Search Results (52)

The airborne distributed position and orientation system (ADPOS), which integrates multi-inertia measurement units (IMUs), a data-processing computer, and a Global Navigation Satellite System (GNSS), serves as a key sensor in new higher-resolution airborne remote sensing applications, such as array SAR and multi-node imaging loads. ADPOS can provide reliable, high-precision and high-frequency spatio-temporal reference information to realize multinode motion compensation with the various nonlinear filter estimation methods such as Central Difference Kalman Filtering (CDKF), and modified CDKF. Although these known nonlinear models demonstrate good performance, their noise estimation performance with its linear minimum variance estimation criterion is limited for ADPOS. For this reason, in this paper, Central Difference Variational Filtering (CDVF) based on the variational optimization process is presented. This method adopts the conjugate gradient algorithm to enhance the estimation performance for mean correction in the filtering update stage. On one hand, the proposed method achieves adaptability by estimating noise covariance through the variational optimization method. On the other hand, robustness is implemented under the minimum variance estimation criterion based on the conjugate gradient algorithm to suppress measurement noise. We conducted a real ADPOS flight test, and the experimental results show that the accuracy of the slave motion parameters has significantly improved compared to the current CDKF. Moreover, the compensation performance shows a clear enhancement. Full article

Forward jammers replicate and retransmit radar signals back to generate coherent jamming signals and false targets, making anti-jamming an urgent issue in electronic warfare. Jamming transmitters work at saturation to maximize the retransmission power such that only the phase information of the angular waveform at the designated direction of arrival (DOA) is retained. Therefore, amplitude modulation of MIMO radar angular waveforms offers an advantage in combating forward jamming. We address both the design of unimodular MIMO waveforms and their associated mismatch filters to confront mainlobe jamming in this paper. Firstly, we design the MIMO waveforms to maximize the discrepancy between the retransmitted jamming and the spatially synthesized radar signal. We formulate the problem as unconstrained non-linear optimization and solve it using the conjugate gradient method. Particularly, we introduce fast Fourier transform (FFT) to accelerate the numeric calculation of both the objection function and its gradient. Secondly, we design a mismatch filter to further suppress the filtered jamming through convex optimization in polynomial time. The simulation results show that for an eight-element MIMO radar, we are able to reduce the correlation between the angular waveform and saturated forward jamming to −6.8 dB. Exploiting this difference, the mismatch filter can suppress the jamming peak by 19 dB at the cost of an SNR loss of less than 2 dB. Full article

In this work, we analyze non-Darcy two-component single-phase isothermal flow in naturally fractured tight gas reservoirs. The model is applied in a scenario of enhanced gas recovery (EGR) with the possibility of carbon dioxide storage. The properties of the gases are obtained via the Peng–Robinson equation of state. The finite volume method is used to solve the governing partial differential equations. This process leads to two subsystems of algebraic equations, which, after linearization and use of an operator splitting method, are solved by the conjugate gradient (CG) and biconjugate gradient stabilized (BiCGSTAB) methods for determining the pressure and fraction molar, respectively. We include inertial effects using the Barree and Conway model and gas slippage via a more recent model than Klinkenberg’s, and we use a simplified model for the effects of effective stress. We also utilize a mesh refinement technique to represent the discrete fractures. Finally, several simulations show the influence of inertial, slippage and stress effects on production in fractured tight gas reservoirs. Full article

This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search direction inherently ensures sufficient descent and trust-region properties, eliminating the need for line search formulas; (iii) Global convergence is established without the necessity of the Lipschitz continuity condition. Benchmark problem numerical results illustrate the proposed algorithm’s effectiveness and competitiveness relative to other three-term algorithms. Additionally, the algorithm is extended to effectively address the image denoising problem. Full article

