scholarly journals Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 50
Author(s):  
Yongjun He ◽  
Bolin Liao ◽  
Lin Xiao ◽  
Luyang Han ◽  
Xiao Xiao
Keyword(s):  
Noise Suppression ◽  
Activation Function ◽  
Matrix Inversion ◽  
Inversion Problem ◽  
Bounded Noise ◽  
Arbitrary Time ◽  
Dynamic Matrix ◽  
Accelerated Convergence ◽  
Fixed Parameter ◽  
The Matrix

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

scholarly journals Efficient Original-Destination Bandwidth: A Novel Model for Arterial Traffic Signal Coordination

2020 ◽  
Vol 53 (5) ◽  
pp. 609-616
Author(s):  
Ying Wang ◽  
Zongzhong Tian
Keyword(s):  
Lag Phase ◽  
Band Model ◽  
Time Dynamic ◽  
Signal Coordination ◽  
Dynamic Matrix ◽  
Phase Sequence ◽  
The Matrix ◽  
Arterial Traffic ◽  
The Relationship

This paper proposes an efficient origin-estimation bandwidth (OD band) model, which provides dedicated progression bands for arterial traffic based on the real-time dynamic matrix of their estimated OD pairs. The innovations of the OD band model are as follows: First, the dynamics of through and turning-in/out traffics are analyzed based on the matrix of their estimated OD pairs, and used to generate the traffic movement sequence at continuous intersections; Second, the end-time of green interval for lag-lag phase sequence at continuous intersections is determined according to the relevant constraints, the relationship between the start/end-time of green interval and the minimum/maximum green intervals; Third, the bandwidths of the two directions of the artery ware produced, after being weighted by their traffic demands. The intuitiveness, convenience, and feasibility of the OD band model were fully demonstrated through a case study. Overall, the OD band model helps to produce bi-directional progression bands for traffic with many turning movements on the artery, and enables the through and turning-in/out traffics to proceed through continuous intersections, when the signals at those intersections are green.

scholarly journals Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait

2019 ◽  
Vol 11 (3) ◽  
pp. 318 ◽  
Author(s):  
Yangyang Liu ◽  
Emmanuel Boss ◽  
Alison Chase ◽  
Hongyan Xi ◽  
Xiaodong Zhang ◽  
...  
Keyword(s):  
Spatial Resolution ◽  
High Performance ◽  
Matrix Inversion ◽  
Percentage Error ◽  
Fram Strait ◽  
Total Chlorophyll ◽  
Concentration Data ◽  
Inversion Technique ◽  
The Matrix ◽  
Gaussian Decomposition

Phytoplankton in the ocean are extremely diverse. The abundance of various intracellular pigments are often used to study phytoplankton physiology and ecology, and identify and quantify different phytoplankton groups. In this study, phytoplankton absorption spectra ( a p h ( λ ) ) derived from underway flow-through AC-S measurements in the Fram Strait are combined with phytoplankton pigment measurements analyzed by high-performance liquid chromatography (HPLC) to evaluate the retrieval of various pigment concentrations at high spatial resolution. The performances of two approaches, Gaussian decomposition and the matrix inversion technique are investigated and compared. Our study is the first to apply the matrix inversion technique to underway spectrophotometry data. We find that Gaussian decomposition provides good estimates (median absolute percentage error, MPE 21–34%) of total chlorophyll-a (TChl-a), total chlorophyll-b (TChl-b), the combination of chlorophyll-c1 and -c2 (Chl-c1/2), photoprotective (PPC) and photosynthetic carotenoids (PSC). This method outperformed one of the matrix inversion algorithms, i.e., singular value decomposition combined with non-negative least squares (SVD-NNLS), in retrieving TChl-b, Chl-c1/2, PSC, and PPC. However, SVD-NNLS enables robust retrievals of specific carotenoids (MPE 37–65%), i.e., fucoxanthin, diadinoxanthin and 19 ′ -hexanoyloxyfucoxanthin, which is currently not accomplished by Gaussian decomposition. More robust predictions are obtained using the Gaussian decomposition method when the observed a p h ( λ ) is normalized by the package effect index at 675 nm. The latter is determined as a function of “packaged” a p h ( 675 ) and TChl-a concentration, which shows potential for improving pigment retrieval accuracy by the combined use of a p h ( λ ) and TChl-a concentration data. To generate robust estimation statistics for the matrix inversion technique, we combine leave-one-out cross-validation with data perturbations. We find that both approaches provide useful information on pigment distributions, and hence, phytoplankton community composition indicators, at a spatial resolution much finer than that can be achieved with discrete samples.

scholarly journals Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200334 ◽  
Author(s):  
Ameya D. Jagtap ◽  
Kenji Kawaguchi ◽  
George Em Karniadakis
Keyword(s):  
Neural Networks ◽  
Adaptive Learning ◽  
Gradient Descent ◽  
Activation Function ◽  
Stochastic Gradient Descent ◽  
Activation Functions ◽  
Gradient Descent Algorithm ◽  
Locally Adaptive ◽  
The Matrix ◽  
Base Method

We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

Electromagnetic modeling of 3-D structures by the method of system iteration using integral equations

