Structural modal shape identification method based on fractional order time domain statistical moment

Abstract

The invention provides a structural modal shape recognition method based on a fractional order time domain statistical moment, and the method comprises the steps: taking a high-rise building structure as an example, carrying out the comparison through theoretical derivation and numerical model analysis in combination with actual measurement response data, and carrying out the recognition of the structural modal shape of the high-rise building. The relation between any fractional order statistical moment and the modal shape is theoretically deduced, the optimal fractional order statistical moment-# imgabs0 # is selected through noise immunity analysis, sensitivity analysis and stability analysis based on # imgabs1 # indexes, and numerical simulation shows that the influence of environmental noise and different excitation on the first-order modal shape recognition result is small. Compared with a random subspace method, the method is accurate and high in efficiency, and the method has good noise immunity and is not only suitable for high-rise building structures, but also suitable for bridges and other building structure types.

Description

Technical Field

[0001] The present invention relates to the field related to modal identification, and in particular to a structural modal vibration shape identification method based on fractional-order time-domain statistical moments. Background Art

[0002] The identification of basic mode vibration types has important applications in structural dynamic characteristics analysis, structural vibration control, optimization design, and damage detection. Therefore, accurate identification of structural modes plays a vital role in early detection of structural abnormalities and avoidance of major accidents.

[0003] At present, the identification method of structural modal parameters based on sensors and acquisition systems has become an efficient and practical dynamic characteristic detection method for structural health monitoring. However, among the existing methods, there is no identification through fractional-order time-domain statistical moments. When identifying structural modal parameters, considering the influence of environmental noise, calculation efficiency and measurement errors, there is still a certain distance from practical application. Therefore, there is a lack of a modal identification method with better accuracy and noise resistance, and a method for applying it to practical engineering. Summary of the invention

[0004] In order to solve the above technical problems, the object of the present invention is to provide a structural mode vibration shape identification method based on fractional-order time-domain statistical moments.

[0005] Based on this, the present invention proposes a structural modal vibration shape identification method based on fractional-order time-domain statistical moments, which includes the following steps:

[0006] Step S1: theoretically derive the relationship between any fractional-order statistical moment and the modal vibration shape;

[0007] S11: First, we analyze the single-degree-of-freedom fractional statistical moment. According to the statistical moment theory, for linear elastic structures, the structural response The time-domain statistical moment of order can be expressed as:

[0008] In the formula, express The order time-domain statistical moment; x and μ represent the structural response and the mean of the response respectively; P(x) represents the probability density function of the structural response, which can be derived from the variance and power spectrum density function Order time domain displacement statistical moment and acceleration statistical moment;

[0009]

[0010] Gamma function; m, k, ξ represent the mass, stiffness and damping ratio of the structure respectively; S0 is the value of the excitation power spectrum density function. When the excitation is ideal white noise, S0 is a constant;

[0012] S12: Then, we analyze the multi-degree-of-freedom structure based on the fractional-order statistical moment. The equation of motion for the excitation is:

[0013] Where M, C, and K represent the structural mass matrix, damping matrix, and stiffness matrix, respectively; Respectively represent the acceleration response vector, velocity response vector and displacement response vector of the structural response; P(t) is the external excitation; I is the unit column vector. By assuming that the structure is Rayleigh damped and decoupling it according to the orthogonality of the vibration mode, the motion equation of the structural vibration mode response is obtained. The similar relationship between the acceleration statistical moment and the mode is derived by calculation. For a multi-degree-of-freedom system, The order fractional displacement statistical moments and acceleration statistical moments have corresponding relationships with vibration modes;

[0014] Step S2: Select the optimal fractional-order statistical moment to identify the basic mode vibration shape of the structure by combining noise resistance analysis, sensitivity analysis and stability analysis;

[0015] S21: During on-site measurement, the interference of ambient noise is inevitable. The effect of noise on stiffness change is only related to the noise intensity. Taking a single degree of freedom structure as a model, the noise resistance of different fractional statistical moments is simulated to determine the impact of noise on the recognition results.

