enforces kinematic constraints such as joint limits, self-collisions, and foot constraints and incorporates a dynamically-consistent redundancy resolution approach to minimize costly joint motions. The efficacy of the proposed algorithm is demonstrated by simulated and real-time experiments of human motion replication on a Honda humanoid robot model. The algorithm closely tracks all input motions while smoothly and automatically transitioning between regimes where different constraints are binding.

The fate of monsters in anti-de Sitter spacetime

Abstract Black hole entropy remains a deep puzzle: where does such enormous amount of entropy come from? Curiously, there exist gravitational configurations that possess even larger entropy than a black hole of the same mass, in fact, arbitrarily high entropy. These are the so-called monsters, which are problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence paradigm since there is far insufficient degrees of freedom on the field theory side to account for the enormous entropy of monsters in AdS bulk. The physics of the bulk however may be considerably modified at semi-classical level due to the presence of branes. We show that this is especially so since monster spacetimes are unstable due to brane nucleation. As a consequence, it is not clear what the final fate of monsters is. We argue that in some cases there is no real threat from monsters since although they are solutions to Einstein’s Field Equations, they are very likely to be completely unstable when embedded in string theory, and thus probably are not solutions to the full quantum theory of gravity. Our analysis, while suggestive and supportive of the claim that such pathological objects are not allowed in the final theory, by itself does not rule out all monsters. We comment on various kin of monsters such as the “bag-of-gold” spacetime, and also discuss briefly the implications of our work to some puzzles related to black hole entropy.

Role of three-body recombination for charge reduction in MALDI process

Ions in Matrix-Assisted Laser Desorption/Ionization (MALDI) are predominantly singly charged for small analyte molecules. With the estimated high number density and low temperature of electrons, the three-body recombination mechanism is attractive and should be considered as an important cause for the charge reduction in the plume. Theoretical calculations indicate that the rate coefficient of the three-body recombination is about 50 times higher than that of the two-body recombination if the analyte molecule has insufficient degrees of freedom. Experimental results show that, for small analyte molecules, the ratio of AH2(2+)/AH(+) is close to the theoretical 5% value from the three-body recombination modeling and this ratio declines with the increasing electron and matrix molecule number density caused by greater laser irradiance. The ratio of [A + 2](+)/[A + 1](+) is higher than the theoretical isotopic value, and the excess [A + 2](+) could exclusively result from the three-body recombination collisions. Further evidence demonstrates that [A + 2](+)/[A + 1](+) increases with electron number density, which is in correspondence with the model. All of these theoretical and experimental results indicate that three-body recombination is an essential charge reduction mechanism for small molecules in the MALDI plume.

Two-Point Floating Clamping Device Based on Fixed Cylinder with Double-Piston and Toggle-Lever Force Amplifier

Two-point floating clamping device, widely used in manufacturing field, can effectively ensure the same clamping force on different workpieces or different surfaces in one workpiece. But due to the application of unitary suspended articulated cylinder, traditional two-point floating devices have disadvantages such as poor working status, great impaction, vibration and noise. A kind of innovatively designed two-point floating clamping devices, with rigidly fixed cylinder replacing unitary suspended articulated cylinder, is presented in this paper. To solve the problem of insufficient degrees of freedom, three different methods are applied. This device has significant advantages in compact structure, small impaction and vibration noise. Moreover, the working principle and mechanical calculation formulas are presented in this paper, which is instructive to the industrial field.

A Novel Algorithm for Simple Hybrid of Adaptive Array and Equalizer

Adaptive array has been used for canceling the interference in communication. When the array cannot suppress all the interference, an equalizer following the array can add to further enhance the capability of canceling the inter-symbol interference (ISI). The adaptive array and equalizer (AE) will suffer the problems of insufficient degrees of freedom and main-beam multi-path ISI. The hybrid of adaptive array and equalizer (HAE) uses a modified training sequence to adjust the weights of adaptive array that leads the array to cancel only the co-channel interference (CCI). The ISI are removed by the equalizer following the array. Thus, the HAE can combat the above problems successfully. Though the HAE improves the performance of AE, a transversal filter is added to generate the modified training sequence. Besides, the weights of equalizer in the HAE, which adjust after the weights of adaptive array, will make the convergent rate slowly. A simple hybrid of adaptive array and equalizer (SHAE) utilizes the output signal of system to adjust the weights of both the adaptive array and equalizer simultaneously. Therefore, the convergent rate of the HAE can improve by the SHAE. Moreover, the ISI can be suppressed by the equalizer instead of the adaptive array in the SHAE that will improve the performance of AE without using the transversal filter. As the mutual coupling present, the convergent rate of the SHAE will slow down. In this paper, a least mean square error algorithm with mutual coupling present is proposed to improve the convergent rate of SHAE, also.

