摘要
在工程结构服役过程中，不可避免地受到来自自身和外界的各方面因素影响，导致结构的抵抗能力下降，可靠度降低，进而引发安全事故，造成巨大的人员和经济财产损失，因此对已经服役的土木工程结构采用有效的手段进行结构健康监测具有重要的意义。目前，结构模态分析已经成为结构健康监测系统的核心技术之一。本文引入欠定的盲源分离理论，应用于结构模态分析，为结构健康监测中传感器数量少于结构活跃模态数量的模态参数识别问题提供了一种新的选择。本文主要的工作和研究如下： 1、研究了基于密度峰值聚类算法的欠定盲源分离方法。首先利用短时傅里叶变换把时域的传感器信号转换到具有稀疏性的时频域，针对无法预知活跃模态数量和高阶振动模态混叠的问题，提出了一种基于密度峰值聚类的算法来识别模态振型；得到模态振型后，利用可以快速重构稀疏信号的SL0算法，重构模态坐标信号，提取各阶模态频率。 2、研究了基于平行因子分析的欠定盲源分离方法。首先利用平滑伪维纳变换把信号转换到时频域，然后构建平行因子模型，利用平行因子分析技术识别模态振型；最后利用子空间方法重构模态坐标信号识别模态频率。
3、通过一个四层剪切型钢框架模型验证以上两种算法的有效性与实用性。通过伪随机振动试验数据，在只布置三个传感器的条件下，两种欠定盲源分离方法都成功地识别了模态振型并且分离了模态坐标信号，
说明了本文提出的方法在模态参数识别实际应用中的可行性。
关键词：模态分析，欠定盲源分离，密度峰值聚类，平行因子分析
ABSTRACT
During the engineering structure servicing life, it is inevitably affected by various factors from itself and the outside world. That makes the structure's resistance performance to decline and reliability to decrease, which in turn leads to safety accidents, and causes huge personnel and economic loss of property. Therefore, it is of great significance to adopt effective means to carry out structural health monitoring of civil engineering structures. At present, structural modal analysis has become one of the core technologies of structural health monitoring system. In this paper, the theory of underdetermined blind source separation is introduced and applied to structural modal analysis, which provides a new choice for the underdetermined modal parameter identification problem that the number of sensors is less than the number of active modes in structural health monitoring. The main work and research of this paper are as follows:
1. The Underdetermined blind source separation method based on density peak clustering algorithm is discussed in this paper. Firstly, the sensor signals in the time domain are transformed to the spars
e time-frequency domain by the short-time Fourier transform. In view of the unpredictable number of active modes and the high-order vibration mode aliasing, a new method based on density peak clustering to identify the mode shapes is proposed. After obtaining vibration mode shapes，the smooth l0 algorithm, which can reconstruct the sparse signals quickly, is used to reconstruct the modal coordinate signals and extract modal frequencies.
2. The underdetermined blind source separation method based on parallel factor analysis is discussed in this paper. Firstly, the signal is transformed to the time-frequency domain by the smoothed pseudo Wigner-Ville distribution. Then, a parallel factor model is constructed, and the modal vibration mode is identified by parallel factor analysis. Finally, modal coordinates are reconstructed using subspace algorithm to identify modal frequencies.
3. The validity and practicability of these two algorithms are verified experimentally by a four-story shear steel frame model. The two underdetermined blind source separation methods both successfully identify the mode shapes and separate the modal coordinate signals with random vibration test data under the condition that only three sensors are arranged, which indicated that the method proposed in this paper can be used in modal parameters.
KEYWORDS: modal analysis, underdetermined blind source separation, density peak clustering, parallel factor analysis
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目录
第一章绪论 (1)
1.1 课题背景及研究目的和意义 (1)
1.2 模态分析 (2)
1.3 盲源分离在模态参数识别中的应用背景 (3)
1.4 本文研究内容 (5)
手动刨冰机第二章基于密度峰值聚类算法的模态参数识别 (8)
2.1 结构振动理论 (8)
2.2 盲源分离基本原理 (8)
2.3 稀疏成分分析算法流程 (9)莲子剥壳机
2.3.1 短时傅里叶变换基本原理 (11)
2.3.2 模态分析中的稀疏性 (12)
2.3.3 振动信号去噪和模态振型矩阵计算原理 (12)
2.3.4 经典聚类算法原理简介 (16)
2.3.5 密度峰值聚类算法原理 (18)
2.4 基于平滑l0算法的单模态信号重构 (20)
2.5 模态识别算例 (22)
2.5.1 计算模态振型 (22)
2.5.2 单模态信号重构 (27)
2.6本章小结 (29)
第三章基于平行因子分析的结构模态参数识别 (31)
3.1 空间时频分布理论 (31)
3.2 多源点与单源点 (31)
3.3 平行因子分析的基本理论 (33)
水力冲洗门3.4 在模态分析中构建平行因子模型 (35)
3.5 CANDECOMP算法的基本原理 (36)
3.6 CANDECOMP算法在模态分析中的应用 (38)
3.7 重构模态坐标信号 (39)
无触点开关3.8 数学求解 (40)
3.9 本章小结 (45)
第四章剪切型钢框架实验与算法验证 (46)
4.1 四层剪切型钢框架模型 (46)
4.2 基于密度峰值聚类算法的实验验证 (48)
4.3 平行因子分析算法的实验验证 (54)
4.4 两种算法识别结果对比 (57)
4.5 本章小结 (59)
第五章结论与展望 (61)
5.1 主要研究工作与结论 (61)
5.2 展望 (61)
参考文献 (63)
附录1 (68)
附录2 (71)
攻读硕士学位期间的学术活动及成果情况 (72)
插图清单
图1.1 一般振动问题组成 (2)
图1.2欠定盲源分离算法流程图 (6)
图2.1混合信号形成的示意图 (9)
图2.2稀疏成分分析算法原理 (10)
图2.3时频域信号的稀疏性示意图 (12)
图2.4混合信号时域图 (13)
图2.5混合信号时频图 (13)
图2.6混合信号幅值散点图 (15)
图2.7去除多源点的混合信号幅值散点图 (16)
图2.8数据点决策图 (19)
图2.9数据点γ值分布图 (20)
图2.10仿真算例决策图 (23)
图2.11 仿真算例γ值分布图 (24)
图2.12 模态振型识别值与理论值对比 (25)
图2.13各种信噪比下的决策图 (26)
图2.14 各种信噪比下识别的模态振型 (26)
图2.15 各阶模态信号时频域三维图 (27)
图2.16各阶模态时域信号 (28)
图2.17各阶模态频域信号 (28)
图3.1源信号的SPWVD自谱与互谱 (32)
图3.2筛选单源点前后的混合信号时频图 (33)
图3.3模态分析中构建三阶张量示意图 (35)
图3.4 分解三阶张量示意图 (36)
图3.5 模态振型识别值与理论值对比 (41)
图3.6 1~5阶模态时频域信号 (42)
高频淬火工艺图3.7各模态E(f)与频率的关系 (43)
图3.8 ξ=0.1时各信噪比平行因子分析算法识别振型结果 (44)
图4.1实验模型尺寸图 (46)
图4.2 4层框架剪切性框架实体图 (47)
图4.3 实验布置图 (47)
图4.4 各传感器的时域信号 (48)
图4.5 各传感器的时频图 (49)
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