A fast Bayesian identification method for structural modal parameters under impact test

Abstract

The present invention discloses a fast Bayesian identification method for structural modal parameters under impact test. The method comprises: firstly obtaining structural vibration data through impact test (such as force hammer test, vehicle jumping test, etc.), and then minimizing the negative log-likelihood function by using the semi-analytical coordinate descent method based on the Laplace approximation algorithm of Bayesian inference to obtain the estimated mean of the modal parameters. The uncertainty of the estimated result is given by the inverse matrix (i.e., covariance matrix) of the Hessian matrix of the negative log-likelihood function at the estimated mean. The proposed method can quickly and accurately identify modal parameters, and the identification process is usually completed within a few seconds, meeting the requirements of online modal parameter identification in the field of structural health monitoring. The algorithm is based on impact vibration test data, and is applicable to both known impact load conditions (such as force hammer test) and unknown impact load conditions (such as vehicle jumping test), with a wide range of applicability and strong practicality.

Description

Technical Field

[0001] The present invention belongs to the field of structural detection and health monitoring, and relates to a structural modal parameter identification method based on impact vibration data, and specifically to a fast Bayesian identification method of structural modal parameters under impact testing. Background Art

[0002] The modal parameters of structures (such as frequency, damping ratio and vibration mode) play an important role in the field of structural inspection and health monitoring. The accurate measurement of these parameters will provide strong support for damage identification, post-earthquake assessment and recovery.

[0003] In recent years, modal parameter identification methods based only on structural response have emerged in the field of structural inspection and health monitoring. They use the dynamic response of the structure under environmental excitations such as wind loads, ground pulsations, and vehicle loads, without the need for special excitation equipment, and are widely used in bridge structural health monitoring. However, such methods generally have disadvantages such as low identification accuracy and complex theories, and cannot meet the requirements of high-precision modal parameters.

[0004] On the contrary, the impact vibration method stimulates the vibration modes of the bridge through impact loads. It is convenient, low-cost, and highly maneuverable, and is more easily applied to load tests on small and medium-sized bridges. Commonly used impact test methods are the force hammer method and the vehicle jump test method. The force hammer method refers to the use of an impact hammer to strike a specific position of the structure. Generally speaking, the hammer force can be directly measured in real time; the vehicle jump test method refers to making the test vehicle drive over the triangular pads on the bridge deck, using the natural fall of the wheels to produce an impact on the bridge, and this impact force is usually not directly measurable.

[0005] The impact vibration method can excite multiple modes at the same time with one impact, and compared with the environmental excitation method, it can significantly increase the signal-to-noise ratio of the data, so that more accurate modal parameters can be identified. Summary of the invention

[0006] The present invention provides a fast Bayesian identification method for structural modal parameters under impact test, aiming to provide a rigorous and systematic solution for fast and accurate acquisition of structural modal parameters.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A fast Bayesian identification method for structural modal parameters under impact test, the method is applicable to both unknown structural input load and known structural input load. If the impact load is unknown, the method comprises the following steps:

[0009] 1) Perform an impact vibration test on the engineering structure of interest. If the structural input load of the impact vibration test is known, collect the structural input load and structural vibration response time history data of the impact vibration test. If the structural input load of the impact vibration test is unknown, only collect the structural vibration response time history data;

[0010] 2) Perform fast Fourier transform on the structural response time history data to obtain the corresponding frequency domain data, select the frequency band where the modal parameters to be identified are located, and perform subsequent calculations based on the frequency domain data in the selected frequency band;

[0011] 3) If the structural input load is known in step 1), a negative log-likelihood function is constructed based on the structural input load and the frequency domain data in the selected frequency band. If the structural input load is unknown, a negative log-likelihood function is constructed based only on the frequency domain data in the selected frequency band. The negative log-likelihood function is related to the modal parameters to be identified; the modal parameters to be identified include the modal frequency f, the modal damping ratio ζ, the unit normalized modal vibration shape Φ, and the power spectral density S of the measurement error. e ;

[0012] 4) Based on the principle of Bayesian inference, the Laplace approximation is used to approximate the posterior solution of the modal parameters, in which the semi-analytical coordinate descent method is used to iteratively solve the mean estimate of the modal parameters; during the iteration process, the unit normalized modal vibration shape Φ and the power spectral density S of the measurement error are e The updated value of is given by analytical expression, and the updated value of modal frequency and modal damping ratio is given by numerical optimization method.

