A real-time identification method for vortex-induced vibration of long-span bridges based on modal confidence criterion

Abstract

The present invention provides a method for real-time identification of vortex-induced vibration of a large-span bridge based on a modal confidence criterion, and the steps are as follows: a section of broadband random acceleration data is selected from existing acceleration response data, and an operational modal analysis is performed on the data using a frequency domain decomposition method to extract modal parameters of the bridge main beam, including frequency and vibration mode; the instantaneous phase and instantaneous envelope are extracted from the acceleration response at the current moment using a Hilbert transform, and the instantaneous envelope of the acceleration response of multiple measuring points is used to form an instantaneous envelope vector according to its instantaneous phase relationship; the possible parametric vibration mode and the analysis window length are determined according to the extreme point time interval, the vibration mode of the possible parametric vibration mode is selected, and the modal confidence criterion thereof and the instantaneous envelope vector is calculated; whether vortex-induced vibration occurs and the modal order of the vortex-induced vibration are determined in real time according to the modal confidence criterion within the analysis window length. The present invention uses the instantaneous envelope vector to be proportional to the vibration mode vector to achieve real-time online identification of different vortex-induced vibration processes.

Description

Technical Field

[0001] The invention belongs to the technical field of structural health monitoring and relates to a real-time identification method of vortex-induced vibration of a long-span bridge based on a modal confidence criterion. Technical Background

[0002] At present, the number of long-span and extra-long-span bridges in my country is increasing year by year, and a large number of bridges with a span of kilometers have been built, such as the Yangsigang Yangtze River Bridge and the Wufengshan Yangtze River Bridge. With the increase of span, the stiffness of the bridge continues to decrease, and the dynamic effect of wind load on the bridge structure becomes more and more significant. Vortex-induced vibration is a wind-induced vibration phenomenon that has frequently occurred in large-span bridges in recent years. It has high vibration amplitude, regular periodicity, and long duration, which can seriously affect driving comfort and safety, and even cause bridge fatigue disasters. For this reason, the real-time identification and online alarm of vortex-induced vibration has become one of the important issues of concern in the health monitoring of large-span bridge structures.

[0003] The current vortex-induced vibration identification technology mainly obtains the characterization parameters of vortex-induced vibration of bridge main beams from two aspects: wind load characteristic analysis and wind-induced bridge vibration characteristic analysis. Then, vortex-induced vibration events are determined by statistically analyzing and clustering the characterization parameters. Among them, Zhang Jian et al. used the similarity of the vibration shape of the main beam to identify vortex-induced vibration. Dan Danhui et al. assumed that the amplitude of the vortex-induced vibration response has a short-term time-invariant characteristic and used the amplitude ratio to identify vortex-induced vibration. Xu Shiqiao et al. used wind speed, wind direction, acceleration root mean square and vibration energy concentration coefficient as the characterization parameters of vortex-induced vibration of Zhoushan Cross-sea Bridge, and determined the threshold of the characterization parameters based on the statistical results to identify vortex-induced vibration. When the above-mentioned characterization parameters are used to distinguish vortex-induced vibration, there are mainly problems of inconsistent judgment criteria and poor real-time performance, which will reduce the online automation level of bridge vortex-induced vibration monitoring and alarm. Among them, the inconsistent judgment criteria are reflected in the fact that the selection of characterization parameters and the determination of their thresholds need to vary from bridge to bridge and from wind load characteristics; the poor real-time performance is reflected in the fact that the characterization parameters are often obtained by offline batch processing of monitoring data over a long period of time.

[0004] Therefore, real-time and reliable acquisition of bridge vortex-induced vibration characterization parameters and improving the degree of automation of its monitoring and analysis are one of the keys to achieving online identification of bridge vortex-induced vibration, which is of great significance for bridge vortex-induced vibration prediction and alarm. Summary of the invention

[0005] The purpose of the present invention is to provide a real-time automatic identification method for vortex-induced vibration of large-span bridges, so as to solve the problem of untimely vortex-induced vibration prediction and alarm caused by poor universality and low extraction timeliness of bridge vortex-induced vibration characterization parameters during online structural health monitoring.

