Non-convergence Problem Research Articles

Error analysis and improved method of time-domain distance protection for wind power transmission lines

Time-domain distance protection has a good transient performance and operation speed when applied to wind power transmission lines. In this paper, the error analysis and improved method of phase-to-phase time-domain distance protection are investigated. Firstly, based on the time-domain mathematical model, the location error caused by fault resistance is analyzed, and then the algorithmic convergence and accuracy of conventional phase-to-phase distance relay are evaluated. To solve the computational non-convergence problem, an improved phase-to-phase distance relay is proposed, in which the instantaneous negative-sequence current is used to improve the location accuracy, especially during the fault transient stage of wind farms. In order to avoid the protection overreach problem, the threshold selection method is designed based on the maximum allowable error of the calculated distance. According to the proposed method, the corresponding protection device is developed. And the hardware-in-the-loop (HIL) test system is built based on the real-time digital simulation (RTDS) platform. Extensive experimental tests are carried out, to verify the feasibility and superiority of the proposed time-domain distance protection.

A survey on training challenges in generative adversarial networks for biomedical image analysis

In biomedical image analysis, the applicability of deep learning methods is directly impacted by the quantity of image data available. This is due to deep learning models requiring large image datasets to provide high-level performance. Generative Adversarial Networks (GANs) have been widely utilized to address data limitations through the generation of synthetic biomedical images. GANs consist of two models. The generator, a model that learns how to produce synthetic images based on the feedback it receives. The discriminator, a model that classifies an image as synthetic or real and provides feedback to the generator. Throughout the training process, a GAN can experience several technical challenges that impede the generation of suitable synthetic imagery. First, the mode collapse problem whereby the generator either produces an identical image or produces a uniform image from distinct input features. Second, the non-convergence problem whereby the gradient descent optimizer fails to reach a Nash equilibrium. Thirdly, the vanishing gradient problem whereby unstable training behavior occurs due to the discriminator achieving optimal classification performance resulting in no meaningful feedback being provided to the generator. These problems result in the production of synthetic imagery that is blurry, unrealistic, and less diverse. To date, there has been no survey article outlining the impact of these technical challenges in the context of the biomedical imagery domain. This work presents a review and taxonomy based on solutions to the training problems of GANs in the biomedical imaging domain. This survey highlights important challenges and outlines future research directions about the training of GANs in the domain of biomedical imagery.

Dynamic displacement measurement of hoisting rope in lateral and longitudinal direction by improving Lucas–Kanade algorithm

The hoisting rope has complex dynamic characteristics under external excitation during operation, characterized by large longitudinal movement and minor lateral oscillation. However, there are no appropriate approaches to acquire the dynamic displacement of the rope currently. In this study, a fast vision-based measurement framework, including initial value forecast (IVF) and target tracking based on Lucas–Kanade (LK) algorithm, called IVF-LK, is proposed to obtain the lateral-longitudinal displacement of the rope. Firstly, an IVF method is proposed to obtain the initial value of iteration, overcoming the problem of non-convergence of LK algorithm under large displacement. Secondly, a parameter update strategy makes the convergence speed of LK significantly improved. Then, the performance of IVF-LK algorithm was tested in the experimental bench, which reveal its superior capacity in rope-structure dynamic measurement both in efficiency and precision. Finally, a field experiment was implemented to analyze the dynamic displacement of the hoisting rope.

A New Performance Optimization Method for Linear Motor Feeding System

The linear motor feeding system is a typical electromechanical coupling system. Conventional characteristic analyses of electromechanical coupling often overlook the influence of flexible deformation in critical components of the linear motor feeding system. Moreover, when employing genetic algorithms to optimize servo system PID control parameters, slow convergence, nonconvergence, or premature convergence problems may arise. To address these issues, this paper proposes a new performance optimization method for a linear motor feeding system. The method uses a combination of “multi-body theory + finite element” to accurately account for the flexible deformation of critical components of the feeding system, establishes a rigid–flexible electromechanical coupling model of the linear motor feeding system, and optimizes the PID parameters of the established model with an improved adaptive genetic algorithm. Simulation results demonstrate that, when utilizing an adaptive genetic algorithm to optimize the rigid–flexible electromechanical coupling model and a control system model that disregards flexible body deformation, the system achieves stability in 0.02 s and 0.027 s with overshoots of 13% and 27%, respectively. These outcomes confirm the accuracy and importance of considering flexible body deformation in the optimization performance of a linear motor feeding system. At the same time, the time required to reach the steady state of the rigid–flexible electromechanical coupling model optimized by the adaptive genetic algorithm is shortened from 0.035 s to 0.02 s. The sinusoidal signal response curve of the optimized system does not exhibit any peak overshoot compared with that of the nonoptimized system, and the response speed is also faster. These results demonstrate the effectiveness of the rigid–flexible electromechanical coupling model optimized by the nonlinear adaptive genetic algorithm. The displacement response curves of the linear motor feeding system under different workbench loads are obtained through experiments and compared with those obtained from simulations to verify the established model and the correctness of the proposed method.

