Existing concrete beam bridge crack diagnosis method based on influence line sparse coefficient

Abstract

The invention discloses an existing concrete beam bridge crack diagnosis method based on an influence line sparse coefficient, which is characterized in that force method graph multiplication and a crack nonlinear damage function are substituted into an analytical solution for solving, and finite element simulation relates to respiration crack simulation. A nonlinear spring is adopted to simulate crack opening and perform grid division and encryption processing on the tip of the crack, bridge section rigidity change caused by the breathing crack is accurately simulated by constructing a crack rigidity damage function, and the model is introduced into an influence line analytical solution to obtain a nonlinear influence line of the cracked bridge. In combination with a sparse coefficient representation method, damage position and damage degree information is extracted from influence line data, and accurate positioning and quantitative evaluation of beam bridge section cracking are achieved; the method not only improves the accuracy and efficiency of damage identification, but also provides a reliable technical means for rapid detection and state evaluation of the existing beam bridge.

Description

Technical Field

[0001] The present invention relates to an analytical solution for the deformation influence line of a reconstructed cross-section cracked concrete beam bridge. The solution involves the use of force method graph multiplication and the substitution of a nonlinear damage function of the crack into the analytical solution. Finite element simulation involves the simulation of breathing cracks, and nonlinear springs are used to simulate crack opening and crack tips are meshed and encrypted. Specifically, the invention relates to a method for diagnosing cracks in existing concrete beam bridges based on the sparse coefficient of the influence line. Background Art

[0002] As an important infrastructure in modern society, bridges are widely used in transportation, urban construction and economic development. However, with the increase of service life and vehicle load, existing beam bridges are often affected by various factors such as fatigue loads and environmental erosion, and damage problems such as cracks and stiffness degradation occur. These damages not only reduce the bearing capacity of the bridge, but also may threaten public safety. Therefore, conducting efficient and accurate bridge damage identification and assessment research is of great significance to the maintenance, reinforcement and service safety of bridges. At present, the mainstream methods for bridge damage identification include technologies based on vibration characteristics, influence line analysis and finite element modeling. However, these methods have the following problems in practical applications:

[0003] 1. Vibration characteristic analysis method: Damage identification is performed by extracting the modal parameters of the bridge (such as natural frequency and vibration mode). However, it is less sensitive to small cracks or slight stiffness changes and cannot effectively capture complex nonlinear damage characteristics.

[0004] 2. Influence Line Analysis: Bridge influence lines are an important tool for analyzing the stress response of bridge structures, reflecting the distribution of structural stiffness. However, traditional influence line models are typically based on linear assumptions and fail to account for the nonlinear mechanical behavior caused by the opening and closing of cracks in bridges (i.e., "breathing cracks"), resulting in reduced identification accuracy.

[0005] 3. Finite element modeling method: Although finite element technology can simulate bridge damage behavior with high precision, the computational cost is high and it is difficult to meet the needs of rapid detection and real-time monitoring of existing beam bridges.

[0006] Breathing cracks are a common form of bridge damage, manifesting as cracks that periodically open and close under load. This nonlinear behavior not only alters the stiffness distribution of the bridge but also produces complex nonlinear effects on the shape of the influence line. However, existing bridge damage identification methods, most of which are based on uniform stiffness degradation models, fail to effectively capture the dynamic characteristics of breathing cracks, making it difficult to accurately locate and quantitatively assess damage.

[0007] Sparse representation methods, a mathematical tool based on signal decomposition, have shown promising application potential in bridge damage identification. By constructing a sparse dictionary and extracting the sparse characteristics of the signal, sparse representation methods can effectively identify structural damage locations in complex noisy environments. However, existing research has primarily modeled linear damage characteristics (such as uniform stiffness variations) and has not fully considered the nonlinear effects of breathing cracks on bridge mechanical behavior. Summary of the Invention

[0008] In response to the problems in the related art, the present invention proposes a method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient to overcome the above-mentioned technical problems existing in the existing related art.

[0009] To achieve the above-mentioned object, according to an embodiment of the first aspect of the present invention, a method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient is proposed. The method comprises the following steps:

[0010] Step S1: Based on the existing crack damage model, simply supported beams with different crack damage models are established using ANSYS finite element method. Influence lines are compared under different load types, load sizes, and damage degrees, and a breathing crack model is selected as the simulation crack model.