[0006] The technical solution of the present invention is to propose a method for real-time identification of vortex-induced vibration of large-span bridges based on the modal confidence criterion. First, a section of broadband random acceleration data is selected from the existing acceleration response data, and the operational modal analysis is performed on it using the frequency domain decomposition method to extract the modal parameters of the bridge main beam, including frequency and vibration mode; secondly, the instantaneous phase and instantaneous envelope are extracted from the acceleration response at the current moment using the Hilbert transform, and the instantaneous envelope of the acceleration response of multiple measuring points is used to form an instantaneous envelope vector according to its instantaneous phase relationship; then, the possible parametric vibration mode and analysis window length are determined according to the extreme point time interval, the vibration mode of the possible parametric vibration mode is selected, and the modal confidence criterion between it and the instantaneous envelope vector is calculated; finally, whether vortex-induced vibration occurs and the modal order of vortex-induced vibration are determined in real time according to the modal confidence criterion within the analysis window length.

[0007] A real-time identification method for vortex-induced vibration of large-span bridges based on modal confidence criterion, the steps are as follows:

[0008] Step 1: Bridge modal parameter identification

[0009] (1) From the historical monitoring data collected by N vertical acceleration sensors installed on the bridge main beam, select broadband random acceleration data with a duration of 1 h, N>1; use the frequency domain decomposition method to identify the modal parameters of the bridge main beam from the broadband random acceleration data, including the order frequencies f1, f2, …, f K and each vibration mode vector Among them, K is the total number of modal orders of the parameter vibration, and the k-th vibration shape vector It is composed of the vibration mode coefficients at each acceleration measuring point, namely The superscript T indicates transposition, order k = 1, 2, ..., K;

[0010] Step 2: Vortex-induced vibration transient characteristics analysis

[0011] (2) At the current time t, collect the vertical acceleration data y from each measuring point i=1, 2, ..., N on the bridge main beam. i (t), the acceleration of multiple measuring points is recorded as y(t) = [y1(t) y2(t) … y N (t)] T ; If the bridge main beam does not experience vortex-induced vibration, the acceleration response expression at the measuring point i is:

[0012]

[0013] In the formula, the subscript i is the measurement point number, is the modal coefficient of the kth modal at the measuring point i, ω k is the k-th order structural circular frequency, θ k is the initial phase, A k(t) is the slowly time-varying amplitude modulation function associated with the excitation;

[0014] When the vortex shedding frequency induced by wind load is close to the p-order frequency of the bridge main beam, the bridge main beam will experience vortex-induced vibration dominated by the p-order mode, where 1≤p≤K; at this time, the acceleration response expression at the measuring point i becomes:

[0015]

[0016] Correspondingly, the acceleration response expression of multiple measuring points when vortex-induced vibration occurs is:

[0017]

[0018] According to formula (3), when the vortex-induced vibration dominated by the p-th order mode occurs, the acceleration response vector y(t) of multiple measuring points and the vibration shape of the p-th order mode are Proportional, the proportionality coefficient is A p (t)cos(ω p t+θ p );

[0019] (3) The modal confidence criterion is used to evaluate the proportional relationship between the two vectors; for the acceleration response vector y(t) and the vibration mode vector The MACs of the two are:

[0020]

[0021] Among them, 0≤MAC≤1, MAC=0 means that the two vectors are completely unrelated, and MAC=1 means that the two vectors are completely related, that is, they are in a proportional relationship;

[0022] According to formula (3), the acceleration response vector of each measuring point changes with time. When the proportional coefficient A p (t)cos(ω p t+θ p )=0, the acceleration response vector of each measuring point satisfies y(t)=0; if y(t) is equal to 0, the MAC value in equation (4) is equal to 0. At this time, the method of using MAC to distinguish vortex-induced vibration fails;

[0023] In order to use MAC for continuous online identification of vortex-induced vibration, it is necessary to use the acceleration response vector y(t) to construct a vector that can represent the vortex-induced vibration and will not be affected by the proportionality coefficient A. p (t)cos(ω p t+θ p )'s periodic oscillations that cause the parameter of discrimination failure, namely, the instantaneous envelope vector;

