CN105787655B - Method for identifying modal parameters of super high-rise structure - Google Patents

Method for identifying modal parameters of super high-rise structure Download PDF

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CN105787655B
CN105787655B CN201610101215.1A CN201610101215A CN105787655B CN 105787655 B CN105787655 B CN 105787655B CN 201610101215 A CN201610101215 A CN 201610101215A CN 105787655 B CN105787655 B CN 105787655B
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李志军
埃德里霍贾特
朴孝善
李高宏
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Abstract

The invention discloses a method for identifying modal parameters of a super high-rise structure, which is used for effectively analyzing non-stationary, nonlinear and strong noise signals based on discrete synchronous extrusion wavelet transform transduction, accurately reconstructing the characteristics of modal components of complex synthetic signals in the form of resonance components, and effectively analyzing the resonance components by combining Hilbert Transform (HT) to obtain the characteristics of instantaneous amplitude and frequency, so that the purpose of identifying the main frequency and damping ratio of the super high-rise structure is achieved, and in order to ensure the accuracy of identifying the modal parameters, a least square linear fitting method (linear least-square fit, LL ST) is introduced to smooth and predict results.

Description

超高层结构模态参数识别方法Modal parameter identification method of super high-rise structure

技术领域technical field

本发明属于结构健康监测领域，具体涉及一种超高层结构模态参数识别方法。The invention belongs to the field of structural health monitoring, in particular to a method for identifying modal parameters of a super high-rise structure.

背景技术Background technique

结构健康监测是评估结构健康状态、识别结构损伤部位和损伤程度的过程。超高层建筑结构的健康监测是延长结构使用寿命关键的一步，鉴于超高层结构自身的重要性，使得针对该结构的健康监测工作具有重大的社会效益和经济效益。结构健康监测需要解决的一个重要问题的就是基于振动信号的结构模态参数识别。目前已有的小波分析方法(wavelet transform,WT)和经验模态解耦方法(empirical mode decomposition,EMD)存在着无法识别相近频率的模态参数以及无法从低幅值、高噪声测量振动信号中有效识别结构基本模态参数的问题。Structural health monitoring is the process of assessing the state of structural health and identifying the site and extent of structural damage. The health monitoring of super high-rise building structures is a key step to prolong the service life of the structure. In view of the importance of the super high-rise structure itself, the health monitoring of the structure has great social and economic benefits. An important problem to be solved in structural health monitoring is the identification of structural modal parameters based on vibration signals. The existing wavelet analysis method (wavelet transform, WT) and empirical mode decoupling method (empirical mode decomposition, EMD) have the problem of not being able to identify modal parameters of similar frequencies and unable to measure vibration signals with low amplitude and high noise. The problem of effectively identifying the fundamental modal parameters of a structure.

同步挤压小波变换能有效地分析非平稳、非线性以及强噪声信号，准确地以谐振分量的形式重构复杂合成信号的模态分量，而这类信号在实际建筑结构中非常普遍，例如地震动、风荷载。Synchro squeeze wavelet transform can effectively analyze non-stationary, nonlinear and strong noise signals, and accurately reconstruct the modal components of complex synthetic signals in the form of resonant components, which are very common in practical building structures, such as earthquakes Dynamic and wind loads.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明的主要目的在于提供一种超高层结构模态参数识别方法。In view of this, the main purpose of the present invention is to provide a method for identifying modal parameters of a super high-rise structure.

为达到上述目的，本发明的技术方案是这样实现的：In order to achieve the above object, the technical scheme of the present invention is achieved in this way:

一种超高层结构模态参数识别方法，其特征在于，该方法通过以下步骤实现：A method for identifying modal parameters of a super high-rise structure, characterized in that the method is realized by the following steps:

步骤1：筛分不同结构层的加速度测量信号，选取包含结构主要基本频率的测量信号

Figure GDA0002053822170000011
进行分析，i＝1,2,…,n为结构相应的层数，根据同步挤压小波变换去除测量信号的噪声，而后基于去噪后的测量信号，分解和重构结构的主要模态分量，则测量信号表示为：Step 1: Screen the acceleration measurement signals of different structural layers, and select the measurement signal containing the main fundamental frequency of the structure
Figure GDA0002053822170000011
For analysis, i=1,2,...,n is the number of layers corresponding to the structure. The noise of the measurement signal is removed according to the synchronous squeeze wavelet transform, and then the main modal components of the structure are decomposed and reconstructed based on the denoised measurement signal. , the measurement signal is expressed as:

Figure GDA0002053822170000021
Figure GDA0002053822170000021

式中，

Figure GDA0002053822170000022
是经同步挤压小波分解后重构的第i层加速度测量信号的前m个主要的模态分量；Fi(t)是第i层加速度测量信号中过滤掉的噪声和高阶模态分量；In the formula,
Figure GDA0002053822170000022
are the first m main modal components of the i-th layer acceleration measurement signal reconstructed after decomposition by synchro-squeezing wavelet; F i (t) is the filtered noise and high-order modal components in the i-th layer acceleration measurement signal;

步骤2：根据希尔伯特变换构建分析信号，之后，根据所述分析信号得到相应瞬时相角和幅值，而后由相应瞬时相角和幅值的自然对数对时间的导数初步识别结构主要频率和阻尼比；Step 2: Construct an analysis signal according to the Hilbert transform, then obtain the corresponding instantaneous phase angle and amplitude according to the analysis signal, and then initially identify the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude against time. frequency and damping ratio;

步骤3：根据最小二乘线性拟合方法对于所述初步识别的主要频率和阻尼比进行平滑预测获得准确的识别结果。Step 3: Perform smooth prediction on the preliminarily identified main frequency and damping ratio according to the least squares linear fitting method to obtain an accurate identification result.

