Calculation Of Inverse Matrix Research Articles

Electric-potential-measurement-based methodology for estimation of electric charge density at the surface of tribocharged insulating slabs

The auto-compensated electrostatic induction probe (ACEIP) is widely used for measuring the electric potential at the surface of conductive or insulating bodies. The aim of this paper is to elaborate a methodology for using this probe in view of performing the estimation of electric charge density at the surface of tribocharged insulating slabs. In such cases, the electric potential is not uniformly distributed on the surface under investigation. Metallic plates trimmed with different shapes were used to characterize the probe. Thus, a first series of experiments enabled a crude evaluation of the shape and size of the area “seen by the probe”: a 10-mm-diameter circle. Other experiments served to determine the transfer function that relates the value measured by the probe to the potential of a small area of constant electric potential located at a well-defined distance from it. By dividing the surface under investigation into a large number of small elementary areas, it was possible to use this transfer function to express the potential measured by the ACEIP as the sum of the contributions of each such element. An inverse matrix computation method enabled the estimation of the actual surface electric potential. Based on the results of a final set of experiments, the distribution of the electric charge density was estimated for slabs charged by corona-respectively triboelectric-effect.

A modified homogenized highly precise direct integration method for time-varying nonhomogeneous systems

This article investigates a novel method for time-varying systems with an impact term; we call it a modified homogenized highly precise direct integration method. Modified homogenized highly precise direct integration method can deal with the time-varying nonhomogeneous systems effectively by direct integration with high precision. Even though it is often difficult to select the time step size of integration properly for stiff problems, modified homogenized highly precise direct integration method can effectively deal with the this problem with a large time step size. By introducing new variants twice, modified homogenized highly precise direct integration method can easily deal with the nonhomogeneous term by a novel way, inherit the advantages of highly precise direct integration method and avoid the calculation of inverse matrix. The convergency and efficiency analyses are given in this article. Several numerical simulations and an application example are presented to demonstrate the high accuracy, eff...

Leak Location of Pipeline with Multibranch Based on a Cyber-Physical System

Data cannot be shared and leakage cannot be located simultaneously among multiple pipeline leak detection systems. Based on cyber-physical system (CPS) architecture, the method for locating leakage for pipelines with multibranch is proposed. The singular point of pressure signals at the ends of pipeline with multibranch is analyzed by wavelet packet analysis, so that the time feature samples could be established. Then, the Fischer-Burmeister function is introduced into the learning process of the twin support vector machine (TWSVM) in order to avoid the matrix inversion calculation, and the samples are input into the improved twin support vector machine (ITWSVM) to distinguish the pipeline leak location. The simulation results show that the proposed method is more effective than the back propagation (BP) neural networks, the radial basis function (RBF) neural networks, and the Lagrange twin support vector machine.

MASERS: A Python package for statistical equilibrium calculations applied to masers

AbstractThe study of astrophysical maser formation provides a useful probe of the chemical composition and physical conditions of the sources they are observed in. This exploration requires continuously solving the SE equations for the populations of the energy levels in search of conditions that will produce an inversion. After evaluation of available implementations applying the Escape Probability approximation, the masers solver was developed to provide an efficient and robust matrix inversion calculation. This open source package is hosted at https://bitbucket.org/ruby_van_rooyen/masers.

Low Complexity ZF and MMSE Detectors for the Uplink MU-MIMO Systems With a Time-Varying Number of Active Users

The classical multiuser detection algorithms such as zero forcing (ZF) and minimum mean square error (MMSE) receivers are designed with the assumption that the number of active users is constant and known. When the number of the active users changes, the receiver may exhibit a serious performance loss if it does not react quickly to such variations. In this paper, we address the problem of reducing the complexity of the reevaluation of the popular ZF and MMSE detectors for multiuser multiple-input multiple-output (MU-MIMO) systems with a time-varying number of users in the channel. For each technique, we propose a detection approach with low complexity and without performance loss. The proposed algorithms avoid the direct computation of matrix inverses required by the ZF and MMSE detectors. Moreover, the performance losses, due to the use of the ZF and MMSE detectors intended for the scenario with a fixed number of active users, are evaluated with Monte Carlo simulation results.

A low-complexity Lanczos-algorithm-based detector with soft-output for multiuser massive MIMO systems

Zero-Forcing (ZF) algorithm achieves the near-optimal detection performance for massive multiple-input multiple-output (MIMO) systems at expense of performing the complicated matrix inversion of a high dimensional matrix. In this paper, a novel Lanczos-algorithm-based signal detection method with soft-output is proposed to iteratively realize ZF algorithm for multiuser massive MIIMO systems, which avoids the exact computation of matrix inversion and in turn reduces the computational complexity from O(K3) to O(K2), where K denotes the number of users. In the development of the proposed method, by analyzing the iterative process of Lanczos algorithm, an approximate low-complexity scheme is proposed to calculate the log likelihood ratios (LLRs) for soft channel decoding. Simulation results show that the proposed detector provides a relatively good tradeoff between the complexity and performance compared with the several recently proposed detectors, and achieves almost the same performance as the ZF algorithm with only 3 iterations.