[0016] The single degree of freedom structure is a model, the mass of which is 276 kg and the lateral stiffness is 4.97*10 5 N / m, the damping ratio is 0.05, the load excitation is set to Gaussian white noise with a mean equal to zero, the duration is 30s, and the sampling frequency is 100Hz;

[0017] S22: Then, a sensitivity analysis is performed to determine that the sensitivity of the displacement statistical moment of the same fractional order is greater than that of the acceleration statistical moment;

[0018] S23: Finally, for the stability analysis of fractional-order statistical moments, 20 groups of randomly generated Gaussian white noise excitations were selected to obtain different time-history responses, and the means and standard deviations of different fractional-order statistical moments and the corresponding coefficients of variation were solved;

[0019] Step S3: Analyze the modal identification results of the indicator in different excitation forms based on numerical simulation;

[0020] S31: Relying on the 33-story high-rise building structure as the analysis model, the Rayleigh damping sum method is used to solve the dynamic response under a given excitation;

[0021] The 33-story high-rise building structure is used as the analysis model, and the elastic modulus of the beams and columns in the model is 7.751×10 9 N / m2, the height of each floor is 0.3m, the span is 0.6m, the damping ratio is 0.05, and the linear density of beams and columns is 43.911kg / m and 7.35kg / m respectively;

[0022] S32: In the field test, first, sensors are arranged on the same vertical line of the structure to obtain the acceleration response; then bandpass filtering is used to obtain the response signal corresponding to the first-order frequency; secondly, the optimal fractional-order statistical moment is calculated. Finally, the modal vibration shape is solved according to the theoretical derivation formula;

[0023] Step S4: Considering other influencing factors in the field test, the modal identification results of the index under 40dB, 30dB, 20dB and 10dB noise conditions are analyzed based on numerical simulation;

[0024] S41: Apply noise with signal-to-noise ratios of 40dB, 30dB, 20dB, and 10dB to the high-rise structure response, and compare the identified first-order vibration mode with the theoretical calculation value of the finite element model according to the identification process to verify Modal vibration shape identification effect;

[0025] S42: To verify the applicability of the proposed method to non-stationary excitation, El-centro wave and Kobe wave are used as excitations, and the recognition effect of the proposed method is analyzed under 40dB, 30dB, 20dB and 10dB conditions, and quantification is also performed using 1-MAC value;

[0026] Step S5: Taking a high-rise building structure as an example, a field test verification is performed;

[0027] S51: A high-rise residential building in Chongqing was used as the test object. The data acquisition instrument and supporting equipment were placed on the middle floor. Horizontal acceleration sensors were arranged at the centroid of the upper and lower floors. The acceleration time history response of different measuring points was filtered, and the displacement response signal was obtained by integration. Then, the displacement response signal was calculated.

[0028] The high-rise residential building in Chongqing is the test object. The high-rise building has 33 floors in total, with a total height of about 102m, 5 underground floors with a floor height of about 4.5m, and 28 above-ground floors with a floor height of about 2.8m.

[0029] S52: Finally, according to the calculated Through analysis, it is found that the method of identifying vibration modes by indicators has good applicability in actual high-rise building structures.

[0030] The present invention has the following advantages: The present invention provides a structural modal vibration shape identification method based on fractional-order time-domain statistical moments through improvements, which has the following improvements:

[0031] Taking high-rise building structure as an example, through theoretical derivation, numerical model analysis, and comparison with measured response data, the relationship between any fractional-order statistical moment and modal vibration shape is theoretically derived, and the optimal fractional-order statistical moment is selected through noise resistance analysis, sensitivity analysis and stability analysis. based on The numerical simulation shows that the environmental noise and different excitations have little effect on the identification of the first-order mode vibration results, and compared with the random subspace method, it shows the accuracy and high efficiency of the proposed method. This method has good noise resistance and is not only suitable for high-rise building structures, but also for bridges and other building structure types. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the method in the present invention;

[0033] Figure 2 It is a point-line diagram of the noise resistance analysis of fractional-order statistical moments in the present invention;

[0034] Figure 3 It is a point-line diagram of the sensitivity analysis of fractional-order statistical moments in the present invention;

[0035] Figure 4 It is a point-line diagram of the stability analysis of fractional-order statistical moments in the present invention;

[0036] Figure 5 This is a plane model diagram of a high-rise structure in the present invention;

