High-rise structure damage identification method based on optimal fractional order statistical moment

Abstract

The invention relates to the technical field of structural damage identification, and discloses a high-rise structure damage identification method based on an optimal fractional order statistical moment, which takes a wind power tower tube structure as an example, and comprises the following steps: obtaining the optimal fractional order statistical moment and a structural modal shape; obtaining an optimal fractional order statistical moment ratio curve of the adjacent measuring points based on the optimal fractional order statistical moment, and judging a structural damage position through the fractional order statistical moment ratio curve; and based on the structural modal shape, identifying the structural damage degree through an improved direct stiffness method. By the adoption of the method, the structure damage position and degree can be recognized only through one-time measurement, structural initial state data are not needed, the method has the advantages of being efficient and accurate, the method is suitable for rapid primary screening of damage of a wind power tower drum structure and other high-rise structures, and a scientific basis is provided for subsequent maintenance measures.

Description

Technical Field

[0001] The invention relates to the technical field of structural damage identification, and in particular to a method for identifying damage of a tall structure based on optimal fractional-order statistical moments. Background Art

[0002] Tall structures are exposed to complex and changeable natural environments for a long time, such as extreme weather and changes in geological conditions. These factors work together to make tall structures prone to various forms of damage. These damages will not only reduce the bearing capacity and stability of tall structures, but may also cause safety accidents, posing a serious threat to the normal operation of tall structures and the safety of personnel. Therefore, timely and accurate identification, positioning and quantitative analysis of the damage to tall structures are of great significance to ensure the safe operation of tall structures, extend the service life of tall structures, and reduce operation and maintenance costs.

[0003] Traditional damage detection methods, such as visual inspection, are simple and easy to use, but they have problems such as low detection efficiency and insufficient accuracy, making it difficult to meet the detection needs of large-scale tall structures. In recent years, with the rapid development of sensor technology, signal processing technology, and artificial intelligence technology, a series of damage identification methods have emerged.

[0004] So far, most damage detection methods for tall structures require analyzing the dynamic response signals before and after structural damage. For the rapid initial screening of the health status of tall structures, multiple tests are time-consuming, labor-intensive, cost-intensive, inefficient, and complex to operate. Summary of the invention

[0005] The present invention mainly provides a method for identifying damage to tall structures based on optimal fractional-order statistical moments, so as to solve the problems of existing damage identification of tall structures, such as multiple detections being time-consuming and labor-intensive, increasing costs, reducing efficiency, and complex operations.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] The damage identification method of tall structures based on optimal fractional statistical moments includes:

[0008] Obtain the optimal fractional statistical moment and structural mode shape;

[0009] Based on the optimal fractional statistical moment, the optimal fractional statistical moment ratio curve of adjacent measuring points is obtained, and the structural damage position is determined by the optimal fractional statistical moment ratio curve;

[0010] Based on the structural mode shapes, the structural damage degree is identified through the improved direct stiffness method.

[0011] Beneficial effects: This method only requires one measurement to identify the location and extent of structural damage, without the need for initial structural state data. It is efficient and accurate and is not only suitable for wind turbine tower structures, but also for rapid initial screening of damage in other tall structures, providing a scientific basis for subsequent maintenance measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flow chart of the wind turbine tower damage identification method based on the optimal fractional statistical moment after obtaining the acceleration signal of the wind turbine tower structure in the same direction;

[0013] Figure 2 This is a schematic diagram of the length, 4.1m diameter, 2.5m diameter, and mass points of a typical 2MW wind turbine tower;

[0014] Figure 3 This is a comparison chart of working conditions 1-4 curves under no noise conditions, 40dB conditions, and 30dB conditions when a 2MW typical wind turbine tower uses White noise;

[0015] Figure 4 This is a comparison chart of working condition 1-4 curves when a 2MW typical wind turbine tower uses EI-centro wave under noiseless conditions, 40dB conditions, and 30dB conditions;

