A method for identifying the degradation degree of vertical stiffness of bridge substructure using time-varying frequency of inspection vehicle

Abstract

The present invention discloses a method for identifying the degradation degree of vertical stiffness of bridge substructure by using time-varying frequency of detection vehicle, comprising the following steps: 1) calculating the damage parameter X based on the time-varying frequency; i ; 2) Based on the time-varying frequency, determine whether the bridge substructure is damaged to the same extent. If so, proceed to step 3), otherwise proceed to step 4); 3) Based on the relationship equation between the damage parameter and the relative stiffness ratio, calculate the damage parameter X i Corresponding relative stiffness ratio; 4) Based on the relationship equation between damage parameter, relative stiffness ratio and stiffness inequality ratio, calculate the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio. The present invention has the advantages of high detection accuracy, low implementation cost, high recognition efficiency, strong real-time performance, etc., and is suitable for bridge health monitoring and maintenance management.

Description

Technical Field

[0001] The present invention relates to the field of bridge safety detection and monitoring, and in particular to a method for identifying the degradation degree of the vertical stiffness of a bridge substructure by utilizing the time-varying frequency of a detection vehicle. Background Art

[0002] Bridges play a vital role in the road traffic network. By the end of 2022, my country had 1.0332 million highway bridges, of which over 80% were small-span bridges. However, long-term exposure of bridge structures to environmental factors (such as temperature fluctuations, humidity, and corrosion) and dynamic traffic loads (such as vehicle loads and wind loads) can easily lead to gradual degradation of the vertical stiffness of their substructures (such as piers and foundations). This degradation can seriously affect the overall structural performance and service life of the bridge, and may even cause safety accidents. Therefore, identifying and monitoring the degree of degradation of the vertical stiffness of the bridge substructure has become an important research topic in the field of bridge engineering.

[0003] Traditional bridge health monitoring methods rely primarily on regular manual inspections and static load tests. However, these methods have limitations, such as long inspection cycles, high costs, and limited accuracy. In recent years, with the advancement of sensor and wireless communication technologies, dynamic detection methods have gained increasing attention. Among these methods, identifying bridge structural parameters by leveraging the coupled vibration characteristics of a testing vehicle (such as a dedicated test vehicle) and the bridge has become an efficient and convenient means of bridge health monitoring.

[0004] Previous research has shown that the coupled vibration system of bridges and vehicles can reflect the dynamic characteristics of bridge structures. For example, by analyzing the frequency response of the bridge-vehicle system, parameters such as the bridge's natural frequency and damping ratio can be extracted, and the health of the bridge structure can be inferred. However, existing methods based on time-varying frequency analysis primarily focus on assessing the stiffness of bridge superstructures, with limited research on identifying vertical stiffness degradation in bridge substructures (such as piers and foundations). Summary of the Invention

[0005] The core concept of this invention is that when a vehicle (inspection vehicle) travels over a bridge, it couples with the bridge, causing the vehicle frequency to change with the overall stiffness of the bridge structure. This means that the vehicle frequency is time-varying. When the bridge substructure deteriorates, this deteriorates the vertical stiffness, which in turn changes the overall stiffness of the bridge structure, ultimately affecting the time-varying frequency characteristics of the inspection vehicle on the bridge. Conversely, the time-varying frequency of the inspection vehicle can be used to indirectly identify the condition of the bridge substructure.

[0006] The purpose of the present invention is to provide a method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, comprising the following steps:

[0007] 1) Place the inspection vehicle at the upper L end of the bridge and collect the time-varying frequency of the inspection vehicle at the current position Then the detection vehicle is placed at the upper R end of the bridge to collect the time-varying frequency of the detection vehicle at the current position.

[0008] 2) Calculate the damage parameter X based on the time-varying frequency i ; Subscript i = l, r;

[0009] 3) Based on time-varying frequency Time-varying frequency Determine whether the bridge substructure is damaged to the same extent. If so, proceed to step 4); otherwise, proceed to step 5.

