Model-Free Detection Method Based on Statistical Moment Ratio

Abstract

The present invention belongs to the technical field of rapid detection of civil engineering structures, and particularly relates to a model-free detection method based on statistical moment ratios, including the following steps: Step 1, obtain the time history response of the measured point displacement; Step 2, calculate the statistical moment ratios; Step 3, plot the statistical moment ratio curve; Step 4, identify the position of sudden change in segment stiffness. Without quantifying the specific value of the segment stiffness of the structure, the present invention does not need to measure the dynamic response data of the structure in the initial reference state. Only by using the idea of relative change before and after the sudden change of the stiffness of each segment of the structure, directly extract the ratio of the second-order statistical moment of the relative displacement response of the equally spaced measured points of the structure, and utilize the mapping relationship between the statistical moment of the measured point response and the corresponding segment stiffness, combined with the preliminary geometric characteristics of the structure, can quickly identify the position of sudden change in the segment stiffness of the structure, and then determine the operating state of the structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of rapid detection of civil engineering structures, and particularly relates to a model-free detection method based on statistical moment ratios. Background Art

[0002] There are numerous civil engineering structures in China. Detecting the structures, finding the regions with sudden changes in structural stiffness, timely discovering and evaluating the location and degree of internal damage in the structures, and predicting the performance changes of the structures are of extremely great significance.

[0003] Currently, the structural detection methods based on dynamic test data can be divided into model-based detection and model-free detection according to whether an original finite element model needs to be established. The model-based detection methods mainly include the residual force vector method, eigenvalue sensitivity method, strain energy method, etc. Such methods can relatively accurately identify the location of changes in local stiffness of the structure, but they need to establish a benchmark finite element model, which invisibly involves the cumbersome operation of establishing the model, and at the same time has defects such as model errors and relatively long time-consuming periods; the model-free detection methods mainly include the frequency change method, mode shape change method, flexibility matrix change method, statistical moment change method, etc. The model-free detection methods do not need to establish an original finite element model, avoiding the influence of model errors on structural detection, and can relatively quickly diagnose whether there are sudden changes in local segment stiffness of the structure, which is more conducive to application and popularization in actual engineering. However, considering the complexity of the actual environment, there is still a large gap from actual application.

[0004] The above model-free detection methods all need to extract the dynamic response data of the structure before the sudden change in stiffness, that is, through traditional model-free detection methods based on frequency change, mode shape change, and flexibility matrix change, etc., which need to be compared with the benchmark index data such as frequency, mode shape, and flexibility matrix under the initial benchmark conditions of the structure. There are short boards such as the need for benchmark model data indicators and the unclear reflection of the location of stiffness changes, and there are also situations such as difficult identification or even misjudgment. Under the influence of actual environmental noise, it is extremely difficult to apply. Summary of the Invention

[0005] In view of the above deficiencies existing in the prior art, the present invention provides a model-free detection method based on statistical moment ratios, which does not need to measure the dynamic response data of the structure in the initial benchmark state. Without quantifying the specific values of the segment stiffness of the structure, only by using the relative change idea before and after the sudden change in the segment stiffness of each height segment of the structure, directly extract the ratio of the second-order statistical moments of the relative displacement responses of the measuring points at equal height intervals of the structure, and utilize the mapping relationship between the statistical moments of the measuring point responses and the corresponding segment stiffness of the structure. Combining the preliminary geometric characteristics of the structure can quickly identify the location of the sudden change in the segment stiffness of the structure, and then determine the operating state of the structure.

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

[0007] Model-free detection method based on statistical moment ratio, comprising the following steps:

[0008] Step 1: Obtain the time history response of the measuring point displacement;

[0009] Step 2: Calculate the statistical moment ratio;

[0010] Step 3: Plot the statistical moment ratio curve;

[0011] Step 4: Identify the position of sudden change in segment stiffness.

[0012] Furthermore, the specific operation of Step 1 is as follows: Arrange the structural response measuring points at equal intervals. At this time, the structure can be regarded as a discrete multi-degree-of-freedom system. The motion equation under the action of ground acceleration excitation can be expressed as:

[0013]

[0014] where: M, C, and K respectively represent the structural mass, damping, and stiffness matrices; X(t) are respectively the time history responses of the acceleration, velocity, and displacement of the structure; P(t) is the external load column vector, I is the ground motion influence coefficient column array. Assume that the ground excitation obeys a Gaussian distribution with a mean of zero, and its power spectral density function is a constant S0;

[0015] Under the assumption condition of Rayleigh damping, Equation (6) can be decoupled by using the orthogonality of vibration modes to obtain the motion equation of the structural vibration mode response:

[0016]

[0017]

[0018] In Equations (7) to (8), Y n (t) is the generalized coordinate corresponding to the nth vibration mode; M n , ξ n , ω n , φ n are respectively the nth generalized mass, damping ratio, natural vibration circular frequency, and standard mode of the structure; P n (t) is the generalized force corresponding to the nth mode, and can be obtained by solving the nth uncoupled vibration mode equation:

[0019]

[0020] For a low-critical damping structural system, in Equation (9):

[0021]

[0022] The displacement response of the i-th measurement point of the 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:

[0023]

[0024] For a linearly elastic structure, its autocorrelation function can be expressed as:

[0025]

[0026] Substitute Equation (11) into Equation (12) for solution and perform variable substitution, the autocorrelation function of the relative displacement response of the i-th measurement point can be obtained as:

[0027]

[0028] In Equation (13) is the covariance function of the external excitations P m (t) and P n (t + τ). Perform Fourier transform on the autocorrelation function of the relative displacement response of the i-th measurement point to obtain its power spectral density function, that is:

[0029]

[0030] Substitute Equation (13) into Equation (14), and solve for the power spectral density function of the relative displacement response of the i-th measurement point as:

[0031]

[0032] In the formula represents the cross-power spectral density function of P m (t) and P n (t), and there is:

[0033]

[0034]

[0035] Among them are the generalized stiffnesses of the m-th and n-th orders of the structure respectively. For a small-damping system, the contribution of the cross-term in Equation (15) to the structural response is extremely small. Therefore, Equation (15) can be simplified to:

[0036]

[0037] When the ground excitation acceleration is a Gaussian distribution with zero mean, the power spectral density function n of the external load P can be expressed as:

[0038]

[0039] Substituting Eqs. (17) and (19) into Eq. (18) can solve the power spectral density function of the relative displacement response at the i-th measurement point. From the relationship between the power spectral density function and the variance, the second central moment of the relative displacement at the i-th measurement point (hereinafter referred to as the second moment of displacement) can be obtained as follows:

[0040]

[0041] Furthermore, the specific content of Step 2 is as follows: The contribution of higher modes to the second moment of displacement in Eq. (20) is relatively small. When calculating the second moment of displacement using the response signal of the first natural frequency of the structure, Eq. (20) can be simplified as:

[0042]

[0043] Similarly, the second moment of displacement of the (i + 1)-th measurement point relative to the i-th measurement point can be obtained and denoted as Using the statistical moment ratio of the relative displacement between the i-th measurement point and the (i - 1)-th measurement point divided by the statistical moment ratio of the relative displacement between the (i + 1)-th measurement point and the i-th measurement point (hereinafter referred to as the statistical moment ratio of the i-th measurement point), that is:

[0044]

[0045] It can be seen from this that the statistical moment ratio of the i-th measurement point can be approximately represented by the ratio of the relative change amount of the i-th measurement point of the first mode shape of the structure. The existence of damage in the structure will inevitably cause a slight change in the mode shape, which is reflected in the measured signal as a change in the statistical moment ratio.