[0016] Figure 5 This is the identification result diagram of working condition 1 under different excitation and different signal-to-noise ratio conditions;

[0017] Figure 6 This is the identification result diagram of working condition 2 under different excitation and different signal-to-noise ratio conditions;

[0018] Figure 7 The identification results of working condition 3 under different excitation and different signal-to-noise ratio conditions;

[0019] Figure 8 The identification results of condition 4 under different excitations and different signal-to-noise ratios. DETAILED DESCRIPTION

[0020] The following will further describe in detail the technical solution of the wind turbine tower damage identification method based on optimal fractional-order statistical moments according to the present invention in combination with embodiments.

[0021] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0022] like Figure 1 As shown, the damage identification method of a tall structure based on the optimal fractional statistical moment of this embodiment, taking a wind turbine tower structure as an example, includes:

[0023] Obtain the optimal fractional statistical moment and structural mode shape;

[0024] Among them, the acceleration signal of the wind turbine tower structure in the same direction is collected, and the acceleration signal is integrated and band-pass filtered to calculate and obtain the optimal fractional statistical moment and the corresponding structural modal vibration shape;

[0025] Based on the optimal fractional statistical moment, the optimal fractional statistical moment ratio curve of adjacent measuring points is obtained, and the structural damage position is determined by the optimal fractional statistical moment ratio curve;

[0026] Based on the structural mode shapes, the structural damage degree is identified through the improved direct stiffness method.

[0027] Further, the obtaining of the optimal fractional-order statistical moment and structural modal vibration shape includes:

[0028] When a multi-degree-of-freedom structure is subjected to ground acceleration When excited, its equation of motion is:

[0029]

[0030] In formula (1), M, C, K, Respectively represent mass matrix, damping matrix, stiffness matrix, acceleration response, velocity response and displacement response; P(t) is the excitation; I is the unit column vector;

[0031] From the orthogonality of the vibration mode, it can be seen that when the structure is Rayleigh damped, the vibration mode response motion equation of the structure can be obtained:

[0032]

[0033] In formula (2), Y n (t) is the generalized coordinate corresponding to the nth vibration mode, M n , N,ξ n ,ω nare the nth-order generalized mass, degree of freedom, nth-order damping ratio and nth-order circular frequency of the structure, respectively. n (t) is the generalized force corresponding to the nth mode;

[0034] For a low critical damping structural system, the modal response to be solved is:

[0035]

[0036] Based on the mode superposition method, the displacement response z of the i-th measuring point of the structure i (t) can be expressed as:

[0037]

[0038] In formula (5), It represents the value of the n-th vibration mode of the structure at the i-th measuring point. Under the condition of steady excitation, the response process of the linear elastic structure will also be steady, and its autocorrelation function is:

[0039]

[0040] Substitute formula (3) into formula (6) to simplify and solve the displacement response autocorrelation function of the i-th measuring point:

[0041]

[0042] In formula (7), Indicates incentive P m (t) and P n covariance function of (τ+t); autocorrelation function R of displacement response of the i-th measuring point zi (τ) is transformed by Fourier transform to obtain the power spectrum function of the displacement response of the i-th measuring point:

[0043]

[0044] Substituting formula (7) into formula (8) can solve the power spectrum density function of the displacement response of the i-th measuring point:

[0045]

[0046] In formula (9), Indicates incentive P m (t) and P n The cross power spectral density function of (τ+t) is:

[0047]

[0048] In formula (10), and They represent the mth and nth order generalized stiffness of the structure respectively. For a small damping system, the cross term in formula (9) contributes very little to the structural response. In this case, formula (9) can be simplified as follows:

[0049]

[0050] In formula (11), 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 S 0 , then the external load P n The autopower spectral density function of (t) It can be expressed as:

[0051]

[0052] Substituting formula (10) and formula (12) into formula (11), we can obtain the power spectrum density function S of the displacement response of the i-th measuring point: zi (ω), using the relationship between the standard deviation and the response power spectrum density function, we can get the j-th order 32 / 7-th order displacement statistical moment of the i-th measuring point, that is, the 32 / 7-th order displacement statistical moment is the optimal fractional-order statistical moment:

