Hierarchical Principle-Based Iterative Parameter Estimation Algorithm for Dual-Frequency Signals

Performance of iterative gradient-based algorithms with different intensity change models in digital image correlation

PurposeIt is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization.Design/methodology/approachThe paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm.FindingsThrough numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma.Originality/valueIt is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.

In this article, we present two new algorithms referred to as the improved modified gradient-based iterative (IMGI) algorithm and its relaxed version (IMRGI) for solving the complex conjugate and transpose (CCT) Sylvester matrix equations, which often arise from control theory, system theory, and so forth. Compared with the gradient-based iterative (GI) (A.-G. Wu, L.-L. Lv, and G.-R. Duan, Iterative algorithms for solving a class of complex conjugate and transpose matrix equations, Appl. Math. Comput. 217 (2011), 8343–8353) and the relaxed GI (RGI) (W.-L. Wang, C.-Q. Song, and S.-P. Ji, Iterative solution to a class of complex matrix equations and its application in time-varying linear system, J. Appl. Math. Comput. 67 (2021), 317–341) algorithms, the proposed ones can make full use of the latest information and need less computations, which leads to higher computational efficiency. With the real representation of a complex matrix as a tool, we establish sufficient and necessary conditions for the convergence of the IMGI and the IMRGI algorithms. Finally, some numerical examples are given to illustrate the effectiveness and advantages of the proposed algorithms.

Graded refractive index media appear in numerous industrial applications such as non-isothermal flows, optics material processing, biological imaging. Refractive index gradient has been an early help for combusting flow visualisation. The numerical treatment of radiative transport is difficult in such media due to the curvature of rays, especially when the media are not optically thick. Computer-aided remote probing (inversion) is done today with the help of the diffusion approximation adapted to varying refractive index media but is unsuitable for thin media. Therefore, it is important to develop an approach allowing the use of the radiative transport equation which is the most complete formalism for radiative transfer to date and to couple it to reconstruction schemes. The aim of this study is to demonstrate the reconstruction of an arbitrary refractive index distribution from a least-squares gradient-based iterative inversion algorithm taking advantage of the full transient Radiative Transfer Equation (tRTE). The finite-difference discrete-ordinates method for the tRTE and its adjoint has been implemented, accounting for spatial changes in the distribution of the refractive index in a semi-transparent medium. A least-squares gradient-based iterative algorithm has been designed and elementary tests have been carried to demonstrate reconstruction possibilities.

New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation

The paper focuses on the identification of discrete-time bilinear forms in the special case when the external noise (disturbance) is an autoregressive average moving process. The proposed estimation procedure is iterative where, at each iteration, two sets of parameter vectors are estimated interactively. Using the hierarchical technique, a hierarchical generalized extended least squares-based iterative (H-GELSI) algorithm is proposed for avoiding estimating the redundant parameters. In contrast to the hierarchical generalized extended gradient-based iterative (H-GEGI) algorithm, the proposed algorithm can give more accurate parameter estimates. The main results derived in this paper are verified by means of both the computational efficiency comparison and two numerical simulations.

The transferability of adversarial examples has been proven to be a potent tool for successful attacks on target models, even in challenging black-box environments. However, the majority of current research focuses on non-targeted attacks, making it arduous to enhance the transferability of targeted attacks using traditional methods. This paper identifies a crucial issue in existing gradient iteration algorithms that generate adversarial perturbations in a fixed manner. These perturbations have a detrimental impact on subsequent gradient computations, resulting in instability of the update direction after momentum accumulation. Consequently, the transferability of adversarial examples is negatively affected. To overcome this issue, we propose an approach called Adversarial Perturbation Transform (APT) that introduces a transformation to the perturbations at each iteration. APT randomly samples clean patches from the original image and replaces the corresponding patches in the iterative output image. This transformed image is then used to compute the next momentum. In addition, APT could seamlessly integrate with other iterative gradient-based algorithms, incurring minimal additional computational overhead. Experimental results demonstrate that APT significantly enhances the transferability of targeted attacks when combined with traditional methods. Our approach achieves this improvement while maintaining computational efficiency.

Time-dependent reliability-based optimization for structural-topological configuration design under convex-bounded uncertain modeling

In this paper, a trajectory planning method of a mobile manipulator with the end-effector's specified path is presented. We derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. The planning problem is formulated as an optimal control problem. To solve the problem, we use the concept of the order of priority. A gradient-based iterative algorithm which synthesize the gradient function in a hierarchical manner based on the order of priority is used. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

This paper proposes two parameter identification methods for a nonlinear membership function. An equation converted method is introduced to turn the nonlinear function into a concise model. Then a stochastic gradient algorithm and a gradient‐based iterative algorithm are provided to estimate the unknown parameters of the nonlinear function. The numerical example shows that the proposed algorithms are effective.