Instability of inverse probability weighting methods and a remedy for nonignorable missing data.

Inverse probability weighting (IPW) methods are commonly used to analyze nonignorable missing data (NIMD) under the assumption of a logistic model for the missingness probability. However, solving IPW equationsnumerically may involve nonconvergence problems when the sample size is moderate and the missingness probability is high. Moreover, those equationsoften have multiple roots, and identifying the best root is challenging. Therefore, IPW methods may have low efficiency or even produce biased results. We identify the pitfall in these methods pathologically: they involve the estimation of a moment-generating function (MGF), and such functions are notoriously unstable in general. As a remedy, we model the outcome distribution given the covariates of the completely observed individuals semiparametrically. After forming an induced logistic regression (LR) model for the missingness status of the outcome and covariate, we develop a maximum conditional likelihood method to estimate the underlying parameters. The proposed method circumvents the estimation of an MGF and hence overcomes the instability of IPW methods. Our theoretical and simulation results show that the proposed method outperforms existing competitors greatly. Two real data examples are analyzed to illustrate the advantages of our method. We conclude that if only a parametric LR is assumed but the outcome regression model is left arbitrary, then one has to be cautious in using any of the existing statistical methods in problems involvingNIMD.

A Model-Based Shrinkage Target to Avoid Non-convergence in Small Sample SEM

Structural equation modeling is prone to a variety of problems when the sample size is small. One solution that attempts to solve the (non-convergence) problem of small sample SEM is found in shrinkage estimation, where a weighted average between the sample variance-covariance matrix (S) and a highly structured shrinkage target (T) is calculated to construct an adjusted sample variance-covariance matrix (), which is then used as input for the analysis. Different target candidates have already been put forward in the literature, but in this paper, we propose using a model-based target matrix specifically tailored for structural equation models. Two simulation studies demonstrate the benefit of using a model-based target over other candidate targets in terms of convergence rate, bias, and MSE, but also emphasize the importance of constructing an optimal shrinkage intensity.

Reliability assessment of passive residual heat removal system using FORM methodology with chaos control

Passive safety systems are adopted extensively to increase the inherent safety of the nuclear reactor. However, their stability of operation is more susceptive to thermal hydraulics uncertainty due to the relatively small driving force of passive systems. Coupled with a shortage of pertinent experimental and operational data, its reliability assessment is still a crucial and challenging task. So far, there are no accepted techniques for this problem and they are not yet frozen. Hasofer-Lind and Rackwitz-Flessler method (HL-RF) is an efficient iterative approach to identify the most probable point (MPP) and calculate the reliability. However, the approach may suffer from instability when dealing with highly nonlinear limit state functions (LSFs) or high-dimensional problems. In this paper, a straightforward and efficient method depending on chaos control was proposed to deal with numerical instability and chaos non-convergence problems. The proposed method was utilized to assess the reliability of the passive residual heat removal system (PRHRS) in Integral-type Pressurized Water Reactor (IPWR200). The results showed that it could efficiently and reliably locate MPP and accurately obtain the reliability index.

Fast Calculation Method for Continuous Power Flow of Microgrid Based on Levenberg-Marquardt Algorithm

There are possible non-convergence problems at load power critical value while using conventional continuous power flow methods. Generally, the step control method is used in the calculation to perform the calculation in small steps at the convergence to the load power critical value, and this method sacrifices the speed of the calculation although the calculation accuracy is high. In this paper, the Levenberg-Marquardt algorithm is used to search for the load power critical value firstly, and after that the step control algorithm is designed to perform fast power flow finding with known load power critical value, which takes into account the computational accuracy and computational efficiency. The case shows that the fast calculation method for continuous power flow of microgrid based on Levenberg-Marquardt algorithm proposed in this paper can guarantee the accuracy while effectively improving the calculation speed, and is suitable for online real-time evaluation of voltage stability and preventive control aided decision online calculation of isolated microgrid with high requirements for real-time.

