Step Size Research Articles

Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.

Eighth-Order Numerov-Type Methods Using Varying Step Length

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community.

Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm

To ensure the safe production of mines, the intelligent trend of underground mining operations is gradually advancing. However, the operational environment of subterranean mining is intricate, making the conventional path-planning algorithm used by mining inspection robots frequently inadequate for real requirements. To safeguard the mining inspection robot, targeting the problem of low search efficiency and path redundancy in the path planning of the existing rapidly exploring random tree (RRT) algorithm in the narrow and complex unstructured environment, a path-planning algorithm combining improved RRT and a probabilistic road map (PRM) is proposed. Initially, the target area is efficiently searched according to the fan-shaped goal orientation strategy and the adaptive step size expansion strategy. Subsequently, the PRM algorithm and the improved RRT algorithm are combined to reduce the redundant points of the planning path. Ultimately, considering the kinematics of the vehicle, the path is optimized by the third-order Bessel curve. The experimental simulation results show that the proposed path-planning algorithm has a higher success rate, smoother path, and shorter path length than other algorithms in complex underground mining environments, which proves the effectiveness of the proposed algorithm.

Efficient Error-Rate Estimation for Optical Transmission Systems Using Artificial Neural Networks

ABSTRACT With the advancement in modulation formats, optical transmission systems are becoming more adaptable and dynamic. Predicting bit errors of higher-order modulation formats is a challenging problem for the optimum design of communication systems. The existing simulation methods have persisted by employing iterative procedures that frequently incur high computing expenses and time consumption. On the other hand, deep learning (DL) algorithms have demonstrated remarkable efficacy as practical computing tools, presenting a viable approach to accelerate modulation simulations. In this paper, an artificial neural network (ANN) based bit error rate (BER) estimation scheme is proposed for the popular modulation forms including 56 Gbps 16-quadrature amplitude modulation (16QAM), 100 Gbps 32QAM, and 120 Gbps 64QAM optical system. Based on constellation diagrams (CDs) acquired with different launch power, laser linewidth, transmission distance, and OSNR, amplitude histograms (AHs) are generated via a manual preprocessing method. The properly trained ANN architecture exhibits a computational speed that surpasses traditional simulation methods by a factor exceeding 347. Moreover, the design considerations including the number of layers, nodes, activation functions, learning rate, optimizers, and evolution epochs are also investigated in detail. This research paves the way for optical transmission systems to use fast DL-based optimization strategies.

Improving performance of WSNs in IoT applications by transmission power control and adaptive learning rates in reinforcement learning

Improving performance of WSNs in IoT applications by transmission power control and adaptive learning rates in reinforcement learning

ICS-ResNet: A Lightweight Network for Maize Leaf Disease Classification

The accurate identification of corn leaf diseases is crucial for preventing disease spread and improving corn yield. Plant leaf images are often affected by factors such as complex backgrounds, climate, light, and sample data imbalance. To address these issues, we propose a lightweight convolutional neural network, ICS-ResNet, based on ResNet50. This network incorporates improved spatial and channel attention modules as well as a deep separable residual structure to enhance recognition accuracy. (1) The residual connections in the ResNet network prevent gradient loss during deep network training. (2) The improved channel attention (ICA) and spatial attention (ISA) modules fully utilize semantic information from different feature layers to accurately localize key features of the network. (3) To reduce the number of parameters and lower computational costs, we replace traditional convolutional computation with a depth-separable residual structure. (4) We also employ cosine annealing to dynamically adjust the learning rate, enhancing the network’s training stability, improving model convergence, and preventing local optima. Experiments on the corn dataset in Plant Village compare the proposed ICS-ResNet with eight popular networks: CSPNet, InceptionNet_v3, EfficientNet, ShuffleNet, MobileNet, ResNet50, ResNet101 and ResNet152. The results show that the ICS-ResNet achieves an accuracy of 98.87%, which is 5.03%, 3.18%, 1.13%, 1.81%, 1.13%, 0.68%, 0.44% and 0.60% higher than the other networks, respectively. Furthermore, the number of parameters and computations are reduced by 69.21% and 54.88%, respectively, compared to the original ResNet50 network, significantly improving the efficiency of corn leaf disease classification. The study provides strong technical support for sustainable agriculture and the promotion of agricultural science and technology innovation.

