Poor Convergence Research Articles

The source-network coordinated planning of active distribution system based on linear constraints

To overcome the problems of poor convergence, high cost and long planning time of traditional methods, a source-network coordinated planning method of active distribution system based on linear constraints is proposed. Firstly, the objective function of source network collaborative planning of active distribution system is established, so as to build the source network collaborative planning model. Then, the system power balance, line power security and other constraints are analysed, and the line power constraints and node voltage constraints are transformed into linear constraints by sensitivity method. Finally, the artificial fish swarm algorithm is used to solve the model, and the output of the model is the source network cooperation planning result of the active distribution system. Experimental results show that this method achieves the convergence of the model solution algorithm in 30 times, the total planning cost is 3.512645 million yuan, and the planning time varies from 0.1 s to 0.5 s.

Improving Numerical Accuracy for the Viscous-Plastic Formulation of Sea Ice

Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the most widely accepted model based on the viscous-plastic (VP) formulation introduced by Hibler in 1979. Due to its highly nonlinear features, this model is intrinsically challenging for computational solvers. In particular, sea ice simulations often significantly differ from satellite observations. This study therefore focuses on improving the numerical accuracy of the VP sea ice model. Since the poor convergence observed in existing numerical simulations stems from the nonlinear nature of the VP formulation, this investigation proposes using the celebrated weighted essentially non-oscillatory (WENO) scheme -- as opposed to the frequently employed centered difference (CD) scheme -- for the spatial derivatives in the VP sea ice model. We then proceed to numerically demonstrate that WENO yields higher-order convergence for smooth solutions, and that furthermore it is able to resolve the discontinuities in the sharp features of sea ice covers -- something that is not possible using CD methods. Finally, our proposed framework integrates a potential function method that utilizes the phase field method to naturally incorporates the physical restrictions of ice thickness and ice concentration in transport equations, resulting in a modified transport equations which includes additional forcing terms. Our method does not require post-processing, thereby avoiding the possible introduction of discontinuities and corresponding negative impact on the solution behavior. Numerical experiments are provided to demonstrate the efficacy of our new methodology.

Hybrid Genetic Firefly Algorithm-Based Routing Protocol for VANETs

Vehicular Adhoc Networks (VANETs) are used for efficient communication among the vehicles to vehicle (V2V) infrastructure. Currently, VANETs are facing node management, security, and routing problems in V2V communication. Intelligent transportation systems have raised the research opportunity in routing, security, and mobility management in VANETs. One of the major challenges in VANETs is the optimization of routing for desired traffic scenarios. Traditional protocols such as Adhoc On-demand Distance Vector (AODV), Optimized Link State Routing (OLSR), and Destination Sequence Distance Vector (DSDV) are perfect for generic mobile nodes but do not fit for VANET due to the high and dynamic nature of vehicle movement. Similarly, swarm intelligence routing algorithms such as Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) routing techniques are partially successful for addressing optimized routing for sparse, dense, and realistic traffic network scenarios in VANET. Also, the majority of metaheuristics techniques suffer from premature convergence, being stuck in local optima, and poor convergence speed problems. Therefore, a Hybrid Genetic Firefly Algorithm-based Routing Protocol (HGFA) is proposed for faster communication in VANET. Features of the Genetic Algorithm (GA) are integrated with the Firefly algorithm and applied in VANET routing for both sparse and dense network scenarios. Extensive comparative analysis reveals that the proposed HGFA algorithm outperforms Firefly and PSO techniques with 0.77% and 0.55% of significance in dense network scenarios and 0.74% and 0.42% in sparse network scenarios, respectively.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods.

Accurate calculation of ab initio potential energy surfaces (PESs) for the NH3 molecule is a difficult task because of the poor convergence of the standard CCSD(T) method with respect to the basis size. Currently, the best available NH3 PESs contain empirically refined parameters. In this paper, we show that CCSD(T)/aug-cc-pCV6Z calculations are not sufficient to properly describe the PES over a large range of nuclear configurations. However, the PES obtained by the extrapolation of the CCSD(T)/aug-cc-pCVXZ (X = T, Q, 5, and 6) energies to the complete basis set limit is closer to that based on the explicitly correlated CCSD(T)-F12a method using the cc-pCVQZ-F12 orbital basis set. All of the ab initio PESs constructed in this work include the following corrections: one electron relativistic effects, diagonal Born-Oppenheimer correction, and high-order electronic correlations (CCSDT, CCSDTQ, and CCSDTQP). Finally, the root-mean-square deviation between the predicted band centers obtained from our final "pure" ab initio PES and the experimental ones in the spectral region [0-7000] cm-1 is divided by two compared to the most accurate ab initio PES available in the literature.