Secure Massive MIMO Systems With Limited RF Chains

In future practical deployments of massive multi-input multi-output (MIMO) systems, the number of radio frequency (RF) chains at the base stations (BSs) may be much smaller than the number of BS antennas to reduce the overall expenditure. In this paper, we propose a novel design framework for joint data and artificial noise (AN) precoding in a multiuser massive MIMO system with limited number of RF chains, which improves the wireless security performance. With imperfect channel state information (CSI), we analytically derive an achievable lower bound on the ergodic secrecy rate of any mobile terminal (MT), for both analog and hybrid precoding schemes. The closed-form lower bound is used to determine optimal power splitting between data and AN that maximizes the secrecy rate through simple one-dimensional search. Analytical and numerical results together reveal that the proposed hybrid precoder, although suffers from reduced secrecy rate compared with theoretical full-dimensional precoder, is free of the high computational complexity of large-scale matrix inversion and null-space calculations, and largely reduces the hardware cost.

An Attitude Determination Method for Comprehensive Inspection Vehicle Based on Track Profile Registration

The attitude of the comprehensive inspection vehicle is one of the important factors that affect the accuracy of the inspection of metro line infrastructure, meanwhile the metro environment restricts the employment of common attitude determination methods. A new method of attitude determination is presented in this paper, which takes the track as reference and employs non-contact measurement to acquire the track profile simulta-neously. By registration of measurement track profile and the standard track profile, the relative position between the vehicle and the track reference can be calculated; and the instantaneous attitude of the vehicle can be determined by the matrix inverse calculation. The performance of the method is verified by an experiment using the road-rail comprehensive inspection vehicle.

Using the method of discrete dipoles to approximate solutions of the problems of light scattering and absorption by particles

A method of approximate calculation of the interaction inverse matrix in the method of discrete dipoles is proposed. The knowledge of this matrix makes it possible to determine the optical response of a system to the action of an electromagnetic wave with an arbitrary shape, which can be represented as a combination of vector spherical wave functions. The number of calculation operations of the matrix in the proposed method is considerably smaller than in the case of its direct calculation. In the case of a change in the refractive index of scattering particles, two methods of approximate calculation of the interaction inverse matrix are also proposed. This makes it possible to calculate the optical response of systems with new characteristics without direct solving equations of a system with a large dimension. The accuracy of the methods is numerically determined for particles with spherical and cubic shapes. It is shown that the methods are computationally efficient and can be used to calculate the values of polarization vectors inside particles and extinction and absorption cross sections of systems.

Time domain equalization method for TS-OFDM signal under higher mobile environments

In higher time-varying fading channels, the signal quality of orthogonal frequency division multiplexing (OFDM) technique would be degraded relatively due to the occurrence of inter-carrier interference (ICI). To solve this problem, this paper firstly proposes a new design of time domain training sequence (TS) in the estimation of channel impulse response (CIR) for the TS-OFDM signal which can reduce the leakage of power spectrum density (PSD) at the outside of OFDM allocated frequency bandwidth with keeping higher CIR estimation accuracy. Secondly, this paper proposes a time domain equalization (TDE) method which can achieve better bit error rate (BER) performance with keeping lower computation complexity even in higher time-varying fading channels. The salient feature of the proposed TDE method is to employ a partial differentiation for the time domain CIR matrix for solving the maximum likelihood (ML) equation in which the time domain CIR matrix becomes a symmetric banded matrix. From this feature, a low-complexity parallel block inverse matrix algorithm can be employed in the calculation of inverse matrix in keeping the same accuracy as that of the direct inverse matrix calculation. This paper presents various computer simulation results to demonstrate the effectiveness of the proposed TDE method for the TS-OFDM signal as compared with conventional frequency domain equalization (FDE) methods under higher mobile environments.

