Stay cable damage identification method of influence line cubic spline interpolation micro separation difference

Abstract

The invention relates to the technical field of bridge health monitoring, and discloses a stay cable damage identification method of influence line cubic spline interpolation micro separation difference, comprising the following steps: S1, constructing an elastic support continuous beam model considering shear deformation and rotational inertia, and establishing a mapping relationship between support stiffness matrix difference before and after damage and cable force influence line change, calculating the cable force influence lines before and after damage, and making a difference to obtain a cable force influence line difference curve; s2, cubic spline interpolation differential is carried out on the cable force influence line difference curve; and S3, sequentially carrying out smoothing processing and mean variance separation calculation on the curvature curve. By constructing an elastic support continuous beam model integrated with shear deformation and rotational inertia and cooperating with a force normal equation of full-bridge support interaction, a cable force influence line difference curve can be accurately calculated, compared with a traditional model, the curve is more accurate, a solid data foundation is laid for damage identification, the identification accuracy is remarkably improved, and it is ensured that damage diagnosis is more reliable.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge health monitoring, in particular to a cable damage identification method based on influence line cubic spline interpolation differential separation. Background Art

[0002] In the field of health monitoring and maintenance of cable-stayed bridges, the damage identification method based on the mean deviation of the curvature of the cable influence line has become an important means of judging the damage status of the cable due to its deep mining and analysis capabilities of structural response data. This method calculates the mean deviation of the curvature of the cable influence line to capture the differences caused by changes in the structural mechanical properties before and after cable damage, thereby achieving accurate judgment of the location and extent of damage. It is of great significance in ensuring the safety of bridge structures and extending their service life.

[0003] The mechanical models relied upon by traditional cable-stayed bridge cable damage identification often ignore key factors such as shear deformation and moment of inertia during the construction process, resulting in large errors in the obtained cable force influence line difference curves. This can easily lead to deviations in the diagnostic results and makes it difficult to meet the needs of accurate cable-stayed bridge cable damage identification in actual engineering projects. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a cable-stayed bridge damage identification method based on differential difference of influence line cubic spline interpolation, which solves the problem that the difference curve of the cable force influence line has large errors, which easily leads to deviations in the diagnosis results and makes it difficult to meet the needs of accurate identification of cable damage in cable-stayed bridges in actual engineering.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: a cable damage identification method based on influence line cubic spline interpolation differential separation, comprising the following steps:

[0006] S1. Construct an elastically supported continuous beam model that considers shear deformation and moment of inertia. Establish a mapping relationship between the difference in support stiffness matrix before and after damage and the change in cable force influence line. Calculate the cable force influence line before and after damage and make the difference to obtain the cable force influence line difference curve.

[0007] S2. performing cubic spline interpolation differentiation on the cable force influence line difference curve to obtain a curvature curve;

[0008] S3, performing smoothing processing and calculating the mean square deviation of the curvature curve in sequence to obtain a mean square deviation curve;

[0009] S4. Position the peak of the mean deviation square curve to determine the position of the damaged cable.

[0010] Preferably, the elastic support continuous beam model considering shear deformation and moment of inertia in S1 is specifically simplified as follows: the main beam of the cable-stayed bridge is simplified into an elastic support continuous beam, the stiffness matrix of the elastic support continuous beam includes shear stiffness GA and moment of inertia I parameters, and the correlation equation between the local stiffness degradation β of the damaged cable and the support reaction force influence line R(x) is established by the principle of virtual work, and the cable force influence line difference expression ΔT(x)=T0(x)-T d (x), where T0(x)=R0(x) / cos 2 α, T d (x) = R d (x) / cos 2 α is the vertical support reaction influence line before and after damage, α is the angle between the cable and the main beam, β = k d / k0, k0 is the cable stiffness before damage, k d is the stiffness of the cable after damage.

[0011] Preferably, the influence lines of the cable forces before and after the damage are calculated in S1 and the difference is made. The overall stiffness matrix K is constructed by the force equation considering the interaction between the whole bridge support. The stiffness matrix K0 before the damage and the stiffness matrix K after the damage are solved by the matrix block technology. d , we can get the influence line of cable force before damage T0(x) and the influence line of cable force after damage T d (x), and make a difference point by point to obtain the difference curve ΔT(x)=T0(x)-T d (x), where the relationship between T(x) and the vertical support reaction force R(x) is T(x)=R(x) / cos 2 α.