[0053]

[0054] Where Γ is the Gamma function, is the j-th order 32 / 7-th order displacement statistical moment of the i-th measuring point;

[0055] Similarly, the j-th 32 / 7-th order displacement statistical moment of the i+1-th measuring point can be obtained, and the optimal fractional-order statistical moments of two adjacent measuring points are compared to obtain:

[0056]

[0057] When the structural inherent parameters are determined, the mode ratio of adjacent measuring points should be a constant. From formula (14), it can be obtained that the mode ratio of adjacent measuring points is the statistical moment ratio. The j-th order statistical moment ratio between the i-th measuring point and the i+1-th measuring point is defined as Set the vibration mode value of measuring point 1 as the reference point, then the vibration mode vector can be calculated for:

[0058]

[0059] In formula (15), It represents the jth 32 / 7th order vibration mode value at the i-th measuring point. Through the above derivation, the structural modal vibration mode can be solved by the 32 / 7th order displacement statistical moment.

[0060] Further, the method of obtaining an optimal fractional-order statistical moment ratio curve of adjacent measuring points based on the optimal fractional-order statistical moment, and judging the structural damage position by the optimal fractional-order statistical moment ratio curve, includes:

[0061] Based on 32 / 7 order displacement statistical moment To obtain damage indicators, the damaged position of the wind turbine tower structure is detected;

[0062] Statistical moment of 32 / 7th order relative displacement of the i-th measuring point That is, the 32 / 7th order displacement statistical moment of the i-th measuring point relative to the i-1-th measuring point can be expressed as:

[0063]

[0064] Similarly, the 32 / 7th order displacement statistical moment of the i+1th measuring point relative to the ith measuring point can be obtained: Then the ratio of adjacent measuring points can be expressed as:

[0065]

[0066] For a tall structure model that can be approximately simplified as a cantilever beam, the first-order bending vibration mode expression of the structure under initial conditions can be obtained:

[0067]

[0068] In formula (16), A 1 is a non-zero constant, aL=1.875; in the field measurement, assuming that the distance between adjacent measuring points is h, and the height of the i-th measuring point is y, then the fractional statistical moment ratio at the measuring point y is:

[0069]

[0070] Substituting formula (18) into formula (19) and taking the derivative of the height y of the measuring point, we can obtain:

[0071]

[0072] In formula (20), C>0, and the ratio is always greater than 0 under the condition of y∈(h, lh), that is, when the lateral stiffness of the high-rise structure does not change, the optimal fractional statistical moment ratio curve between the adjacent lower measuring point and the upper measuring point increases with the height of the measuring point, showing a smooth and continuous increasing trend;

[0073] When the stiffness changes, the matrix perturbation method shows that the structural mass matrix and stiffness matrix will change accordingly, as shown below:

[0074] M=M 0 +εM 1

[0075] K=K 0 +εK 1 (twenty one)

[0076] In formula (21), M 0 , K 0 are the mass matrix and stiffness matrix corresponding to the original system respectively, ε is the damage parameter, when ε=0, it is the original system, εM 1 , εK 1 They represent the mass matrix change and the stiffness matrix change respectively. The solution to the structural eigenvalue problem can be expressed as:

[0077]

[0078] In formula (22), φ n is the nth-order vibration mode vector, is the square value of the nth order circular frequency; when the mass matrix and stiffness matrix change, that is, εM 1 ,εK 1 When changes occur, the eigenvalues ​​and eigenvectors will change; according to the perturbation method, φ n and λ n Expanding into a power series according to ε, we can get:

[0079] λ n =λ 0n +ελ 1n +ε 2 λ 2n +…

[0080] φ n =φ 0n tεφ 1n +ε 2 φ 2n +… (23)

