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Article(id=1322907626882867620, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322907425740825534, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1721232000000, receivedDateStr=2024-07-18, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793335356684, onlineDateStr=2026-10-30, pubDate=1750780800000, pubDateStr=2025-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793335356684, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793335356684, creator=13701087609, updateTime=1793335356684, updator=13701087609, issue=Issue{id=1322907425740825534, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='6', pageStart='1', pageEnd='300', issueExtLink='null', onlineDate='null', pubDate='1750780800000', pubDateStr='2025-06-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793335308726, creator='13701087609', updateTime=1793335308726, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=272, endPage=279, ext={EN=ArticleExt(id=1322907627075805605, articleId=1322907626882867620, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Study on Separation Method of Magnetite Ore Based on Fuzzy Wavelet Neural Network, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to improve the separation accuracy of magnetite ore with particle size of 20−50 mm and adapt to the change of ore quality, a magnetite ore classification method based on fuzzy wavelet neural network (IGWO-FWNN) was proposed. Firstly, feature extraction was performed on the data set, and the adaptability of the model was enhanced by fuzzification and quantization. Then, the improved grey wolf algorithm was used to optimize the initial parameters of the model, which ensured the efficiency of model training. In the training process, the fuzzy rule parameters were continuously updated by the gradient descent algorithm to optimize the performance of the network model. Experiment results show that compared with the GWO-FWNN model, the accuracy of the optimized network model reaches 0.966 7, the F1 value reaches 0.951 2, and the convergence speed of the model is also improved by 24%. The results have verified the effectiveness of the proposed method on the iden tification and classification of magnetite ore, which provides a new thought for the development of magnetic separation technology.

, authors=Caiyong LING1, Chunrong PAN1, Kai FENG1, 2, Decan ZENG1, authorsList=Caiyong LING, Chunrong PAN, Kai FENG, Decan ZENG, authorCompany=null, correspAuthors=Chunrong PAN, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322907644230509053, articleId=1322907626882867620, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于模糊小波神经网络的磁铁矿石分选方法研究, columnId=1226462297560892399, journalTitle=矿业研究与开发, columnName=选矿与资源综合利用, runingTitle=null, highlight=null, articleAbstract=

为了提高20~50 mm粒度磁铁矿石的分选精度并适应矿石品质的变化，提出了一种基于模糊小波神经网络的磁铁矿石分类方法(IGWO-FWNN)。首先，对数据集进行特征提取，并通过模糊化和量化处理来增强模型的适应性。然后，采用改进的灰狼算法优化模型的初始参数，确保了模型训练的高效性。在训练过程中，通过梯度下降算法不断更新模糊规则参数，以优化网络模型的性能。试验表明，与优化前的GWO-FWNN模型相比，优化后的IGWO-FWNN模型准确率达到0.966 7, F1值提升到0.951 2，同时模型的收敛速度也提高了24%。验证了该方法在磁铁矿石识别分类中的有效性，为磁铁矿石分选技术的发展提供了新的思路。

, authors=凌彩勇1, 潘春荣1, 冯凯1, 2, 曾德灿1, authorsList=凌彩勇, 潘春荣, 冯凯, 曾德灿, authorCompany=null, correspAuthors=潘春荣, authorNote=

凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

, correspAuthorsNote=
潘春荣（1973—），男，广东龙川人，博士，教授，主要从事机电一体化系统、智能制造研究。E-mail:
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凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

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凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

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figureFileSmall=aKuiTbPrftqSlR67Ic09ag==, figureFileBig=RgA7MiaAiBVyOuEY3G6K6A==, tableContent=null), ArticleFig(id=1322907649003627051, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907626882867620, language=EN, label=Fig.6, caption=Confusion matrix, figureFileSmall=y6xYneNTm6+revQVDh0ryQ==, figureFileBig=95LykqxPPeQcou/qCgKDuw==, tableContent=null), ArticleFig(id=1322907649066541612, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907626882867620, language=CN, label=图6, caption=混淆矩阵, figureFileSmall=y6xYneNTm6+revQVDh0ryQ==, figureFileBig=95LykqxPPeQcou/qCgKDuw==, tableContent=null), ArticleFig(id=1322907649137844781, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907626882867620, language=EN, label=Table 1, caption=