[0013] Preferably, in step 3), the negative log-likelihood function constructed based on the structural input load and the frequency domain data in the selected frequency band is:

[0014]

[0015] in, is the set of modal parameters to be identified, is the modal mass normalized mode shape, S e is the power spectral density of the measurement error; n is the number of degrees of freedom of the measurement, N f is the number of fast Fourier transform points in the selected frequency band, is the fast Fourier transform value of the measured structural response, p k is the fast Fourier transform value of the impact load; the superscript “*” is the conjugate transpose symbol, the superscript T represents the matrix transpose, tr[.] is the matrix trace symbol, Re(.) is the symbol for taking the real part; l is a distribution vector whose elements are all 1, H k =diag[h 1k ,h 2k ,…,h mk] is the diagonal matrix of the frequency response function, diag[·] represents the matrix diagonalization symbol, h ik is the i-th order frequency response function, h ik The expression is:

[0016]

[0017] Among them, f k is the kth frequency domain coordinate corresponding to the data, q is the applicable factor of the data type, and the value of q is changed according to the type of structural vibration response time history data. ik is the ratio of the i-th modal frequency to the k-th frequency domain coordinate, ζ i is the i-th order modal damping ratio, f i is the i-th order modal frequency.

[0018] Preferably, in step 3), the negative log-likelihood function constructed based only on the frequency domain data in the selected frequency band is:

[0019]

[0020] in, is the normalized mode shape of impact quantity-modal mass, Q is a constant, which represents the impact quantity.

[0021] Preferably, in step 4), the semi-analytical coordinate descent method is used to iteratively solve and obtain the mean value estimation of the modal parameters, which specifically includes the following steps:

[0022] 4.1) Take the derivative of the constructed negative log-likelihood function to obtain the unit normalized mode shape Φ and the power spectral density S of the measurement error e An analytical expression to update the value;

[0023] 4.2) Using Φ and S e Update the analytical expression of the value and solve for Φ and S e The updated value of

[0024] 4.3) The solved Φ and S e Substitute the updated value of into the negative log-likelihood function constructed in step 3), and numerically optimize the negative log-likelihood function by the simplex method to obtain the updated values ​​of the modal frequency f and the modal damping ratio ζ;

[0025] 4.4) Repeat steps 4.2) and 4.3) until the negative log-likelihood function no longer decreases, and the modal frequency f, modal damping ratio ζ, unit normalized modal vibration shape Φ and power spectral density S of the measurement error are obtained. e The mean estimate of .

[0026] Preferably, if the input load of the structure is known, in the step 4.1), the constructed negative log-likelihood function is differentiated to obtain the unit normalized modal vibration shape Φ and the power spectral density S of the measurement error. e The analytical expression for the updated value is:

[0027] The negative log-likelihood function constructed in step 3) is derived with respect to the power spectral density of the modal mass normalized modal vibration shape and the measurement error, and the modal mass normalized modal vibration shape is The first-order derivative of is equal to zero, and the solution is obtained to obtain the normalized modal vibration shape of the modal mass Parsing expression to update the value:

[0028]

[0029] right By performing unit normalization, we can get the updated value of the unit normalized modal vibration shape Φ; let the power spectrum density S of the measurement error be e The first-order derivative of is equal to zero, that is, the power spectral density S of the measurement error is obtained by solving e Parsing expression to update the value:

[0030] .

