The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not on...The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function . An efficient ‘Combinatorial-Probabilistic Dual-Fusion’ version of the modification of Bernstein’s Polynomial Operator is proposed. The potential of the aforesaid improvement is tried to be brought forth and illustrated through an empirical study, for which the function is assumed to be known in the sense of simulation.展开更多
This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We der...This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .展开更多
[目的]本文旨在解决在自然环境下不同成熟度苹果目标检测精度较低的问题。[方法]提出了一种改进的YOLOv5s模型SODSTR-YOLOv5s(YOLOv5s with small detection layer and omni-dimensional dynamic convolution and swin transformer bloc...[目的]本文旨在解决在自然环境下不同成熟度苹果目标检测精度较低的问题。[方法]提出了一种改进的YOLOv5s模型SODSTR-YOLOv5s(YOLOv5s with small detection layer and omni-dimensional dynamic convolution and swin transformer block),用于不同成熟度苹果检测。首先改进YOLOv5s的多尺度目标检测层,在Prediction中构建检测160×160特征图的检测头,提高小尺寸的不同成熟度苹果的检测精度;其次在Backbone结构中融合Swin Transformer Block,加强同级成熟度的苹果纹理特征融合,弱化纹理特征分布差异带来的消极影响,提高模型泛化能力;最后将Neck结构的Conv模块替换为动态卷积模块ODConv,细化局部特征映射,实现局部苹果细粒度特征的充分提取。基于不同成熟度苹果数据集进行试验,验证改进模型的性能。[结果]改进模型SODSTR-YOLOv5s检测的精确率、召回率、平均精度均值分别为89.1%、95.5%、93.6%,高、中、低成熟度苹果平均精度均值分别为94.1%、93.1%、93.7%,平均检测时间为16 ms,参数量为7.34 M。相比于YOLOv5s模型,改进模型SODSTR-YOLOv5s精确率、召回率、平均精度均值分别提高了3.8%、5.0%、2.9%,参数量和平均检测时间分别增加了0.32 M和5 ms。[结论]改进模型SODSTR-YOLOv5s提升了在自然环境下对不同成熟度苹果的检测能力,能较好地满足实际采摘苹果的检测要求。展开更多
针对煤矿高噪声、低照度、运动模糊与大批量煤矸混杂等复杂工况环境因素导致煤矸识别存在误检、漏检以及检测精度低的问题,提出一种基于CFS-YOLO算法的煤矸智能识别模型。采用ConvNeXt V2(Convolutional Neural Network with NeXt Units...针对煤矿高噪声、低照度、运动模糊与大批量煤矸混杂等复杂工况环境因素导致煤矸识别存在误检、漏检以及检测精度低的问题,提出一种基于CFS-YOLO算法的煤矸智能识别模型。采用ConvNeXt V2(Convolutional Neural Network with NeXt Units Version 2)特征提取模块替换主干网络末端的2个C3(Cross Stage Partial Bottle Neck Mudule)模块,通过将掩码自动编码器(Masked Autoencoders,MAE)和全局响应归一化(Global Response Normalization,GRN)层添加到ConvNeXt架构中,有效缓解特征崩溃问题以及保持特征在网络传递过程中的多样性;采用Focal-EIOU(Focal and Efficient Intersection Over Union)损失函数替换原CIOU(Computer Intersection Over Union)损失函数,通过其Focal-Loss机制和调整样本权重的方式优化边界框回归任务中的样本不平衡问题,提高模型的收敛速度和定位精度;添加无参注意力机制(Simple Attention Mechanism,SimAM)于主干网络每个C3模块的后端,凭借其注意力权重自适应调整策略,提升模型对尺度变化较大或低分辨率煤矸目标关键特征的提取能力。通过消融试验和对比试验验证所提CFS-YOLO模型的有效性与优越性。试验结果表明:CFS-YOLO模型对于煤矸在煤矿高噪声、低照度、运动模糊与大批量煤矸混杂等复杂环境下的检测效果均得到有效提高,模型的平均精度均值达到90.2%,相较于原YOLOv5s模型的平均精度均值提高了3.7%,平均检测速度达到90.09 FPS,可充分满足煤矸实时检测的需求。同时与YOLOv5s、YOLOv7-tiny与YOLOv8n等6种YOLO系列算法相比,CFS-YOLO模型对煤矿复杂环境的适应性最强且综合检测性能最佳,可为煤矸的智能高效分选提供技术支持。展开更多
文摘The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function . An efficient ‘Combinatorial-Probabilistic Dual-Fusion’ version of the modification of Bernstein’s Polynomial Operator is proposed. The potential of the aforesaid improvement is tried to be brought forth and illustrated through an empirical study, for which the function is assumed to be known in the sense of simulation.