[0010] 4) Based on the relationship equation between damage parameter and relative stiffness ratio, calculate the damage parameter X i The corresponding relative stiffness ratio;

[0011] 5) Based on the relationship equation between damage parameter, relative stiffness ratio and stiffness inequality ratio, calculate the damage parameter X i Corresponding relative stiffness ratio and stiffness inequality ratio.

[0012] Furthermore, the detection vehicle is equipped with an acceleration sensor; the acceleration sensor is used to collect the acceleration of the vehicle during driving to extract the vehicle frequency.

[0013] Furthermore, when the frequency When , the bridge substructure is damaged to the same extent;

[0014] When the frequency The substructure of the bridge was damaged to varying degrees.

[0015] Furthermore, the damage parameter X i As shown below:

[0016]

[0017] In the formula, when i=r, X i represents the damage parameter of the lower R end of the bridge; when i=l, X i represents the damage parameter of the lower L end of the bridge; Indicates the natural frequency of the test vehicle; k v 、m v Indicates the stiffness and mass of the test vehicle; when i=r, represents the measured time-varying frequency at the R end of the bridge; when i=l, Represents the measured time-varying frequency at the L end of the bridge.

[0018] Furthermore, when the bridge substructure suffers the same degree of damage, the relationship between the damage parameter and the relative stiffness ratio is as follows:

[0019]

[0020] Where μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio;

[0021] Further, calculate the damage parameter X i The corresponding relative stiffness ratio steps include:

[0022] a1) Fit formula (2) and obtain:

[0023]

[0024] a2) Calculate the damage parameter X i The corresponding relative stiffness ratio is:

[0025]

[0026] Where, is the relative stiffness ratio.

[0027] Furthermore, when the bridge substructure is damaged to varying degrees, the relationship equations between the damage parameters and the relative stiffness ratio and stiffness inequality ratio are constructed through the following steps:

[0028] b1) Construct the relationship equations between the damage parameters at the R end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, as well as the relationship equations between the damage parameters at the L end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, namely:

[0029]

[0030]

[0031] Where α is the stiffness inequality ratio; μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio; β is the natural frequency ratio of the inspection vehicle;

[0032] b2) Fit formula (5)-formula (6) to construct the relationship equation between damage parameters and relative stiffness ratio and stiffness inequality ratio, namely:

[0033]

[0034] Where p 00 is a constant; p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 is the fitting coefficient.

[0035] Furthermore, the fitting coefficient p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 Determined by the mass ratio of the measuring vehicle and obtained by looking up the coefficient table.

[0036] Further, calculate the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio methods include Newton's method.

[0037] The technical benefits of this invention are undeniable. By deploying an inspection vehicle atop the bridge and leveraging the coupled vibration characteristics of the vehicle and bridge, the invention accurately identifies the degree of vertical stiffness degradation of the bridge substructure. Compared to traditional methods, this method, which uses an inspection vehicle for bridge substructure inspection, offers advantages such as speed, high mobility, real-time performance, and low labor and economic costs. It also avoids the safety hazards associated with traditional inspections requiring engineers to work under the bridge, significantly improving the on-site inspection environment and efficiency, making it more suitable for bridge health monitoring and maintenance management. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 For measuring vehicle-elastic support beam system;

[0039] Figure 2 To measure the vehicle-bridge-pier system;

[0040] Figure 3 X under different mass ratios under equal damage conditions i varies with κ;

[0041] Figure 4 For equal damage situation X i The fitting of

[0042] Figure 5 is the parameter X calculated under different mass ratios under different damage conditions i : Figure 5 (a) Parameter X calculated under different mass ratios with different damage conditions l ; Figure 5 (b) Parameter X calculated under different damage conditions and different mass ratios r ;

[0043] Figure 6 Flowchart for identifying vertical stiffness damage of the lower junction. DETAILED DESCRIPTION

[0044] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0045] Example 1:

[0046] See also Figures 1 to 6 A method for identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency of a detection vehicle comprises the following steps:

[0047] 1) Place the detection vehicle at the L end of the upper part of the bridge (in this embodiment, the L end is set to the left end) and collect the time-varying frequency of the current position detection vehicle Then the detection vehicle is placed at the R end of the upper part of the bridge (in this embodiment, the R end is set to the right end), and the time-varying frequency of the detection vehicle at the current position is collected.

