Rapid structural damage identification method based on vertical array seismic records of super high-rise building

Abstract

The invention belongs to the technical field of structural damage identification, and provides a rapid structural damage identification method based on a vertical array seismic record of a super high-rise building, and the method comprises the following steps: segmenting a seismic oscillation record according to a normalized cumulative energy curve; according to seismic oscillation records in different time periods, determining a structure basic period and shear wave reference propagation time in each time period; determining the actual propagation time of shear waves from the bottom to the top of the structure in different time periods by using a seismic interferometry method based on deconvolution and referring to the shear wave reference propagation time; according to the change amplitude of the equivalent shear stiffness of the structure in different time periods, the damage degree of the structure is evaluated; the method has the advantages of being high in precision, simple in calculation and clear in physical significance, and accurate evaluation of the structural damage of the super high-rise building after the earthquake can be rapidly achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural damage identification, and in particular to a method for rapid structural damage identification based on vertical array seismic records of super high-rise buildings. Background Art

[0002] According to statistics from the Council on Tall Buildings and Urban Habitat, by April 2025, my country had over 3,400 supertall buildings over 150 meters tall, accounting for approximately 50% of the world's total. Furthermore, since 2020, several major cities, including Beijing, Guangzhou, Wuhan, and Shanghai, have implemented structural seismic arrays for supertall buildings. In Wuhan, over 150 supertall buildings have been equipped with structural seismic arrays, which can be used to rapidly assess damage after an earthquake.

[0003] However, existing methods for identifying damage in super-high-rise structures primarily rely on inverting the natural frequency or damping ratio of the structure from its response, and then determining whether the structure has sustained damage based on changes in the natural frequency or damping ratio. However, due to limitations in the accuracy of the inversion results, existing methods struggle to accurately determine whether the structure has sustained minor damage or whether the damage has recovered by the time the earthquake wave ends.

[0004] To this end, technicians in this field have proposed a method for rapid identification of structural damage based on vertical array seismic records of super-high-rise buildings, which is used to accurately assess the damage to buildings after an earthquake. The method aims to use high-precision seismic interferometry to extract the propagation time of shear waves from the top to the bottom of the structure from the vertical array seismic records of the structure, and then determine the degree of structural damage by the change in the equivalent shear stiffness of the structure when the seismic wave just arrives and when it is about to end. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings to solve the problems raised in the background technology.

[0006] A rapid structural damage identification method based on vertical array seismic records of super high-rise buildings includes the following steps:

[0007] S1. Segment the ground motion record according to the normalized cumulative energy curve;

[0008] S2. Determine the structural fundamental period and shear wave reference propagation time in each period based on the seismic motion records at different periods;

[0009] S3. Determine the actual propagation time of shear waves from the bottom to the top of the structure during different time periods using seismic interferometry based on deconvolution, with reference to the shear wave reference propagation time;

[0010] S4. Evaluate the degree of structural damage based on the change in the equivalent shear stiffness of the structure at different time periods.

[0011] Preferably, in step S1, the normalized cumulative energy curve is calculated using the seismic record in the horizontal direction of the top of the structure using the following formula:

[0012]

[0013] Where t1 is the total duration of the earthquake record; a(τ) is the earthquake acceleration history; τ represents time; I(t) is the normalized cumulative energy from the start of the earthquake record to time t;

[0014] The seismic records in the period from 0 to 20% of the normalized cumulative energy are selected as the pre-seismic record segment when the seismic wave just arrives, and the seismic records in the period from 80% to 100% of the normalized cumulative energy are selected as the post-seismic record segment when the seismic wave is about to end. Then, the seismic records in different time periods are removed by averaging, and a tapered cosine window is added to prevent spectrum leakage. The window function expression of the tapered cosine window is:

[0015]

[0016] Where N is the number of sampling points of the intercepted seismic record; n is the half-width of the cosine window, and the calculation formula is:

[0017]

[0018] in, Indicates the floor symbol; r is 0.05.

[0019] Preferably, in step S2, the acceleration response spectrum ratio of the earthquake records at the top and bottom of the structure in different time periods is calculated, and the reference propagation time of the shear wave is determined using the following formula:

[0020]

[0021] Among them, the damping ratio of the acceleration response spectrum is 5%, T1 is the period corresponding to the maximum peak of the response spectrum ratio, that is, the basic period of the structure, and T ref is one quarter of the fundamental period of the structure and serves as the reference propagation time of the shear wave.