所述步骤1具体包括以下步骤：The step 1 specifically includes the following steps:

步骤101：筛分测量信号，为保证计算的精度，采样点的数量满足2n的要求，其中n为一正整数，建议n为10或11，即采用点的数量为1024或2048，选取包含结构主要基本频率的测量信号进行分析；Step 101: Sieve the measurement signal. In order to ensure the accuracy of the calculation, the number of sampling points meets the requirement of 2 n , where n is a positive integer. It is recommended that n be 10 or 11, that is, the number of points used is 1024 or 2048. The measurement signal of the main fundamental frequency of the structure is analyzed;

步骤102：对于筛分的测量信号进行离散小波变换，首先定义测量信号

Figure GDA0002053822170000023
的连续小波变换(continuous wavelet transform,CWT)，Wf(a,·)为Step 102: Perform discrete wavelet transform on the sieved measurement signal, first define the measurement signal
Figure GDA0002053822170000023
The continuous wavelet transform (CWT) of , W f (a, ) is

Figure GDA0002053822170000024
Figure GDA0002053822170000024

式中ψ是选择的基小波函数；a为比例系数；“*”表示卷积；where ψ is the selected fundamental wavelet function; a is the scale coefficient; "*" means convolution;

在频域空间，小波变换Wf(a,·)表示为In the frequency domain space, the wavelet transform W f (a, ) is expressed as

Figure GDA0002053822170000025
Figure GDA0002053822170000025

则对于任意位置(aj,tk)，这里tk是任意的离散时间点，对应的离散时间形式的比例系数

Figure GDA0002053822170000026
L为一非负整数，nv为影响比例系数的参数，通常取32或64，我们用下面的公式计算离散小波变换(discrete wavelet transform,DWT)Then for any position ( aj , t k ), where t k is any discrete time point, the corresponding proportional coefficient of discrete time form
Figure GDA0002053822170000026
L is a non-negative integer, n v is a parameter that affects the scale coefficient, usually 32 or 64, we use the following formula to calculate the discrete wavelet transform (DWT)

Figure GDA0002053822170000027
Figure GDA0002053822170000027

式中，Γn和

Figure GDA0002053822170000031
是标准的离散傅里叶变换(Fourier Transform)以及它的逆变换；“·”表示点乘；
Figure GDA0002053822170000032
是频域空间的采样间隔；In the formula, Γ n and
Figure GDA0002053822170000031
is the standard discrete Fourier Transform (Fourier Transform) and its inverse transform; "·" indicates dot product;
Figure GDA0002053822170000032
is the sampling interval of the frequency domain space;

步骤103：基于连续小波变换系数，Wf(a,·)，由下面的公式得对应的实值频率Step 103: Based on the continuous wavelet transform coefficient, W f (a, ·), the corresponding real-valued frequency is obtained by the following formula

Figure GDA0002053822170000033
Figure GDA0002053822170000033

式中，

Figure GDA0002053822170000034
In the formula,
Figure GDA0002053822170000034

为了有效过滤噪声，选用硬门槛参数(hard threshold parameter)γ为In order to effectively filter noise, the hard threshold parameter γ is selected as

Figure GDA0002053822170000035
Figure GDA0002053822170000035

MAD是离散小波系数，

Figure GDA0002053822170000036
的平均绝对偏差；bl是与MAD相关的增大系数，建议取值为1.2～1.7；
Figure GDA0002053822170000037
是离散小波系数的幅值；MAD is the discrete wavelet coefficient,
Figure GDA0002053822170000036
The average absolute deviation of ; b l is the increase coefficient related to MAD, and the recommended value is 1.2 to 1.7;
Figure GDA0002053822170000037
is the magnitude of discrete wavelet coefficients;

由式(6)可知，离散小波变换系数的幅值小于γ的点被舍弃，从而有效地过滤噪声影响，基于公式(5)，则得基于离散小波变换的实值频率为It can be seen from equation (6) that the points whose amplitudes of discrete wavelet transform coefficients are less than γ are discarded, thereby effectively filtering the influence of noise. Based on equation (5), the real-valued frequency based on discrete wavelet transform is

Figure GDA0002053822170000038
Figure GDA0002053822170000038

式中，

Figure GDA0002053822170000039
且
Figure GDA00020538221700000310
In the formula,
Figure GDA0002053822170000039
and
Figure GDA00020538221700000310

步骤104：基于由公式(4)和(7)所得的

Figure GDA00020538221700000311
和
Figure GDA00020538221700000312
定义去噪加速度信号
Figure GDA00020538221700000313
的离散同步挤压小波变换为Step 104: Based on the obtained from equations (4) and (7)
Figure GDA00020538221700000311
and
Figure GDA00020538221700000312
Defining the Denoised Acceleration Signal
Figure GDA00020538221700000313
The discrete synchro-squeezing wavelet transform of

Figure GDA00020538221700000314
Figure GDA00020538221700000314

式中，二分频率ωl满足条件

Figure GDA00020538221700000315
In the formula, the bisection frequency ω l satisfies the condition
Figure GDA00020538221700000315

步骤105：设置相应m个带通滤波器，而后进行离散同步挤压小波逆变换，则去噪加速度信号

Figure GDA00020538221700000316
的每个模态分量能被重构为Step 105: Set corresponding m band-pass filters, and then perform discrete synchronous squeeze wavelet inverse transform, then denoise the acceleration signal
Figure GDA00020538221700000316
Each modal component of can be reconstructed as

Figure GDA00020538221700000317
Figure GDA00020538221700000317

式中，

Figure GDA0002053822170000041
是一标准化常数。In the formula,
Figure GDA0002053822170000041
is a normalization constant.