Performance comparison of different models

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算法ERMSEMAPEMAA
FNN0.027 51.964 60.013 50.843 3
FWNN0.009 71.021 20.004 40.933 3
GWO-FWNN0.009 31.323 20.005 30.940 0
IGWO-FWNN0.008 60.811 60.004 10.966 7
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不同模型的性能比较

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算法ERMSEMAPEMAA
FNN0.027 51.964 60.013 50.843 3
FWNN0.009 71.021 20.004 40.933 3
GWO-FWNN0.009 31.323 20.005 30.940 0
IGWO-FWNN0.008 60.811 60.004 10.966 7
), ArticleFig(id=1322907649318199855, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322907626882867620, language=EN, label=Table 2, caption=

Evaluation index of each model

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算法PRF1
FNN0.618 00.750 00.660 3
FWNN0.854 80.941 00.894 8
GWO-FWNN0.860 80.945 00.899 8
IGWO-FWNN0.931 80.973 50.951 2
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各模型评估指标

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算法PRF1
FNN0.618 00.750 00.660 3
FWNN0.854 80.941 00.894 8
GWO-FWNN0.860 80.945 00.899 8
IGWO-FWNN0.931 80.973 50.951 2
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基于模糊小波神经网络的磁铁矿石分选方法研究
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凌彩勇 1 , 潘春荣 1 , 冯凯 1, 2 , 曾德灿 1
矿业研究与开发 | 选矿与资源综合利用 2025,45(6): 272-279
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矿业研究与开发 |选矿与资源综合利用 2025 , 45 (6) : 272 -279
基于模糊小波神经网络的磁铁矿石分选方法研究
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凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

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凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

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凌彩勇1 , 潘春荣1 , 冯凯1, 2, 曾德灿1
作者信息
  • 1.江西理工大学 机电工程学院，江西　赣州市　341000
  • 2.赣南科技学院，江西　赣州市　341000
通讯作者:
潘春荣（1973—），男，广东龙川人，博士，教授，主要从事机电一体化系统、智能制造研究。E-mail:
作者简介:

凌彩勇（1999—），男，江西赣州人，硕士研究生，主要从事智能选矿设备制造研究。E-mail:

Study on Separation Method of Magnetite Ore Based on Fuzzy Wavelet Neural Network
Caiyong LING1 , Chunrong PAN1 , Kai FENG1, 2, Decan ZENG1
Affiliations
  • 1.School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, China
  • 2.Gannan University of Science and Technology, Ganzhou, Jiangxi 341000, China
出版时间: 2025-06-25
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摘要
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为了提高20~50 mm粒度磁铁矿石的分选精度并适应矿石品质的变化，提出了一种基于模糊小波神经网络的磁铁矿石分类方法(IGWO-FWNN)。首先，对数据集进行特征提取，并通过模糊化和量化处理来增强模型的适应性。然后，采用改进的灰狼算法优化模型的初始参数，确保了模型训练的高效性。在训练过程中，通过梯度下降算法不断更新模糊规则参数，以优化网络模型的性能。试验表明，与优化前的GWO-FWNN模型相比，优化后的IGWO-FWNN模型准确率达到0.966 7, F1值提升到0.951 2，同时模型的收敛速度也提高了24%。验证了该方法在磁铁矿石识别分类中的有效性，为磁铁矿石分选技术的发展提供了新的思路。

磁铁矿  /  霍尔传感器  /  模糊小波神经网络  /  改进灰狼算法

In order to improve the separation accuracy of magnetite ore with particle size of 20−50 mm and adapt to the change of ore quality, a magnetite ore classification method based on fuzzy wavelet neural network (IGWO-FWNN) was proposed. Firstly, feature extraction was performed on the data set, and the adaptability of the model was enhanced by fuzzification and quantization. Then, the improved grey wolf algorithm was used to optimize the initial parameters of the model, which ensured the efficiency of model training. In the training process, the fuzzy rule parameters were continuously updated by the gradient descent algorithm to optimize the performance of the network model. Experiment results show that compared with the GWO-FWNN model, the accuracy of the optimized network model reaches 0.966 7, the F1 value reaches 0.951 2, and the convergence speed of the model is also improved by 24%. The results have verified the effectiveness of the proposed method on the iden tification and classification of magnetite ore, which provides a new thought for the development of magnetic separation technology.

