Convergence Issues Research Articles

Convergence of power sequences of operators via their stability

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where “convergence” and “stability” are considered with respect to weak, strong and norm topologies. It is proved that an operator has a convergent power sequence if and only if it is a (not necessarily orthogonal) direct sum of an identity operator and a stable operator. This reduces the issue of convergence of the power sequence of an operator T to the study of stability of T. The question of when the limit of the power sequence is an orthogonal projection is investigated. Among operators sharing this property are hyponormal and contractive ones. In particular, a hyponormal or a contractive operator with no identity part is stable if and only if its power sequence is convergent. In turn, a unitary operator has a weakly convergent power sequence if and only if its singular-continuous part is weakly stable and its singular-discrete part is the identity. Characterizations of the convergence of power sequences and stability of subnormal operators are given in terms of semispectral measures.

An explicit finite element discrete crack analysis of open hole tension failure in composites

Developing efficient, robust methods for predicting the progressive failure of carbon fiber composites under tension is essential for optimal design, balancing weight reduction, damage tolerance, and service life. Implicit finite element (FE) methods struggle with the complex interplay of failure mechanisms, leading to a heavy reliance on costly, time-consuming experimental testing. This study introduces a novel explicit algorithm designed for laminate-level mesh models, capable of simulating cohesive cracks without predefined paths. Utilizing an explicit finite element software approach, our method effectively addresses convergence issues associated with the non-linear and unstable nature of composite failures during quasi-static loading. Contrasting with implicit FE method, this mesh-independent approach is both practical and numerically robust. The algorithm’s performance, tested on carbon-fiber reinforced composites with varying ply configurations [452/-452]s, [45n/90n/-45n/0n]s and [45/90/-45/0]ns (n=1/2/4/8), demonstrates improved simulation accuracy and efficiency over implicit FE methods, aligning well with prior experimental and simulation data. This advancement offers a promising solution for accurately simulating and understanding the complex failure behavior of these composites.

PD-DETR: towards efficient parallel hybrid matching with transformer for photovoltaic cell defects detection

Defect detection for photovoltaic (PV) cell images is a challenging task due to the small size of the defect features and the complexity of the background characteristics. Modern detectors rely mostly on proxy learning objectives for prediction and on manual post-processing components. One-to-one set matching is a critical design for DEtection TRansformer (DETR) in order to provide end-to-end capability, so that does not need a hand-crafted Efficient Non-Maximum Suppression NMS. In order to detect PV cell defects faster and better, a technology called the PV cell Defects DEtection Transformer (PD-DETR) is proposed. To address the issue of slow convergence caused by DETR’s direct translation of image feature mapping into target detection results, we created a hybrid feature module. To achieve a balance between performance and computation, the image features are passed through a scoring network and dilated convolution, respectively, to obtain the foreground fine feature and contour high-frequency feature. The two features are then adaptively intercepted and fused. The capacity of the model to detect small-scale defects under complex background conditions is improved by the addition of high-frequency information. Furthermore, too few positive queries will be assigned to the defect target via one-to-one set matching, which will result in sparse supervision of the encoder and impair the decoder’s ability of attention learning. Consequently, we enhanced the detection effect by combining the original DETR with the one-to-many matching branch. Specifically, two Faster RCNN detection heads were added during training. To maintain the end-to-end benefits of DETR, inference is still performed using the original one-to-one set matching. Our model implements 64.7% AP on the PVEL-AD dataset.

Novel cell-based smoothed extended finite element method for simulating the interactions of ultrasonic waves with randomly distributed cracks in solid structures

The conventional extended finite element method (XFEM) is a powerful tool for simulating crack-related problems in materials; however, several limitations exist, such as numerical instabilities and convergence issues. These problems arise because enriched elements have higher stiffness than standard elements, and this difference can cause computational difficulties. To overcome these limitations, we developed the cell-based smoothed extended finite element method (CS-XFEM), an advanced computational technique designed to simulate the intricate interactions between ultrasonic waves and randomly distributed cracks within solid materials. This innovative approach integrates a cell-based smoothing technique into the XFEM, effectively softening the stiffness of the enriched elements around crack tips. Therefore, the CS-XFEM eliminates numerical instability, providing a more stable and reliable computational framework. In this study, numerical experiments were conducted in which plasticity properties were assigned to both the crack bodies and tips to reflect crack yielding. Further, frictional contact in the crack body elements was formulated using the Heaviside function, and deformation around the crack tips was approximated using a singular function. Through comprehensive numerical investigations, we demonstrated that the conventional XFEM fails to converge and, instead, diverges when ultrasonic waves interact with randomly distributed cracks. By contrast, our proposed CS-XFEM method demonstrates strong convergence capabilities, rendering it well-suited for exploring the interactions between ultrasonic waves and randomly distributed cracks under varying crack quantities, lengths, and friction coefficients. Overall, the proposed CS-XFEM is an efficient, accurate, and robust method for investigating the acoustic nonlinearity induced by randomly distributed cracks with frictional contact in solid structures.