所述步骤2具体包括以下步骤：The step 2 specifically includes the following steps:

步骤201：对于每一个由离散同步挤压小波变换重构得到的模态分量，即由式(9)得到的模态分量，首先基于希尔伯特变换得到相应的第j阶模态分量的分析信号形式为Step 201: For each modal component reconstructed by the discrete synchronous squeezing wavelet transform, that is, the modal component obtained by formula (9), first obtain the corresponding jth-order modal component based on the Hilbert transform. The analysis signal is in the form of

Figure GDA0002053822170000042
Figure GDA0002053822170000042

式中，Aij(t)是与频率ωj相应的重构模态分量在t时刻的幅值；θij(t)是相应时刻的相角；where A ij (t) is the amplitude of the reconstructed modal component corresponding to the frequency ω j at time t; θ ij (t) is the phase angle at the corresponding time;

步骤202：基于公式(10)，结构的瞬态频率和阻尼比由下面的公式获得Step 202: Based on equation (10), the transient frequency and damping ratio of the structure are obtained by the following equations

Figure GDA0002053822170000043
Figure GDA0002053822170000043

Figure GDA0002053822170000044
Figure GDA0002053822170000044

式中，

Figure GDA0002053822170000045
为第j阶模态的阻尼体系模态频率。In the formula,
Figure GDA0002053822170000045
is the modal frequency of the damped system for the jth mode.

所述步骤3具体包括以下步骤：The step 3 specifically includes the following steps:

步骤301：在相角θij(t)随时间t变化图中，根据最小二乘线性拟合方法得到相应的一条平均直线来近似表示相角θij(t)随时间t变化的关系，则由该拟合直线的斜率可得预测的阻尼体系模态频率ωdj，即利用公式(11)所得；Step 301: In the graph of the change of the phase angle θ ij (t) with time t, a corresponding average straight line is obtained according to the least squares linear fitting method to approximate the relationship between the change of the phase angle θ ij (t) with time t, then The predicted damping system modal frequency ω dj can be obtained from the slope of the fitted straight line, which is obtained by using formula (11);

步骤302：在幅值的自然对数lnAij(t)随时间t变化图中，选取相应的时段利用最小二乘线性拟合方法得到相应的一条平均直线来近似表示该时段内lnAij(t)随t变化的关系，则由该拟合直线的斜率可得公式(12)中ξjωj的值；Step 302: In the graph of the natural logarithm lnA ij (t) of the amplitude versus time t, select a corresponding time period and use the least squares linear fitting method to obtain a corresponding average straight line to approximately represent lnA ij (t in this time period. ) changes with t, then the value of ξ j ω j in formula (12) can be obtained from the slope of the fitted straight line;

步骤303：根据由前两步中所得的ωdj和ξjωj的值，并利用已知关系式

Figure GDA0002053822170000046
则可得预测的结构模态频率值和阻尼比值。Step 303: According to the values of ω dj and ξ j ω j obtained in the previous two steps, and using the known relationship
Figure GDA0002053822170000046
Then the predicted structural modal frequency value and damping ratio can be obtained.

与现有技术相比，本发明的有益效果：Compared with the prior art, the beneficial effects of the present invention:

本发明能够从超高层结构的状态反应传感器所测的低幅值、强噪声以及具有相近频率特征的振动测量信号中有效地识别结构基本模态频率和相应的阻尼比。从而克服了传统小波分析方法和经验模态解耦方法存在的缺陷。The invention can effectively identify the basic modal frequency and the corresponding damping ratio of the structure from the low amplitude, strong noise and vibration measurement signals with similar frequency characteristics measured by the state response sensor of the super high-rise structure. Thus, the defects of traditional wavelet analysis method and empirical mode decoupling method are overcome.

附图说明Description of drawings

图1为本发明实施例的实施流程；Fig. 1 is the implementation flow of the embodiment of the present invention;

图2为本发明实施例的具体超高层建筑-韩国首尔的乐天世界塔(Lotte WorldTower,LWT)；Fig. 2 is the concrete super high-rise building of the embodiment of the present invention - the Lotte World Tower (Lotte World Tower, LWT) in Seoul, South Korea;

图3(a)为本发明实施例—乐天世界塔的加速度传感器沿高度的位置布置图；Fig. 3 (a) is an embodiment of the present invention - the positional arrangement diagram of the acceleration sensor of Lotte World Tower along the height;

图3(b)为本发明实施例加速度传感器沿楼层的位置和方位布置图；Figure 3(b) is a diagram of the position and orientation arrangement of the acceleration sensor along the floor according to the embodiment of the present invention;

图4(a)为本发明实施例选择的72层北侧沿x方向加速度传感器所测信号；Figure 4(a) is the signal measured by the acceleration sensor along the x-direction on the north side of the 72th floor selected in the embodiment of the present invention;

图4(b)为本发明实施例筛分的分析信号；Fig. 4 (b) is the analysis signal of the screening of the embodiment of the present invention;

图5为本发明实施例信号的时频分布图；5 is a time-frequency distribution diagram of a signal according to an embodiment of the present invention;

图6为本发明实施例的模态分量重构；Fig. 6 is the modal component reconstruction of the embodiment of the present invention;