The Specification and Impact of Prior Distributions for Categorical Latent Variable Models

ABSTRACT Latent class models can exhibit poor parameter recovery and low convergence rates under the traditional frequentist estimation approach. Bayesian estimation may be a viable alternative for estimating latent class models–especially when categorical items are present and priors can be placed directly on the categorical item-thresholds. We present a simulation study involving Bayesian latent class analysis (LCA) with categorical items. We demonstrate that the frequentist framework and the Bayesian framework with diffuse (non-informative) priors are unable to properly recover parameters (e.g., latent class item-thresholds); a substantive interpretation of the obtained results would lead to improper conclusions under these estimation conditions. However, specifying (weakly) informative priors within the Bayesian framework generally produced accurate parameter recovery, indicating that this may be a more viable estimation approach for LCA models with categorical indicators. The paper concludes with a general discussion surrounding the advantages of Bayesian estimation for LCA models.

A Numerical Convex Lens for the State-Discretized Modeling and Simulation of Megawatt Power Electronics Systems as Generalized Hybrid Systems

Modeling and simulation have emerged as an indispensable approach to create numerical experiment platforms and study engineering systems. However, the increasingly complicated systems that engineers face today dramatically challenge state-of-the-art modeling and simulation approaches. Such complicated systems, which are composed of not only continuous states but also discrete events, and which contain complex dynamics across multiple timescales, are defined as generalized hybrid systems (GHSs) in this paper. As a representative GHS, megawatt power electronics (MPE) systems have been largely integrated into the modern power grid, but MPE simulation remains a bottleneck due to its unacceptable time cost and poor convergence. To address this challenge, this paper proposes the numerical convex lens approach to achieve state-discretized modeling and simulation of GHSs. This approach transforms conventional time-discretized passive simulations designed for pure-continuous systems into state-discretized selective simulations designed for GHSs. When this approach was applied to a largescale MPE-based renewable energy system, a 1000-fold increase in simulation speed was achieved, in comparison with existing software. Furthermore, the proposed approach uniquely enables the switching transient simulation of a largescale megawatt system with high accuracy, compared with experimental results, and with no convergence concerns. The numerical convex lens approach leads to the highly efficient simulation of intricate GHSs across multiple timescales, and thus significantly extends engineers’ capability to study systems with numerical experiments.

Ensemble-based constrained optimization using an exterior penalty method

In science and engineering, non-linear constrained optimization has been a useful mathematical technique for many practical applications. Of interest to us is its applicability in the modeling and prediction of hydrocarbon reservoir production. In this paper, a new efficient, robust, and accurate optimal solution strategy based on the exterior penalty function (EPF) method and the adaptive ensemble-based optimization (EnOpt) approach (with backtracking line-search technique) for non-linear constrained optimization problems is presented. The purpose of this work is to provide a better user-friendly strategy which mitigates the problem often faced with the current constraints handling technique utilized when using the EnOpt method to solve constrained problems of water or EOR flooding. This study notes that the problem contributes to uncertainties in the gradient computation of the objective function and hence leads to the poor convergence rate of the standard EnOpt method. In this work, we used the EPF method to transform a given constrained optimization problem to a sequence of unconstrained subproblems and then sequentially solve the subproblems by unconstrained EnOpt procedure until convergence to the solution of the original problem. To demonstrate the advantage of the proposed methodology, we used it to solve analytical 2D bound constrained Rosenbrock’s problem and a practical high dimensional bound constrained water flooding optimization problem associated with a 2D 5Spot field and a 3D Reek reservoir field. The numerical results are compared with EnOpt using classical Lagrangian approach, as well as the traditional EnOpt. Our findings showed that the proposed solution method has a fast convergence rate and is more accurate and robust.