Magnetite  /  Hall sensor  /  Fuzzy wavelet neural network  /  Improved grey wolf optimizer
凌彩勇, 潘春荣, 冯凯, 曾德灿. 基于模糊小波神经网络的磁铁矿石分选方法研究. 矿业研究与开发, 2025 , 45 (6) : 272 -279 .
Caiyong LING, Chunrong PAN, Kai FENG, Decan ZENG. Study on Separation Method of Magnetite Ore Based on Fuzzy Wavelet Neural Network[J]. Mining Research and Development, 2025 , 45 (6) : 272 -279 .
正文
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0　引言
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铁矿石是钢铁行业的主要原料，对社会经济的发展至关重要。虽然我国拥有丰富的铁矿石资源，储量在全球排名靠前，但是，我国铁矿石的平均品位较低，贫矿占比高，开采和分选的难度较大，导致国内资源供给不足而长期依赖进口。因此，充分利用国内资源，提高铁矿石自给率势在必行，新型选矿设备的研究变得愈发重要[1-3]。柳衡琪等[4]提出了新型磁力预选设备ZCLA磁选机，该设备采用外磁系与内选筒式结构，巧妙地利用了重力、磁力和离心力协同作用，可使各种磁性矿物得到高效预选，并在钒钛磁铁矿上验证了该设备的有效性。程志勇等[5]进行了履带式磁选机磁场特性的优化研究，设计了3种平面磁系结构，并利用COMSOL Multiphysics对3种平面磁系分别进行模型构建、网格划分和仿真计算，最终确定了最佳磁系类型和结构参数。
磁感应式分选机作为一种重要的分选设备，能够通过霍尔传感器检测磁铁矿石的磁场强度判别矿石品质，对矿石进行有效分选，具有广泛的应用前景。然而，受限于单一阈值，传统阈值分割方法无法适应不同类型矿石的磁场强度变化，难以准确区分不同品质的矿石；而且阈值分割方法对弱磁性矿石的分选精度较低，容易出现错选和漏选的情况。机器学习是近年来一个热门的研究方向，广泛应用于各个领域[6-8]。模糊神经网络(Fuzzy Neural Network, FNN)作为机器学习的一个分支，充分利用了模糊逻辑的强大结构表达能力和神经网络的自学习及定量数据处理能力[9-10]，能更好地适应不同类型和性质的矿石以及处理矿石磁场信号中的复杂非线性关系。目前模糊神经网络在电力领域[11-12]、非线性系统领域[13-14]、汽车领域[15-16]、电机控制[17-18]等都具有很大的应用价值。
李烨等[19]利用模糊小波神经网络研究了高功率微波武器在传统舰艇防空体系中的协同防空效果和系统贡献率，并对高功率微波与中近程防空武器的协同作战效能进行了合理评估。SAEID等[20]运用模糊小波神经网络通过气象参数和电厂参数对风电场的输出功率进行预测，使用梯度下降法对所提出的模糊小波神经网络模型的参数进行更新调节，获得更合理的模型并与传统方法比较，预测精度较高。
本文提出了一种基于改进灰狼算法优化模糊小波神经网络（Improve Grey Wolf Optimizer Fuzzy Wavelet Neural Network, IGWO-FWNN)的铁矿石信号分类方法。网络参数初值通常是随机生成的，因而模型收敛速度较慢，为了获得更好的初始参数，采用改进灰狼算法优化网络模型。首先，去除采集磁铁信号中的直流分量，并利用小波变换进行去噪，提取出具有时域信息的特征。然后，将提取的特征模糊化和量化后输入到模糊小波神经网络中进行训练，利用网络的非线性映射能力实现对磁铁矿石信号的有效建模。最后，采用梯度下降法更新模型参数，实现磁铁矿石信号的准确分类。通过对比研究，使用改进灰狼优化的模糊小波神经网络提高了模型对矿石的分类准确率，并利用混淆矩阵和F1得分等指标评估模型的识别效果。
1　磁铁矿石识别分类方法