IQoR-LSE: An Intelligent QoS On-Demand Routing Algorithm With Link State Estimation

With the rapid development of Internet applications, diversified Quality of Service (QoS) has been required in packet routing to meet the demand of various types of applications. In this article, an Intelligent QoS on-demand Routing (IQoR) framework has been proposed to support multiclass QoS Provisioning for packet forwarding. In addition, we present an IQoR with Link State Estimation (IQoR-LSE) algorithm with the assistance of link congestion inference to guide the exploration of action space in deep reinforcement learning, to seek optimal routing policies. The IQoR-LSE algorithm is proposed to solve the non-convergence problem at exploring the high-dimensional action space by jointly estimating the link congestion. Extensive simulations show that IQoR-LSE algorithm outperforms other benchmark routing algorithms with efficient learning and a significant reduction in average delay, jitter and packet loss.

A mixed selective edge-based smoothed PFEM with second-order cone programming for geotechnical large deformation analysis

Traditional particle finite element method (PFEM) with a six-node triangular (T6) element using an iteration algorithm often suffers from high computational costs and non-convergence problems. This paper proposes a novel dynamic implicit optimisation based smoothed PFEM for solving geotechnical large deformation problems. The governing equations are treated as an equivalent min–max optimisation that is recast as a second-order cone programming (SOCP) problem. Owing to the particularity of the min–max optimisation problem, which needs to simultaneously interpolate displacement and stress field, a novel mixed constant-stress selective edge-based smoothed strain element is proposed in which strain and stress are constant in the smoothing domain. The two-level mesh repartitioning scheme is implemented into the proposed method to overcome volumetric locking. Next, a mass lumping scheme using nodal integration is developed to improve computational efficiency. An efficient and simple variable mapping scheme is finally proposed and implemented into PFEM to tackle large deformation problems. Several classical statics and dynamics examples are used to validate the proposed method. All results demonstrate that the proposed method only using the lower-order element offers high accuracy, high efficiency, mesh insensitivity and is free of volumetric locking for geotechnical problems under both small and large deformation.

A Design Method of Two-Dimensional Subwavelength Grating Filter Based on Deep Learning Series Feedback Neural Network.

Subwavelength grating structure has excellent filtering characteristics, and its traditional design method needs a lot of computational costs. This work proposed a design method of two-dimensional subwavelength grating filter based on a series feedback neural network, which can realize forward simulation and backward design. It was programed in Python to study the filtering characteristics of two-dimensional subwavelength grating in the range of 0.4–0.7 µm. The shape, height, period, duty cycle, and waveguide layer height of two-dimensional subwavelength grating were taken into consideration. The dataset, containing 46,080 groups of data, was generated through numerical simulation of rigorous coupled-wave analysis (RCWA). The optimal network was five layers, 128 × 512 × 512 × 128 × 61 nodes, and 64 batch size. The loss function of the series feedback neural network is as low as 0.024. Meanwhile, it solves the problem of non-convergence of the network reverse design due to the non-uniqueness of data. The series feedback neural network can give the geometrical structure parameters of two-dimensional subwavelength grating within 1.12 s, and the correlation between the design results and the theoretical spectrum is greater than 0.65, which belongs to a strong correlation. This study provides a new method for the design of two-dimensional subwavelength grating, which is quicker and more accurate compared with the traditional method.

An Alternative Perspective on the Robust Poisson Method for Estimating Risk or Prevalence Ratios.

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or prevalence ratios. In addition, it does not suffer from frequent nonconvergence problems such as the most common implementations of maximum likelihood estimators of the log-binomial model. However, using a Poisson distribution to model a binary outcome may seem counterintuitive. Methodologic papers have often presented this as a good approximation to the more natural binomial distribution. In this article, we provide an alternative perspective to the robust Poisson method based on the semiparametric theory. This perspective highlights that the robust Poisson method does not require assuming a Poisson distribution for the outcome. In fact, the method only assumes a log-linear relation between the risk or prevalence of the outcome and the explanatory variables. This assumption and the consequences of its violation are discussed. We also provide suggestions to reduce the risk of violating the modeling assumption. Additionally, we discuss and contrast the robust Poisson method with other approaches for estimating exposure risk or prevalence ratios. See video abstract at, http://links.lww.com/EDE/B987 .