文摘This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .
文摘[目的]本文旨在解决在自然环境下不同成熟度苹果目标检测精度较低的问题。[方法]提出了一种改进的YOLOv5s模型SODSTR-YOLOv5s(YOLOv5s with small detection layer and omni-dimensional dynamic convolution and swin transformer block),用于不同成熟度苹果检测。首先改进YOLOv5s的多尺度目标检测层,在Prediction中构建检测160×160特征图的检测头,提高小尺寸的不同成熟度苹果的检测精度;其次在Backbone结构中融合Swin Transformer Block,加强同级成熟度的苹果纹理特征融合,弱化纹理特征分布差异带来的消极影响,提高模型泛化能力;最后将Neck结构的Conv模块替换为动态卷积模块ODConv,细化局部特征映射,实现局部苹果细粒度特征的充分提取。基于不同成熟度苹果数据集进行试验,验证改进模型的性能。[结果]改进模型SODSTR-YOLOv5s检测的精确率、召回率、平均精度均值分别为89.1%、95.5%、93.6%,高、中、低成熟度苹果平均精度均值分别为94.1%、93.1%、93.7%,平均检测时间为16 ms,参数量为7.34 M。相比于YOLOv5s模型,改进模型SODSTR-YOLOv5s精确率、召回率、平均精度均值分别提高了3.8%、5.0%、2.9%,参数量和平均检测时间分别增加了0.32 M和5 ms。[结论]改进模型SODSTR-YOLOv5s提升了在自然环境下对不同成熟度苹果的检测能力,能较好地满足实际采摘苹果的检测要求。
文摘针对煤矿高噪声、低照度、运动模糊与大批量煤矸混杂等复杂工况环境因素导致煤矸识别存在误检、漏检以及检测精度低的问题,提出一种基于CFS-YOLO算法的煤矸智能识别模型。采用ConvNeXt V2(Convolutional Neural Network with NeXt Units Version 2)特征提取模块替换主干网络末端的2个C3(Cross Stage Partial Bottle Neck Mudule)模块,通过将掩码自动编码器(Masked Autoencoders,MAE)和全局响应归一化(Global Response Normalization,GRN)层添加到ConvNeXt架构中,有效缓解特征崩溃问题以及保持特征在网络传递过程中的多样性;采用Focal-EIOU(Focal and Efficient Intersection Over Union)损失函数替换原CIOU(Computer Intersection Over Union)损失函数,通过其Focal-Loss机制和调整样本权重的方式优化边界框回归任务中的样本不平衡问题,提高模型的收敛速度和定位精度;添加无参注意力机制(Simple Attention Mechanism,SimAM)于主干网络每个C3模块的后端,凭借其注意力权重自适应调整策略,提升模型对尺度变化较大或低分辨率煤矸目标关键特征的提取能力。通过消融试验和对比试验验证所提CFS-YOLO模型的有效性与优越性。试验结果表明:CFS-YOLO模型对于煤矸在煤矿高噪声、低照度、运动模糊与大批量煤矸混杂等复杂环境下的检测效果均得到有效提高,模型的平均精度均值达到90.2%,相较于原YOLOv5s模型的平均精度均值提高了3.7%,平均检测速度达到90.09 FPS,可充分满足煤矸实时检测的需求。同时与YOLOv5s、YOLOv7-tiny与YOLOv8n等6种YOLO系列算法相比,CFS-YOLO模型对煤矿复杂环境的适应性最强且综合检测性能最佳,可为煤矸的智能高效分选提供技术支持。
