Multiple-input-multiple-output bridge modal parameter identification method and device based on corrected periodogram method power spectrum

Abstract

The invention discloses a multiple-input-multiple-output bridge modal parameter identification method and device based on a corrected periodogram method power spectrum, and the method comprises the steps: obtaining a section of multi-point input excitation and multi-point output response, and equally dividing the excitation and response data according to the dimension of an excitation vector; the equant excitation and response data are substituted into a response power spectrum matrix calculation formula for separating excitation, singular value decomposition is carried out on the obtained matrix to obtain a maximum singular value curve and a singular vector, the frequency corresponding to the peak value of the curve is the inherent frequency of the bridge, the corresponding singular vector is the vibration mode of the bridge, and the maximum singular value curve is obtained. The frequency corresponding to the half of the peak value of the curve is a half-power point, and the half-power point is substituted into a damping ratio calculation formula to obtain the damping ratio of the bridge. And substituting the damping ratio, the vibration mode and the inherent frequency into a vibration mode scaling coefficient calculation formula to obtain the vibration mode scaling coefficient of the bridge. In the bridge operation modal parameter identification process, the problem that an excited autopower spectrum ill-conditioned condition is difficult to invert is solved, and the identification precision of the bridge modal parameters is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of engineering structure detection data analysis, and relates to a multi-input multi-output bridge modal parameter identification method and device based on a modified cycle diagram method power spectrum. BACKGROUND

[0002] Bridge health monitoring usually needs to collect bridge data through sensors to analyze the safety in-service state of the bridge. Data analysis modal parameters are an effective way of bridge health monitoring. Bridge modal parameters include natural frequency, damping ratio and mode shape. Changes in the in-service state of the bridge are usually reflected in changes in the physical parameters of the bridge. Changes in physical parameters will inevitably cause changes in modal parameters. Therefore, the safety in-service state of the bridge can be indirectly reflected through modal parameters.

[0003] Multi-input multi-output modal identification surpasses the limitations of traditional single-input single-output methods in bridge structure health monitoring, captures the complex dynamic behavior of bridge structures under multiple degrees of freedom, and can more comprehensively and accurately depict the dynamic characteristics and in-service state of the bridge, thereby improving the precision and stability of modal parameter extraction.

[0004] There are many kinds of multi-input multi-output modal identification of bridges. In 2019, Zhou Xiaohang proposed a time-domain identification method based on sliding window technology and deterministic-stochastic subspace identification in "Multi-input multi-output bridge structure time-varying modal parameter sliding window time domain identification" to track and identify the time-varying modal parameters of multi-input multi-output bridge structure. The method can realize tracking identification of bridge modal parameters in time domain, but it cannot solve the problem of irreversible input power spectrum because it is based on state space modal parameter identification. In 2021, Zhang Guowen proposed a multi-reference least squares complex frequency domain optimization method in "Numerical problem analysis and optimization of multi-reference least squares complex frequency domain method", which can automatically obtain clear and stable figures without losing accuracy. Since it is also based on state space modal parameter identification, it cannot solve the problem of difficult inverse of input power spectrum, and the determination of modal order also has a great influence on identification. In 2023, Huang Tianli proposed a bridge structure modal parameter identification method based on AR-EWT and SSI in "Bridge structure modal parameter identification based on AR-EWT and SSI", which can avoid the system order determination problem when directly using SSI to identify modal parameters and improve the efficiency of modal parameter identification. In 2004, Catbas proposed and implemented a parameter estimation method using complex modal indicator function in "Parameter estimation for multiple-input multiple-output modal analysis of large structures" to determine modal characteristics and obtain modal flexibility by appropriate scaling, but it uses exciter excitation, which is difficult to meet in large bridges. At present, the problem of multi-input multi-output modal identification of bridges is that the self-power spectrum matrix of excitation is ill-conditioned and difficult to invert, which leads to low accuracy of modal bridge modal parameter identification. SUMMARY

[0005] The present application aims to provide a multi-input multi-output bridge modal parameter identification method and device based on modified periodogram method power spectrum, which solves the problem of ill-conditioned self-power spectrum of excitation in the identification process of bridge modal parameters, which leads to inaccurate modal parameter identification.

[0006] The technical scheme of the present application is:

[0007] A multi-input multi-output bridge modal parameter identification method based on a modified cycle graph method power spectrum, first obtains a long period of multi-point input excitation and multi-point output response, according to the dimension of the excitation vector, the excitation and response data are equally divided. Then the equally divided excitation and response data are brought into the calculation formula of the response power spectrum matrix of the separated excitation, and the maximum singular value curve and the singular vector are obtained by singular value decomposition of the calculated matrix, the frequency corresponding to the peak value of the curve is the natural frequency of the bridge, and the corresponding singular vector is the vibration mode of the bridge. The frequency corresponding to the half power point of the curve is the half power point, and the half power point is brought into the damping ratio calculation formula to obtain the damping ratio of the bridge. The identified damping ratio, mode shape and natural frequency are brought into the mode shape scaling coefficient calculation formula to obtain the mode shape scaling coefficient of the bridge.