[0022] Preferably, in step S3, the seismic records at the top and bottom of the structure in different time periods are processed by fourth-order Butterworth low-pass filtering to reduce the influence of the high-order modes of the structure on the results, wherein the cutoff frequency f c Take the inverse of the reference propagation time of the structural shear wave and express it as;

[0023]

[0024] The deconvolution function between the seismic records at the top and bottom of the structure is calculated in the frequency domain using the following formula:

[0025]

[0026] Where f is the frequency; S1(f) and S2(f) are the Fourier spectra of the acceleration records at the top and bottom of the structure, respectively; * is the complex conjugate; ε is the stability factor, which is 1% of the average power spectrum of the acceleration record at the bottom of the structure;

[0027] The deconvolution function is converted from the frequency domain to the time domain by inverse Fourier transform, and the sampling frequency of the deconvolution function in the time domain is increased to 10000 Hz using the cubic spline interpolation method; the shear wave reference propagation time T is used as the reference propagation time. ref , in [0.5T ref , 1.5T ref ] is searched for the maximum value of the deconvolution function within the range of , and the corresponding time is the actual propagation time tt of the shear wave from the bottom to the top of the structure.

[0028] Preferably, in step S4, the variation range K of the equivalent shear stiffness of the structure in different time periods is calculated by the following formula:

[0029]

[0030] Where G1 and G2 represent the equivalent shear stiffness of the recording section before and after the earthquake, respectively; V S1 and V S2 represent the average shear wave velocity of the structure in the recording section before and after the earthquake, respectively; tt1 and tt2 represent the actual propagation time of the shear wave from the bottom to the top of the structure in the recording section before and after the earthquake, respectively;

[0031] The degree of structural damage is determined based on the value of K: when K is less than 5%, the structure is undamaged; when K is between 5% and 20%, the structure is slightly damaged; when K is between 20% and 50%, the structure is moderately damaged; and when K exceeds 50%, the structure is severely damaged and faces the risk of failure.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The deconvolution-based seismic interferometry method used in the present invention has been proven to be a high-precision shear wave velocity imaging method suitable for vertical seismic arrays. Its error is generally no higher than 1%. Therefore, this method can accurately determine whether a structure has suffered minor damage. At the same time, the seismic interferometry method is computationally simple. Therefore, the present invention is both accurate and efficient.

[0034] 2. The present invention utilizes the close relationship between shear wave velocity and shear stiffness and proposes using the variation amplitude of equivalent shear stiffness as an indicator for evaluating structural damage. This has the advantages of clear physical meaning and is easy to understand and demonstrate. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings of the present invention;

[0036] Figure 2 This is the acceleration record of the top and bottom of the Wuhan Jinyinhu Building in Example 2 of the present invention during the 7.7 magnitude Sagaing earthquake in Myanmar on March 28, 2025;

[0037] Figure 3 This is a diagram of the shear wave propagation time extraction process in the second embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0039] Example 1: As shown in the attached Figure 1 As shown, the present invention provides a method for quickly identifying structural damage based on vertical array seismic records of high-rise buildings, comprising the following steps:

[0040] S1. Segment the ground motion record according to the normalized cumulative energy curve;

[0041] S2. Determine the structural fundamental period and shear wave reference propagation time in each period based on the seismic motion records at different periods;

[0042] S3. Determine the actual propagation time of shear waves from the bottom to the top of the structure during different time periods using seismic interferometry based on deconvolution, with reference to the shear wave reference propagation time;

[0043] S4. Evaluate the degree of structural damage based on the change in the equivalent shear stiffness of the structure at different time periods.

[0044] The normalized cumulative energy curve is calculated using the following formula using the horizontal ground motion data at the top of the structure:

[0045]

[0046] Where t1 is the total duration of the earthquake record; a(τ) is the earthquake acceleration history; τ represents time; I(t) is the normalized cumulative energy from the start of the earthquake record to time t;

[0047] The seismic records in the period from 0 to 20% of the normalized cumulative energy are selected as the pre-seismic recording segment when the seismic wave just arrives, and the seismic records in the period from 80% to 100% of the normalized cumulative energy are selected as the post-seismic recording segment when the seismic wave is about to end. Then, the seismic records in different time periods are removed by mean value processing, and a tapered cosine window is added to prevent spectrum leakage. The window function expression of the tapered cosine window is as follows:

[0048]

[0049] Where N is the number of sampling points of the intercepted seismic record; n is the half-width of the cosine window, and the calculation formula is as follows:

[0050]

[0051] in, Indicates the floor symbol; r is 0.05.

