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Article(id=1243304969835753980, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.02.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1723996800000, receivedDateStr=2024-08-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774356604298, onlineDateStr=2026-03-24, pubDate=1739980800000, pubDateStr=2025-02-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774356604298, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774356604298, creator=13701087609, updateTime=1774356604298, updator=13701087609, issue=Issue{id=1243304968753623545, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='2', pageStart='171', pageEnd='335', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1774356604040, creator=13701087609, updateTime=1774356967523, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243306493370544137, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243306493370544138, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243304968753623545, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=288, endPage=299, ext={EN=ArticleExt(id=1243304970053857791, articleId=1243304969835753980, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Vibration control of pump duct based on macro fiber composite, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

The pump-jet thrusters produce structural noise during operation.The pump-jet propulsors made of conventional materials often have heavy structure weights. And in this case it is difficult to balance the stern weight. The use of composite materials in the pump-jet propulsor structure can not only greatly reduce the overall weight, but also have good corrosion resistance and fatigue resistance. Focusing on the vibration control problem of composite duct structure of pump-jet propulsors, this paper presents the research on experimental modeling, algorithm optimization design, hardware platform construction and test for MFC-based structural vibration active control system construction and verification based on macro fiber composite (MFC). The genetic algorithm was applied to the optimization design of linear quadratic Gaussian (LQG) controller, and the control effects of the algorithm before and after optimization were compared by experiments. A model identification platform and an active control test platform were built for the composite duct. The control model was obtained by experimental modeling method and the active vibration control test under harmonic excitation was carried out in the air environment. The research attempts to push MFC-based active vibration control method to application scenarios.

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泵喷推进器在工作过程中会产生结构噪声。常规材料加工的泵喷推进器往往结构重量大，难以进行尾部配重。而使用复合材料的泵喷推进器结构不仅可以大幅降低整体重量，还具备良好的耐腐蚀性与抗疲劳能力。本文围绕泵喷推进器复合材料导管结构振动控制问题，开展基于宏纤维复合材料（Macro Fiber Composite，MFC）的结构振动主动控制系统构建及验证的相关试验建模、算法优化设计、硬件平台搭建与试验等研究。将遗传算法应用于线性二次高斯（LQG）控制器优化设计中，通过试验对优化前后的算法控制效果进行对比。针对复合材料导管搭建模型辨识平台与主动控制试验平台，通过实验建模的方法获得控制模型并在空气环境中进行了谐波激励下的振动主动控制试验，尝试将基于MFC的振动主动控制推向应用场景。

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通讯作者，E-mail：。
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乌德木（1998-），男，硕士研究生，通讯作者，E-mail：。

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乌德木（1998-），男，硕士研究生，通讯作者，E-mail：。

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乌德木（1998-），男，硕士研究生，通讯作者，E-mail：。