[0048] 2) Calculate the damage parameter X based on the time-varying frequency i ; Subscript i = l, r;

[0049] 3) Based on time-varying frequency Time-varying frequency Determine whether the bridge substructure is damaged to the same extent. If so, proceed to step 4); otherwise, proceed to step 5.

[0050] 4) Based on the relationship equation between damage parameter and relative stiffness ratio, calculate the damage parameter X i The corresponding relative stiffness ratio;

[0051] 5) Based on the relationship equation between damage parameter, relative stiffness ratio and stiffness inequality ratio, calculate the damage parameter X i Corresponding relative stiffness ratio and stiffness inequality ratio.

[0052] The detection vehicle is equipped with an acceleration sensor; the acceleration sensor is used to collect the acceleration of the vehicle during driving to extract the vehicle frequency.

[0053] When the frequency When , the bridge substructure is damaged to the same extent;

[0054] When the frequency The substructure of the bridge was damaged to varying degrees.

[0055] Damage parameter X i As shown below:

[0056]

[0057] In the formula, when i=r, Xi represents the damage parameter of the lower R end of the bridge; when i=l, X i represents the damage parameter of the lower L end of the bridge; Indicates the natural frequency of the test vehicle; k v 、m v Indicates the stiffness and mass of the test vehicle; when i=r, represents the measured time-varying frequency at the R end of the bridge; when i=l, Represents the measured time-varying frequency at the L end of the bridge.

[0058] When the bridge substructure is damaged to the same extent, the relationship between the damage parameter and the relative stiffness ratio is as follows:

[0059]

[0060] Where μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio;

[0061] Calculate the damage parameter X i The corresponding relative stiffness ratio steps include:

[0062] a1) Fit formula (2) and obtain:

[0063]

[0064] a2) Calculate the damage parameter X i The corresponding relative stiffness ratio is:

[0065]

[0066] Where, is the relative stiffness ratio.

[0067] When the bridge substructure is damaged to varying degrees, the relationship equations between the damage parameters and the relative stiffness ratio and stiffness inequality ratio are constructed through the following steps:

[0068] b1) Construct the relationship equations between the damage parameters at the R end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, as well as the relationship equations between the damage parameters at the L end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, namely:

[0069]

[0070]

[0071] Where α is the stiffness inequality ratio; μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio; β is the natural frequency ratio of the inspection vehicle;

[0072] b2) Fit formula (5)-formula (6) to construct the relationship equation between damage parameters and relative stiffness ratio and stiffness inequality ratio, namely:

[0073]

[0074] Where p 00 is a constant; p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 is the fitting coefficient.

[0075] Fitting coefficient p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 Determined by the mass ratio of the measuring vehicle and obtained by looking up the coefficient table.

[0076] Calculate the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio methods include Newton's method.

[0077] Example 2:

[0078] A method for identifying the degree of degradation of vertical stiffness of a bridge substructure using a time-varying frequency of a detection vehicle comprises the following steps:

[0079] 1) Place the inspection vehicle at the upper L end of the bridge and collect the time-varying frequency of the inspection vehicle at the current position Then the detection vehicle is placed at the upper R end of the bridge to collect the time-varying frequency of the detection vehicle at the current position.

[0080] 2) Calculate the damage parameter X based on the time-varying frequency i ; Subscript i = l, r;

[0081] 3) Based on time-varying frequency Time-varying frequency Determine whether the bridge substructure is damaged to the same extent. If so, proceed to step 4); otherwise, proceed to step 5.

[0082] 4) Based on the relationship equation between damage parameter and relative stiffness ratio, calculate the damage parameter X i The corresponding relative stiffness ratio;

[0083] 5) Based on the relationship equation between damage parameter, relative stiffness ratio and stiffness inequality ratio, calculate the damage parameter X i Corresponding relative stiffness ratio and stiffness inequality ratio.