图7为本发明实施例的相角θij(t)随时间t变化图及最小二乘线性拟合直线。其中，图(a)为第一模态反应；图(b)为第二模态反应；图(c)为第三模态反应；FIG. 7 is a graph showing the variation of the phase angle θ ij (t) with time t and a least squares linear fitting straight line according to an embodiment of the present invention. Among them, Figure (a) is the first modal response; Figure (b) is the second modal response; Figure (c) is the third modal response;

图8为本发明实施例的幅值的自然对数lnAij(t)随时间t变化图及最小二乘线性拟合直线。其中，图(a)为第一模态反应；图(b)为第二模态反应；图(c)为第三模态反应。FIG. 8 is a graph showing the variation of the natural logarithm lnA ij (t) of the amplitude with time t and a least squares linear fitting straight line according to an embodiment of the present invention. Among them, Figure (a) is the first modal response; Figure (b) is the second modal response; Figure (c) is the third modal response.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

本发明基于离散同步挤压小波变换(discretized synchrosqueezed wavelettransform,DSWT)能有效地分析非平稳、非线性以及强噪声信号，准确地以谐振分量的形式重构复杂合成信号的模态分量的特点，并结合希尔伯特变换(Hilbert transform,HT)能有效分析谐振分量，得到瞬时幅值和频率的特点，从而达到识别超高层结构主要频率和阻尼比的目的。为了保证识别模态参数的准确性，引入最小二乘线性拟合方法(linear least-square fit,LLST)来平滑预测的结果。Based on discrete synchrosqueezed wavelet transform (DSWT), the invention can effectively analyze non-stationary, nonlinear and strong noise signals, accurately reconstruct the modal components of complex synthetic signals in the form of resonance components, and Combined with the Hilbert transform (HT), the resonance components can be effectively analyzed, and the characteristics of the instantaneous amplitude and frequency can be obtained, so as to achieve the purpose of identifying the main frequency and damping ratio of the super high-rise structure. In order to ensure the accuracy of identifying modal parameters, a linear least-square fit (LLST) method is introduced to smooth the predicted results.

本发明实施例提供一种超高层结构模态参数识别方法，该方法通过以下步骤实现：An embodiment of the present invention provides a method for identifying modal parameters of a super high-rise structure, and the method is implemented by the following steps:

步骤1：筛分不同结构层的加速度测量信号，选取包含结构主要基本频率(一般选择前9阶)的测量信号

Figure GDA0002053822170000061
(i＝1,2,…,n为结构相应的层数)进行分析，根据同步挤压小波变换去除测量信号的噪声，而后基于去噪后的测量信号，分解和重构结构的主要模态分量(滤掉影响较小的高阶模态分量)，则测量信号表示为：Step 1: Screen the acceleration measurement signals of different structural layers, and select the measurement signals containing the main fundamental frequencies of the structure (usually the first 9 orders are selected)
Figure GDA0002053822170000061
(i=1,2,...,n is the number of layers corresponding to the structure) for analysis, remove the noise of the measurement signal according to the synchronous squeezing wavelet transform, and then decompose and reconstruct the main mode of the structure based on the denoised measurement signal component (filtering out higher-order modal components with less influence), the measurement signal is expressed as:

Figure GDA0002053822170000062
Figure GDA0002053822170000062

式中，

Figure GDA0002053822170000063
是经同步挤压小波分解后重构的第i层加速度测量信号的前m个主要的模态分量；Fi(t)是第i层加速度测量信号中过滤掉的噪声和高阶模态分量；In the formula,
Figure GDA0002053822170000063
are the first m main modal components of the i-th layer acceleration measurement signal reconstructed after decomposition by synchro-squeezing wavelet; F i (t) is the filtered noise and high-order modal components in the i-th layer acceleration measurement signal;

具体地，所述步骤1具体包括以下步骤：Specifically, the step 1 specifically includes the following steps:

步骤101：筛分测量信号，为保证计算的精度，采样点的数量满足2n的要求，其中n为一正整数，建议n为10或11，即采用点的数量为1024或2048，选取测量信号中结构基本频率成分最为丰富的部分进行分析(主要是前9阶频率)；Step 101: Sieve the measurement signal. To ensure the accuracy of the calculation, the number of sampling points meets the requirement of 2 n , where n is a positive integer. It is recommended that n be 10 or 11, that is, the number of points used is 1024 or 2048, and the measurement is selected. Analyze the part of the signal with the most abundant fundamental frequency components of the structure (mainly the first 9 frequencies);

步骤102：对于筛分的测量信号进行离散小波变换，首先定义测量信号

Figure GDA0002053822170000064
的连续小波变换(continuous wavelet transform,CWT)，Wf(a,·)为Step 102: Perform discrete wavelet transform on the sieved measurement signal, first define the measurement signal
Figure GDA0002053822170000064
The continuous wavelet transform (CWT) of , W f (a, ) is

Figure GDA0002053822170000065
Figure GDA0002053822170000065

式中ψ是选择的基小波函数；a为比例系数；“*”表示卷积；where ψ is the selected fundamental wavelet function; a is the scale coefficient; "*" means convolution;

在频域空间，小波变换Wf(a,·)表示为In the frequency domain space, the wavelet transform W f (a, ) is expressed as