[0011] Step S2: Substitute the stiffness damage function of the breathing crack model into the displacement influence line theory to obtain the analytical solution of the displacement influence line at different positions;

[0012] Step S3: using ANSYS finite element method to simulate a simply supported beam under a breathing crack to obtain the displacement influence line and verify the accuracy of the analytical solution of the theoretical displacement influence line;

[0013] Among them, nonlinear springs are used at the cracks to model the opening and closing breathing of the cracks;

[0014] Step S4: Calculate analytical solutions for the cracking displacement influence lines of different types of bridge structure sections;

[0015] Step S5: A sparse mathematical model is established by combining the influence lines of the cross-section cracked bridge and the influence lines of the normal bridge. The sparse coefficient is used as the bridge damage identification index. The damage degree is quantified with the energy damage index and the damage energy index is normalized to identify the damage degree and damage location of the bridge.

[0016] Preferably, the stiffness damage function of the breathing crack model is substituted into the displacement influence line theory in step S2 to obtain the displacement influence line analytical solution at different positions by taking a simply supported beam as an example, and the steps are as follows:

[0017] S211: The finite element model is used for the simply supported beam, and the stiffness at the crack is replaced by the breathing crack damage function;

[0018] S212: Find the expressions of the bending moment under the action of unit force and moving unit force, that is,

[0019] The expression for the bending moment of a simply supported beam under a moving unit load is:

[0020]

[0021] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0022]

[0023] S213: Graph multiplication method is used to obtain the analytical solution expression of the displacement influence line, that is,

[0024] when hour

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] (

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] .

[0045] Preferably, the specific steps of step S3 are:

[0046] S311, selecting parameters;

[0047] S312, the finite element displacement influence line is compared with the analytical solution of the theoretical displacement influence line, taking the midpoint and one-quarter of the simply supported beam respectively;

[0048] Take the maximum point of the displacement influence line for comparison.

[0049] Preferably, the analytical solution of the cracking displacement influence line of different types of bridge structure sections is solved in the following steps:

[0050] S411, solve the analytical expressions for the bending moments of different types of bridges under the action of moving unit loads and unit forces at measuring points;

[0051] S412, according to the different crack areas, the damage function is substituted into the force method diagram to obtain the bridge displacement influence line;

[0052] S413, taking the cracking displacement influence line of continuous beam bridge section as an example;

[0053] when When: The bending moment expression of a simply supported beam under moving unit load is:

[0054]

[0055] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0056]

[0057] when When: The bending moment expression of a simply supported beam under moving unit load is:

[0058]

[0059] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0060]

[0061] .

[0062] Preferably, a sparse mathematical model is established by combining the influence lines of the cross-section cracked bridge and the influence lines of the normal bridge. The sparse coefficient is used as the bridge damage identification index. The damage degree is quantified by the energy damage index and the damage energy index is normalized to identify the damage degree and damage location of the bridge, including:

[0063] S511, data preprocessing;

[0064] Obtain the influence line data of the bridge in the undamaged state, construct a dictionary matrix A, each column of which represents the response of different load positions, and obtain the influence line y in the damaged state;

[0065] S512, establishing a sparse mathematical model;

[0066] Assume that the damage distribution is sparse, that is, Can be represented by a linear combination of a small number of basis vectors;

[0067] The mathematical model is:

[0068]

[0069] in: : dictionary matrix, influence line in lossless state;

[0070] : sparse coefficient vector, only a few elements are non-zero;

[0071] : Noise vector, used to describe the measurement error.

[0072] The optimization problem can be expressed as:

[0073]

[0074] in:

[0075] : Reconstruction error, ensuring Close to the observed data y;

[0076] : L1 norm regularization, solving sparse solutions;

[0077] : Regularization parameter, which controls the trade-off between sparsity and reconstruction error;

[0078] S513, constructing a dictionary matrix A;

[0079] Assume that the bridge is divided into segments, and the contribution of each segment to the influence line under load is ; Dictionary matrix ,Each column represents the response feature of a segment;

[0080] It can be obtained through finite element simulation or test data under healthy conditions;

[0081] S514, solve the sparse coefficient ;

[0082] The optimization problem uses LASSO (Least Absolute Shrinkage and Selection Operator):

[0083]

[0084] : regularization parameter.

[0085] Preferably, the solution method adopts the coordinate descent method, and the steps are:

[0086] 1. Initialization

[0087] 2. For each Update one by one:

[0088]

[0089] in:

[0090] is a soft threshold function;

[0091] Indicates that the first Matrix after column

[0092] Indicates that x vector is removed Vector of elements

[0093] 3. Iterate until convergence.