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1.1　磁铁矿石的磁感应识别原理
磁铁矿石中含有的磁性物质主要是Fe3O4，即磁性四氧化三铁。通过模糊小波神经网络识别矿石通过传感器产生的感应信号特征，判断矿石蕴含磁性矿物的含量，从而实现对矿石的分类。磁铁矿石检测原理如图1所示。
1.2　磁铁矿石信号分类指标
均值、方差和峰值等时域特征可以提供关于信号波形的各种重要信息。
（1）均值：信号波形在时间序列上的平均值，反映信号的整体水平。对于周期性信号，均值可以显示信号的偏移程度。根据经验，将其分为5个等级：小、较小、中等、较大、大，并依次量化为2, 4，6, 8，10。
（2）方差：信号波形在时间序列上的离散程度或波动程度。较大的方差表示信号的波动范围广，而较小的方差表示信号的波动范围窄。根据经验，将其分为5个等级：小、较小、中等、较大、大，依次量化为2, 4，6, 8，10。
（3）峰值：信号波形在时间序列上的最大振幅绝对值，代表了信号的动态范围或振幅变化幅度。根据经验，将其分为5个等级：小、较小、中等、较大、大，依次量化为2, 4，6, 8，10。
2　基于改进灰狼算法的模糊小波神经网络结构
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2.1　模糊小波神经网络原理
由于小波神经网络对输入信息为不确定信息的适应性较差，为了增强网络的自学习能力和快速适应变化，实现对目标矿石的准确分类，将小波神经网络集成在网络模型的后半部分，形成模糊小波神经网络。
模糊小波神经网络的具体结构如图2所示，A11、A21、⋯、A12、Anm是以模糊隶属度为特征的模糊语言集合，m表示模糊IF-THEN规则的数量，R1、R2、⋯、Rm是模糊IF-THEN规则，、⋯、表示模糊层中每个模糊规则占该层总输出的比例，为求和，u表示去模糊化的网络输出。整个网络分为5层。
第一层为输入层，x1、x2、⋯、xn分别为系统的输入特征，n为输入变量的数量。
第二层为隶属度层，由于Gaussian形隶属度函数能有效捕捉和描述数据特征的非线性关系以及适应数据的分布特征，因此，选择Gaussian函数作为隶属度函数，其表达式为：
式中：i=1，⋯,n；y=1，⋯，m；cij、σij分别表示第j个模糊规则下的中心参数和宽度参数。
第三层为模糊规则层，由一系列模糊规则R组成，其输出可以表示为：
式中，表示逻辑“与”操作。
第四层为小波函数层，选用了高斯函数的一阶导数φ(x)=x⋅exp(−0.5x)2作为基础小波函数。此函数在拟合数据时表现出了优异的性能。通过对其进行尺度和位移的变换，该函数被嵌入到第二层的神经元之中，充当激活函数φr。网络的第四层输出结果为。其中，wr是连接隐藏层和输出层的权值，Nw为小波神经元的总数，r=1，⋯，Nw。
第五层为输出层，其作用是将第四层（小波层）输出乘以第三层（模糊规则层）节点输出。第五层的输出值表达式为：
模糊小波神经网络的能量函数为：
式中：uq代表期望的输出；u代表网络的输出；k代表训练次数。通过采用梯度下降法，有效调整网络参数c、σ、t、d、w，实现自主学习，使用参数的最优值为模型预测的参数值，以期得到更好的预测结果。
2.2　动态学习率
为了提高FWNN的收敛速度和泛化能力，建立了一种让学习率动态变化的网络模型。鉴于持续时间及多次迭代，模糊小波神经网络的参数调整公式为：
式中，α为学习率，调整α使模型具有更强的自适应能力。基于误差反馈的原则，随着模型的变化，α随之变化，从而有效地搜索最优解。通过使用S形曲线，确定α在(0, 1)的学习效果。计算方法为：
式中，e为每次输出的误差。
2.3　改进灰狼优化算法
灰狼算法（Grey Wolf Optimizer, GWO）是一种于2014年提出的群体智能优化算法，它通过分析灰狼的社会地位、捕食行为、协同行动以及共同狩猎目标，旨在优化其捕食行为[21-23]。
GWO算法是基于个体适应度值的搜索方法，通过分析种群中每个灰狼个体的适应度值来进行搜寻。因此，选择合适的适应度函数非常关键，这决定了算法的收敛速度和最优解，适应度函数为交叉熵损失函数。使用灰狼优化算法求解模糊小波神经网络模型的最佳初始权重矩阵，以加快收敛速度，减少训练时间；增强模型的稳定性，减少训练中的振荡和不稳定。