Figure GDA0002053822170000066
Figure GDA0002053822170000066

则对于任意位置(aj,tk)，这里tk是任意的离散时间点，对应的离散时间形式的比例系数

Figure GDA0002053822170000071
(L为一非负整数，nv为影响比例系数的参数，通常取32或64)，我们用下面的公式计算离散小波变换(discrete wavelet transform,DWT)Then for any position ( aj , t k ), where t k is any discrete time point, the corresponding proportional coefficient of discrete time form
Figure GDA0002053822170000071
(L is a non-negative integer, n v is a parameter that affects the scale coefficient, usually 32 or 64), we use the following formula to calculate the discrete wavelet transform (DWT)

Figure GDA0002053822170000072
Figure GDA0002053822170000072

式中，Γn和

Figure GDA0002053822170000073
是标准的离散傅里叶变换(Fourier Transform)以及它的逆变换；“·”表示点乘；
Figure GDA0002053822170000074
是频域空间的采样间隔；In the formula, Γ n and
Figure GDA0002053822170000073
is the standard discrete Fourier Transform (Fourier Transform) and its inverse transform; "·" indicates dot product;
Figure GDA0002053822170000074
is the sampling interval of the frequency domain space;

步骤103：基于连续小波变换系数，Wf(a,·)，由下面的公式得对应的实值频率Step 103: Based on the continuous wavelet transform coefficient, W f (a, ·), the corresponding real-valued frequency is obtained by the following formula

Figure GDA0002053822170000075
Figure GDA0002053822170000075

式中，

Figure GDA0002053822170000076
In the formula,
Figure GDA0002053822170000076

为了有效过滤噪声，选用硬门槛参数(hard threshold parameter)γ为In order to effectively filter noise, the hard threshold parameter γ is selected as

Figure GDA0002053822170000077
Figure GDA0002053822170000077

MAD是离散小波系数，

Figure GDA0002053822170000078
的平均绝对偏差；bl是与MAD相关的增大系数，建议取值为1.2～1.7；
Figure GDA0002053822170000079
是离散小波系数的幅值；MAD is the discrete wavelet coefficient,
Figure GDA0002053822170000078
The average absolute deviation of ; b l is the increase coefficient related to MAD, and the recommended value is 1.2 to 1.7;
Figure GDA0002053822170000079
is the magnitude of discrete wavelet coefficients;

由式(6)可知，离散小波变换系数的幅值小于γ的点被舍弃，从而有效地过滤噪声影响，基于公式(5)，则得基于离散小波变换的实值频率为It can be seen from equation (6) that the points whose amplitudes of discrete wavelet transform coefficients are less than γ are discarded, thereby effectively filtering the influence of noise. Based on equation (5), the real-valued frequency based on discrete wavelet transform is

Figure GDA00020538221700000710
Figure GDA00020538221700000710

式中，

Figure GDA00020538221700000711
且
Figure GDA00020538221700000712
In the formula,
Figure GDA00020538221700000711
and
Figure GDA00020538221700000712

步骤104：基于由公式(4)和(7)所得的

Figure GDA00020538221700000713
和
Figure GDA00020538221700000714
定义去噪加速度信号
Figure GDA00020538221700000715
的离散同步挤压小波变换为Step 104: Based on the obtained from equations (4) and (7)
Figure GDA00020538221700000713
and
Figure GDA00020538221700000714
Defining the Denoised Acceleration Signal
Figure GDA00020538221700000715
The discrete synchro-squeezing wavelet transform of

Figure GDA00020538221700000716
Figure GDA00020538221700000716

式中，二分频率ωl满足条件

Figure GDA0002053822170000081
In the formula, the bisection frequency ω l satisfies the condition
Figure GDA0002053822170000081

步骤105：设置相应m个带通滤波器，而后进行离散同步挤压小波逆变换，则去噪加速度信号

Figure GDA0002053822170000082
的每个模态分量能被重构为Step 105: Set corresponding m band-pass filters, and then perform discrete synchronous squeeze wavelet inverse transform, then denoise the acceleration signal
Figure GDA0002053822170000082
Each modal component of can be reconstructed as

Figure GDA0002053822170000083
Figure GDA0002053822170000083

式中，

Figure GDA0002053822170000084
是一标准化常数。In the formula,
Figure GDA0002053822170000084
is a normalization constant.

步骤2：根据希尔伯特变换构建分析信号，之后，根据所述分析信号得到瞬时相角和幅值，而后由相应瞬时相角和幅值的自然对数对时间的导数初步识别结构主要频率和阻尼比；Step 2: Construct an analysis signal according to the Hilbert transform, then obtain the instantaneous phase angle and amplitude according to the analysis signal, and then preliminarily identify the main frequency of the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude with respect to time and damping ratio;

具体地，所述步骤2具体包括以下步骤：Specifically, the step 2 specifically includes the following steps:

步骤201：对于每一个由离散同步挤压小波变换重构得到的模态分量，即由式(9)得到的模态分量，首先基于希尔伯特变换得到相应的第j阶模态分量的分析信号形式为Step 201: For each modal component reconstructed by the discrete synchronous squeezing wavelet transform, that is, the modal component obtained by formula (9), first obtain the corresponding jth-order modal component based on the Hilbert transform. The analysis signal is in the form of

Figure GDA0002053822170000085
Figure GDA0002053822170000085

式中，Aij(t)是与频率ωj相应的重构模态分量在t时刻的幅值；θij(t)是相应时刻的相角；where A ij (t) is the amplitude of the reconstructed modal component corresponding to the frequency ω j at time t; θ ij (t) is the phase angle at the corresponding time;

步骤202：基于公式(10)，结构的瞬态频率和阻尼比由下面的公式获得Step 202: Based on equation (10), the transient frequency and damping ratio of the structure are obtained by the following equations

Figure GDA0002053822170000086
Figure GDA0002053822170000086

Figure GDA0002053822170000087
Figure GDA0002053822170000087

式中，

Figure GDA0002053822170000088
为第j阶模态的阻尼体系模态频率。In the formula,
Figure GDA0002053822170000088
is the modal frequency of the damped system for the jth mode.