Dynamic gait stability in people with mild to moderate Parkinson's disease

BackgroundFalls are a serious health threat for people with Parkinson's disease. Dynamic gait stability has been associated with fall risk. Developing effective fall prevention interventions requires a sound understanding of how Parkinson's disease affects dynamic gait stability. This study compared dynamic gait stability within the Feasible Stability Region framework between people with and without Parkinson's disease during level walking at a self-selected speed. MethodsTwenty adults with Parkinson's disease and twenty age- and gender-matched healthy individuals were recruited. Dynamic gait stability at two gait instants: touchdown and liftoff, was assessed as the primary outcome measurement. Spatiotemporal gait parameters, including stance phase duration, step length, gait speed, and cadence were determined as explanatory variables. FindingsPeople with Parkinson's disease walked more slowly (p < 0.001) with a shorter step (p = 0.05), and prolonged stance phase (p = 0.04) than their healthy peers with moderate to large effect sizes. Dynamic gait stability did not show any group-associated differences (p > 0.36). InterpretationDespite the different gait parameters between groups, people with Parkinson's disease exhibited similar dynamic gait stability to their healthy counterparts. To compensate for the potential dynamic gait stability deficit resulting from slow gait speed, individuals with Parkinson's disease adopted a short step length to shift the center of mass motion state closer to the Feasible Stability Region. Our findings could provide insight into the impact of Parkinson's disease on the control of dynamic gait stability.

A Real-Time Adaptive Station Beamforming Strategy for Next Generation Phased Array Radio Telescopes.

The next generation phased array radio telescopes, such as the Square Kilometre Array (SKA) low frequency aperture array, suffer from RF interference (RFI) because of the large field of view of antenna element. The classical station beamformer used in SKA-low is resource efficient but cannot deal with the unknown sidelobe RFI. A real-time adaptive beamforming strategy is proposed for SKA-low station, which trades the capability of adaptive RFI nulling at an acceptably cost, it doesn't require hardware redesign but only modifies the firmware accordingly. The proposed strategy uses a Parallel Least Mean Square (PLMS) algorithm, which has a computational complexity of 4N+2 and can be performed in parallel. Beam pattern and output SINR simulation results show deeply nulling performance to sidelobe RFI, as well as good mainlobe response similar to the classical beamformer. The convergence performance depends on the signal-and-interference environments and step size, wherein too large a step size leads to a non-optimal output SINR and too small a step size leads to slow convergence speed. FPGA implementation demonstrations are implemented and tested on a NI FPGA module, and test results demonstrate good real-time performance and low slice resource consumption.

Fractional-Order Tabu Learning Neuron Models and Their Dynamics

In this paper, by replacing the exponential memory kernel function of a tabu learning single-neuron model with the power-law memory kernel function, a novel Caputo’s fractional-order tabu learning single-neuron model and a network of two interacting fractional-order tabu learning neurons are constructed firstly. Different from the integer-order tabu learning model, the order of the fractional-order derivative is used to measure the neuron’s memory decay rate and then the stabilities of the models are evaluated by the eigenvalues of the Jacobian matrix at the equilibrium point of the fractional-order models. By choosing the memory decay rate (or the order of the fractional-order derivative) as the bifurcation parameter, it is proved that Hopf bifurcation occurs in the fractional-order tabu learning single-neuron model where the value of bifurcation point in the fractional-order model is smaller than the integer-order model’s. By numerical simulations, it is shown that the fractional-order network with a lower memory decay rate is capable of producing tangent bifurcation as the learning rate increases from 0 to 0.4. When the learning rate is fixed and the memory decay increases, the fractional-order network enters into frequency synchronization firstly and then enters into amplitude synchronization. During the synchronization process, the oscillation frequency of the fractional-order tabu learning two-neuron network increases with an increase in the memory decay rate. This implies that the higher the memory decay rate of neurons, the higher the learning frequency will be.

Projective integration methods in the Runge–Kutta framework and the extension to adaptivity in time

Projective Integration methods are explicit time integration schemes for stiff ODEs with large spectral gaps. In this paper, we show that all existing Projective Integration methods can be written as Runge–Kutta methods with an extended Butcher tableau including many stages. We prove consistency and order conditions of the Projective Integration methods using the Runge–Kutta framework. Spatially adaptive Projective Integration methods are included via partitioned Runge–Kutta methods. New time adaptive Projective Integration schemes are derived via embedded Runge–Kutta methods and step size variation while their accuracy, stability, convergence, and error estimators are investigated analytically and numerically.

Effects of acupuncture combined with trunk strengthening training on balance and gait abilities in stroke hemiplegic patients.