[0046] Furthermore, the specific content of Step 3 is as follows: Corresponding to the actual structure, under the condition that the stiffness of the segment is constant and there is no sudden change, it can be regarded as a distributed parameter system. The stiffness of the structural segment and the mass per unit length can be expressed as EI(x) = EI and m(x) = m. Then the undamped free vibration equation of this structural system is:

[0047]

[0048] In Eq. (23), v(x, t) is the displacement response of the structure, which is a function of time t and height x;

[0049] Using the method of separation of variables, assuming that the solution conditions are satisfied: v(x, t) = φ(x)Y(t). At this time, the mode shape φ(x) is a continuous function. Taking the high-rise building structure as an example, it can be regarded as a cantilever beam model. 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 conditions can be obtained as:

[0050]

[0051] In Equation (24), C1 is a non-zero constant coefficient, aL = 1.875. Assuming that the interval between each measurement point of the structure is h, and the corresponding position of the i-th measurement point is x, it can be known from Equation (22) that the statistical moment ratio of the i-th measurement point under the condition of no sudden change in the stiffness of each segment of the structure can be expressed as:

[0052]

[0053] Taking the derivative of Equation (25) with respect to the measurement point position x, we can obtain:

[0054]

[0055] In the formula, G is greater than zero. It is easy to obtain that Equation (34) is always greater than zero when x ∈ (h, l - h), that is, for the corresponding high-rise structure under the conditions of constant and non-sudden change in segment stiffness, the curve of the statistical moment ratio of the structural displacement response shows a continuous and monotonically increasing trend with the change of the measurement point position. If a discrete vibration mode array is adopted, the statistical moment ratio will also show a smooth and monotonically increasing trend with the change of the measurement point position under the condition of constant segment stiffness. Without loss of generality, when applied to structures such as bridges, taking a simply supported beam as an example, the first-order vibration mode function relationship of the structure shown in Equation (24) will change, and the solved statistical moment ratio curve will no longer be monotonic. However, under the condition of sufficient number of measurement points, the connection of the statistical moment ratio curve with the change of the measurement point position will necessarily approach smoothness.

[0056] Furthermore, the specific content of Step 4 is as follows: When damage occurs in a local segment of the structure, it can be regarded as a reduction in the stiffness of the local segment of the structure. According to the structural matrix perturbation theory, when the structural parameters change slightly, the structural mass matrix and stiffness matrix will change accordingly, which can be expressed as:

[0057] M = M0 + εM1, K = K0 + εK1 (27)

[0058] 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 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:

[0059] Kφ n =λ n Mφ n =ω n 2 Mφ n (28)

[0060] In Equation (28), the eigenvalue λ n =ω n 2 , and the eigenvector φ n is the n-th order vibration mode vector. When εM1 and εK1 are relatively small, the eigenvalue and eigenvector will have a small change. According to the perturbation theory, the eigenvector φn The eigenvalue λ and the eigenvector φ are expanded as power series in terms of the small parameter ε, i.e.:

[0061]

[0062] In the above equation, λ 0n and φ 0n are the eigenvalue and eigenvector of the original system, and λ 1n and λ 2n are the first-order perturbation and second-order perturbation of the eigenvalue respectively, and φ 1n and φ 2n are the first-order perturbation and second-order perturbation of the eigenvector respectively. When the change in structural parameters is small, a relatively accurate result can be obtained using the first-order perturbation. Substituting equations (27) and (29) into (28) for solution, neglecting higher-order infinitesimals and combining like terms, the first-order perturbation of the structural eigenvalue and eigenvector can be solved. After structural damage, only the structural stiffness matrix changes, and the structural mass matrix remains unchanged, i.e., M1 is a zero matrix. The first-order perturbation of the structural eigenvalue and eigenvector can be simplified as:

[0063]

[0064]

[0065] Taking the example of the stiffness reduction of a single local segment of a high-rise structure, when there is stiffness reduction in the s-th segment of the structure, we have:

[0066]

[0067] Substituting equations (30), (31) and (32) into equation (29) for solution, when the change in segment stiffness is small, i.e., ε is small, a relatively accurate solution can be obtained using the first-order perturbation as:

[0068]

[0069] In the equation, represents the s-th element of the n-th mode of the original system. Substituting equation (33) into (22), the statistical moment ratio of the i-th layer can be expressed as:

[0070]

[0071] When the stiffness of the s-th segment of the structure is reduced, the change in the statistical moment ratio δ , at the measuring points of the structure before and after damage for i (i = 1 i 2... s... N) can be solved by the matrix perturbation theory as:

[0072]

[0073] Substitute Equation (34) into Equation (35) for solution, which can be simplified to:

[0074]

[0075] In Equation (36), represents the s-th element of the first-order vibration mode of the original system, and K is a non-zero term. It can be seen that when s≠i, the change amount δ of the statistical moment ratio of the corresponding measurement points before and after damage approaches 0. When s≈i, Equation (36) can be further simplified, and the result is not zero. When the section stiffness mutation section s is far from the measurement point i for solving the statistical moment ratio, the change amount δ of the statistical moment ratio approaches 0. When the section stiffness mutation section s is close to the measurement point i for solving the statistical moment ratio, the change amount δ of the statistical moment ratio is large, that is, the statistical moment ratio curve of the structure can be considered to be still continuous and smooth at the place where the section stiffness does not mutate, and only large fluctuations occur at the place where the section stiffness changes, and the ratio curve is no longer smooth. Based on this, the position of the section stiffness mutation can be quickly judged.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] 1) The present invention calculates the second-order statistical moment of the relative displacement by using the equally spaced measured displacement responses, and draws the relationship curve of the ratio changing with the corresponding structural height, which can effectively identify the position of the section stiffness mutation of the structure;

[0078] 2) The present invention is still applicable to the structure with gradually changing section stiffness and also has a certain identification effect under the influence of different external excitations and environmental noises, and has strong robustness;