[0012] Preferably, the cubic spline interpolation differentiation of the cable force influence line difference curve in S2 is specifically as follows: in the full length interval [x1,x n ], set the interpolation node x i (i=1,2,...,n), construct a cubic spline function S(x)=a that satisfies the natural boundary conditions of the second-order derivatives at both ends being 0 and the continuity constraints of the third-order derivatives in adjacent intervals i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , we can obtain the curvature curve k(x)=S″(x)=2c by taking the second derivative of S(x) i +6d i (xx i ), where a i , b i, c i , d i are the coefficients of the cubic spline polynomial.

[0013] Preferably, a regularization constraint term is introduced in the cubic spline interpolation process to suppress high-order derivative oscillations, where λ is a regularization parameter adaptively adjusted according to the signal-to-noise ratio of the data, and c i is the coefficient of the second derivative term.

[0014] Preferably, in S3, the curvature curve is smoothed successively using a Gaussian filter function to suppress high-frequency noise, median filtering to eliminate impulse noise, and local polynomial regression LOESS(x)=∑w i (x)y i to correct systematic trend errors, forming a three-level smoothing process, where σ is the Gaussian kernel standard deviation, w i (x) is the local weighting coefficient, and y i =k(x i ) is the curvature sample value.

[0015] Preferably, in S3, the improved formula for calculating the mean square deviation from the mean is used to calculate the degree of curvature fluctuation, where is the mean curvature of the local window with the current point x j as the center and a width of 2k + 1, is the standard deviation of the local window curvature, and k(x j +i) is the curvature value after differentiating the difference curve ΔT(x) of the cable force influence line by cubic spline interpolation.

[0016] Preferably, in S4, peak localization of the mean square deviation from the mean curve is performed by modeling background noise of the mean square deviation from the mean curve using the K-means clustering algorithm, calculating the mean μ and standard deviation σ of the background noise, dynamically generating a damage threshold T = μ + 3σ, using the non-maximum suppression algorithm to eliminate pseudo-peaks with a spacing less than L / 2, and determining the damaged cable number j according to the geometric correspondence |x m and the support position x j =jL as |x m -x j |<L / 2, where L is the adjacent support spacing.

[0017] Preferably, in the elastic support continuous beam model, the conversion relationship between the cable force T(x) of the stay cable and the vertical support reaction R(x) is T(x)=R(x) / cos 2 α, where α is the angle between the stay cable and the main girder, and cos 2 α is the angle correction coefficient.

[0018] Preferably, the cubic spline interpolation nodes are arranged adaptively by the curvature change rate, the nodes are densely packed at an L / 4 spacing in the area near the cable support, and the nodes are sparsely packed at a 2L spacing in the mid-span area, and the node density is proportional to the curvature change rate |d k / d x |Positive correlation, where L is the distance between adjacent supports.

[0019] The present invention provides a cable damage identification method based on differential separation of influence line cubic spline interpolation. It has the following beneficial effects:

[0020] 1. By constructing an elastically supported continuous beam model that incorporates shear deformation and moment of inertia, and combining it with the force equation for the interaction between the entire bridge support, the present invention can accurately calculate the cable force influence line difference curve. Compared with traditional models, this curve is more accurate, creating a solid data foundation for damage identification, significantly improving identification accuracy, and ensuring more reliable damage diagnosis.

[0021] 2. The present invention uses cubic spline interpolation differentiation and combines it with regularization constraints to adaptively arrange nodes according to the curvature change rate. It can effectively suppress noise interference and accurately capture damage characteristics. Even minor damage can be accurately identified. At the same time, it improves the accuracy of interpolation and makes data processing more scientific.

[0022] 3. The present invention eliminates various types of noise through three-level smoothing processing and highlights the damage characteristics with the help of an improved deviation from the mean square formula. The two work together to enable the deviation from the mean square curve to clearly show the damage location, thereby improving the accuracy and reliability of damage location and providing precise guidance for bridge maintenance.