[0037] Figure 6 Identify the flow chart in the present invention;

[0038] Figure 7 The noise under the influence of the present invention Point and line diagram of modal identification results;

[0039] Figure 8 It is a dot-line diagram of the El-centro wave mode recognition result in the present invention;

[0040] Fig. 9 It is a dot-line diagram of the Kobe wave vibration type identification result in the present invention;

[0041] Fig.10 It is a dot-line diagram of the recognition results of different methods in the present invention;

[0042] Fig.11 It is a dot-line diagram of the recognition results in the present invention. DETAILED DESCRIPTION

[0043] For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0044] The specific implementation of the present invention is further described in detail below in conjunction with 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.

[0045] Please refer to Figure 1-11 This embodiment provides a structural modal vibration shape identification method based on fractional-order time-domain statistical moments, the method comprising the following steps:

[0046] Step S1: theoretically derive the relationship between any fractional-order statistical moment and the modal vibration shape;

[0047] Step S11: According to the statistical moment theory, for a linear elastic structure, the structural response The time-domain statistical moment of order can be expressed as:

[0048]

[0049] In the formula, express The order time-domain statistical moment; x and μ represent the structural response and the mean of the response respectively; P(x) represents the probability density function of the structural response, which can be derived from the variance and power spectrum density function Order time domain displacement statistical moment and acceleration statistical moment:

[0050]

[0051] in, and Respectively The sum of the fractional statistical moments of the order displacement The first-order acceleration fractional statistical moment; Γ is the Gamma function; m, k, ξ represent the mass, stiffness and damping ratio of the structure respectively; S0 is the excitation power spectrum density function value, when the excitation is ideal white noise, S0 is a constant;

[0052] Step S12: The multi-degree-of-freedom structure is subjected to ground acceleration The equation of motion for the excitation is:

[0053]

[0054] Where M, C, and K represent the structural mass matrix, damping matrix, and stiffness matrix, respectively; They represent the acceleration response vector, velocity response vector and displacement response vector of the structural response respectively; P(t) is the external excitation; I is the unit column vector. Assuming that the structure is Rayleigh damped, the orthogonality of the vibration mode is used to decouple formula (4) and the motion equation of the structural vibration mode response is obtained:

[0055]

[0056] Among them, Y n (t) is the generalized coordinate corresponding to the nth vibration mode of the structure, M n ,N,ξ n ,ω n are the nth-order generalized mass, degree of freedom, damping ratio and circular frequency of the structure, P n (t) is the generalized force corresponding to the nth-order mode. When the structure satisfies low damping, the vibration response to be solved is:

[0057]

[0058] From the vibration mode superposition method, we can know that the displacement response D of the i-th measuring point is i (t) can be expressed as the linear superposition of n vibration modes:

[0059]

[0060] If the stimulus is stationary, the reaction process will also be stationary, then D i The autocorrelation function R of (t) Di (τ) is:

[0061]

[0062] Substituting formula (6) into formula (9) and simplifying the solution, we can obtain the displacement response autocorrelation function of the i-th measuring point:

[0063]

[0064] in, Indicates incentive P m (t) and P n The covariance function of (τ+t) and the autocorrelation function R of the displacement response to the i-th measuring point Di (τ) is transformed by Fourier transform to obtain the power spectrum function of the displacement response of the i-th measuring point:

[0065]

[0066] Substituting formula (10) into formula (11) can solve the power spectrum density function of the displacement response of the i-th measuring point:

[0067]

[0068] in, Indicates incentive P m (t) and P n The cross power spectral density function of (τ+t) is:

[0069]

[0070] In the formula, and represent the order generalized stiffness of the structure respectively. For a small damping system, formula (12) can be simplified as follows:

[0071]

[0072] In the formula, Indicates incentive P n (t) is the power spectral density function, when the surface excitation acceleration When it obeys a Gaussian distribution with a mean of zero, its autopower spectrum function is a constant S0, then the external load P n The autopower spectral density function of (t) It can be expressed as:

[0073]

[0074] Substituting formula (13) and formula (15) into formula (14), we can obtain the power spectrum density function S of the displacement response of the i-th measuring point: Di (ω):

[0075]