[0094] 7. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 5, further comprising:

[0095] S515, Damage Diagnosis Methods;

[0096] The x obtained by solving the optimization problem is:

[0097]

[0098] in is a sparse vector:

[0099] Qualitative damage occurs: the non-zero element position of the sparse vector x corresponds to the damaged area;

[0100] Locate the injury: If Rule No. There is damage to the segment;

[0101] Quantitative damage degree: The amplitude of non-zero elements reflects the damage degree, The absolute value of The bridge section cracking model is a stiffness drop model, and the stiffness drop of each bridge section has a linear relationship with the change of the influence line:

[0102]

[0103] in:

[0104] : No. Beam stiffness in the segment health state

[0105] : The decrease in bridge stiffness

[0106] :The sparse solution An element reflects the relative proportion of stiffness change caused by damage;

[0107] The actual stiffness change is calculated as:

[0108]

[0109] Known , you can convert the sparse vector Converted into actual stiffness change;

[0110] S516, further quantify the extent of damage;

[0111] Bridge damage can be further quantified using the damage energy metric. The unit strain energy of a beam is defined as:

[0112]

[0113] in: : No. Energy loss caused by segment damage;

[0114] : beam bending moment expression;

[0115] : flexural stiffness;

[0116] : No. Segment length

[0117] Bridge damage is mainly manifested as a decrease in stiffness, resulting in changes in bending moment , which in turn causes the strain energy to change ;

[0118] The strain energy after damage is:

[0119]

[0120] Simplifying assumptions:

[0121] 1. The injury only causes changes, no significant changes ,Right now ;

[0122] 2.

[0123] 3.

[0124] Substitute and simplify:

[0125]

[0126] in:

[0127] , indicating the relative change in the degree of damage (corresponding to the sparse representation physical meaning of ).

[0128] The final formula is:

[0129]

[0130] Further simplification and engineering application

[0131] In the project, it is assumed that each bridge 、 and is approximately a constant, then:

[0132]

[0133] in: : No. Average bending moment of the segment;

[0134] : No. Bending stiffness of the segment;

[0135] : No. The length of the segment;

[0136] : No. Sparsity coefficient of segment damage (relative stiffness reduction);

[0137] Normalization of damage energy index

[0138] For ease of comparison, the damage energy can be normalized:

[0139]

[0140] in is the total number of bridge sections.

[0141] Compared with the prior art, the present invention has the following beneficial effects:

[0142] This method accurately simulates the changes in bridge cross-section stiffness caused by breathing cracks by constructing a crack stiffness damage function. This model is then incorporated into an influence line analytical solution to obtain nonlinear influence lines for cracked bridges. Combined with a sparse coefficient representation method, damage location and severity information is extracted from the influence line data, enabling precise localization and quantitative assessment of cracks in beam bridge sections. This method not only improves the accuracy and efficiency of damage identification but also provides a reliable technical means for rapid detection and condition assessment of existing beam bridges.

[0143] The analytical solution of the deformation influence line of the cross-section cracked beam bridge described in the present invention is more accurate than the analytical solution of the traditional stiffness reduction damage deformation influence line, can better reflect the real cross-section cracked beam bridge influence line and can be applied to various bridge structures. The breathing crack model described in the present invention can better simulate the nonlinear analysis of real cracks and use nonlinear springs to simulate the nonlinear behavior of cracks in the finite element model. The use of grid encryption at the crack tip greatly improves the accuracy. The damage identification index described in the present invention can more accurately identify the damage location and damage degree of the bridge and has strong robustness to noise, and can be applied to high-noise and sparse data. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] In order to more clearly illustrate the technical solutions of the embodiments of the invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, they can also obtain drawings based on these drawings without paying any creative work.

[0145] Figure 1 This is a flow chart of a method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient proposed by the present invention.