步骤3：根据最小二乘线性拟合方法对于所述初步识别的主要频率和阻尼比进行平滑预测获得准确的识别结果。Step 3: Perform smooth prediction on the preliminarily identified main frequency and damping ratio according to the least squares linear fitting method to obtain an accurate identification result.

具体地，所述步骤3具体包括以下步骤：Specifically, the step 3 specifically includes the following steps:

步骤301：在相角θij(t)随时间t变化图中，根据最小二乘线性拟合方法得到相应的一条平均直线来近似表示相角θij(t)随时间t变化的关系，则由该拟合直线的斜率可得预测的阻尼体系模态频率ωdj，即利用公式(11)所得；Step 301: In the graph of the change of the phase angle θ ij (t) with time t, a corresponding average straight line is obtained according to the least squares linear fitting method to approximate the relationship between the change of the phase angle θ ij (t) with time t, then The predicted damping system modal frequency ω dj can be obtained from the slope of the fitted straight line, which is obtained by using formula (11);

步骤302：在幅值的自然对数lnAij(t)随时间t变化图中，选取相应的时段利用最小二乘线性拟合方法得到相应的一条平均直线来近似表示该时段内lnAij(t)随t变化的关系，则由该拟合直线的斜率可得公式(12)中ξjωj的值；Step 302: In the graph of the natural logarithm lnA ij (t) of the amplitude versus time t, select a corresponding time period and use the least squares linear fitting method to obtain a corresponding average straight line to approximately represent lnA ij (t in this time period. ) changes with t, then the value of ξ j ω j in formula (12) can be obtained from the slope of the fitted straight line;

步骤303：根据由前两步中所得的ωdj和ξjωj的值，并利用已知关系式

Figure GDA0002053822170000091
则可得预测的结构模态频率值和阻尼比值。Step 303: According to the values of ω dj and ξ j ω j obtained in the previous two steps, and using the known relationship
Figure GDA0002053822170000091
Then the predicted structural modal frequency value and damping ratio can be obtained.

实施例：Example:

本发明的具体实施流程如图1所示。在图1中，外部激励的具体形式可为风荷载、地震荷载、爆炸荷载等。选用的具体实例为坐落于韩国首尔的一个超高层摩天大楼，乐天世界塔，如图2所示。该建筑总高555米，地上123层，地下6层，目前正在施工，预计于2016年底竣工。加速度传感器分别布置在地下第6层，地上第1层、24层、39层、64层和72层，总计34个传感器，具体位置详见图3。在图3(b)中：(1)显示了传感器的具体布置位置，分别为南侧(South)、北侧(North)以及中部(Center)；(2)显示了传感器的具体布置方位，分别为x、y和z向。在2015年4月2日晚间9时至10时，加速度信号被记录，采样周期为0.005(秒)，最大风速为14米/秒，风向为西南。The specific implementation process of the present invention is shown in FIG. 1 . In Fig. 1, the specific form of external excitation can be wind load, seismic load, explosion load and so on. The specific example chosen is a super high-rise skyscraper located in Seoul, South Korea, Lotte World Tower, as shown in Figure 2. The building has a total height of 555 meters, 123 floors above ground and 6 floors underground. It is currently under construction and is expected to be completed by the end of 2016. The acceleration sensors are arranged on the sixth underground floor, the first, 24, 39, 64 and 72 floors above ground, with a total of 34 sensors. The specific locations are shown in Figure 3. In Figure 3(b): (1) shows the specific arrangement positions of the sensors, which are the south side (South), the north side (North) and the center (Center) respectively; (2) shows the specific arrangement positions of the sensors, respectively for the x, y and z directions. From 9:00 pm to 10:00 pm on April 2, 2015, the acceleration signal was recorded with a sampling period of 0.005 (seconds), the maximum wind speed was 14 m/s, and the wind direction was southwest.

步骤1：利用离散同步挤压小波变换重构x方向前3阶模态分量。具体实现步骤为：Step 1: Reconstruct the first 3-order modal components in the x-direction using discrete synchro-extrusion wavelet transform. The specific implementation steps are:

(1)通过筛分各层信号，选用72层北侧位置沿x向布置的加速度传感器测试的数据，即图4(a)。采样点的数量取2048，则信号的分段时长为2048x0.005＝10.24(秒)，经分析，选用该位置传感器所测信号数据的最后10.24(秒)段作为用于参数识别的分析信号时段，即图4(b)。(1) By sifting the signals of each layer, select the test data of the acceleration sensor arranged along the x-direction on the north side of the 72nd floor, that is, Figure 4(a). The number of sampling points is 2048, then the segment duration of the signal is 2048x0.005=10.24 (seconds). After analysis, the last 10.24 (seconds) segment of the signal data measured by the position sensor is selected as the analysis signal period for parameter identification. , namely Figure 4(b).

(2)利用离散同步挤压小波变换过滤噪声后的测量信号的时间-频率带关系如图5所示。变换中的参数nv取32；硬门槛参数γ取1.48。(2) The time-frequency band relationship of the measurement signal after filtering the noise by discrete synchronous squeezing wavelet transform is shown in Fig. 5 . The parameter n v in the transformation is 32; the hard threshold parameter γ is 1.48.