在求解实际问题时，灰狼算法的寻优过程较为复杂，线性递减的收敛因子a可能导致搜索过早集中在局部区域，从而错过全局最优解。因此，采用非线性递减方式改进收敛因子a。寻优过程如图3所示。
采用随机初始化种群，包围猎物的数学模型为：
式中：、分别是当前猎物和灰狼的位置向量；为当前个体与被捕食者之间的距离；系数向量、系数向量。其中，、为[0, 1]间的随机变量。追捕猎物的数学模型为：
式中：、、分别为α狼、β狼、γ狼的位置向量；、、分别为当前个体与α狼、β狼、γ狼间的距离。
灰狼个体的位置更新如下：
式中：分别为τ狼向α狼、β狼、γ狼位置移动的方向和步长；决定了τ狼的最终位置。
2.4　基于FWNN的磁铁矿石识别分类方法
基于FWNN的铁矿石分类方法分为以下5个步骤，流程如图4所示。
（1）磁铁矿感应信号采集。利用霍尔传感器采集磁铁矿石的感应信号，将永磁体放置在霍尔传感器下方，实现矿石的磁化并提升信号的显著性。
（2）构建信号数据集。根据铁的百分比含量将20~50 mm范围内的磁铁矿石划分为4个等级：超过50%的为高品位矿石，35%至50%的为中等品位矿石，25%至35%的为低品位矿石，低于25%的为最低品位矿石，即贫矿。
（3）感应信号数据预处理。对采集到的磁感应信号进行预处理，包括信号去噪和归一化处理等。提取信号的峰值、均值及方差作为特征参数，这些参数能有效地反映信号波形的基本特性，为后续的分类提供依据。通过对参数进行量化，构建了模糊小波神经网络模型的训练集和测试集，用于训练模型和测试评估其性能。
（4）FWNN模型建立与训练：使用改进灰狼算法优化的初始权重和随机的初始隶属度等参数，构建FWNN模型。将经过预处理的训练集输入模糊小波神经网络模型中进行训练，在训练过程中，利用梯度下降法调整预先设定的参数值，并在达到设定的迭代次数后停止训练。然后在测试集中测试训练出的模型性能，并保存性能最优的模型参数。
（5）磁铁矿的识别分类：使用性能最佳的模型，对经过量化和归一化的未知磁铁矿石指标数据进行识别与分类。
3　试验分析
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3.1　构建试验数据集
为验证本研究所提出的矿石分类技术的实际应用能力，开展了一系列针对磁铁矿石磁场特性的信号采集和分类试验。试验所依托的信号采集系统由工业计算机、传输装置、霍尔效应传感器、永磁铁以及数据采集装置等关键部件组成。该系统能够对不同铁含量等级的磁铁矿石进行磁感应信号的采集与分析。
在试验操作过程中，选用了灵敏度高达30 mV/GS的霍尔效应传感器来捕捉磁铁矿石的磁场变化。数据采集装置的采样频率设定为1 000 Hz，确保了信号采集的高分辨率。每块矿石的信号采集时间设定为5 s，使每个样本均采集到5 000个数据点，充分覆盖了信号的时域特征。此外，传输带的运行速度被精确调控在0.5 m/s, 以保证矿石在传感器下稳定通过，实现信号的准确采集。
通过上述试验设计，旨在全面评估所提出的矿石分类方法在实际磁场信号处理中的性能表现，确保分类结果的准确性和可靠性。
3.2　磁铁矿石识别分类试验设计
模糊小波神经网络的设计架构依据输入输出数据的特征维度来定制。该网络的首层配备了3个输入单元，分别对应均值、方差与峰值的隶属函数值，构成了网络的初始感知能力。随后，第二层扩展为3×5个节点，用于深化特征的处理。继续深入，第三层与第四层各配备了5个处理单元，以增强网络的非线性表达能力。最终，第五层负责输出预测的分类结果。整个训练周期在预设的迭代轮数内完成后终止。
模型的构建与测试工作是在MATLAB R2018b版本环境下利用 MATLAB语言完成的。在数据分配上，遵循了7∶2∶1的划分比例，分别用于训练、测试和验证模型的性能。训练阶段的迭代轮数设定为100 次，同时，网络的初始学习率被调整为0.08，以期在训练初期获得较快的收敛速度，并在训练过程中逐步精细化调整。通过上述配置，旨在实现模型参数的有效优化，确保网络在处理模糊小波数据时的准确性和鲁棒性。