[0081] In formula (23), λ 0n ,φ 0n are the eigenvalue and eigenvector of the original system, λ 1n ,φ 1n are the first-order perturbations of eigenvalues ​​and eigenvectors, respectively, 2n ,φ 2n are the second-order perturbations of eigenvalues ​​and eigenvectors respectively; when the structural lateral stiffness changes and the mass matrix does not change, the first-order perturbation value can be expressed as:

[0082]

[0083] When the lateral stiffness of the mth section of the tall structure, that is, between measuring points m and m-1, changes, we can get:

[0084]

[0085] Substituting formula (24) and (25) into formula (23), we can solve:

[0086]

[0087] In formula (26), represents the mth element corresponding to the nth vibration mode of the original system; Substituting formula (26) into formula (19), the optimal fractional-order statistical moment ratio of the i-th measuring point can be expressed as:

[0088]

[0089] When the lateral stiffness of the structure changes at the mth segment, it can be seen from formula (13) that the optimal fractional statistical moment of the i-th measuring point will change accordingly; define Δ i It represents the optimal fractional statistical moment change of the measuring point i before and after the sudden change of the structural stiffness, as shown below:

[0090]

[0091] Substituting formula (27) into formula (28) and solving it, we can obtain:

[0092]

[0093] In formula (29), U is a non-zero constant term; when m≠i, the change Δ i Approaches 0; when the mth segment of the structural stiffness mutation is close to the measuring point i, that is, m≈i, the change Δ i Not 0; when the structure lateral stiffness mutation m segment is not equal to the measuring point i, the change Δ i Close to 0, when the structure lateral stiffness mutation m segment is close to the measuring point i, the change Δ i The change is large; combined with formula (20), it can be obtained that the optimal fractional statistical moment ratio curve only produces large fluctuations at the position where the stiffness changes suddenly, and maintains a continuous and smooth state at the position where the stiffness does not change suddenly;

[0094] The structural damage location is judged based on the state of the optimal fractional statistical moment ratio curve, and the place where the curve suddenly changes is the damage location.

[0095] Furthermore, the identification of the degree of structural damage based on the structural modal vibration shape and through an improved direct stiffness method includes:

[0096] If the modal vibration shape changes uniformly and linearly within the unit, and only the first-order modal vibration shape is considered, we can get:

[0097]

[0098] In formula (30), M i and Mi+1 The bending moment values ​​at both ends of the i-th unit; V i and V i+1 Respectively represent the shear force values ​​at both ends of the i-th unit; ω 1 ,ρ,λ,φ 1 (x) represents the first-order frequency, density, cross-sectional area and the first-order vibration mode value at the x position respectively; the unit node bending moment M obtained by formula (30) i Substituting into the following formula, the element stiffness can be calculated:

[0099]

[0100] In formula (31), EI i is the bending stiffness of the i-th unit, φ″ i is the modal curvature of the ith unit, which can be calculated by the central difference method.

[0101] In order to study the effectiveness of the proposed method in identifying damage of tall structures, the theoretical derivation is verified by taking a typical 2MW wind turbine tower as an example.

[0102] like Figure 2 As shown in the figure, the wind turbine tower structure is 81.5m, with a bottom diameter of 4.1m and a top diameter of 2.5m, and a wall thickness of 20mm. The structural material is Q345D steel, with a Poisson's ratio of 0.3 and a density of 7850kg / m 3 , the elastic modulus is 210GPa. The focus of this paper is the tower of the wind power generation structure, so the upper mass of the structure is simplified to a mass point, which is 90t. The structure is evenly divided into 20 sections according to the height. Next, the two-step method of damage identification is simulated and verified.