(3)根据图5，设置相应3个带通滤波器，分别为0.1Hz＝ω1L<ω1<ω1U＝0.17Hz,0.3Hz＝ω1L<ω1<ω1U＝0.75Hz以及0.75Hz＝ω1L<ω1<ω1U＝1.7Hz，而后进行离散同步挤压小波逆变换，则可得到沿x方向的前3阶重构模态分量，具体见图6。(3) According to Fig. 5, set corresponding three band-pass filters, respectively 0.1Hz=ω 1L <ω 1 <ω 1U =0.17Hz, 0.3Hz=ω 1L <ω 1 <ω 1U =0.75Hz and 0.75Hz =ω 1L <ω 1 <ω 1U =1.7Hz, and then perform discrete synchronous squeeze wavelet inverse transform, the first three-order reconstructed modal components along the x direction can be obtained, see Figure 6 for details.

步骤2：利用希尔伯特变换得到相角θij(t)随时间t变化关系以及幅值的自然对数lnAij(t)随时间t变化关系。具体实现步骤为：Step 2: Use the Hilbert transform to obtain the variation relation of the phase angle θ ij (t) with time t and the variation relation of the natural logarithm lnA ij (t) of the amplitude with time t. The specific implementation steps are:

(1)利用公式(10)，得到相应重构模态分量的分析信号形式。(1) Using the formula (10), the analysis signal form of the corresponding reconstructed modal component is obtained.

(2)根据相应的分析信号，得到相角θij(t)随时间t变化关系图，即图7中相应虚线所示曲线。(2) According to the corresponding analysis signal, a graph of the variation of the phase angle θ ij (t) with time t is obtained, that is, the curve shown by the corresponding dotted line in FIG. 7 .

(3)根据相应的分析信号，得到幅值的自然对数lnAij(t)随时间t变化关系图，即图8中相应虚线所示曲线。(3) According to the corresponding analysis signal, obtain the relationship diagram of the natural logarithm lnA ij (t) of the amplitude with time t, that is, the curve shown by the corresponding dotted line in FIG. 8 .

步骤3：基于最小二乘线性拟合方法，准确预测该超高层结构沿x方向前3阶模态频率和阻尼比。具体实现步骤为：Step 3: Based on the least squares linear fitting method, accurately predict the first 3-order modal frequencies and damping ratios of the super high-rise structure along the x-direction. The specific implementation steps are:

(1)利用最小二乘线性拟合方法得到相应的一条平均直线来预测相角θij(t)随时间t变化的关系，即图7中相应实线所示直线，由该拟合直线的斜率可得预测的阻尼体系模态频率ωdj，即公式(11)的运用。(1) Use the least squares linear fitting method to obtain a corresponding average straight line to predict the relationship of the phase angle θ ij (t) with time t, that is, the straight line shown by the corresponding solid line in Fig. 7, from the fitted straight line The slope yields the predicted modal frequency ω dj of the damped system, ie the application of Equation (11).

(2)同理，选取相应的时段利用最小二乘线性拟合方法得到相应的一条平均直线来预测该时段内lnAij(t)随t变化的关系，即图8中相应实线所示直线，由该拟合直线的斜率可得公式(12)中ξjωj的值。(2) In the same way, select a corresponding time period and use the least squares linear fitting method to obtain a corresponding average straight line to predict the relationship between lnA ij (t) and t in this time period, that is, the straight line shown by the corresponding solid line in Figure 8 , the value of ξ j ω j in formula (12) can be obtained from the slope of the fitted straight line.

(3)根据由前两步中所得的ωdj和ξjωj的值，并利用已知关系式

Figure GDA0002053822170000101
则可得预测的结构模态频率值和阻尼比值，实际工程中，自振周期的表达形式更为工程师所接受，因而转变结构模态频率值为自振周期值，具体数值见表1。在表1中，本发明识别的自振周期值与有限元模型所得值进行了相应对比，以显示本发明所提方法的有效性。需要注意的是，所提的有限元模型所得自振周期值未考虑施工因素，因而并未进行相应阶段的调整。(3) According to the values of ω dj and ξ j ω j obtained in the previous two steps, and use the known relation
Figure GDA0002053822170000101
Then the predicted structural modal frequency value and damping ratio can be obtained. In actual engineering, the expression form of natural vibration period is more acceptable to engineers. Therefore, the modal frequency value of the transformed structure is the natural vibration period value. The specific values are shown in Table 1. In Table 1, the value of the natural vibration period identified by the present invention is compared with the value obtained by the finite element model to show the effectiveness of the method proposed by the present invention. It should be noted that the natural vibration period value obtained by the proposed finite element model does not consider the construction factors, so the corresponding stage adjustment is not carried out.

表1Table 1

Figure GDA0002053822170000111
Figure GDA0002053822170000111

以上所述，仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention.