[0084] Example 3:

[0085] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure by using the time-varying frequency of an inspection vehicle. The technical content is the same as that of Example 2. Furthermore, the inspection vehicle is equipped with an acceleration sensor; the acceleration sensor is used to collect the acceleration of the vehicle during driving to extract the vehicle frequency.

[0086] Example 4:

[0087] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, the technical content of which is the same as any one of embodiments 2-3, further, when the time-varying frequency When , the bridge substructure is damaged to the same extent;

[0088] When the frequency The substructure of the bridge was damaged to varying degrees.

[0089] Example 5:

[0090] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, the technical content of which is the same as any one of Examples 2-4, furthermore, the damage parameter X i As shown below:

[0091]

[0092] In the formula, when i=r, X i represents the damage parameter of the lower R end of the bridge; when i=l, X i represents the damage parameter of the lower L end of the bridge; Indicates the natural frequency of the test vehicle; k v 、m v Indicates the stiffness and mass of the test vehicle; when i=r, represents the measured time-varying frequency at the R end of the bridge; when i=l, Represents the measured time-varying frequency at the L end of the bridge.

[0093] Example 6:

[0094] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency of an inspection vehicle, the technical content of which is the same as any one of Examples 2-5. Furthermore, when the bridge substructure is damaged to the same degree, the relationship equation between the damage parameter and the relative stiffness ratio is as follows:

[0095]

[0096] Where μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio;

[0097] Example 7:

[0098] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, the technical content of which is the same as any one of Examples 2-6, and furthermore, calculating the damage parameter X i The corresponding relative stiffness ratio steps include:

[0099] a1) Fit formula (2) and obtain:

[0100]

[0101] a2) Calculate the damage parameter X i The corresponding relative stiffness ratio is:

[0102]

[0103] Where, is the relative stiffness ratio.

[0104] Example 8:

[0105] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency of an inspection vehicle, the technical content of which is the same as any one of Examples 2-7. Furthermore, when the bridge substructure is damaged to varying degrees, the relationship equations between the damage parameter and the relative stiffness ratio and the stiffness inequality ratio are constructed by the following steps:

[0106] b1) Construct the relationship equations between the damage parameters at the R end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, as well as the relationship equations between the damage parameters at the L end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, namely:

[0107]

[0108]

[0109] Where α is the stiffness inequality ratio; μ is the mass ratio of the inspection vehicle to the bridge; κ represents the relative stiffness ratio; β is the natural frequency ratio of the inspection vehicle;

[0110] b2) Fit formula (5)-formula (6) to construct the relationship equation between damage parameters and relative stiffness ratio and stiffness inequality ratio, namely:

[0111]

[0112] Where p 00 is a constant; p 10 、p 01 、p20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 is the fitting coefficient.

[0113] Example 9:

[0114] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, the technical content of which is the same as any one of Examples 2-8, and further, the fitting coefficient p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 Determined by the mass ratio of the measuring vehicle and obtained by looking up the coefficient table.

[0115] Example 10:

[0116] A method for identifying the degree of degradation of the vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, the technical content of which is the same as any one of Examples 2-9, and furthermore, calculating the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio methods include Newton's method.

[0117] Example 11:

[0118] A method for identifying the degree of degradation in the vertical stiffness of a bridge substructure using the time-varying frequency of a detection vehicle. The core concept of this method is that when a vehicle travels on a bridge, the vehicle and bridge couple to form a dynamic system, and the vehicle-bridge frequency varies with the vehicle's position on the bridge. When the vertical support stiffness of the bridge substructure decreases due to damage, the vehicle's time-varying frequency also changes. The vehicle frequency contains information about the bridge substructure's support stiffness, making it possible to identify bridge substructure damage using the vehicle frequency.