[0103] The first step is damage location:

[0104] like Figure 3 As shown in the figure, the optimal fractional statistical moment is used to preliminarily judge whether the wind turbine tower structure is damaged. This method only requires one on-site measurement and has the characteristics of rapid detection. Structural damage is simulated by reducing the stiffness of the tower segment, while considering the influence of environmental noise and external excitation. Environmental noise is achieved by applying noise with a signal-to-noise ratio of 40dB and 30dB on the structural response, and white noise and EI-centro waves are used for external excitation to verify the feasibility of the proposed method. The damage conditions set are: Condition 1, the structure is not damaged; Condition 2, the stiffness of unit 15 is reduced by 10%; Condition 3, the stiffness of unit 11 is reduced by 20%; Condition 4, the stiffness of units 7 and 13 is reduced by 20%.

[0105] Table 1 below is a table showing the working conditions of a 2MW typical wind turbine tower using White noise and EI-centro waves:

[0106] Table 1 Working condition table

[0107]

[0108] like Figure 3 As shown in the figure, when the external excitation is Gaussian white noise, the identification results of the four working conditions under different signal-to-noise ratio conditions. Under noise-free conditions, the curve of working condition 1 is smooth, without mutation, indicating that the structure is not damaged, which is consistent with the working condition setting. Working conditions 2, 3 and 4 have mutations in units 15, 11, 7 and 13, respectively, indicating that damage has occurred at the location. At the same time, it can be obtained that the greater the degree of damage, the more obvious the curve mutation. Under 40dB and 30dB conditions, the curve fluctuates in a small range compared to when there is no noise, but mutations occur at the damaged location, and the damage location is accurately determined.

[0109] To verify the applicability of the proposed method under different incentive conditions, such as Figure 4 As shown in the figure, four working conditions are simulated using EI-centro waves, and the recognition results under different signal-to-noise ratio conditions are obtained. It can be seen that under noise-free conditions, the curve is smooth, and only a mutation occurs at the damage location. Under different signal-to-noise ratio conditions, due to the interference of noise, the curve has certain fluctuations, but a drastic mutation occurs at the damage location, and the damage location can still be accurately determined. The first step is to make a preliminary judgment on the location of structural damage, which can be achieved with only one measurement, so it is suitable for rapid detection of wind turbine tower clusters. The second step is to identify the degree of damage at the damage location and compare and verify the recognition results of the first step.

[0110] The second step is to identify the extent of structural damage:

[0111] After identifying the damage location of the wind turbine tower structure, the optimal fractional statistical moment

[0112] Identify the basic modal vibration type of the structure. Then use the improved direct stiffness method to identify the degree of structural damage. This will achieve the positioning and quantification of wind turbine tower structure damage identification.

[0113] Firstly, the optimal fractional statistical moment is obtained and the structural modal vibration shape is verified.

[0114] Feasibility of identifying fundamental vibration modes. Figure 6 Consistent, will The identified result is compared with the theoretical value. The MAC value is usually used to judge the similarity between different vibration modes of the structure and perform quantitative analysis. The closer it is to 1, the higher the correlation. The present invention uses 1-MAC as the evaluation index. Therefore, the closer the value is to 0, the more similar the identified vibration mode is to the theoretical value. Secondly, the principle of the improved direct stiffness method is to perform central difference on the identified basic mode to obtain the modal curvature, and then calculate the corresponding bending moment, and calculate the structural unit stiffness through formula (31). Figure 2 , 3 As shown in Figures 4 and 5, the wind turbine tower structure is divided into 20 units and 21 nodes, where E and N represent units and nodes, respectively. It should be noted that the stiffness value identified by the improved direct stiffness method is the stiffness of each node. Taking working condition 2 as an example, if the stiffness of unit 15 is set to be reduced by 10%, the stiffness values ​​of adjacent nodes 15 and 16 will be reduced by 5% respectively. In this study, the steps for damage degree identification are to first use the optimal fractional statistical moment to identify the damage degree. After identifying the basic vibration mode, the damage degree of the structure is then identified by the improved direct stiffness method. The identification results of conditions 1 to 4 are as follows: Figures 5 to 8 and as shown.

