WO2022111423A1 - 大跨悬索桥涡振事件的实时识别和监测预警方法 - Google Patents

大跨悬索桥涡振事件的实时识别和监测预警方法 Download PDF

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WO2022111423A1
WO2022111423A1 PCT/CN2021/132169 CN2021132169W WO2022111423A1 WO 2022111423 A1 WO2022111423 A1 WO 2022111423A1 CN 2021132169 W CN2021132169 W CN 2021132169W WO 2022111423 A1 WO2022111423 A1 WO 2022111423A1
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real
bridge
signal
time
vortex vibration
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淡丹辉
李厚金
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同济大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0066—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by exciting or detecting vibration or acceleration
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H13/00—Measuring resonant frequency
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/04—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring tension in flexible members, e.g. ropes, cables, wires, threads, belts or bands
    • G01L5/042—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring tension in flexible members, e.g. ropes, cables, wires, threads, belts or bands by measuring vibrational characteristics of the flexible member
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm

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  • the invention relates to the field of large-span bridge structure monitoring, in particular to a real-time identification, monitoring and early warning method for vortex vibration events of a long-span suspension bridge.
  • Vortex-induced resonance of bridges is an important vibration problem in bridge operation.
  • bridge vortex vibration is not like flutter, gallop and other divergent vibrations, which can lead to bridge dynamic instability and damage, vortex vibration can easily occur at low wind speeds, and a large amplitude will cause fatigue of bridge cables and other structures, and also It will affect the driving comfort and driving safety. Therefore, the real-time online identification and early warning of bridge vortex vibration is very important, and it is the basis for bridge operation and maintenance management and subsequent vibration control.
  • the current bridge vortex vibration identification is mainly to identify the stable sinusoidal vibration segment in the bridge monitoring data by artificial eyes, or by performing spectrum analysis on a segment of data and manually judging whether there is only a single spectrum peak.
  • the disadvantage of the method is that the judgment error by the human eye is large, inaccurate, and easy to be misjudged or missed; the batch spectrum analysis method cannot be judged online and in real time. And the above two methods cannot accurately perceive the occurrence and end time of vortex vibration. This is where this application needs to focus on improving.
  • the technical problem to be solved by the present invention is to provide a real-time identification, monitoring and early warning method for vortex vibration events of large-span suspension bridges based on Hilbert transform.
  • the present invention provides a real-time identification, monitoring and early warning method for vortex vibration events of large-span suspension bridges, including the following steps:
  • Step S1 Based on the time history of the bridge acceleration monitoring signal, the frequency spectrum is calculated by the fast Fourier transform (FFT), the abscissa corresponding to the first-order energy peak value of the frequency spectrum is read, the first-order frequency f s of the structure is obtained, and the filter cut-off frequency f c is determined:
  • FFT fast Fourier transform
  • ⁇ is the filter proportional coefficient; for long-span bridges, ⁇ is taken as 1/4 to 1/3;
  • Step S2 remove low-frequency noise interference in the acceleration signal through a recursive high-pass filtering method.
  • the recursive filter is in the form of:
  • Step S3 Use the recursive acceleration integration method to calculate the vibration displacement of the bridge:
  • the baseline of the bridge acceleration monitoring signal is corrected by the recursive least square method, and then the low-frequency noise in the acceleration signal is eliminated by the recursive high-pass filter. Finally, the acceleration signal is integrated by the time domain quadratic integration method to obtain the bridge vibration and displacement data;
  • Step S4 perform short-time recursive Hilbert transform on the integral displacement data, construct an analytical signal in the complex domain, obtain the real part and imaginary part of the signal data, and express the signal in a complex plane:
  • x(m) is the sampling signal
  • N is the signal sampling length
  • h(i) is the impulse response multiplier
  • the real part and imaginary part of the complex domain analytical signal are obtained by calculation, and the real part is the x-axis and the imaginary part is the y-axis to draw the complex plane vector image of the data;
  • Step S5 vortex vibration judgment:
  • the image will show circular features; the image in the non-vortex vibration area is chaotic and irregular, and the occurrence of vortex vibration can be recognized and warned in real time;
  • the image will appear approximately circular; the image in the non-vortex vibration area is chaotic and irregular, and the occurrence of vortex vibration can be identified and warned in real time.