[0052] Calculate the acceleration response spectrum ratio of the earthquake records at the top and bottom of the structure in different time periods (the damping ratio is 5%). The period corresponding to the maximum peak of the response spectrum ratio is the fundamental period T1 of the structure, and take one quarter of the fundamental period of the structure as the reference propagation time T of the shear wave. ref :

[0053]

[0054] The seismic records at the top and bottom of the structure in different time periods are processed by fourth-order Butterworth low-pass filtering to reduce the influence of the high-order modes of the structure on the results. The cutoff frequency f c Taking the inverse of the reference propagation time of the structural shear wave, it can be expressed as;

[0055]

[0056] The deconvolution function between the seismic records at the top and bottom of the structure is calculated in the frequency domain using the following formula:

[0057]

[0058] Where f is the frequency; S1(f) and S2(f) are the Fourier spectra of the acceleration records at the top and bottom of the structure, respectively; * is the complex conjugate; ε is the stability factor, which is 1% of the average power spectrum of the acceleration record at the bottom of the structure;

[0059] The deconvolution function is converted from the frequency domain to the time domain by inverse Fourier transform, and the sampling frequency of the deconvolution function in the time domain is increased to 10000 Hz using the cubic spline interpolation method; the shear wave reference propagation time T is used as the reference propagation time. ref , in [0.5T ref, 1.5T ref ] is searched for the maximum value of the deconvolution function within the range of , and the corresponding time is the actual propagation time tt of the shear wave from the bottom to the top of the structure.

[0060] The variation K of the equivalent shear stiffness of the structure in different time periods is calculated using the following formula:

[0061]

[0062] Where G1 and G2 represent the equivalent shear stiffness of the recording section before and after the earthquake, respectively; V S1 and V S2 represent the average shear wave velocity of the structure in the recording sections before and after the earthquake, respectively; tt1 and tt2 represent the actual propagation time of the shear wave from the bottom to the top of the structure in the recording sections before and after the earthquake, respectively.

[0063] The degree of structural damage can be determined based on the value of K: when K is less than 5%, the structure is undamaged; when K is between 5% and 20%, the structure is slightly damaged; when K is between 20% and 50%, the structure is moderately damaged; when K exceeds 50%, the structure is severely damaged and there is a risk of failure.

[0064] Example 2: Using the solution in Example 1, this example uses earthquake records in the north-south direction collected from the Wuhan Jinyinhu Building (building height 198 meters) during the 7.7 magnitude Sagaing earthquake in Myanmar on March 28, 2024 to assess whether the structure has been damaged. The sampling frequency of the earthquake record is 100Hz, and the recording time is 1800 seconds. Figure 2 The specific implementation process is as follows:

[0065] S1. Using north-south component seismic motion data from the top of the Wuhan Jinyinhu Building structure, we calculated the normalized cumulative energy curve. We selected the 0-468 second segment of the seismic record as the pre-seismic recording period, representing the initial arrival of the seismic wave (the period corresponding to the normalized cumulative energy from 0 to 20%), and the 883.8-1800 second segment of the seismic record as the post-seismic recording period, representing the end of the seismic wave (the period corresponding to the normalized cumulative energy from 80 to 100%). We then removed the mean of the seismic records for each of these two time periods, and added a tapered cosine window to prevent spectral leakage.

[0066] S2. Calculate the acceleration response spectrum ratio of the top and bottom of the Jinyinhu Building in the recording section before and after the earthquake (damping ratio is 5%). It can be determined that the fundamental period of the building structure before and after the earthquake is 4.11 seconds and 4.22 seconds respectively. According to the calculation formula of the shear wave reference propagation time (T ref =T1 / 4), the reference propagation times of shear waves before and after the earthquake are 1.0275 seconds and 1.055 seconds respectively.

[0067] S3. Perform fourth-order Butterworth low-pass filtering on the earthquake records at the top and bottom of the Jinyinhu Building structure in different time periods, where the cutoff frequency f c Take the inverse of the structural shear wave reference propagation time f c =1 / T ref , after substituting, we can obtain: the low-pass filter cutoff frequencies of the pre-earthquake and post-earthquake recording segments are 0.973Hz and 0.948Hz respectively; calculate the deconvolution function between the earthquake records at the top and bottom of the Jinyinhu Building structure in the frequency domain, then convert the deconvolution function from the frequency domain to the time domain through the inverse Fourier transform, and use the cubic spline interpolation method to increase the sampling frequency of the deconvolution function in the time domain to 10000Hz; refer to the shear wave reference propagation time T ref , search for the maximum value of the deconvolution function corresponding to the pre-earthquake and post-earthquake recording segments within [0.51s, 1.54s] and [0.53s, 1.58s], respectively. The corresponding time is the actual propagation time tt of the shear wave from the bottom to the top of the structure (the actual propagation time corresponding to the pre-earthquake and post-earthquake recording segments is 0.9105s and 0.909s, respectively).

[0068] S4. Calculate the variation K of the equivalent shear stiffness of the structure at different time periods using the following formula:

[0069]

[0070] Substituting the propagation time of the shear wave before and after the earthquake, we can get K = -0.33%. Therefore, it can be determined that the Jinyinhu Building did not suffer structural damage in the earthquake. In addition, through this embodiment, it can be found that the structural natural vibration periods corresponding to the pre-earthquake and post-earthquake recording segments are 4.11 seconds and 4.22 seconds respectively, with a difference of more than 2.5%; considering that the peak acceleration at the top of the structure is less than 2 cm / s 2 , the structure will not be damaged, which further verifies that the error of the shear stiffness variation amplitude extracted in this embodiment is smaller than the error of the natural vibration period variation amplitude.