[0146] Figure 2 Schematic diagram of torsion spring connection in the constant stiffness torsion spring model of the present invention;

[0147] Figure 3 Schematic diagram of torsion spring connection;

[0148] Figure 4 is the damage function model in the open crack model;

[0149] Figure 5 is the damage function model in the breathing crack model;

[0150] Figure 6 is the influence line under different loads;

[0151] Figure 7 is the influence line under different loads;

[0152] Figure 8 Comparison of influence lines of different models;

[0153] Figure 9 Simplified schematic diagram of a simply supported beam;

[0154] Figure 10 Comparison between theoretical displacement influence line and finite element displacement influence line;

[0155] Figure 11 It is a virtual continuous beam model;

[0156] Figure 12 It is a virtual continuous beam model. DETAILED DESCRIPTION

[0157] The following will clearly and completely describe the technical solutions in the embodiments of the invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0158] like Figure 1 As shown, one embodiment of the present invention provides a method for diagnosing cracks in existing concrete beam bridges based on an influence line sparsity coefficient. The method comprises the following steps:

[0159] Step S1: Select a crack damage model, establish simply supported beams with different crack damage models using ANSYS finite element method based on the existing crack damage model, select appropriate parameters to compare influence lines under different load types, load sizes, and damage degrees, and select a breathing crack model as the simulated crack model;

[0160] Step S2: Substitute the stiffness damage function of the breathing crack model into the displacement influence line theory and obtain the analytical solutions of the displacement influence lines at different positions by taking a simply supported beam as an example;

[0161] Step S3: The displacement influence line is obtained by ANSYS finite element simulation of a simply supported beam under a breathing crack to verify the accuracy of the analytical solution of the theoretical displacement influence line.

[0162] Among them, nonlinear springs are used at the cracks to model the opening and closing breathing of the cracks;

[0163] Step S4: Calculate analytical solutions for the cracking displacement influence lines of different types of bridge structure sections;

[0164] Step S5: A sparse mathematical model is established by combining the influence lines of cross-section cracked bridges and normal bridges. The sparse coefficient is proposed as a bridge damage identification indicator and its accuracy is verified. On this basis, an energy damage index is proposed to further quantify the damage extent and normalize the damage energy index. This allows for accurate identification of the damage extent and location of the bridge, providing the necessary basis for research such as damage identification and health monitoring.

[0165] In one embodiment of the present invention, the specific steps of selecting the crack damage model in step S1 are:

[0166] S111: Constant stiffness torsion spring model, that is:

[0167] Consider only the cracked Euler-Bernoulli beam under bending moment. Figure 2 .

[0168] The beam length is L, the beam height is h, and the nominal depth of the crack is a. It represents the nominal local rotation angle of the crack under the bending moment M.

[0169] If the flexibility coefficient of the crack section is ,but:

[0170] Flexibility coefficient Through fracture mechanics analysis, we can get:

[0171] Where: E is the elastic modulus, I is the moment of inertia of the section, is the nominal damage ratio, and the dimensionless function value can be obtained from the literature:

[0172]

[0173] The beam is separated at the fracture and connected with a torsion spring in the middle. The torsion spring stiffness is , the torsion spring connection diagram is as follows Figure 3 :

[0174] S112: Open crack model, namely:

[0175] like Figure 4 The figure shows the distribution of the elastic modulus of the damaged area along the length of the beam. The damage is most severe in the center of the area, and the degree of damage changes gradually from the center of the area to the undamaged area.

[0176] The bridge stiffness damage function is expressed as:

[0177]

[0178] Where L is the length of the beam; is the elastic modulus of the healthy beam; x is the distance from the center line of the damaged area of ​​the beam; Indicates the degree of damage, and its variation range is [0,1]. When the beam is completely destroyed, When , it means that the beam has not been damaged; It represents the length coefficient of the damaged area, which determines the impact range of the open crack on the adjacent area, and the variation range is [0,1]. If the crack damage is localized, it means that the damage is relatively concentrated. When , the entire beam is damaged and the stiffness is reduced accordingly; is the stiffness variation coefficient of the damaged area, generally ranging from 0.5 to 2. The larger the value, the flatter the stiffness curve. The smaller it is, the steeper the stiffness curve is.

[0179] S113: Breathing crack model, i.e.,

[0180] On the basis of opening the crack, a breathing coefficient is introduced To simulate the breathing of cracks. Figure 5 As shown, the remaining parameters are the same as those for the open crack.

[0181] Assume that the elastic modulus corresponding to the fully open crack state is , then the bridge damage stiffness is expressed as:

[0182]

[0183]

[0184] In the formula is the coefficient of the opening degree of the breathing crack caused by the bending moment under the deadweight of the bridge, is the vehicle speed, then .

[0185] when When the breathing crack is open, When , it indicates that the breathing crack is closed.

[0186] S121: Different load-displacement influence line analysis, i.e.,

[0187] The influence lines of the constant stiffness torsion spring model and the breathing crack model are studied under different loads. The displacement influence lines of the simply supported beam of the constant stiffness torsion spring model and the breathing crack model are measured under the action of 100N, 1000N and 10000N moving loads respectively. Figure 6 shown.

