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Article(id=1322506264375046940, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506263716541212, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.10.487, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1729785600000, receivedDateStr=2024-10-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239664404, onlineDateStr=2026-10-29, pubDate=1757865600000, pubDateStr=2025-09-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239664404, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239664404, creator=13701087609, updateTime=1793239664404, updator=13701087609, issue=Issue{id=1322506263716541212, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='9', pageStart='881', pageEnd='990', issueExtLink='null', onlineDate='null', pubDate='1757865600000', pubDateStr='2025-09-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239664248, creator='13701087609', updateTime=1793239664248, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=899, endPage=904, ext={EN=ArticleExt(id=1322506264706396957, articleId=1322506264375046940, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=LS+Informer in Polar Motion Prediction, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to improve the medium and long term prediction accuracy of polar motion, the LS+Informer(least-squares extrapolation and Informer, LS+Informer) prediction model is proposed based on the traditional LS+AR prediction model combined with deep learning method. The mean absolute error(MAE) was used as the evaluation index based on LS+AR forecast model and Bulletin A forecast results. After LS+Informer method is adopted, the medium and long term prediction accuracy of PMX and PMY components of polar motion can be significantly improved, and the amplitude can reach 61.94% and 64.86% respectively. At the same time, the MAE value can be controlled within 10 mas in the medium and long term 365-day phase. The results show that the prediction accuracy of LS+Informer model is better than that of LS+AR model, and better than that of Bulletin A. The results demonstrate that the LS+Informer model can be effectively used in medium and long term polar motion prediction.

, authors=Dandan WANG1, Shubo QIAO1, *, Dongliang CHENG1, Hailong XU2, Yaming YAN1, authorsList=Dandan WANG, Shubo QIAO, Dongliang CHENG, Hailong XU, Yaming YAN, authorCompany=null, correspAuthors=Shubo QIAO, authorNote=

WANG Dandan, majors in spatial geodesy and navigation positioning, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., 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=1322506267587883821, articleId=1322506264375046940, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=LS+Informer用于极移预报的方法研究, columnId=1322506169105633839, journalTitle=大地测量与地球动力学, columnName=现代大地测量, runingTitle=null, highlight=null, articleAbstract=

为提高极移中长期预报精度，在传统LS+AR预报模型的基础上结合深度学习方法，提出LS+Informer(least-squares extrapolation and Informer)预报模型。以LS+AR预报模型和Bulletin A的预报结果为参考，采用平均绝对误差(mean absolute error，MAE)作为评价指标。采用LS+Informer方法后，极移的PMX分量和PMY分量的中长期预报精度得到显著提升，幅度分别可达61.94%和64.86%。同时，在中长期(365 d)阶段可以将MAE值控制在10 mas以内。研究结果显示，在极移的中长期预报中，LS+Informer模型的预报精度明显优于LS+AR模型，且优于Bulletin A的预报结果。该结果表明，LS+Informer模型可有效应用于中长期极移预测。

, authors=王丹丹1, 乔书波1, *, 程栋梁1, 徐海龙2, 闫亚明1, authorsList=王丹丹, 乔书波, 程栋梁, 徐海龙, 闫亚明, authorCompany=null, correspAuthors=乔书波, authorNote=

王丹丹，主要研究方向为空间大地测量与导航定位，E-mail：

, correspAuthorsNote=

乔书波，博士，教授，主要研究方向为空间大地测量与导航定位，E-mail：

QIAO Shubo, PhD, professor, majors in spatial geodesy and navigation positioning, E-mail:

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WANG Dandan, majors in spatial geodesy and navigation positioning, E-mail:

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王丹丹，主要研究方向为空间大地测量与导航定位，E-mail：