[0115] Table 2 below shows the 1-MAC values ​​of the identification results of the four working conditions:

[0116] Table2(1-MAC)valueunderdifferentcases(×10 -7 )

[0117]

[0118] Figure 5 The identification results of working condition 1 under different excitations and different signal-to-noise ratios are shown in Figure 1. Working condition 1 is the intact structure. The vibration mode identification results under white noise excitation and EI-centro wave excitation are basically consistent with the theoretical values. When the excitation is white noise and the signal-to-noise ratio is 30dB, the maximum 1-MAC value is 9.40×10 -7 , verified Accuracy of identifying the basic vibration mode of the wind turbine tower structure. Based on the vibration mode identified in the previous step, the node stiffness identified by the improved direct stiffness method is also basically consistent with the theoretical stiffness in the undamaged state, with a maximum error of only 2.74%, indicating that the structure is not damaged, which verifies the identification of the damage position in the first stage.

[0119] Figure 6 The identification results of working condition 2 under different excitation and signal-to-noise ratio conditions are shown in Figure 2. Working condition 2 is that the stiffness of unit 15 is reduced by 10%, which means that the stiffness of the corresponding nodes 15 and 16 are reduced by 5% respectively. Under different signal-to-noise ratios and excitation conditions, the identified vibration modes are consistent with the theoretical values, and the maximum 1-MAC value is only 9.96×10-7, indicating that It also has a high accuracy in identifying the basic vibration mode of the damaged wind turbine tower structure. The node stiffness identified by the improved direct stiffness method is offset from the lossless stiffness of the structure at nodes 15 and 16. Taking the structure under E I-centro wave excitation and 30dB noise as an example, the offsets are 6.03% and 5.88% respectively, accurately identifying the degree of damage to the corresponding nodes.

[0120] Figure 7 The identification results of working condition 3 under different excitation and different signal-to-noise ratio conditions. Working condition 3 is that the stiffness of unit 11 is reduced by 20%, which means that the stiffness of the corresponding nodes 11 and 12 is reduced by 10% respectively. The identification of the basic vibration mode is also accurate, with the maximum 1-MAC value of only 16.5×10-7. The identified node stiffness has a large offset at nodes 11 and 12. The maximum offset occurs when the signal-to-noise ratio is 30dB under white noise excitation, which is 11.57% and 12.20% respectively. Figure 6 It can be found that the greater the degree of damage to the structural unit stiffness, the greater the offset at the corresponding node.

[0121] Figure 8 The identification results of condition 4 under different excitation and signal-to-noise ratio conditions are shown in Figure 4. In condition 4, the stiffness of unit 7 and unit 13 is reduced by 20%, and the stiffness of nodes 7, 8, 13 and 14 is reduced by 10% respectively. Under multiple loss conditions, the basic vibration mode identification results are also accurate, with the maximum 1-MAC value of 9.08×10-7. Nodes 7, 8, 13 and 14 are offset, with the maximum offsets of 11.20%, 11.13%, 11.74% and 11.57% respectively.

[0122] In summary, The accurately identified basic vibration modes of the wind turbine tower structure provide a good condition for improving the direct stiffness method to identify the degree of structural damage. The damage locations identified by the ratios are mutually verified. The two-step method has good noise resistance and accurate identification results. Only one measurement is required during on-site measurement, and no initial value is required, which greatly improves the detection efficiency.

[0123] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A damage identification method for tall structures based on optimal fractional statistical moments, characterized in that: include: Obtain the optimal fractional statistical moment and structural mode shape; Based on the optimal fractional statistical moment, the optimal fractional statistical moment ratio curve of adjacent measuring points is obtained, and the structural damage position is determined by the optimal fractional statistical moment ratio curve; Based on the structural mode shapes, the structural damage degree is identified through the improved direct stiffness method.

