Non-model detection method for abrupt change position of lateral stiffness of high-rise structure

Abstract

The application belongs to the technical field of building structure damage identification, and particularly relates to a model-free detection method for lateral stiffness mutation position of a high-rise structure, comprising the following steps: step one, obtaining the displacement time history response of the same height interval measuring points in the same vertical line of the high-rise structure in the same horizontal direction; step two, calculating the second-order statistical moment of the relative displacement of each measuring point according to the time history response, and solving the lower-to-upper value corresponding to the statistical moment of the measuring point; step three, taking the height of each measuring point as the horizontal coordinate and the lower-to-upper value corresponding to the statistical moment of the measuring point as the vertical coordinate to draw a curve; and step four, observing the mutation of the curve to identify the lateral stiffness mutation position.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of building structure damage identification, and particularly relates to a model-free detection method for a lateral stiffness mutation position of a high-rise structure. BACKGROUND

[0002] There are many high-rise structures in China, which are typical and common engineering projects in civil engineering structures. It is of great significance to detect high-rise structures, find the lateral stiffness mutation area of the high-rise structure, timely find and evaluate the position and degree of internal damage of the structure, and predict the performance change of the structure.

[0003] The structure detection method based on dynamic test data can be divided into model-based detection and model-free detection according to whether a original finite element model needs to be established. The model-based detection method mainly includes residual force vector method, eigenvalue sensitivity method, strain energy method, etc. This kind of method can relatively accurately identify the change position of the local lateral stiffness of the structure, but needs to establish a benchmark finite element model, which in turn has the defects of cumbersome operation of establishing the model, model error, and relatively long time period. The model-free detection method mainly includes frequency change method, mode shape change method, flexibility matrix change method, and statistical moment change method. The model-free detection method does not need to establish an original finite element model, avoids the influence of model error on structure detection, and can quickly diagnose whether the local lateral stiffness of the structure is mutated, which is more conducive to the application and promotion in practical engineering. However, considering the complexity of the actual environment, there is still a big gap from practical application.

[0004] Corresponding to the detection of high-rise structures, the above-mentioned model-free detection methods all need to extract the dynamic response data of the high-rise structure before the lateral stiffness mutation, that is, the traditional model-free detection method based on frequency change, mode shape change and flexibility matrix change needs to be compared with the benchmark indicators such as frequency, mode shape and flexibility matrix under the initial benchmark condition of the structure. There are shortcomings such as the need for benchmark model data indicators and the fact that the mutation position of the stiffness is not obvious, and it is difficult to identify and even misjudge, which makes it difficult to apply in the actual environment with noise. SUMMARY

[0005] In view of the above-mentioned deficiencies in the prior art, the application provides a model-free detection method for a lateral stiffness mutation position of a high-rise structure, to solve the problems mentioned in the background art.

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

[0007] The model-free detection method for the lateral stiffness mutation position of the high-rise structure comprises the following steps:

[0008] Step one. Obtain the time history response of the displacement of the measuring points with the same height and interval in the same vertical line of the high-rise structure in the same horizontal direction;

[0009] Step two. Calculate the second order statistical moment of the relative displacement of each measuring point according to the time history response, and solve the lower-upper ratio of the statistical moment of the corresponding measuring point;

[0010] Step three. Draw a curve with the height of each measuring point as the horizontal coordinate and the lower-upper ratio of the statistical moment of the corresponding measuring point as the vertical coordinate;

[0011] Step four. Observe the mutation of the curve and identify the position of the lateral stiffness mutation.

[0012] Further, when the structure parameters change slightly, according to the perturbation theory of the structure matrix, the mass matrix and the stiffness matrix of the structure will change, which can be represented as:

[0013] M = M0 + εM1, K = K0 + εK1 (27)

[0014] In equation (27), ε is a small parameter. When ε = 0, the system is called the original system. M0 and K0 are the mass matrix and the stiffness matrix of the original system. εM1 and εK1 represent the change in the mass matrix and the stiffness matrix, respectively. The eigenvalue problem of the structure vibration can be represented as:

[0015] Kφ n = λ n Mφ n = ω n 2 Mφ n (28)

[0016] In equation (28), λ n = ω n 2 is the square of the nth order circular frequency of the structure, and φ n is the nth order mode shape vector. When εM1 and εK1 are small, the eigenvalue and the eigenvalue will change slightly from the original system. According to the perturbation theory, the eigenvalue φ n and the eigenvalue λ n can be expanded as a power series according to the small parameter ε, i.e.:

[0017]

[0018] In the above equation, λ 0n and φ 0n are the eigenvalue and the eigenvalue of the original system, λ 1n and λ 2n are the first order perturbation and the second order perturbation of the eigenvalue, respectively, and φ 1n and φ 2nThese are the first-order and second-order perturbations of the eigenvectors, respectively. When the structural parameters change only slightly, the first-order perturbation can be used to obtain a more accurate result. Substituting equations (27) and (29) into (28) for solution, ignoring higher-order infinitesimals, and combining like terms, the structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be obtained. The reduction of the lateral stiffness of the structural segments is used to characterize the abrupt change in stiffness. After the abrupt change, only the structural stiffness matrix changes, while the structural mass matrix remains unchanged, i.e., M1 is a zero matrix. The structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be simplified as follows:

[0019]

[0020]

[0021] Taking a sudden change in lateral stiffness in a single local segment of the structure as an example, when there is a reduction in lateral stiffness in the s-th segment of the structure, then:

[0022]

[0023] Substituting equations (30), (31), and (32) into equation (29) for solution, when the change in lateral stiffness is small, i.e., ε is small, a more accurate solution can be obtained using the first-order perturbation:

[0024]