  • the bridge vibration displacement data is obtained, and the instantaneous frequency, phase and amplitude in the bridge vortex vibration process are obtained;
  • the real-time amplitude At of the bridge during vortex vibration is calculated from the real and imaginary parts of the analytical signal in the complex domain:
  • the invention Based on the quasi-sine vibration characteristics of bridge vortex vibration, the invention adopts Hilbert transform to process the one-dimensional monitoring signal in the time domain and convert it into a two-dimensional complex plane vector.
  • the two-dimensional complex plane vector graphics Present a standard circle, clearly and intuitively identify the occurrence of bridge vortex vibration.
  • the present invention is based on the recursive processing of monitoring acceleration data and short-time recursive Hilbert transformation, which can display the vibration state of the bridge in real time, and the display results under the random vibration of the bridge environment and the vortex vibration are obviously different, and can be intuitive and accurate. It can sense the occurrence of bridge vortex vibrations, serve the vibration control and operation and maintenance of bridges, and meet the requirements of real-time and continuity in the online monitoring environment. It is easy to implement, and has high engineering application value and broad application prospects;
  • the method of the present invention has a simple process, and the real-time monitoring data processing and analysis results show that it is extremely easy to identify and perceive the generation of bridge vortex vibration, and by calculating the instantaneous index of the vortex vibration, real-time early warning and online measurement of the vortex vibration can be realized, and the calculation efficiency is high, Sustainable and stable operation;
  • the method of the present invention has the characteristics of high real-time performance (second level), high precision, accuracy and intuition;
  • the method of the present invention can be used for online real-time perception of the start and end times of the bridge vortex vibration, and identification and measurement of the vibration characteristics of the bridge vortex vibration, such as instantaneous frequency, phase, amplitude, etc. Online Monitoring;
  • the method of the present invention has wide application scenarios.
  • Fig. 1 is the flow chart of the method of the present invention
  • Figure 2a is the Hilbert transform complex plane vector diagram of the original acceleration signal when vortex vibration occurs
  • Figure 2b is a complex plane vector diagram of Hilbert transform after signal integration processing when vortex vibration occurs
  • Fig. 3a is the Hilbert transform complex plane vector diagram of the original acceleration signal when the environment is randomly vibrated
  • Figure 3b is a complex plane vector diagram of the Hilbert transform after signal integration processing when the environment is randomly vibrated.
  • FIG. 1 shows a flowchart of a method according to an embodiment of the present invention.
  • the present invention provides a real-time identification and monitoring and early warning method for vortex vibration events of a large-span suspension bridge, using real-time acceleration data obtained by an acceleration sensor of a real bridge health monitoring system for calculation and analysis, and the sampling frequency is 50Hz, including The following steps:
  • ⁇ is the filter proportional coefficient; for long-span bridges, ⁇ is taken as 1/4 to 1/3;
  • S2 The low-frequency noise interference in the acceleration signal is removed by the recursive high-pass filtering method.