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tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, orderNo=1, keyword=宏纤维复合压电材料), Keyword(id=1243304983244944278, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, orderNo=2, keyword=泵喷推进器), Keyword(id=1243304983333024663, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, orderNo=3, keyword=振动控制), Keyword(id=1243304983450465179, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, orderNo=4, keyword=LQG最优控制), Keyword(id=1243304983572100001, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, orderNo=5, keyword=遗传算法)], refs=[Reference(id=1243304989309907007, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, doi=null, pmid=null, pmcid=null, year=2023, volume=null, issue=null, 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(in Chinese), articleTitle=Research on vibration control of low stiffness thin plate based on macrofiber composite, refAbstract=null), Reference(id=1243304991985872988, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, doi=null, pmid=null, pmcid=null, year=2023, volume=43, issue=4, pageStart=1, pageEnd=6, url=null, language=null, rfNumber=[10], rfOrder=13, authorNames=李志欣, 郑智伟, 黄修长, journalName=噪声与振动控制, refType=null, unstructuredReference=李志欣，郑智伟，黄修长. 泵喷推进器压电复合材料导管及定子结构的振动控制[J]. 噪声与振动控制，2023, 43(4):1-6., articleTitle=泵喷推进器压电复合材料导管及定子结构的振动控制, refAbstract=null), Reference(id=1243304992124285023, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, doi=null, pmid=null, pmcid=null, year=2023, volume=43, issue=4, pageStart=1, pageEnd=6, url=null, language=null, rfNumber=[10], rfOrder=14, authorNames=Li Z X, Zheng Z W, Huang X Z, journalName=Noise and Vibration Control, refType=null, unstructuredReference=Li Z X, Zheng Z W, Huang X Z. Vibration control of piezoelectric composite conduit and stator structure of pump-jet thruster[J]. Noise and Vibration Control, 2023, 43(4): 1-6. (in Chinese), articleTitle=Vibration control of piezoelectric composite conduit and stator structure of pump-jet thruster, refAbstract=null), Reference(id=1243304992199782496, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, doi=null, pmid=null, pmcid=null, year=2006, volume=84, issue=22, pageStart=1402, pageEnd=1414, url=null, language=null, rfNumber=[11], rfOrder=15, authorNames=Vasques C M A, Dias Rodrigues J, journalName=Computers & Structures, refType=null, unstructuredReference=Vasques C M A, Dias Rodrigues J. Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies[J]. Computers & Structures, 2006, 84(22): 1402-1414., articleTitle=Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies, refAbstract=null), Reference(id=1243304992308834402, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, doi=null, pmid=null, pmcid=null, year=2015, volume=62, issue=1, pageStart=484, pageEnd=493, url=null, language=null, rfNumber=[12], rfOrder=16, authorNames=Ufnalski B, Kaszewski A, Grzesiak L M, journalName=IEEE Transactions on Industrial Electronics, refType=null, unstructuredReference=Ufnalski B, Kaszewski A, Grzesiak L M. Particle swarm optimization of the multioscillatory LQR for a three-phase four-wire voltage-source inverter with an LC output filter[J]. 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Optimal analysis of the weighted matrices in LQR based on the differential evolution algorithm [C]//2017 29th Chinese Control and Decision Conference（CCDC），2017:832-836., articleTitle=Optimal analysis of the weighted matrices in LQR based on the differential evolution algorithm, refAbstract=null)], funds=[Fund(id=1243304989167300664, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, awardId=JCKY2023207CI02, language=CN, fundingSource=船舶振动噪声重点实验室基金项目(JCKY2023207CI02), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1243304980120187711, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, xref=null, ext=[AuthorCompanyExt(id=1243304980124382016, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, companyId=1243304980120187711, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=China Ship 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label=图13, caption=20 Hz和30 Hz复合波激励下观测点响应, figureFileSmall=sN3ZTvLQvqEJARH0fPR+Ag==, figureFileBig=PiWgDWbBqoXF5oEpW/39NQ==, tableContent=null), ArticleFig(id=1243304987867066382, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Fig.14, caption=Response of the observed points under 20 Hz and 40 Hz compound wave excitation, figureFileSmall=b+7W9ZFCf1PKgT4DQwLNKw==, figureFileBig=AqyBHi0LI0DJQNXMd57+bg==, tableContent=null), ArticleFig(id=1243304987938369553, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=图14, caption=20 Hz和40 Hz复合波激励下观测点响应, figureFileSmall=b+7W9ZFCf1PKgT4DQwLNKw==, figureFileBig=AqyBHi0LI0DJQNXMd57+bg==, tableContent=null), ArticleFig(id=1243304988034838548, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.1, caption=

Structural specifications of composite duct model

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序号部件名称材料尺寸/mm数量
1导管框架Q355BΦ11231
2导管上侧内蒙皮碳纤维t=81
3导管上侧外蒙皮碳纤维t=88
4导管下侧内蒙皮碳纤维t=81
5导管下侧外蒙皮碳纤维t=88
), ArticleFig(id=1243304988127113240, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表1, caption=

复合材料导管模型结构规格

, figureFileSmall=null, figureFileBig=null, tableContent=
序号部件名称材料尺寸/mm数量
1导管框架Q355BΦ11231
2导管上侧内蒙皮碳纤维t=81
3导管上侧外蒙皮碳纤维t=88
4导管下侧内蒙皮碳纤维t=81
5导管下侧外蒙皮碳纤维t=88
), ArticleFig(id=1243304988210999323, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.2, caption=

Material properties of composite duct model

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序号材料密度/（kg·m-3）杨氏模量/GPa泊松比
1碳纤维18002800.3
2Q355B78502060.3
), ArticleFig(id=1243304988311662621, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表2, caption=