[0031] Preferably, if the unknown structure input load, in the step 4.1), the constructed negative log-likelihood function is differentiated to obtain the unit normalized modal vibration shape Φ and the power spectral density S of the measurement error e The analytical expression for the updated value is,

[0032] Derivative the negative log-likelihood function constructed in step 3) with respect to the power spectral density of the normalized modal vibration shape of the impact quantity-modal mass and the measurement error, and let The first-order derivative of is equal to zero, and the normalized modal vibration shape of the impact amount-modal mass is obtained by solving Parsing expression to update the value:

[0033]

[0034] right By performing unit normalization, we can get the updated value of the unit normalized modal vibration shape Φ; let the power spectrum density S of the measurement error be e The first-order derivative of is equal to zero, that is, the power spectral density S of the measurement error is obtained by solving e Parsing expression to update the value:

[0035]

[0036] Preferably, in step 4.2), Φ and S are solved for the first time. e When updating the value of , first set the initial value of the modal frequency f and the modal damping ratio ζ, and solve Φ and S for the non-first time. e When the updated value is used, the values ​​of the modal frequency f and the modal damping ratio ζ are both taken as the last updated values ​​of the modal frequency f and the modal damping ratio ζ.

[0037] Preferably, the initial value of the modal damping ratio is 1%; the initial value of the modal frequency to be identified is determined by the following method: calculating the structural power spectrum density matrix and its eigenvalues ​​based on the acquired structural output data, plotting a graph of the eigenvalues ​​versus frequency, i.e., a singular value spectrum of the structural response, and selecting the peak value of the singular value spectrum of the structural response to determine the initial value of the modal frequency.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) The method proposed in the present invention is applicable to both known impact loads (such as hammer test) and unknown impact loads (such as vehicle jumping test), meeting the application requirements of different impact and vibration tests, with wide adaptability and strong robustness.

[0040] (2) The method proposed in the present invention is implemented through a Bayesian framework. Compared with classical statistical methods, it can quantify the identification uncertainty of the identification results while giving the mean estimate of the modal parameters, thus providing a systematic framework for modal parameter identification and uncertainty analysis.

[0041] (3) The method proposed in the present invention only selects data within the frequency band of interest during the solution process, and only a very small part of the parameters are calculated through numerical optimization methods. Therefore, the modal parameters can be quickly solved. The identification process is usually completed within a few seconds, which meets the requirements of online and real-time modal parameter identification in the structural health monitoring system.

[0042] (4) The method proposed in the present invention effectively reduces the uncertainty of modal parameter identification and enhances the reliability of identified modal parameters by obtaining complete structural input and output information or increasing the signal-to-noise ratio of structural vibration response.

[0043] (5) The method proposed in the present invention is applicable to measuring three types of data: displacement, velocity and acceleration time history, and can meet the requirements of different test equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the process of the present invention.

[0045] Figure 2 An eight-layer shear frame model and test arrangement diagram according to an embodiment of the present invention.

[0046] Figure 3Root SV spectra of input and output measured according to an embodiment of the present invention.

[0047] Figure 4 This is a modal parameter identification result of an embodiment of the present invention when the impact load is known.

[0048] Figure 5 This is a modal parameter identification result of an embodiment of the present invention when the impact load is unknown. DETAILED DESCRIPTION

[0049] The present invention is further described and illustrated below in conjunction with specific embodiments. The examples are merely exemplary of the present disclosure and do not define the scope of limitation. The technical features of each embodiment of the present invention may be combined accordingly without conflicting with each other.

[0050] How to identify modal parameters based on impact vibration data is the core purpose of the present invention; how to propose a unified solution framework for known or unknown impact load amplitude conditions is the key technical point solved by the present invention. Based on this, the present invention proposes a structural modal parameter identification method based on impact vibration testing, and the impact vibration testing scheme is as follows:

[0051] For the engineering structure of interest, impact equipment (such as a hammer, vehicle, etc.) is used to perform impact vibration testing, and the structural input load (if any) and structural vibration response time history data are collected by the vibration pickup. The data collection type can be acceleration, velocity or displacement time history data. For impact vibration testing, the structural input load is the impact load.

[0052] Combination Figure 1 The key theories of the technical solution of the present invention are divided into three parts: ① establishing physical expressions of measurement signals and modal parameters in the frequency domain; ② constructing the relationship between the posterior distribution of modal parameters and the distribution of measurement data (i.e., negative log-likelihood function) through the Bayesian formula; ③ using a semi-analytical coordinate descent method to iteratively solve the modal parameter mean estimate that minimizes the negative log-likelihood function; ④ calculating the Hessian matrix of the negative log-likelihood function, and taking its inverse matrix at the modal parameter mean estimate as the covariance matrix to quantify the uncertainty of the modal parameter identification results.