An enhanced fast non-dominated solution sorting genetic algorithm for multi-objective problems

Multi-modal multi-objective optimization problem (MMOPs) has attracted more and more attention in evolutionary computing recently. It is not easy to solve these problems using the existing evolutionary algorithms. The non-dominated solution sorting genetic algorithm (NSGA-II) has poor PS distribution and convergence. In this paper, an enhanced fast NSGA-II based on a special congestion strategy and adaptive crossover strategy, namely ASDNSGA-II is proposed. In the ASDNSGA-II, the strategy with a special congestion degree is used to improve the selection strategy. Then a new adaptive crossover strategy is designed by evaluating the advantages and disadvantages of the SBX crossover strategy with the ability to solve high dimensions and the BLX-α with the ability of Pareto solution to produce offspring solutions. These can ensure the generation of offspring solutions around individuals with large crowding degrees and balance the convergence and diversity of decision space and object space. It can improve PS distribution and convergence and maintain PF precision. Eight functions of MMF1-MMF8 from the CEC2020 are selected to prove the effectiveness of the ASDNSGA-II. By comparing several latest multi-modal multi-objective evolutionary algorithms, the results show that the ASDNSGA-II can effectively find the global Pareto solution set and improve the distribution and convergence of PS.

Unusual Presentation of PLA2G6-Related Neurodegeneration with Retinal Vasculitis.

Unusual Presentation of PLA2G6-Related Neurodegeneration with Retinal Vasculitis.

Sub-space iteration based Monte Carlo scheme for simultaneous computation of multiple dominant k-eigenmodes and acceleration of fission source iterations

Monte Carlo neutron transport codes are widely used for criticality simulation of full reactor core owing to their ability to model complex geometry in exact details, and of using the best available nuclear data. These codes are generally based on the Power Iteration (PI) method which is used to estimate only the fundamental eigenmode, and suffers from poor convergence rate specially when the dominance ratio is close to unity. Estimation of higher modes are required for various applications such as modal analysis, perturbation theory, etc. Computation of the dominance ratio is essential for determining the convergence rate of the power iterations. To overcome these issues, we have utilized a more robust Sub-Space Iteration (SSI) based Monte Carlo algorithm for simultaneous and efficient computation of multiple dominant eigenmodes for the general geometry full-core reactor problems. We have done an extensive investigation of the scheme on variety of problems with multi-group cross-section data, including the realistic full-core reactor benchmark (OECD/NEA 3D C5G7) to exemplify its validity, accuracy, and effectiveness. It was observed that the scheme works well for various kinds of systems, with good accuracy and has distinctly superior convergence properties than the PI method. The SSI based Monte Carlo scheme is built on top of the PI based neutron transport algorithm, and hence can be easily incorporated in the existing PI-based Monte Carlo codes for accelerating the fission source convergence and also for simultaneous computation of multiple eigenmodes.

Analytical solution for arbitrary large deflection of geometrically exact beams using the homotopy analysis method

Beam-like compliant elements have found wide-ranging application in many fields of engineering and science often where 3D large deflections can be of concern such as soft robotics, DNA mechanics and helicopter/wind turbine rotor blades. The homotopy analysis method (HAM) is used for the first time to obtain a novel analytical solution in converged series form for the arbitrary large deflection of geometrically exact beams subject to both conservative and follower loading scenarios. The homotopy analysis method, which offers desirable characteristics such as being free from small or large parameters, coupled with auxiliary parameters controlling convergence, is applied directly to the intrinsic governing equations of a geometrically exact beam theory. The system of first-order differential governing equations of geometrically exact beams with intrinsic formulation is free from rotation and displacement variables, and offers a low degree of nonlinearity (quadratic at most) and compact mathematical form, making it suitable for analytical solutions. Due to the relatively poor convergence of the original HAM algorithm, the iterative HAM technique is employed which is known to accelerate convergence and to improve the computational efficiency of the homotopy analysis method. The obtained homotopy series offers a number of novel features in the context of the analytical solutions for the large deflection of beams, including (a) the direct calculation of internal forces and moments which is significant for engineering design purposes, (b) being able to capture 3D deflections, (c) considering transverse shear effects which can be important for thicker beams or when the Young’s modulus to shear modulus ratio is significant (such as composite materials) and (d) considering conservative and follower tip and distributed loads, in a unified framework. In order to investigate the efficacy, applicability and accuracy of the proposed method, a number of numerical examples are considered in which a cantilever beam subject to tip or distributed loads undergoes large deflection. Large deflection results for both conservative and follower loads are compared against those of less comprehensive analytical solutions as well as against numerical methods including finite element and Chebyshev collocation methods where good agreement is observed. These results demonstrate the applicability and effectiveness of HAM for the large deflection analysis of geometrically exact beams.

