CN117473263A - A method and system for automatic identification of frequency and damping ratio for bridge vibration monitoring - Google Patents

A method and system for automatic identification of frequency and damping ratio for bridge vibration monitoring Download PDF

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CN117473263A
CN117473263A CN202311478266.2A CN202311478266A CN117473263A CN 117473263 A CN117473263 A CN 117473263A CN 202311478266 A CN202311478266 A CN 202311478266A CN 117473263 A CN117473263 A CN 117473263A
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张尧
陈思佳
陈志为
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Xiamen University
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Abstract

A frequency and damping ratio automatic identification method and system for bridge vibration monitoring comprises the following steps: s1, carrying out Fourier transformation on actual monitoring data of a bridge to obtain approximate first-order self-vibration frequency of the bridge, and constructing a free damping vibration signal of a damped single-degree-of-freedom spring vibrator by setting an initial damping ratio; s2, positioning and screening out a plurality of signals with the highest degree of correlation with the constructed free damping vibration signals in the actual monitoring data by using a cross-correlation function; s3, dividing the screened first plurality of segments of signals into single-frequency free damping vibration signals and multi-frequency free damping vibration signals according to frequency spectrum analysis, and respectively calculating the single-frequency free damping vibration signals and the multi-frequency free damping vibration signals to obtain frequency and damping ratios. The invention has the advantages of wide applicability, high identification precision, high working efficiency and no need of priori information.

Description

一种桥梁振动监测的频率与阻尼比自动识别方法和系统A method and system for automatic identification of frequency and damping ratio for bridge vibration monitoring

技术领域Technical field

本发明涉及桥梁健康监测领域,特别是指一种桥梁振动监测的频率与阻尼比自动识别方法和系统。The invention relates to the field of bridge health monitoring, and in particular to a method and system for automatic identification of frequency and damping ratio for bridge vibration monitoring.

背景技术Background technique

频率与阻尼比是桥梁结构的重要模态参数,反映了桥梁的整体安全水平,在桥梁健康监测中发挥了重要的作用。桥梁频率通常由傅里叶变换得到。然而,由于通行车辆的影响,频率的测量往往会出现一定的误差。另一方面,如何根据监测数据对阻尼比进行准确估计仍然是一个挑战。Frequency and damping ratio are important modal parameters of the bridge structure, which reflect the overall safety level of the bridge and play an important role in bridge health monitoring. The bridge frequency is usually obtained from the Fourier transform. However, due to the influence of passing vehicles, certain errors often occur in frequency measurement. On the other hand, how to accurately estimate the damping ratio based on monitoring data remains a challenge.

阻尼比的计算方法一般有半功率带宽法、指数衰减法(EA)、随机子空间辨识法(SSI)、特征系统实现算法(ERA)、具有外源输入的自回归模型、频域分解、子空间状态空间辨识数值算法、连续小波变换等。在这些方法中,EA方法通常被认为是一个相对可靠和准确的方法。然而,该方法需要结构自由振动响应,因此只能用于可以施加可控激励的振动试验,如下落的重量以及跳跃的卡车。The calculation methods of damping ratio generally include half-power bandwidth method, exponential decay method (EA), stochastic subspace identification method (SSI), eigensystem implementation algorithm (ERA), autoregressive model with external source input, frequency domain decomposition, subspace Numerical algorithm for spatial state space identification, continuous wavelet transform, etc. Among these methods, the EA method is generally considered to be a relatively reliable and accurate method. However, this method requires a free vibration response of the structure and therefore can only be used for vibration tests where controlled excitation can be applied, such as falling weights and jumping trucks.

事实上,在桥梁的日常运行过程中,桥梁所受到的激励通常是桥上的车流带来的。这是一种典型的非平稳随机激励。桥梁在随机车流作用下往往不会产生自由振动。而桥梁周边车流通过土壤结构耦合作用传递的激励可以近似认为是脉冲激励,即作用在桥梁上的时间相比桥梁振动响应的时间可以忽略。桥梁在此激励的作用下,会产生明显的自由衰减振动。如果无法从桥梁的监测数据中找到类似的自由衰减振动信号,就很难准确提取出桥梁的阻尼比和频率。然而,通过人工的方式从大量数据中手动提取这样的响应是不切实际的。In fact, during the daily operation of the bridge, the stimulation received by the bridge is usually brought by the traffic flow on the bridge. This is a typical non-stationary random excitation. Bridges often do not vibrate freely under the action of random traffic flow. The excitation transmitted by the traffic flow around the bridge through the coupling effect of the soil structure can be approximately considered as pulse excitation, that is, the time acting on the bridge can be ignored compared to the time of the bridge vibration response. Under the influence of this excitation, the bridge will produce obvious free attenuation vibration. If similar free attenuation vibration signals cannot be found from the monitoring data of the bridge, it will be difficult to accurately extract the damping ratio and frequency of the bridge. However, it is impractical to manually extract such responses from large amounts of data.

因此,从桥梁的监测数据中识别桥梁的频率与阻尼比还存在着技术难题。Therefore, there are still technical difficulties in identifying the frequency and damping ratio of the bridge from the bridge monitoring data.

发明内容Contents of the invention

本发明的主要目的在于克服现有技术中的上述缺陷,提出一种桥梁振动监测的频率与阻尼比自动识别方法和系统,具有适用性广、识别精度高、工作效率高且无需先验信息的优点。The main purpose of the present invention is to overcome the above-mentioned defects in the prior art and propose a method and system for automatic identification of frequency and damping ratio for bridge vibration monitoring, which has wide applicability, high identification accuracy, high work efficiency and does not require prior information. advantage.