[0025] In the formula Let represent the element corresponding to the sth element of the nth mode shape of the original system. Substituting equation (33) into (22), the ratio of the lower to upper statistical moments of the i-th layer can be expressed as:

[0026]

[0027] To explore the structure before and after the abrupt change in lateral stiffness at segment s, i (i=1) , The change in the ratio of the statistical moments of the 2...s...N) measurement points to the upper value is introduced as follows: δ represents the change in the ratio of the statistical moments of the measurement points before and after the abrupt change in structural stiffness. Then, the change in the ratio of the statistical moments of the i-th measurement point before and after the abrupt change is δ. i for:

[0028]

[0029] Substituting equation (34) into equation (35) and solving, we can simplify it to:

[0030]

[0031] Similarly, in equation (36) Let represent the s-th element of the first mode shape of the original system, where K is a non-zero term and will not be further expanded. It is easy to see that when s≠i, the change in quantity δ... iApproaching to 0, when s≈i formula (36) can be further simplified, and the result is not zero. That is, when the lateral stiffness mutation section s and the statistical moment under the ratio value solving measuring point i are far apart, the statistical moment ratio change δ i Approaching to 0, when the lateral stiffness mutation section s and the statistical moment under the ratio value solving measuring point i are far apart, the statistical moment ratio change δ i Large, referring to formula (26) the conclusion can be further formed The method for quickly judging the section stiffness mutation position of the high-rise structure, that is, the local lateral stiffness mutation of the structure will cause the statistical moment ratio curve to only produce large fluctuations at the lateral stiffness change position, and the ratio curve produces large folds, and the lateral stiffness is still continuous and smooth at the non-mutation position.

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

[0033] 1. The present application only needs to consider single measurement data results, without the need for comparison of structure data indicators before and after the lateral stiffness mutation of the high-rise structure, and the applicability is stronger.

[0034] 2. The present application directly uses the structure time history response to perform statistical moment index mathematical calculation, the data processing is simpler, and the calculation efficiency is higher.

[0035] 3. The present application uses the statistical moment index for diagnosis, only needs to perform simple solving of the structure response frequency domain index, and the identification result is good or bad depends on the time domain data, is not limited by the structure modal index identification method, and the engineering applicability is stronger.

[0036] 4. The statistical moment of the horizontal dynamic response of the high-rise structure is made into a ratio by using the same vertical line equidistant measuring points, the ratio curve with the height of the measuring point is drawn, and the section lateral stiffness mutation position can be identified through the curve mutation position.

[0037] 5. The numerical model and the measured conical wind power tower data of the high-rise structure show that the section lateral stiffness of the high-rise structure gradually changes, and the statistical moment ratio curve can still quickly diagnose the position of the section lateral stiffness mutation.

[0038] 6. Compared with other model-free detection methods, the method proposed in the present application does not need to compare and analyze the measured data before the structure section stiffness mutation, has great advantages in data processing, and does not have to depend on the advantages and disadvantages of the structure modal parameter extraction method. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 It is a schematic diagram of a planar multi-degree-of-freedom structure in the embodiment of the model-free detection method for the lateral stiffness mutation position of the high-rise structure.

[0040] Figure 2Figure of the simplified model of the high-rise structure in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0041] Figure 3 Figure of the numerical model of the high-rise tower in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application (29 measuring points);

[0042] Figure 4 Figure of the curve of the D value changing with the structure height in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0043] Figure 5 Figure of the curve of the derivative of the lower value to the upper value of the statistical moment in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0044] Figure 6 Figure of the curve of the δ value changing in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0045] Figure 7 Figure of the diagnosis result of the abrupt lateral stiffness position of the structure under the condition of the Gaussian white noise excitation (working condition 1) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0046] Figure 8 Figure of the diagnosis result of the abrupt lateral stiffness position of the structure under the condition of the Gaussian white noise excitation (working condition 2) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0047] Figure 9 Figure of the diagnosis result of the abrupt lateral stiffness position of the structure under the condition of the Gaussian white noise excitation (working condition 3) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0048] Figure 10 Figure of the diagnosis result of the abrupt lateral stiffness position of the structure under the condition of the Gaussian white noise excitation (working condition 4) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0049] Figure 11 Figure of the recognition result of the abrupt lateral stiffness position of the structure under the condition of the EI-Centro wave excitation (working condition 1) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0050] Figure 12 Figure of the recognition result of the abrupt lateral stiffness position of the structure under the condition of the EI-Centro wave excitation (working condition 2) in the embodiment of the model-free detection method for the abrupt lateral stiffness position of the high-rise structure of the application;

[0051] Figure 13Figure for identifying result of the abrupt position of lateral stiffness of the high-rise structure in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application under the excitation condition of EI-Centro wave (working condition 3);

[0052] Figure 14 Figure for identifying result of the abrupt position of lateral stiffness of the high-rise structure in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application under the excitation condition of EI-Centro wave (working condition 4);

[0053] Figure 15 Figure for identifying result of the high-rise structure with gradual change of lateral stiffness under the excitation condition of Gaussian white noise in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application (working condition 1);

[0054] Figure 16 Figure for identifying result of the high-rise structure with gradual change of lateral stiffness under the excitation condition of Gaussian white noise in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application (working condition 2);

[0055] Figure 17 Figure for identifying result of the high-rise structure with gradual change of lateral stiffness under the excitation condition of Gaussian white noise in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application (working condition 3);

[0056] Figure 18 Figure for identifying result of the high-rise structure with gradual change of lateral stiffness under the excitation condition of Gaussian white noise in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application (working condition 4);

[0057] Figure 19 Figure for identifying result of the frequency change method under the working condition 3;