[0008] A multi-input multi-output bridge modal parameter identification method based on a modified cycle graph method power spectrum, steps as follows:

[0009] (1) Bridge input excitation acquisition and output response acquisition;

[0010] The bridge is excited by an excitation device such as a vehicle, and sensors are arranged on the bridge to collect the excitation applied to the bridge and the corresponding response of the bridge , wherein I is the number of input excitation sensors, and M is the number of output response sensors. According to the number I of input excitation sensors, the collected bridge excitation and response are equally divided into I sections, that is and .

[0011] (2) Multi-input multi-output modified cycle graph method power spectrum calculation;

[0012] The collected excitation applied to the bridge and the collected response of the bridge are transformed into the frequency domain to obtain and , the frequency domain values of the bridge excitation and the frequency domain values of the bridge response are brought into the following formula to calculate the modified cycle graph self-power spectrum of the bridge excitation and the mutual power spectrum of the bridge excitation-response .

[0013]

[0014] (3) Bridge frequency response function matrix acquisition;

[0015] One of the core links of the multi-input multi-output modal parameters of the bridge is to calculate the frequency response function of the bridge, and and Substitute the values ​​into the following formula to calculate the frequency response function matrix:

[0016]

[0017] (4) Singular value decomposition of the frequency response function matrix;

[0018] The frequency response function matrix of the bridge obtained by singular value decomposition. Obtain the maximum singularity curve and the singular vectors corresponding to different frequencies Maximum singularity curve and singular vectors Modal parameters used to reflect the bridge, maximum singular value curves There are a total of N peaks. Let the initial solution order be... ;

[0019] (5) Bridge modal parameter identification;

[0020] Picking the maximum singular value curve The The peak value corresponds to the frequency of the bridge. natural frequency of the order The natural frequency corresponds to the singular vector, which is the first singular vector of the bridge. Mode shape The curve was obtained on the [number]th [day]. The two frequencies corresponding to half of the peak value and That is, the first The half-power points of the first mode are used to identify the damping ratio of the bridge by substituting the two half-power points into the following formula.

[0021]

[0022] (6) Identification of bridge mode scaling factor;

[0023] The first bridge identified natural frequency of the order , mode shape Damping ratio and curves exist numerical value Substitute into the following formula to calculate the bridge's first... Mode scaling factor :

[0024]

[0025] (7) Order Repeat (5) to (6) until... , obtain the modal parameters of each order of the bridge.

[0026] A multi-input multi-output bridge modal parameter identification device based on a modified cycle graph method power spectrum, comprising: an acquisition module for obtaining measured response data of a bridge;

[0027] a storage for storing measured data and a data processing program;

[0028] a processor for executing the data processing program in the storage, when the data processing program is executed, the processor will be used for:

[0029] reading the measured response data of the bridge, the response data being collected and stored at the same time; using the data processing program, analyzing the modal parameters of the bridge.

[0030] The beneficial effects of the present application: in the process of multi-input multi-output modal parameter identification of the bridge, the problem of ill-conditioned self-power spectrum of excitation is difficult to solve, which is an important reason affecting the identification accuracy. By dividing the data and combining the modified cycle graph method power spectrum to calculate the self-power of the excitation, the problem of difficult to solve is solved, and the identification accuracy of the bridge modal parameters is improved. DETAILED DESCRIPTION

[0031] The specific embodiments of the present application are further illustrated below in combination with the technical solutions.

[0032] Taking an equal cross-section simply supported beam model as an example, the length of the equal cross-section simply supported beam is 20m, the mass is 150Kg / m, the stiffness is 3×10 6 N / m 2 . The damping ratio of each order mode is set to 0.005, and a sensor is placed every 2.5m to collect the response, and there are 7 sensors in total.

[0033] The form of excitation is randomly generated vehicle excitation, the wheelbase of the vehicle is set to 2~4m, the axle load of the vehicle is set to 3~5kN and 10~15kN, and the speed is set to 10~15m / s. The response signal is the displacement response collected by the sensor.

[0034] (1) obtaining the input excitation of the bridge and the output response;

[0035] The bridge is excited by a vehicle excitation device, and sensors are arranged on the bridge to collect the excitation and the corresponding response of the bridge, wherein I is the number of input excitation sensors, and M is the number of output response sensors. The collected bridge excitation and response are divided into I segments according to the number I of input excitation sensors, i.e. and .

[0036] (2) MIMO modified periodicity diagram method power spectrum calculation;

[0037] The collected excitation applied on the bridge and the collected response of the bridge are transformed into frequency domain to obtain and the frequency domain values of the bridge excitation and the frequency domain values of the bridge response are brought into the following formula to calculate the modified periodicity diagram method self-power spectrum of the bridge excitation and the cross-power spectrum of the bridge excitation-response .