First and Second Reductions in an Aprotic Solvent: Comparing Computational and Experimental One-Electron Reduction Potentials for 345 Quinones.

Using reference reduction potentials of quinones recently measured relative to the saturated calomel electrode (SCE) in N,N-dimethylformamide (DMF), we benchmark absolute one-electron reduction potentials computed for 345 Q/Q•- and 265 Q•-/Q2- half-reactions using adiabatic electron affinities computed with density functional theory and solvation energies computed with four continuum solvation models: IEF-PCM, C-PCM, COSMO, and SM12. Regression analyses indicate a strong linear correlation between experimental and absolute computed Q/Q•- reduction potentials with Pearson's correlation coefficient (r) between 0.95 and 0.96 and the mean absolute error (MAE) relative to the linear fit between 83.29 and 89.51 mV for different solvation methods when the slope of the regression is constrained to 1. The same analysis for Q•-/Q2- gave a linear regression with r between 0.74 and 0.90 and MAE between 95.87 and 144.53 mV, respectively. The y-intercept values obtained from the linear regressions are in good agreement with the range of absolute reduction potentials reported in the literature for the SCE but reveal several sources of systematic error. The y-intercepts from Q•-/Q2- calculations are lower than those from Q/Q•- by around 320-410 mV for IEF-PCM, C-PCM, and SM12 compared to 210 mV for COSMO. Systematic errors also arise between molecules having different ring sizes (benzoquinones, naphthoquinones, and anthraquinones) and different substituents (titratable vs nontitratable). SCF convergence issues were found to be a source of random error that was slightly reduced by directly optimizing the solute structure in the continuum solvent reaction field. While SM12 MAEs were lower than those of the other solvation models for Q/Q•-, SM12 had larger MAEs for Q•-/Q2- pointing to a larger error when describing multiply charged anions in DMF. Altogether, the results highlight the advantages of, and further need for, testing computational methods using a large experimental data set that is not skewed (e.g., having more titratable than nontitratable substituents on different parent groups or vice versa) to help further distinguish between sources of random and systematic errors in the calculations.

Ensemble Deep Random Vector Functional Link Network Using Privileged Information for Alzheimer's Disease Diagnosis.

Alzheimer's disease (AD) is a progressive brain disorder. Machine learning models have been proposed for the diagnosis of AD at early stage. Recently, deep learning architectures have received quite a lot attention. Most of the deep learning architectures suffer from the issues of local minima, slow convergence and sensitivity to learning rate. To overcome these issues, non-iterative learning based deep randomized models especially random vector functional link network (RVFL) with direct links have proven to be successful. However, deep RVFL and its ensemble models are trained only on normal samples. In this paper, deep RVFL and its ensembles are enabled to incorporate privileged information, as the standard RVFL model and its deep models are unable to use privileged information. To fill this gap, we have incorporated learning using privileged information (LUPI) in deep RVFL model, and propose deep RVFL with LUPI framework (dRVFL+). Privileged information is available while training the models. As RVFL is an unstable classifier, we propose ensemble deep RVFL+ with LUPI framework (edRVFL+) which exploits the LUPI as well as the diversity among the base leaners for better classification. Unlike traditional ensemble approach wherein multiple base learners are trained, the proposed edRVFL+ model optimises a single network and generates an ensemble via optimization at different levels of random projections of the data. Both dRVFL+ and edRVFL+ efficiently utilise the privileged information which results in better generalization performance. In LUPI framework, half of the available features are used as normal features and rest as the privileged features. However, we propose a novel approach for generating the privileged information. We utilise different activation functions while processing the normal and privileged information in the proposed deep architectures. To the best of our knowledge, this is first time that a separate privileged information is generated. The proposed dRVFL+ and edRVFL+ models are employed for the diagnosis of Alzheimer's disease. Experimental results demonstrate the superiority of the proposed dRVFL+ and edRVFL+ models over baseline models. Thus, the proposed edRVFL+ model can be utilised in clinical setting for the diagnosis of AD.