  • the form of the recursive filter is:
  • the baseline of the bridge acceleration monitoring signal is corrected by the recursive least square method, and then the low-frequency noise in the acceleration signal is eliminated by the recursive high-pass filter. Finally, the acceleration signal is integrated by the time domain quadratic integration method to obtain the bridge vibration and displacement data;
  • x(m) is the sampling signal
  • N is the signal sampling length
  • h(i) is the impulse response multiplier
  • the real and imaginary parts of the analytical signal in the complex domain are obtained by calculation, and the complex plane vector image of the data is drawn with the real part as the x-axis and the imaginary part as the y-axis; if vortex vibration occurs, the image presents circular features, as shown in Figure 2b ;
  • the image in the non-vortex vibration area is chaotic and irregular, as shown in Figure 3b, to identify and warn in real time the generation of vortex vibration;
  • the present invention also provides a real-time tracking and measurement method for vortex vibration events of a large-span suspension bridge, comprising the following steps: 1): measuring the magnitude of the vibration displacement at the current moment in real time:
  • the baseline of the bridge acceleration monitoring signal is corrected by the recursive least square method, and then the low-frequency noise in the acceleration signal is eliminated by the recursive high-pass filter. Finally, the acceleration signal is integrated by the time domain quadratic integration method to obtain the bridge vibration and displacement data;
  • the real-time amplitude At during the bridge vortex vibration is calculated from the real and imaginary parts of the analytical signal in the complex domain:
  • the invention can be used for vortex vibration monitoring and early warning of main beams and slender load-bearing members of large-span bridges such as suspension bridges and cable-stayed bridges, such as stay cables, main cables and suspension cables, to provide monitoring and management services for bridge owners;