Cuts for two-body decays at colliders

Fixed-order perturbative calculations of fiducial cross sections for two-body decay processes at colliders show disturbing sensitivity to unphysically low momentum scales and, in the case of H → γγ in gluon fusion, poor convergence. Such problems have their origins in an interplay between the behaviour of standard experimental cuts at small transverse momenta (pt) and logarithmic perturbative contributions. We illustrate how this interplay leads to a factorially divergent structure in the perturbative series that sets in already from the first orders. We propose simple modifications of fiducial cuts to eliminate their key incriminating characteristic, a linear dependence of the acceptance on the Higgs or Z-boson pt, replacing it with quadratic dependence. This brings major improvements in the behaviour of the perturbative expansion. More elaborate cuts can achieve an acceptance that is independent of the Higgs pt at low pt, with a variety of consequent advantages.

Performance optimization of differential evolution with slime mould algorithm for multilevel breast cancer image segmentation

Breast cancer is one of the most dangerous diseases for women's health, and it is imperative to provide the necessary diagnostic assistance for it. The medical image processing technology is one of the most critical of all complementary diagnostic technologies. Image segmentation is the core step of image processing, where multilevel image segmentation is considered one of the most efficient and straightforward methods. Many multilevel image segmentation methods based on evolutionary and population-based methods have been proposed in recent years, but many have the fatal weakness of poor convergence accuracy and the tendency to fall into local optimum. Therefore, to overcome these weaknesses, this paper proposes a modified differential evolution (MDE) algorithm with a vision based on the slime mould foraging behavior, where the recently proposed slime mould algorithm (SMA) inspires it. Besides, to obtain high-quality breast cancer image segmentation results, this paper also develops an excellent MDE-based multilevel image segmentation model, the core of which is based on non-local means 2D histogram and 2D Kapur's entropy. To effectively validate the performance of the proposed method, a comparison experiment between MDE and its similar algorithms was first carried out on IEEE CEC 2014. Then, an initial validation of the MDE-based multilevel image segmentation model was performed by utilizing a reference image set. Finally, the MDE-based multilevel image segmentation model was compared with peers using breast invasive ductal carcinoma images. A series of experimental results have proved that MDE is an evolutionary algorithm with high convergence accuracy and the ability to jump out of the local optimum, as well as effectively demonstrated that the developed model is a high-quality segmentation method that can provide practical support for further research of breast invasive ductal carcinoma pathological image processing.

Automatic Annotation Algorithm of Medical Radiological Images using Convolutional Neural Network

In order to address the problems of time-consuming, low accuracy and poor convergence effect of traditional image automatic annotation algorithm, an Automatic annotation algorithm of medical radiological images based on convolutional neural network (CNN) is proposed. First of all, the image gradient information model was constructed, the edge contour feature of medical radiation image was initialized, the automatic segmentation model of medical radiation image was established by block template matching method, and the automatic segmentation processing of medical radiation image was completed. Secondly, by fusing the contour and gray information of image segmentation, the multi-resolution feature is extracted by using the three-dimensional distributed pixel sequence of image. The fusion feature decomposition of the image was obtained based on CNN, and the automatic annotation of medical radiation image was completed. The results show that the image segmentation effect of the proposed algorithm is good, the number of feature points is accurate, and the accuracy of multi-resolution feature extraction is as high as 98.7%. The convergence of image annotation is good, short time-consumption, and the F1 measurement value of the algorithm is high, and the overall performance is good.

Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks

Engineering data are often highly nonlinear and contain high-frequency noise, so the Levenberg–Marquardt (LM) algorithm may not converge when a neural network optimized by the algorithm is trained with engineering data. In this work, we analyzed the reasons for the LM neural network’s poor convergence commonly associated with the LM algorithm. Specifically, the effects of different activation functions such as Sigmoid, Tanh, Rectified Linear Unit (RELU) and Parametric Rectified Linear Unit (PRLU) were evaluated on the general performance of LM neural networks, and special values of LM neural network parameters were found that could make the LM algorithm converge poorly. We proposed an adaptive LM (AdaLM) algorithm to solve the problem of the LM algorithm. The algorithm coordinates the descent direction and the descent step by the iteration number, which can prevent falling into the local minimum value and avoid the influence of the parameter state of LM neural networks. We compared the AdaLM algorithm with the traditional LM algorithm and its variants in terms of accuracy and speed in the context of testing common datasets and aero-engine data, and the results verified the effectiveness of the AdaLM algorithm.