[0188] The maximum values ​​of the displacement influence lines are compared in Table 1. The results show that the displacement influence line of the constant stiffness torsion spring model varies linearly with the load size, while the displacement influence line of the breathing crack model varies nonlinearly with the load size, which better reflects the actual bridge cracks.

[0189] Table 1 Analysis of influence lines of different loads and displacements

[0190] Load (N) 100N 1000N 10000N Simply supported beam with constant stiffness torsion spring model <![CDATA[3.20659×10 -9 ]]> <![CDATA[3.20659×10 -8 ]]> <![CDATA[3.20659×10 -7 ]]> Linear change Breathing crack model simply supported beam <![CDATA[3.65643×10 -9 ]]> <![CDATA[3.65643×10 -8 ]]> <![CDATA[3.65645×10 -7 ]]> Nonlinear changes

[0191] S122: Different damage displacement influence line analysis, i.e.

[0192] Taking the opening crack model and the breathing crack model as examples, the influence line changes under different damage conditions are studied. The stiffness change coefficient 𝛄 of the damaged area is set to 2, the length coefficient 𝛃 of the damaged area is set to 0.1, and the moving load is 10000N. The displacement influence line of the midpoint position of the simply supported beam bridge is analyzed with damage degrees of 0.2, 0.3, 0.4, and 0.5 respectively. The influence lines of the bridge under different damage conditions can be obtained as follows: Figure 7 shown.

[0193] The maximum value of the displacement influence line is compared and shown in Table 2. The results show that the bridge displacement changes nonlinearly with damage under the same load.

[0194] Table 2 Analysis of influence lines of different damage displacements

[0195] Degree of injury 0.2 0.3 0.4 0.5 Displacement influence lines -3.52316e-7 -3.74638e-7 -4.03509e-7 -4.42496e-7 Displacement influence line difference 6.35% 14.53% 25.6%

[0196] S123: Displacement influence line analysis of different models, i.e.

[0197] Select the same damage degree 0.3 and moving load 10 6 The influence lines of different crack models are studied using three crack models, a simply supported beam and a normal simply supported beam, under the action of N. The parameters of the crack damage function are the same as those in the previous section.

[0198] By analyzing the displacement influence lines of the midpoint of the simply supported beam bridge, the influence lines of the bridge under different crack models can be obtained as follows: Figure 8 shown.

[0199] The maximum values ​​of the displacement influence lines are compared in Table 3. The results show that the constant stiffness torsion spring model, due to its constant stiffness and small torsion spring length, has minimal difference from the influence line of a normal bridge, and the change is linear. The crack in the opening crack model remains open, resulting in an exaggerated result. The breathing crack model better simulates real cracks: when the moving load is before the damaged area, the crack is closed. As the moving load moves into the damaged area, the crack gradually opens. When it reaches the crack, it is fully open. As the load continues to move, the crack gradually closes again. When it moves into the undamaged area, the crack is completely closed. Therefore, the breathing crack model will be used in subsequent studies to simulate cracking in real bridge sections.

[0200] Table 3 Displacement influence line analysis of different models

[0201] Model Normal simply supported beam Simply supported beam with constant stiffness torsion spring model Simply supported beam with opening crack model Breathing crack model simply supported beam Displacement influence lines -3.1989e-7 -3.2308e-7 -3.7464e-7 -3.67719e-7 Displacement influence line difference 0.9% 17.1% 14.95%

[0202] Substituting the stiffness damage function of the breathing crack model into the displacement influence line theory in step S2 and taking a simply supported beam as an example to obtain the analytical solution of the displacement influence lines at different positions, the specific steps are as follows:

[0203] S211, taking the simply supported beam as an example for theoretical derivation, the simply supported beam adopts the above finite element model, and the virtual beam model is as follows Figure 9 , the stiffness at the crack is replaced by the breathing crack damage function.

[0204] S212, respectively find the expressions for the bending moment under the action of unit force and moving unit force, that is,

[0205] The expression for the bending moment of a simply supported beam under a moving unit load is:

[0206]

[0207] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0208]

[0209] S213, the displacement influence line analytical solution expression is obtained by graph multiplication, that is,

[0210] when hour

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218] (

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231] The accuracy of the theoretical displacement influence line solution is verified by simulating the simply supported beam under the breathing crack using ANSYS finite element method in step S3. Nonlinear springs are used at the crack to model the opening and closing breathing of the crack. The specific steps are as follows:

[0232] S311, select appropriate parameters, that is,

[0233] The cross section is rectangular, length × width = 0.3m × 0.5m, beam length 10m, elastic modulus E = 2.1 × 10 5 , the damage degree is 0.3, the stiffness variation coefficient of the damaged area 𝛄 is 2, the length coefficient of the damaged area 𝛃 is 0.1, and the moving load is 10 6 N. The coefficient of the opening degree of the breathing crack caused by the bending moment under the deadweight of the bridge is taken as 0.3.