This study aimed to observe the effects of acupuncture combined with trunk strengthening training on balance and gait abilities in stroke hemiplegic patients. Sixty stroke hemiplegic patients were selected and randomly divided into a treatment group and a control group, with 30 patients in each group. The control group received conventional rehabilitation training and trunk strengthening exercises, while the treatment group received acupuncture in addition to the same interventions. Before and after 8 weeks of treatment, patients were assessed using the Holden Functional Ambulation Categories and Berg Balance Scale, and measurements were taken for step length, step width, and gait speed. Prior to treatment, there were no significant differences in Holden scores, Berg scores, step length, step width, or gait speed between the 2 groups (P > .05). After 8 weeks of treatment, significant improvements were observed in the aforementioned parameters in both groups (P < .05), with the acupuncture group showing significantly greater improvement compared to the control group (P < .05). Acupuncture combined with trunk strengthening training can significantly improve balance and gait impairments in stroke hemiplegic patients.

Does a Standardized Load Carriage Increase Spatiotemporal Gait Asymmetries in Police Recruits? A Population-based Study.

Although the effects of carrying loads on gait biomechanics have been well-documented, to date, little evidence has been provided whether such loads may impact spatial and temporal gait asymmetries under the different foot regions. Therefore, the main purpose of the study was to examine the effects of carrying a standardized police equipment on spatiotemporal gait parameters. In this population-based study, participants were 845 first-year police recruits (age: 21.2 ± 2.3 years; height: 178.1 ± 10.2 cm; weight: 78.4 ± 11.3 kg; body mass index: 24.7 ± 3.2 kg/m2; 609 men and 236 women; 72.1% men and 27.9% women) measured in 2 conditions: (i) "no load" and (ii) "a 3.5 kg load." Spatiotemporal gait parameters were derived from the FDM Zebris pressure platform. Asymmetry was calculated as (xright-xleft)/0.5*(xright + xleft)*100%, where "x" represented a given parameter being calculated and a value closer to 0 denoted greater symmetry. When compared to "no load" condition, a standardized 3.5 kg/7.7 lb load significantly increased asymmetries in spatial gait parameters as follows: gait phases of stance (mean diff. = 1.05), load response (mean diff. = 0.31), single limb support (mean diff. = 0.56), pre-swing (mean diff. = 0.22), and swing (mean diff. = 0.90) phase, while no significant asymmetries in foot rotation, step, and stride length were observed. For temporal gait parameters, we observed significant asymmetries in step time (mean diff. = -0.01), while no differences in cadence and gait speed were shown. The findings indicate that the additional load of 3.5 kg/7.7 lb is more likely to increase asymmetries in spatial gait cycle components, opposed to temporal parameters. Thus, external police load may have hazardous effects in increasing overall body asymmetry, which may lead to a higher injury risk and a decreased performance for completing specific everyday tasks.

Multi-Point Seawall Settlement Prediction with Limited Data Volume Using an Improved Fractional-Order Grey Model

Settlement prediction based on monitoring data holds significant importance for engineering maintenance of seawalls. In practical engineering, the volume of the collected monitoring data is often limited due to the restrictions of devices and engineering budgets. Previous studies have applied the fractional-order grey model to time series prediction under the situation of limited data volume. However, the performance of the fractional-order grey model is easily affected by the inappropriate settings of fractional order. Also, the model cannot make dynamic predictions due to the characteristic of fixed step size. To solve the above problems, in this paper, the genetic algorithm with enhanced search capabilities was employed to solve the premature convergence problem. Additionally, to solve the problem of the fractional-order grey model associated with fixed step size, the real-time tracing algorithm was introduced to conduct equal-dimensionally recursive calculation. The proposed model was validated using monitoring data of four monitoring points at Haiyan seawall in Zhejiang province, China. The prediction performance of the proposed model was then compared with those of the fractional-order GM(1,1), integer-order GM(1,1), and fractal theory model. Results indicate that the proposed model significantly improves the prediction performance compared to other models.