To introduce a modified 3D stack-of-spirals trajectory and efficient SENSE reconstruction for improved through-plane undersampling, while maintaining SNR efficiency and other benefits of spiral acquisitions. A novel spiral staircase trajectory is introduced. This trajectory is a modified stack of spirals, in which spiral arms are distributed between partitions along kz . The trajectory maintains the efficient separable reconstruction with a Cartesian fast Fourier transform along the kz direction, followed by a 2D slice-by-slice gridding reconstruction. An additional intermediate step introduces a phase correction to collapse the spiral arms into the prescribed slice planes. For data undersampled through plane, this produces aliasing with reduced coherence, controlled by the arm-ordering. Undersampled data can then be reconstructed with reduced g-factor using a conjugate gradient-based iterative SENSE algorithm. The trajectory significantly improves g-factor for through-plane accelerated acquisitions. Improvement manifests through both reduced overall g-factor and reduced structure in the g-factor maps. In the presented experiments, the mean g-factor decreased from 1.26 to 0.93 and the maximum g-factor decreased from 3.89 to 1.15 for R = 2 spiral staircase when compared with stack of spirals, and the mean g-factor decreased from 2.51 to 0.94 and the maximum g-factor decreased from 8.26 to 1.35 for R = 3 spiral staircase when compared with stack of spirals. The novel spiral staircase trajectory offers improved aliasing characteristics for through-plane parallel imaging acceleration in 3D spiral acquisitions.

A pixel-wise accurate and interactive video segmentation technique is proposed in this paper to generate a binary mask of moving objects optimized for MPEG-4 object-based video coding. The initial object mask is tracked temporally, and regions are classified into the background region, the object region, and the uncertain region where the pixel is within a certain distance from the tracked object boundary. We exploit the color feature in the L*u*v* space, and use a non-parametric gradient-based iterative color clustering algorithm, known as the mean shift algorithm, to generate the region marker in the background and the object regions. Furthermore, we use the watershed technique to classify pixels in the uncertain region into the background and the object. Finally, by employing a variable bandwidth region boundary, the final mask for moving objects is optimized for MPEG-4 shape coding efficiency. The shape coding efficiency can be improved up to 30% with negligible loss of perceptual quality.

Effective reservoir management relies heavily on the accurate prediction of reservoir flow performance over the entire life of the reservoir. Accurate prediction of flow performance is possible only if reservoir flow parameters are known with reasonable accuracy. Consequently, a major challenge in reservoir management is the estimation of reservoir parameters that affect the flow and distribution of reservoir fluids the most. Estimation of distributed reservoir parameters has been done using mainly gradient-based optimization algorithms because these algorithms are relatively faster than global (stochastic) optimization algorithms. However, the gradient-based algorithms are local in nature and thus limited in their search ability. In this paper, we present a local-global optimization method that generates multiple realizations of reservoir parameters at coarse scale. The method involves the use of a local search optimization algorithm to parameterize the model space at a coarse scale followed by a stochastic search for better estimates in the vicinity of the local estimate. At the end of the search, the method produces a distribution of estimates that can be used for uncertainty quantification. To test the effectiveness of the method, the local-global optimization algorithm was applied to a sample reservoir with a known distributed permeability field. Results obtained indicate that the method is able to produce multiple history-matched realizations of the permeability field, some of which are closer to the true reservoir permeability distribution than the estimate obtained from an exhaustive local search.

We consider the problem of parameter estimation from real-valued multi-tone signals. Such problems arise frequently in spectral estimation. More recently, they have gained new importance in finite-rate-of-innovation signal sampling and reconstruction. The annihilating filter is a key tool for parameter estimation in these problems. The standard annihilating filter design has to be modified to result in accurate estimation when dealing with real sinusoids, particularly because the real-valued nature of the sinusoids must be factored into the annihilating filter design. We show that the constraint on the annihilating filter can be relaxed by making use of the Hilbert transform. We refer to this approach as the Hilbert annihilating filter approach. We show that accurate parameter estimation is possible by this approach. In the single-tone case, the mean-square error performance increases by 6 dB for signal-to-noise ratio (SNR) greater than 0 dB. We also present experimental results in the multi-tone case, which show that a significant improvement (about 6 dB) is obtained when the parameters are close to 0 or pi. In the mid-frequency range, the improvement is about 2 to 3 dB.

ABSTRACTThis article considers the parameter estimation problems of multivariable autoregressive output‐error autoregressive moving‐average systems. To alleviate the identification difficulty of systems, we decompose the multivariable autoregressive output‐error autoregressive moving‐average system into several subsystems. To reduce the impact of colored noises on parameter estimation accuracy, we propose an auxiliary model maximum likelihood generalized extended gradient‐based iterative algorithm using the auxiliary model idea and the maximum likelihood principle. In addition, we use the multi‐innovation identification theory to introduce a moving data window and propose an auxiliary model maximum likelihood moving‐data‐window generalized extended gradient‐based iterative algorithm. These two proposed algorithms produce more accurate parameter estimates than the existing auxiliary model generalized extended gradient‐based iterative algorithm. Simulation examples illustrate the effectiveness of the proposed algorithms.