朱敏 , 许爱强 , 许晴 , 等 . 基于改进多层核超限学习机的模拟电路故障诊断 [J ] . 兵工学报 , 2021 , 42 ( 2 ): 356 - 369 . DOI: 10.3969/j.issn.1000-1093.2021.02.013 http://doi.org/10.3969/j.issn.1000-1093.2021.02.013 为兼顾模拟电路多故障诊断的实用性和诊断精度，基于仿真诊断模型的测试性应用框架，结合深度学习与核方法的优势，提出一种多层单纯形优化核超限学习机（ML-SOKELM）方法。将有效初选后的数据集输入多层核超限学习机逐层提取故障特征并进行诊断；训练过程中，将各层核参数向量视为待优化变量，运用单纯形法对其进行联合优化。实验结果表明：与常见的深度学习方法相比，ML-SOKELM方法对主观经验依赖性更低，在训练时间大大缩短的同时，还能获得与之相当的准确率；与流行的核方法相比，ML-SOKELM方法在不同模糊度阈值下均能获得较高的诊断准确率。

ZHU M , XU A Q , XU Q , et al. Fault diagnosis of analog circuit based on improved multilayer kernel extreme learning machine [J ] . Acta Armamentarii , 2021 , 42 ( 2 ): 356 - 369 . (in Chinese)

郭伟超 , 赵怀山 , 李成 , 等 . 基于小波包能量谱与主成分分析的轴承故障特征增强诊断方法 [J ] . 兵工学报 , 2019 , 40 ( 11 ): 2370 - 2377 . DOI: 10.3969/j.issn.1000-1093.2019.11.022 http://doi.org/10.3969/j.issn.1000-1093.2019.11.022 滚动轴承出现损伤时，采集的振动信号呈非平稳性，采用一般的时域和频域分析方法不能准确提取出振动信号的故障特征。根据小波包多分辨、精细化的分解特性，提出一种基于小波包能量谱与主成分分析（PCA）方法的滚动轴承故障诊断算法。将振动信号进行小波包分解，得到重点频率段信息的能量谱，提取能量谱作为特征向量；利用PCA方法对特征向量降维并减小噪声信号的干扰，获得增强的故障特征；利用层次聚类方法和改进的模糊c均值聚类算法对不同类型的滚动轴承故障进行识别，两种聚类方法都准确地识别出了不同的故障类型。实例验证结果表明，所提方法能够有效地提取振动信号中的有用故障特征，实现轴承故障类型的精确诊断。

GUO W C , ZHAO H S , LI C , et al. Fault feature enhancement method for rolling bearing fault diagnosis based on wavelet packet energy spectrum and principal component analysis [J ] . Acta Armamentarii , 2019 , 40 ( 11 ): 2370 - 2377 . (in Chinese)

王大轶 , 符方舟 , 刘成瑞 , 等 . 控制系统可诊断性的内涵与研究综述 [J ] . 自动化学报 , 2018 , 44 ( 9 ): 1537 - 1553 .

WANG D Y , FU F Z , LIU C R , et al. Connotation and research status of diagnosability of control systems: a review [J ] . Acta Automatica Sinica , 2018 , 44 ( 9 ): 1537 - 1553 . (in Chinese)

李文博 , 王大轶 , 刘成瑞 . 卫星姿态控制系统的故障可诊断性评价研究 [J ] . 空间控制技术与应用 , 2014 , 40 ( 5 ): 8 - 13 .

LI W B , WANG D Y , LIU C R . Evaluating fault diagnosability of satellite attitude control system [J ] . Aerospace Control and Application , 2014 , 40 ( 5 ): 8 - 13 . (in Chinese)

ERIKSSON D , FRISK E , KRYSANDER M . A method for quantitative fault diagnosability analysis of stochastic linear descriptor models [J ] . Automatica , 2013 , 49 ( 6 ): 1591 - 600 . DOI: 10.1016/j.automatica.2013.02.045 http://doi.org/10.1016/j.automatica.2013.02.045 https://linkinghub.elsevier.com/retrieve/pii/S0005109813001349 https://linkinghub.elsevier.com/retrieve/pii/S0005109813001349

LIN L X , WANG Q , HE B W , et al. Evaluation of fault diagnosability for nonlinear uncertain system with multiple faults occuring simutaneously [J ] . Journal of Systems Engineering and Electronics , 2020 , 31 ( 3 ): 634 - 646. DOI: 10.23919/JSEE.5971804 http://doi.org/10.23919/JSEE.5971804 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5971804 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5971804

PENG X F , LIN L X , ZHONG X Y , et al. Methods for fault diagnosability analysis of a calss of affine nonlinear systems [J ] . Mathematical Problems in Engineering , 2015 : 409184 .