本发明采用如下技术方案:The present invention adopts the following technical solutions:

一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,包括:An automatic identification method of frequency and damping ratio for bridge vibration monitoring, which is characterized by including:

S1,对桥梁的实际监测数据进行傅里叶变换,得到近似的桥梁一阶自振频率,拟定初始阻尼比并构造有阻尼的单自由度弹簧振子的自由衰减振动信号;S1, perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, formulate the initial damping ratio and construct the free attenuation vibration signal of the damped single-degree-of-freedom spring oscillator;

S2,利用互相关函数定位筛选出所述实际监测数据中与构造的所述自由衰减振动信号之间的相关性程度最大的所述前若干段信号;S2, use the cross-correlation function to locate and filter out the first several segments of signals in the actual monitoring data that have the greatest degree of correlation with the constructed free attenuation vibration signal;

S3,根据频谱分析将筛选出的所述前若干段信号分为单频自由衰减振动信号与多频自由衰减振动信号,对于所述单频自由衰减振动信号和所述多频自由衰减振动信号分别计算得到频率和阻尼比;S3. According to spectrum analysis, the first several segments of the screened signals are divided into single-frequency free attenuation vibration signals and multi-frequency free attenuation vibration signals. For the single-frequency free attenuation vibration signal and the multi-frequency free attenuation vibration signal, respectively Calculate the frequency and damping ratio;

S4,将所述前若干段信号的频率和阻尼绘制成频率-阻尼散点图,并分别对计算得到的所述频率和阻尼比分别取平均数得到最终识别结果。S4, draw the frequency and damping of the first several segments of signals into a frequency-damping scatter plot, and average the calculated frequencies and damping ratios to obtain the final identification result.

步骤S1中具体包括:Step S1 specifically includes:

对实际监测数据进行预处理;Preprocess actual monitoring data;

将经过预处理的实际监测数据的加速度信号定义为X(t),加速度信号X(t)是采样频率为fs、采样时间为TX的时间序列,其信号长度为LX,LX=fsTX The acceleration signal of the preprocessed actual monitoring data is defined as X(t). The acceleration signal X(t) is a time series with a sampling frequency of f s and a sampling time of T f s T X ;

对X(t)进行傅里叶变换:Perform Fourier transform on X(t):

其中,e是自然对数,i是虚数单位,ω是圆频率;Among them, e is the natural logarithm, i is the imaginary unit, and ω is the circular frequency;

通过峰值拾取判断频谱中最高峰的位置,得到近似的桥梁一阶自振频率 Determine the position of the highest peak in the spectrum through peak picking, and obtain the approximate first-order natural frequency of the bridge.

拟定初始阻尼比并构造有阻尼单自由度弹簧振子的自由衰减振动的信号Y(t):Proposed initial damping ratio And construct the signal Y(t) of the free attenuated vibration of the damped single-degree-of-freedom spring oscillator:

信号Y(t)是采样频率同为fs、采样时间为TY的时间序列,其信号长度为LY,LY=fsTYSignal Y(t) is a time series with the same sampling frequency f s and sampling time TY . Its signal length is LY , and LY =f s TY .

所述预处理包括:The preprocessing includes:

首先,对所述实际监测数据进行去除趋势项处理以去除原始信号中的偏移量;First, perform detrend processing on the actual monitoring data to remove the offset in the original signal;

其次,对所述实际监测数据进行低通滤波减少测量噪声的干扰。Secondly, low-pass filtering is performed on the actual monitoring data to reduce the interference of measurement noise.

步骤S2中具体包括:Step S2 specifically includes:

计算所述加速度信号X(t)与所述自由衰减振动的信号Y(t)的互相关函数:Calculate the cross-correlation function of the acceleration signal X(t) and the free attenuated vibration signal Y(t):

由此得到信号X(t)与Y(t)之间的相关性向量并同时得到相关性的滞后索引向量/> From this, the correlation vector between signals X(t) and Y(t) is obtained And at the same time get the lagged index vector of the correlation/>

取相关性向量R中绝对值最大的前k个值,并在滞后索引向量L中找到其对应的位置索引,筛选出所述实际监测数据与构造的所述自由衰减振动信号之间的相关性程度最大的前k段信号,X1(t),X2(t),……,Xk(t)。Take the top k values with the largest absolute values in the correlation vector R, find their corresponding position index in the lag index vector L, and filter out the correlation between the actual monitoring data and the constructed free attenuation vibration signal. The first k-segment signals with the largest degree, X 1 (t), X 2 (t), ..., X k (t).

步骤S3中具体包括:Step S3 specifically includes:

对所述前若干段信号X1(t),X2(t),……,Xk(t)进行傅里叶变换:Perform Fourier transform on the first several segments of signals X 1 (t), X 2 (t),..., X k (t):

其中,e是自然对数,i是虚数单位,ω是圆频率,k的取值范围10-30;Among them, e is the natural logarithm, i is the imaginary unit, ω is the circular frequency, and the value range of k is 10-30;

通过峰值拾取得到每个频谱中的高峰,其中,峰值大于初始设定阈值的记为有效高峰;有效高峰数为1的信号为所述单频自由衰减振动信号,有效高峰数大于1的信号为所述多频自由衰减振动信号。Peak peaks in each spectrum are obtained through peak picking, where the peak value greater than the initial set threshold is recorded as a valid peak value; a signal with a valid peak number of 1 is the single-frequency free attenuation vibration signal, and a signal with a valid peak number greater than 1 is The multi-frequency freely attenuates vibration signals.

步骤S3中,对于所述单频自由衰减振动信号直接利用指数衰减法计算得到频率和阻尼比,通过峰值拾取得到信号中的波峰值Am及其对应的时间tm和序号m,将波峰值的对数与其对应的序号通过最小二乘法进行线性拟合,得到:In step S3, for the single-frequency free attenuation vibration signal, the frequency and damping ratio are directly calculated using the exponential decay method, and the wave peak value A m in the signal and its corresponding time t m and sequence number m are obtained through peak picking, and the wave peak value is obtained The logarithm of and its corresponding serial number are linearly fitted by the least squares method to obtain:

lnA=a·n+blnA=a·n+b

其中,lnA为波峰对数值,n为波数,Among them, lnA is the logarithmic value of the wave crest, n is the wave number,

其中,M为所述单频自由衰减振动信号的总波数;Where, M is the total wave number of the single-frequency free attenuated vibration signal;

计算阻尼比:Calculate damping ratio:

计算频率:Calculate frequency:

步骤S3中,对于所述多频自由衰减振动信号,通过变分非线性分量分解方法将该信号分解为多个单频自由衰减振动信号,对每个所述单频自由衰减振动信号利用指数衰减法计算各自的频率和阻尼比。In step S3, for the multi-frequency free attenuating vibration signal, the signal is decomposed into multiple single-frequency free attenuating vibration signals through a variational nonlinear component decomposition method, and exponential attenuation is used for each of the single-frequency free attenuating vibration signals. method to calculate their respective frequencies and damping ratios.