[0023] 4. The present invention dynamically generates damage thresholds with the help of the K-means clustering algorithm and combines it with the non-maximum suppression algorithm to eliminate pseudo-peaks to determine the damaged cable number, effectively avoiding misjudgment and accurately locking the position of the damaged cable, greatly improving the reliability of damage identification and ensuring the accuracy of bridge safety monitoring.

[0024] 5. The present invention establishes a conversion relationship between cable force and support reaction force, and relies on the identification process of the square of the mean deviation of the curvature of the cable force influence line. The two cooperate with each other to closely fit the actual working conditions of the cable-stayed bridge, thereby enhancing practicality and versatility. It can be widely applied to various types of cable-stayed bridges and has stronger adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a flow chart of a method for identifying damage of a stay cable based on differential separation of influence line cubic spline interpolation. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solution of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0027] Please see the attached Figure 1 The embodiment of the present invention provides a cable damage identification method based on influence line cubic spline interpolation differential separation, comprising the following steps:

[0028] S1. Construct an elastically supported continuous beam model that considers shear deformation and moment of inertia. Establish a mapping relationship between the difference in support stiffness matrix before and after damage and the change in cable force influence line. Calculate the cable force influence line before and after damage and make the difference to obtain the cable force influence line difference curve.

[0029] S2. Perform cubic spline interpolation differentiation on the cable force influence line difference curve to obtain the curvature curve;

[0030] S3, performing smoothing processing and calculating the mean square error on the curvature curve in sequence to obtain a mean square error curve;

[0031] S4. Locate the peak of the deviation from the mean square curve to determine the location of the damaged cable.

[0032] Specifically, in step S1, by constructing an elastically supported continuous beam model that takes into account shear deformation and moment of inertia, a mapping relationship between the support stiffness matrix and the cable force influence line changes before and after damage is established. The cable force influence line difference curve is calculated and subtracted to fully reflect the effect of the cable-stayed bridge structural characteristics on the cable force influence line, providing more realistic initial data.

[0033] In step S2, the curvature curve is obtained by performing cubic spline interpolation differentiation on the difference curve of the cable influence line. The difference curve can be further processed into a form that can highlight the change characteristics. The difference caused by the damage is magnified through mathematical methods to make the damage characteristics more obvious.

[0034] In step S3, the mean deviation square curve is obtained by smoothing the curvature curve and calculating the mean deviation square. Smoothing removes noise interference in the data, while the mean deviation square calculation quantifies the degree of curvature fluctuation, highlights the abnormal characteristics of the damage location, and makes the damage characteristics easier to identify on the mean deviation square curve.

[0035] In step S4, the damaged cable position is determined by locating the peak of the deviation from the mean square curve. By finding the peak of the deviation from the mean square curve, the damaged cable position can be directly locked. Based on the data processed in the previous steps, accurate conversion from data to damage location is achieved, ultimately achieving the goal of improving damage identification accuracy.

[0036] In S1, the elastically supported continuous beam model considering shear deformation and moment of inertia is constructed by simplifying the main beam of the cable-stayed bridge into an elastically supported continuous beam. The stiffness matrix of the elastically supported continuous beam contains the shear stiffness GA and moment of inertia I parameters. The correlation equation between the local stiffness degradation β of the damaged cable and the support reaction influence line R(x) is established through the principle of virtual work, and the cable force influence line difference expression ΔT(x)=T0(x)-T d (x), where T0(x)=R0(x) / cos 2 α, T d (x) = R d (x) / cos 2 α is the vertical support reaction influence line before and after damage, α is the angle between the cable and the main beam, β = k d / k0, k0 is the cable stiffness before damage, k d is the stiffness of the cable after damage.

[0037] Specifically, by simplifying the main beam of the cable-stayed bridge into an elastically supported continuous beam taking into account the shear stiffness GA and moment of inertia I parameters, the principle of virtual work is used to establish the correlation equation between the local stiffness degradation β of the damaged cable and the support reaction influence line R(x), and the cable force influence line difference expression is derived. This can more accurately reflect the changes in the mechanical properties of the cable-stayed bridge structure before and after damage, provide accurate cable force influence line difference data for damage identification, lay a solid data foundation for damage identification, and improve the accuracy of identification.