A Novel Numerical Method for Theoretical Tire Model Simulation

Theoretical tire models are often used in tire dynamics analysis and tire design. In the past, scholars have carried out a lot of research on theoretical model modeling; however, little progress has been made on its solution. This paper focuses on the numerical solution of the theoretical model. New force and moment calculation matrix equations are constructed, and different iterative methods are compared. The results show that the modified Richardson iteration method proposed in this paper has the best convergence-stability in the steady and unsteady state calculation, which mathematically solves the problem of nonconvergence of discrete theoretical models in the published reference. A novel discrete method for solving the total deformation of tires is established based on the Euler method. The unsteady characteristics of tire models are only related to the path frequency without changing its parameters, so the unsteady state ability of the tire model can be judged based on this condition. It shows that the method in the references have significant differences at different speeds with the same path frequency under turn slip or load variations input, but the method proposed in this paper has good results.

Multiagent Reinforcement-Learning-Aided Service Function Chain Deployment for Internet of Things

Nowadays, the compelling applications of the Internet of Things (IoT) bring unexpected economic benefits to our daily lives. But at the same time, it also poses huge challenges to service providers. Diverse proprietary hardware (i.e., firewall and code conversion) have to be deployed in networks for meeting different applications’ requirements. Recently, network functions virtualization (NFV) is considered a promising technique. In the NFV-enabled architecture, network services can be implemented via a set of orderly virtual network functions (VNFs) on standardized compute nodes, which is termed service function chains (SFCs). However, with the explosion of IoT applications, embedding multiple SFCs in a shared NFV-enabled infrastructure becomes a challenging problem. Centralized schemes suffer from the scalability and private issue, while distributed schemes suffer from the nonconvergence problem. In this article, we propose a hybrid intelligent control architecture, which adopts the centralized training and distributed execution paradigm. A centralized critic is introduced to ease the training process of the distributed network nodes. Besides, considering the competitive behavior of users, we formulate the resource allocation problem as a multiuser competition game model. Based on this, we proposed a multiagent reinforcement learning-based SFCs deployment algorithm.

Member importance prediction and failure response analysis for cable network antennas

Cable network antennas are likely to experience damage from the extreme space environment. This will deteriorate the antennas’ performance and even lead to the scrapping of antennas. To date, effective means for on-orbit maintenance of cable network antennas are lacking. Therefore, it is necessary to investigate the influence of each member failure on the antenna and find the most important ones before launching. But the method of exhaustion to analyze each member failure response is inefficient. Hence, we propose an importance prediction method for finding the key members of the antenna based on the sensitivity analysis. The sensitivity analyses with respect to the failure member are carried out, in which the condition of cable slack caused by member failure is considered. The node displacement sensitivity is used to predict the member importance. After that, based on the vector form intrinsic finite element method, a response analysis method for the incomplete antenna after member failure is proposed. The proposed method can accurately capture the transient response of the antenna and effectively avoid the non-convergence problem caused by slack cables. A numerical example is provided, and the most important members are predicted, which should be given special concern in the design stage.

Study of non-convergence problem of the integral method for polarizer design on the ECRH system

On the electron cyclotron resonance heating system, the integral method represents a class of classical mathematical methods for polarizer design. However, the non-convergence problem caused by the Fredholm integral equation of the integral method usually leads to an incorrect result. This sometimes may confuse the beginners. The simplified kernel function based on the infinitesimal approximation is presented in this paper, which effectively solves the non-convergence problem, making it easier to use and simplifying the code of calculation for beginners. A code is developed based on this method, then the calculation results are compared with the calculation results of the coordinate transformation method, and the experimental results of the low power test platform. The comparison results and low power test results indicate that this method can be used for polarizer design.