ZHAO D , AHN C K , PASZKE W , et al. Fault diagnosability analysis of two-dimensional linear discrete systems [J ] . IEEE Transactions on Automatic Control , 2021 , 66 ( 2 ): 826 - 832 . DOI: 10.1109/TAC.9 http://doi.org/10.1109/TAC.9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9

李文博 , 王大轶 , 刘成瑞 . 一类非线性系统的故障可诊断性量化评价方法 [J ] . 宇航学报 , 2015 , 36 ( 4 ): 455 - 462 .

LI W B , WANG D Y , LIU C R . An approach to fault diagnosability quantitative evaluation for a class of nonlinear systems [J ] . Journal of Astronautics , 2015 , 36 ( 4 ): 455 - 462 . (in Chinese)

李文博 , 王大轶 , 刘成瑞 . 动态系统实际故障可诊断性的量化评价研究 [J ] . 自动化学报 , 2015 , 41 ( 3 ): 497 - 507 .

LI W B , WANG D Y , LIU C R . Quantitative evaluation of actual fault diagnosability for dynamic systems [J ] . Acta Automatica Sinica , 2015 , 41 ( 3 ): 497 - 507 . (in Chinese)

LIU J , HUA Y Z , LI Q D , et al. Fault diagnosability qualitative analysis of spacecraft based on temporal fault signature matrix [C ] // Proceedings of 2016 IEEE Chinese Guidance, Navigation and Control Conference. London, UK:IEEE , 2016 : 1496 - 500 .

MEKKI T , TRIKI S , KAMOUN A . A qualitative approach to single fault isolation in switching systems [C ] //Proceedings of the 14th International Conference on Science and Techniques of Automatic Control & Computer Engineering. London, UK:IEEE , 2013 : 220 - 4 .

LI B C , WANG H G , MU L Y , et al. A configuration design method for a redundant inertial navigation system based on diagnosability analysis [J ] . Measurement Science and Technology , 2020 , 32 ( 2 ): 025111 . DOI: 10.1088/1361-6501/abbdf0 http://doi.org/10.1088/1361-6501/abbdf0 Redundant design can improve the performance of an inertial navigation system, and the configuration is an important factor in determining the accuracy and reliability of the redundant inertial navigation system. As well as the sensor quantity and the reliability of single sensors, the reliability of the redundant inertial navigation system also depends on the capability of the fault diagnosis, which has been neglected in much of the previous research. This paper verifies that configurations designed using the previous method cannot maintain optimal performance in fault diagnosis. To optimize the performance in fault detection and isolation through the configuration design, an evaluation function for fault detectability and isolability is proposed based on Kullback–Leibler divergence. On this basis, the inherent diagnosability analysis method is proposed, and the configuration design method is developed with the analysis results. Simulation experiments prove that the proposed diagnosability analysis method can find the defects in the fault detection and isolation, and the diagnosability can be assessed correctly. Configurations designed using the proposed methodensure the optimal accuracy and reliability of the system, and effectively improve the fault diagnosis ability, too.

FU F Z , WANG D Y , LI W B , et al. Data-driven fault identifiability analysis for discrete-time dynamic systems [J ] . International Journal of Systems Science , 2020 , 51 ( 2 ): 402 - 412 .

DUNIA R , QIN S J . Subspace approach to multidimensional fault identification and reconstruction [J ] . AIChE Journal , 1998 , 44 ( 8 ): 1813 - 1831 . DOI: 10.1002/(ISSN)1547-5905 http://doi.org/10.1002/(ISSN)1547-5905 http://doi.wiley.com/10.1002/%28ISSN%291547-5905 http://doi.wiley.com/10.1002/%28ISSN%291547-5905

YUE H H , QIN S J . Reconstruction-based fault identification using a combined index [J ] . Industrial & Engineering Chemistry Research , 2001 , 40 ( 20 ): 4403 - 4414 . DOI: 10.1021/ie000141+ http://doi.org/10.1021/ie000141+ https://pubs.acs.org/doi/10.1021/ie000141%2B https://pubs.acs.org/doi/10.1021/ie000141%2B

刘文静 , 刘成瑞 , 王南华 , 等 . 定量与定性相结合的动量轮故障可诊断性评价 [J ] . 中国空间科学技术 , 2011 , 31 ( 4 ): 54 - 63 .

LIU W J , LIU C R , WANG N H , et al. Quantitative and qualitative model based fault diagnosability evaluation of momentum wheel [J ] . Chinese Space Science and Technology , 2011 , 31 ( 4 ): 54 - 63 . (in Chinese)

吕琛 , 马剑 , 刘红梅 , 等 . 基于认知计算与几何空间变换的故障诊断与预测 [M ] . 北京 : 国防工业出版社 , 2021 .

