AN EFFICIENT NUMERICAL METHOD FOR SOLVING AN INVERSE WAVE PROBLEM

2013 ◽  
Vol 10 (03) ◽  
pp. 1350009 ◽  
Author(s):  
REZA POURGHOLI ◽  
AMIN ESFAHANI
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Auxiliary Problem ◽  
Linear Wave ◽  
Singular Value Decomposition Method ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
The Stability ◽  
Stability And Accuracy ◽  
Value Decomposition

In this paper, we will first study the existence and uniqueness of the solution of a one-dimensional inverse problem for an inhomogeneous linear wave equation with initial and boundary conditions via an auxiliary problem. Then a stable numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization to the matrix form of Duhamel's principle for solving this inverse problem is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition method. Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data.

scholarly journals Quantitative motion detection of in-hand objects for robotic grasp manipulation

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984633
Author(s):  
Xueyong Li ◽  
Kai Zhao ◽  
Changhou Lu ◽  
Yonghui Wang
Keyword(s):  
Motion Detection ◽  
Decomposition Method ◽  
Quantitative Measurement ◽  
Singular Value ◽  
Singular Value Decomposition Method ◽  
Innovative Method ◽  
The Stability ◽  
Coordinate Changes ◽  
Value Decomposition ◽  
Robotic Grasp

In an actual grasp operation, grasp accidents (slant, rolling, turning over, and dropping) of in-hand objects occur frequently. Quantitative motion detection of in-hand objects is critical to optimize the grasp configuration and to improve the stability and dexterity of a grasp manipulation. In this article, an innovative method for quantitative measurement of the motions of in-hand objects is presented. Firstly, the slip information at object–finger interface between adjacent states is detected by three omnidirectional slip sensors; next, singular value decomposition method is applied to calculate the rotation and translation matrices according to the relative coordinate changes extracted from the slip information. Finally, Euler angles and the linear displacements which illustrate the motion of in-hand objects are quantitatively measured from the translation matrix and the rotation matrix, and the continuous motion track can be further established. Experiment results show that the proposed method is effective in detecting multiple motion information of in-hand objects.

scholarly journals Global Calibration Method of a Camera Using the Constraint of Line Features and 3D World Points

2016 ◽  
Vol 16 (4) ◽  
pp. 190-196 ◽  
Author(s):  
Guan Xu ◽  
Xinyuan Zhang ◽  
Xiaotao Li ◽  
Jian Su ◽  
Zhaobing Hao
Keyword(s):  
Calibration Method ◽  
Original Method ◽  
Transformation Matrix ◽  
Mean Values ◽  
Global Calibration ◽  
The Stability ◽  
Stability And Accuracy ◽  
Value Decomposition ◽  
Projective Lines ◽  
Mean Square Errors

Abstract We present a reliable calibration method using the constraint of 2D projective lines and 3D world points to elaborate the accuracy of the camera calibration. Based on the relationship between the 3D points and the projective plane, the constraint equations of the transformation matrix are generated from the 3D points and 2D projective lines. The transformation matrix is solved by the singular value decomposition. The proposed method is compared with the point-based calibration to verify the measurement validity. The mean values of the root-mean-square errors using the proposed method are 7.69×10−4, 6.98×10−4, 2.29×10−4, and 1.09×10−3 while the ones of the original method are 8.10×10−4, 1.29×10−2, 2.58×10−2, and 8.12×10−3. Moreover, the average logarithmic errors of the calibration method are evaluated and compared with the former method in different Gaussian noises and projective lines. The variances of the average errors using the proposed method are 1.70×10−5, 1.39×10−4, 1.13×10−4, and 4.06×10−4, which indicates the stability and accuracy of the method.

Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂t β u = −(− Δ) α/2 u − (− Δ) γ/2 u

2021 ◽  
Vol 24 (3) ◽  
pp. 818-847
Author(s):  
Ngartelbaye Guerngar ◽  
Erkan Nane ◽  
Ramazan Tinaztepe ◽  
Suleyman Ulusoy ◽  
Hans Werner Van Wyk
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Fractional Laplacian ◽  
Space Time ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Simultaneous Inversion ◽  
Error Functional ◽  
Uniqueness Of The Solution ◽  
Least Squares Approach

Abstract In this article, we consider the space-time fractional (nonlocal) equation characterizing the so-called “double-scale” anomalous diffusion ∂ t β u ( t , x ) = − ( − Δ ) α / 2 u ( t , x ) − ( − Δ ) γ / 2 u ( t , x ) , t > 0 , − 1 < x < 1 , $$\begin{array}{} \displaystyle \partial_t^\beta u(t, x) = -(-\Delta)^{\alpha/2}u(t,x) - (-\Delta)^{\gamma/2}u(t,x), \, \, t \gt 0, \, -1 \lt x \lt 1, \end{array}$$ where ∂ t β $\begin{array}{} \displaystyle \partial_t^\beta \end{array}$ is the Caputo fractional derivative of order β ∈ (0, 1) and 0 < α ≤ γ < 2. We consider a nonlocal inverse problem and show that the fractional exponents β, α and γ are determined uniquely by the data u(t, 0) = g(t), 0 < t ≤ T. The existence of the solution for the inverse problem is proved using the quasi-solution method which is based on minimizing an error functional between the output data and the additional data. In this context, an input-output mapping is defined and its continuity is established. The uniqueness of the solution for the inverse problem is proved by means of eigenfunction expansion of the solution of the forward problem and some basic properties of fractional Laplacian. A numerical method based on discretization of the minimization problem, namely the steepest descent method and a least squares approach, is proposed for the solution of the inverse problem. The numerical method determines the fractional exponents simultaneously. Finally, numerical examples with noise-free and noisy data illustrate applicability and high accuracy of the proposed method.