[0076] Using the relationship between the standard deviation and the response power spectral density function, combined with the relationship between the statistical moment and the standard deviation, it can be concluded that The formula for the j-th order response of the j-th order displacement fractional statistical moment at the i-th measuring point is:

[0077]

[0078] Similarly, we can find The expression of the j-th order response of the fractional statistical moment of the displacement at the i+1 measuring point By comparing the fractional statistical moments of the two measuring points, we can get:

[0079]

[0080] It can be seen that the fractional statistical moment ratio of adjacent measuring points is only related to the mode shape ratio. The mode shape belongs to the inherent property of the structure. Therefore, the ratio of the statistical moment of adjacent measuring points is a constant. The ratio of the i measuring point and the i+1 measuring point of the j-th order response of the structure is defined as The order fractional statistical moment ratio is Then the statistical moment ratio vector of all adjacent measuring points is It can be expressed as:

[0081]

[0082] In formula (19) Order statistical moment ratio vector Only related to the mode vibration shape, set the vibration shape value at the measurement point 1 As the reference point, the j-th mode vibration value can be calculated

[0083]

[0084] Similarly, for the acceleration fractional statistical moment, only the order acceleration frequency response function and the order displacement frequency response function are different. The similar relationship between the acceleration statistical moment and the mode can be derived by calculation. Therefore, for the multi-degree-of-freedom system, the order fractional displacement statistical moment and the acceleration statistical moment have a corresponding relationship with the vibration mode;

[0085] Step S2: Select the optimal fractional-order statistical moment to identify the basic mode vibration shape of the structure by combining noise resistance analysis, sensitivity analysis and stability analysis;

[0086] Step S21: During on-site measurement, the interference of ambient noise is inevitable. The noise intensity α is the root mean square ratio of the noise ε and the structural response x:

[0087]

[0088] When the effect of noise is considered, the structural response y can be expressed as:

[0089] y=x+ε

[0090] Formula 22

[0091] Assume that the noise intensity is γ, that is From formula (22), we can get:

[0092]

[0093] Combining formulas (2) and (3), we can find the displacement and acceleration under the influence of noise: The order fractional statistical moment,

[0094]

[0095]

[0096] In the formula, and Respectively represent the The order fractional displacement statistical moment and acceleration statistical moment can be calculated to obtain the stiffness value of the structure under the influence of noise:

[0097]

[0098] In the formula, and They represent the displacement statistical moment stiffness value and acceleration statistical moment stiffness value after adding noise, respectively, k d and k a They represent the stiffness values ​​without noise. From formulas (26) and (27), it can be concluded that the effect of adding noise on the change of stiffness is only related to the noise intensity, but has nothing to do with the order of statistical moments. When the noise intensity is 5%, the stiffness identification result with displacement statistical moment as the indicator is compared with the stiffness identification result without noise, and the stiffness value error is -0.17%; the stiffness identification result with acceleration statistical moment as the indicator is compared with the stiffness identification result without noise, and the stiffness value error is 0.5%. Theoretical derivation shows that both indicators have good noise resistance.

[0099] Next, a single degree of freedom structure is used as a model to simulate the noise resistance of different fractional statistical moments; the mass of the structure is 276kg, and the lateral stiffness is 4.97*10 5 N / m, the damping ratio is 0.05, the load excitation is set to Gaussian white noise with a mean of zero, the duration is 30s, the sampling frequency is 100Hz, the commonly used statistical moment orders are between 2 and 8, and they are all integer orders. When selecting the optimal fractional-order statistical moment, the interval is set to [2, 8]. From theoretical derivation, it can be seen that the fractional-order statistical moment is meaningful only when the denominator of the fractional-order statistical moment is an odd number and the numerator is an even number. When selecting the fractional-order scale, it is considered that it must be different from the integer-order statistical moment and be representative. Therefore, the fractional-order scale is selected as 2 / 7, that is, the order of the fractional-order statistical moment is Through MATLAB simulation, noise with signal-to-noise ratios of 40dB, 30dB, 20dB and 10dB was applied to the structural response to observe the noise resistance of different fractional statistical moments and define the identification error. M and M ε Respectively represent the fractional statistical moments before and after adding noise. The recognition results are as follows: Figure 2 As shown;