[0058] Figure 20 Figure for identifying result of the mode change method under the working condition 3;

[0059] Figure 21 Figure for identifying result of the flexibility curvature method under the working condition 3;

[0060] Figure 22 Figure for identifying result of the statistical moment change method under the working condition 3;

[0061] Figure 23 Figure for identifying result of the method of the application under the working condition 3;

[0062] Figure 24 Figure for measured acceleration time history response signal in the embodiment of the model-free detection method of the abrupt position of lateral stiffness of the high-rise structure of the application;

[0063] Figure 25Acceleration signal amplitude-frequency curve diagram in a high-rise structure anti-lateral stiffness mutation position model-free detection method embodiment of the present application;

[0064] Figure 26 Statistical moment lower than upper value identification result diagram in a high-rise structure anti-lateral stiffness mutation position model-free detection method embodiment of the present application. DETAILED DESCRIPTION

[0065] In order for those skilled in the art to better understand the present application, the technical solutions of the present application are further described below in combination with the drawings and examples.

[0066] 1 Theoretical analysis

[0067] 1.1 Single degree of freedom statistical moment theory derivation

[0068] The motion equation of a single degree of freedom linear elastic structure can be expressed as:

[0069]

[0070] In formula (1), m, c and k respectively represent the mass, damping and stiffness of the structure. x(t), respectively represent the displacement, velocity and acceleration response of the structure, represents the base excitation, and formula (1) can be further simplified as:

[0071]

[0072] Wherein ξ is the damping ratio of the structure, and ω0 is the circular frequency of the structure. For a linear elastic structure, the variance σ 2 The solution expression is as follows:

[0073]

[0074] In the formula, S f (ω) is the power spectral density function of the excitation. When the excitation is ideal white noise, S f (ω) can be regarded as a constant S0 in the frequency domain range; H(ω) is the frequency response function of the structure, wherein the displacement frequency response function expression is as follows:

[0075]

[0076] According to the above formula, the variance of the displacement response, i.e. the second order statistical moment expression of the displacement response, can be derived as:

[0077]

[0078] As can be seen from formula (5), the change of the structure stiffness will inevitably lead to the change of the statistical moment of the structure response, i.e. the statistical moment can be considered as a structure anti-lateral stiffness mutation discrimination index.

[0079] 1.2 Multi-degree of freedom statistical moment theory derivation

[0080] For high-rise structures, the measurement points are arranged at equal intervals, which can be regarded as a discrete multi-degree of freedom system as shown in Figure 1 , and the motion equation under the action of ground acceleration excitation can be expressed as:

[0081]

[0082] wherein M, C, K represent the mass, damping, and stiffness matrices of the structure, respectively; X(t) is the time history response of acceleration, velocity, and displacement of the structure, respectively; P(t) is the external load column vector, and I is the ground motion influence coefficient matrix corresponding Figure 1 to the structure, which is a column vector with all elements being 1, same as equation (1), and the excitation obeys the Gaussian distribution with a mean of zero, and its power spectral density function is a constant S0.

[0083] Under the condition of Rayleigh damping assumption, equation (6) can be decoupled using the orthogonality of modes to obtain the motion equation of the mode shape response of the structure:

[0084]

[0085]

[0086] In equations (7)-(8), Y n (t) is the generalized coordinate corresponding to the nth mode shape; M n , ξ n , ω n , φ n are the nth generalized mass, damping ratio, circular frequency, and standard mode shape of the structure, respectively; P n (t) is the generalized force corresponding to the nth mode. By solving the nth uncoupled mode shape equation, we can obtain:

[0087]

[0088] For a low-critical damping structure system, in equation (9):

[0089]

[0090] The displacement response Z i (t) of the i-th measurement point of the high-rise structure relative to the i-1-th measurement point (hereinafter referred to as the relative displacement response of the i-th measurement point) can be further expressed as:

[0091]

[0092] wherein The value corresponding to the nth mode shape at the i-th measuring point, under stationary excitation, the response autocorrelation function of a linear elastic structure can be expressed as:

[0093]

[0094] Substituting equation (11) into equation (12) and performing variable substitution, the relative displacement response autocorrelation function of the i-th measuring point can be obtained as:

[0095]

[0096] In equation (13), C is the covariance function of external excitation P m (t) and P n (t+τ). The power spectral density function of the relative displacement response of the i-th measuring point can be obtained by performing Fourier transform on the relative displacement response autocorrelation function, that is:

[0097]

[0098] Substituting equation (13) into equation (14), the power spectral density function of the relative displacement response of the i-th measuring point is obtained as:

[0099]

[0100] In the equation, G is the cross power spectral density function of P m (t) and P n (t), and has:

[0101]

[0102]

[0103] where K m and K n are the m-th and n-th generalized stiffness of the structure, respectively. For a small damping system, the cross term in equation (15) has little contribution to the structural response, so equation (15) can be simplified as:

[0104]

[0105] When the ground excitation acceleration is a Gaussian distribution with a mean of zero, the power spectral density function of the external load P n (t) can be expressed as:

[0106]

[0107] Substitute formula (17) and (19) into formula (18), the relative displacement response power spectral density function of the ith measuring point can be solved. According to the relationship between the power spectral density function and the variance, the second central moment of the relative displacement of the ith measuring point (hereinafter referred to as the displacement second moment) is:

[0108]

[0109] From the above formula, it is not difficult to see that if the lateral stiffness of the structure changes suddenly, the modal shape of the structure will change, thereby causing the statistical moment of the structure response to change. Therefore, for a multi-degree-of-freedom structure system, the statistical moment index can still be used as a basis for judging the sudden change of lateral stiffness.