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Informer, figureFileSmall=96KyoV/FGjGeRwEBxBamEQ==, figureFileBig=x/FYk+PTHgVtflaoSFb3Ig==, tableContent=null), ArticleFig(id=1322506273401189220, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=CN, label=图7, caption=AR和Informer滚动预测的MAE值, figureFileSmall=96KyoV/FGjGeRwEBxBamEQ==, figureFileBig=x/FYk+PTHgVtflaoSFb3Ig==, tableContent=null), ArticleFig(id=1322506273468298085, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=EN, label=Tab. 1, caption=

Corresponding parameters of LS+AR model

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(LS模型)拟合项 (AR模型)模型阶数
线性趋势项 周年项 X Y
钱德勒项 半周年项 180 180
), ArticleFig(id=1322506273543795559, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=CN, label=表1, caption=

LS+AR模型对应参数

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(LS模型)拟合项 (AR模型)模型阶数
线性趋势项 周年项 X Y
钱德勒项 半周年项 180 180
), ArticleFig(id=1322506273824813928, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=EN, label=Tab. 2, caption=

Average MAE and PAIP values for 200 sets of PMX rolling predictions

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预测时间/d Bulletin A /mas LS+AR /mas LS+ Informer /mas 对比Bulletin A PAIP/% 对比LS+AR PAIP/%
35 6.94 7.46 6.36 9.12 14.74
45 7.68 8.79 7.83 -1.92 10.84
65 8.56 11.35 8.01 6.87 29.38
95 9.68 13.68 7.86 23.16 42.53
135 9.97 15.09 8.34 19.55 44.75
185 9.05 14.58 8.44 7.23 42.12
245 8.47 16.02 8.20 3.29 48.80
295 10.27 18.58 7.74 32.69 58.34
355 12.49 20.59 7.83 59.52 61.94
365 12.48 20.68 7.89 58.18 61.84
), ArticleFig(id=1322506273925477225, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=CN, label=表2, caption=

进行200组滚动预测PMX的平均MAE和PAIP值

, figureFileSmall=null, figureFileBig=null, tableContent=
预测时间/d Bulletin A /mas LS+AR /mas LS+ Informer /mas 对比Bulletin A PAIP/% 对比LS+AR PAIP/%
35 6.94 7.46 6.36 9.12 14.74
45 7.68 8.79 7.83 -1.92 10.84
65 8.56 11.35 8.01 6.87 29.38
95 9.68 13.68 7.86 23.16 42.53
135 9.97 15.09 8.34 19.55 44.75
185 9.05 14.58 8.44 7.23 42.12
245 8.47 16.02 8.20 3.29 48.80
295 10.27 18.58 7.74 32.69 58.34
355 12.49 20.59 7.83 59.52 61.94
365 12.48 20.68 7.89 58.18 61.84
), ArticleFig(id=1322506273996780394, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=EN, label=Tab. 3, caption=

Average MAE and PAIP values for 200 sets of PMY rolling predictions

, figureFileSmall=null, figureFileBig=null, tableContent=
预测时间/d Bulletin A /mas LS+AR /mas LS+ Informer /mas 对比Bulletin A PAIP/% 对比LS+AR PAIP/%
35 6.95 6.87 6.82 1.90 0.73
45 7.11 9.20 7.62 -6.70 17.17
65 7.44 13.88 8.31 -10.47 40.09
95 8.03 19.77 9.53 -15.74 51.81
135 9.73 25.53 9.66 7.25 62.15
185 13.30 27.76 10.04 32.47 63.86
245 15.12 27.41 10.78 40.26 60.67
295 13.83 26.39 10.21 35.46 61.29
355 11.17 24.98 8.78 27.22 64.86
365 11.01 24.39 9.14 20.46 62.51
), ArticleFig(id=1322506274059694955, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506264375046940, language=CN, label=表3, caption=