Practical guidelines for Bayesian phylogenetic inference using Markov Chain Monte Carlo (MCMC)

Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible solutions and possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Modern statistical methods involve not just the estimation of a tree, but also solutions to more complex models involving fossil record information and other data sources. Markov Chain Monte Carlo (MCMC) is a leading method for approximating the posterior distribution of parameters in a mathematical model. It is deployed in all Bayesian phylogenetic tree estimation software. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. In this manuscript, we will offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them.

Discontinuum Micromodelling of Unstrengthened and FRCM-Strengthened Masonry Cross-Vaults Subjected to Seismic Excitation

ABSTRACT Many historical buildings employ masonry cross-vaults as flooring systems. The structural response of such cross-vaults to seismic excitation still needs to be fully understood and requires investigation through experimental studies or accurate numerical simulations. This article presents a finite element discontinuum micromodelling technique to simulate a full-scale mortared masonry cross-vault (unstrengthened and subsequently strengthened with textile-reinforced mortar) recently tested on a shake table as part of a blind prediction competition. The numerical technique uses shell elements to model the brick and mortar geometry explicitly within the STKO+OpenSees finite element framework. Both brick and mortar materials are modeled using an advanced damage-plasticity constitutive model, addressing potential convergence issues associated with strain-softening materials through a novel implicit-explicit integration algorithm. The numerical models predicted the failure mechanisms and crack patterns in close agreement with the experimental results. The strengthened model displayed severe cracks spreading across a larger part of the cross-vault, whereas the unstrengthened model exhibited in-plane shear failure along the groin lines. The strengthened vault showed an almost twofold increase in peak ground acceleration capacity, demonstrating the effectiveness of textile-reinforced mortar. The proposed numerical technique will be helpful in the design of effective retrofit measures for heritage structures.

Parameter‐free predictive control with flexibility in power adjustment for grid‐connected converters under unbalanced grid conditions

AbstractThis paper introduces a novel finite control set predictive direct power control method for grid‐connected converters without cost function evaluations. Unlike conventional predictive direct power control, since the proposed method does not use the model parameters, their uncertainties do not cause prediction error and inappropriate voltage vector selection. The method employs a new form of voltage vector selection based on the slopes of active and reactive powers. The slopes are predicted in a manner with a low sensitivity to sampling noise, without updating a look‐up table, and recursive methods. Hence, there are no stagnation and convergence issues. Also, the proposed method avoids startup problems caused by data‐lacking due to directly regulating the active and reactive power by a switching logic. Flexible power oscillations control with balanced sinusoidal grid currents without any signal sequence extraction can also be achieved under this method in unbalanced grid conditions. The proposed method is assessed by both simulation and experimental studies, and its performance is compared with existing robust combined and model predictive control methods. The outcomes highlight the influence of the proposed approach and establish its superiority over the other considered methods.

Rational capacity investment for renewable hydrogen-based steelmaking systems: A multi-stage expansion planning strategy

To improve energy efficiency and mitigate environmental impact, the iron and steel industry (ISI) is responsible for implementing a low-carbon transition. The renewable hydrogen-based steelmaking system (RHSS) has emerged as an innovative energy system in the pathway of reducing the carbon footprint of ISI. Nonetheless, the sustainable development requirements of RHSS emphasize the critical need for well-planned capacity investments to boost its economic viability. This study introduces a novel planning strategy for RHSS referred to as a multi-stage expansion planning (MSEP) model, which is aimed to minimize the levelized cost of crude steel over the planning horizon from 2025 to 2050 (EU climate neutrality year). The MSEP model incorporates the construction sequence and dynamic techno-economic parameters to formulate investment strategies that adapt to changing system requirements and external conditions over the planning horizon. To address the complexity of the MSEP model, a rolling-horizon approach (RHA) is proposed to solve the model sequentially while integrating updated information. The proposed approach is benchmarked against both the single-stage approach and the perfect-sight approach through case studies. The numerical results show that the proposed RHA (i) guarantees a rational capacity investment strategy for RHSS considering the construction sequence and dynamic techno-economic parameters over multiple planning stages; (ii) achieves a reduction in the levelized cost of crude steel by approximately 50% relative to the single-stage approach; (iii) resolves the convergence issues encountered with the perfect-sight approach while achieving an optimal solution in a reasonable time frame. Additionally, sensitivity analysis evaluates the uncertainties of multiple factors on the planning results, while the robustness analysis confirms the applicability and adaptability of RHA across various scenarios.