[0024] Step 3: Extraction of instantaneous envelope vector

[0025] (4) Acceleration data y at measuring point i i (t) Perform Hilbert transform to obtain its analytical signal z i (t) is:

[0026] z i (t) = y i (t)+jH[y i (t)] (5)

[0027] Where j is the imaginary unit, H[·] represents the Hilbert transform;

[0028] If the acceleration data is vortex-induced vibration, the analytical signal expression in equation (5) is transformed into:

[0029]

[0030] Analyze the analytical signal in equation (6) and extract the acceleration response y i The instantaneous envelope and instantaneous phase of (t) are:

[0031]

[0032]

[0033]

[0034] Among them, x Ui (t) and x Li (t) are defined as the instantaneous upper envelope and the instantaneous lower envelope, Re[·] and Im[·] represent the real part and the imaginary part, and |·| represents the absolute value. Defined as the instantaneous phase, its range is set to

[0035] According to the instantaneous phase at the initial time τ Determine the relative vibration direction of each measuring point and select the instantaneous envelope x of the acceleration response of each measuring point i (t) is:

[0036]

[0037] Correspondingly, when the p-th order mode undergoes vortex-induced vibration, the instantaneous envelope vector of the acceleration response of each measuring point is proportional to the vibration mode, that is:

[0038]

[0039] When vortex-induced vibration occurs, the acceleration instantaneous envelope vector x(t) and the vibration mode vector The proportionality coefficient is A p (t) rather than A p(t)cos(ω p t+θ p ), A p (t) is a slowly varying amplitude modulation function and is not equal to 0;

[0040] Therefore, the instantaneous envelope vector x(t) is used to replace the acceleration vector y(t), and its relationship with the vibration mode vector The modal confidence criterion MAC, if MAC is close to 1, it means that the two are in proportional relationship;

[0041] Step 4: Online identification of vortex-induced vibrations of various orders

[0042] (5) When the bridge girder measurement points satisfy N>>K, the vibration mode vectors of each order mode can be distinguished, that is, the MAC of each vibration mode vector satisfies Where p = 1, 2, ..., K, q = 1, 2, ..., K, and p ≠ q; at this time, it is only necessary to extract the instantaneous envelope vector x(t) of the acceleration at the current moment and calculate its relationship with the vibration mode vector Modal Assurance Criterion MAC; if in the time period t0 = t-T + Δt, t-T + 2Δt, ..., t, there is only satisfy Then vortex-induced vibration occurs, and the vibration mode is the pth order. Otherwise, vortex-induced vibration does not occur. Wherein, Δt is the sampling time interval, and T represents the analysis window length that changes with time, which is calculated as follows:

[0043] T(t)=t -1 -t -2 (12)

[0044] Among them, t -1 represents the time point closest to t and at which the acceleration reaches a maximum value; t -2 It indicates the time point close to the tth time and the acceleration reaches the maximum value;

[0045] (6) When the acceleration measurement points of the main beam satisfy 1<N<K, the vibration mode vectors of each order mode may be aliased, that is, Where p≠q; In order to avoid the misjudgment of the modal order of vortex-induced vibration caused by vibration mode vector aliasing, it is necessary to first select M possible parametric vibration modes occurring in the acceleration response at the current time t from the K-order modes, where M≤K;

[0046] First, the possible vibration frequency band of the acceleration response is determined to be [0.8 / T(t), 1.2 / T(t)] Hz according to the analysis window length T(t);

[0047] If the p-th order frequency of the structure is within [0.8 / T(t),1.2 / T(t)] Hz, it means that the p-th order mode is a possible parametric vibration mode; screen f1, f2, …, f KFor all the modal orders that meet the above requirements, calculate the modal confidence criteria of their vibration shape vectors and acceleration instantaneous envelope vectors respectively;

[0048] If in the time period t0 = t-T + Δt, t-T + 2Δt, ..., t, for a modal order p that satisfies [0.8 / T(t), 1.2 / T(t)], then the vibration mode vector and the acceleration instantaneous envelope vector satisfy Then vortex-induced vibration occurs, and the vibration mode is the pth order, otherwise vortex-induced vibration does not occur.