复合材料导管模型材料属性

, figureFileSmall=null, figureFileBig=null, tableContent=
序号材料密度/（kg·m-3）杨氏模量/GPa泊松比
1碳纤维18002800.3
2Q355B78502060.3
), ArticleFig(id=1243304988403937312, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.3, caption=

Genetic algorithm parameter setting

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个体数目最大遗传代数代沟交叉概率变异概率
401000.950.70.01
), ArticleFig(id=1243304988492017698, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表3, caption=

遗传算法参数设置

, figureFileSmall=null, figureFileBig=null, tableContent=
个体数目最大遗传代数代沟交叉概率变异概率
401000.950.70.01
), ArticleFig(id=1243304988601069607, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.4, caption=

Parameter setting for model identification

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状态空间阶数信号采样速率激励信号类型激励信号频段输出信号类型
651.200 kS/s白噪声0~10 000 Hz加速度
), ArticleFig(id=1243304988663984169, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表4, caption=

模型辨识参数设置

, figureFileSmall=null, figureFileBig=null, tableContent=
状态空间阶数信号采样速率激励信号类型激励信号频段输出信号类型
651.200 kS/s白噪声0~10 000 Hz加速度
), ArticleFig(id=1243304988739481644, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.5, caption=

Parameter setting of vibration active control test

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模型阶数采样周期信号放大倍率输出信号类型
60.004 s200位移
), ArticleFig(id=1243304988840144943, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表5, caption=

振动主动控制试验参数设置

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模型阶数采样周期信号放大倍率输出信号类型
60.004 s200位移
), ArticleFig(id=1243304988945002548, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=EN, label=Tab.6, caption=

Effect of active vibration control of composite duct model

, figureFileSmall=null, figureFileBig=null, tableContent=
激励信号未控制时振幅/mm优化前控制时振幅/mm优化后控制时振幅/mm优化前控制率（%）优化后控制率（%）
20 Hz单频0.00590.00280.002352.8060.60
40 Hz单频0.01110.00540.004351.4361.65
20 Hz+30 Hz双频0.01340.00730.006345.8852.97
20 Hz+40 Hz双频0.01120.00730.006435.1843.00
), ArticleFig(id=1243304989037277238, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1243304969835753980, language=CN, label=表6, caption=

复合材料导管模型振动主动控制效果

, figureFileSmall=null, figureFileBig=null, tableContent=
激励信号未控制时振幅/mm优化前控制时振幅/mm优化后控制时振幅/mm优化前控制率（%）优化后控制率（%）
20 Hz单频0.00590.00280.002352.8060.60
40 Hz单频0.01110.00540.004351.4361.65
20 Hz+30 Hz双频0.01340.00730.006345.8852.97
20 Hz+40 Hz双频0.01120.00730.006435.1843.00
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基于宏纤维复合材料的泵喷导管振动控制研究
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乌德木 , 严斌 , 吴文伟
船舶力学 | 流体与结构声学 2025,29(2): 288-299
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船舶力学 | 流体与结构声学 2025, 29(2): 288-299
基于宏纤维复合材料的泵喷导管振动控制研究
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乌德木 , 严斌, 吴文伟
作者信息
  • 中国船舶科学研究中心，江苏　无锡　214082

    • 乌德木（1998-），男，硕士研究生，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：。
Vibration control of pump duct based on macro fiber composite
De-mu WU , Bin YAN, Wen-wei WU
Affiliations
  • China Ship Scientific Research Center, Wuxi 214082, China
出版时间: 2025-02-20 doi: 10.3969/j.issn.1007-7294.2025.02.012
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摘要
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泵喷推进器在工作过程中会产生结构噪声。常规材料加工的泵喷推进器往往结构重量大，难以进行尾部配重。而使用复合材料的泵喷推进器结构不仅可以大幅降低整体重量，还具备良好的耐腐蚀性与抗疲劳能力。本文围绕泵喷推进器复合材料导管结构振动控制问题，开展基于宏纤维复合材料（Macro Fiber Composite，MFC）的结构振动主动控制系统构建及验证的相关试验建模、算法优化设计、硬件平台搭建与试验等研究。将遗传算法应用于线性二次高斯（LQG）控制器优化设计中，通过试验对优化前后的算法控制效果进行对比。针对复合材料导管搭建模型辨识平台与主动控制试验平台，通过实验建模的方法获得控制模型并在空气环境中进行了谐波激励下的振动主动控制试验，尝试将基于MFC的振动主动控制推向应用场景。