[0038] In S1, the influence lines of cable forces before and after damage are calculated and the difference is made. The overall stiffness matrix K is constructed by the force method equation considering the interaction between the entire bridge support. The stiffness matrix K0 before damage and the stiffness matrix K after damage are solved by matrix block technology. d , we can get the influence line of cable force before damage T0(x) and the influence line of cable force after damage T d (x), and make a difference point by point to obtain the difference curve ΔT(x)=T0(x)-T d (x), where the relationship between T(x) and the vertical support reaction force R(x) is T(x)=R(x) / cos 2 α.

[0039] Specifically, by constructing an elastically supported continuous beam model considering shear deformation and moment of inertia, and combining the principle of virtual work, a mapping relationship between the difference in support stiffness matrix before and after damage and the change in cable force influence line is established, and the force method equation considering the interaction between the supports of the entire bridge is used to solve the cable force influence line before and after damage and make the difference. The cable force influence line difference curve can be accurately obtained, reflecting the influence of the structural characteristics of the cable-stayed bridge on the cable force influence line, providing an accurate data basis for subsequent damage identification, effectively improving the accuracy of damage identification, and achieving the effect of building a solid data foundation for damage identification and improving identification accuracy. At the same time, the combination of this mechanical model and calculation method also enhances the practicality and versatility of the entire damage identification method, and can be widely used in damage identification of cables of different types of cable-stayed bridges.

[0040] In S2, the cubic spline interpolation differentiation of the cable force influence line difference curve is as follows: in the full length interval [x1,x n ], set the interpolation node x i (i=1,2,...,n), construct a cubic spline function S(x)=a that satisfies the natural boundary conditions of the second-order derivatives at both ends being 0 and the continuity constraints of the third-order derivatives in adjacent intervals i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , we can obtain the curvature curve k(x)=S″(x)=2c by taking the second derivative of S(x) i +6d i (xx i ), where a i , b i , c i , d i are the cubic spline polynomial coefficients.

[0041] Specifically, within the entire length of the main beam of the cable-stayed bridge, a cubic spline function that meets specific boundary conditions and derivative continuity constraints is constructed by setting interpolation nodes, and the curvature curve is obtained by calculating its second-order derivative. This can effectively process the difference curve of the cable influence line, capture the curve change characteristics through mathematical means, further highlight the differences caused by damage, provide more obvious data for subsequent damage identification, and improve the accuracy of damage identification.

[0042] Introducing regularization constraints in the cubic spline interpolation process Suppress high-order derivative oscillations, where λ is a regularization parameter that is adaptively adjusted according to the data signal-to-noise ratio, c i is the coefficient of the second-order derivative term.

[0043] Specifically, a regularization constraint is introduced in the cubic spline interpolation process Among them, the regularization parameter is adaptively adjusted according to the data signal-to-noise ratio, and the nodes are adaptively arranged according to the curvature change rate. The nodes are denser near the cable support and sparser in the mid-span. This not only ensures the accurate capture of damage characteristics in key areas, but also takes into account computational efficiency. It is beneficial to suppress high-order derivative oscillations and avoid interpolation result deviations caused by noise interference. The curvature curve obtained by interpolation can more accurately reflect the true characteristics of the cable force influence line difference curve, improve interpolation accuracy, provide more reliable data for subsequent damage identification, and enhance the accuracy and reliability of damage location.

[0044] In S3, the curvature curve is smoothed in turn using Gaussian filter function Suppress high-frequency noise, median filtering to eliminate impulse noise, local polynomial regression LOESS(x)=∑w i (x)y i Correct the systematic trend error and form a three-level smoothing process, where σ is the Gaussian kernel standard deviation, w i (x) is the local weighting coefficient, y i =k(x i ) is the curvature sample value.

[0045] Specifically, by sequentially using Gaussian filter functions Median filtering, local polynomial regression LOESS(x)=∑w i (x)y i Performing three-level smoothing on the curvature curve can remove high-frequency noise, impulse noise, and systematic trend errors, making the curvature curve smoother and more accurate, highlighting the damage characteristics, providing more reliable data for subsequent mean square error calculations, and enhancing the ability of subsequent calculation results to reflect abnormal characteristics of the damage location.