[0079] 3) The present invention does not need to measure the displacement response data of the structure under the initial reference conditions, and only discriminates by comparing the relative change of the statistical moment of adjacent measurement points, which is especially suitable for the on-site rapid preliminary detection after disasters such as earthquakes of high-rise structures, and has high engineering application value;

[0080] 4) The present invention is especially suitable for the large-area rapid cluster detection on the post-disaster site of structures such as earthquakes and typhoons, and can quickly identify the weak parts. Although a high-rise structure is used for simulation verification, it is still applicable to bridge structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a simplified model diagram of a high-rise structure in an embodiment of the model-free detection method based on the statistical moment ratio of the present invention;

[0082] Figure 2 is a plan view of a high-rise structure (28 segments) in an embodiment of the model-free detection method based on the statistical moment ratio of the present invention;

[0083] Figure 3It is the curve graph of the change of D value with the structural height in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention;

[0084] Figure 4 It is the curve graph of the derivative value of the statistical moment ratio in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention;

[0085] Figure 5 It is the curve graph of the change of δ value in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention;

[0086] Figure 6 It is the diagnostic result graph of the stiffness mutation position of the structural segment under the condition of Gaussian white noise excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 1);

[0087] Figure 7 It is the diagnostic result graph of the stiffness mutation position of the structural segment under the condition of Gaussian white noise excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 2);

[0088] Figure 8 It is the diagnostic result graph of the stiffness mutation position of the structural segment under the condition of Gaussian white noise excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 3);

[0089] Figure 9 It is the diagnostic result graph of the stiffness mutation position of the structural segment under the condition of Gaussian white noise excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 4);

[0090] Figure 10 It is the identification result graph of the stiffness mutation position of the structural segment under the condition of EI-Centro wave excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 1);

[0091] Figure 11 It is the identification result graph of the stiffness mutation position of the structural segment under the condition of EI-Centro wave excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 2);

[0092] Figure 12 It is the identification result graph of the stiffness mutation position of the structural segment under the condition of EI-Centro wave excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 3);

[0093] Figure 13 It is the identification result graph of the stiffness mutation position of the structural segment under the condition of EI-Centro wave excitation in the embodiment of the model-free detection method based on the statistical moment ratio of the present invention (working condition 4);

[0094] Figure 14Identification result diagram (operating condition 1) of a high-rise structure with gradually changing segment stiffness in the embodiment of the model-free detection method based on statistical moment ratios of the present invention under Gaussian white noise excitation;

[0095] Figure 15 Identification result diagram (operating condition 2) of a high-rise structure with gradually changing segment stiffness in the embodiment of the model-free detection method based on statistical moment ratios of the present invention under Gaussian white noise excitation;

[0096] Figure 16 Identification result diagram (operating condition 3) of a high-rise structure with gradually changing segment stiffness in the embodiment of the model-free detection method based on statistical moment ratios of the present invention under Gaussian white noise excitation;

[0097] Figure 17 Identification result diagram (operating condition 4) of a high-rise structure with gradually changing segment stiffness in the embodiment of the model-free detection method based on statistical moment ratios of the present invention under Gaussian white noise excitation;

[0098] Figure 18 Identification result diagram of the frequency change method under operating condition 3;

[0099] Figure 19 Identification result diagram of the mode shape change method under operating condition 3;

[0100] Figure 20 Identification result diagram of the flexibility curvature method under operating condition 3;

[0101] Figure 21 Identification result diagram of the statistical moment change method under operating condition 3;

[0102] Figure 22 Identification result diagram of the model-free detection method based on statistical moment ratios of the present invention under operating condition 3;

[0103] Figure 23 Measured acceleration time history response signal diagram in the embodiment of the model-free detection method based on statistical moment ratios of the present invention;

[0104] Figure 24 Acceleration signal amplitude-frequency curve diagram in the embodiment of the model-free detection method based on statistical moment ratios of the present invention;

[0105] Figure 25 Statistical moment ratio identification result diagram in the embodiment of the model-free detection method based on statistical moment ratios of the present invention;

[0106] Figure 26 Detection flow chart of the embodiment of the model-free detection method based on statistical moment ratios of the present invention. Detailed implementation manners

[0107] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0108] Based on the analysis of the displacement response statistical moment theory, the present invention deduces the calculation principle, that is, by calculating the ratio of the structural response statistical moment from the displacement response data results of a single sampling, and identifying the damage location according to the mutation position of the ratio. For the sake of concise description, only the numerical model of the high-rise structure is used to analyze the identification effect of this method under different external excitations and environmental noise conditions, and the measured results of the on-site tower barrel structure are used for comparative verification analysis.

[0109] 1 Theoretical analysis

[0110] 1.1 Theoretical analysis of single-degree-of-freedom statistical moment

[0111] For a single-degree-of-freedom linear elastic structure, its motion equation can be expressed as:

[0112]

[0113] In Equation (1), m, c, and k represent the mass, damping, and stiffness of the structure respectively. x(t), represent the displacement, velocity, and acceleration responses of the structure respectively, represents the acceleration of the ground excitation, and Equation (1) can be further simplified as:

[0114]

[0115] where 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 of its structural response 2 The solution expression is as follows:

[0116]

[0117] In the formula, S f (ω) is the power spectral density function of the ground excitation. When the ground excitation is ideal white noise, S f (ω) can be regarded as a constant S0 in the frequency domain; H(ω) is the frequency response function of the structure, and the expression of the displacement frequency response function is as follows:

[0118]

[0119] According to the above formula, the variance of the displacement response, that is, the expression of the second-order statistical moment of the displacement response, can be deduced as:

[0120]

[0121] As can be seen from Equation (5), the change in structural stiffness will inevitably lead to a change in the statistical moments of the structural response. That is, the statistical moments can be considered as the structural damage discrimination index.

[0122] 1.2 Theoretical Analysis of Statistical Moments of Multiple Degrees of Freedom

[0123] By arranging measuring points at equal height intervals, an engineering structure can be regarded as a discrete multi-degree-of-freedom system. Under the action of ground acceleration excitation The motion equation can be expressed as:

[0124]

[0125] Where: M M, C, and K represent the structural mass, damping, and stiffness matrices respectively; X(t) are the time-history responses of the acceleration, velocity, and displacement of the structure respectively; P(t) is the external load column vector, I is the ground motion influence coefficient column matrix, and for the corresponding simplified model, it can be considered as a column vector with all elements equal to 1. Assuming that the ground excitation obeys a Gaussian distribution with a mean of zero, and its power spectral density function is a constant S0.