宏纤维复合压电材料  /  泵喷推进器  /  振动控制  /  LQG最优控制  /  遗传算法

The pump-jet thrusters produce structural noise during operation.The pump-jet propulsors made of conventional materials often have heavy structure weights. And in this case it is difficult to balance the stern weight. The use of composite materials in the pump-jet propulsor structure can not only greatly reduce the overall weight, but also have good corrosion resistance and fatigue resistance. Focusing on the vibration control problem of composite duct structure of pump-jet propulsors, this paper presents the research on experimental modeling, algorithm optimization design, hardware platform construction and test for MFC-based structural vibration active control system construction and verification based on macro fiber composite (MFC). The genetic algorithm was applied to the optimization design of linear quadratic Gaussian (LQG) controller, and the control effects of the algorithm before and after optimization were compared by experiments. A model identification platform and an active control test platform were built for the composite duct. The control model was obtained by experimental modeling method and the active vibration control test under harmonic excitation was carried out in the air environment. The research attempts to push MFC-based active vibration control method to application scenarios.

macro fiber composite (MFC)  /  pump-jet thruster  /  vibration control  /  linear quadratic Gaussian (LQG)  /  genetic algorithm (GA)
乌德木, 严斌, 吴文伟. 基于宏纤维复合材料的泵喷导管振动控制研究. 船舶力学, 2025 , 29 (2) : 288 -299 . DOI: 10.3969/j.issn.1007-7294.2025.02.012
De-mu WU, Bin YAN, Wen-wei WU. Vibration control of pump duct based on macro fiber composite[J]. Journal of Ship Mechanics, 2025 , 29 (2) : 288 -299 . DOI: 10.3969/j.issn.1007-7294.2025.02.012
正文
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0　引言
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振动是日常生产和生活中难以避免的现象。通常情况下，结构振动会影响设备的正常工作，降低设备元件的使用寿命，甚至危害使用人员的生命安全。对于高精密装备而言，运行环境需要进行更为严格的减振降噪工作。推进装置是船舶上不容忽视的主要噪声源之一，针对船舶推进装置的减振降噪研究逐渐受到人们重视。