进行200组滚动预测PMY的平均MAE和PAIP值

, figureFileSmall=null, figureFileBig=null, tableContent=
预测时间/d Bulletin A /mas LS+AR /mas LS+ Informer /mas 对比Bulletin A PAIP/% 对比LS+AR PAIP/%
35 6.95 6.87 6.82 1.90 0.73
45 7.11 9.20 7.62 -6.70 17.17
65 7.44 13.88 8.31 -10.47 40.09
95 8.03 19.77 9.53 -15.74 51.81
135 9.73 25.53 9.66 7.25 62.15
185 13.30 27.76 10.04 32.47 63.86
245 15.12 27.41 10.78 40.26 60.67
295 13.83 26.39 10.21 35.46 61.29
355 11.17 24.98 8.78 27.22 64.86
365 11.01 24.39 9.14 20.46 62.51
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LS+Informer用于极移预报的方法研究
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王丹丹 1 , 乔书波 1, * , 程栋梁 1 , 徐海龙 2 , 闫亚明 1
大地测量与地球动力学 | 现代大地测量 2025,45(9): 899-904
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大地测量与地球动力学 |现代大地测量 2025 , 45 (9) : 899 -904
LS+Informer用于极移预报的方法研究
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王丹丹1 , 乔书波1, * , 程栋梁1, 徐海龙2, 闫亚明1
作者信息
  • 1 信息工程大学地理空间信息学院，郑州市科学大道62号，450001
  • 2 31121部队，南京市，210042
通讯作者:

乔书波，博士，教授，主要研究方向为空间大地测量与导航定位，E-mail：

QIAO Shubo, PhD, professor, majors in spatial geodesy and navigation positioning, E-mail:

作者简介:

王丹丹，主要研究方向为空间大地测量与导航定位，E-mail：

LS+Informer in Polar Motion Prediction
Dandan WANG1 , Shubo QIAO1, * , Dongliang CHENG1, Hailong XU2, Yaming YAN1
Affiliations
  • 1 School of Surveying and Mapping, Information Engineering University, 62 Kexue Road, Zhengzhou 450001, China
  • 2 31121 Troops, Nanjing 210042, China

    • WANG Dandan, majors in spatial geodesy and navigation positioning, E-mail:

出版时间: 2025-09-15 doi: 10.14075/j.jgg.2024.10.487
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摘要
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为提高极移中长期预报精度，在传统LS+AR预报模型的基础上结合深度学习方法，提出LS+Informer(least-squares extrapolation and Informer)预报模型。以LS+AR预报模型和Bulletin A的预报结果为参考，采用平均绝对误差(mean absolute error，MAE)作为评价指标。采用LS+Informer方法后，极移的PMX分量和PMY分量的中长期预报精度得到显著提升，幅度分别可达61.94%和64.86%。同时，在中长期(365 d)阶段可以将MAE值控制在10 mas以内。研究结果显示，在极移的中长期预报中，LS+Informer模型的预报精度明显优于LS+AR模型，且优于Bulletin A的预报结果。该结果表明，LS+Informer模型可有效应用于中长期极移预测。

Transformer模型  /  Informer模型  /  LS+AR模型  /  极移  /  平均绝对误差

In order to improve the medium and long term prediction accuracy of polar motion, the LS+Informer(least-squares extrapolation and Informer, LS+Informer) prediction model is proposed based on the traditional LS+AR prediction model combined with deep learning method. The mean absolute error(MAE) was used as the evaluation index based on LS+AR forecast model and Bulletin A forecast results. After LS+Informer method is adopted, the medium and long term prediction accuracy of PMX and PMY components of polar motion can be significantly improved, and the amplitude can reach 61.94% and 64.86% respectively. At the same time, the MAE value can be controlled within 10 mas in the medium and long term 365-day phase. The results show that the prediction accuracy of LS+Informer model is better than that of LS+AR model, and better than that of Bulletin A. The results demonstrate that the LS+Informer model can be effectively used in medium and long term polar motion prediction.