A 2D generic multi-surface cohesive zone model for simulating FRP-to-concrete mixed-mode debonding failure

This paper proposes a 2D generic multi-surface cohesive zone model to simulate the debonding failure process of FRP-to-concrete joints within the framework of plasticity theory. The model combines a tension cut-off yield surface with a Coulomb friction yield surface, which can accurately predict the coupled mixed-mode debonding behaviour. Non-associated flow rule is adopted by the Coulomb friction yield formulation to reproduce the dilation effect, while the tension cut-off criterion is responsible for simulating the separation in the normal direction between two bonded substrates. Given the potential non-convergence problems caused by the presence of vertex region at the intersections between two yield surfaces, a remedy measure using the implicit backward Euler integration method incorporating Koiter’s rule and coupled independent state variables is applied. The proposed 2D interface model is versatile, and its accuracy has been validated by comparing the predicted results with their test counterparts from literature in different aspects, including the capacities of capturing mixed-mode failure, dilation behaviour, lateral compression effect, FRP deformation, and local bond stress-slip relationship. The model’s good compatibility with the constitutive relationship of CDP (concrete damaged plasticity) is also demonstrated.

A LiDAR-based single-shot global localization solution using a cross-section shape context descriptor

Fusing LiDAR and high definition (HD) maps is a feasible way to achieve global localization in GNSS-denied environments, which is necessary in driverless vehicle and robotic technologies. This paper proposes a single-shot global localization solution that uses only a single current scan of a rotating multiple-beam LiDAR sensor to locate its own location and pose with respect to an HD map in the form of georeferenced point clouds. This single-shot global localization solution estimates the state of the current moment without the previous moment state and thus avoids the nonconvergence problems that plague filter-based methods. The proposed solution allows HD maps from diverse LiDAR sensors to be used for global localization and is more robust than existing methods. The proposed solution consists of two procedures: offline preprocessing and online global localization. In the offline procedure, diverse HD maps are preprocessed to construct a global prior map for the localization process. The online global localization procedure includes two elements: place recognition, location and pose estimation. A novel Cross-Section Shape Context (CSSC) descriptor that is highly descriptive and rotation-invariant is proposed for subsequent processes. Two strategies, two-stage similarity estimation and Nearest Cluster Distance Ratio (NCDR), based on the CSSC descriptor are proposed to improve place recognition precision. A Selective Generalized Iterative Closest Point (SGICP) algorithm is proposed to calculate location and pose accurately using the CSSC descriptor. Comprehensive experiments were performed to evaluate this solution. A comparison of the precision-recall curve of multiple scenes, particularly under changed viewpoint scenes, shows that the CSSC descriptor is more robust than existing descriptors. Experimental analysis also confirms that the proposed strategies, two-stage similarity estimation and NCDR, improve place recognition precision. Also, compared to the generalized iterative closest point algorithm, the SGICP algorithm achieved better accuracy by 31% and efficiency by 60%. The proposed solution achieves a mean relative translation error (RTE) improvement of 27% over the OneShot algorithm on the KITTI dataset. The proposed solution had an average 77% improvement over 1σ RTE relative to the benchmark in tests with the long-term localization NCLT dataset. The mean RTE of the proposed solution was 0.13 m using HD maps from different LiDAR sensors. Our code is available at: https://github.com/Dongxu05/CSSC.

General solution to the Kohn–Luttinger nonconvergence problem

A simple, but general solution is proposed for the Kohn–Luttinger problem, i.e., the nonconvergence of the finite-temperature many-body perturbation theory with its zero-temperature counterpart as temperature is lowered to zero under some circumstances. How this nonconvergence can be avoided by altering the reference wave function is illustrated numerically by using up to the fifth order of the perturbation theory.

Research on Real-time Simulation of Power Electronic Circuits Based on Simscape

In order to realize hardware-in-the-loop simulation of commonly used power electronic circuits, a method of joint simulation using Simcape and field programmable gate array (FPGA) is proposed. This article adopts a switch modeling method suitable for high-frequency characteristics, namely the switch function method. It effectively solves the problem of rigidity non-convergence in the modeling of the binary resistance method, as well as the transient error caused by the binary LC method when the system state is switched with the increase of the switching frequency, which reduces the simulation accuracy. Taking the single-phase full-bridge inverter circuit as an example, a Simscape model based on the state-space averaging method was established, and the HDL code was automatically generated using the Simscape HDL Workflow Advisor tool, and the hardware-in-the-loop simulation was completed with FPGA. Finally, the simulation results with Simulink comparison verify the effectiveness and feasibility of the method.