scholarly journals 2D and 3D fault basis for fuel cell diagnosis by external magnetic field measurements

2017 ◽  
Vol 79 (2) ◽  
pp. 20901 ◽  
Author(s):  
Lyes Ifrek ◽  
Gilles Cauffet ◽  
Olivier Chadebec ◽  
Yann Bultel ◽  
Sébastien Rosini ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Fuel Cell ◽  
External Magnetic Field ◽  
Current Density ◽  
Field Measurements ◽  
Magnetic Field Measurements ◽  
Uniqueness Of The Solution ◽  
Ill Posed ◽  
Value Decomposition

An original approach used for the identification of faults in fuel cell stacks is presented. It is based on the 3D reconstruction of the current density from external magnetic field measurements which is an ill-posed magnetostatic linear inverse problem. A suitable and original current density and magnetic field basis are proposed in order to define both local and global faults on a fuel cell stack. The inverse problem is regularized by truncated singular value decomposition (SVD) to ensure the uniqueness of the solution.

scholarly journals Бинарные соответствия и обратная задача химической кинетики

2018 ◽  
Author(s):  
L.I. Kononenko ◽  
A.E. Gutman
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Chemical Kinetics ◽  
Unique Solvability ◽  
Auxiliary Problem ◽  
Problem Definition ◽  
Finite Sets ◽  
The Stability ◽  
Definition Of ◽  
The Right

We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions. In particular, formalization of the following notions is presented: condition, data, unknowns, and solutions of a problem, solvability and unique solvability, inverse problem, composition and restriction of problems, isomorphism between problems. We also consider topological problems and the related notions of stability and correctness. A connection is indicated between the stability and continuity of a uniquely solvable topological problem. The definition of parametrized set is given. The notions are introduced of parametrized problem, the problem of reconstruction of an object by the values of parameters, as well as the notions of locally free set of parameters and stability with respect to a set of parameters. As an illustration, we consider a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning. Direct and inverse problems are stated for such a system. We extend the class of problems under study by considering polynomials of arbitrary degree as the right-hand sides of the differential equations. It is shown how the inverse problem of chemical kinetics can be corrected and made more practical by means of the composition with a simple auxiliary problem which represents the relation between functions and finite sets of numerical characteristics being measured. For the corrected inverse problem, formulas for the solution are presented and the conditions of unique solvability are indicated. Within the study of solvability, a criterion is established for linear independence of functions in terms of finite sets of their values. With the help of the criterion, realizability is clarified of the condition for unique solvability of the inverse problem of chemical kinetics.

scholarly journals Applying the R-solution method for designing a tsunami observational system

2021 ◽  
Vol 2099 (1) ◽  
pp. 012063
Author(s):  
T A Voronina ◽  
A V Loskutov
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Least Squares Method ◽  
Tsunami Wave ◽  
Singular Value Decomposition Method ◽  
Spatial Modes ◽  
The Matrix ◽  
Wave Heights ◽  
Value Decomposition ◽  
Tsunami Energy

Abstract One of the promising methods of the early warning of a tsunami is obtaining data of the wave heights based on the numerical solution of the inverse tsunami problem by using the truncated singular value decomposition method as a variant of the least-squares method. The problem is considered within the framework of the linear theory of wave propagation. The technique proposed allows one to avoid the inevitable instability of the numerical solution. It is possible to choose the most informative directions for the placement of the observation stations, which is based on the analysis of the energy transfer by the spatial modes generated by each right singular vector. As it has turned out, the best location of the stations is closely related to the directions of the most intense distribution of the tsunami energy. One of the significant advantages of the approach presented is the possibility, without additional calculations of the tsunami wave propagation from a reconstructed source, to obtain the tsunami wave heights at the points at which there are no observations but which are associated when calculating the matrix of the direct problem operator. The implementation of the approach proposed of the actual event of the Chilean Illapel Tsunami of September 16, 2015, is presented.

scholarly journals Underground Microseismic Event Monitoring and Localization within Sensor Networks

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2830
Author(s):  
Sili Wang ◽  
Mark P. Panning ◽  
Steven D. Vance ◽  
Wenzhan Song
Keyword(s):  
Sensor Networks ◽  
Real Time ◽  
Information Needs ◽  
Localization Algorithm ◽  
Distributed Sensors ◽  
Distributed Sensor ◽  
Microseismic Events ◽  
The Stability ◽  
Stability And Accuracy

Locating underground microseismic events is important for monitoring subsurface activity and understanding the planetary subsurface evolution. Due to bandwidth limitations, especially in applications involving planetarily-distributed sensor networks, networks should be designed to perform the localization algorithm in-situ, so that only the source location information needs to be sent out, not the raw data. In this paper, we propose a decentralized Gaussian beam time-reverse imaging (GB-TRI) algorithm that can be incorporated to the distributed sensors to detect and locate underground microseismic events with reduced usage of computational resources and communication bandwidth of the network. After the in-situ distributed computation, the final real-time location result is generated and delivered. We used a real-time simulation platform to test the performance of the system. We also evaluated the stability and accuracy of our proposed GB-TRI localization algorithm using extensive experiments and tests.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

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