准确率、精确率、召回率和F1得分是评估分类模型性能的4个关键指标，尤其是在处理多分类问题时，这些指标可以体现模型在预测时的表现情况。准确率（Accuracy, A）、精确率（Precision, P）、召回率(Recall, R）、F1值。
式中：TP表示真阳性；TN是真阴性；FP表示假阳性；FN表示假阴性。
为了进一步证明IGWO-FWNN在矿石分类预测上的优越性，将其与使用相同训练和测试数据集的其他未改进方法（FNN、FWNN和GWO-FWNN)进行比较。本文采用了4种评价指标：平均绝对误差（MAE, EMA）、平均绝对百分比误差(MAPE, EMAP)、均方根误差（RMSE, ERMS）和准确率(A)。EMA、EMAP和ERMS的值越小，说明对应模型与实际之间的差别越小，A的值越高意味着预测的准确性越好。
式中：yi为实际值；ŷi为模型预测值。
3.3　磁铁矿石识别分类试验结果分析
为了验证改进灰狼算法的有效性，设计了对比试验，比较了不同模型的性能，包括(FNN、FWNN、GWO-FWNN)，试验结果如图5所示。由图5可知，IGWO-FWNN模型在第19次迭代时达到收敛，GWO-FWNN模型在第25次迭代时达到收敛。由此可得，改进灰狼算法优化的网络模型收敛速度提升了约24%，改进算法优化的网络模型在系统稳定性和收敛速度上都更具优势。模型性能比较结果见表1。结合表1可知，IGWO-FWNN模型对于所有的性能指标都是最优的，分类的准确率为0.966 7。因此，本文提出的基于IGWO-FWNN的铁矿石信号分类方法在预测分类上效果更佳。
通过混淆矩阵（见图6），可以准确比较模型的预测结果和实际情况，矩阵中的行代表矿石的实际类别，而列则代表模型的预测类别，其中类别1、类别2、类别3、类别4分别对应贫矿、低品矿、中品矿和高品矿。通过分析图6中的混淆矩阵，可以看出，在试验测试中，本文所提出的磁铁矿石识别方法和分类方法显示出对弱磁性矿石具有较高的分类准确性。
针对磁铁矿石分选问题，本文更注重降低假阴性率，以提高铁的产量。因此选择F1分数作为衡量模型的指标，由表2可知，本文所提出的模型的综合评价指标F1值最高，为0.951 2，相比GWO-FWNN模型，提升了0.056 4。
4　结论
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本文提出了一种基于改进灰狼算法优化模糊小波神经网络的磁铁信号分选方法，并在实际应用中取得了良好效果。
（1）提出了一种改进灰狼算法优化的模糊小波神经网络的磁铁矿石识别分类方法，用于解决粒度为20~50 mm的磁铁矿石分选问题。该模型能够模糊化识别磁感应信号特征，从而实现磁铁矿石分类。
（2）将该磁铁矿石识别分类模型与其他模型进行了对比，通过收敛速度和平均绝对误差等评价指标验证了改进灰狼算法优化的模糊小波神经网络模型的有效性。通过混淆矩阵及精确率等指标分析，该模型的整体识别准确率为0.966 7，综合评价指标F1值为0.951 2，验证了其识别分类的准确性。
本研究为矿石分选技术的发展提供了新的思路和方法，未来将进一步优化模型结构，以提高模型的自适应性。
基金
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  • 江西省研究生创新专项项目(YC2021-S577)
文献
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  • 接收时间：2024-07-18
  • 首发时间：2026-10-30
  • 出版时间：2025-06-25
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  • 收稿日期：2024-07-18
基金
江西省研究生创新专项项目(YC2021-S577)
作者信息
    1.江西理工大学 机电工程学院，江西　赣州市　341000
    2.赣南科技学院，江西　赣州市　341000

通讯作者:

潘春荣（1973—），男，广东龙川人，博士，教授，主要从事机电一体化系统、智能制造研究。E-mail:
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