如今，工程应用中出现较多的船舶推进器为泵类推进器和螺旋桨推进器。泵类推进器包括喷水推进器和泵喷推进器等[1]。其中，喷水推进器设计过程中更需要优先考虑推进器的工作效率、快速性能和推力大小；而泵喷推进器主要考虑工作过程中的声隐身性能[2]。作为一种性能优秀的推进装置，泵喷推进器不仅可以作为传统水面船舶的推进器，还可以用于许多水下航行体，例如自主水下潜航器（AUV）、无人水下潜航器（UUV）和潜艇等[3-4]。常规材料加工的泵喷推进器往往结构重量大，难以进行尾部配重[5]。使用复合材料的泵喷推进器结构不仅可以大幅降低整体重量，还具备良好的耐腐蚀性与抗疲劳能力。因此，研究复合材料泵喷推进器导管的振动控制具有重要意义。
复合材料具有质量轻、强度大等特点，将复合材料应用于泵喷推进器结构的设计与优化时，既可以减轻整体重量，又能够提升结构的减振降噪能力。Bammidi等[6]于2018年将铝合金材料的螺旋桨替换为玻璃纤维增强复合材料桨，通过动力学和静力学分析比较了两种结构的性能，其中复合材料螺旋桨的叶片刚度更大、工作频带更宽、最高转速更大，最终证明使用复合材料可以在不牺牲结构机械性能的情况下显著降低重量。An等[7]于2020年利用双向流固耦合方法分析了碳纤维增强塑料复合材料制成的导管螺旋桨，分析了导管螺旋桨的叶尖间隙对其性能的影响，同时证明了复合材料可以提升转子的机械性能。
压电驱动器具有分辨率高、体积小、速度快、带宽高等特点[8]，为振动主动控制提供了新思路，将压电材料应用到振动控制领域时，其振动幅度与输出能力同样非常可观[9]。此外，性能强大的主动控制器不仅需要传感器、作动器与被控结构互动，还依赖有效的对象模型与控制算法。压电结构的动力学建模是指建立传感器、压电作动器和被控结构的机电耦合模型。常见的压电结构建模主要包括理论建模和实验建模两种方法，其中理论建模是指利用力学原理和数学方法推导出动力学方程，而实验建模则是指通过实验数据的分析处理和系统辨识方法进行数学模型的建立。本文将采用系统辨识的方法建立复合材料导管控制模型。
李志欣等[10]于2023年围绕泵喷推进器导管-定子结构减振降噪问题，将压电复合材料导管-定子结构作为研究对象，利用压电分流被动控制方法以及压电自适应主动控制方法对泵喷推进器结构进行了振动控制。现有研究主要集中于对泵喷推进器的设计与动力学特性分析，针对泵喷推进器结构振动控制的研究较少。本文以泵喷推进器导管结构作为振动控制模型，利用宏纤维压电复合材料（MFC）对复合材料导管在空气环境中进行谐波激励下的振动主动控制试验，为泵喷推进器导管结构的减振降噪研究提供参考。
线性二次最优控制（LQR）以控制输入和性能输出的加权二次型为优化指标，兼顾了控制能量和系统状态能量指标，而线性二次高斯控制（LQG）在LQR的基础上考虑了过程噪声和测量噪声对结构动力学特性的影响，可以对系统的状态空间和控制输出做出精确的估计，提升了算法的实用性。Vasques等[11]于2006年利用智能压电梁模型对LQR控制器和LQG控制器进行了分析与比较，利用代价函数对控制系统进行了量化；Ufnalski等[12]于2015年利用粒子群算法对LQR的权重矩阵进行了优化，并利用实验证明了该方案的实用性；Deng等[13]于2017年采用差分进化算法（DEA）对LQR的加权矩阵进行了优化，并利用仿真对结果进行了分析，证明了加权矩阵优化的合理性与有效性。因此，利用最优化控制算法进行压电结构的振动主动控制具有可行性，且对其加权矩阵的优化改进具有必要性。
本文围绕泵喷推进器复合材料导管结构振动控制问题，将遗传算法应用于LQG控制器优化设计，通过试验对优化前后的算法控制效果进行对比。采用实验建模的方式建立复合材料导管结构的控制模型，搭建泵喷导管振动主动控制试验系统，对空气环境中的复合材料导管进行谐波激励下的振动主动控制试验。
1　研究对象
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本文选用的复合材料导管模型由定子、转子和导管组件共同组成，其中导管组件由导管框架、2块内蒙皮和16块外蒙皮组成。复合材料导管模型的规格尺寸如表1所示，实物如图1所示。
复合材料导管模型主要由碳纤维和Q355B两种材料组成，总重467.67 kg，材料属性如表2所示。其中，碳纤维构成的蒙皮具有高强度、轻质、耐腐蚀性和耐高温性等优点；构成框架的Q355B是一种低合金高强度结构钢，广泛应用于桥梁、车辆、船舶等工业场景中。复合材料导管模型直立放置，由定子与地面接触，对本文主要研究的导管蒙皮而言，该试验边界条件接近实际应用中的边界条件。