[0038]

[0039] (3) Bridge frequency response function matrix acquisition;

[0040] One of the core links of the MIMO modal parameters of the bridge is to calculate the frequency response function of the bridge, and and are brought into the following formula to calculate the frequency response function matrix:

[0041]

[0042] (4) Singular value decomposition of the frequency response function matrix;

[0043] The frequency response function matrix of the bridge calculated by singular value decomposition obtains the maximum singular value curve and the singular vectors corresponding to different frequencies , the maximum singular value curve and the singular vector are used to reflect the modal parameters of the bridge, and the maximum singular value curve has N peaks in total. Let the initial solving order be ;

[0044] (5) Bridge modal parameter identification;

[0045] Pick up the th peak of the maximum singular value curve , and the frequency corresponding to the peak is the th natural frequency of the bridge , and the singular vector corresponding to the natural frequency is the th mode shape of the bridge . Obtain the two frequencies corresponding to the half of the th peak of the curve , that is, the The half-power points of the mode shape are brought into the following formula to identify the damping ratio of the bridge.

[0046]

[0047] (6) Identification of the mode shape scaling coefficient of the bridge;

[0048] The identified first order natural frequency , mode shape , damping ratio and curve of the bridge are brought into the following formula to calculate the first order mode shape scaling coefficient of the bridge:

[0049]

[0050] (7) Let , repeat (5)~(6) until , and obtain the modal parameters of each order of the bridge.

[0051] The natural frequencies of each stage of the bridge are as follows:

[0052]

[0053] The mode shapes of each order of the bridge are as follows:

[0054]

[0055] The damping ratios of each order of the bridge are as follows:

[0056]

[0057] The mode shape scaling coefficients of each order of the bridge are as follows:

[0058]

[0059] The excitation and response data of the bridge are brought into the complex modal indicator function method to show that the present application can effectively improve the identification precision of the modal parameters, and the identification results of the natural frequency and the mode shape scaling coefficient are as follows:

[0060]

[0061] It can be found that the identification precision of the present application is improved compared with the complex modal indicator function method, and the self-power spectrum of the bridge excitation is calculated by combining the modified cycle diagram method power spectrum, so that the problem of ill-conditioned inverse can be effectively solved, and the identification precision of the bridge modal parameters is improved.​​

Claims

1. A method for identifying multi-input multi-output bridge modal parameters based on the power spectrum of the modified periodogram method, characterized in that, The steps are as follows: (1) Acquisition of the bridge's input excitation and output response; The bridge is stimulated by an excitation device, and sensors are deployed on the bridge to collect the excitation applied to it. And the corresponding bridge response Where I represents the number of input excitation sensors and M represents the number of output response sensors; based on the number I of input excitation sensors, the collected excitation and response data from the bridge are divided into I segments, i.e. as well as ; (2) Power spectrum calculation using the multi-input multi-output corrected periodogram method; The collected excitations were applied to the bridge. And the collected bridge responses Transform to the frequency domain to obtain as well as The frequency domain value of the bridge excitation and the frequency domain value of the bridge response Substitute the values ​​into the following formula to calculate the power spectrum of the bridge excitation using the modified periodogram method. and the cross-power spectrum of bridge excitation-response ; ； (3) Obtaining the frequency response function matrix of the bridge; The modified periodogram method for bridge excitation is used to analyze the self-power spectrum. and the cross-power spectrum of bridge excitation-response Substitute the values ​​into the following formula to calculate the frequency response function matrix of the bridge: ； (4) Singular value decomposition of the frequency response function matrix; The frequency response function matrix of the bridge obtained by singular value decomposition. Obtain the maximum singularity curve and the singular vectors corresponding to different frequencies Maximum singularity curve and singular vectors Modal parameters used to reflect the bridge, maximum singular value curves There are a total of N peaks; let the initial solution order be... ; (5) Bridge modal parameter identification; Picking the maximum singular value curve The The peak value corresponds to the frequency of the bridge. natural frequency of the order The natural frequency corresponds to the singular vector, which is the first singular vector of the bridge. Mode shape Obtain the maximum singular value curve. In the The two frequencies corresponding to half of the peak value and That is, the first The half-power points of the first mode are used to identify the damping ratio of the bridge by substituting the two half-power points into the following formula: ； (6) Identification of bridge mode scaling factor; The first bridge identified natural frequency of the order , vibration shape Damping ratio and the maximum singularity curve At the natural frequency numerical value Substitute into the following formula to calculate the bridge's first... Mode scaling factor : ； (7) Order Repeat steps (5) to (6) until... The modal parameters of the bridge at each stage were obtained.

2. A multi-input multi-output bridge modal parameter identification device based on the modified periodogram method power spectrum, characterized in that, include: The data acquisition module is used to obtain the measured response data of the bridge. Storage, used to store measured data and data processing programs; The processor is used to execute data processing programs stored in memory. When a data processing program is executed, the processor will be used for: Read the measured response data of the bridge, which is collected and stored over the same period of time; use a data processing program to analyze the modal parameters of the bridge.

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