Transformer model  /  Informer model  /  LS+AR model  /  polar motion  /  MAE
王丹丹, 乔书波, 程栋梁, 徐海龙, 闫亚明. LS+Informer用于极移预报的方法研究. 大地测量与地球动力学, 2025 , 45 (9) : 899 -904 . DOI: 10.14075/j.jgg.2024.10.487
Dandan WANG, Shubo QIAO, Dongliang CHENG, Hailong XU, Yaming YAN. LS+Informer in Polar Motion Prediction[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (9) : 899 -904 . DOI: 10.14075/j.jgg.2024.10.487
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极移(polar motion，PM)预报方法正从单一预报模型向组合预报模型、从线性预报模型向非线性预报模型的方向发展。线性预报模型，如最小二乘(least squares，LS)外推模型，在短期预报中具有一定的实用性[1]，但在长期预报中存在较大的预报误差；而非线性预报模型，如神经网络方法，在中长期预报中取得了较好的结果，但预报效率较低[2]。有学者对最小二乘与自回归组合模型(LS+AR)和最小二乘与人工神经网络组合模型(least squares and artificial neural network, LS+ANN)2种极移预报方法进行了分析对比，结果表明，LS+AR的短期预报精度较高，而LS+ANN的中长期预报精度较高[3-4]。近年来，Transformer模型被视为人工智能的新一代浪潮[5]，因此，本文引入基于Transformer模型的Informer模型进行极移预报。
在各种预报方法中，LS+AR模型对极移的预报精度较高，是应用较为广泛的方法之一。国际地球自转和参考服务局(International Earth Rotation and Reference Systems Service, IERS)快速产品服务中心的A公报目前就是利用LS+AR模型生成极移预报值[6]。因此，本文应用最小二乘方法，分别通过线性的AR模型和非线性的Informer模型对最小二乘极移残差序列进行预报，结果表明，引入Informer模型后，中长期记忆时间预报精度得到显著提升。同时，本文还将有效角动量(effective angular momentum，EAM)、日长变化(length of day，LOD)、世界时与协调世界时之差(universal time1 and coordinated universal time，UT1-UTC)、PMX、PMY分别作为PMX和PMY在Informer模型预测中的影响因子，提出一种基于LS+Informer的多参数输入-单参数输出的联合预报方法，有效提高了极移中长期预报的精度。
1 预报方法
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1.1 LS拟合外推
通常采用LS拟合来分离极移时序中的周期项和随机项。LS模型为[7]：
$f_{x_i}=a+b t+\sum\limits_{i=1}^k A_i \cos \left(2 \pi t / \mathrm{PE}_i+\mathrm{PH}_i\right)$
式中，t为时间变量；k为ERP序列中周期信号个数；PEi、Ai和PHi分别为周期信号的振荡周期、振幅和相位。其中周期项个数k及其振荡周期PEi由频谱分析方法确定，而Ai、PHi、a和b为待求参数。为计算方便，令ci=AisinPHi, di=AicosPHi，通过变换，式(1)可以转化为：
$\begin{gathered}X_t=a+b t+\sum\limits_{i=1}^k c_i \cos \left(2 \pi t / \mathrm{PE}_i\right)+ \\d_i \sin \left(2 \pi / \mathrm{PE}_i\right)\end{gathered}$
式中，未知参数a、b、ci和di可以通过最小二乘法求得。LS模型拟合出周期项(Chandler摆动、周年项、半年项)，剩余序列为含有非线性成分的残差序列(准周期变化成分和其他不规则变化成分)。
1.2 AR模型
AR自回归模型通过线性组合过去的观测值来进行预测。假设平稳的随机时序{Zt，t=1，2，…，N}, 自回归模型描述了当前时刻的随机变量值与前P个随机变量值的线性组合及误差项之间的函数关系。P阶自回归模型的数学表达式为：