[0046] The improved square deviation formula is used to calculate the square deviation from the mean in S3. Calculate the degree of curvature fluctuation, where The current point x j The mean curvature of the local window with a center and a width of 2k+1, is the standard deviation of the local window curvature, k(x j +i) is the curvature value of the cable force influence line difference curve ΔT(x) after differential interpolation by cubic spline.

[0047] Specifically, the improved mean square error formula is used Calculate the degree of curvature fluctuation and comprehensively consider the local window mean curvature and the standard deviation of the local window curvature σ k, it can more accurately quantify the curvature fluctuations, highlight the curvature anomalies at the damage locations, make the damage features more prominent in the deviation-from-mean square curve, provide a strong basis for accurately locating the damaged stay cables subsequently, and improve the accuracy of damage identification.

[0048] In S4, peak localization of the deviation-from-mean square curve models the background noise of the deviation-from-mean square curve through the K-means clustering algorithm, calculates the mean μ and standard deviation σ of the background noise, dynamically generates the damage threshold T = μ + 3σ, uses the non-maximum suppression algorithm to eliminate the pseudo-peaks with a spacing less than L / 2, and determines the damaged stay cable number j according to the geometric correspondence between the peak position x m and the support position x j = jL, i.e., |x m -x j |< L / 2, where L is the adjacent support spacing.

[0049] Specifically, the background noise of the deviation-from-mean square curve is modeled through the K-means clustering algorithm, the mean μ and standard deviation σ of the background noise are calculated, the damage threshold is dynamically generated using the formula T = μ + 3σ, the non-maximum suppression algorithm is combined to eliminate the pseudo-peaks with a spacing less than L / 2, and the damaged stay cable number is determined based on the geometric correspondence between the peak position and the support position, which can distinguish the damage signal from the background noise, eliminate interference factors, and provide a basis for the maintenance decision of the cable-stayed bridge.

[0050] In the elastic support continuous beam model, the conversion relationship between the stay cable force T(x) and the vertical support reaction R(x) is T(x) = R(x) / cos 2 α, where α is the angle between the stay cable and the main girder, and cos 2 α is the angle correction coefficient.

[0051] Specifically, in the elastic support continuous beam model, it is clear that the conversion relationship between the stay cable force T(x) and the vertical support reaction R(x) is T(x) = R(x) / cos 2 α. This formula is corrected considering the angle α between the stay cable and the main girder, can realize the conversion of mechanical quantities between the two, provides an accurate mechanical relationship basis for steps such as constructing the model and calculating the influence line of the cable force, makes the entire damage identification method more in line with the actual mechanical characteristics of the cable-stayed bridge, enhances the practicability and generality of the method, and enhances the ability to identify damage.

[0052] The cubic spline interpolation nodes are adaptively arranged according to the curvature change rate. The nodes are densified at a spacing of L / 4 in the area near the stay cable supports, and sparsified at a spacing of 2L in the mid-span area. The node density is positively correlated with the curvature change rate |d k / d x |, where L is the adjacent support spacing.

[0053] Specifically, the cubic spline interpolation nodes are based on the curvature change rate |d k / d x Adaptive node arrangement: nodes are densely packed at L / 4 spacing near the cable-stayed supports and sparsely packed at 2L spacing in the mid-span area. This allows for flexible adjustment of node density based on the curvature variations in different structural regions. Nodes are densely packed near supports with large curvature variations to accurately capture damage characteristics, while nodes are sparsely packed in the mid-span area to ensure computational efficiency.

[0054] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A cable damage identification method based on influence line cubic spline interpolation differential separation, characterized by: The following steps are involved: S1. Construct an elastically supported continuous beam model that considers shear deformation and moment of inertia. Establish a mapping relationship between the difference in support stiffness matrix before and after damage and the change in cable force influence line. Calculate the cable force influence line before and after damage and make the difference to obtain the cable force influence line difference curve. S2. performing cubic spline interpolation differentiation on the cable force influence line difference curve to obtain a curvature curve; S3, performing smoothing processing and calculating the mean square deviation of the curvature curve in sequence to obtain a mean square deviation curve; S4. Position the peak of the mean deviation square curve to determine the position of the damaged cable.

2. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: The elastic support continuous beam model considering shear deformation and moment of inertia constructed in S1 is specifically to simplify the main beam of the cable-stayed bridge into an elastic support continuous beam. The stiffness matrix of the elastic support continuous beam includes the shear stiffness GA and the moment of inertia I parameters. The correlation equation between the local stiffness degradation β of the damaged cable and the support reaction force influence line R(x) is established through the principle of virtual work, and the cable force influence line difference expression ΔT(x)=T0(x)-T d (x), where T0(x)=R0(x) / cos 2 α, T d (x) = R d (x) / cos 2 α is the vertical support reaction influence line before and after damage, α is the angle between the cable and the main beam, β = k d / k0, k0 is the cable stiffness before damage, k d is the stiffness of the cable after damage.

3. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: In S1, the influence lines of cable forces before and after damage are calculated and the difference is made. The overall stiffness matrix K is constructed by the force equation considering the interaction between the whole bridge support. The stiffness matrix K0 before damage and the stiffness matrix K after damage are solved by matrix block technology. d , we can get the influence line of cable force before damage T0(x) and the influence line of cable force after damage T d (x), and make a difference point by point to obtain the difference curve ΔT(x)=T0(x)-T d (x), where the relationship between T(x) and the vertical support reaction force R(x) is T(x)=R(x) / cos 2 α.

4. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: The cubic spline interpolation differentiation of the cable force influence line difference curve in S2 is specifically as follows: in the full length interval [x1,x n ], set the interpolation node x i (i=1,2,...,n), construct a cubic spline function S(x)=a that satisfies the natural boundary conditions of the second-order derivatives at both ends being 0 and the continuity constraints of the third-order derivatives in adjacent intervals i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , we can obtain the curvature curve k(x)=S″(x)=2c by taking the second derivative of S(x) i +6d i (xx i ), where a i , b i , c i , d i are the cubic spline polynomial coefficients.

5. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 4 is characterized in that: The regularization constraint term is introduced in the cubic spline interpolation process Suppress high-order derivative oscillations, where λ is a regularization parameter that is adaptively adjusted according to the data signal-to-noise ratio, c i is the coefficient of the second-order derivative term.

6. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: In S3, the curvature curve is smoothed in sequence using Gaussian filter functions. Suppress high-frequency noise, median filtering to eliminate impulse noise, local polynomial regression LOESS(x)=Σw i (x)y i Correct the systematic trend error and form a three-level smoothing process, where σ is the Gaussian kernel standard deviation, w i (x) is the local weighting coefficient, y i =k(x i ) is the curvature sample value.

7. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: The calculation of the deviation from the mean square in S3 adopts the improved deviation from the mean square formula Calculate the degree of curvature fluctuation, where The current point x j The mean curvature of the local window with a center and a width of 2k+1, is the standard deviation of the local window curvature, k(x j +i) is the curvature value of the cable force influence line difference curve ΔT(x) after differentially interpolating with cubic spline.

8. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: The peak positioning of the deviation-from-mean square curve in S4 is to model the background noise of the deviation-from-mean square curve through the K-means clustering algorithm, calculate the mean μ and standard deviation σ of the background noise, dynamically generate the damage threshold T = μ + 3σ, use the non-maximum suppression algorithm to eliminate the pseudo-peaks with a spacing less than L / 2, and determine the damage cable number j according to the geometric correspondence between the peak position x m and the support position x j = jL |x m -x j |< L / 2, where L is the adjacent support spacing.

9. The cable damage identification method based on influence line cubic spline interpolation differential error according to claim 1 is characterized in that: In the elastically supported continuous beam model, the conversion relationship between the cable force T(x) and the vertical support reaction force R(x) is T(x)=R(x) / cos 2 α, where α is the angle between the cable and the main beam, cos 2 α is the angle correction coefficient.

10. The cable damage identification method based on influence line cubic spline interpolation and differential separation according to claim 1 is characterized in that: The cubic spline interpolation nodes are arranged adaptively according to the curvature change rate. The nodes are densely packed at L / 4 spacing in the area near the cable support and sparsely packed at 2L spacing in the mid-span area. The node density is proportional to the curvature change rate |d k / d x |Positive correlation, where L is the distance between adjacent supports.

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