如图2所示，将复合材料导管模型外蒙皮拆下后，在内蒙皮上选定的最优区域处使用双组份环氧树脂胶粘剂粘贴MFC片，用相同方法每隔90°粘贴一片，共粘贴4处。其中一组对位粘贴的MFC作为激励作动器，另一组对位粘贴的MFC作为控制作动器。加速度传感器选定为内蒙皮振型波峰分布区域的任一位置。
完成MFC粘贴后，将外蒙皮以同样的方式进行安装，安装完成的模型如图3所示。MFC作为薄型作动器在布置前后既不会影响壳体的正常安装，也不会影响模型的整体力学性能，大大降低了模型的设计难度且减少了性能分析的工作步骤。
2　基于遗传算法的LQG控制器设计
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为了建立导管振动主动控制试验系统，本文设计了基于遗传算法的线性二次高斯型（LQG）最优控制器。LQG控制器通过对受噪声扰动的线性系统进行状态反馈来实现最优化控制，其优化指标为最小化系统线性二次型的泛函取值。LQG算法控制框图如图4所示。
作为最优控制，LQG反馈控制方法的目标是最小化成本函数或性能指标，因此其代价函数选择为状态向量与控制输入的二次型表达形式，即衡量代价的目标函数为
式中，Q为状态向量误差权重矩阵，R为输入权重矩阵，x（t）和u（t）分别为状态向量和系统输入。设定存在最优的反馈矩阵K，则系统的状态反馈为
此时，最优的反馈增益可以由K=R-1BTP（t）求得，其中P（t）为如下Riccati方程的解：
式中，A和B分别为状态空间方程中的系统矩阵和控制矩阵。
基于遗传算法的LQG控制方法，是将遗传算法与最优控制方法LQG相结合，利用遗传算法对LQG控制器目标函数中的Q矩阵进行优化。计算得到最佳的状态反馈矩阵K，最终提升LQG的控制性能。Q矩阵作为状态误差权重矩阵，其对角线上每个元素对应状态向量中的一阶，在状态反馈中，Q矩阵的取值将决定反馈信号在每一阶的分配情况。
重新设6维加权矩阵Q=diag（q1，q2，⋯，q6），R=0.001，令qi ∈[0，1×105]，i ∈ Z+且i ∈[1，6]，设置遗传算法参数如表3所示。
适应度的遗传进化过程如图5所示，图5展示了在Q矩阵优化搜索过程中，适应度随进化代数的变化而变化的情况。从图中可以看出，当遗传代数达到25代之后，种群各代间的适应度变化显著减小，进化结果逐渐收敛到了最优值。将此时染色体中的Q矩阵信息代入LQG控制器，通过解Riccati方程可以得到最优控制所需的增益反馈矩阵K。
3　复合材料导管模型辨识
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使用解析法进行复合材料导管结构建模时，需要考虑几方面因素造成的误差：
（1）各厂家的工艺水平不同造成碳纤维性能参数的差异；
（2）碳纤维本身存在各向异性等复杂的力学特性，无法简单准确地定义材料特性；
（3）复合材料导管模型加工过程中存在不可控的误差；
（4）导管安装过程中螺栓预紧力不同等因素带来的影响。
综合上述不可控因素，本文决定使用模型辨识的方法对复合材料导管进行建模。模型辨识与精确的理论建模方法相比，其有效性和工作范围有限。通过辨识得到的控制模型在某些情况下没有直接的物理意义，但是模型辨识的结果非常容易获得与使用，最为关键的是这一方法能够确保所得模型足够简洁，这有利于后续控制算法的设计。
3.1　模型辨识试验
本文基于NI CompactRIO系统，使用LabVIEW图形化编程语言，利用FPGA快速响应逻辑模块和实时操作系统RT模块，对复合材料导管模型进行系统辨识的嵌入式平台搭建。
根据模型辨识算法原理，进行系统辨识需要为辨识程序提供真实系统的输入与输出信号，并且二者需保证高度的同步性，同时辨识系统需要具备监测、传输、保存数据等功能。因此，设定嵌入式系统平台的功能要求为：
（1）能够产生正弦信号、脉冲信号、白噪声信号等激励信号，能够将激励信号通过作动器作用至复合材料导管模型；
（2）能够采集复合材料导管实时响应的输出信号，可以对输出信号进行预处理；
（3）能够将输入、输出信号实时传输至上位机进行监测；
（4）能够对输入、输出数据进行保存、后处理和校验。
根据上述功能要求，设计模型辨识试验任务流程如图6所示，其中涉及的主要硬件模块为LabVIEW FPGA模块与实时Real-Time模块。
LabVIEW中FPGA模块可与NI-9234采集模块和NI-9269输出模块直接连接。与其他系统相比，该系统几乎不会为辨识系统带来信号采集与信号输出的延迟。这种连接方式能够在保持高采样速率的情况下，将采集到的传感器信号与激励输出信号一同进行保存，降低了编程工作的难度。NI LabVIEW Real-Time模块是LabVIEW开发环境中用于实时控制和数据采集的特殊模块。这一模块广泛应用于工业控制中，可以极大地增加系统的实时性。模型辨识试验平台如图7所示。
3.2　模型辨识结果分析
给出复合材料导管模型的n阶状态空间表达，得到如下的离散线性时不变状态空间模型：