A novel correlation-based approach for combined estimation of state of charge and state of health of lithium-ion batteries

State of charge(SOC) and state of health(SOH) estimation are two critical aspects for the secure operation and echelon utilisation of lithium-ion batteries. Considering the two states are interrelated, combined estimation methods are desired in practice. However, previous machine learning-based or traditional filter-based techniques have high computational requirements or suffer from convergence issues. To this end, the combined SOC and SOH estimation method of lithium-ion batteries using the novel correlation between SOC and SOH is proposed in this study. Specifically, a correlation between the capacity ratio for constant-current charging process and constant-voltage charging process and capacity loss is established. Extended Kalman filter is adopted to track SOC values at the end of constant current charging process instead of relying on the entire charging process during online application and SOH estimation can be accomplished in only one step based on the established correlation. The results show that the proposed combined SOC and SOH estimation method enables precise SOC estimation during both charging and discharging processes and achieves reliable estimation results during battery degradation. Additionally, the proposed method offers a swift means of estimating SOH with guaranteed estimation accuracy.

Coordinated finite‐time control of multiple motors with saturation constraints

AbstractA multi‐motor coordinated tracking control strategy based on a disturbance sliding‐mode observer and an anti‐saturation non‐singular fast‐terminal sliding mode is proposed to address the issues of slow convergence and controller output saturation in multi‐motor coordinated control systems. Firstly, a mathematical model of a multi‐motor traction system considering uncertain parameter perturbations, external disturbances, and dead zones was established. Secondly, a disturbance sliding‐mode observer was designed based on the mathematical model to eliminate motor disturbances and estimate the torque. The observer's forward compensation was added to design a total‐consensus‐based fast non‐singular terminal sliding‐mode controller. Then, a fast anti‐saturation auxiliary system with fast finite‐time convergence was constructed. Finally, a comparative experiment was conducted with traditional anti‐saturation sliding‐mode control to demonstrate that the proposed method had faster convergence, stronger disturbance rejection, and better tracking performance in the presence of multi‐motor parameter perturbations, unknown disturbances, and input saturation.

Solving the Travelling Salesman Problem Using the PSO Optimization

This article examines a potential solution to the well-known Travelling Salesman Problem (TSP), which is classified as an NP-hard problem. We also provide a theoretical synopsis of several approaches that have been employed to tackle this problem. A prominent example of a combinatorial problem is the traveling salesman problem (TSP). To address the fundamental PSO algorithm's premature convergence issue and stagnation behavior on TSP, a scout characteristic-based PSO algorithm is suggested.We address Particle Swarm Optimization (PSO), a member of the evolutionary methods class, and outline the methodology for applying PSO to the TSP. Among population-based metaheuristic optimization methods, Particle Swarm Optimization (PSO) is one of the most widely used. Scientific domains such as engineering, chemistry, medicine, advanced physics, and humanities have all effectively employed PSO. Numerous theoretical and empirical results on the convergence and parameterization of PSO versions have been produced as a result of the method's extensive investigation since its introduction in 1995. Hundreds of PSO versions have been developed. It is well recognized that population size has a significant impact on the effectiveness of metaheuristics; nevertheless, no comprehensive research has been done on the appropriate selection of PSO swarm size to date.Through the application of this approach, we examine the effects of various control settings. The ideal solution and the quality of the solution are contrasted.