  • large-span bridges such as suspension bridges and cable-stayed bridges, such as stay cables, main cables and suspension cables
  • the invention can also be used for other engineering structures with cross-wind vortex-induced vibration monitoring requirements, such as long-span cable-membrane structures, cables , towers, high-rise buildings, etc.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

一种大跨悬索桥涡振事件的实时识别和监测预警方法，包括：先对桥梁监测加速度信号计算频谱；根据频谱一阶能量峰值对应桥梁一阶频率来确定高通滤波截止频率，通过滤波去除信号中的低频噪声干扰，并采用递归加速度积分方法计算桥梁实时振动位移；再通过对积分位移数据进行实时递归希尔伯特变换获得信号数据的实部和虚部，对信号进行复平面表达并评估，实现了涡振的识别预警。该方法具有实时性高、精度高，准确和直观的特点，能够在线实时进行涡振识别并测量桥梁涡振时的振动特性，从而实现桥梁的涡振预警和在线监测。

Description

大跨悬索桥涡振事件的实时识别和监测预警方法 技术领域
本发明涉及大跨桥梁结构监测领域，特别涉及一种大跨悬索桥涡振事件的实时识别和监测预警方法。
背景技术
桥梁涡激共振是桥梁运营中的一个重要振动问题，是由周期性交替脱落的漩涡引起的主梁限幅振动现象。虽然桥梁涡振不像颤振、驰振等发散性振动会导致桥梁动力失稳和破坏，但是涡振很容易在低风速下发生，并且较大的振幅会造成桥梁缆索等结构的疲劳，也会影响行车舒适性和行车安全，因此，桥梁涡振的实时在线识别和预警十分重要，并且是桥梁运维管理以及进行后续振动控制的基础。
目前，桥梁的涡振响应及特性研究相对成熟，但主要是基于振动后数据的批处理，具有一定的后效性，以及大量的桥梁涡振半主动控制研究的前提是要实时在线识别出桥梁涡振的产生。因此，迫切需要一种针对在线监测环境下的桥梁涡振事件发生的实时识别方法。
桥梁正常运营状态下的环境激励随机振动和涡激共振时的振动特性有明显区别，涡振发生时，桥梁振动近似一种单模态的振动形式，其频谱呈现单一能量峰值，其余峰值能量很小，桥梁响应类似标准正弦函数。基于桥梁的涡振特性，目前的桥梁涡振识别主要是对通过人工肉眼识别桥梁监测数据中的稳定正弦振动段，或者通过对一段数据进行频谱分析并人工判断是否只有单一频谱峰值，这两种方法的缺点在于人工肉眼判断误差大，不准确，容易误判或漏判断；批处理频谱分析方法不能在线实时判断。并且上述两种方法均无法准确感知涡振的发生和结束时刻。这是本申请需要着重改善的地方。
发明内容
本发明所要解决的技术问题是要提供一种基于希尔伯特变换的大跨悬索桥涡振事件的实时识别和监测预警方法。
为了解决以上的技术问题，本发明提供了一种大跨悬索桥涡振事件的实时识别和监测预警方法，包括以下的步骤：
步骤S1：基于桥梁加速度监测信号时程，通过快速傅里叶变换FFT计算频谱，读取频谱一阶能量峰值对应的横坐标，获得结构的一阶频率f s，并确定滤波截止频率f c：
f c＝αf s；
式中，α为滤波比例系数；对于大跨桥梁，α取为1/4～1/3；
步骤S2：通过递归高通滤波方法去除加速度信号中的低频噪声干扰，递归滤波器的形式为：
Figure PCTCN2021132169-appb-000001
式中，x j和y j(j＝1，2，3…)分别为输入和输出信号，q为近似于1的常数；
步骤S3：采用递归加速度积分方法计算桥梁的振动位移：
先采用递归最小二乘法对桥梁加速度监测信号进行基线校正，再采用递归高通滤波消除加速度信号中的低频噪声，最后通过时域二次积分方法将加速度信号积分得到桥梁振动位移数据；
步骤S4：对积分位移数据进行短时递归希尔伯特变换，构造复数域的解析信号，并获得信号数据的实部和虚部，对信号进行复平面表达：
Figure PCTCN2021132169-appb-000002
式中，
Figure PCTCN2021132169-appb-000003
为对时域信号x(t)进行希尔伯特变换：
Figure PCTCN2021132169-appb-000004
对于离散监测信号数据，其希尔伯特变换计算式为：
Figure PCTCN2021132169-appb-000005
式中，x(m)为采样信号；
N为信号采样长度，h(i)为脉冲响应乘子，表达形式为：
Figure PCTCN2021132169-appb-000006
通过计算得到复数域解析信号的实部和虚部，以实部为x轴，虚部为y轴绘制数据复平面向量图像；
或通过直接对实时加速度监测信号进行短时希尔伯特变换，并且以实部为x轴，虚部为y轴绘制数据复平面向量图像；
步骤S5：涡振判断：
1)复数域解析信号的实部和虚部生成的向量图像：
若涡振产生，图像呈现圆形特征；非涡振区的图像杂乱无章无规律，对涡振的产生进行实时识别和预警；