[0126] Under the assumption of Rayleigh damping, Equation (6) can be decoupled using the orthogonality of the vibration modes to obtain the motion equation of the structural vibration mode response:

[0127]

[0128]

[0129] In Equations (7) to (8), Y n (t) is the generalized coordinate corresponding to the nth vibration mode; M n , ξ n , ω n , φ n are the nth generalized mass, damping ratio, natural circular frequency, and standard mode of the structure respectively; P n (t) is the generalized force corresponding to the nth mode. By solving the nth uncoupled vibration mode equation, we can obtain:

[0130]

[0131] For a low-critical damping structural system, in Equation (9):

[0132]

[0133] The relative displacement response of the ith measuring point of the structure with respect to the (i - 1)th measuring point (hereinafter referred to as the relative displacement response of the ith measuring point) can be further expressed as:

[0134]

[0135] For a linearly elastic structure, under stationary excitation conditions, the response process should satisfy a stationary distribution, and its autocorrelation function can be expressed as:

[0136]

[0137] Substitute Equation (11) into Equation (12) for solution and perform variable substitution, and the autocorrelation function of the relative displacement response at the i-th measurement point can be obtained as:

[0138]

[0139] In Equation (13) is the covariance function of the external excitations P m (t) and P n (t + τ). Fourier transform of the autocorrelation function of the relative displacement response at the i-th measurement point can obtain its power spectral density function, that is:

[0140]

[0141] Substitute Equation (13) into Equation (14), and solve to obtain the power spectral density function of the relative displacement response at the i-th measurement point as:

[0142]

[0143] In the formula represents the cross-power spectral density function of P m (t) and P n (t), and there is:

[0144]

[0145]

[0146] Among them are the generalized stiffnesses of the m-th and n-th orders of the structure respectively. For a small-damping system, the cross terms in Equation (15) contribute very little to the structural response. Therefore, Equation (15) can be simplified to:

[0147]

[0148] When the ground excitation acceleration is a Gaussian distribution with zero mean, the power spectral density function of the external load Pn(t) can be expressed as:

[0149]

[0150] Substituting Eqs. (17) and (19) into Eq. (18) can solve the power spectral density function of the relative displacement response at the i-th measurement point. According to the relationship between the power spectral density function and the variance, the second-order central moment of the relative displacement at the i-th measurement point (hereinafter referred to as the displacement second moment) can be obtained as follows:

[0151]

[0152] 1.3 Theoretical Analysis of Model-Free Damage Diagnosis

[0153] It can be seen from Eq. (20) that the higher modes contribute less to the displacement second moment. When calculating the displacement second moment using the first-order main frequency response signal of the structure, Eq. (20) can be simplified as:

[0154]

[0155] Similarly, the second moment of the displacement of the (i + 1)-th measurement point relative to the i-th measurement point can be obtained and denoted as Using the ratio of the statistical moment of the relative displacement between the i-th measurement point and the (i - 1)-th measurement point to the statistical moment of the relative displacement between the (i + 1)-th measurement point and the i-th measurement point (hereinafter referred to as the statistical moment ratio of the i-th measurement point), that is:

[0156]

[0157] It can be seen from this that the statistical moment ratio of the i-th measurement point can be approximately expressed by the ratio of the relative change amount of the i-th measurement point in the first-order vibration mode of the structure. Eq. (22) is the derivation result under the discrete multi-degree-of-freedom structural system, and it is difficult to see its particularity. For the actual structure, under the condition that the section stiffness is constant and there is no sudden change, it can be regarded as a distributed parameter system, as Figure 1 shown. The section stiffness and the mass per unit length of the structure can be expressed as EI(x) = EI, m(x) = m. Then the undamped free vibration equation of this structural system is:

[0158]

[0159] In Eq. (23), v(x, t) is the displacement response of the structure, which is a function of time t and height x.

[0160] Using the method of separation of variables, assuming that the solution conditions are satisfied: v(x, t) = φ(x)Y(t). At this time, the vibration mode φ(x) is a continuous function. Considering the simplicity of the description, only the high-rise building structure is taken as an example here. The high-rise building structure can be regarded as a cantilever beam model. Substituting the boundary conditions of the cantilever beam and solving, the expression of the first-order bending vibration mode of the structure under the initial conditions can be obtained as:

[0161]

[0162] In Equation (24), C1 is a non-zero constant coefficient, aL = 1.875. Suppose the interval between each measurement point of the structure is h, and the corresponding position of the i-th measurement point is x. Then, according to Equation (22), the statistical moment ratio of the i-th measurement point under the condition of no sudden change in the stiffness of each segment of the structure can be expressed as:

[0163]

[0164] Taking the derivative of Equation (25) with respect to the measurement point position x, we can obtain:

[0165]

[0166] In the formula, G is greater than zero. It is easy to obtain that Equation (34) is always greater than zero when x ∈ (h, l - h), that is, for the corresponding high-rise structure under the condition of constant and no sudden change in the segment stiffness, the curve of the statistical moment ratio of the structural displacement response shows a continuous and monotonically increasing trend with the change of the measurement point position. If a discrete vibration mode array is adopted, the statistical moment ratio will also show a smooth and monotonically increasing trend with the change of the measurement point position under the condition of constant segment stiffness. Without loss of generality, when applied to structures such as bridges, taking a simply supported beam as an example, the relational expression of the first-order vibration mode function of the structure shown in Equation (24) will change, and the solved curve of the statistical moment ratio will no longer be monotonic. However, under the condition of sufficient measurement points, the connection of the statistical moment ratio curve with the change of the measurement point position will necessarily approach smoothness.

[0167] When damage occurs in a local segment of the structure, it can be regarded as a reduction in the stiffness of the local segment of the structure. According to the structural matrix perturbation theory, when the structural parameters change slightly, the structural mass matrix and stiffness matrix will change accordingly, which can be expressed as:

[0168] M = M0 + εM1, K = K0 + εK1 (27)

[0169] 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 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:

[0170] Kφ n =λ n Mφ n =ω n 2 Mφ n (28)

[0171] In Equation (28), the eigenvalue λ n =ω n 2 , and the eigenvector φ n is the n-th order vibration mode vector. When εM1 and εK1 are relatively small, the eigenvalue and eigenvector will have small changes. According to the perturbation theory, the eigenvector φ nAnd the eigenvalue λ is expanded as a power series in terms of the small parameter ε, i.e.:

[0172]

[0173] In the above formula, λ 0n and φ 0n are the eigenvalues and eigenvectors of the original system, λ 1n and λ 2n are the first-order perturbation and second-order perturbation of the eigenvalue respectively, and φ 1n and φ 2n are the first-order perturbation and second-order perturbation of the eigenvector respectively. When the structural parameters change slightly, more accurate results can be obtained by using the first-order perturbation. Substitute equations (27) and (29) into (28) to solve, ignore the higher-order infinitesimals, and combine like terms to solve for the first-order perturbation of the structural eigenvalues and eigenvectors. After structural damage, only the structural stiffness matrix changes, and the structural mass matrix does not change, that is, M1 is a zero matrix. The first-order perturbation of the structural eigenvalues and eigenvectors can be simplified as:

[0174]

[0175]

[0176] Similarly, taking the stiffness reduction of a single local segment of a high-rise structure as an example, when there is stiffness reduction in the s-th segment of the structure, there is:

[0177]

[0178] Substitute equations (30), (31) and (32) into equation (29) to solve. When the change in segment stiffness is small, that is, ε is small, a more accurate solution can be obtained using the first-order perturbation as:

[0179]

[0180] In the formula represents the s-th element of the n-th mode of the original system. Substitute equation (33) into (22), and the statistical moment ratio of the i-th layer can be expressed as:

[0181]

[0182] When the stiffness of the s-th segment of the structure is reduced, the change in the statistical moment ratio δ , at the measuring points of the structure before and after damage for i (i = 1 i 2... s... N) can be solved by the matrix perturbation theory as:

[0183]

[0184] Substitute equation (34) into equation (35) to solve, and it can be simplified as:

[0185]

[0186] In formula (36), represents the s-th element of the first-order vibration mode of the original system, and K is a non-zero term. It can be seen that when s≠i, the change amount δ of the statistical moment ratio of the corresponding measurement points before and after damage approaches 0. When s≈i, formula (36) can be further simplified, and the result is non-zero. When the section stiffness mutation section s is far from the measurement point i for solving the ratio of the statistical moment from bottom to top, the change amount δ of the statistical moment ratio approaches 0. When the section stiffness mutation section s is close to the measurement point i for solving the statistical moment ratio, the change amount δ of the statistical moment ratio is large, that is, the statistical moment ratio curve of the structure can be considered to be still in a continuous and smooth state at the place where the section stiffness does not mutate, and only large fluctuations occur at the place where the section stiffness changes, and the ratio curve is no longer smooth. Based on this, the position of the section stiffness mutation can be quickly judged.

[0187] 2 Numerical simulation analysis

[0188] 2.1 Model introduction

[0189] Based on the numerical model of the previous research of the team, corrections were made, and a high-rise structure model was established for the applicability study of the method. This plane structure model was divided into 28 segments in total. The initial elastic modulus value of the column was E0 = 7.751×10 9 N·m 2 , the height h of a single segment of the column was 0.3 m, the linear density m 柱 = 7.35 kg / m, the beam was regarded as a rigid body, the span l was 0.6 m, the mass m was 26.35 kg, the damping ratio was set as ξ i = 0.05 (i = 1, 2). The model is as Figure 2 shown. The applicability of this model has been verified. The element stiffness matrix and element mass matrix obtained by solving were combined into the overall stiffness matrix and mass matrix of the structure. The Rayleigh damping hypothesis was adopted, and the time-history response of the structure under the given excitation was solved by the Newmark-β method. Numerical calculations were carried out for the theoretical derivation of the detection of the section stiffness mutation position without a model proposed in the present invention. At the same time, the applicability of the method for diagnosing the section stiffness mutation position proposed in the present invention was verified for influencing factors such as environmental noise, external excitation, and the section stiffness distribution of the actual structure. Based on the literature, the section stiffness damage of the high-rise structure was simulated by reducing the elastic modulus of the column to characterize the stiffness mutation, and the following working conditions were set:

[0190] Working condition 1: The section stiffness of each section of the structure was not reduced;

[0191] Working condition 2: The section stiffness of the 15th section of the structure was reduced by 10%;

[0192] Working condition 3: The section stiffness of the 15th section of the structure was reduced by 20%;

[0193] Condition 4: The stiffness of the 10th and 20th segments of the structure is reduced by 20%.

[0194] 2.2 Numerical verification

[0195] 2.2.1 Theoretical derivation and numerical verification of the method for detecting the position of segment stiffness mutation based on the ratio of statistical moments

[0196] For Figure 2 the base of the model shown, a random stationary white noise excitation is input, and the first-order main frequency displacement response of the corresponding measuring point is extracted. The statistical moment ratio of the relative displacement response of the corresponding measuring point can be solved. At the same time, by solving the eigenvalue equation using the stiffness matrix and mass matrix of the model under known structural parameter conditions, the first-order vibration mode of the structure can be solved. Introduce the variable D and denote it as:

[0197]

[0198] Using the numerical model to numerically solve Equation (37), the curve of the D value changing with height under Conditions 1 to 4 can be plotted as Figure 3 shown.

[0199] It can be seen from the above figure that the fitting degree between the statistical moment ratio solved from the structural response and the ratio of the relative change amount of the first-order vibration mode of the structure solved under the conditions of the known structural mass matrix and stiffness matrix has a maximum error of no more than 5% under different working conditions, which verifies the correctness of Equation (22) to a certain extent, that is, there is a numerical calculation relationship between the statistical moment ratio of the corresponding measuring point response of the high-rise structure and the first-order vibration mode of the structure. The same method can also be used to verify the ratio of the upper statistical moment to the lower statistical moment, and good fitting degrees can be obtained.

[0200] When there is no mutation in the segment stiffness of the structure (Condition 1), using the numerical model as Figure 2 shown, the derivative formula (34) of the statistical moment ratio of the structural displacement response can be solved, and the result is as Figure 4 shown.

[0201] It is not difficult to see from the result curve that when the statistical moment ratio is differentiated with respect to the height of the structural measuring point, its derivative value is always greater than 0 within the range of x ∈ (h, l - h), that is, when the segment stiffness value of the structure is constant and there is no mutation, the statistical moment ratio changes continuously and monotonically with the change of the measuring point height. Similarly, it can be proved that when the segment stiffness value of the structure is constant and there is no mutation, the ratio of the upper statistical moment to the lower statistical moment decreases continuously with the increase of height.

[0202] When the segment stiffness value of the structure mutates, the present invention uses stiffness reduction to simulate the change of the segment stiffness value of the structure. The curve relationship between the change amount δ of the statistical moment ratio before and after damage and the height is as Figure 5 shown.

[0203] It is not difficult to see that under the condition of a single segment stiffness reduction, the change in the statistical moment ratio is generally small, but the change in the statistical moment ratio will produce a relatively large mutation value near the location where the stiffness of the structural segment is reduced. That is, compared with the case where there is no mutation in stiffness, after the stiffness of the local segment of the structure is reduced, the smooth monotonic curve of the statistical moment ratio will show a mutation at the stiffness reduction location, breaking the original continuous smooth state. Similarly, it can be calculated that at this location, the continuous smooth state of the upper value of the statistical moment ratio will also be broken. This feature can be used to locate and judge the location of the stiffness mutation of the segment of the tall structure.