Adaptive Conformal Inference for Computing Market Risk Measures: An Analysis with Four Thousand Crypto-Assets

This paper investigates the estimation of the value at risk (VaR) across various probability levels for the log-returns of a comprehensive dataset comprising four thousand crypto-assets. Employing four recently introduced adaptive conformal inference (ACI) algorithms, we aim to provide robust uncertainty estimates crucial for effective risk management in financial markets. We contrast the performance of these ACI algorithms with that of traditional benchmark models, including GARCH models and daily range models. Despite the substantial volatility observed in the majority of crypto-assets, our findings indicate that ACI algorithms exhibit notable efficacy. In contrast, daily range models, and to a lesser extent, GARCH models, encounter challenges related to numerical convergence issues and structural breaks. Among the ACI algorithms, Fully Adaptive Conformal Inference (FACI) and Scale-Free Online Gradient Descent (SF-OGD) stand out for their ability to provide precise VaR estimates across all quantiles examined. Conversely, Aggregated Adaptive Conformal Inference (AgACI) and Strongly Adaptive Online Conformal Prediction (SAOCP) demonstrate proficiency in estimating VaR for extreme quantiles but tend to be overly conservative for higher probability levels. These conclusions withstand robustness checks encompassing the market capitalization of crypto-assets, time-series size, and different forecasting methods for asset log-returns. This study underscores the promise of ACI algorithms in enhancing risk assessment practices in the context of volatile and dynamic crypto-asset markets.

Active suspension control using novel HB3C optimized LQR controller for vibration suppression and ride comfort enhancement

This article addresses the optimization of a Vehicle Active Suspension System (VASS) through the application of a Linear Quadratic Regulator (LQR) controller. The primary objective is to enhance ride comfort and ensure vehicle stability by addressing the divergent needs of vibration control. The research identifies key issues in existing optimization algorithms, namely, the exploration stage inefficiency in Big Bang Big Crunch Optimization (B3C) and the slow convergence rate in Coyote Optimization (CO). To overcome these challenges, a novel hybrid algorithm, Hybrid Coyote optimization based Big Bang Big Crunch (HB3C), is proposed. The research objective is to optimize the LQR weighting matrices using the HB3C algorithm, aiming for improved ride comfort and vehicle safety. The problem statement involves the inadequacies of existing algorithms in addressing the exploration and convergence issues. The motivation lies in enhancing the efficiency of VASS through optimal control, leading to better ride comfort and safety. The methodology involves integrating CO within a loop with B3C to compute the optimum reduction rate for the algorithm. Since, B3C algorithm’s success is highly dependent on selecting the ideal reduction rate. This hybrid approach is then applied to optimize the existing LQR weighting matrices. The results are evaluated in terms of time domain and frequency domain response analysis, with a focus on ride comfort based on ISO 2631-1 standards. The study demonstrates a maximum reduction of approximately 74% achieved by the optimized HB3C-LQR controllers.

Transfer Learning-Based Specific Emitter Identification for ADS-B over Satellite System

In future aviation surveillance, the demand for higher real-time updates for global flights can be met by deploying automatic dependent surveillance–broadcast (ADS-B) receivers on low Earth orbit satellites, capitalizing on their global coverage and terrain-independent capabilities for seamless monitoring. Specific emitter identification (SEI) leverages the distinctive features of ADS-B data. High data collection and annotation costs, along with limited dataset size, can lead to overfitting during training and low model recognition accuracy. Transfer learning, which does not require source and target domain data to share the same distribution, significantly reduces the sensitivity of traditional models to data volume and distribution. It can also address issues related to the incompleteness and inadequacy of communication emitter datasets. This paper proposes a distributed sensor system based on transfer learning to address the specific emitter identification. Firstly, signal fingerprint features are extracted using a bispectrum transform (BST) to train a convolutional neural network (CNN) preliminarily. Decision fusion is employed to tackle the challenges of the distributed system. Subsequently, a transfer learning strategy is employed, incorporating frozen model parameters, maximum mean discrepancy (MMD), and classification error measures to reduce the disparity between the target and source domains. A hyperbolic space module is introduced before the output layer to enhance the expressive capacity and data information extraction. After iterative training, the transfer learning model is obtained. Simulation results confirm that this method enhances model generalization, addresses the issue of slow convergence, and leads to improved training accuracy.