一种桥梁振动监测的频率与阻尼比自动识别系统,其特征在于,包括:An automatic identification system of frequency and damping ratio for bridge vibration monitoring, which is characterized by including:

加速度传感器,安装于桥梁的主梁的下方,用于将桥梁的振动加速度转换为电压信号,从而测量桥梁的振动加速度;The acceleration sensor is installed under the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal to measure the vibration acceleration of the bridge;

信号采集模块,接收采集加速计传来的电压信号,并将其从模拟信号转换为数字信号,然后记录下信号;The signal acquisition module receives and collects the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal;

相关性分析模块,接收信号采集模块记录的时程信号,利用互相关函数筛选出信号中的自由衰减振动信号;The correlation analysis module receives the time course signal recorded by the signal acquisition module, and uses the cross-correlation function to filter out the free attenuation vibration signal in the signal;

时频分析模块,接收相关性分析模块输出的自由衰减振动信号,利用傅里叶变换将自由衰减振动信号分为单频自由衰减振动信号与多频自由衰减振动信号,再利用变分非线性分量分解将多频自由衰减振动信号分解为多个单频自由衰减振动信号;The time-frequency analysis module receives the free attenuation vibration signal output from the correlation analysis module, uses Fourier transform to divide the free attenuation vibration signal into a single-frequency free attenuation vibration signal and a multi-frequency free attenuation vibration signal, and then uses the variational nonlinear component Decompose the multi-frequency free attenuation vibration signal into multiple single-frequency free attenuation vibration signals;

线性拟合模块,接收时频分析模块输出的单频自由衰减振动信号,利用线性拟合计算桥梁的频率与阻尼。The linear fitting module receives the single-frequency free attenuation vibration signal output from the time-frequency analysis module, and uses linear fitting to calculate the frequency and damping of the bridge.

由上述对本发明的描述可知,与现有技术相比,本发明具有如下有益效果:From the above description of the present invention, it can be seen that compared with the prior art, the present invention has the following beneficial effects:

1、本发明可以实现从实测信号中自由衰减信号提取到阻尼比识别的全过程自动识别,在无需人工筛选信号段建立数据库的情况下实现自动识别,可以很好地应用于实时、连续信号处理,在桥梁健康检测中具有广阔的应用前景。1. The present invention can realize automatic identification of the entire process from free attenuation signal extraction to damping ratio identification in measured signals. It can realize automatic identification without manually screening signal segments to establish a database, and can be well applied to real-time and continuous signal processing. , which has broad application prospects in bridge health detection.

2、本发明同传统的阻尼识别方法相比,基于实际信号进行傅里叶变换得到的结构自振频率构造的有阻尼单自由衰减信号,对实测信号中自由衰减信号振动形式不敏感,具有强大的鲁棒性,较适用于在运营环境下工作。2. Compared with the traditional damping identification method, the present invention constructs a damped single free attenuation signal based on the natural vibration frequency of the structure obtained by Fourier transformation of the actual signal. It is insensitive to the vibration form of the free attenuation signal in the actual measured signal and has powerful The robustness makes it more suitable for working in operational environments.

附图说明Description of the drawings

图1为本发明方法流程图;Figure 1 is a flow chart of the method of the present invention;

图2为某桥某一分布测点的加速度时程响应曲线;Figure 2 shows the acceleration time history response curve of a certain distributed measuring point on a certain bridge;

图3为构造的有阻尼的单自由度弹簧振子的自由衰减振动的信号;Figure 3 shows the free attenuated vibration signal of the constructed damped single-degree-of-freedom spring oscillator;

图4为03B0105分布测点的实际监测数据与构造的衰减信号之间的相关系数;Figure 4 shows the correlation coefficient between the actual monitoring data of the 03B0105 distributed measuring points and the constructed attenuation signal;

图5为03B0105分布测点的实际监测数据与识别出的衰减段示意图;Figure 5 is a schematic diagram of the actual monitoring data of the 03B0105 distributed measuring points and the identified attenuation section;

图6为阻尼比计算过程;Figure 6 shows the damping ratio calculation process;

图7为03B0105分布测点频率-阻尼比散点分布及其平均值示意图;Figure 7 is a schematic diagram of the frequency-damping ratio scatter distribution and its average value of the 03B0105 distribution measuring points;

图8为03B0114分布测点的实测信号与构造的衰减信号之间的相关系数;Figure 8 shows the correlation coefficient between the measured signal at the 03B0114 distributed measuring point and the constructed attenuated signal;

图9为03B0114分布测点的实测信号与识别出的衰减段示意图;Figure 9 is a schematic diagram of the measured signal and the identified attenuation section of 03B0114 distributed measuring points;

图10为信号分解示意图;Figure 10 is a schematic diagram of signal decomposition;

图11为阻尼比计算过程;Figure 11 shows the damping ratio calculation process;

图12为为一阶频率-阻尼比、二阶频率-阻尼比散点分布及其平均值示意图。Figure 12 is a schematic diagram of the first-order frequency-damping ratio, second-order frequency-damping ratio scatter distribution and their average value.

以下结合附图和具体实施例对本发明作进一步详述。The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

具体实施方式Detailed ways

以下通过具体实施方式对本发明作进一步的描述。The present invention will be further described below through specific embodiments.

下面将结合所附带的图示以及具体的实施算例,对本发明进行更为深入和详细的描述。这些附图和实施算例将为读者提供一个更加直观的认识,使得本发明的结构、工作原理及应用场景能够被更为清晰地呈现和理解。The present invention will be described in more depth and detail below with reference to the accompanying diagrams and specific implementation examples. These drawings and implementation examples will provide readers with a more intuitive understanding, so that the structure, working principle and application scenarios of the present invention can be more clearly presented and understood.

参见图1,一种桥梁振动监测的频率与阻尼比自动识别方法,包括:Referring to Figure 1, an automatic identification method of frequency and damping ratio for bridge vibration monitoring includes:

S1,对桥梁的实际监测数据进行傅里叶变换,得到近似的桥梁一阶自振频率,拟定初始阻尼比并构造有阻尼的单自由度弹簧振子的自由衰减振动信号。S1, perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, formulate the initial damping ratio and construct the free attenuation vibration signal of the damped single-degree-of-freedom spring oscillator.