物理モデル同定による剛体加振源の加振力同定手法

This paper proposes identification method of excitation force of rigid body vibration source by physical model identification. If the reworking occurs after the assembly of the prototype in mechanical product, the cost increases due to the retrofit countermeasures and development period extension. Pre-prediction of vibration at the design stage is important to avoid these problems. Prior prediction of vibration needs to grasp the excitation force of the vibration source. As conventional methods, the mount stiffness method and the matrix inversion method have been proposed. However, mount stiffness method calculates the mount transmission force. Therefore, if the development machine changes the structure, preliminary evaluation does not apply. The matrix inversion method can solve this problem. However, when the frequency response function contains a measurement error, the error spreading propagates in inverse matrix calculation. Therefore, in order to avoid the inverse matrix calculation, we propose identification method of excitation force of rigid body vibration source by physical model identification. In this paper, it was investigated features of the inverse matrix method and the identification method of excitation force by physical model identification using the basic experiment. As a result of study, the method by physical model identification showed that the influence of measurement error is smaller than the matrix inversion method. In addition, it showed that it is possible to identify the excitation force with fewer excitation points than the matrix inversion method.

Inverting Matrix Using a Graph in the Theory of Dynamic Systems

Abstract To obtain the transfer equation in dynamic system theory, we need to calculate an inverse matrix. In this work we show both the classic methods and the methods used in automation theory of inverse matrix calculation. However, they are both time consuming and difficult. In the second section, we will show a simpler method. We will define how to create a graph for a given matrix and how to invert it. The matrix for the inverse graph is inverse of the original. We illustrate this method on an example and compare it to a classic solution.

Near‐optimal practical convergent method for interference alignment in MIMO interference channels

A practical distributed Gauss–Newton method for the near-optimal computation of interference alignment solutions is proposed, based on the block-wise structure of Jacobian matrix of the residual interference function. Also, a simple practical matrix inverse computation algorithm to solve the rank-deficient problem due to the interference sparse matrix is adopted. This proposal achieves convergent performance comparable to centralised Gauss–Newton method, with the major advantage of being practically implemented in a distributed manner.

Contrast variation by dynamic nuclear polarization and time-of-flight small-angle neutron scattering. I. Application to industrial multi-component nanocomposites.

Dynamic nuclear polarization (DNP) at low temperature (1.2 K) and high magnetic field (3.3 T) was applied to a contrast variation study in small-angle neutron scattering (SANS) focusing on industrial rubber materials. By varying the scattering contrast by DNP, time-of-flight SANS profiles were obtained at the pulsed neutron source of the Japan Proton Accelerator Research Complex (J-PARC). The concentration of a small organic molecule, (2,2,6,6-tetramethylpiperidine-1-yl)oxy (TEMPO), was carefully controlled by a doping method using vapour sorption into the rubber specimens. With the assistance of microwave irradiation (94 GHz), almost full polarization of the paramagnetic electronic spin of TEMPO was transferred to the spin state of hydrogen (protons) in the rubber materials to obtain a high proton spin polarization (PH). The following samples were prepared: (i) a binary mixture of styrene-butadiene random copolymer (SBR) with silica particles (SBR/SP); and (ii) a ternary mixture of SBR with silica and carbon black particles (SBR/SP/CP). For the binary mixture (SBR/SP), the intensity of SANS significantly increased or decreased while keeping its q dependence for PH = -35% or PH = 40%, respectively. The q behaviour of SANS for the SBR/SP mixture can be reproduced using the form factor of a spherical particle. The intensity at low q (∼0.01 Å-1) varied as a quadratic function of PH and indicated a minimum value at PH = 30%, which can be explained by the scattering contrast between SP and SBR. The scattering intensity at high q (∼0.3 Å-1) decreased with increasing PH, which is attributed to the incoherent scattering from hydrogen. For the ternary mixture (SBR/SP/CP), the q behaviour of SANS was varied by changing PH. At PH = -35%, the scattering maxima originating from the form factor of SP prevailed, whereas at PH = 29% and PH = 38%, the scattering maxima disappeared. After decomposition of the total SANS according to inverse matrix calculations, the partial scattering functions were obtained. The partial scattering function obtained for SP was well reproduced by a spherical form factor and matched the SANS profile for the SBR/SP mixture. The partial scattering function for CP exhibited surface fractal behaviour according to q-3.6, which is consistent with the results for the SBR/CP mixture.

Directivity control of a compact circular loudspeaker array based on selected orders of circular harmonic expansion

We investigated directivity control of a compact circular loudspeaker array that can be attached to the arm. The loudspeaker array can be used for various wearable systems, such as personal audio reproduction systems. A personal audio system often requires that sound leakage outside the listening area in three-dimensional space be minimized. Digital filters that control directivity are usually designed using the multi-point control method. However, the multi-point method causes large filter gains at low frequencies, owing to unstable inverse matrix calculation, which results in sound distortion during practical use. Many methods that use a regularization parameter to overcome the unstable inverse matrix have been proposed; however, they are difficult to apply directly. Thus, after studying the relationship between orders of circular harmonic expansion and filter gain, we propose a stable digital filter design based on appropriately selected orders of circular harmonic expansion for each frequency band. Directivity simulations conducted using the measured circular loudspeaker array response based on the proposed method indicate that the proposed method achieves a more stable filter gain than the multi-point control method. Further, it controls three-dimensional directivity by sacrificing a narrow directivity at low frequencies.