[0110] 1.3 Theoretical derivation of lateral stiffness mutation position detection based on statistical moment ratio

[0111] From formula (20), it can be seen that the higher order modes have less contribution to the displacement statistical moment, and the displacement statistical moment value mainly depends on the first order modal parameters of the structure. Therefore, formula (20) can be simplified as:

[0112]

[0113] Similarly, the second central moment of the displacement of the ith+1 measuring point relative to the ith measuring point is denoted as The relative displacement statistical moment of the ith+1 measuring point relative to the ith measuring point is denoted as

[0114]

[0115] Therefore, the value of the statistical moment of the ith measuring point can be approximately represented by the square of the relative change of the first order mode of the ith measuring point. Formula (22) is the result of a discrete multi-degree-of-freedom system, and it is difficult to see the special nature from it. For a real distributed parameter system, it can be simplified as shown in formula (23): Figure 2 The Euler cantilever beam structure is shown in formula (23). Under the condition that the lateral stiffness of the structure is constant and there is no sudden change, the stiffness and the mass per unit length can be represented as EI(x) = EI, m(x) = m. The undamped free vibration equation of the structure system is:

[0116]

[0117] In formula (23), v(x, t) is the displacement response of the structure, which is a function of time t and height x. Using the separation of variables method, the solution is assumed to satisfy the following conditions: v(x, t) = φ(x)Y(t), where the mode shape φ(x) is a continuous function. After substituting the boundary conditions of the cantilever beam and solving, the expression of the first order bending mode shape of the structure under the initial condition is obtained as:

[0118]

[0119] C1 is a non-zero constant, aL=1.875. Assuming that the height interval of each measuring point of the high-rise structure is h, and the height of the i-th measuring point is x, it can be seen from equation (22) that the statistical moment ratio of the i-th measuring point under the condition that the structure has no lateral stiffness mutation can be expressed as:

[0120]

[0121] Taking the derivative of equation (25) with respect to the height x of the measuring point, we can obtain:

[0122]

[0123] In the above equation, G is always greater than zero, and it is easy to obtain that equation (26) is always greater than zero under the condition that x∈(h, l-h). That is, under the condition that the lateral stiffness of the high-rise structure is constant and has no mutation, the statistical moment ratio curve of the structure displacement response is continuously and monotonously increasing with the increase of the height of the measuring point. Without loss of generality, when a discrete mode vector array is used to represent, the connecting line of the calculated values of equation (22) will also tend to be smooth, and the statistical moment ratio of the i-th measuring point will increase with the increase of the height of the measuring point.

[0124] Accordingly, an important law of the change of the statistical moment ratio of the measuring point of the high-rise structure with the height of the measuring point under the condition that the lateral stiffness is constant and has no mutation has been solved. When the structure parameters change slightly, the mass matrix and the stiffness matrix of the structure will change accordingly according to the perturbation theory of the structure matrix, which can be expressed as:

[0125] M=M0+εM1, K=K0+εK1 (27)

[0126] In equation (27), ε is a small parameter, and the system is called the original system when ε=0. M0 and K0 are the mass matrix and the stiffness matrix of the original system. εM1 and εK1 represent the change of the mass matrix and the stiffness matrix, respectively. The structure vibration eigenvalue problem can be expressed as:

[0127] Kφ n =λ n Mφ n =ω n 2 Mφ n (28)

[0128] In equation (28), the eigenvalue λ n =ω n 2 is the square of the nth order circular frequency of the structure, and the eigenvector φ n is the nth order mode vector. When εM1 and εK1 are small, the eigenvalue and the eigenvector will change slightly compared with the original system. According to the perturbation theory, the eigenvector φ n and the eigenvalue λ nExpanding this series by the smaller parameter ε, we get:

[0129] λ n =λ 0n +ελ 1n +ε 2 λ 2n +... (29)

[0130] φ n =φ 0n +εφ 1n +ε 2 φ 2n +...

[0131] In the above formula, λ 0n and φ 0n Let λ be the eigenvalues ​​and eigenvectors of the original system. 1n and λ 2n These are the first-order and second-order perturbations of the eigenvalues, φ. 1n and φ 2n These are the first-order and second-order perturbations of the eigenvectors, respectively. When the structural parameters change only slightly, the first-order perturbation can be used to obtain a more accurate result. Substituting equations (27) and (29) into (28) for solution, ignoring higher-order infinitesimals, and combining like terms, the structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be obtained. The reduction of the lateral stiffness of the structural segments is used to characterize the abrupt change in stiffness. After the abrupt change, only the structural stiffness matrix changes, while the structural mass matrix remains unchanged, i.e., M1 is a zero matrix. The structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be simplified as follows:

[0132]

[0133]

[0134] like Figure 1 Taking the tall structure shown as an example, with a sudden change in lateral stiffness in a single local segment, when the s-th segment of the structure experiences a reduction in lateral stiffness, then:

[0135]

[0136] Substituting equations (30), (31), and (32) into equation (29) for solution, when the change in lateral stiffness is small, i.e., ε is small, a more accurate solution can be obtained using the first-order perturbation:

[0137]

[0138] In the formula Let represent the element corresponding to the sth element of the nth mode shape of the original system. Substituting equation (33) into (22), the ratio of the lower to upper statistical moments of the i-th layer can be expressed as:

[0139]

[0140] To explore the structure in the s section of lateral stiffness mutation before and after the i (i = 1 , 2...s...N) measurement point statistical moment ratio change, the introduction of delta represents the structure stiffness mutation before and after the measurement point statistical moment ratio change, then the mutation before and after the i measurement point statistical moment ratio change delta i For:

[0141]

[0142] Substitute equation (34) into equation (35) to solve, which can be simplified as:

[0143]

[0144] Similarly, in equation (36) The first order mode of the original system s element, K is not zero, not further expansion. It is not difficult to find that when s≠i, the change delta i Tends to 0, when s≈i equation (36) can be further simplified, the result is not zero. That is, when the structure lateral stiffness mutation segment s and statistical moment ratio value solving measurement point i interval far, the statistical moment ratio change delta i Tends to 0, when the lateral stiffness mutation segment s and statistical moment ratio value solving measurement point i interval close, the statistical moment ratio change delta i Large, refer to equation (26) conclusion can be further formed high-rise structure rapid judgment segment stiffness mutation position method, namely the structure of local lateral stiffness mutation will lead to statistical moment ratio curve only in the lateral stiffness change place produces larger fluctuation, ratio curve produces larger fold, in the lateral stiffness does not mutate still maintains continuous smooth state.