该步骤具体包括:This step specifically includes:

先对实际监测数据进行预处理。预处理包括:首先,对实际监测数据进行去除趋势项处理以去除原始信号中的偏移量;其次,对实际监测数据进行低通滤波减少测量噪声的干扰。First, preprocess the actual monitoring data. Preprocessing includes: first, detrending the actual monitoring data to remove the offset in the original signal; second, performing low-pass filtering on the actual monitoring data to reduce the interference of measurement noise.

将经过预处理的实际监测数据的加速度信号定义为X(t),信号X(t)是采样频率为fs、采样时间为TX的时间序列,其信号长度为LX,LX=fsTX The acceleration signal of the preprocessed actual monitoring data is defined as X(t). The signal X(t) is a time series with a sampling frequency of f s and a sampling time of TX . Its signal length is L s T X ;

对X(t)进行傅里叶变换:Perform Fourier transform on X(t):

其中,e是自然对数,i是虚数单位,ω是圆频率。Among them, e is the natural logarithm, i is the imaginary unit, and ω is the circular frequency.

通过峰值拾取判断频谱中最高峰的位置,得到近似的桥梁一阶自振频率 Determine the position of the highest peak in the spectrum through peak picking, and obtain the approximate first-order natural frequency of the bridge.

拟定初始阻尼比并构造有阻尼单自由度弹簧振子的自由衰减振动的信号Y(t):Proposed initial damping ratio And construct the signal Y(t) of the free attenuated vibration of the damped single-degree-of-freedom spring oscillator:

信号Y(t)是采样频率同为fs、采样时间为TY(推荐时长为桥梁近似一阶周期的10倍至20倍)的时间序列,其信号长度为LY,LY=fsTYSignal Y(t) is a time series with the same sampling frequency f s and sampling time T Y (the recommended duration is 10 to 20 times the approximate first-order period of the bridge). Its signal length is LY , LY = f s TY .

S2,利用互相关函数定位筛选出实际监测数据中与构造的自由衰减振动信号之间的相关性程度最大的前若干段信号。具体包括:S2, use the cross-correlation function to locate and screen out the first few signals in the actual monitoring data that have the greatest correlation with the constructed free attenuation vibration signal. Specifically include:

计算加速度信号X(t)与自由衰减振动的信号Y(t)的互相关函数:Calculate the cross-correlation function between the acceleration signal X(t) and the free attenuated vibration signal Y(t):

由此得到信号X(t)与Y(t)之间的相关性向量并同时得到相关性的滞后索引向量/> From this, the correlation vector between signals X(t) and Y(t) is obtained And at the same time get the lagged index vector of the correlation/>

取相关性向量R中绝对值最大的前k个值,并在滞后索引向量L中找到其对应的位置索引,筛选出实际监测数据与构造的自由衰减振动信号之间的相关性程度最大的前k段信号,X1(t),X2(t),……,Xk(t)。Take the top k values with the largest absolute value in the correlation vector R, find their corresponding position index in the lag index vector L, and filter out the top k values with the largest degree of correlation between the actual monitoring data and the constructed free attenuation vibration signal. K-segment signal, X 1 (t), X 2 (t), ..., X k (t).

S3,根据频谱分析将筛选出的前若干段信号分为单频自由衰减振动信号与多频自由衰减振动信号,对于单频自由衰减振动信号和多频自由衰减振动信号分别计算得到频率和阻尼比;S3, according to the spectrum analysis, the first few selected signals are divided into single-frequency free attenuation vibration signals and multi-frequency free attenuation vibration signals. For the single-frequency free attenuation vibration signals and multi-frequency free attenuation vibration signals, the frequencies and damping ratios are calculated respectively. ;

具体包括:Specifically include:

对前若干段信号X1(t),X2(t),……,Xk(t)进行傅里叶变换:Perform Fourier transform on the first several segments of signals X 1 (t), X 2 (t),..., X k (t):

其中,e是自然对数,i是虚数单位,ω是圆频率。k的取值范围10~30。Among them, e is the natural logarithm, i is the imaginary unit, and ω is the circular frequency. The value of k ranges from 10 to 30.

通过峰值拾取得到每个频谱中的高峰,其中,峰值大于初始设定阈值的记为有效高峰;有效高峰数为1的信号为单频自由衰减振动信号,有效高峰数大于1的信号为多频自由衰减振动信号。Peak peaks in each spectrum are obtained through peak picking. The peak value greater than the initial set threshold is recorded as a valid peak value; a signal with a valid peak number of 1 is a single-frequency free attenuation vibration signal, and a signal with a valid peak number greater than 1 is a multi-frequency signal. Freely attenuates vibration signals.

对于单频自由衰减振动信号直接利用指数衰减法计算得到频率和阻尼比,通过峰值拾取得到信号中的波峰值Am及其对应的时间tm和序号m,将波峰值的对数与其对应的序号通过最小二乘法进行线性拟合,得到:For single-frequency free attenuation vibration signals, the frequency and damping ratio are directly calculated using the exponential decay method. The peak value A m in the signal and its corresponding time t m and sequence number m are obtained through peak picking. The logarithm of the wave peak value and its corresponding The serial number is linearly fitted by the least squares method to obtain:

lnA=a·n+blnA=a·n+b

其中,lnA为波峰对数值,n为波数,Among them, lnA is the logarithmic value of the wave crest, n is the wave number,

其中,M为单频自由衰减振动信号的总波数;Among them, M is the total wave number of single-frequency free attenuation vibration signal;

计算阻尼比:Calculate damping ratio:

计算频率:Calculate frequency:

对于多频自由衰减振动信号,通过变分非线性分量分解方法将该信号分解为多个单频自由衰减振动信号,再对每个单频自由衰减振动信号利用指数衰减法计算各自的频率和阻尼比。For multi-frequency free attenuated vibration signals, the signal is decomposed into multiple single-frequency free attenuated vibration signals through the variational nonlinear component decomposition method, and then the exponential decay method is used to calculate the respective frequency and damping of each single-frequency free attenuated vibration signal. Compare.

S4,将前若干段信号的频率和阻尼绘制成频率-阻尼散点图,并分别对计算得到的频率和阻尼比分别取平均数得到最终识别结果。S4, draw the frequency and damping of the first several segments of the signal into a frequency-damping scatter plot, and average the calculated frequency and damping ratio to obtain the final identification result.