[0053] Assume that in the shock vibration test, the sampling frequency is f s (unit: Hz), the sampling time is T (unit: second), and the measured time-history response of the n-degree-of-freedom structure is The fast Fourier transform value can be expressed as Where i is the imaginary unit, The corresponding frequency is f k =kf s / N (k is the index number of the data in the frequency domain). Based on the linear, time-invariant system and classical damping assumptions, assuming that there are m modes of interest in the selected frequency band, the frequency domain signal of the measured structural acceleration response can be expressed as:

[0054]

[0055] where φ i is the vibration shape vector of the i-th mode at the measured degree of freedom; ε k Represents the measurement error, which satisfies zero mean and covariance S e The complex Gaussian distribution of I (I is the identity matrix, S e is the power spectral density of the measurement error, assuming that S e is a constant within the selected frequency band); At frequency f k The i-th order modal acceleration response at , its corresponding time domain expression satisfies under impact load:

[0056]

[0057] in, η i (t) are the acceleration, velocity and displacement time history responses of the single degree of freedom system respectively; ω i =2πf i , f i and i are the frequency and damping ratio of the i-th mode respectively; is the i-th order modal mass, M is the mass matrix of the measured structure, and the superscript T indicates the matrix transpose; L is the distribution vector of the impact load, whose elements are 1 at the degree of freedom where the impact force acts and 0 at other degrees of freedom; p k Enter the load for the structure at f k In the impact vibration test, since the initial and final values ​​of the structural acceleration response are almost zero, and Gradually established.

[0058] Performing fast Fourier transform on formula (2) and substituting it into formula (1) yields:

[0059]

[0060]

[0061] Among them, h ik is the frequency response function of the i-th order mode. In formula (3), the vibration mode vector φ i It can be normalized arbitrarily. To facilitate problem solving, define And construct the normalized vibration shape of the i-th order modal mass Thus, formula (3) depends linearly on the unconstrained parameter So far, the set of modal parameters to be identified is defined ζ=[ζ1,ζ2,…,ζ m ] T , ). Formula (3) is expressed in matrix form as:

[0062]

[0063] Among them, H k =diag[h 1k ,h 2k ,…,h mk ].

[0064] Assuming that within the selected frequency band, Satisfies independent complex Gaussian distribution, and its mean is The covariance matrix is ​​S e I n ,Right now Assuming uniformly distributed prior information, according to Bayes' theorem, the posterior probability density function of the modal parameter set θ can be expressed as:

[0065]

[0066] Among them, L(θ) is the negative log-likelihood function, that is,

[0067]

[0068] Where N f is the number of fast Fourier transform values ​​in the selected frequency band; the superscript * indicates the conjugate transpose. The maximum a posteriori estimate of the modal parameter set θ It can be determined by solving the minimum value of the negative log-likelihood function shown in formula (7). The present invention will use a semi-analytical coordinate descent method to solve the problem through iteration. This is because the negative log-likelihood function is nonlinearly dependent on f and ζ, and the updated values ​​of both need to be given by numerical optimization methods rather than analytical expressions. Since the optimization process only involves 2m parameters (m is usually not more than 3), an efficient solution can be achieved using a simplex search method (such as the function "fminsearch" in MATLAB). If a numerical optimization method is used to obtain the updated value of the vibration mode, the computational efficiency will be greatly reduced as the measurement degrees of freedom increase, so an analytical expression of the updated value of the vibration mode is required to achieve a rapid solution of the modal parameters. Specifically, formula (7) is rewritten as:

[0069]

[0070] Where: tr[.] is the symbol for finding the matrix trace, Re(.) is the symbol for taking the real part; let formula (8) be about The first-order derivative of is equal to zero, and we can get The updated value of is:

[0071]

[0072] Normalized vibration shape for modal mass By performing unit normalization processing, the unit normalized mode vibration shape Φ can be obtained.