[0204] 2.2.2 Application simulation of a new method for detecting the location of segment stiffness mutation based on statistical moment ratio

[0205] In order to verify the diagnostic method proposed in this invention, Gaussian white noise and EI-Centro wave in the literature are used as external excitations, and the noise resistance of the method of this invention is analyzed by considering the noise-free, signal-to-noise ratio 40db and 30db environmental noise. At the same time, in order to further fit the actual engineering application, Figure 2 The segment stiffness of the numerical model is reduced layer by layer, and the applicability of the method of the present invention is verified by simulation when the segment stiffness of the actual high-rise structure gradually changes with the height. Referring to the new method for detecting the position of sudden change of segment stiffness without model proposed in the present invention, the specific operation steps are as follows:

[0206] 1. Obtain the displacement time-history response of measuring points with equal height spacing in the same vertical plane of a tall structure in the same horizontal direction;

[0207] 2. Calculate the second-order statistical moment of the relative displacement of each measuring point and solve the statistical moment ratio of the corresponding measuring point;

[0208] 3. Draw a curve with the height of each measuring point as the horizontal coordinate and the corresponding measuring point displacement statistical moment ratio as the vertical coordinate;

[0209] 4. Observe the sudden change of the curve and identify the sudden change position of lateral stiffness;

[0210] According to the diagnostic steps, the method verification simulation analysis is carried out under the conditions of constant segment stiffness and gradual segment stiffness. The simulation conditions are shown in Table 1:

[0211] Table 1 Detailed list of numerical simulation conditions

[0212]

[0213] ① Constant stiffness of structural segments

[0214] Assuming that the stiffness of each segment of the high-rise structure is the same in the initial state, a steady Gaussian white noise is used as the external excitation to extract the time-history response of the corresponding measuring point of the structure and solve the statistical moment. The statistical moment ratio is used to determine the position of the segment stiffness mutation. The results are as follows: Figure 6 , Figure 7 ,Figure 8 , Figure 9 as shown.

[0215] It is not difficult to see from the recognition result diagram that under Condition 1, the statistical moment ratio curve shows a smooth and monotonically increasing trend without noise interference, without sudden changes, which is consistent with the theoretical derivation result of the statistical moment ratio under the condition of no sudden change in segment stiffness. Referring to the signal-to-noise ratio calculation formula, the statistical moment ratio of the interlayer relative displacement at the position without sudden change in stiffness gradually approaches a fixed value under the influence of noise. As shown in the figure, under 40DB and 30DB noise, the statistical moment ratio curve no longer shows an obvious monotonically increasing trend with the increase in height and has serrated protrusions, but the coefficient of variation of the statistical moment ratio data points does not exceed 0.076, so it can be considered that there is no obvious sudden change position, and it is basically determined that there is no segment stiffness mutation in this high-rise structure. Under Condition 2, when there is no noise interference, there is an obvious sudden change in the statistical moment ratio at the stiffness reduction position; under the influence of 40DB noise in the signal-to-noise ratio, the coefficient of variation of the statistical moment ratio at the stiffness reduction position is 0.16, which is twice that of the corresponding data at the position where no stiffness reduction occurs, so it can be determined that the sudden change at this position is obvious; under the influence of 30DB noise in the signal-to-noise ratio near the stiffness reduction position, the change of the statistical moment ratio is the most drastic, and the maximum coefficient of variation is 0.105, which is 1.5 times that of other positions, so it can be determined that there is a stiffness mutation at this position. Under Condition 3, as the stiffness reduction increases, under the conditions of no noise, 40DB noise in the signal-to-noise ratio and 30DB noise in the signal-to-noise ratio, the coefficient of variation of the statistical moment ratio at the segment stiffness reduction position reaches up to 0.35, which is 7 times that of other positions, so it can be judged that the segment stiffness mutation is obvious; similarly, under the condition of double-segment stiffness reduction in Condition 4, the new detection method proposed by the present invention can effectively diagnose the segment stiffness mutation position under the conditions of no noise, 40DB in the signal-to-noise ratio and 30DB in the signal-to-noise ratio.

[0216] Considering the influence of different external excitations on the method proposed by the present invention, the EI-Centro wave signal is used to simulate the input of external excitation, and the simulation calculation results are as Figure 10 , Figure 11 , Figure 12 , Figure 13 shown.

[0217] After the external excitation changes, it is not difficult to see from the result curve diagram that under the conditions of no noise, 40DB noise in the signal-to-noise ratio and 30DB noise in the signal-to-noise ratio, the method for diagnosing the segment stiffness mutation position proposed by the present invention can effectively identify the segment stiffness mutation position, that is, the method proposed by the present invention still has strong applicability in the face of non-stationary external excitation conditions.

[0218] ② Gradual change of segment stiffness

[0219] Considering that in actual engineering structures, the stiffness of high-rise structure segments generally shows a decreasing trend with increasing height, the numerical simulation model is adjusted. As the height increases, the elastic modulus of the columns in the numerical model is E0 = (1 - 0.01×n)×7.751×10 9 N·m 2 (n = 1, 2... 28). That is, as the height increases, the elastic modulus of the frame columns is distributed in an arithmetic progression with a decreasing trend. Similarly, white noise is used as the external excitation for simulation calculation, and the results are as shown in Figure 14 、 Figure 15 、 Figure 16 、 Figure 17 shown. It can be seen from the figure that when the stiffness of the high-rise structure segment gradually decreases with the increase of the structure height, under the preset working conditions (working conditions 1 to 4), the method proposed in the present invention can still effectively identify the position of the stiffness mutation of the segment. At the same time, considering the influence of environmental noise with a signal-to-noise ratio of 40 DB and 30 DB, the identification results are still relatively accurate. That is, the method proposed in the present invention is still applicable to high-rise structures with gradually changing stiffness.

[0220] 2.3 Comparative analysis of model-free detection methods

[0221] Compare the new model-free method for detecting the position of segment stiffness mutation proposed in the present invention with the existing model-free detection methods: frequency change method, mode change method, flexibility curvature method, and response statistical moment change method in the detection of the position of segment stiffness mutation in high-rise structures. Through the above numerical model, the working condition 3 under the condition of no noise, that is, the segment stiffness of the 15th floor is reduced by 20%, is selected as the comparison working condition for analysis. The first-order frequency and the first-order mode before and after the local mutation of the segment stiffness of the structure are extracted respectively, and the frequency change index, mode change index, flexibility curvature difference index, and structure response statistical moment change index are calculated according to the literature. The analysis of the calculation results is as shown in Figure 18 、 Figure 19 、 Figure 20 、 Figure 21 、 Figure 22 shown. Analyze the identification results of different methods. The comparative analysis of the identification effects of each method is shown in Table 2:

[0222] Table 2 Comparative analysis table of identification results of different detection methods

[0223]

[0224] Comprehensively analyze the identification effects of the above model-free methods for detecting the position of segment stiffness mutation. The advantages of the present invention are mainly reflected in:

[0225] 1. The present invention only needs to consider the results of single measurement data, without comparing the structural data indexes before and after the stiffness mutation of the high-rise structure segment, and has stronger applicability;

[0226] 2. The present invention directly uses the structural time history response for the mathematical calculation of statistical moment indicators, with simpler data processing and higher calculation efficiency.