2. The method according to claim 1, characterized in that The obtaining of the optimal fractional-order statistical moment and structural modal vibration shape comprises: When a multi-degree-of-freedom structure is subjected to ground acceleration When excited, its equation of motion is: In formula (1), M, C, K, X(t) represents the mass matrix, damping matrix, stiffness matrix, acceleration response, velocity response and displacement response respectively; P(t) is the excitation; I is the unit column vector; From the orthogonality of the vibration mode, it can be seen that when the structure is Rayleigh damped, the vibration mode response motion equation of the structure can be obtained: In formula (2), Y n (t) is the generalized coordinate corresponding to the nth vibration mode, M n , N,ξ n ,ω n are the nth-order generalized mass, degree of freedom, nth-order damping ratio and nth-order circular frequency of the structure, respectively. n (t) is the generalized force corresponding to the nth mode; For a low critical damping structural system, the modal response to be solved is: Based on the mode superposition method, the displacement response z of the i-th measuring point of the structure i (t) can be expressed as: In formula (5), It represents the value of the nth-order vibration mode of the structure at the i-th measuring point. Under the condition of steady excitation, the response process of the linear elastic structure will also be steady, and its autocorrelation function is: Substitute formula (3) into formula (6) to simplify and solve the displacement response autocorrelation function of the i-th measuring point: In formula (7), Indicates incentive P m (t) and P n covariance function of (τ+t); autocorrelation function R of displacement response of the i-th measuring point zi (τ) is transformed by Fourier transform to obtain the power spectrum function of the displacement response of the i-th measuring point: Substituting formula (7) into formula (8) can solve the power spectrum density function of the displacement response of the i-th measuring point: In formula (9), Indicates incentive P m (t) and P n The cross power spectral density function of (τ+t) is: In formula (10), and They represent the mth and nth order generalized stiffness of the structure respectively. For a small damping system, the cross term in formula (9) contributes very little to the structural response. In this case, formula (9) can be simplified as follows: In formula (11), 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: Substituting formula (10) and formula (12) into formula (11), we can obtain the power spectrum density function S of the displacement response of the i-th measuring point: zi (ω), using the relationship between the standard deviation and the response power spectrum density function, we can get the j-th order 32 / 7-th order displacement statistical moment of the i-th measuring point, that is, the 32 / 7-th order displacement statistical moment is the optimal fractional-order statistical moment: Where Γ is the Gamma function, is the j-th order 32 / 7-th order displacement statistical moment of the i-th measuring point; Similarly, the j-th 32 / 7-th order displacement statistical moment of the i+1-th measuring point can be obtained, and the optimal fractional-order statistical moments of two adjacent measuring points are compared to obtain: When the structural inherent parameters are determined, the mode ratio of adjacent measuring points should be a constant. From formula (14), it can be obtained that the mode ratio of adjacent measuring points is the statistical moment ratio. The j-th order statistical moment ratio between the i-th measuring point and the i+1-th measuring point is defined as Set the vibration mode value of measuring point 1 as the reference point, then the vibration mode vector can be calculated for: In formula (15), It represents the jth 32 / 7th order vibration mode value at the i-th measuring point. Through the above derivation, the structural modal vibration mode can be solved by the 32 / 7th order displacement statistical moment.