基于此,本发明还提出一种桥梁振动监测的频率与阻尼比自动识别系统,包括:Based on this, the present invention also proposes an automatic identification system of frequency and damping ratio for bridge vibration monitoring, including:

加速度传感器,安装于桥梁的主梁的下方,用于将桥梁的振动加速度转换为电压信号,从而测量桥梁的振动加速度;The acceleration sensor is installed under the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal to measure the vibration acceleration of the bridge;

信号采集模块,接收采集加速计传来的电压信号,并将其从模拟信号转换为数字信号,然后记录下信号;The signal acquisition module receives and collects the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal;

相关性分析模块,接收信号采集模块记录的时程信号,利用互相关函数筛选出信号中的自由衰减振动信号;The correlation analysis module receives the time course signal recorded by the signal acquisition module, and uses the cross-correlation function to filter out the free attenuation vibration signal in the signal;

时频分析模块,接收相关性分析模块输出的自由衰减振动信号,利用傅里叶变换将自由衰减振动信号分为单频自由衰减振动信号与多频自由衰减振动信号,再利用变分非线性分量分解将多频自由衰减振动信号分解为多个单频自由衰减振动信号;The time-frequency analysis module receives the free attenuation vibration signal output from the correlation analysis module, uses Fourier transform to divide the free attenuation vibration signal into a single-frequency free attenuation vibration signal and a multi-frequency free attenuation vibration signal, and then uses the variational nonlinear component Decompose the multi-frequency free attenuation vibration signal into multiple single-frequency free attenuation vibration signals;

线性拟合模块,接收时频分析模块输出的单频自由衰减振动信号,利用线性拟合计算桥梁的频率与阻尼。The linear fitting module receives the single-frequency free attenuation vibration signal output from the time-frequency analysis module, and uses linear fitting to calculate the frequency and damping of the bridge.

本发明的系统采用上述的一种桥梁振动监测的频率与阻尼比自动识别方法,将前若干段信号的频率和阻尼绘制成频率-阻尼散点图,并分别对计算得到的频率和阻尼比分别取平均数得到最终识别结果。The system of the present invention adopts the above-mentioned automatic identification method of frequency and damping ratio for bridge vibration monitoring, draws the frequency and damping of the first several segments of signals into frequency-damping scatter diagrams, and compares the calculated frequencies and damping ratios respectively. The average is taken to obtain the final recognition result.

本发明能够实现从结构振动监测信号中自动提取桥梁的低阶频率与阻尼比,具有适用性广、识别精度高、工作效率高且无需先验信息的优点,在桥梁健康检测中具有广阔的应用前景。The invention can automatically extract the low-order frequency and damping ratio of the bridge from the structural vibration monitoring signal. It has the advantages of wide applicability, high recognition accuracy, high work efficiency and no need for prior information, and has broad applications in bridge health detection. prospect.

应用举例Application examples

以某Z24桥为例,其为一座经典的后张拉预应力混凝土双单元箱梁桥,主跨为30米,两侧跨度为14米。对桥梁进行了持续近一年的监测,在监测后期逐步施加了人工可控的损伤。研究人员以Z24桥为土木工程系统的工程背景,确定了研究课题SIMCES,建立了Z24桥梁的基准问题,研究了健康监测领域的一系列问题,包括固有频率、振型、桥梁损伤下的阻尼比以及环境因素引起的结构模态参数变换,Z24桥成为了很多学者研究桥梁健康监测的基桥。因此,选择该桥作为试验的研究对象具有很强的现实意义。Take a certain Z24 bridge as an example. It is a classic post-tensioned prestressed concrete double-unit box girder bridge with a main span of 30 meters and a span of 14 meters on both sides. The bridge was monitored for nearly a year, and artificially controllable damage was gradually applied during the later stages of the monitoring period. Taking the Z24 bridge as the engineering background of civil engineering systems, the researchers determined the research topic SIMCES, established the benchmark problem of the Z24 bridge, and studied a series of issues in the field of health monitoring, including natural frequencies, vibration shapes, and damping ratios under bridge damage. As well as the transformation of structural modal parameters caused by environmental factors, the Z24 bridge has become the foundation bridge for many scholars to study bridge health monitoring. Therefore, choosing this bridge as the research object of the experiment has strong practical significance.

某Z24桥监测分为9个分布,每个分布有33个通道,其中28个通道位于桥面上,5个固定通道为参考点,其中3个参考点通道位于桥面,2个测试通道位于桥墩。某Z24桥传感器以100Hz的采样率采集了65536个样本,将SVS网站提供的bin格式数据在MATLAB中转换为mat格式后,可得到Z24桥某一分布测点的加速度时程响应曲线,如图2所示。在环境激励下,振动信号存在许多典型的自由衰减信号。值得一提的是,用于识别的实测数据无需多个测点,单一加速度传感器采集的监测数据即可用于此方法进行识别,因此采用此方法的自动识别技术正好可以避免安装多个传感器的缺陷。The monitoring of a Z24 bridge is divided into 9 distributions, each distribution has 33 channels, of which 28 channels are located on the bridge deck, 5 fixed channels are reference points, 3 reference point channels are located on the bridge deck, and 2 test channels are located on the bridge deck. pier. A Z24 bridge sensor collected 65536 samples at a sampling rate of 100Hz. After converting the bin format data provided by the SVS website into mat format in MATLAB, the acceleration time history response curve of a distributed measuring point of the Z24 bridge can be obtained, as shown in the figure 2 shown. Under environmental excitation, there are many typical free attenuation signals in vibration signals. It is worth mentioning that the measured data used for identification does not require multiple measurement points. The monitoring data collected by a single acceleration sensor can be used for identification by this method. Therefore, the automatic identification technology using this method can avoid the disadvantages of installing multiple sensors. .

首先,对实际监测数据进行傅里叶变换,得到近似的桥梁一阶自振频率,拟定初始阻尼比,构造有阻尼的单自由度弹簧振子自由衰减振动的信号。图3显示了构造的有阻尼自由衰减时程曲线。First, Fourier transform is performed on the actual monitoring data to obtain the approximate first-order natural frequency of the bridge, the initial damping ratio is formulated, and the free attenuated vibration signal of the damped single-degree-of-freedom spring oscillator is constructed. Figure 3 shows the constructed damped free decay time history curve.