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

Purpose It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity. Design/methodology/approach The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings. Findings The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy. Originality/value Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

Review of the strain-based formulation for analysis of plane structures Part I: Formulation of basics and the existing elements

Since the introduction of the finite element approach, as a numerical solution scheme for structural and solid mechanics applications, various for mulation methodologies have been proposed. These ways offer different advantages and shortcomings. Among these techniques, the standard displacement-based approach has attracted more interest due to its straightforward scheme and generality. Investigators have proved that the other strategies, such as the force-based, hybrid, assumed stress, and as sumed strain provides special advantages in comparison with the classicfinite elements. For instance, the mentioned techniques are able to solve difficulties, like shear locking, shear parasitic error, mesh sensitivity, poor convergence, and rotational dependency. The main goal of this two-part study is to present a brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane finite elements. In this article, which is the first part of this study, assump tions and the basics of this method are introduced. Then, a detailed review of all the existing strain-based membrane elements is presented. Although the strain formulation is applicable for different types of structures, most of the existing elements pertain to the plane structures. The second part of this study deals with the application and performance of the reviewed elements in the analysis of plane stress/strain problems.

Impact Force Reconstruction of Composite materials based on Improved Regularization Technology

In the structural health monitoring of composite materials, in order to solve the ill-posed problem of impact force reconstruction, regularization techniques are often used to deal with it. Due to the poor convergence of the traditional Tikhonov regularization method, in order to accurately reconstruct the time history of the impact force, this paper improves Tikhonov regularization method and constructs homotopy function with strong convergence. Since the optimal regularization parameters need to be found in the homotopy function, the Newton downhill method is used to find the optimal parameters and the homotopy function can be calculated, which can accurately reconstruct the time history of the impact force. In order to verify the universality of the method in this paper, impact hammers of different materials were used in the experiment in this paper to study and compare the reconstruction effect of impact time history of different impact hammers.

An Improved Extended Kalman Filter for Radar Tracking of Satellite Trajectories

Nonlinear state estimation problem is an important and complex topic, especially for real-time applications with a highly nonlinear environment. This scenario concerns most aerospace applications, including satellite trajectories, whose high standards demand methods with matching performances. A very well-known framework to deal with state estimation is the Kalman Filters algorithms, whose success in engineering applications is mostly due to the Extended Kalman Filter (EKF). Despite its popularity, the EKF presents several limitations, such as exhibiting poor convergence, erratic behaviors or even inadequate linearization when applied to highly nonlinear systems. To address those limitations, this paper suggests an improved Extended Kalman Filter (iEKF), where a new Jacobian matrix expansion point is recommended and a Frobenius norm of the cross-covariance matrix is suggested as a correction factor for the a priori estimates. The core idea is to maintain the EKF structure and simplicity but improve its accuracy. In this paper, two case studies are presented to endorse the proposed iEKF. In both case studies, the classic EKF and iEKF are implemented, and the obtained results are compared to show the performance improvement of the state estimation by the iEKF.

A Multigrid Method for a Nitsche-based Extended Finite Element Method

We present a tailored multigrid method for linear problems stemming from a Nitsche-based extended finite element method (XFEM). Our multigrid method is robust with respect to highly varying coefficients and the number of interfaces in a domain. It shows level independent convergence rates when applied to different variants of Nitsche’s method. Generally, multigrid methods require a hierarchy of finite element (FE) spaces which can be created geometrically using a hierarchy of nested meshes. However, in the XFEM framework, standard multigrid methods might demonstrate poor convergence properties if the hierarchy of FE spaces employed is not nested. We design a prolongation operator for the multigrid method in such a way that it can accommodate the discontinuities across the interfaces in the XFEM framework and recursively induces a nested FE space hierarchy. The prolongation operator is constructed using so-called pseudo-L^2-projections; as common, the adjoint of the prolongation operator is employed as the restriction operator.