2)对实时加速度监测信号进行短时希尔伯特变换，其实部和虚部生成的向量图像：
若涡振产生，图像呈现近似圆形特征；非涡振区的图像杂乱无章无规律,对涡振的产生进行实时识别和预警。
基于所述步骤S3中的加速度信号积分得到桥梁振动位移数据，得到桥梁涡振过程中的瞬时频率、相位以及振幅；
1)计算桥梁涡振的瞬时相位：
基于加速度积分所得位移信号的短时递归希尔伯特变换，得到复数域解析信号的实部和虚部，则桥梁涡振的瞬时相位
Figure PCTCN2021132169-appb-000007
Figure PCTCN2021132169-appb-000008
2)计算桥梁涡振的瞬时频率：
对瞬时相位关于时间求一次导数，得到桥梁涡振的瞬时频率f t：
Figure PCTCN2021132169-appb-000009
3)计算桥梁涡振的实时振幅：
涡振期间的桥梁实时振幅A t由复数域解析信号的实部和虚部计算求得：
Figure PCTCN2021132169-appb-000010
对桥梁涡振实时跟踪测量。
本发明基于桥梁涡振时的类正弦振动特性，采用了希尔伯特变换将时域一维监测信号进行处理转换为二维复平面向量，当涡振发生时，该二维复平面向量图形呈现标准的圆形，清晰、直观地识别桥梁涡振的发生。
本发明的优越功效在于：
1)本发明基于监测加速度数据的递归处理和短时递归希尔伯特变换，可实时显示出桥梁的振动状态，并且桥梁环境随机振动和涡振下的显示结果有明显差异，能直观、准确地感知桥梁涡振的发生，服务于桥梁的振动控制和运营维护工作，并且满足在线监测环境下的实时性、连续性的要求，易于实现，具有很高的工程应用价值和广阔的应用前景；
2)本发明方法过程简单，通过实时监测数据处理分析结果表明，极易识别和感知桥梁涡振的产生，通过计算涡振的瞬时指标可实现涡振实时预警和在线测量，并且计算效率高，可持续稳定运行；
3)本发明方法具有实时性高(秒级)、高精度，准确和直观等特点；
4)本发明方法可用于在线实时感知桥梁涡振的开始和结束时刻以及识别和测量桥梁涡振时的振动特性，如瞬时频率、相位、幅值等，并据此进行桥梁的涡振预警和在线监测；
5)本发明方法的应用场景广泛。
附图说明
构成本申请的一部分的说明书附图用来提供对本发明的进一步理解，本发明的示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。在附图中：
图1为本发明方法的流程图；
图2a为涡振发生时原始加速度信号希尔伯特变换复平面向量图；
图2b为涡振发生时信号积分处理后希尔伯特变换复平面向量图；
图3a为环境随机振动时原始加速度信号希尔伯特变换复平面向量图；
图3b为环境随机振动时信号积分处理后希尔伯特变换复平面向量图。
具体实施方式
以下结合附图对本发明的实施例进行详细说明。
图1示出了本发明实施例的方法流程图。如图1所示，本发明提供了一种大跨悬索桥涡振事件的实时识别和监测预警方法，采用实桥健康监测系统的加速度传感器获取的实时加速度数据进行计算分析，采样频率为50Hz，包括以下步骤：
S1：基于桥梁加速度监测信号时程，通过快速傅里叶变换FFT计算频谱，读取频谱一阶能量峰值对应的横坐标，获得结构的一阶频率f s，并确定滤波截止频率f c：
f c＝αf s；
式中，α为滤波比例系数；对于大跨桥梁，α取为1/4～1/3；
S2：通过递归高通滤波方法去除加速度信号中的低频噪声干扰，递归滤波器的形式为：
Figure PCTCN2021132169-appb-000011
式中，x j和y j(j＝1，2，3…)分别为输入和输出信号，q为近似于1的常数；
S3：采用递归加速度积分方法计算桥梁的振动位移：
先采用递归最小二乘法对桥梁加速度监测信号进行基线校正，再采用递归高通滤波消除加速度信号中的低频噪声，最后通过时域二次积分方法将加速度信号积分得到桥梁振动位移数据；
S4：对积分位移数据进行短时递归希尔伯特变换，构造复数域的解析信号，并获得信号数据的实部和虚部，对信号进行复平面表达：
Figure PCTCN2021132169-appb-000012
式中，
Figure PCTCN2021132169-appb-000013
为对时域信号x(t)进行希尔伯特变换：
Figure PCTCN2021132169-appb-000014
对于离散监测信号数据，其希尔伯特变换计算式为：
Figure PCTCN2021132169-appb-000015
式中，x(m)为采样信号；
N为信号采样长度，h(i)为脉冲响应乘子，表达形式为：
Figure PCTCN2021132169-appb-000016
通过计算得到复数域解析信号的实部和虚部，并且以实部为x轴，虚部为y轴绘制数据复平面向量图像；若涡振产生，图像呈现圆形特征，如图2b所示；非涡振区的图像杂乱无章无规律，如图3b所示，对涡振的产生进行实时识别和预警；
通过直接对实时加速度监测信号进行短时希尔伯特变换，并且以实部为x轴，虚部为y轴绘制数据复平面向量图像；若涡振产生，图像呈现近似圆形特征，如图2a所示；非涡振区的图像杂乱无章无规律,如图3a所示，对涡振的产生进行实时识别和预警。
本发明还提供了一种大跨悬索桥涡振事件的实时跟踪测量方法，包括如下的步骤：1)：实时测量当前时刻的振动位移大小：