接下来,利用互相关函数确定实测信号中与构造的自由衰减振动信号之间的相关性系数,如图4所示,并利用两者信号之间的相关性大小定位筛选处最大的前若干段信号,结果显示如图5所示。Next, the cross-correlation function is used to determine the correlation coefficient between the measured signal and the constructed free attenuation vibration signal, as shown in Figure 4, and the correlation between the two signals is used to locate the largest first few segments at the screening point. signal, and the result is shown in Figure 5.

最后,进一步筛选,根据频谱分析将筛选出的前若干段信号分为单频自由衰减振动信号与多频自由衰减振动信号。通过峰值拾取得到每个频谱中的峰值,其中,峰值大于初始设定阈值的记为有效高峰。有效高峰数为1的信号为单频自由衰减振动信号,有效高峰数大于1的信号为多频自由衰减振动信号。Finally, further screening is performed, and the first few selected signals are divided into single-frequency free attenuation vibration signals and multi-frequency free attenuation vibration signals based on spectrum analysis. The peak value in each spectrum is obtained through peak picking, where the peak value greater than the initial set threshold is recorded as a valid peak value. A signal with an effective peak number of 1 is a single-frequency free attenuation vibration signal, and a signal with an effective peak number greater than 1 is a multi-frequency free attenuation vibration signal.

对于单频信号,直接利用傅里叶变换和指数衰减法得到阻尼比和频率,将波峰值的对数与其对应的序号通过最小二乘法进行线性拟合,如图6所示,其中(a)为某一提取衰减段,(b)为峰值对数值与波数线性拟合。进一步,计算阻尼比和频率,结果如图7所示分布测点频率-阻尼比散点分布及其平均值(★)。由于此实例中,原始数据中只含有一阶自由衰减振动信号,从实测数据中提取出的衰减段进行傅里叶变换后只能得到一阶频率。将本发明提出的自动识别结果与基于参考的组合确定性-随机子空间和基于DBSCAN识别的固有频率和阻尼比进行比较,如表1所示。For single-frequency signals, the damping ratio and frequency are obtained directly using Fourier transform and exponential decay method, and the logarithm of the wave peak value and its corresponding serial number are linearly fitted by the least squares method, as shown in Figure 6, where (a) is a certain extracted attenuation section, (b) is the linear fitting of peak logarithm value and wave number. Further, the damping ratio and frequency are calculated, and the results are shown in Figure 7. The distribution of measuring point frequency-damping ratio scatter point distribution and its average value (★). Since in this example, the original data only contains the first-order free attenuation vibration signal, only the first-order frequency can be obtained after Fourier transform of the attenuation segment extracted from the measured data. The automatic identification results proposed by the present invention are compared with the natural frequencies and damping ratios of the reference-based combined deterministic-random subspace and DBSCAN-based identification, as shown in Table 1.

表1Table 1

为了进一步测试,该方法也可运用于多频自由衰减振动信号阻尼比的识别,选取Z24桥某个时刻通道5的加速度数据(03B0114),还是利用如图3构造的有阻尼的单自由度自由衰减振动的信号来定位筛选实测信号中的自由衰减信号。For further testing, this method can also be used to identify the damping ratio of multi-frequency free attenuated vibration signals. Select the acceleration data of channel 5 of the Z24 bridge at a certain moment (03B0114), or use the damped single degree of freedom constructed as shown in Figure 3. The attenuated vibration signal is used to locate and screen the free attenuated signal in the measured signal.

接下来,利用互相关函数确定实测信号中与构造的自由衰减振动信号之间的相关性系数,如图8所示,并利用两者信号之间的相关性大小定位筛选处最大的前若干段信号,结果显示如图9所示。Next, the cross-correlation function is used to determine the correlation coefficient between the measured signal and the constructed free attenuation vibration signal, as shown in Figure 8, and the correlation between the two signals is used to locate the largest first few segments at the screening point. signal, and the result is shown in Figure 9.

对于多频信号,首先利用变分非线性分量分解法将其分解为多个单频信号,如图10所示,(a)为原始信号;(b)为分解出的一阶单频信号;(c)为分解出的二阶单频信号。图11展示了对分解出的某一单频信号利用指数衰减法计算阻尼比的过程,(a)为某一分解出的单频信号;(b)为峰值对数值与波数线性拟合。再对每个单频信号利用傅里叶变换得到频率,并取算数平均值,自由衰减振动信号的频率-阻尼散点图,如图12的一阶频率-阻尼比、二阶频率-阻尼比散点分布及其平均值(★)示意图。将本发明提出的自动识别结果与基于参考的组合确定性-随机子空间和基于DBSCAN识别的固有频率和阻尼比进行比较,如表2所示。所提出的基于结构振动监测数据的阻尼比自动识别方法实现频率和阻尼比自动识别,可以很好地应用于实时、连续地信号处理。For multi-frequency signals, first use the variational nonlinear component decomposition method to decompose them into multiple single-frequency signals, as shown in Figure 10, (a) is the original signal; (b) is the decomposed first-order single-frequency signal; (c) is the decomposed second-order single-frequency signal. Figure 11 shows the process of calculating the damping ratio using the exponential decay method for a decomposed single-frequency signal. (a) is a decomposed single-frequency signal; (b) is the linear fitting of the peak logarithm value and the wave number. Then use Fourier transform to obtain the frequency of each single-frequency signal, and take the arithmetic average. The frequency-damping scatter plot of the free attenuated vibration signal is as shown in Figure 12: first-order frequency-damping ratio and second-order frequency-damping ratio. Schematic diagram of scatter distribution and its mean (★). The automatic identification results proposed by the present invention are compared with the natural frequencies and damping ratios of the reference-based combined deterministic-random subspace and DBSCAN-based identification, as shown in Table 2. The proposed automatic identification method of damping ratio based on structural vibration monitoring data realizes automatic identification of frequency and damping ratio, and can be well applied to real-time and continuous signal processing.