3. The method according to claim 2, characterized in that The method of obtaining an optimal fractional-order statistical moment ratio curve of adjacent measuring points based on the optimal fractional-order statistical moment, and judging the structural damage position by the optimal fractional-order statistical moment ratio curve, comprises: Based on 32 / 7 order displacement statistical moment To detect the damage position of the tall structure as a damage indicator; Statistical moment of 32 / 7th order relative displacement of the i-th measuring point That is, the 32 / 7th order displacement statistical moment of the i-th measuring point relative to the i-1-th measuring point can be expressed as: Similarly, the 32 / 7th order displacement statistical moment of the i+1th measuring point relative to the ith measuring point can be obtained: Then the ratio of adjacent measuring points can be expressed as: For a tall structure model that can be approximately simplified as a cantilever beam, the first-order bending vibration mode expression of the structure under initial conditions can be obtained: In formula (16), A1 is a non-zero constant, aL=1.875; in field measurement, assuming that the distance between adjacent measuring points is h, and the height of the i-th measuring point is y, the fractional-order statistical moment ratio at the measuring point y is: Substituting formula (18) into formula (19) and taking the derivative of the height y of the measuring point, we can obtain: In formula (20), C>0, and the ratio is always greater than 0 under the condition of y∈(h, lh), that is, when the lateral stiffness of the high-rise structure does not change, the ratio curve of the fractional statistical moment between the adjacent lower measuring point and the upper measuring point shows a smooth and continuous increasing trend as the height of the measuring point increases; When the stiffness changes, the matrix perturbation method shows that the structural mass matrix and stiffness matrix will change accordingly, as shown below: M=M0+εM1 K=K0+εK1 (21) In formula (21), M0, K0 are the mass matrix and stiffness matrix corresponding to the original system, ε is the damage parameter, when ε = 0, it is the original system, εM1, εK1 represent the mass matrix change and stiffness matrix change, respectively. The solution to the structural eigenvalue problem can be expressed as: In formula (22), φ n is the nth-order vibration mode vector, is the square value of the nth order circular frequency; when the mass matrix and stiffness matrix change, that is, εM1 and εK1 change, the eigenvalue and eigenvector will change; according to the perturbation method, φ n and λ n Expanding into a power series according to ε, we can get: l n =λ 0n +el 1n +e 2 l 2n +… f n =φ 0n +ef 1n +e 2 φ2 n+ …(23) In formula (23), λ 0n ,φ 0n are the eigenvalue and eigenvector of the original system, λ 1n ,φ 1n are the first-order perturbations of eigenvalues ​​and eigenvectors, respectively, 2n ,φ 2n are the second-order perturbations of eigenvalues ​​and eigenvectors respectively; when the structural lateral stiffness changes and the mass matrix does not change, the first-order perturbation value can be expressed as: When the lateral stiffness of the mth section of the tall structure, that is, between measuring points m and m-1, changes, we can get: Substituting formula (24) and (25) into formula (23), we can solve: In formula (26), represents the mth element corresponding to the nth vibration mode of the original system; Substituting formula (26) into formula (19), the fractional-order statistical moment ratio of the i-th measuring point can be expressed as: When the lateral stiffness of the structure changes at the mth segment, it can be seen from formula (13) that the fractional statistical moment of the i-th measuring point will change accordingly; define Δ i It represents the change of fractional statistical moment of measuring point i before and after the sudden change of structural stiffness, as shown below: Substituting formula (27) into formula (28) and solving it, we can obtain: In formula (29), U is a non-zero constant term; when m≠i, the change Δ i Approaches 0; when the mth segment of the structural stiffness mutation is close to the measuring point i, that is, m≈i, the change Δ i Not 0; when the structure lateral stiffness mutation m segment is not equal to the measuring point i, the change Δ i Close to 0, when the structure lateral stiffness mutation m segment is close to the measuring point i, the change Δ i The change is large; combined with formula (20), it can be obtained that the fractional statistical moment ratio curve only produces large fluctuations at the position where the stiffness changes suddenly, and maintains a continuous and smooth state at the position where the stiffness does not change suddenly; The structural damage location is determined based on the state of the fractional statistical moment ratio curve.

4. The method according to claim 3, characterized in that The method for identifying the degree of structural damage based on structural modal vibration shape and through an improved direct stiffness method includes: If the modal vibration shape changes uniformly and linearly within the unit, and only the first-order modal vibration shape is considered, we can get: In formula (30), M i and M i+1 The bending moment values ​​at both ends of the i-th unit; V i and V i+1 Respectively represent the shear force values ​​at both ends of the i-th unit; ω1, ρ, A, φ1(x) represent the first-order frequency, density, cross-sectional area and the first-order vibration mode value at the x position; the unit node bending moment M obtained by formula (30) i Substituting into the following formula, the element stiffness can be calculated: In formula (31), EI i is the bending stiffness of the i-th unit, φ i is the modal curvature of the ith unit, which can be calculated by the central difference method.

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