式中，k时刻的激励作动器输入向量，k时刻的控制作动器输入向量，状态向量和输出向量，系统矩阵，激励力输入矩阵，控制力输入矩阵，观测矩阵，直接传递矩阵。
预设模型辨识的各项参数如表4所示。系统辨识的实验流程为：将输入输出信号序列由FPGA模块传输至RT模块中，运行编写好的LabVIEW模型辨识程序，调用子空间模型辨识法计算，最终获得复合材料导管的离散状态空间方程。
经过系统辨识得到复合材料导管离散状态空间模型，将其转换为连续状态空间模型后，得到系统矩阵[A，B，C，D]分别为
为验证辨识结果的有效性，对系统辨识模型和导管实物模型同时施加激励信号，对比其响应输出。导管实物模型中，对压电片控制器输入激励电信号，将接收到的传感器加速度信号进行后处理，得到对应的位移输出信号并记录。辨识模型利用Matlab进行数值仿真，计算相同输入下辨识模型的响应输出。设置两组输入信号，分别为25 Hz的正弦信号和20 Hz与30 Hz正弦信号叠加得到的复合谐波信号，幅值均为1 V。最终对比辨识模型响应与实物模型响应结果，如图8所示。
对比两组响应结果可知，辨识模型与实物模型响应信号拟合结果较好，证明模型辨识结果比较准确，可以用于后续的复合材料导管控制器设计。
4　复合材料导管振动主动控制试验
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4.1　控制系统设计
硬件系统设计的技术框架图如图9所示。硬件系统由被控对象、信号传感和采集系统、cRIO控制模块、功率放大器和PC组成。控制系统工作流程为：传感器采集被控对象振动信号，被采集信号由传感器经输入模块送至控制模块。控制模块进行数据处理后产生控制信号，并发送至输出模块。最终，输出模块经功率放大器后驱动MFC产生振动，达到控制目的。上位机不直接参与控制，其作用是数据监控与数据存储。
硬件系统的核心部件是控制模块，本试验采用NI CompactRIO控制器。利用CompactRIO中的FPGA快速响应逻辑模块和Real-Time实时操作模块，实现采集信号的接收、信号处理、控制信号的产生及发射。硬件系统具体工作流程如下：
（1）FPGA使用输出模块发射激励信号，功率放大器驱动激励MFC使得被控对象开始振动；
（2）传感器采集到振动信号后通过输入模块传送至FPGA，由FPGA将待处理信号传输至Real-Time模块内；
（3）Real-Time模块中的LQG控制算法计算出本次循环所需的反馈信号值，处理并返回至FPGA；
（4）FPGA通过输出模块和功率放大器驱动控制MFC完成对被控对象的控制；
（5）运行期间控制系统的数据由Real-Time模块传输至上位机进行监控与保存，以便后续对试验过程与结果的分析。
本试验基于NI CompactRIO系统，利用CompactRIO中的FPGA模块和RT模块搭建了振动控制系统的硬件部分。硬件系统由PC机、cRIO-9039测控系统、NI-9234采样模块、NI-9269电压输出模块、HVA1500/500型压电驱动器、复合材料导管模型、M-8557-P1MFC片、352C33型加速度传感器组成。试验平台硬件布置如图10所示。PC机与嵌有各输入输出模块的cRIO主机连接，NI-9269电压输出模块通过压电驱动器与MFC作动器连通，加速度传感器与NI-9234采样模块连接。
设置试验参数如表5所示。为了简化控制程序编写逻辑，将系统控制步长与传感器采样周期均选为4 ms。在上一章中由模型辨识得到了6阶状态空间方程，对该模型进行对应采样周期的离散化后即可作为振动控制模型使用。FPGA通过输出模块发射激励信号，HVA1500/500型压电驱动器可以将信号放大200倍后输出。352C33传感器标定后测量值为加速度形式，为了便于对控制效果进行直观的评估，将传感器测量值进行两次积分获得位移形式的输出信号。
4.2　正弦激励下振动主动控制试验
本节叙述了复合材料导管振动的主动控制试验，实验目的是测试在不同激励输入下LQG算法的振动主动控制效果。每组激励分别设置遗传算法优化前的初始矩阵Q0和经过遗传算法优化的优化矩阵Q'以进行对比。其取值如下所示：
优化前的初始矩阵Q0为
Q0=diag (1000, 1000, 1000, 1000, 1000, 1000)
优化100代后的优化矩阵Q'为
Q'=diag (134.70, 53.88, 4660.62, 9752.27, 11 449.49, 99 974.26)
设置激励MFC的激励电压为1 V，激励频率为20 Hz，得到如图11的控制效果。图11（a）和图11（b）为进行振动主动控制试验时测点接收到的位移响应，其中图11（a）为优化前振动控制效果，图11（b）为Q矩阵经过遗传算法优化后振动控制效果，未控制、控制但未优化和优化且进行控制的幅频响应如图11（c）所示。