Three‐phase state estimation in transmission networks with unbalanced loading utilising SCADA measurements

AbstractState estimation stands as one of the most crucial applications in energy management systems of control centres, ensuring the secure operation of the power system. The real‐time availability of accurate system variables, including voltages, currents, and power flows, presents an excellent opportunity to consider the actual network characteristics, including imbalances. This paper presents a linear and non‐iterative method to solve the three‐phase state estimation problem in transmission systems with unbalanced loading. The method utilises supervisory control and data acquisition measurements obtained from remote terminal units. The formulation is based on complex variables derived from traditional supervisory control and data acquisition measurements, with assumptions made regarding the availability of certain three‐phase bus voltages, as well as a number of three‐phase currents and active and reactive power flows. The proposed algorithm employs the classical weighted least squares technique for solving the three‐phase state estimation problem. Due to its straightforward and linear nature, the method ensures no convergence issues. To validate its effectiveness, the proposed method is validated on a three‐bus network and the IEEE 39‐bus network simulated using the three‐phase model within the DIgSILENT Power Factory environment.

A structural after measurement approach to structural equation modeling.

In structural equation modeling (SEM), the measurement and structural parts of the model are usually estimated simultaneously. In this article, we revisit the long-standing idea that we should first estimate the measurement part, and then estimate the structural part. We call this the "structural-after-measurement" (SAM) approach to SEM. We describe a formal framework for the SAM approach under settings where the latent variables and their indicators are continuous. We review earlier SAM methods and establish how they are specific instances of the SAM framework. Decoupled estimation for the measurement and structural parts using SAM possesses three key advantages over simultaneous estimation in standard SEM. First, estimates are more robust against local model misspecifications. Second, estimation routines are less vulnerable to convergence issues in small samples. Third, estimates exhibit smaller finite sample biases under correctly specified models. We propose two variants of the SAM approach. "Local" SAM expresses the mean vector and variance-covariance matrix of the latent variables as a function of the observed summary statistics and the parameters of the measurement model. "Global" SAM holds the parameters of the measurement part fixed while estimating the parameters of the structural part. Our framework includes two-step corrected standard errors, and permits computing both local and global fit measures. Nonetheless, the SAM approach is an estimation strategy, and should not be regarded as a model-building tool. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Research on a Multi-Strategy Improved Sand Cat Swarm Optimization Algorithm for Three-Dimensional UAV Trajectory Path Planning

In response to the issues of premature convergence, lack of population diversity, and poor convergence accuracy in the traditional Sand Cat Swarm Optimization (SCSO) algorithm, a Multi-Strategy Improved SCSO (MISCSO) algorithm is proposed. Firstly, multiple population strategies are used to avoid premature convergence and falling into local optima traps. Secondly, a distribution estimation learning strategy is introduced to represent the relationships between individuals, using probability models to improve algorithm performance. Next, the diversity of candidate solutions in the elite pool is utilized to expand the search space and enhance the algorithm’s ability to avoid local solutions. Lastly, a Cauchy disturbance strategy is adopted to accelerate the convergence speed of the algorithm, thereby improving the search efficiency and convergence accuracy. The experimental results of CEC2017 tests show that the improved algorithm balances convergence speed and global search capabilities effectively. Finally, the algorithm is applied to actual drone path planning and compared with six other intelligent algorithms, demonstrating the practicality and effectiveness of the improved algorithm.

Differential evolutionary optimization fuzzy entropy for gland segmentation based on breast mammography imaging

ObjectiveThe integration of fuzzy entropy into image segmentation techniques has proven effective in addressing issues related to ambiguous boundaries and uncertainties in complex image structures. This study aims to improve breast mammography image segmentation by optimizing minimum fuzzy entropy. The primary challenges identified are the presence of glandular burrs and irregular edges, as well as premature convergence and local optima in entropy optimization. MethodsWe propose an enhanced differential evolution algorithm combined with fuzzy entropy to address these challenges. This algorithm specifically targets glandular burrs, irregular edges, premature convergence, and local optimal entropy issues. The algorithm's performance was evaluated using breast mammography images representing four types of glands and benchmarked against five state-of-the-art algorithms. ResultsExperimental results demonstrate that the proposed algorithm significantly improves segmentation accuracy compared to the other advanced algorithms. It effectively resolves issues related to glandular burrs, irregular edges, premature convergence, and local optimal entropy, leading to superior segmentation outcomes. ConclusionThe proposed algorithm, which combines an improved differential evolution approach with fuzzy entropy, delivers the best segmentation results for breast gland segmentation. It successfully overcomes the challenges of glandular burrs, irregular edges, premature convergence, and local optimal entropy, thus enhancing breast mammography image segmentation.