The subspace minimization conjugate gradient (SMCG) methods proposed by Yuan and Store are efficient iterative methods for unconstrained optimization, where the search directions are generated by minimizing the quadratic approximate models of the objective function at the current iterative point. Although the SMCG methods have illustrated excellent numerical performance, they are only used to solve unconstrained optimization problems at present. In this paper, we extend the SMCG methods and present an efficient SMCG method for solving nonlinear monotone equations with convex constraints by combining it with the projection technique, where the search direction is sufficiently descent.Under mild conditions, we establish the global convergence and R-linear convergence rate of the proposed method. The numerical experiment indicates that the proposed method is very promising. Full article

Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point system of equations where the coefficient matrix of this system is dense and ill conditioned (it has a huge condition number). The ill-conditioned property leads to slowing of the convergence of any iterative method, such as Krylov subspace methods. One treatment for the slowness property is to apply the preconditioning technique. In this paper, we propose a block triangular preconditioner because we know that using the exact triangular preconditioner leads to a preconditioned matrix with exactly two distinct eigenvalues. This means that we need at most two iterations to converge to the exact solution. However, we cannot use the exact preconditioner because the Shur complement of our system is of the form $S=K^{*}K+\lambda L_{\alpha }$ which is a huge and dense matrix. The first matrix, $K{}^{*}K$, comes from the blurred operator, while the second one is from the TFOV regularization model. To overcome this difficulty, we propose two preconditioners based on the circulant and standard TV matrices. In our algorithm, we use the flexible preconditioned GMRES method for the outer iterations, the preconditioned conjugate gradient (PCG) method for the inner iterations, and the fixed point iteration (FPI) method to handle the nonlinearity. Fast convergence was found in the numerical results by using the proposed preconditioners. Full article

We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time. Full article

In studying planar multi-bar mechanisms with multiple degrees of freedom, mathematical modeling is undoubtedly a way to get closer to the expected trajectory. Compared with the analytical method, the optimization method has higher accuracy in solving nonlinear equations, and it can be searched and iterated in an extensive range until it meets the real engineering solution. The research on the overlap ratio of the Slitting Shear essentially aims to study the kinematics of the two-DOF mechanism. In this study, a one-DOF mathematical model of mechanical motion was established for the Slitting Shear without considering the overlap ratio. The mathematical model was then verified through simulation. The overlap ratio was introduced based on the above mathematic model, and the three-DOF mathematic model of the shear mechanism was established. Finally, the setting of the overlap ratio was optimized using the conjugate gradient method and the global optimal NMinmize function. Under the condition of satisfying the overlap ratio, the recommended value for the overlap ratio setting of the two-DOF mechanism, which approximates the pure rolling cut, was determined. Full article

In this paper, a two-point step-size gradient technique is proposed by which the approximate solutions of a non-linear system are found. The two-point step-size includes two types of parameters deterministic and random. A new adaptive backtracking line search is presented and combined with the two-point step-size gradient to make it globally convergent. The idea of the suggested method depends on imitating the forward difference method by using one point to estimate the values of the gradient vector per iteration where the number of the function evaluation is at most one for each iteration. The global convergence analysis of the proposed method is established under actual and limited conditions. The performance of the proposed method is examined by solving a set of non-linear systems containing high dimensions. The results of the proposed method is compared to the results of a derivative-free three-term conjugate gradient CG method that solves the same test problems. Fair, popular, and sensible evaluation criteria are used for comparisons. The numerical results show that the proposed method has merit and is competitive in all cases and superior in terms of efficiency, reliability, and effectiveness in finding the approximate solution of the non-linear systems. Full article

The motive of this study is to provide the numerical performances of the monkeypox transmission system (MTS) by applying the novel stochastic procedure based on the radial basis scale conjugate gradient deep neural network (RB-SCGDNN). Twelve and twenty numbers of neurons were taken in the deep neural network process in first and second hidden layers. The MTS dynamics were divided into rodent and human, the human was further categorized into susceptible, infectious, exposed, clinically ill, and recovered, whereas the rodent was classified into susceptible, infected, and exposed. The construction of dataset was provided through the Adams method that was refined further by using the training, validation, and testing process with the statics of 0.15, 0.13 and 0.72. The exactness of the RB-SCGDNN is presented by using the comparison of proposed and reference results, which was further updated through the negligible absolute error and different statistical performances to solve the nonlinear MTS. Full article