[0049] The beneficial effects of the present invention are as follows: the vortex-induced vibration characteristic that the instantaneous envelope of the acceleration response of multiple measuring points is proportional to the vibration mode vector is used as a characterization parameter, which is suitable for online identification of different bridges or different vortex-induced vibration development processes; the instantaneous envelope characteristic does not require long-term batch data processing, and can perceive the entire vortex-induced vibration process in real time, which is an important prerequisite for online prediction and alarm of vortex-induced vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the vertical acceleration data of vortex-induced vibration of bridge main beam.

[0051] Figure 2 It is a schematic diagram of the vibration mode of the bridge main beam.

[0052] Figure 3 It is the MAC between the acceleration response vector and the vibration mode vector.

[0053] Figure 4 is the instantaneous envelope of acceleration at each measuring point.

[0054] Figure 5 It is the MAC between the vibration mode vectors of each order.

[0055] Figure 6 It is the MAC between the instantaneous envelope vector and the vibration shape vector. DETAILED DESCRIPTION

[0056] The following is a technical solution to further illustrate the implementation of the present invention.

[0057] Taking a long-span suspension bridge as an example, its health monitoring system has N = 3 acceleration sensors deployed at 1 / 4, 1 / 2 and 3 / 4 of the main span of the bridge to collect the vertical acceleration response of the main beam. The sampling frequency of each acceleration sensor is 50Hz. The vortex-induced vibration acceleration data of the fifth-order vertical mode is used as the data set for the verification of the vortex-induced vibration identification method. The acceleration data of each measuring point is as follows: Figure 1 shown.

[0058] The specific implementation is as follows:

[0059] (1) 1 h of broadband random acceleration data was selected from historical monitoring data, and modal parameter identification was performed using the frequency domain decomposition method. The first K = 9 modal frequencies of the bridge main beam were obtained as follows: f1 = 0.095 Hz, f2 = 0.133 Hz, f3 = 0.183 Hz, f4 = 0.230 Hz, f5 = 0.275 Hz, f6 = 0.326 Hz, f7 = 0.379 Hz, f8 = 0.436 Hz, and f9 = 0.499 Hz. The vibration shapes of the first 9 modes are as follows: Figure 2 As shown, the vibration mode values ​​at the measuring points are

[0060]

[0061] (2) Collect vertical acceleration data y from the acceleration measurement points i=1, 2, and 3 on the bridge main beam. i (t), the acceleration of multiple measuring points is recorded as y(t) = [y1(t) y2(t) y3(t)] T .

[0062] (3) Since the vortex-induced vibration data analyzed occurs in the fifth-order mode, the acceleration response vector y(t) and the vibration mode vector of the fifth-order mode are calculated. The modal confidence criterion The results are as follows Figure 3 As shown. It can be seen that during the vortex-induced vibration process, when the acceleration response vector y(t) is close to 0, the modal confidence criterion is much smaller than 1. At this time, the acceleration response vector y(t) and the vibration mode vector The modal confidence criterion cannot continuously and reliably identify vortex-induced vibration.

[0063] (4) Acceleration data y at acceleration measurement point i i (t) Perform Hilbert transform to obtain its analytical signal z i (t). According to equations (7) to (9), the analytical signal z i (t) Analyze and extract the acceleration response y i The instantaneous upper envelope x of (t) Ui (t), instantaneous lower envelope x Li (t) and the instantaneous phase at the initial time τ = 0 Then, according to formula (10), the instantaneous envelope x is determined i (t). The instantaneous envelope of each measuring point at each moment is as follows: Figure 4 As shown. Using the instantaneous envelope x of each measuring point i (t) Construct the instantaneous envelope vector x(t). Taking the current time t = 10s as an example, its instantaneous envelope vector is x(t) = [-0.099 -0.014 0.120] T .

[0064] (5) Since the number of acceleration measurement points N = 3 is less than the modal order K = 9, the vibration mode vectors of each mode may be aliased, that is, when the modal order p ≠ q, there is still like Figure 5 To this end, it is necessary to first select M possible parametric vibration modes occurring in the acceleration response at the current time t from the K-order modes.