[0100] from Figure 2It can be seen that the noise resistance of the fractional statistical moment of the same order is better than that of the acceleration, which is consistent with the theoretical derivation. Under the conditions of 40dB and 30dB, the maximum identification error of the displacement fractional statistical moment and the acceleration fractional statistical moment is only 2.62%. Under the condition of 20dB, the maximum identification error of the fractional displacement statistical moment is 4.06%, and the identification error of the acceleration statistical moment less than 34 / 7 order is less than 5%. Under the condition of 10dB, the identification error of any order acceleration statistical moment exceeds 5%, and the minimum value is 5.29%. The identification error of the displacement statistical moment less than 34 / 7 order is less than 5%. Under the same signal-to-noise ratio, with the increase of the order, the identification error of the fractional statistical moment of displacement and acceleration increases, and the discreteness of the identification error of the fractional statistical moment of acceleration is greater than that of the fractional statistical moment of displacement. However, the theoretical derivation shows that the influence of adding noise on the recognition result is only related to the noise intensity, and has nothing to do with the order of the statistical moment. In addition to the influence of noise, the sensitivity and stability of the fractional statistical moment index have a certain influence on the recognition result. Therefore, the sensitivity and stability of the fractional statistical moment index are analyzed.

[0101] Step S22: Differentiate both ends of formula (2) and (3) and divide them by the original formula to obtain the sensitivity of the fractional displacement statistical moment and acceleration statistical moment:

[0102]

[0103] From the above formula, we can get: the sensitivity of fractional displacement statistical moment to stiffness is greater than that of fractional acceleration statistical moment, which is 3 times greater; the displacement statistical moment and acceleration statistical moment have opposite directions to the change of stiffness, the displacement statistical moment decreases with the increase of stiffness, and the acceleration statistical moment increases with the increase of stiffness; when the order is larger, the statistical moment is more sensitive to the change of stiffness. Taking the above single degree of freedom structural model as an example, the working conditions of different degrees of damage such as 5%, 10% and 15% stiffness reduction are set respectively to observe the sensitivity of fractional statistical moment. Due to space limitations, some fractional statistical moment identification results are selected for display, such as Figure 3 As shown;

[0104] Figure 3 The sensitivity analysis results of eight fractional statistical moments are given. The sensitivity of displacement statistical moments of the same fractional order is greater than that of acceleration statistical moments, which is consistent with the theoretical derivation. When the order increases, the sensitivity of displacement and acceleration statistical moments increases accordingly. If only the sensitivity of fractional statistical moments is considered, high-order fractional statistical moments seem to be the most ideal indicators. However, the calculation of statistical moments is based on the assumption of a stable Gaussian time-history response under arbitrary excitation. In actual numerical calculations, due to the influence of limited duration and unstable transient dynamic response in the initial stage, the statistical moments of structural response are unstable. Therefore, the stability of fractional statistical moments will be analyzed in the next section.

[0105] Step S23: Select 20 groups of randomly generated Gaussian white noise excitations to obtain different time-history responses, and solve the means and standard deviations of different fractional-order statistical moments and the corresponding coefficients of variation, which can be specifically expressed as:

[0106]

[0107] Among them, δ i represents the coefficient of variation of the i-th order statistical moment, σ(M i ) and μ(M i ) represent the standard deviation and mean of the i-th order statistical moment, respectively. The coefficient of variation of each order fractional statistical moment is as follows: Figure 4 As shown;

[0108] Depend on Figure 4 It can be seen that the displacement statistical moment of the same fractional order is more stable than the acceleration statistical moment. The higher the order, the larger the coefficient of variation, that is, the more unstable the identification result. According to the noise resistance analysis results, under the condition of 10dB, the identification error of the fractional acceleration statistical moment is greater than 5%. When the order is less than 34 / 7, the displacement statistical moment identification error is less than 5%. From the sensitivity analysis results, it can be seen that with the increase of the order, the sensitivity of the fractional displacement statistical moment and the acceleration statistical moment increases accordingly. Combining the above analysis, it can be concluded that the optimal fractional statistical moment suitable for solving the vibration mode is That is, the 32 / 7 order displacement statistical moment;

[0109] Step S3: Analyze the modal identification results of the indicator in different excitation forms based on numerical simulation;