Low-Complexity Channel Estimation and Detection for MIMO-OFDM Receiver With ESPAR Antenna

Multiple-input–multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) receivers with an electronically steerable passive array radiator (ESPAR) antenna can improve bit error rate (BER) performance and obtain additional diversity gain without increasing the number of radio-frequency (RF) front-end circuits. In this scheme, a minimum-mean-square-error (MMSE) channel estimator is employed for obtaining the channel state information. However, its drawbacks include insufficient estimation accuracy and high computational complexity due to the inverse matrix calculation. In this paper, we propose using a low-complexity compressed-sensing-based channel estimation for the MIMO-OFDM receiver with an ESPAR antenna. We also propose a low-complexity detection scheme to further reduce the computational cost required for the detection. The simulation results show that with using the proposed channel estimation method, the BER performance is improved, while its complexity is reduced. The simulations also show that the proposed detection scheme successfully reduces the required computational cost while minimizing the degradation in the BER.

Algebraic Connectivity Estimation Based on Decentralized Inverse Power Iteration

AbstractIn this work, we propose a new scheme to estimate the algebraic connectivity of the graph describing the network topology of a multi‐agent system. We consider network topologies modeled by undirected graphs. The main idea is to propose a new decentralized conjugate gradient algorithm and a decentralized compound inverse power iteration scheme. The matrix inversion computation in this scheme is replaced by solving the non‐homogeneous linear equations relying on the proposed decentralized conjugate gradient algorithm. With this scheme, we can achieve a fast convergence rate in estimating the algebraic connectivity by setting the parameter μ properly. Simulation results demonstrate the effectiveness of the proposed scheme.

Parallel regressions for variable selection using GPU

This paper proposes a parallel regression formulation to reduce the computational time of variable selection algorithms. The proposed strategy can be used for several forward algorithms in order to select uncorrelated variables that contribute for a better predictive capability of the model. Our demonstration of the proposed method include the use of Successive Projections Algorithm (SPA), which is an iterative forward technique that minimizes multicollinearity. SPA is traditionally used for variable selection in the context of multivariate calibration. Nevertheless, due to the need of calculating an inverse matrix for each insertion of a new variable in the model calibration, the computational performance of the algorithm may become impractical as the matrix size increases. Based on such limitation, this paper proposes a new strategy called Parallel Regressions (PR). PR strategy was implemented in the SPA to avoid the matrix inverse calculation of original SPA in order to increase the computational performance of the algorithm. It uses a parallel computing platform called Compute Unified Device Architecture (CUDA) in order to exploit a Graphics Processing Unit, and was called SPA-PR-CUDA. For this purpose, we used a case study involving a large data set of spectral variables. The results obtained with SPA-PR-CUDA presented 37$$\times $$× times better performance compared to a traditional SPA implementation. Additionally, when compared to traditional algorithms we demonstrated that SPA-PR-CUDA may be a more viable choice for obtaining a model with a reduced prediction error value.

物理モデル構築による加振力同定に関する研究

This paper proposes excitation force identification method based on a physical model building. If reworking occurs after the assembly of the prototype in mechanical product, cost increases due to the retrofit countermeasures and development period extension. As conventional methods, the mount stiffness method and the matrix inversion method have been proposed. However, mount stiffness method calculates the mount transmission force. Therefore, if the development machine has structure change, preliminary evaluation does not apply. matrix inversion method can solve this problem. However, when the frequency response function contains a measurement error, there is problem that error at the time of invers matrix calculation is propagated to expand. Therefore, in order to avoid the inverse matrix calculation, we propose excitation force identification method based on a physical model construction of the vibration source. In this paper, it was investigated features of the inverse matrix method and physical model construction technique using the basic experiment and analysis. Study a result, the physical model building techniques showed that less than affected by the measurement error inverse matrix method.

표적기동분석을 위한 Levenberg-Marquardt 적용에 관한 연구

The Levenberg-Marquardt method is a well known solution about the least square problem. However, in a Target Motion Analysis(TMA) application most of researches have used the Gauss-Newton method as a batch estimator, which of inverse matrix calculation may causes instability problem. In this paper, Levenberg-Marquardt method is applied to TMA problem to prevent its divergence. In experiment, its performance is compared with Gauss-Newton in domain of range, course and speed. Monte Carlo simulation reveals the convergence time and reliability of the TMA based on Levenberg-Marquardt.