[0073] Let formula (8) be about S e The first-order derivative of is equal to zero, and the updated value of the measurement noise can be obtained, that is:

[0074]

[0075] At this time, except for the frequency and damping ratio, other unknown parameters are updated in the form of analytical solutions. The updated values ​​of the frequency and damping ratio can be obtained by directly numerically optimizing formula (8) using the function "fminsearch" in MATLAB.

[0076] Usually, impact vibration testing can be achieved through hammer tests or car-jump tests. The former can generally measure the magnitude of the impact force in real time, providing complete information for modal parameter identification, thereby reducing the uncertainty in modal parameter identification. However, impact methods such as car-jump tests are difficult to directly measure the impact force, so separate modeling is required for unknown impact load amplitudes. Specifically, when the impact load is unknown, it can be modeled as p(t) = Qδ(t), where Q represents the impact amount and δ(t) is the Dirac function. At this time, the fast Fourier transform value p of the impact load p(t) is k =Q, that is, the value of the impact load is a constant in the frequency domain. At this time, formula (7) can be rewritten as

[0077]

[0078] in, is the normalized vibration mode matrix of impact quantity-modal mass. Let formula (11) be about The first-order derivative of is equal to zero, and we can get The updated value of is:

[0079]

[0080] Since the vibration mode can be arbitrarily scaled, the solution and solve The physical meaning is equivalent, and there is no need to solve the specific value of Q. Normalized vibration mode of impact quantity-modal mass The unit normalized mode shape Φ can be obtained by performing unit normalization processing.

[0081] Let formula (11) be about S e The first-order derivative of is equal to zero, and the updated value of the measurement noise can be obtained, that is:

[0082]

[0083] Similarly, by directly optimizing formula (11) numerically using the function “fminsearch” in MATLAB, the updated values ​​of the frequency and damping ratio can be obtained.

[0084] In addition, before using the proposed algorithm for modal parameter identification, it is necessary to first give some initial values ​​of modal parameters to drive the coordinate descent method for iterative solution:

[0085] (1) The method for setting the initial value of the frequency to be identified is: based on the obtained structural output data, the structural power spectrum density matrix is ​​calculated and its eigenvalue is calculated, and a graph of the eigenvalue versus frequency is plotted, i.e., the singular value spectrum of the structural response, and the peak value of the singular value spectrum of the structural response is selected to determine the initial value of the frequency.

[0086] (2) The method for setting the initial value of the damping ratio to be identified is: assuming that the initial value of the damping ratio of all modes is 1%.

[0087] In summary, Figure 1 The modal parameter identification algorithm flow based on impact vibration testing is demonstrated.

[0088] Based on the above algorithm flow, a description is given below in conjunction with specific embodiments.

[0089] like Figure 2 As shown, the test structure is an eight-story shear frame model, each floor height is 150mm, and each floor is composed of a rigid aluminum floor slab with a size of 250mm×350mm. Use an impact hammer to apply an impact load along the negative direction of the X-axis at degree of freedom 1. The accelerometers are arranged diagonally on each floor, and 5 seconds of structural vibration signals are collected at a sampling frequency of 2048Hz. In order to reduce the amount of calculation, the original data is downsampled to 256Hz, and the first 5 seconds of data with larger amplitude are selected for modal identification. So far, in this impact vibration test, a total of 1 structural input and 16 structural output acceleration time history data have been collected. The data are subjected to fast Fourier transform to obtain the corresponding frequency domain data, and the singular value spectral density diagrams are drawn based on this, which are shown in Figure 3 In. From Figure 3 It can be seen from (b) that the acceleration singular value spectral density of the impact load is approximately constant with frequency, which is close to the nature of pulse excitation. Figure 3In (c), the root singular value spectral density diagram of the structural acceleration response shows that there are three obviously excited modes in the first 40 Hz, and the frequency bands and initial values ​​selected for identifying the three modes are represented by square brackets and circles in the figure. The feasibility of the present invention will be explained from two cases of known impact load and unknown impact load.