[0110] Step S31: Relying on the 33-story high-rise building structure as the analysis model, Figure 5 As shown, the elastic modulus of the beam and column is 7.751×10 9 N / m2, the height of each floor is 0.3m, the span is 0.6m, the damping ratio is 0.05, the linear density of beams and columns is 43.911kg / m and 7.35kg / m respectively, and the Rayleigh damping and Newmark-β method are used to solve the dynamic response under given excitation;

[0111] Step S32: In the field test, the first-order mode is easy to obtain and relatively accurate. Therefore, only the basic modal vibration response of the high-rise building is considered in the vibration mode analysis. First, sensors are arranged on the same vertical line of the structure to obtain the acceleration response; then, band-pass filtering is used to obtain the response signal corresponding to the first-order frequency; secondly, the optimal fractional-order statistical moment is calculated. Finally, the modal vibration shape is solved according to the theoretical derivation formula. The specific identification process is as follows: Figure 6 As shown;

[0112] Step S4: Considering other influencing factors in the field test, the modal identification results of the index under 40dB, 30dB, 20dB and 10dB noise conditions are analyzed based on numerical simulation;

[0113] Step S41: During the field test, the signal will inevitably be interfered by the environmental noise, thus affecting the accuracy of modal identification. Noises with signal-to-noise ratios of 40dB, 30dB, 20dB and 10dB are applied to the high-rise structure response respectively. Figure 5 The process compares the identified first-order vibration mode with the theoretical calculated value of the finite element model to verify The results of modal vibration shape identification are as follows: Figure 7 As shown, 1-MAC (MAC is the modal assurance criterion) is used to quantitatively analyze the recognition results. The recognition results are shown in Table 1. The closer the 1-MAC value is to 0, the closer the mode identified by the method is to the theoretical solution, and vice versa.

[0114] Table 1. Vibration mode identification (1-MAC) values ​​under noise (×10 -5 )

[0115]

[0116] from Figure 7 As shown in Table 1, under noise conditions, the vibration modes identified by the proposed method are in good agreement with the theoretical values. As the noise intensity increases, the 1-MAC value of the identified vibration mode gradually increases, which means that the deviation from the theoretical value is larger. Even under the condition of 10 dB, the 1-MAC value is only 3.18×10 -5 The results show that the The index identifies the basic mode shape with good noise resistance;

[0117] Step S42: To verify the applicability of the proposed method to non-stationary excitation, El-centro wave and Kobe wave are used as excitations, and the recognition effect of the proposed method is analyzed under the conditions of 40dB, 30dB, 20dB and 10dB. The 1-MAC value is also used for quantification. The recognition results are as follows: Figure 8 , Fig. 9 As shown in Table 2;

[0118] Table 2 Vibration mode identification (1-MAC) values ​​under different excitations (×10 -5 )

[0119]

[0120] From the recognition results, it can be seen that the modal curves identified by El-centro wave and Kobe wave as excitations basically coincide with the theoretical curves, and the basic vibration mode can still be accurately identified. The greater the noise interference, the greater the impact on the recognition results. Under the condition of 10dB, the maximum 1-MAC value is 56.10×10 -5 , the results show that, The indicator also has good mode identification effect under non-stationary excitation;

[0121] Step S43: To further illustrate the advantages of the proposed method in identifying vibration modes, the random subspace method (SSI) commonly used in actual engineering modal identification of civil structures is selected for comparison. This method can accurately identify the modal parameters of the structure to a certain extent and is currently a widely recognized method for identifying modal parameters of structural environmental vibration. Based on the above numerical model, Kobe waves are used as excitation to compare the recognition accuracy and efficiency of different methods under 20 dB conditions. The results are as follows: Fig.10 As shown in Table 3;

[0122] Table 3 Different vibration mode identification (1-MAC) values ​​(×10 -5 )

[0123]

[0124] from Fig.10 It can be seen that under the 20dB condition, The index is better in agreement with the theoretical value compared with the mode identified by the random subspace method. Similarly, it can be found from Table 3 that the 1-MAC value of the first-order vibration mode identified by the proposed method is smaller than that of the random subspace method, and the recognition accuracy is higher. In terms of computational efficiency, the random subspace method takes nearly 10 seconds to run once on a computer with the same configuration, while the proposed method only takes no more than 1 second, which is more efficient.