[0065] First, from the acceleration y1(t), the times of the two closest and second closest maximum points to the current time t = 10s are extracted, which are t -1 =8.54s, t -2 =4.98s. Accordingly, the analysis window length T(t) is determined to be 3.56s.

[0066] According to the inverse of the analysis window length 1 / T(t), the possible vibration frequency band of the acceleration response is determined to be [0.8 / T(t), 1.2 / T(t)] = [0.225, 0.337] Hz.

[0067] Among the 1st to 9th order frequencies, 0.225≤f5<f6≤0.337Hz, indicating that the 5th and 6th order modes are possible parametric vibration modes, that is, M=2.

[0068] Calculate the vibration shape vectors of the 5th and 6th order modes respectively And the acceleration instantaneous envelope vector x(t) = [-0.099 -0.014 0.120] T The modal assurance criterion MAC of It can be found that only It satisfies the single-mode characteristics when vortex-induced vibration occurs.

[0069] In order to avoid the possibility that the random vibration signal may have MAC>0.9 due to measurement noise, which may lead to misjudgment, we further select the time period of t0=t-T+Δt, t-T+2Δt,…, t=6.46, 6.48,…, 10s to calculate The results are as follows Figure 6 As shown. Since the time period t0 = 6.46 ~ 10s is always satisfied Vortex-induced vibration occurs, and the vibration mode is p=5th order.