Claims (2)

1. A method for identifying modal parameters of a super high-rise structure is characterized by comprising the following steps:
step 1: screening acceleration measurement signals of different structural layers, and selecting measurement signals containing main fundamental frequencies of the structure
Figure FDA0002548682590000011
Analysis was carried out with p ═ 1,2, …, nsRemoving the measurement signal according to the synchronous squeeze wavelet transform for the corresponding number of layers of the structureThen, based on the denoised measurement signal, the main modal components of the structure are decomposed and reconstructed, and then the measurement signal is expressed as:
Figure FDA0002548682590000012
wherein g is 1,2, …, ms，
Figure FDA0002548682590000013
Is the g-th main modal component, F, of the p-th layer acceleration measurement signal reconstructed after the synchronous extrusion wavelet decompositionp(t) is the noise and higher-order modal components filtered out of the p-th layer acceleration measurement signal;
step 2: constructing an analysis signal according to Hilbert transform, then obtaining a corresponding instantaneous phase angle and amplitude according to the analysis signal, and then preliminarily identifying the main frequency and the damping ratio of the structure by the derivative of the natural logarithm of the corresponding instantaneous phase angle and amplitude to time;
and step 3: performing smooth prediction on the primary frequency and the damping ratio of the primary identification according to a least square linear fitting method to obtain an accurate identification result;
the step 1 specifically comprises the following steps:
step 101: screening the measurement signals, the number of sampling points satisfying 2 to ensure the accuracy of the calculationnSelecting a measurement signal containing the main fundamental frequency of the structure for analysis;
step 102: for discrete wavelet transform of screened measuring signal, firstly defining measuring signal
Figure FDA0002548682590000014
Continuous Wavelet Transform (CWT), Wf(a,. is) is
Figure FDA0002548682590000015
Where ψ is a selected base wavelet function; a is a proportionality coefficient; "+" indicates convolution;
in the frequency domain space, wavelet transform Wf(a,. cndot.) is represented by
Figure FDA0002548682590000016
For an arbitrary position (a)j,tk) Here tkIs a scaling factor of any discrete time point and corresponding discrete time form
Figure FDA0002548682590000021
j＝1,2,…,LnvL is a non-negative integer, nvTo influence the parameters of the scaling factor, a Discrete Wavelet Transform (DWT) is calculated using the following formula, usually 32 or 64
Figure FDA0002548682590000022
In the formula (I), the compound is shown in the specification,nand
Figure FDA0002548682590000023
is the standard discrete Fourier Transform (Fourier Transform) and its inverse; "·" denotes a point multiplication;
Figure FDA0002548682590000024
λk2 pi k/n, k 0, …, n-1 being the sampling interval of the frequency domain space;
step 103: based on continuous wavelet transform coefficients, Wf(a,. cndot.) the corresponding real-valued frequency is obtained by the following equation
Figure FDA0002548682590000025
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000026
for effective noise filtering, a hard threshold parameter (gamma) is selected as
Figure FDA0002548682590000027
The MAD is a discrete wavelet coefficient of the matrix,
Figure FDA0002548682590000028
average absolute deviation of (d); blThe coefficient of increase related to the MAD is 1.2-1.7;
Figure FDA0002548682590000029
is the magnitude of the discrete wavelet coefficient;
from equation (6), the point where the amplitude of the discrete wavelet transform coefficient is smaller than γ is discarded to effectively filter the noise effect, and based on equation (5), the real-valued frequency based on the discrete wavelet transform is obtained as
Figure FDA00025486825900000210
In the formula (I), the compound is shown in the specification,
Figure FDA00025486825900000211
and is
Figure FDA00025486825900000212
k＝0,…,n-1；
Step 104: based on the results obtained from equations (4) and (7)
Figure FDA00025486825900000213
And
Figure FDA00025486825900000214
defining de-noised acceleration signals
Figure FDA00025486825900000215
Discrete synchronous extrusion ofWavelet transform
Figure FDA00025486825900000216
In the formula, the frequency of two divisions omegalSatisfies the conditions
Figure FDA0002548682590000031
Step 105: set corresponding msThe acceleration signal is denoised by a band-pass filter and then a discrete synchronous extrusion wavelet inverse transformation
Figure FDA0002548682590000032
Can be reconstructed as
Figure FDA0002548682590000033
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000034
is a normalization constant;
the step 2 specifically comprises the following steps:
step 201: for each modal component reconstructed by discrete simultaneous wavelet transform, i.e. the modal component obtained by equation (9), the analytical signal form of the corresponding g-th order modal component is obtained based on Hilbert transform
Figure FDA0002548682590000035
In the formula, Apg(t) is related to the frequency ωgThe amplitude of the corresponding reconstructed modal component at time t; thetapg(t) is the phase angle at the respective time instant;
step 202: based on equation (10), the transient frequency and damping ratio of the structure are obtained from the following equations
Figure FDA0002548682590000036
Figure FDA0002548682590000037
In the formula (I), the compound is shown in the specification,
Figure FDA0002548682590000038
the damping system modal frequency is a g-order modal;
the step 3 specifically comprises the following steps:
step 301: at a phase angle thetapg(t) in the time t-dependent change diagram, obtaining a corresponding average straight line according to a least square linear fitting method to approximately represent the phase angle thetapg(t) the relation of the change along with the time t, and the predicted modal frequency omega of the damping system can be obtained by the slope of the fitting straight linedgNamely, obtained by using formula (11);
step 302: natural logarithm at amplitude lnApg(t) in the time t-dependent graph, selecting a corresponding time interval, and obtaining a corresponding average straight line by using a least square linear fitting method to approximately represent lnA in the time intervalpg(t) as a function of t, the slope of the fitted line can be used to derive ξ in equation (12)gωgA value of (d);
step 303: according to ω obtained from the first two stepsdgAnd ξgωgAnd using a known relationship
Figure FDA0002548682590000041
The predicted structural modal frequency value and damping ratio value can be obtained.
2. The method for identifying modal parameters of super high-rise structure according to claim 1, wherein n is a positive integer and n is 10 or 11, i.e. the number of points used is 1024 or 2048.
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