表2Table 2

进一步说明,实测信号中筛选出的自由衰减信号振动情况并非与构造的有阻尼的单自由度自由衰减振动的信号振动情况非常相近,但最终都可被识别、提取出来。只要实测数据中存在的衰减响应曲线近似满足所构造的有阻尼自由衰减曲线形状,就可以识别出数据中的衰减段。在本次Z24桥实测数据测试中,证明了本发明提出的自动模态识别方法具有很强的鲁棒性,并有望应用于实时健康监测。It is further explained that the vibration conditions of the free attenuation signal filtered out from the measured signals are not very similar to the vibration conditions of the constructed damped single-degree-of-freedom free attenuation vibration signal, but they can all be identified and extracted in the end. As long as the attenuation response curve existing in the measured data approximately satisfies the shape of the constructed damped free attenuation curve, the attenuation segment in the data can be identified. In this Z24 bridge actual measurement data test, it was proved that the automatic mode recognition method proposed by the present invention has strong robustness and is expected to be applied to real-time health monitoring.

需要强调的是,前述的实例只是为了解释本发明的技术内容,并不表示其唯一界定。虽然我们已经通过优选实例详细介绍了本发明,但相关领域的技术专家应当知道,他们可以对这些技术内容进行适当的调整或与之等效的替换,这些变更应当仍然遵循本发明的核心理念并不超出其定义范围,这些都应当包括在本发明的权益范围内。It should be emphasized that the foregoing examples are only for explaining the technical content of the present invention and do not represent its sole definition. Although we have introduced the present invention in detail through preferred examples, technical experts in relevant fields should know that they can make appropriate adjustments or equivalent replacements to these technical contents. These changes should still follow the core concept of the present invention and Without exceeding the scope of its definition, these should be included within the scope of the invention.

Claims (8)