Claims

1. A real-time identification method for vortex-induced vibration of a large-span bridge based on modal confidence criterion, characterized in that: Here are the steps: Step 1: Bridge modal parameter identification (1) From the historical monitoring data collected by N vertical acceleration sensors installed on the bridge main beam, select broadband random acceleration data with a duration of 1 h, N>1; use the frequency domain decomposition method to identify the modal parameters of the bridge main beam from the broadband random acceleration data, including the order frequencies f1, f2, …, f K and each vibration mode vector Among them, K is the total number of modal orders of the parameter vibration, and the k-th vibration shape vector It is composed of the vibration mode coefficients at each acceleration measuring point, namely The superscript T indicates transposition, order k = 1, 2, ..., K; Step 2: Vortex-induced vibration transient characteristics analysis (2) At the current time t, collect the vertical acceleration data y from each measuring point i=1, 2, ..., N on the bridge main beam. i (t), the acceleration of multiple measuring points is recorded as y(t) = [y1(t) y2(t)…y N (t)] T ; If the bridge main beam does not experience vortex-induced vibration, the acceleration response expression at the measuring point i is: In the formula, the subscript i is the measurement point number, is the vibration mode coefficient of the kth vibration mode at the measuring point i, ω k is the k-th order structural circular frequency, θ k is the initial phase, A k (t) is the slowly time-varying amplitude modulation function associated with the excitation; When the vortex shedding frequency induced by wind load is close to the p-order frequency of the bridge main beam, the bridge main beam will experience vortex-induced vibration dominated by the p-order mode, where 1≤p≤K; at this time, the acceleration response expression at the measuring point i becomes: Correspondingly, the acceleration response expression of multiple measuring points when vortex-induced vibration occurs is: According to formula (3), when the vortex-induced vibration dominated by the p-th order mode occurs, the acceleration response vector y(t) of multiple measuring points and the vibration shape of the p-th order mode are Proportional, the proportionality coefficient is A p (t)cos(ω p t+θ p ); (3) The modal confidence criterion is used to evaluate the proportional relationship between the two vectors; for the acceleration response vector y(t) and the vibration mode vector The MACs of the two are: Among them, 0≤MAC≤1, MAC=0 means that the two vectors are completely unrelated, and MAC=1 means that the two vectors are completely related, that is, they are in a proportional relationship; According to formula (3), the acceleration response vector of each measuring point changes with time. When the proportional coefficient A p (t)cos(ω p t+θ p )=0, the acceleration response vector of each measuring point satisfies y(t)=0; if y(t) is equal to 0, the MAC value in equation (4) is equal to 0. At this time, the method of using MAC to distinguish vortex-induced vibration fails; In order to use MAC for continuous online identification of vortex-induced vibration, it is necessary to use the acceleration response vector y(t) to construct a vector that can represent the vortex-induced vibration and will not be affected by the proportionality coefficient A. p (t)cos(ω p t+θ p )'s periodic oscillations that cause the parameter of discrimination failure, namely, the instantaneous envelope vector; Step 3: Extraction of instantaneous envelope vector (4) Acceleration data y at measuring point i i (t) Perform Hilbert transform to obtain its analytical signal z i (t) is: z i (t)=y i (t)+jH[y i (t)] (5) Where j is the imaginary unit, H[·] represents the Hilbert transform; If the acceleration data is vortex-induced vibration, the analytical signal expression in equation (5) is transformed into: Analyze the analytical signal in equation (6) and extract the acceleration response y i The instantaneous envelope and instantaneous phase of (t) are: Among them, x Ui (t) and x Li (t) are defined as the instantaneous upper envelope and the instantaneous lower envelope, Re[·] and Im[·] represent the real part and the imaginary part, and |·| represents the absolute value. Defined as the instantaneous phase, its range is set to According to the instantaneous phase at the initial time τ Determine the relative vibration direction of each measuring point and select the instantaneous envelope x of the acceleration response of each measuring point i (t) is: Correspondingly, when the p-th order mode undergoes vortex-induced vibration, the instantaneous envelope vector of the acceleration response of each measuring point is proportional to the vibration mode, that is: When vortex-induced vibration occurs, the acceleration instantaneous envelope vector x(t) and the vibration mode vector The proportionality coefficient is A p (t) rather than A p (t)cos(ω p t+θ p ), A p (t) is a slowly varying amplitude modulation function and is not equal to 0; Therefore, the instantaneous envelope vector x(t) is used to replace the acceleration vector y(t), and its relationship with the vibration mode vector The modal confidence criterion MAC, if MAC is close to 1, it means that the two are in proportional relationship; Step 4: Online identification of vortex-induced vibrations of various orders (5) When the bridge girder measurement points satisfy N>>K, the vibration mode vectors of each order mode can be distinguished, that is, the MAC of each vibration mode vector satisfies Where p = 1, 2, ..., K, q = 1, 2, ..., K, and p ≠ q; at this time, it is only necessary to extract the instantaneous envelope vector x(t) of the acceleration at the current moment and calculate its relationship with the vibration mode vector Modal Assurance Criterion MAC; if in the time period t0 = t-T + Δt, t-T + 2Δt, ..., t, there is only satisfy Then vortex-induced vibration occurs, and the vibration mode is the pth order. Otherwise, vortex-induced vibration does not occur. Wherein, Δt is the sampling time interval, and T represents the analysis window length that changes with time, which is calculated as follows: T(t)=t -1 -t -2 (12) Among them, t -1 represents the time point closest to t and at which the acceleration reaches a maximum value; t -2 It indicates the time point close to the tth time and the acceleration reaches the maximum value; (6) When the acceleration measurement points of the main beam satisfy 1<N<K, the vibration mode vectors of each order mode may be aliased, that is, Where p≠q; In order to avoid the misjudgment of the modal order of vortex-induced vibration caused by vibration mode vector aliasing, it is necessary to first select M possible parametric vibration modes occurring in the acceleration response at the current time t from the K-order modes, where M≤K; First, the possible vibration frequency band of the acceleration response is determined to be [0.8 / T(t), 1.2 / T(t)] Hz according to the analysis window length T(t); If the p-th order frequency of the structure is within [0.8 / T(t),1.2 / T(t)] Hz, it means that the p-th order mode is a possible parametric vibration mode; screen f1, f2, …, f K For all the modal orders that meet the above requirements, calculate the modal confidence criteria of their vibration shape vectors and acceleration instantaneous envelope vectors respectively; If in the time period t0 = t-T + Δt, t-T + 2Δt, ..., t, for a modal order p that satisfies [0.8 / T(t), 1.2 / T(t)], then the vibration mode vector and the acceleration instantaneous envelope vector satisfy Then vortex-induced vibration occurs, and the vibration mode is the pth order, otherwise vortex-induced vibration does not occur.

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