LÜ C , MA J , LIU H M , et al. Fault diagnosis and prognostics based on cognitive computing and geometric space transformation [M ] . Beijing : National Defense Industry Press , 2021 . (in Chinese)

化永朝 , 李清东 , 任章 , 等 . 连续系统故障可诊断性评价方法综述 [J ] . 控制与决策 , 2016 , 31 ( 12 ): 2113 - 2121 .

HUA Y Z , LI Q D , REN Z , et al. Overview of fault diagnosability evaluation methods for continuous systems [J ] . Control and Decision , 2016 , 31 ( 12 ): 2113 - 2121 . (in Chinese)

符方舟 , 王大轶 , 李文博 . 复杂动态系统的实际非完全失效故障的可诊断性评估 [J ] . 自动化学报 , 2017 , 43 ( 11 ): 1941 - 1949 .

FU F Z , WANG D Y , LI W B . Quantitative evaluation of actual loe fault diagnosability for dynamic systems [J ] . Acta Automatica Sinica , 2017 , 43 ( 11 ): 1941 - 1949 . (in Chinese)

LIU Q Y , WANG Z D , ZHANG J F , et al. Necessary and sufficient conditions for fault diagnosability of linear open- and closed-loop stochastic systems under sensor and actuator faults [J ] . IEEE Transactions on Automatic Control , 2022 , 67 ( 8 ): 4178 - 4185. DOI: 10.1109/TAC.2021.3108587 http://doi.org/10.1109/TAC.2021.3108587 https://ieeexplore.ieee.org/document/9525215/ https://ieeexplore.ieee.org/document/9525215/

刘文静 , 李文博 , 张秀云 , 等 . 基于图论的深空探测航天器故障可诊断性评价 [J ] . 控制理论与应用 , 2019 , 36 ( 12 ): 2074 - 2084 .

LIU W J , LI W B , ZHANG X Y , et al. Fault diagnosability evaluation of deep space exploration spacecraft based on graph theory [J ] . Control Theory & Applications , 2019 , 36 ( 12 ): 2074 - 2084 . (in Chinese)

李巍华 , 张小丽 , 严如强 . 复杂机电系统智能故障诊断与健康评估 [M ] . 北京 : 国防工业出版社 , 2021 .

LI W H , ZHANG X L , YAN R Q . Intellifent fault diagnosis and health assessment for complex electro-mechanical systems [M ] . Beijing : National Defense Industry Press , 2021 . (in Chinese)

BORZOU A , YOUSEFI R , SADYGOV R G . Another look at matrix correlations [J ] . Bioinformatics , 2019 , 35 ( 22 ): 4748 - 4753 . DOI: 10.1093/bioinformatics/btz281 http://doi.org/10.1093/bioinformatics/btz281 High throughput technologies are widely employed in modern biomedical research. They yield measurements of a large number of biomolecules in a single experiment. The number of experiments usually is much smaller than the number of measurements in each experiment. The simultaneous measurements of biomolecules provide a basis for a comprehensive, systems view for describing relevant biological processes. Often it is necessary to determine correlations between the data matrices under different conditions or pathways. However, the techniques for analyzing the data with a low number of samples for possible correlations within or between conditions are still in development. Earlier developed correlative measures, such as the RV coefficient, use the trace of the product of data matrices as the most relevant characteristic. However, a recent study has shown that the RV coefficient consistently overestimates the correlations in the case of low sample numbers. To correct for this bias, it was suggested to discard the diagonal elements of the outer products of each data matrix. In this work, a principled approach based on the matrix decomposition generates three trace-independent parts for every matrix. These components are unique, and they are used to determine different aspects of correlations between the original datasets.Simulations show that the decomposition results in the removal of high correlation bias and the dependence on the sample number intrinsic to the RV coefficient. We then use the correlations to analyze a real proteomics dataset.The python code can be downloaded from http://dynamic-proteome.utmb.edu/MatrixCorrelations.aspx.Supplementary data are available at Bioinformatics online.© The Author(s) 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

刘成瑞 , 刘文静 , 王南华 , 等 . 基于相关性模型的液浮陀螺可诊断性分析方法 [J ] . 空间控制技术与应用 , 2013 , 39 ( 1 ): 10 - 4 , 22.

LIU C R , LIU W J , WANG N H , et al. Fault diagnosability analysis method based on dependency model for liquid-floated gyros [J ] . Aerospace Control and Application , 2013 , 39 ( 1 ): 10 - 4 , 22. (in Chinese)