[0119] The specific steps are as follows:

[0120] Installing accelerometers and other sensing elements on the measuring vehicle to collect the acceleration of the vehicle during driving and extract the vehicle frequency;

[0121] Place the vehicles on the left and right ends of the bridge and collect the time-varying frequency of the vehicles at these locations. and The time-varying frequency is used to determine whether the bridge substructure is damaged to the same degree. When , it can be judged that the substructures at both ends of the bridge are damaged to the same extent, otherwise the damage extents at both ends are different;

[0122] Calculate the damage parameter X based on the vehicle's time-varying frequency i , and select different damage index back-calculation methods according to whether the damage is the same;

[0123] If the damage is the same, then X i Substituting the equation provided by this method into the equation and solving it directly, we can obtain the relative stiffness ratio κ of the substructure;

[0124] Otherwise, a set of cubic equations concerning the relative stiffness ratio κ and the stiffness inequality ratio α is constructed by interpolation from the coefficient table of cubic equations provided in this paper based on the mass ratio μ of the vehicle to the bridge. The relative stiffness ratio κ and the stiffness inequality ratio α of the bridge substructure are obtained by solving this set of equations using Newton's method to identify damage.

[0125] Example 12:

[0126] The verification of the method for identifying the degree of degradation of the vertical stiffness of the bridge substructure using the time-varying frequency of the inspection vehicle described in any one of Examples 1-11 is as follows:

[0127] 1. Theoretical verification (simulating the substructures at both ends of the bridge as vertical supports and replacing the moving vehicles with sprung masses):

[0128] The bridge is simplified into an Euler-Bernoulli beam, EI represents the vertical flexural stiffness of the bridge, and the bridge line density is The length is L, the bridge damping ratio is ξ, and the vehicle stiffness is k v , the damping is c v , mass is m v , moves on the bridge at a speed of v; the left substructure support stiffness is K l , the right lower structure support stiffness is K r ;u v represents the vehicle displacement, u b is the vertical displacement of the bridge. The natural frequency of the vehicle is:

[0129]

[0130] It should be noted that when the lower structure support stiffness K l =K r =∞, the bridge is a simply supported beam. This method must meet the following prerequisites when used:

[0131] This method is only used to detect the degradation of vertical support stiffness caused by various bridge damages and does not involve the determination of the cause of the damage;

[0132] The initial state of the bridge is simply supported, that is, the vertical stiffness of the substructure is assumed to be infinite before damage;

[0133] The design parameters of the bridge are known. Before the substructure is damaged, the first-order natural frequency of the bridge can be calculated using the following formula:

[0134]

[0135] Defining the relative stiffness ratio Unequal ratio of stiffness If the left side stiffness ratio is taken as the reference value, the relative stiffness ratio of the left side support is κ=κ l , and ακ is on the right. The equations of motion for the bridge and the vehicle are

[0136]

[0137]

[0138] where q v is the vehicle displacement, u b (x, t) is the vertical deformation displacement of the bridge. The superscript “·” indicates the partial derivative with respect to time t, and ' indicates the partial derivative with respect to displacement. Figure 1 The elastic support beam model shown can be approximated by the elastic deformation of the simply supported beam and the displacement of the steel beam. The mode shape expression is as follows

[0139]

[0140] The displacement of the bridge can be expressed using the modal superposition method as:

[0141] u b (x,t)=q(t)φ(x) (6)

[0142] Substituting equations (5) and (6) into equation (3), multiplying both sides by the vibration mode φ(x) and integrating from 0 to L can transform it into:

[0143]

[0144] Where χ is the integral of the square of the mode shape:

[0145]

[0146] ω esb The natural frequency of the elastically supported beam can be expressed as Multiplying by an elastic support beam frequency amplification factor yields:

[0147] ω esb =ω ssb ε (9)

[0148] The frequency amplification factor is:

[0149]

[0150] When the tire mass is neglected and the tire is assumed to be tightly fitted, the external force P(x c ,t) is

[0151]

[0152] Substituting equations (5) and (11) into (7), and combining equations (5) and (4), we can obtain the coupling equations of the VBI system:

[0153]

[0154]

[0155] In order to achieve uniformity in form, the parameters are defined In the above formula, μ is the mass ratio of the vehicle to the bridge, which can be expressed as:

[0156]

[0157] Arrange equations (12) and (13) into matrix form

[0158]

[0159] Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, and {F} is the external load matrix, which are expressed as follows:

[0160]

[0161]

[0162]

[0163]

[0164] From equations (16) to (19), we can see that the mass matrix, stiffness matrix, and damping matrix all change with the vehicle position x. c changes, so Equation (15) is a time-varying system.