[0227] 3. The present invention uses statistical moment indicators for diagnosis, only requiring simple solution of the frequency domain indicators of the structural response. The quality of the identification results depends on the time domain data and is not restricted by the structural mode indicator identification method, with stronger engineering applicability.

[0228] 3 Field test analysis and verification

[0229] The measured data of the newly built wind turbine tower structure in Fengdu Jilong Wind Farm, Chongqing, is selected for the verification analysis of the method applicability. The typical newly built 2.5 MW tower (No. 24 machine) in this area is measured. The total height of the tower is 87.3 meters and it is divided into 5 sections. Considering conditions such as the setting of the on-site work platform, the installation conditions of sensors, the number of interfaces of the data acquisition instrument, and the length of the data acquisition line, 5 acceleration sensors are used to synchronously collect acceleration signals. Among them, the data acquisition instrument and the supporting acquisition computer are placed on the work platform near the flange at the connection between the 3rd and 4th sections of the tower. The corresponding sensors are installed at 85m, 64m, 43m, 24m, and 3m respectively according to the existing placement conditions inside the tower and the requirements of the method proposed in the present invention, to obtain the acceleration responses of the measuring points at equal height intervals on the same vertical line of the tower body in the same horizontal direction.

[0230] During the test measurement process, the external wind force is small, the fan is in the shutdown state, and there is no blade rotation. The collected data of the tower acceleration response and its corresponding amplitude-frequency curve are as Figure 23 、 Figure 24 shown.

[0231] The relatively stable acceleration response data from 25 s to 65 s is selected for analysis, and the height interval between the measuring points is about 21 m. It can be seen from the amplitude-frequency curve Figure 24 that the test data of each acceleration sensor basically coincide in the frequency domain and all contain the main frequency signal of 0.25 - 0.26 HZ. The integral of the measured acceleration data is used to solve the structural displacement response, and the method proposed in the present invention is used to judge the position of the sudden change in the stiffness of the section. Referring to the principle of the diagnosis method mentioned in the article, the ratio of the relative displacement statistical moment of each measuring point is calculated by extracting the main frequency signal corresponding to 0.25 - 0.26 HZ. The measured data is analyzed using the diagnosis method mentioned in the article. Due to the limitation of the measurement conditions and the small number of measuring points, the statistical moment ratios are connected by a smooth curve, and the analysis curve can be obtained as Figure 25 shown.

[0232] As can be seen from the above figure, when using the main frequency time-domain response signal to solve the statistical moment ratio, the curve of the statistical moment ratio increases monotonically with the increase of the tower barrel height, and there is no obvious mutation. It can be determined that there is no obvious stiffness mutation in this tower barrel section, indicating that the bolt connections between sections meet the regulations. Combining the operation data of this wind farm, this tower barrel is a newly built tower barrel, which meets the quality acceptance regulations and is ready for grid connection and power generation. The calculation results show that the model-free diagnosis method proposed in the present invention can be implemented in the diagnosis of the stiffness mutation position of the actual high-rise structure segments.

[0233] The detection flow chart of the model-free detection method based on the statistical moment ratio of the present invention is as Figure 26 shown.

[0234] 4 Conclusions

[0235] The present invention uses the numerical model of high-rise structures for numerical demonstration, and combines the measured displacement response data of the actual wind turbine tower structure for analysis, and summarizes the following conclusions:

[0236] 1) The present invention calculates the ratio of the second-order statistical moment of the relative displacement by using the equally spaced measured displacement response, and draws the relationship curve of the ratio changing with the corresponding structure height, which can effectively identify the stiffness mutation position of the structure segment;

[0237] 2) The present invention is still applicable to structures with gradually changing segment stiffness, and also has a certain recognition effect under the influence of different external excitations and environmental noises, and has strong robustness;

[0238] 3) The present invention does not need to measure the displacement response data of the structure under the initial reference conditions, and only judges by comparing the relative changes of the statistical moments of adjacent measuring points. It is especially suitable for on-site rapid preliminary detection after disasters such as earthquakes in high-rise structures, and has high engineering application value;

[0239] 4) The recognition method of the present invention is also applicable to bridge structures, and has a wide range of applications.

[0240] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A model-free detection method based on the ratio of statistical moments, characterized in that, It includes the following steps: Step 1: Obtain the time history response of the measuring point displacement; Step 2: Calculate the statistical moment ratio; Step 3: Plot the statistical moment ratio curve; Step 4: Identify the position of sudden change in segment stiffness; The specific content of the first step is as follows: Structural response measuring points are arranged at equal intervals. At this time, the structure can be regarded as a discrete multi-degree-of-freedom system. Under the ground acceleration excitation The motion equation can be expressed as: Where: M, C, and K represent the structural mass, damping, and stiffness matrices, respectively; X(t) are the time-history responses of the acceleration, velocity, and displacement of the structure, respectively; P(t) is the external load column vector, I is the ground motion influence coefficient array, assuming that the ground surface excitation obeys a Gaussian distribution with a mean of zero, and its power spectral density function is a constant S0; Under the Rayleigh damping assumption condition, the motion equation of the structural mode response can be obtained by using the mode orthogonality and decoupling in Equation (6): In formulas (7) to (8), Y n (t) is the generalized coordinate corresponding to the nth-order vibration mode; M n , ξ n , ω n , φ n are respectively the nth-order generalized mass, damping ratio, natural circular frequency, and standard mode of the structure; P n (t) is the generalized force corresponding to the nth-order mode, which can be obtained by solving the nth uncoupled vibration mode equation: For a low critical damping structural system, in Equation (9): The displacement response of the i-th measuring point of the structure relative to the i-1-th measuring point (hereinafter referred to as the relative displacement response of the i-th measuring point) can be further expressed as: For a linear elastic structure, its autocorrelation function can be expressed as: Substitute Equation (11) into Equation (12) for solution and perform variable substitution, and the autocorrelation function of the relative displacement response of the i-th measuring point can be obtained as: In Equation (13) is the external excitation P m (t) and the covariance function of P n (t + τ). By performing a Fourier transform on the autocorrelation function of the relative displacement response at the i-th measurement point, its power spectral density function can be obtained, i.e.: Substitute Equation (13) into Equation (14), and the power spectral density function of the relative displacement response of the i-th measuring point is solved as: where denotes P m (t) and the cross-power spectral density function of P n (t), and there is: Among them They are the m-th and n-th order generalized stiffnesses of the structure respectively. For a small-damping system, the cross-term in Equation (15) contributes very little to the structural response. Therefore, Equation (15) can be simplified as follows: The ground surface excitation acceleration is a Gaussian distribution with zero mean, and the power spectral density function of the external load P n (t) can be expressed as: Substitute Equations (17) and (19) into Equation (18) to solve the power spectral density function of the relative displacement response of the i-th measuring point. From the relationship between the power spectral density function and the variance, the second-order central moment of the relative displacement of the i-th measuring point (hereinafter referred to as the displacement second moment) can be obtained as:

2. The model-free detection method based on the statistical moment ratio according to claim 1, wherein The specific content of the said Step 2 is: The contribution of higher modes to the displacement second moment in Equation (20) is relatively small. When calculating the displacement second moment using the response signal of the first natural frequency of the structure, Equation (20) can be simplified as: Similarly, the second moment of the displacement of the (i + 1)-th measurement point relative to the i-th measurement point can be obtained and denoted as Using the statistical moment of the relative displacement between the i-th measurement point and the (i - 1)-th measurement point divided by the statistical moment of the relative displacement between the (i + 1)-th measurement point and the i-th measurement point (hereinafter referred to as the statistical moment ratio of the i-th measurement point), i.e.: It can be seen from this that the statistical moment ratio of the i-th measuring point can be approximately expressed by the ratio of the relative change amount of the i-th measuring point of the first mode of the structure. The existence of damage in the structure will inevitably cause a slight change in the mode, which is reflected in the measured signal as a change in the statistical moment ratio.

3. The model-free detection method based on statistical moment ratio according to claim 2, wherein The specific content of the said Step 3 is: Corresponding to the actual structure, under the condition that the segment stiffness is constant and there is no sudden change, it can be regarded as a distributed parameter system. The segment stiffness and the mass per unit length of the structure can be expressed as EI(x) = EI, m(x) = m. Then the undamped free vibration motion equation of this structural system is: In Equation (23), v(x, t) is the displacement response of the structure, which is a function of time t and height x; Using the method of separation of variables, assume that the definite solution conditions are satisfied: v(x, t) = φ(x)Y(t). At this time, the mode φ(x) is a continuous function. Taking the high-rise building structure as an example only, it can be regarded as a cantilever beam model. Substitute it into the cantilever beam boundary conditions for solution, and the expression of the first-order bending mode of the structure under the initial conditions can be obtained as: In Equation (24), C1 is a non-zero constant coefficient, aL = 1.

875. Let the interval between each measuring point of the structure be h, and the corresponding position of the i-th measuring point be x. Then from Equation (22), it can be known that the statistical moment ratio of the i-th measuring point under the condition of no sudden change in segment stiffness of the structure can be expressed as: Take the derivative of Equation (25) with respect to the measuring point position x, and we can get: Where G is greater than zero, and it is easy to obtain that formula (34) is always true when x∈(h,lh) is greater than zero. That is, for high-rise structures, under the condition of constant segment stiffness and no mutation, the statistical moment ratio curve of structural displacement response shows a continuous single-increasing trend with the change of measuring point position. If a discrete vibration mode array is used, under the condition of constant segment stiffness, the statistical moment ratio will also show a smooth single-increasing trend with the change of measuring point position without loss of generality. When applied to structures such as bridges, taking a simply supported beam as an example, the first-order vibration mode function relationship of the structure shown in formula (24) will change, and the solved statistical moment ratio curve will no longer be monotonic. However, under the condition of sufficient number of measuring points, the line connecting the statistical moment ratio curve with the change of measuring point position will inevitably approach smoothness.

4. The model-free detection method based on the statistical moment ratio according to claim 3, wherein The step 4 is specifically as follows: damage to the local segment of the structure can be regarded as a reduction in the stiffness of the local segment of the structure. According to the structural matrix perturbation theory, when the structural parameters change slightly, the structural mass matrix and stiffness matrix will change accordingly, which can be expressed as: M=M0+εM1,K=K0+εK1 (27) In formula (27), ε is a small parameter. When ε = 0, the system is called the original system. M0 and K0 are the mass matrix and stiffness matrix of the original system. εM1 and εK1 represent the changes of 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) The eigenvalue λ in Equation (28) n = ω n 2 , and the eigenvector φ n is the nth-order mode shape vector. When εM1 and εK1 are small, the eigenvalue and eigenvector will have small changes. According to perturbation theory, the eigenvector φ n and the eigenvalue λ can be expanded as power series in terms of the small parameter ε, that is: In the above formula, λ 0n and φ 0n are the eigenvalues and eigenvectors of the original system. λ 1n and λ 2n are the first-order perturbation and second-order perturbation of the eigenvalues respectively. φ 1n and φ 2n are the first-order perturbation and second-order perturbation of the eigenvectors respectively. When the change of structural parameters is small, a relatively accurate result can be obtained by using the first-order perturbation. Substitute equations (27) and (29) into (28) for solution. Ignoring the higher-order infinitesimals and combining like terms, the first-order perturbation amounts of the structural eigenvalues and eigenvectors can be solved. After structural damage, only the structural stiffness matrix changes, and the structural mass matrix does not change, that is, M1 is a zero matrix. The first-order perturbation amounts of the structural eigenvalues and eigenvectors can be simplified as: Taking the single local segment stiffness reduction of a high-rise structure as an example, when there is stiffness reduction in the sth segment of the structure, we have: Substituting equations (30), (31) and (32) into equation (29) for solution, when the change in segment stiffness is small, that is, ε is small, a more accurate solution can be obtained by using the first-order perturbation: where represents the sth element of the nth mode shape of the original system. Substituting equation (33) into (22), the statistical moment ratio of the ith layer can be expressed as: The stiffness reduction occurs in the sth section of the structure. The change in the statistical moment ratio δi of the i-th (i=1,2...s...N) measuring point of the structure before and after damage can be solved by matrix perturbation theory: Substituting equation (34) into equation (35) to solve it, it can be simplified to: In formula (36) represents the s-th element of the first-order vibration mode of the original system. K is a non-zero term. It can be seen that when s≠i, the change amount δ of the statistical moment ratio corresponding to the measured points before and after damage approaches 0. When s≈i, formula (36) can be further simplified and its result is not zero. When the section stiffness mutation section s is far from the measured point i for solving the statistical moment ratio, the change amount δ of the statistical moment ratio approaches 0. When the section stiffness mutation section s is close to the measured point i for solving the statistical moment ratio, the change amount δ of the statistical moment ratio is large. That is, the structural statistical moment ratio curve can be considered to be still in a continuous and smooth state at the location where the section stiffness does not mutate, and only large fluctuations occur at the location where the section stiffness changes, and the ratio curve is no longer smooth. Based on this, the location of the section stiffness mutation can be quickly judged.

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