Tongchuan City, located in Shaanxi Province, northwest China, has limited groundwater resources. Rational planning and exploitation of groundwater are crucial to the sustainable development of the city, for which investigating the distribution of groundwater is the premise. Traditional resistivity sounding methods are often used to detect groundwater; however, these methods are not applicable in the study area where thick Quaternary loess is extensively distributed. In this study, we arranged five audio-frequency magnetotelluric (AMT) profiles to detect the deep clastic rock groundwater and carbonate karst fissure groundwater in Tongchuan. Firstly, we analyzed the electromagnetic interference (EMI) noises in Tongchuan City, revealing that the main EMI is power frequency interference (PFI). We used the dictionary learning processing technology to suppress the PFI. Secondly, the two-dimensional (2D) nonlinear conjugate gradient method was employed to invert a 2D electrical structure model for the area shallower than 1 km. We analyzed the characteristics of the electrical structure and its geological significance. Lastly, the three-dimensional (3D) electrical structure model of the study area was inverted using the 3D nonlinear conjugate gradient method, and the spatial distribution characteristics of the water-bearing strata were further analyzed. The results show that the PFI in urban environment can be suppressed by the dictionary learning processing technology. In Tongchuan city, the distribution of clastic rock fissure water is controlled by folds and faults, as well as the thickness of sandstone layers, and that of the carbonate karst fissure water is mainly controlled by faults. On this basis, we infer that the water-bearing areas are in the middle east and south of the study area. Full article

This paper presents an approach for the solution of a zero-sum differential game associated with a nonlinear state-feedback ${\mathcal{H}}_{\infty }$ control problem. Instead of using the approximation methods for solving the corresponding Hamilton–Jacobi–Isaacs (HJI) partial differential equation, we propose an algorithm that calculates the explicit inputs to the dynamic system by directly performing minimization with simultaneous maximization of the same objective function. In order to achieve numerical robustness and stability, the proposed algorithm uses: quasi-Newton method, conjugate gradient method, line search method with Wolfe conditions, Adams approximation method for time discretization and complex-step calculation of derivatives. The algorithm is evaluated in computer simulations on examples of first- and second-order nonlinear systems with analytical solutions of ${\mathcal{H}}_{\infty }$ control problem. Full article

In this work, we propose the use of non-homogeneous grids in 1D and 2D for the study of various nonlinear physical equations using spectral methods. As is well known, the use of spectral methods allow a faster resolution of the problem via the application of the ubiquitous Fast Fourier Transform (FFT) algorithm. We will center our investigation on the search of fast and accurate schemes to solve the spectral operators in the Fourier space. In particular, we will use the Conjugate Gradient (CG) iterative method, with a preconditioning matrix to accelerate the inversion process of the non-uniform Fast Fourier Transform (NFFT). As it will be shown, the results obtained are in good agreement with the expected values. Full article

Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations with convex constraints is proposed. The new approach is based on a modified symmetric rank-one updating formula. The search direction of the proposed algorithm mimics the behavior of a spectral conjugate gradient algorithm where the spectral parameter is determined so that the direction is sufficiently descent. Based on the assumption that the underlying function satisfies monotonicity and Lipschitz continuity, the convergence result of the proposed algorithm is discussed. Subsequently, the efficiency of the new method is revealed. As an application, the proposed algorithm is successfully implemented on image deblurring problem. Full article

We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The algorithm is always applicable for any given initial matrix and will arrive at an LS solution within finite steps. When the matrix equation has many LS solutions, the algorithm can search for the one with minimal Frobenius-norm. Moreover, given a matrix Y, the algorithm can find a unique LS solution closest to Y. Numerical experiments show the relevance of the algorithm for square/non-square dense/sparse matrices of medium/large sizes. The algorithm works well in both the number of iterations and the computation time, compared to the direct Kronecker linearization and well-known iterative methods. Full article