[0234] S312, the finite element displacement influence line is compared with the analytical solution of the theoretical displacement influence line, that is,

[0235] like Figure 10 As shown: take the midpoint and one-quarter of the simply supported beam respectively.

[0236] Comparisons were made at the maximum displacement influence line values. The difference in the maximum displacement influence line values ​​at the midpoint was 0.564%, and the difference at the quarter-point values ​​was 0.568%. These results demonstrate that the analytical solution for the displacement influence line of a beam bridge with cracked sections is highly accurate and can accurately reflect the true bridge influence line when the bridge section is cracked.

[0237] Step S4: Analytical solutions for the cracking displacement influence lines of different types of bridge structure sections are obtained. The specific steps are as follows:

[0238] S411, solve the analytical expressions for the bending moments of different types of bridges under the action of moving unit loads and unit forces at measuring points;

[0239] S412, according to the different crack areas, the damage function is substituted into the force method diagram to obtain the bridge displacement influence line;

[0240] S413, taking the cracking displacement influence line of continuous beam bridge section as an example;

[0241] when When: Virtual beam model is as follows Figure 11

[0242] The expression for the bending moment of a simply supported beam under a moving unit load is:

[0243]

[0244] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0245]

[0246] when When: Virtual beam model is as follows Figure 12

[0247] The expression for the bending moment of a simply supported beam under a moving unit load is:

[0248]

[0249] Bending moment when unit force acts on the midpoint of a simply supported beam:

[0250]

[0251]

[0252] In step S5, a sparse mathematical model is established by combining the influence lines of the cracked bridge section and the normal bridge section. The sparse coefficient is proposed as a bridge damage identification indicator and its accuracy is verified. The energy damage index is proposed to further quantify the damage extent and normalize the damage energy index. This allows for accurate identification of the damage extent and location of the bridge, providing the necessary basis for research such as damage identification and health monitoring. The specific steps are as follows:

[0253] S511, data preprocessing;

[0254] The influence line data of the bridge in the undamaged state are obtained, and a dictionary matrix A is constructed, in which each column represents the response of different load positions, and the influence line y in the damaged state is obtained.

[0255] S512, establishing a sparse mathematical model;

[0256] Assume that the damage distribution is sparse, that is, It can be represented by a linear combination of a small number of basis vectors.

[0257] The mathematical model is:

[0258]

[0259] in: : dictionary matrix, influence line in lossless state;

[0260] : sparse coefficient vector, only a few elements are non-zero;

[0261] : Noise vector, used to describe the measurement error.

[0262] The optimization problem can be expressed as:

[0263]

[0264] in:

[0265] : Reconstruction error, ensuring Close to the observed data y;

[0266] : L1 norm regularization, solving sparse solutions

[0267] : Regularization parameter that controls the trade-off between sparsity and reconstruction error.

[0268] S513, constructing a dictionary matrix A;

[0269] Assume that the bridge is divided into segments, and the contribution of each segment to the influence line under load is . Dictionary matrix ,Each column represents the response feature of a segment.

[0270] It can be obtained through finite element simulation or test data under healthy conditions.

[0271] S514, solve the sparse coefficient ;

[0272] The optimization problem uses LASSO (Least Absolute Shrinkage and Selection Operator):

[0273]

[0274] : Regularization parameter. When it is larger, the sparsity is enhanced but the accuracy is reduced. When it is smaller, the sparsity is weakened but the fitting effect is better.

[0275] The solution method uses the coordinate descent method, and the specific steps are:

[0276] 1. Initialization

[0277] 2. For each Update one by one:

[0278]

[0279] in:

[0280] is a soft threshold function;

[0281] Indicates that the first Matrix after column

[0282] Indicates that x vector is removed Vector of elements

[0283] 3. Iterate until convergence.

[0284] S515, Damage Diagnosis Methods;

[0285] The x obtained by solving the optimization problem is:

[0286]

[0287] in is a sparse vector:

[0288] Qualitative damage occurs: the non-zero element position of the sparse vector x corresponds to the damaged area.