The impact of foot orthoses on gait in children with Osteogenesis Imperfecta type I, III and IV – a cross-sectional study

BackgroundFor children with Osteogenesis Imperfecta (OI), a rare genetic bone disease, walking can be difficult to carry out due to a combination of bone fragility and deformity, muscle weakness, joint hypermobility, and pain. Bisphosphonate treatment has facilitated more children being able to walk, but for many, foot and ankle hypermobility is a limiting factor. Current evidence on foot orthoses in children with OI is sparse. This study aimed to evaluate gait characteristics in children with OI walking barefoot as compared to walking with foot orthoses.MethodsTwenty-three children with OI and hypermobility (mean age 8.3 ± 3.0 years) were included in this cross-sectional study. Children conducted three-dimensional gait analysis barefoot, and with foot orthoses and appropriate foot wear (stable yet light-weight), respectively. Walking speed, step length, lower limb kinematics and kinetics were collected. Differences in gait characteristics between test conditions were evaluated using paired sample t-tests.ResultsWhen walking with foot orthoses, the external foot progression angle was reduced, peak ankle dorsiflexion angle increased, and peak plantarflexion moment increased as compared to barefoot. No difference was found in walking speed between test conditions, however, children with OI walked with longer steps with foot orthoses as compared to barefoot.ConclusionThe observed gait alterations suggest that foot orthoses, aiming to support the foot and ankle joint, contributed to reduced overall foot rotation as measured by external foot progression, increased peak plantarflexion moment, and increased step length. In a wider perspective, the ability to walk provides the opportunity to be physically active, and thereby increase skeletal loading and prevent fractures, thus, foot orthoses may be an important treatment option to consider in children with OI.Level of evidenceIII.

The Basics of Evolution Strategies: The Implementation of the Biomimetic Optimization Method in Educational Modules.

With a focus on education and teaching, we provide general background information on bioinspired optimization methods by comparing the concept of optimization and the search for an optimum in engineering and biology. We introduce both the principles of Darwinian evolution and the basic evolutionary optimization procedure of evolution strategies. We provide three educational modules in work sheets that can be used by teachers and students to improve their understanding of evolution strategies. The educational module "Optimization of a Milk Carton" shows that the material consumption in producing a milk carton can be minimized using an evolution strategy with a mutative step size control. The use of a standard dice and a pocket calculator enables new milk cartons to be generated, with the offspring having the lowest material consumption becoming the parent of the next generation. The other educational modules deal with the so-called brachistochrone problem. The module "Fastest and Shortest Marble Track" provides a construction plan for a marble track whereby students can experimentally compare the "path of shortest length" with the "path of shortest time". The EvoBrach software, is used in the module "Various Marble Track Shapes" to compare the running times of a marble on a straight line, a parabola, and a brachistochrone. In conclusion, the introduction to the biomimetic method of evolution strategies and the educational modules should deepen the understanding of both optimization problems and biological evolution.

A Multitask Learning-Based Vision Transformer for Plant Disease Localization and Classification

Plant disease detection is a critical task in agriculture, essential for ensuring crop health and productivity. Traditional methods in this context are often labor-intensive and prone to errors, highlighting the need for automated solutions. While computer vision-based solutions have been successfully deployed in recent years for plant disease identification and localization tasks, these often operate independently, leading to suboptimal performance. It is essential to develop an integrated solution combining these two tasks for improved efficiency and accuracy. This research proposes the innovative Plant Disease Localization and Classification model based on Vision Transformer (PDLC-ViT), which integrates co-scale, co-attention, and cross-attention mechanisms and a ViT, within a Multi-Task Learning (MTL) framework. The model was trained and evaluated on the Plant Village dataset. Key hyperparameters, including learning rate, batch size, dropout ratio, and regularization factor, were optimized through a thorough grid search. Early stopping based on validation loss was employed to prevent overfitting. The PDLC-ViT model demonstrated significant improvements in plant disease localization and classification tasks. The integration of co-scale, co-attention, and cross-attention mechanisms allowed the model to capture multi-scale dependencies and enhance feature learning, leading to superior performance compared to existing models. The PDLC-ViT model evaluated on two public datasets achieved an accuracy of 99.97%, a Mean Average Precision (MAP) of 99.18%, and a Mean Average Recall (MAR) of 99.11%. These results underscore the model's exceptional precision and recall, highlighting its robustness and reliability in detecting and classifying plant diseases. The PDLC-ViT model sets a new benchmark in plant disease detection, offering a reliable and advanced tool for agricultural applications. Its ability to integrate localization and classification tasks within an MTL framework promotes timely and accurate disease management, contributing to sustainable agriculture and food security.

Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

In this work, we introduce a new inertial hybrid algorithm that combines the subgradient extragradient, Halpern, and S-iteration methods. We provide an approximate solution to variational inequality and common fixed point problem of relatively non-expansive mappings in real Banach spaces, where our cost operator is Lipschitz continuous and quasimonotone, and our step size is self-adaptive, non-monotone, and non-reliant on any line-search principle. We provide two strong convergence results with (and without) recourse to the monotonicity property, and further conduct several relevant numerical experiments to reveal the efficiency of our method over others in the literature.