$Z_i=\sum\limits_{i=1}^P \varphi_i Z_{t-i}+\xi_t$
式中，ξt为高斯白噪声；φi为自回归模型的系数；P为模型阶数，表示过去参与运算的值的个数，可以选用赤池信息量准则(akaike information criterion, AIC)来确定，其数学表达式为：
$\mathrm{AIC}_P=\ln \sigma_p^2+\frac{2 P}{N}$
式中，σ2P为拟合残差序列的方差；N为输入时序的长度。当AICP的值为最小时，对应的P值为AR模型的最优阶数。表 1为LS+AR模型的各个对应参数[8]，其中LS参数对应于LS+Informer中的LS参数，2个模型的基础序列长度均为10 a。
1.3 Informer模型
Informer模型与传统的Transformer模型相比，引入了ProbSparse自注意力机制，从而在时间复杂度和内存使用上实现了显著优化，能够有效捕捉序列之间的长期依赖关系[9]。
Informer模型结构如图 1所示，由编码器提取输入变量间的依赖关系，解码器生成极移时间序列预测结果。
图 1左侧为编码器，其接收到的长序列输入通过概率稀疏自注意力模块和自注意力蒸馏模块，得到特征表示，获取极移输入变量间的依赖关系。编码器能够捕捉极移长序列输入之间的远程依赖关系，从而提取出相关性较高的数值进行输入。通过注意力蒸馏机制，编码器将单层特征的时间维度减半，从而可处理更长的极移输入序列，提高长序列预测输出的效率[10]，同时拥有更高的预报精度。图 1右侧为解码器及最终输出过程，在Informer模型的极移预测任务中，多头注意力机制负责处理两路输入；编码器输出的长序列特征(包含历史极移数据的时间模式)和解码器输入的预测目标序列(初始设置为占位符“0”)[11-12]。
地球系统应用角动量守恒原理来展示固体地球自转的变化。其中，角动量(包括海洋角动量(oceanic angular momentum, OAM)、大气角动量(atmospheric angular momentum, AAM)、陆地水圈角动量(hydrospheric angular momentum, HAM)以及海平面角动量(sea level angular momentum, SLAM))对极移产生不同程度的影响[13]。UT1-UTC和日长变化也与极移分量的变化密切相关[2]。在极移时间序列预测中，本文采用多参数输入-单参数输出的预测方法，充分利用不同数据源，将LOD、UT1-UTC、EAM、PMX和PMY等数据作为影响因子纳入Informer模型的运算。Shahvandi等[2]指出，结合OAM、HAM和AAM的EAM数值对极移预测精度的提升作用更为显著。因此，本文在使用EAM数据时，综合考虑了AAM、HAM和OAM的数值。Informer输入LOD、UT1-UTC、EAM-X、EAM-Y、PMX、PMY等多个变量作为影响因子，处理过程可以表示为图 2。
2 实验数据处理
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实验分为2个部分：第一部分通过最小二乘方法对极移时间序列进行拟合和外推求出残差项，以及对周期项进行外推；第二部分通过AR和Informer方法对残差值进行输入预测(图 3)。
将最小二乘投入的基础输入序列长度设置为10年期，对2005-01-01—2014-12-31数据进行最小二乘拟合外推处理。处理结果如图 4、图 5所示，图 4为2005-01-01—2014-12-31极移分量X和Y的观测序列、线性模型拟合值序列和残差序列，图 5为2015-01-01—2019-10-24最小二乘拟合值和残差值。
本文输入的数据包括从IERS的官方网站上获取的EOP 14 C04序列、Bulletin A预报值和从德国地球科学研究中心(German Research Centre for Geosciences，GFZ)的官方网站上获取的EAM序列。其中，EOP 14 C04序列中的LOD、UT1-UTC、PMX、PMY数据的时间分辨率是24 h，角动量数据中AAM和OAM序列的时间分辨率是3 h，HAM序列的时间分辨率是12 h。为使角动量数据与ERP序列的时间分辨率统一，预处理得到时间分辨率为24 h的序列，以确保与PMX、PMY有相同的分辨率。需要注意的是，有关研究表明，在预测极移2个分量时[2]，质量项比运动项更重要。在PMX中，质量项比运动项重要约54%；而在PMY中，质量项比运动项重要约37%，故在本文中仅使用了质量项而没有使用运动项。质量项加权处理结果如图 6所示。
本文选用平均绝对误差(mean absolute error, MAE，为预测数据与真实数据之间真实的误差) 和预报精度提升百分比(prediction accuracy improvement percentage, PAIP) 作为模型的性能评价指标：