[0145] 2 Numerical simulation analysis

[0146] 2.1 Model introduction

[0147] Based on the technical data of China Electric Power Construction Group Fengdu Wudongyan area wind power engineering, referring to the previous numerical model of the research group, MATLAB is used to establish a simple dynamic numerical model of high-rise tower. The tower model is 87m high, the outer diameter of the tower is 3.845m, the wall thickness of the tower is 10cm, the tower material is steel, the elastic modulus E0=200×10 9 N / m 2 , the material density is ρ=7850kg / m 3The top generator rotor weighs 100 tons, the generator stator weighs 140 tons, and the total weight of the wind turbine blades is 210 tons. Considering the upper part of the wind turbine unit, including the motor and blades, as a concentrated mass unit, the total weight is 450 tons. Assuming 29 measuring points are evenly spaced along the same vertical line on the tower, the tower is divided into 29 segments for numerical modeling. The height of a single segment is h = 3m, and the damping ratio is set to ξ. i =0.05 (i=1,2), the model is as follows Figure 3 As shown, the solved element stiffness matrix and element mass matrix are combined to form the overall stiffness matrix and mass matrix of the structure. The first-order frequency of the model is 0.26 Hz, which is consistent with the actual monitoring data. Using the Rayleigh damping assumption, the time history response of the structure under a given excitation is solved using the Newmark-β method. Numerical calculations are performed to derive the proposed theory for detecting abrupt changes in lateral stiffness. The applicability of the proposed method is verified by considering factors such as environmental noise, external excitation form, and the actual lateral stiffness distribution of the structure. Based on existing technology, the abrupt change in lateral stiffness of a segment is characterized by the reduction of the elastic modulus of the corresponding tower section. The following working conditions are set:

[0148] Condition 1: The lateral stiffness of each section of the structure is not reduced;

[0149] Condition 2: The lateral stiffness of the 15th section of the structure (at a height of 42m to 45m) is reduced by 10%;

[0150] Condition 3: The lateral stiffness of the 15th section of the structure (at a height of 42m to 45m) is reduced by 20%;

[0151] Condition 4: The lateral stiffness of the 10th section (27m-30m height) and the 20th section (57m-60m height) of the structure is reduced by 20%;

[0152] 2.2 Numerical Verification

[0153] 2.2.1 Theoretical Derivation and Numerical Verification of a Method for Detecting Abrupt Changes in Lateral Stiffness Based on Statistical Moment Ratio

[0154] Simplifying equation (20) to equation (21), it is assumed that the higher-order modes contribute less to the statistical moment of the relative displacement at the i-th measurement point, thus further deriving equation (22). Now, using... Figure 3 The numerical model shown illustrates this simplification through calculation. A variable D is introduced to represent the goodness of fit between the lower and upper ratios of the statistical moments of relative displacement of the structure at the corresponding measuring point and the square of the ratio of the relative changes in the first-order mode shape of the structure, denoted as:

[0155]

[0156] use Figure 3 The numerical model solves equation (37) numerically, and the curves showing the change of D value with height under working conditions 1 to 4 are plotted as follows: Figure 4As shown in the figure:

[0157] As can be seen from the above figure, the maximum error of the fitting degree of the square of the relative change of the structure first-order mode solved by the structural response under the condition of the statistical moment ratio and the known structure mass matrix and stiffness matrix is not more than 2.5% under different working conditions, which shows that the simplification of formula (20) to formula (21) is reasonable and is conducive to the subsequent deduction.

[0158] The derivative of the statistical moment ratio with respect to the measuring point height x can be obtained as formula (26), assuming that the total height of the structure is L and the interval distance between the measuring points is h, then the corresponding Figure 3 The numerical model must be: L = 29h, and the numerical solution of formula (26) is as follows: Figure 5 As shown in the figure:

[0159] Figure 5 The derivative calculation value in the height range of h / L to 28h / L (i.e. h to L-h) is shown, and it is not difficult to see that the derivative value is greater than 0 in the range of x∈(h, L-h), that is, under the condition that the lateral stiffness value of the structure is constant and has no mutation, the statistical moment ratio value changes continuously and monotonically with the measuring point height.

[0160] Through the solution of the derivative of the statistical moment ratio, the basic shape of the statistical moment ratio curve of the high-rise structure under the condition that the lateral stiffness is constant and has no mutation is obtained. When the lateral stiffness value of the structure is mutated, the statistical moment ratio change Figure 3 The numerical model shown can be used to calculate the statistical moment ratio change i The curve relationship with the change of the structure height is as follows: Figure 6 As shown in the figure:

[0161] It is not difficult to see that the statistical moment ratio change will have a relatively large mutation value near the position where the lateral stiffness of the structure is reduced, that is, compared with the case where the stiffness has no mutation, after the local lateral stiffness of the structure is reduced, the smooth and monotonic curve of the statistical moment ratio will present a mutation at the position where the stiffness is reduced, breaking the original continuous and smooth state. Figure 6 From the numerical calculation, it is confirmed that the mutation position of the statistical moment ratio curve can be used to identify the lateral stiffness mutation position of the high-rise structure.