Geophysics ◽  
1992 ◽  
Vol 57 (12) ◽  
pp. 1556-1561 ◽  
Author(s):  
Zonghou Xiong
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Computation Time ◽  
Iterative Solution ◽  
Matrix Inversion ◽  
Electromagnetic Modeling ◽  
Direct Inversion ◽  
Conductivity Structure ◽  
The Matrix ◽  
Earth Conductivity

A new approach for electromagnetic modeling of three‐dimensional (3-D) earth conductivity structures using integral equations is introduced. A conductivity structure is divided into many substructures and the integral equation governing the scattering currents within a substructure is solved by a direct matrix inversion. The influence of all other substructures are treated as external excitations and the solution for the whole structure is then found iteratively. This is mathematically equivalent to partitioning the scattering matrix into many block submatrices and solving the whole system by a block iterative method. This method reduces computer memory requirements since only one submatrix at a time needs to be stored. The diagonal submatrices that require direct inversion are defined by local scatterers only and thus are generally better conditioned than the matrix for the whole structure. The block iterative solution requires much less computation time than direct matrix inversion or conventional point iterative methods as the convergence depends on the number of the submatrices, not on the total number of unknowns in the solution. As the submatrices are independent of each other, this method is suitable for parallel processing.

scholarly journals A hypothesis of state covariance decorrelation effects to partial observability SLAM

2019 ◽  
Vol 14 (2) ◽  
pp. 588 ◽  
Author(s):  
H Ahmad ◽  
N.A Othman ◽  
M M Saari ◽  
M S Ramli ◽  
M M Mazlan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Matrix Inversion ◽  
Matrix Norm ◽  
Main Element ◽  
Partial Observability ◽  
Localization And Mapping ◽  
The Matrix ◽  
Simulation Results ◽  
Partially Observable

<span>This paper analyze the performance of partial observability in simultaneous localization and mapping(SLAM) problem. The study focuses mainly on the effect of having a decorrelation technique known as Covariance Inflation to the estimation. The matrix inversion will be the main element to be investigated through two conditions with respect to some defined environment namely as unstable partially observable SLAM and partially observable SLAM via matrix norm analysis. For assessment purposes, the Extended Kalman Filter estimation is referred as the estimator to understand how the conditions can influence the results. The simulation results depicted that, the matrix norm is able to determine the efficiency of estimation and is proportional to the uncertainties of the system.</span>

scholarly journals Modified Conjugate Gradient Algorithms for Gram Matrix Inversion of Massive MIMO Downlink Linear Precoding

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2834-2840
Keyword(s):  
Conjugate Gradient ◽  
Massive Mimo ◽  
Mimo Systems ◽  
Mimo System ◽  
Low Complexity ◽  
Matrix Inversion ◽  
Gram Matrix ◽  
Linear Precoding ◽  
Inversion Algorithm ◽  
The Matrix

This paper deals with various low complexity algorithms for higher order matrix inversion involved in massive MIMO system precoder design. The performance of massive MIMO systems is optimized by the process of precoding which is divided into linear and nonlinear. Nonlinear precoding techniques are most complex precoding techniques irrespective of its performance. Hence, linear precoding is generally preferred in which the complexity is mainly contributed by matrix inversion algorithm. To solve this issue, Krylov subspace algorithm such as Conjugate Gradient (CG) was considered to be the best choice of replacement for exact matrix inversions. But CG enforces a condition that the matrix needs to be Symmetric Positive Definite (SPD). If the matrix to be inverted is asymmetric then CG fails to converge. Hence in this paper, a novel approach for the low complexity inversion of asymmetric matrices is proposed by applying two different versions of CG algorithms- Conjugate Gradient Squared (CGS) and Bi-conjugate Gradient (Bi-CG). The convergence behavior and BER performance of these two algorithms are compared with the existing CG algorithm. The results show that these two algorithms outperform CG in terms of convergence speed and relative residue.

scholarly journals Rubber Stiffness Optimization for Floor Vibration Attenuation of a Light Bus Based on Matrix Inversion TPA

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hui Shi ◽  
Wenku Shi ◽  
Changhai Yang ◽  
Guozheng Liu ◽  
Zhaomeng Fan ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Optimization Procedure ◽  
Matrix Inversion ◽  
Vibration Test ◽  
Transfer Path ◽  
Stiffness Optimization ◽  
Market Competitiveness ◽  
Vibration Attenuation ◽  
The Matrix ◽  
Floor Vibration

The NVH characteristics of light buses are a very important performance for market competitiveness. To solve the serious floor vibration of a light bus at speed of 60 km/h and 90 km/h, we first derive the matrix inversion TPA (MITPA) method, and then transfer path contribution is analyzed by applying matrix inversion TPA with TPA model establishment, operational vibration test, and FRF measurement. Next, the energy decoupling rate of the powertrain mount system (PMS) is optimized by rubber stiffness optimization based on the path contribution analysis taking both amplitude and phase into consideration. The optimized natural frequencies and energy decoupling rate indicate that energy decoupling rate (EDR) of each DoF of the powertrain mount system is improved. Finally, to verify the optimization effect, this paper implements an operational vibration test with optimized mount installed. The results indicate that floor vibration of postoptimization is improved significantly compared with that of preoptimization. This paper offers a method for engineers to improve vibration problem of vehicle by combining experimental TPA for identification of dominant paths with optimization procedure.

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