Bilinear equation method for unbiased identification of linear FIR systems in the presence of input and output noises

The presence of contaminating noises in both the input and output of an FIR system usually results in a biased least squares (LS) parameter estimate. The total least squares (TLS) methods are known to be efficient in achieving unbiased estimation, if the ratio of the input noise variance to the output noise variance (NNR) is known. However, when the NNR is unknown, a simple analysis shows that the classical LS and TLS estimation methods usually have such insufficient degree of freedom that they can achieve the unbiased solution. In this paper, it is shown by analyzing the algebraic structure of the correlation matrix that the unbiased estimate of FIR parameters can be obtained by solving a special bilinear equation. Then we develop a bilinear equation method (BEM) for solving the bilinear equation associated with the unbiased solution of the FIR system or filtering under the unknown NNR. Unlike the available unbiased estimators, the main advantage is that the proposed method exploits much sufficiently the special structure of the correlation matrix and obtains much accurate estimation for FIR filtering in the presence of input and output noises. Two simulation examples are presented that show the good performance of the proposed method, including its superiority over the classical LS and TLS approaches, and the instrumental variable methods.

Adaptive Hybrid Beamformer for Mobile Reception of ATSC DTV

An adaptive hybrid beamformer is proposed to improve the reception performance of the advanced television system committee (ATSC) digital television (DTV) in a mobile environment. Dynamic multipaths and Doppler shifts severely degrade the reception performance of the ATSC DTV receiver. Accordingly, a hybrid beamformer, called a Capon and least mean square (CLMS) beamformer, is presented that uses direction of arrival (DOA) information and the least mean square (LMS) beamforming algorithm. The proposed CLMS algorithm efficiently removes dynamic multipaths and compensates for the phase distortion caused by Doppler shifts in mobile receivers. When the CLMS beamformer has an insufficient degree of freedom (DOF), the subsequent use of an equalizer removes any residual multipath effects, thereby significantly improving the performance of DTV receivers. The performances of the proposed CLMS, Capon, and LMS beamformers are compared based on computer simulations. In addition, the overall performance of the CLMS beamformer followed by an equalizer is also considered.

不完全な接触をもつ把持の力学的多面凸解析

Contacts with insufficient degrees of freedom are defined as defective contacts. Although defective contacts are found in the power-grasp and the enveloping grasp of a multifingered robot hand, the mechanical characteristics are not yet studied in depth. In this paper, an approach to the mechanical analysis of grasps with defective contacts is presented. The relations among joint torque space, contact force space, friction cone, admissible external force space are made clear. By using the convex analysis, we represent these sets in the external or internal representation of polyhedral convex set. Finally, the validity of our approach is illustrated by a numerical example.

全腕式電動義手(TDU ys-86)のメカニズムと工学的評価

Many handicapped persons have had both arms amputated from the shoulder due to accidents or malignant tumors; these individuals need help in their daily life, especially for taking meals, and such needs can some-times be filled by a high-performance shoulder prosthesis. About 20 years ago electrical prostheses were developed for thalidomide victims in many countries; however, insufficient degree of freedom, problems in controlling, increase in weight in proportion to freedom degree improvement, and other problems gradually put them out of use. We therefore have developed over the past several years a new type of total-arm electrical prosthesis (right arm) with DC motors controlled by 3 single-chip microcomputers, and have developed technical support system for the arms using a CAD system. The arm consists of a space linkage shoulder mechanism capable of giving the arm 6 degrees of freedom, with a modular gripper including forward and side raising, rotation of upper arm and elbow bending, inside and outside direction forearm turning, and grippers opening and closing. A battery and control printed circuit board was made in order to keep the weight light. The arm is basically operated by chin switches. The main movement is divided into two kinds, i. e., manually controlled and combined movement by DDA (digital differential analyzer). With the cooperation of 3 disabled persons, we are currently undertaking training in wearing and operating the arm using a personal computer.

An algorithm for pattern synthesis improvement

When shaped beams are synthesized using array antennas with a limited number of elements, insufficient degrees of freedom sometimes result in practically unsatisfactory patterns. In such cases, it is very convenient if the unsatisfactory patterns can be improved to satisfactory ones using some techniques. An example is presented of such pattern improvement techniques. First, an algorithm necessary for the improvement technique is derived by modifying an algorithm commonly used for adaptive array antennas into a form not requiring real time information of receiving signals. Then, three application examples of this technique are presented. In the example of a shaped beam array antenna of which two elements are removed out of ten elements, measured results are compared to the calculated pattern to show the validity and usefulness of this technique.