[0090] (1) When the impact load is known, the updated value of the corresponding modal vibration shape can be calculated by formula (9) using the selected initial frequency value and the artificially set initial damping ratio value of 1%, as well as the structural input and output data within the frequency band. Then, the updated values ​​of the frequency and damping ratio are obtained by minimizing formula (8) using the simplex method. Subsequently, the updated value of the measurement error can be calculated according to formula (10). Finally, the updated values ​​of the corresponding vibration shape, frequency, damping ratio, and measurement error are substituted into the negative log-likelihood function to calculate its function value. Repeat the above process until the change in the function value meets the convergence requirements. At this time, the above parameter values ​​obtained are the mean estimates of the modal parameters of the test structure, and they are displayed in Figure 4 middle.

[0091] (2) When the impact load is unknown, the updated value of the corresponding modal vibration shape can be calculated by formula (12) using the selected initial frequency value and the artificially set initial damping ratio value of 1%, as well as the structural output data within the frequency band. Next, the updated values ​​of the frequency and damping ratio are obtained by minimizing formula (11) using the simplex method. Subsequently, the updated value of the measurement error can be calculated according to formula (13). Finally, the updated values ​​of the corresponding vibration shape, frequency, damping ratio, and measurement error are substituted into the negative log-likelihood function to calculate its function value. Repeat the above process until the change in the function value meets the convergence requirements. At this time, the above parameter values ​​obtained are the mean estimates of the modal parameters of the test structure, and they are displayed in Figure 5 middle.

[0092] In summary, it can be seen that the method proposed in the present invention is able to identify the first and second order translation modes (TX1, TX2) and the first order torsional mode (R1) of the structure along the X-axis direction.

[0093] The above-mentioned embodiments only express several implementation modes of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. For those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A fast Bayesian identification method for structural modal parameters under impact test, characterized in that: The method comprises the following steps: 1) Performing an impact vibration test on the engineering structure to be tested. If the structural input load of the impact vibration test is known, collecting the structural input load and structural vibration response time history data of the impact vibration test; if the structural input load of the impact vibration test is unknown, only collecting the structural vibration response time history data; 2) Perform fast Fourier transform on the structural vibration response time history data to obtain the corresponding frequency domain data, and select the frequency band where the modal parameters to be identified are located; 3) If the structural input load is known in step 1), a negative log-likelihood function is constructed based on the structural input load and the frequency domain data in the selected frequency band. If the structural input load is unknown, a negative log-likelihood function is constructed based only on the frequency domain data in the selected frequency band. The negative log-likelihood function is related to the modal parameters to be identified; the modal parameters to be identified include the modal frequency f, the modal damping ratio ζ, the unit normalized modal vibration shape Φ, and the power spectral density S of the measurement error. e ; 4) Based on the constructed negative log-likelihood function, the semi-analytical coordinate descent method is used to iteratively solve the mean estimate of the modal parameters; during the iteration process, the unit normalized modal vibration shape φ and the power spectral density S of the measurement error are e The updated value of is given by analytical expression, and the updated value of modal frequency and modal damping ratio is given by numerical optimization method; In step 3), the negative log-likelihood function is constructed based on the structural input load and the frequency domain data in the selected frequency band: in, is the set of modal parameters to be identified, is the modal mass normalized mode shape, S e is the power spectral density of the measurement error; n is the number of degrees of freedom of the measurement, N f is the number of fast Fourier transform points in the selected frequency band, is the fast Fourier transform value of the measured structural response, p k is the fast Fourier transform value of the impact load; the superscript "*" is the conjugate transpose symbol, the superscript T represents the matrix transpose, tr[.] is the matrix trace symbol, Re(.) is the symbol for taking the real part; l is a distribution vector whose elements are all 1, H k =diag[h 1k ,h 2k ,…,h mk ] is the diagonal matrix of the frequency response function, diag[·] represents the matrix diagonalization symbol, h ik is the i-th order frequency response function, h ik The expression is: Among them, f k is the kth frequency domain coordinate corresponding to the data, q is the applicable factor of the data type, and the value of q is changed according to the type of structural vibration response time history data. ik is the ratio of the i-th modal frequency to the k-th frequency domain coordinate, ζ i is the i-th order modal damping ratio, f i is the i-th order modal frequency; In step 3), the negative log-likelihood function is constructed based only on the frequency domain data in the selected frequency band: in, is the normalized mode shape of impact quantity-modal mass, Q is a constant, which represents the impact quantity.