[0162] 2.2.2 Application simulation of the lateral stiffness mutation position detection method based on the statistical moment ratio

[0163] In order to verify the applicability of the detection method to different excitation forms, Gaussian white noise and EI-Centro wave in the prior art are used as external excitation, and the noise resistance of the method is analyzed considering noiseless, signal-to-noise ratio of 40db and 30db environment noise, and at the same time, in order to further fit the actual engineering application, the Figure 3The lateral stiffness of the numerical model is taken in a step-by-step decreasing manner, and the applicability of the method is demonstrated under the condition that the lateral stiffness of the actual high-rise structure gradually changes with the height. The specific operation steps of the method for detecting the position of the sudden change of the model-free lateral stiffness are as follows:

[0164] 1. Obtain the time history response of the displacement of the measuring points at the same height and interval in the same vertical line of the high-rise structure in the same horizontal direction;

[0165] 2. According to the time history response, calculate the second-order statistical moment of the relative displacement of each measuring point, and solve the lower-to-upper value corresponding to the statistical moment of the measuring point;

[0166] 3. Take the height of each measuring point as the abscissa and the lower-to-upper value corresponding to the statistical moment of the measuring point as the ordinate to draw a curve;

[0167] 4. Observe the sudden change of the curve to identify the position of the sudden change of the lateral stiffness;

[0168] According to the detection steps, the method verification simulation analysis is carried out under the conditions of constant lateral stiffness and gradually changing lateral stiffness. The simulation conditions are shown in Table 1:

[0169] Table 1 Numerical simulation condition detail table

[0170]

[0171] (1) Structure with constant lateral stiffness

[0172] It is assumed that the lateral stiffness of each section of the high-rise structure is the same in the initial state, and a stationary Gaussian white noise is used as the external excitation. The time history response of the corresponding measuring point of the structure is extracted, and the statistical moment is solved. The statistical moment ratio is used to judge the position of the sudden change of the lateral stiffness, and the results are shown in Figure 7 、 Figure 8 、 Figure 9 、 Figure 10

[0173] ​From the identification result graph, it is not difficult to see that in the case of working condition 1, the statistical moment ratio curve shows a smooth single-increasing trend without noise influence, and there is no mutation phenomenon, which is consistent with the theoretical derivation result of the statistical moment ratio curve under the condition that the lateral stiffness has no mutation; in the case of 40DB and 30DB noise, the statistical moment ratio curve still shows a single-increasing trend with the increase of height, and there is only burr phenomenon near the top data, but the data point variation coefficient of the statistical moment ratio curve at the top is not more than 0.0043, and it can be considered that there is no obvious mutation position, and it is basically determined that the high-rise structure does not have lateral stiffness mutation. In the case of working condition 2, under the influence of noise, the statistical moment ratio curve shows a smooth single-increasing trend without noise influence, and there is no mutation phenomenon, which is consistent with the theoretical derivation result of the statistical moment ratio curve under the condition that the lateral stiffness has no mutation; in the case of 40DB and 30DB noise, the statistical moment ratio curve still shows a single-increasing trend with the increase of height, and there is only burr phenomenon near the top data, but the data point variation coefficient of the statistical moment ratio curve at the top is not more than 0.0043, and it can be considered that there is no obvious mutation position, and it is basically determined that the high-rise structure does not have lateral stiffness mutation. In the case of working condition 3, with the increase of stiffness reduction, under the conditions of no noise, signal-to-noise ratio 40DB noise and signal-to-noise ratio 30DB noise, the variation coefficient of the statistical moment ratio curve at the lateral stiffness reduction position is up to 0.35, which is 8.89 times that of the remaining positions, and it can be judged that the lateral stiffness mutation is obvious; similarly, under the condition of working condition 4, double lateral stiffness reduction, the detection method proposed in the present application can effectively detect the lateral stiffness mutation position under the conditions of no noise, signal-to-noise ratio 40DB and signal-to-noise ratio 30DB.

[0174] Considering the influence of different external excitations on the method proposed in the present application, EI-Centro wave signals are used for simulation external excitation input, and the simulation calculation results are shown in Figure 11 、 Figure 12 、 Figure 13 and Figure 14 .

[0175] When the external excitation changes, it is not difficult to see from the result curve that under the conditions of no noise, signal-to-noise ratio 40DB noise and signal-to-noise ratio 30DB noise, the lateral stiffness mutation position diagnosis method proposed in the present application can effectively identify the lateral stiffness mutation position, that is, the method proposed in the present application still has strong applicability to non-stationary external excitation conditions.

[0176] (2) Lateral stiffness gradually changing structure

[0177] Considering that in actual engineering structures, the lateral stiffness of high-rise structures generally decreases with the increase of height, the numerical simulation model is adjusted according to the conical shape of the actual tower cylinder model, and the wall thickness of the numerical model is kept unchanged at 10cm, and the outer diameter is taken as D 外径=4.35-nx0.035m(n=1,2...29). That is, with the increase of height, the outer diameter of the high-rise tower drum is in an arithmetic decreasing sequence, and the white noise is used as an external excitation for simulation calculation, and the results are shown in Figure 15 、 Figure 16 、 Figure 17 and Figure 18

[0178] From Figure 15 、 Figure 16 、 Figure 17 and Figure 18 , when the lateral stiffness of the high-rise structure gradually decreases with the increase of the structure height, under the preset working conditions (working condition 1 to working condition 4), the method can still effectively identify the lateral stiffness mutation position, and the identification result is still relatively accurate under the influence of environmental noise with a signal-to-noise ratio of 40DB and 30DB, that is, the method is still applicable to the gradually changing lateral stiffness of the high-rise structure.