Application of Local Search Particle Swarm Optimization Based on the Beetle Antennae Search Algorithm in Parameter Optimization

Intelligent control algorithms have been extensively utilized for adaptive controller parameter adjustment. While the Particle Swarm Optimization (PSO) algorithm has several issues: slow convergence speed requiring a large number of iterations, a tendency to get trapped in local optima, and difficulty escaping from them. It is also sensitive to the distribution of the solution space, where uneven distribution can lead to inefficient contraction. On the other hand, the Beetle Antennae Search (BAS) algorithm is robust, precise, and has strong global search capabilities. However, its limitation lies in focusing on a single individual. As the number of iterations increases, the step size decays, causing it to get stuck in local extrema and preventing escape. Although setting a fixed or larger initial step size can avoid this, it results in poor stability. The PSO algorithm, which targets a population, can help the BAS algorithm increase diversity and address its deficiencies. Conversely, the characteristics of the BAS algorithm can aid the PSO algorithm in finding the optimal solution early in the optimization process, accelerating convergence. Therefore, considering the combination of BAS and PSO algorithms can leverage their respective advantages and enhance overall algorithm performance. This paper proposes an improved algorithm, W-K-BSO, which integrates the Beetle Antennae Search strategy into the local search phase of PSO. By leveraging chaotic mapping, the algorithm enhances population diversity and accelerates convergence speed. Additionally, the adoption of linearly decreasing inertia weight enhances algorithm performance, while the coordinated control of the contraction factor and inertia weight regulates global and local optimization performance. Furthermore, the influence of beetle antennae position increments on particles is incorporated, along with the establishment of new velocity update rules. Simulation experiments conducted on nine benchmark functions demonstrate that the W-K-BSO algorithm consistently exhibits strong optimization capabilities. It significantly improves the ability to escape local optima, convergence precision, and algorithm stability across various dimensions, with enhancements ranging from 7 to 9 orders of magnitude compared to the BAS algorithm. Application of the W-K-BSO algorithm to PID optimization for the Pointing and Tracking System (PTS) reduced system stabilization time by 28.5%, confirming the algorithm’s superiority and competitiveness.

Laser-induced breakdown spectroscopy as a method for millimeter-scale inspection of surface flatness

A non-contact method for millimeter-scale inspection of material surface flatness via Laser-Induced Breakdown Spectroscopy (LIBS) is investigated experimentally. The experiment is performed using a planished surface of an alloy steel sample to simulate its various flatness, ranging from 0 to 4.4 mm, by adjusting the laser focal plane to the surface distance with a step length of 0.2 mm. It is found that LIBS measurements are successful in inspecting the flatness differences among these simulated cases, implying that the method investigated here is feasible. It is also found that, for achieving the inspection of surface flatness within such a wide range, when univariate analysis is applied, a piecewise calibration model must be constructed. This is due to the complex dependence of plasma formation conditions on the surface flatness, which inevitably complicates the inspection procedure. To solve the problem, a multivariate analysis with the help of Back-Propagation Neural Network (BPNN) algorithms is applied to further construct the calibration model. By detailed analysis of the model performance, we demonstrate that a unified calibration model can be well established based on BPNN algorithms for unambiguous millimeter-scale range inspection of surface flatness with a resolution of about 0.2 mm.

Clustering Methods for the Characterization of Synchrotron Radiation X‐Ray Fluorescence Images of Human Carotid Atherosclerotic Plaque

This study employs computational algorithms to automatically identify and classify features in X‐Ray fluorescence (XRF) microscopy images. Principal component analysis (PCA) and unsupervised machine learning algorithms, such as Gaussian mixture (GM) clustering, are implemented to label features on a collection of XRF maps of human atherosclerotic plaque samples. The investigation involves the hard X‐Ray nanoprobe (NanoMAX) at MAX IV synchrotron radiation facility, utilizing scanning transmission X‐Ray microscopy (STXM) and XRF techniques. The analysis covers regions of interest scanned by the beam with a step size of 200 nm, yielding XRF maps of elements like calcium, iron, and zinc. These maps reveal intricate structures unsuitable for manual labeling. However, they can be accurately classified in an automated fashion using GM. Prior to clustering, PCA is used to deal with repeated patterns and background areas. The resulting clusters are associated with different types of features, which can be identified as specific tissues confirmed by histology. Regions of high concentrations of phosphorus, sulfur, calcium, and iron are found in the samples. These regions are also observed in the STXM results as spots of low transmission that typically are associated with calcium deposits only.