2. The method for rapid Bayesian identification of structural modal parameters under impact test according to claim 1, characterized in that: In the step 4), the semi-analytical coordinate descent method is used to iteratively solve and obtain the mean value estimation of the modal parameters, which specifically includes the following steps: 4.1) Take the derivative of the constructed negative log-likelihood function to obtain the unit normalized mode shape Φ and the power spectral density S of the measurement error e An analytical expression to update the value; 4.2) Using Φ and S e Update the analytical expression of the value and solve for Φ and S e The updated value of 4.3) The solved Φ and S e Substitute the updated value of into the negative log-likelihood function constructed in step 3), and numerically optimize the negative log-likelihood function by the simplex method to obtain the updated values ​​of the modal frequency f and the modal damping ratio ζ; 4.4) Repeat steps 4.2) and 4.3) until the negative log-likelihood function no longer decreases, and the modal frequency f, modal damping ratio ζ, unit normalized modal vibration shape Φ and power spectral density S of the measurement error are obtained. e The mean estimate of .

3. The method for rapid Bayesian identification of structural modal parameters under impact test according to claim 2, characterized in that: If the structural input load is known, in step 4.1), the constructed negative log-likelihood function is differentiated to obtain the unit normalized modal vibration shape Φ and the power spectral density S of the measurement error. e The analytical expression for updating the value is: The negative log-likelihood function constructed in step 3) is derived with respect to the power spectral density of the modal mass normalized modal vibration shape and the measurement error, and the modal mass normalized modal vibration shape is The first-order derivative of is equal to zero, and the solution is obtained to obtain the normalized modal vibration shape of the modal mass Parsing expression to update the value: right By performing unit normalization, we can get the updated value of the unit normalized modal vibration shape Φ; let the power spectrum density S of the measurement error be e The first-order derivative of is equal to zero, that is, the power spectral density S of the measurement error is obtained by solving e Parsing expression to update the value:

4. The method for rapid Bayesian identification of structural modal parameters under impact test according to claim 2, characterized in that: If the unknown structure input load is used, in step 4.1), the constructed negative log-likelihood function is differentiated to obtain the unit normalized modal vibration shape Φ and the power spectral density S of the measurement error. e The analytical expression for the updated value is, Derivative the negative log-likelihood function constructed in step 3) with respect to the power spectral density of the normalized modal vibration shape of the impact quantity-modal mass and the measurement error, and let The first-order derivative of is equal to zero, and the normalized modal vibration shape of the impact amount-modal mass is obtained by solving Parsing expression to update the value: right By performing unit normalization, we can get the updated value of the unit normalized modal vibration shape φ; let the power spectrum density S of the measurement error be e The first-order derivative of is equal to zero, that is, the power spectral density S of the measurement error is obtained by solving e Parsing expression to update the value:

5. The method for rapid Bayesian identification of structural modal parameters under impact test according to claim 2, characterized in that: In step 4.2), Φ and S are first solved e When updating the value of , first set the initial value of the modal frequency f and the modal damping ratio ζ, and solve Φ and S for the non-first time. e When the updated value is used, the values ​​of the modal frequency f and the modal damping ratio ζ are both taken as the last updated values ​​of the modal frequency f and the modal damping ratio ζ.

6. The method for rapid Bayesian identification of structural modal parameters under impact test according to claim 5, characterized in that: The initial value of the modal damping ratio is 1%; The initial value of the modal frequency is determined by the following method: calculating the structural power spectrum density matrix and its eigenvalues ​​based on the acquired structural output data, plotting the variation of the eigenvalues ​​with frequency, i.e., the singular value spectrum of the structural response, and selecting the peak value of the singular value spectrum of the structural response to determine the initial value of the modal frequency.

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