[0179] 2.3 Comparison and analysis of model-free detection methods

[0180] The applicability of the model-free lateral stiffness mutation position detection method in the present application and the existing model-free detection methods, frequency change method, mode shape change method, flexibility curvature method and response statistical moment change method, in the lateral stiffness mutation position detection of high-rise structures is compared. Through the above numerical model, under the condition of no noise, working condition 3, that is, the 15th section of the lateral stiffness is reduced by 20%, is selected as the comparative working condition for analysis, the first-order frequency and the first-order mode shape before and after the local mutation of the lateral stiffness of the structure are extracted, and the frequency change index, the mode shape change index, the flexibility curvature difference index and the structure response statistical moment change index are calculated according to the prior art, and the calculation result analysis is shown in Figure 19 、 Figure 20 、 Figure 21 、 Figure 22 and Figure 23

[0181] The analysis Figure 19 、 Figure 20 、 Figure 21 、 Figure 22 and Figure 23 The identification results of different methods are shown in Table 2:

[0182] Table 2 Comparison and analysis of identification results of different detection methods

[0183]

[0184] Based on the analysis of the identification effect of the above model-free lateral stiffness mutation position detection methods, the advantages of the new method for judging the lateral stiffness mutation position based on the statistical moment ratio in the present application mainly include: ​​

[0185] 1. The proposed diagnosis method only needs to consider single measurement data results, without comparing structure data indicators before and after the lateral stiffness mutation of the high-rise structure, and has stronger applicability;

[0186] 2. The proposed diagnosis method directly uses structure time response for statistical moment indicator mathematical calculation, and the data processing is simpler and the calculation efficiency is higher;

[0187] 3. The proposed diagnosis method uses statistical moment indicators for diagnosis, only needs to perform simple solving of structure response frequency domain indicators, and the identification result depends on time domain data, is not limited by structure modal indicator identification method, and has stronger engineering applicability.

[0188] 3. Field test analysis and verification

[0189] The measured data of a newly-built wind power tower structure in Jilong wind farm in Fengdu, Chongqing is selected for method applicability verification analysis. A typical newly-built 2.5MW tower (No. 24 machine) in the region is measured, the total height of the tower is 87.3 meters, and according to the design regulation, it is divided into 5 segments for assembly. Considering the field work platform setting, sensor installation conditions, data acquisition instrument interface quantity and data acquisition line length and other conditions, 5 acceleration sensors are used for synchronous acceleration signal acquisition, among which the data acquisition instrument and the matching acquisition computer are placed near the flange of the connection between the 3rd and 4th segments of the tower on the work platform, and the corresponding sensors are installed at 85m, 64m, 43m, 24m and 3m respectively according to the existing placement conditions in the tower and the requirements of the method, to obtain the acceleration response of the tower body at the same vertical line and the same height interval measuring points in the same horizontal direction:

[0190] During the test measurement process, the external wind is small, the wind turbine is in a shutdown state, and there is no blade rotation. The tower acceleration response acquisition data and the corresponding amplitude-frequency curve are shown in Figure 24 and Figure 25 .

[0191] According to the equal-interval measuring point arrangement requirement of the method, the actual measuring point interval height is about 21m. As can be seen from the figure, the test data of each sensor basically agrees in the frequency domain, and the first-order main frequency is 0.26HZ, which further verifies the correctness of the measured data. The measured acceleration data is used for integral solving of structure displacement response, and the lateral stiffness mutation position is identified by using the method. According to the principle of the diagnosis method, the relative displacement statistical moment lower-to-upper ratio of each measuring point is calculated, and the measured data is analyzed by using the diagnosis method. Due to the limitation of measurement conditions, the number of measuring points is small, the statistical moment lower-to-upper ratio is connected by a smooth curve, and the analysis curve is obtained as Figure 26 .

[0192] As can be seen from the above figure, the statistical moment ratio curve is increased with the increase of the tower height, and the statistical moment is lower than the upper value, which is a single increase state without obvious mutation. It can be determined that the tower section has no stiffness mutation, combined with the operation data of the wind power plant, the tower is a newly built tower, which meets the quality acceptance regulation and is ready for grid connection. The calculation results show that the model-free diagnosis method proposed in the application can be implemented in the diagnosis process of the lateral stiffness mutation position of the actual high-rise structure.

[0193] 4. Conclusion

[0194] The application proposes a lateral stiffness mutation position detection method suitable for high-rise structures, and related theoretical derivation is carried out. Numerical demonstration is carried out by using a numerical model of a high-rise structure, and analysis is carried out combined with actual wind turbine tower structure measured response data, and the following conclusions are summarized:

[0195] 1. The statistical moment of the horizontal dynamic response of the same vertical line of the high-rise structure is used to make a ratio, and the ratio curve with the height of the measuring point is drawn, and the segment lateral stiffness mutation position can be identified by the curve mutation position.

[0196] 2. The numerical model of the high-rise structure and the measured conical wind turbine tower data analysis show that the high-rise structure with gradually changing segment lateral stiffness, the statistical moment ratio curve can still quickly diagnose the position of the segment lateral stiffness mutation.

[0197] 3. Compared with other model-free detection methods, the method proposed in the application does not need to compare and analyze the measured data before the segment stiffness mutation of the structure, and has great advantages in data processing, and does not have to depend on the advantages and disadvantages of the structure modal parameter extraction method.

[0198] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the application and are not limiting, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the application can be modified or replaced by equivalents without departing from the purpose and scope of the application, which should be covered in the scope of the claims of the application.