[0289] Locate the injury: If Rule No. There is damage in the segment.

[0290] Quantitative damage degree: The amplitude of non-zero elements reflects the damage degree, The absolute value of The bridge section cracking model is a stiffness drop model, and the stiffness drop of each bridge section has a linear relationship with the change of the influence line:

[0291]

[0292] in:

[0293] : No. Beam stiffness in the segment health state

[0294] : The decrease in bridge stiffness

[0295] :The sparse solution An element that reflects the relative proportion of stiffness change caused by damage.

[0296] The actual stiffness change is calculated as:

[0297]

[0298] Known , you can convert the sparse vector Converted into actual stiffness change.

[0299] S516, further quantify the extent of damage;

[0300] Bridge damage can be further quantified using the damage energy metric. The unit strain energy of a beam is defined as:

[0301]

[0302] in: : No. Energy loss caused by segment damage;

[0303] : beam bending moment expression;

[0304] : flexural stiffness;

[0305] : No. Segment length

[0306] Bridge damage is mainly manifested as a decrease in stiffness, resulting in changes in bending moment , which in turn causes the strain energy to change .

[0307] The strain energy after damage is:

[0308]

[0309] Simplifying assumptions:

[0310] 1. The injury only causes changes, no significant changes ,Right now ;

[0311] 2.

[0312] 3.

[0313] Substitute and simplify:

[0314]

[0315] in:

[0316] , indicating the relative change in the degree of damage (corresponding to the sparse representation physical meaning of ).

[0317] The final formula is:

[0318]

[0319] Further simplification and engineering application

[0320] In the project, it is assumed that each bridge 、 and is approximately a constant, then:

[0321]

[0322] in: : No. Average bending moment of the segment;

[0323] : No. Bending stiffness of the segment;

[0324] : No. The length of the segment;

[0325] : No. The sparsity coefficient of the segment damage (relative stiffness reduction).

[0326] Normalization of damage energy index

[0327] For ease of comparison, the damage energy can be normalized:

[0328]

[0329] in is the total number of bridge sections.

[0330] The damage degree is further quantified based on the damage energy index and a specific formula is proposed. The damage energy index is further simplified based on engineering applications and normalized to make damage identification more accurate and practical.

[0331] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0332] The preferred embodiments of the invention disclosed above are intended only to help illustrate the invention. These preferred embodiments do not exhaust all details, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient, characterized in that: The method comprises the following steps: Step S1: Based on the existing crack damage model, simply supported beams with different crack damage models are established using ANSYS finite element method. Influence lines are compared under different load types, load sizes, and damage degrees, and a breathing crack model is selected as the simulation crack model. Step S2: Substitute the stiffness damage function of the breathing crack model into the displacement influence line theory to obtain the analytical solution of the displacement influence line at different positions; Step S3: using ANSYS finite element method to simulate a simply supported beam under a breathing crack to obtain the displacement influence line and verify the accuracy of the analytical solution of the theoretical displacement influence line; Among them, nonlinear springs are used at the cracks to model the opening and closing breathing of the cracks; Step S4: Calculate analytical solutions for the cracking displacement influence lines of different types of bridge structure sections; Step S5: A sparse mathematical model is established by combining the influence lines of the cross-section cracked bridge and the influence lines of the normal bridge. The sparse coefficient is used as the bridge damage identification index. The damage degree is quantified with the energy damage index and the damage energy index is normalized to identify the damage degree and damage location of the bridge.

2. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 1, characterized in that: Substituting the stiffness damage function of the breathing crack model into the displacement influence line theory in step S2 and obtaining the analytical solution of the displacement influence lines at different positions using a simply supported beam as an example, the steps are as follows: S211: The finite element model is used for the simply supported beam, and the stiffness at the crack is replaced by the breathing crack damage function; S212: Find the expressions of the bending moment under the action of unit force and moving unit force, that is, The expression for the bending moment of a simply supported beam under a moving unit load is: ; Bending moment when unit force acts on the midpoint of a simply supported beam: ; S213: Graph multiplication method is used to obtain the analytical solution expression of the displacement influence line, that is, hour ； ； ； ； ； ； ； ； ； 。 3. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 1, characterized in that: The specific steps of step S3 are: S311, selecting parameters; S312, the finite element displacement influence line is compared with the analytical solution of the theoretical displacement influence line, taking the midpoint and one-quarter of the simply supported beam respectively; Take the maximum point of the displacement influence line for comparison.

4. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 1, characterized in that: The analytical solution of the cracking displacement influence line of different types of bridge structure sections is solved in the following steps: S411, solve the analytical expressions for the bending moments of different types of bridges under the action of moving unit loads and unit forces at measuring points; S412, according to the different crack areas, the damage function is substituted into the force method diagram to obtain the bridge displacement influence line; S413, taking the cracking displacement influence line of continuous beam bridge section as an example; when When: The bending moment expression of a simply supported beam under moving unit load is: ; Bending moment when unit force acts on the midpoint of a simply supported beam: ； when When: The bending moment expression of a simply supported beam under a moving unit load: The bending moment expression of a simply supported beam under a moving unit load: ； Bending moment when unit force acts on the midpoint of a simply supported beam: ； 。 5. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 1, characterized in that: A sparse mathematical model is established by combining the influence lines of cross-section cracked bridges and normal bridges. The sparse coefficient is used as a bridge damage identification indicator. The damage degree is quantified by the energy damage index and the damage energy index is normalized. This allows the damage degree and location of the bridge to be identified, including: S511, data preprocessing; Obtain the influence line data of the bridge in the undamaged state, construct a dictionary matrix A, each column of which represents the response of different load positions, and obtain the influence line y in the damaged state; S512, establishing a sparse mathematical model; Assume that the damage distribution is sparse, that is, y can be represented by a linear combination of a small number of basis vectors; The mathematical model is: ; Where: A: dictionary matrix, influence line in lossless state; : sparse coefficient vector, only a few elements are non-zero; : noise vector, used to describe the measurement error; The optimization problem can be expressed as: ; in: : Reconstruction error, ensuring Close to the observed data y; Norm regularization to find sparse solutions; : Regularization parameter, which controls the trade-off between sparsity and reconstruction error; S513, constructing a dictionary matrix A; Assume that the bridge is divided into segments, and the contribution of each segment to the influence line under load is ; Dictionary matrix , where each column represents the response feature of a segment; It can be obtained through finite element simulation or test data under healthy conditions; S514, solve the sparse coefficient ; The optimization problem uses LASSO (Least Absolute Shrinkage and Selection Operator): ； : regularization parameter.

6. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 5, characterized in that: The solution method uses the coordinate descent method, and the steps are: A1. Initialization ; A2. For each Update one by one: ; in: is a soft threshold function; Indicates that the first The matrix after the columns; Indicates that x vector is removed a vector of elements; A3. Iterate until convergence.

7. The method for diagnosing cracks in existing concrete beam bridges based on the influence line sparsity coefficient according to claim 5, characterized in that: Also includes: S515, Damage Diagnosis Methods; The x obtained by solving the optimization problem is: ； in is a sparse vector; Qualitative damage occurs: the non-zero element position of the sparse vector x corresponds to the damaged area; Locate the injury: If , then There is damage to the segment; Quantitative damage degree: The amplitude of non-zero elements reflects the damage degree, The absolute value of The damage degree of the bridge section; the bridge section cracking model is a stiffness reduction model, and the stiffness reduction of each bridge section has a linear relationship with the change of the influence line: ； in: No. The stiffness of the beam in the healthy state; : the decrease in bridge stiffness; The sparse solution An element reflects the relative proportion of stiffness change caused by damage; The actual stiffness change is calculated as: ; Known , you can convert the sparse vector Converted into actual stiffness change; S516, further quantify the extent of damage; Bridge damage can be further quantified using the damage energy index, where the unit strain energy of the beam is defined as; ； in: No. Energy loss caused by segment damage; Beam bending moment expressions; flexural stiffness; No. Segment length; Bridge damage is mainly manifested as a decrease in stiffness, resulting in changes in bending moment , which in turn causes the strain energy to change ; The strain energy after damage is: ; Simplifying assumptions: B1. The injury only causes changes, no significant changes ,Right now ; B2、 ； B3、 ； Substitute and simplify: ; in: , indicating the relative change in the degree of damage (corresponding to the sparse representation physical meaning); The final formula is: ; Further simplification and engineering application; In the project, it is assumed that each bridge is approximately a constant, then: ； in: No. Average bending moment of the segment; No. Bending stiffness of the segment; No. The length of the segment; No. Sparsity coefficient of segment damage (relative stiffness reduction); Normalization of damage energy index For ease of comparison, the damage energy can be normalized: ； in is the total number of bridge sections.

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