为了更简洁直观地对控制效果进行评估，设定振幅控制率为
式中，AmpC为施加控制后位移响应的包络线幅值，AmpU为未施加控制时位移响应的包络线幅值。
由试验结果可知，在开启控制MFC后，测点振幅较快地降低并趋于稳定，振幅控制率为52.81%；经过遗传算法优化后，振幅控制率提高了7.79%。由幅频响应图可知，与未控状态相比，20 Hz处的峰值在未优化控制时降低了9.49 dB，遗传算法优化后降低了13.16 dB。
设置激励MFC的激励电压为1 V，激励频率为40 Hz，得到如图12所示的控制效果。未优化控制时振幅控制率为51.43%，经过遗传算法优化后，振幅控制率提高了10.21%。由幅频响应图可知，与未控状态相比，40 Hz处峰值在未优化控制时降低了9.81 dB，遗传算法优化后降低了11.50 dB。
4.3　复合谐波激励下振动主动控制试验
令激励MFC的输入信号为不同的正弦波叠加形成的复合波信号，设定正弦波频率分别为20 Hz和30 Hz，幅值均为1 V，得到如图13所示的控制效果。未优化控制时振幅控制率为45.88%，经过遗传算法优化后，振幅控制率提高了7.09%。由幅频响应图可知，与未控状态相比，20 Hz处峰值在未优化控制时降低了7.59 dB，遗传算法优化后降低了9.84 dB；30 Hz处峰值在未优化控制时降低了5.67 dB，遗传算法优化后降低了6.14 dB。
设定正弦波频率分别为20 Hz和40 Hz，幅值均为1 V，得到如图14所示的控制效果。未优化控制时振幅控制率为35.18%，经过遗传算法优化后，振幅控制率提高了7.82%。由幅频响应图可知，与未控状态相比，20 Hz处峰值在未优化控制时降低了1.46 dB，遗传算法优化后降低了1.39 dB；40 Hz处峰值在未优化控制时降低了9.17 dB，遗传算法优化后降低了11.54 dB。虽然20 Hz处幅频响应峰值在优化后反而少量增加，但是由图可知40 Hz处为振动幅值的主要贡献频率，优化后整体的振动控制效果还是有所提升。
对不同激励信号下复合材料导管模型在遗传算法优化前后的振动控制效果进行了总结，如表6所示。遗传算法优化前LQG控制器可对导管模型的振动进行较为良好的抑制，平均控制率能够达到46.32%。而利用遗传算法对LQG控制器的权重矩阵Q进行优化后，控制器的性能得到了进一步提升，平均控制率达到了54.56%左右，证明了基于遗传算法的LQG控制系统拥有较好的振动抑制能力。
5　结语
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本文将复合材料导管的振动主动控制作为研究方向，基于NI CompactRIO系统，使用LabVIEW图形化编程语言，利用FPGA快速响应逻辑模块和实时RT模块，搭建了空气环境中的导管抑振试验系统。利用子空间模型辨识方法的实验建模方式，对复合材料导管进行了模型辨识。分析了遗传算法优化对导管振动控制系统性能的提升。试验结果表明，经过遗传算法优化后振幅控制率平均提升了8%左右。结果证明，本文通过实验建模得到的系统模型准确有效，搭建的复合材料导管抑振试验系统能够有效降低结构振动幅值，且遗传算法可以进一步改善系统控制效果。
基金
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  • 船舶振动噪声重点实验室基金项目(JCKY2023207CI02)
文献
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doi: 10.3969/j.issn.1007-7294.2025.02.012
  • 接收时间：2024-08-19
  • 首发时间：2026-03-24
  • 出版时间：2025-02-20
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  • 收稿日期：2024-08-19
基金
船舶振动噪声重点实验室基金项目(JCKY2023207CI02)
作者信息
    中国船舶科学研究中心，江苏　无锡　214082

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https://castjournals.cast.org.cn/joweb/cblx/CN/10.3969/j.issn.1007-7294.2025.02.012
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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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