Claims

1. A model-free method for detecting abrupt changes in the lateral stiffness of tall structures, characterized in that, Includes the following steps: Step 1. Obtain the displacement time history response of the tall structure at equally spaced measuring points along the same vertical line in the same horizontal direction; Step 2. Based on the time history response, calculate the second-order statistical moments of the relative displacement of each measuring point, and solve for the lower ratio of the statistical moments of the corresponding measuring points; Step 3. Plot a curve with the height of each measuring point as the abscissa and the ratio of the lower to the upper statistical moments of the corresponding measuring points as the ordinate. Step 4. Observe the abrupt changes in the curve and identify the locations of abrupt changes in lateral stiffness; The equation of motion for a single-degree-of-freedom linear elastic structure can be expressed as: In equation (1), m, c, and k represent the structural mass, damping, and stiffness, respectively, and x(t), These represent the displacement, velocity, and acceleration responses of the structure, respectively. To represent the basis excitation, equation (1) can be further simplified to: Where ξ is the damping ratio of the structure, ω0 is the angular frequency of the structure, and for a linear elastic structure, the variance of its structural response σ 2 The expression to be solved is as follows: In the formula, S f (ω) is the power spectral density function of the excitation. When the excitation is ideal white noise, S f H(ω) can be considered as a constant S0 in the frequency domain; H(ω) is the frequency response function of the structure, where the expression for the displacement frequency response function is as follows: Based on the above formula, the expression for the variance of the displacement response, i.e., the second-order statistical moment of the displacement response, can be derived as follows: As can be seen from equation (5), changes in structural stiffness will inevitably lead to changes in the statistical moments of structural response. Therefore, the statistical moments can be used as a criterion for discriminating sudden changes in structural lateral stiffness.

2. The model-free detection method for abrupt changes in lateral stiffness of tall structures according to claim 1, characterized in that: When the structural parameters undergo a slight change, according to the structural matrix perturbation theory, the structural mass matrix and stiffness matrix will change accordingly, which can be expressed as: M = M0 + εM1, K = K0 + εK1 (27) In equation (27), ε is a small parameter, corresponding to the system when ε = 0, which is called the original system. M0 and K0 are the mass matrix and stiffness matrix of the original system, respectively. εM1 and εK1 represent the changes in the mass matrix and stiffness matrix, respectively. The structural vibration eigenvalue problem can be expressed as: Kφ n =λ n Mφ n =ω n 2 Mφ n (28) In equation (28), the eigenvalue λ n =ω n 2 The square of the nth-order circumfrequency of the structure, and the eigenvector φ n Let φ be the nth order mode shape vector. When εM1 and εK1 are small, the eigenvalues ​​and eigenvectors will undergo slight changes compared to the original system. According to perturbation theory, the eigenvector φ can be... n and eigenvalue λ n Expanding this series by the smaller parameter ε, we get: In the above formula, λ 0n and φ 0n Let λ be the eigenvalues ​​and eigenvectors of the original system. 1n and λ 2n These are the first-order and second-order perturbations of the eigenvalues, φ. 1n and φ 2n These are the first-order and second-order perturbations of the eigenvectors, respectively. When the structural parameters change relatively little, the first-order perturbation can be used to obtain a more accurate result. Substituting equations (27) and (29) into (28) for solution, ignoring higher-order infinitesimals, and combining like terms, the structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be solved. The reduction of the lateral stiffness of the structural segments is used to characterize the stiffness mutation. After the mutation, only the structural stiffness matrix changes, while the structural mass matrix remains unchanged, i.e., M1 is a zero matrix. The structural eigenvalues ​​and the first-order perturbation of the eigenvectors can be simplified as follows: Taking a sudden change in lateral stiffness in a single local segment of the structure as an example, when there is a reduction in lateral stiffness in the s-th segment of the structure, then: Substituting equations (30), (31), and (32) into equation (29) for solution, when the change in lateral stiffness is small, i.e., ε is small, a more accurate solution can be obtained using the first-order perturbation: In the formula Representing the element corresponding to the sth element of the nth mode of the original system, substituting equation (33) into (22), the ratio of the lower to upper statistical moments of the i-th layer can be expressed as: To explore the change in the ratio of the lower to upper statistical moments of the i-th (i = 1, 2, ..., s...N) measuring point before and after the abrupt change in the lateral stiffness of the structure at segment s, δ is introduced to represent the change in the ratio of the statistical moments of the measuring point before and after the abrupt change in structural stiffness. The change in the ratio of the statistical moments of the i-th measuring point before and after the abrupt change is δ. i for: Substituting equation (34) into equation (35) and solving, we can simplify it to: Similarly, in equation (36) This represents the s-th element of the first mode shape of the original system, where K is a non-zero term. Without further expansion, it is easy to see that when s≠i, the change in quantity δ i Approaching 0, when s≈i, equation (36) can be further simplified, and the result is not zero. That is, when the interval between the abrupt change segment s of the structural lateral stiffness and the measurement point i in the calculation of the lower ratio of the statistical moment is far, the change in the statistical moment ratio δ i When the abrupt change in lateral stiffness s is close to 0, and the interval between the measurement point i used to solve the lower ratio of the statistical moments is relatively small, the change in the statistical moment ratio δ approaches 0. i The results are relatively large. Based on the derivation of formula (26), a method for quickly determining the location of abrupt changes in segment stiffness of tall structures can be further developed. That is, abrupt changes in the local lateral stiffness of the structure will cause the statistical moment ratio curve to fluctuate significantly only at the location of changes in lateral stiffness, and the ratio curve will have large undulations. At the location where there is no abrupt change in lateral stiffness, it will remain in a continuous and smooth state.

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