[0071] It is important to note that the construction and arrangement of the present application shown in a plurality of different exemplary embodiments are merely illustrative. Although only a few embodiments are described in detail in this disclosure, it will be readily understood by those who consult this disclosure that many modifications are possible without departing substantially from the novel teachings and advantages of the subject matter described in this application. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the exemplary embodiments without departing from the scope of the present invention. Therefore, the present invention is not limited to specific embodiments, but extends to a variety of modifications that still fall within the scope of the appended claims.

[0072] It will be understood that in the development of any actual embodiment, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort may be complex and time-consuming, but for those of ordinary skill having the benefit of this disclosure, the development effort will be a routine task of design, fabrication, and production without undue experimentation.

[0073] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings, characterized by: The following steps are involved: S1. Segment the ground motion record according to the normalized cumulative energy curve; S2. Determine the structural fundamental period and shear wave reference propagation time in each period based on the seismic motion records at different periods; S3. Determine the actual propagation time of shear waves from the bottom to the top of the structure during different time periods using seismic interferometry based on deconvolution, with reference to the shear wave reference propagation time; S4. Evaluate the degree of structural damage based on the change in the equivalent shear stiffness of the structure at different time periods.

2. The method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings according to claim 1, characterized in that: In step S1, the normalized cumulative energy curve is calculated using the seismic record in the horizontal direction of the top of the structure using the following formula: Where t1 is the total duration of the earthquake record; a(τ) is the earthquake acceleration history; τ represents time; I(t) is the normalized cumulative energy from the start of the earthquake record to time t; The seismic records in the period from 0 to 20% of the normalized cumulative energy are selected as the pre-seismic record segment when the seismic wave just arrives, and the seismic records in the period from 80% to 100% of the normalized cumulative energy are selected as the post-seismic record segment when the seismic wave is about to end. Then, the seismic records in different time periods are removed by averaging, and a tapered cosine window is added to prevent spectrum leakage. The window function expression of the tapered cosine window is: Where N is the number of sampling points of the intercepted seismic record; n is the half-width of the cosine window, and the calculation formula is: in, Indicates the floor symbol; r is 0.

05.

3. The method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings according to claim 1, characterized in that: In step S2, the acceleration response spectrum ratios of the earthquake records at the top and bottom of the structure in different time periods are calculated, and the reference propagation time of the shear wave is determined using the following formula: Among them, the damping ratio of the acceleration response spectrum is 5%, T1 is the period corresponding to the maximum peak of the response spectrum ratio, that is, the basic period of the structure, and T ref is one quarter of the fundamental period of the structure and serves as the reference propagation time of the shear wave.

4. The method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings according to claim 1, characterized in that: In step S3, the seismic records at the top and bottom of the structure in different time periods are processed by fourth-order Butterworth low-pass filtering to reduce the influence of the high-order modes of the structure on the results, where the cutoff frequency f c Take the inverse of the reference propagation time of the structural shear wave and express it as; The deconvolution function between the seismic records at the top and bottom of the structure is calculated in the frequency domain using the following formula: Where f is the frequency; S1(f) and S2(f) are the Fourier spectra of the acceleration records at the top and bottom of the structure, respectively; * is the complex conjugate; ε is the stability factor, which is 1% of the average power spectrum of the acceleration record at the bottom of the structure; The deconvolution function is converted from the frequency domain to the time domain by inverse Fourier transform, and the sampling frequency of the deconvolution function in the time domain is increased to 10000 Hz using the cubic spline interpolation method; the shear wave reference propagation time T is used as the reference propagation time. ref , in [0.5T ref , 1.5T ref ] is searched for the maximum value of the deconvolution function within the range of , and the corresponding time is the actual propagation time tt of the shear wave from the bottom to the top of the structure.

5. The method for rapid identification of structural damage based on vertical array seismic records of super high-rise buildings according to claim 1, characterized in that: In step S4, the variation range K of the equivalent shear stiffness of the structure in different time periods is calculated by the following formula; Where G1 and G2 represent the equivalent shear stiffness of the recording section before and after the earthquake, respectively; V S1 and V S2 represent the average shear wave velocity of the structure in the recording section before and after the earthquake, respectively; tt1 and tt2 represent the actual propagation time of the shear wave from the bottom to the top of the structure in the recording section before and after the earthquake, respectively; The degree of structural damage is determined based on the value of K: when K is less than 5%, the structure is undamaged; when K is between 5% and 20%, the structure is slightly damaged; when K is between 20% and 50%, the structure is moderately damaged; and when K exceeds 50%, the structure is severely damaged and faces the risk of failure.

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