$\mathrm{MAE}=\frac{\sum\limits_{n=1}^N\left|P_n-\hat{P}_n\right|}{N}$
$\mathrm{PAIP}_{\mathrm{FE}}^i=\frac{\mathrm{MAE}_{\mathrm{F}}^i-\mathrm{MAE}_{\mathrm{E}}^i}{\mathrm{MAE}_{\mathrm{F}}^i} \times 100 \%$
式中，Pn为真实值；$ \hat{P}_n$为预测值；N是预测总数量；MAEiF与MAEiE分别对应LS+AR和LS+Informer方法在第i天的MAE值；PAIPFEi表示在第i天方法E相对于方法F的提升百分比。
3 实验结果
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分别通过AR和Informer方法对LS求得的残差数据进行输入处理，以2005-01-01—2014-12-31十年周期为基础时间序列输入到模型中。预报实验于2015-01-01开始，于2019-10-24结束。采用滚动预报，预测200期，7 d为一个滚动周期，每组实验预报窗口均为1~365 d。每组预报值求出一组1~365 d的MAE值，每组MAE值由图 7表示，可以得到每组滚动预报值。由图可见，从整体来看，无论是极移PMX分量还是极移PMY分量，AR残差处理的影像图中黄色区域(黄色区域越大MAE值越高，精度越低)均多于Informer残差处理的区域，即精度在35 d以后均变得波动较大，预测精度并不稳定；Informer模型则表现良好，全程处于一个较为稳定且精度较高的状态。
Bulletin A、LS+AR和LS+Informer对极移时间序列滚动预测200组的MAE值的平均值以及PAIP值如表 2~3所示。在35~365 d的中长期预测中，LS+Informer模型的预测精度相对稳定，精度提升的PAIP值相较于LS+AR模型在PMX和PMY预测上最优分别可达到61.94%和64.86%，相较于Bulletin A模型也有所提高。据此预测稳定性估计，未来有望进行更长时间序列的预测，预计可达到2 a期、3 a期甚至更高周期，为未来较长时间预测工作提供保障。
4 结语
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针对极移中长期时间序列预测精度过低且不稳定等问题，本文提出一种极移中长期时间序列预测的LS+Informer模型。采用概率稀疏自注意力机制，广泛捕获输入序列的长期依赖信息，采用多参数输入-单参数输出方法对极移中长期时间序列进行预报。预报结果表明, 与LS+AR模型极移预报结果相比，本文方法在35~365 d跨度的中长期预报中精度显著高于LS+AR的预报结果，在长期预报中优于Bulletin A的预报结果，可以将MAE值控制在10 max以内。PMX分量和PMY分量的预报精度改进最高分别可达61.94%和64.86%，验证了LS+Informer方法对极移中长期预报结果改进的有效性。
基金
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  • 国家自然科学基金面上项目(42474043)
文献
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doi: 10.14075/j.jgg.2024.10.487
  • 接收时间：2024-10-25
  • 首发时间：2026-10-29
  • 出版时间：2025-09-15
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  • 收稿日期：2024-10-25
基金
National Natural Science Foundation of China(42474043)
国家自然科学基金面上项目(42474043)
作者信息
    1 信息工程大学地理空间信息学院，郑州市科学大道62号，450001
    2 31121部队，南京市，210042

通讯作者:

乔书波，博士，教授，主要研究方向为空间大地测量与导航定位，E-mail：

QIAO Shubo, PhD, professor, majors in spatial geodesy and navigation positioning, E-mail:

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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