先采用递归最小二乘法对桥梁加速度监测信号进行基线校正，再采用递归高通滤波消除加速度信号中的低频噪声，最后通过时域二次积分方法将加速度信号积分得到桥梁振动位移数据；
2)计算桥梁涡振的瞬时相位：
基于加速度积分所得位移信号的短时递归希尔伯特变换，得到复数域解析信号的实部和虚部，则桥梁涡振的瞬时相位
Figure PCTCN2021132169-appb-000017
Figure PCTCN2021132169-appb-000018
3)计算桥梁涡振的瞬时频率：
对瞬时相位关于时间求一次导数，得到桥梁涡振期间的瞬时频率f t：
Figure PCTCN2021132169-appb-000019
4)计算桥梁涡振的实时振幅：
桥梁涡振期间的实时振幅A t由复数域解析信号的实部和虚部计算求得：
Figure PCTCN2021132169-appb-000020
实现对涡振的实时全过程测量。
本发明可用于悬索桥、斜拉桥等大跨桥梁的主梁和细长承力构件的涡振监测和预警，如拉索、主缆和吊索中，为桥梁业主监控管理服务；也可用于上述大跨桥梁风洞试验室内的缩尺模型气动试验和节段气动试验的过程监控之中；亦可用于其它具备横风向涡激振动监控需求的其它工程结构，如大跨索膜结构、缆索、塔、高层建筑等。
以上所述仅为本发明的优先实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (2)

  1. 一种大跨悬索桥涡振事件的实时识别和监测预警方法，包括以下的步骤：
    步骤S1：基于桥梁加速度监测信号时程，通过快速傅里叶变换FFT计算频谱，读取频谱一阶能量峰值对应的横坐标，获得结构的一阶频率f s，并确定滤波截止频率f c：
    f c＝αf s；
    式中，α为滤波比例系数；
    步骤S2：通过递归高通滤波方法去除加速度信号中的低频噪声干扰，递归滤波器的形式为：
    Figure PCTCN2021132169-appb-100001
    式中，x j和y j(j＝1，2，3…)分别为输入和输出信号，q为近似于1的常数；
    步骤S3：采用递归加速度积分方法计算桥梁的振动位移：
    先采用递归最小二乘法对桥梁加速度监测信号进行基线校正，再采用递归高通滤波消除加速度信号中的低频噪声，最后通过时域二次积分方法将加速度信号积分得到桥梁振动位移数据；
    步骤S4：对积分位移数据进行短时递归希尔伯特变换，构造复数域的解析信号，并获得信号数据的实部和虚部，对信号进行复平面表达：
    Figure PCTCN2021132169-appb-100002
    式中，
    Figure PCTCN2021132169-appb-100003
    为对时域信号x(t)进行希尔伯特变换：
    Figure PCTCN2021132169-appb-100004
    对于离散监测信号数据，其希尔伯特变换计算式为：
    Figure PCTCN2021132169-appb-100005
    式中，x(m)为采样信号；
    N为信号采样长度，h(i)为脉冲响应乘子，表达形式为：
    Figure PCTCN2021132169-appb-100006
    通过计算得到复数域解析信号的实部和虚部，以实部为x轴，虚部为y轴绘制数据复平面向量图像；
    或通过直接对实时加速度监测信号进行短时希尔伯特变换，并且以实部为x轴，虚部为y轴绘制数据复平面向量图像；
    步骤S5：涡振判断：
    复数域解析信号的实部和虚部生成的向量图像：
    若涡振产生，图像呈现圆形特征；非涡振区的图像杂乱无章无规律，对涡振的产生进行实时识别和预警；
    对实时加速度监测信号进行短时希尔伯特变换，其实部和虚部生成的向量图像：
    若涡振产生，图像呈现近似圆形特征；非涡振区的图像杂乱无章无规律,对涡振的产生进行实时识别和预警。
  2. 根据权利要求1所述的大跨悬索桥涡振事件的实时识别和监测预警方法，其特征在于：基于所述步骤S3中的加速度信号积分得到桥梁振动位移数据，得到桥梁涡振过程中的瞬时频率、相位以及振幅；
    1)计算桥梁涡振的瞬时相位：
    基于加速度积分所得位移信号的短时递归希尔伯特变换，得到复数域解析信号的实部和虚部，则桥梁涡振的瞬时相位
    Figure PCTCN2021132169-appb-100007
    Figure PCTCN2021132169-appb-100008
    2)计算桥梁涡振的瞬时频率：
    对瞬时相位关于时间求一次导数，得到桥梁涡振的瞬时频率f t：
    Figure PCTCN2021132169-appb-100009
    3)计算桥梁涡振的实时振幅：
    涡振期间的桥梁实时振幅A t由复数域解析信号的实部和虚部计算求得：
    Figure PCTCN2021132169-appb-100010
    对桥梁涡振实时跟踪测量。
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