1.一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,包括:1. An automatic identification method of frequency and damping ratio for bridge vibration monitoring, which is characterized by including: S1,对桥梁的实际监测数据进行傅里叶变换,得到近似的桥梁一阶自振频率,拟定初始阻尼比并构造有阻尼的单自由度弹簧振子的自由衰减振动信号;S1, perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, formulate the initial damping ratio and construct the free attenuation vibration signal of the damped single-degree-of-freedom spring oscillator; S2,利用互相关函数定位筛选出所述实际监测数据中与构造的所述自由衰减振动信号之间的相关性程度最大的所述前若干段信号;S2, use the cross-correlation function to locate and filter out the first several segments of signals in the actual monitoring data that have the greatest degree of correlation with the constructed free attenuation vibration signal; S3,根据频谱分析将筛选出的所述前若干段信号分为单频自由衰减振动信号与多频自由衰减振动信号,对于所述单频自由衰减振动信号和所述多频自由衰减振动信号分别计算得到频率和阻尼比;S3. According to spectrum analysis, the first several segments of the screened signals are divided into single-frequency free attenuation vibration signals and multi-frequency free attenuation vibration signals. For the single-frequency free attenuation vibration signal and the multi-frequency free attenuation vibration signal, respectively Calculate the frequency and damping ratio; S4,将所述前若干段信号的频率和阻尼绘制成频率-阻尼散点图,并分别对计算得到的所述频率和阻尼比分别取平均数得到最终识别结果。S4, draw the frequency and damping of the first several segments of signals into a frequency-damping scatter plot, and average the calculated frequencies and damping ratios to obtain the final identification result. 2.如权利要求1所述的一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,步骤S1中具体包括:2. An automatic identification method of frequency and damping ratio for bridge vibration monitoring as claimed in claim 1, characterized in that step S1 specifically includes: 对实际监测数据进行预处理;Preprocess actual monitoring data; 将经过预处理的实际监测数据的加速度信号定义为X(t),加速度信号X(t)是采样频率为fs、采样时间为TX的时间序列,其信号长度为LX,LX=fsTX The acceleration signal of the preprocessed actual monitoring data is defined as X(t). The acceleration signal X(t) is a time series with a sampling frequency of f s and a sampling time of T f s T X ; 对X(t)进行傅里叶变换:Perform Fourier transform on X(t): 其中,e是自然对数,i是虚数单位,ω是圆频率;Among them, e is the natural logarithm, i is the imaginary unit, and ω is the circular frequency; 通过峰值拾取判断频谱中最高峰的位置,得到近似的桥梁一阶自振频率 Determine the position of the highest peak in the spectrum through peak picking, and obtain the approximate first-order natural frequency of the bridge. 拟定初始阻尼比并构造有阻尼单自由度弹簧振子的自由衰减振动的信号Y(t):Proposed initial damping ratio And construct the signal Y(t) of the free attenuated vibration of the damped single-degree-of-freedom spring oscillator: 信号Y(t)是采样频率同为fs、采样时间为TY的时间序列,其信号长度为LY,LY=fsTYSignal Y(t) is a time series with the same sampling frequency f s and sampling time TY . Its signal length is LY , and LY =f s TY . 3.如权利要求2所述的一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,所述预处理包括:3. An automatic identification method of frequency and damping ratio for bridge vibration monitoring according to claim 2, characterized in that the preprocessing includes: 首先,对所述实际监测数据进行去除趋势项处理以去除原始信号中的偏移量;First, perform detrend processing on the actual monitoring data to remove the offset in the original signal; 其次,对所述实际监测数据进行低通滤波减少测量噪声的干扰。Secondly, low-pass filtering is performed on the actual monitoring data to reduce the interference of measurement noise. 4.如权利要求2所述的一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,步骤S2中具体包括:4. An automatic identification method of frequency and damping ratio for bridge vibration monitoring as claimed in claim 2, characterized in that step S2 specifically includes: 计算所述加速度信号X(t)与所述自由衰减振动的信号Y(t)的互相关函数:Calculate the cross-correlation function of the acceleration signal X(t) and the free attenuated vibration signal Y(t): 由此得到信号X(t)与Y(t)之间的相关性向量并同时得到相关性的滞后索引向量/> From this, the correlation vector between signals X(t) and Y(t) is obtained And at the same time get the lagged index vector of the correlation/> 取相关性向量R中绝对值最大的前k个值,并在滞后索引向量L中找到其对应的位置索引,筛选出所述实际监测数据与构造的所述自由衰减振动信号之间的相关性程度最大的前k段信号,X1(t),X2(t),……,Xk(t)。Take the top k values with the largest absolute values in the correlation vector R, find their corresponding position index in the lag index vector L, and filter out the correlation between the actual monitoring data and the constructed free attenuation vibration signal. The first k-segment signals with the largest degree, X 1 (t), X 2 (t), ..., X k (t). 5.如权利要求1所述的一种桥梁振动监测的频率与阻尼比自动识别方法,其特征在于,步骤S3中具体包括:5. An automatic identification method of frequency and damping ratio for bridge vibration monitoring as claimed in claim 1, characterized in that step S3 specifically includes: 对所述前若干段信号X1(t),X2(t),……,Xk(t)进行傅里叶变换:Perform Fourier transform on the first several segments of signals X 1 (t), X 2 (t),..., X k (t): 中,e是自然对数,i是虚数单位,ω是圆频率。k的取值范围10-30;where, e is the natural logarithm, i is the imaginary unit, and ω is the circular frequency. The value range of k is 10-30; 通过峰值拾取得到每个频谱中的高峰,其中,峰值大于初始设定阈值的记为有效高峰;有效高峰数为1的信号为所述单频自由衰减振动信号,有效高峰数大于1的信号为所述多频自由衰减振动信号。Peak peaks in each spectrum are obtained through peak picking, where the peak value greater than the initial set threshold is recorded as a valid peak value; a signal with a valid peak number of 1 is the single-frequency free attenuation vibration signal, and a signal with a valid peak number greater than 1 is The multi-frequency freely attenuates vibration signals. 6.根据权利要求1所述基于桥梁振动监测数据的频率与阻尼比自动识别方法,其特征在于:步骤S3中,对于所述单频自由衰减振动信号直接利用指数衰减法计算得到频率和阻尼比,通过峰值拾取得到信号中的波峰值Am及其对应的时间tm和序号m,将波峰值的对数与其对应的序号通过最小二乘法进行线性拟合,得到:6. The automatic identification method of frequency and damping ratio based on bridge vibration monitoring data according to claim 1, characterized in that: in step S3, the frequency and damping ratio are directly calculated using the exponential decay method for the single-frequency free attenuation vibration signal. , the wave peak value A m in the signal and its corresponding time t m and sequence number m are obtained through peak picking. The logarithm of the wave peak value and its corresponding sequence number are linearly fitted by the least squares method to obtain: ln A=a·n+bln A=a·n+b 其中,ln A为波峰对数值,n为波数,Among them, ln A is the logarithmic value of the wave crest, n is the wave number, 其中,M为所述单频自由衰减振动信号的总波数;Where, M is the total wave number of the single-frequency free attenuated vibration signal; 计算阻尼比:Calculate damping ratio: 计算频率:Calculate frequency: 7.根据权利要求1所述基于桥梁振动监测数据的频率与阻尼比自动识别方法,其特征在于:步骤S3中,对于所述多频自由衰减振动信号,通过变分非线性分量分解方法将该信号分解为多个单频自由衰减振动信号,对每个所述单频自由衰减振动信号利用指数衰减法计算各自的频率和阻尼比。7. The automatic identification method of frequency and damping ratio based on bridge vibration monitoring data according to claim 1, characterized in that: in step S3, for the multi-frequency free attenuation vibration signal, the variational nonlinear component decomposition method is used to decompose the frequency and damping ratio. The signal is decomposed into multiple single-frequency free-attenuated vibration signals, and the exponential decay method is used to calculate the respective frequency and damping ratio of each single-frequency free-attenuated vibration signal. 8.一种桥梁振动监测的频率与阻尼比自动识别系统,其特征在于,包括:8. An automatic identification system of frequency and damping ratio for bridge vibration monitoring, which is characterized by including: 加速度传感器,安装于桥梁的主梁的下方,用于将桥梁的振动加速度转换为电压信号,从而测量桥梁的振动加速度;The acceleration sensor is installed under the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal to measure the vibration acceleration of the bridge; 信号采集模块,接收采集加速计传来的电压信号,并将其从模拟信号转换为数字信号,然后记录下信号;The signal acquisition module receives and collects the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal; 相关性分析模块,接收信号采集模块记录的时程信号,利用互相关函数筛选出信号中的自由衰减振动信号;The correlation analysis module receives the time course signal recorded by the signal acquisition module, and uses the cross-correlation function to filter out the free attenuation vibration signal in the signal; 时频分析模块,接收相关性分析模块输出的自由衰减振动信号,利用傅里叶变换将自由衰减振动信号分为单频自由衰减振动信号与多频自由衰减振动信号,再利用变分非线性分量分解将多频自由衰减振动信号分解为多个单频自由衰减振动信号;The time-frequency analysis module receives the free attenuation vibration signal output from the correlation analysis module, uses Fourier transform to divide the free attenuation vibration signal into a single-frequency free attenuation vibration signal and a multi-frequency free attenuation vibration signal, and then uses the variational nonlinear component Decompose the multi-frequency free attenuation vibration signal into multiple single-frequency free attenuation vibration signals; 线性拟合模块,接收时频分析模块输出的单频自由衰减振动信号,利用线性拟合计算桥梁的频率与阻尼。The linear fitting module receives the single-frequency free attenuation vibration signal output from the time-frequency analysis module, and uses linear fitting to calculate the frequency and damping of the bridge.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117688480A (en) * 2024-02-04 2024-03-12 四川华腾公路试验检测有限责任公司 Bridge damage identification method based on damage frequency panorama and random forest
CN118797322A (en) * 2024-09-14 2024-10-18 四川中图三维信息技术有限公司 A coordinated control method and system of multi-scale hybrid strategy for bridge damping
CN119829893A (en) * 2025-03-17 2025-04-15 湖南大学 Damping ratio identification method, device, electronic device and storage medium

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117688480A (en) * 2024-02-04 2024-03-12 四川华腾公路试验检测有限责任公司 Bridge damage identification method based on damage frequency panorama and random forest
CN117688480B (en) * 2024-02-04 2024-05-14 四川华腾公路试验检测有限责任公司 Bridge damage identification method based on damage frequency panorama and random forest
CN118797322A (en) * 2024-09-14 2024-10-18 四川中图三维信息技术有限公司 A coordinated control method and system of multi-scale hybrid strategy for bridge damping
CN119829893A (en) * 2025-03-17 2025-04-15 湖南大学 Damping ratio identification method, device, electronic device and storage medium

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