[0125] Step S5: Taking a high-rise building structure as an example, a field test verification is performed;

[0126] Step S51: The test object is a high-rise residential building in Chongqing. The high-rise building has 33 floors in total, with a total height of about 102m, 5 underground floors with a floor height of about 4.5m, and 28 above-ground floors with a floor height of about 2.8m. The main structure construction has been completed, and it is a regular structure in plane and vertical layout, such as Fig. 9 As shown, the data acquisition instrument and supporting equipment are placed on the middle floor, and horizontal acceleration sensors are arranged at the centroids of the upper and lower floors. The acquisition time is 50s and the sampling frequency is 100Hz.

[0127] Step S52: The first-order frequency of the high-rise building structure in the X direction is 0.891 Hz. The acceleration time history response of different measuring points is filtered, integrated to obtain the displacement response signal, and then calculated. The basic mode shape solved is as follows Fig.11 As shown, and compared with the results identified by random subspace;

[0128] from Fig.11 Can get, The first-order vibration mode identified by the index is basically consistent with the first-order vibration mode identified by the random subspace, with only a slight deviation, indicating that the proposed The method of identifying vibration modes by indicators has good applicability in actual high-rise building structures. Although the identification results are basically the same, the computational efficiency of the proposed method is much higher than that of the random subspace method.

[0129] Through theoretical derivation, numerical model analysis of high-rise building structures, and comparison with measured response data of a high-rise building, the relationship between any fractional-order statistical moment and modal vibration shape is theoretically derived, and the optimal fractional-order statistical moment is selected through noise resistance analysis, sensitivity analysis and stability analysis. based on Indicators, numerical simulation shows that environmental noise and different excitations have little effect on the identification of the first-order mode vibration results, and compared with the random subspace method, it shows that the proposed method is accurate and efficient. This method has good noise resistance, and the engineering applicability is verified through a field test of a high-rise building structure.

[0130] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A structural mode shape identification method based on fractional-order time-domain statistical moments, characterized in that: The method comprises the following steps: Step S1: theoretically derive the relationship between any fractional-order statistical moment and the modal vibration shape; Step S2: Select the optimal fractional-order statistical moment to identify the basic mode vibration shape of the structure by combining noise resistance analysis, sensitivity analysis and stability analysis; Step S3: Analyze the modal identification results of the indicator in different excitation forms based on numerical simulation; Step S4: Considering other influencing factors in the field test, the modal identification results of the index under 40dB, 30dB, 20dB and 10dB noise conditions are analyzed based on numerical simulation; Step S5: Perform on-site testing and verification using a high-rise building structure as an example.

2. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 1 is characterized in that: The specific steps of theoretically deriving the relationship between any fractional statistical moment and the modal vibration shape as described in step S1 above are: S11: First, we analyze the single-degree-of-freedom fractional statistical moment. According to the statistical moment theory, for linear elastic structures, the structural response The time-domain statistical moment of order can be expressed as: In the formula, express The order time-domain statistical moment; x and μ represent the structural response and the mean of the response respectively; P(x) represents the probability density function of the structural response, which can be derived from the variance and power spectrum density function Order time domain displacement statistical moment and acceleration statistical moment; S12: Then, we analyze the multi-degree-of-freedom structure based on the fractional-order statistical moment. The equation of motion for the excitation is: Where M, C, and K represent the structural mass matrix, damping matrix, and stiffness matrix, respectively; X(t) represents the acceleration response vector, velocity response vector and displacement response vector of the structural response respectively; P(t) is the external excitation; I is the unit column vector. By assuming that the structure is Rayleigh damped and decoupling it according to the orthogonality of the vibration mode, the motion equation of the structural vibration mode response is obtained. The similar relationship between the acceleration statistical moment and the mode is derived by calculation. For a multi-degree-of-freedom system, The order fractional displacement statistical moments and acceleration statistical moments have corresponding relationships with vibration modes.

3. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 1 is characterized in that: The specific steps of theoretically deriving the relationship between any fractional statistical moment and the modal vibration shape as described in step S2 above are: S21: During on-site measurement, the interference of ambient noise is inevitable. The effect of noise on stiffness change is only related to the noise intensity. Taking a single degree of freedom structure as a model, the noise resistance of different fractional statistical moments is simulated to determine the impact of noise on the recognition results. S22: Then, a sensitivity analysis is performed to determine that the sensitivity of the displacement statistical moment of the same fractional order is greater than that of the acceleration statistical moment; S23: Finally, for the stability analysis of the fractional-order statistical moments, 20 different groups of randomly generated Gaussian white noise excitations were selected to obtain different time-history responses, and the means and standard deviations of different fractional-order statistical moments and the corresponding coefficients of variation were solved.

4. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 1 is characterized in that: The specific steps of theoretically deriving the relationship between any fractional statistical moment and the modal vibration shape as described in step S3 above are: S31: Relying on the 33-story high-rise building structure as the analysis model, the Rayleigh damping sum method is used to solve the dynamic response under a given excitation; S32: In the field test, first, sensors are arranged on the same vertical line of the structure to obtain the acceleration response; then bandpass filtering is used to obtain the response signal corresponding to the first-order frequency; secondly, the optimal fractional-order statistical moment is calculated. Finally, the modal vibration shape is solved according to the theoretical derivation formula.

5. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 1 is characterized in that: The specific steps of theoretically deriving the relationship between any fractional statistical moment and the modal vibration shape as described in step S4 above are: S41: Apply noise with signal-to-noise ratios of 40dB, 30dB, 20dB, and 10dB to the high-rise structure response, and compare the identified first-order vibration mode with the theoretical calculation value of the finite element model according to the identification process to verify Modal vibration shape identification effect; S42: To verify the applicability of the proposed method to non-stationary excitation, El-centro wave and Kobe wave are used as excitations, and the recognition effect of the proposed method is analyzed under 40dB, 30dB, 20dB and 10dB conditions, and quantification is also performed using 1-MAC value; S43: To further illustrate the advantages of the proposed method in identifying vibration modes, the random subspace method, which is commonly used in actual engineering modal identification of civil structures, is selected for comparison.

6. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 1 is characterized in that: The specific steps of theoretically deriving the relationship between any fractional statistical moment and the modal vibration shape as described in step S5 above are: S51: A high-rise residential building in Chongqing was used as the test object. The data acquisition instrument and supporting equipment were placed on the middle floor. Horizontal acceleration sensors were arranged at the centroids of the upper and lower floors. The acceleration time-history responses at different measuring points were filtered, and the displacement response signals were obtained by integration. Then, the displacement response signals were calculated. S52: Finally, according to the calculated Through analysis, it is found that the method of identifying vibration modes by indicators has good applicability in actual high-rise building structures.

7. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 2 is characterized in that: The The order time domain displacement statistical moment and acceleration statistical moment are calculated by the following formula: Gamma function; m, k, ξ represent the mass, stiffness and damping ratio of the structure respectively; S0 is the value of the excitation power spectrum density function. When the excitation is ideal white noise, S0 is a constant.

8. The structural mode vibration shape identification method based on fractional-order time-domain statistical moments according to claim 3 is characterized in that: The single degree of freedom structure is a model, the mass of which is 276 kg and the lateral stiffness is 4.97*10 5 N / m, the damping ratio is 0.05, the load excitation is set to Gaussian white noise with a mean equal to zero, the duration is 30s, and the sampling frequency is 100Hz.

9. The structural modal vibration shape identification method based on fractional-order time-domain statistical moments according to claim 4 is characterized in that: The 33-story high-rise building structure is used as the analysis model, and the elastic modulus of the beams and columns in the model is 7.751×10 9 N / m2, the height of each floor is 0.3m, the span is 0.6m, the damping ratio is 0.05, and the linear densities of beams and columns are 43.911kg / m and 7.35kg / m respectively.

10. The structural mode vibration shape identification method based on fractional-order time-domain statistical moments according to claim 6, characterized in that: The high-rise residential building in Chongqing is the test object. The high-rise building has 33 floors in total and a total height of about 102 meters, including 5 underground floors with a floor height of about 4.5 meters and 28 above-ground floors with a floor height of about 2.8 meters.

Images