[0165] To derive a closed-form solution, the system damping is temporarily ignored, and the influence of damping will be studied through numerical examples. It can be obtained by solving the following characteristic equation:

[0166]

[0167] For the sake of convenience, the superscript “~” here represents the time-varying frequency. Substituting the vibration mode expression of formula (5) into the above formula, we can get:

[0168]

[0169] Note that “±” in formula (21) indicates the following situations: ① ② and③ In this method, only Therefore, the time-varying frequency of the bridge is:

[0170]

[0171] Substitute equation (9) into equation (22), and let x c If it is equal to 0 or L, the values ​​of the vehicle time-varying frequency on the left and right sides of the vehicle can be obtained respectively as follows:

[0172]

[0173]

[0174] According to the above equations (23) and (24), the damage calculation parameters are established as follows:

[0175]

[0176] The subscript "i" indicates the left or right end of the bridge. is the on-site measurement value, ω v is the natural frequency of the measuring vehicle. When the measuring vehicle is located at the left and right ends of the bridge, the measuring vehicle and the lower support form a series spring, see Figure 2 Physically, a change in the stiffness of any part of the series spring causes a change in the overall stiffness, which in turn causes a change in the frequency of the measuring vehicle. This is the principle of using a measuring vehicle to identify substructure damage.

[0177] According to the different damage conditions of the lower structures on the left and right sides, this method is divided into two categories: the left and right supports are damaged to the same extent; the left and right supports are damaged to different degrees.

[0178] Case 1: Identification of equal damage to the left and right lower structures

[0179] At this time, α = 1. Substituting the expression of γ into equations (23) and (24), the vehicle frequency is equal on the left and right sides of the bridge:

[0180]

[0181] Substituting equation (26) into equation (25), we can get

[0182]

[0183] Where β is the bridge-vehicle natural frequency ratio:

[0184]

[0185] To enhance the recognition effect, the bridge-vehicle natural frequency ratio of the measuring vehicle is set to β = 1, and Equation (27) can be simplified as:

[0186]

[0187] Formula (29) shows that X is the equation of mass ratio μ and stiffness ratio κ. Where μ is the known data of the measured vehicle and κ is the parameter to be identified. Next, by assigning values ​​to μ, we explore the sensitivity of formula (29) to μ in the range of μ∈[0,0.12]. Figure 3 .

[0188] Figure 3 It shows that under the same damage X i The sensitivity to μ is not high, so an intermediate curve can be used as a general curve, see Figure 3 In view of the complex form of Equation (29), this method will fit the curve through a quadratic function to obtain a simple expression, see Figure 4 The fitting curve expression is:

[0189]

[0190] By inversely solving equation (30), we can obtain κ:

[0191]

[0192] In this description, the superscript “^” indicates the measured value, and the value without this symbol indicates the actual value.

[0193] From the above derivation, it can be concluded that: This method proposes equations (25) and (31), which can be used as the core formulas for calculating the substructure on both sides of the bridge under the condition of equal damage. By measuring the frequency of the vehicle at both ends of the bridge, the relative stiffness ratio of the substructure can be calculated, and the damage can be identified.

[0194] Case 2: Identification of unequal damage to the left and right lower structures

[0195] When the left and right lower structures are damaged unequally, α≠1, then substituting γ into equations (23) and (24) yields the vehicle frequencies at the left and right ends of the bridge:

[0196]

[0197]

[0198] When β = 1, Equations (32) and (33) are functions of the stiffness ratio κ, the stiffness inequality ratio α, and the mass ratio μ, where μ is a known parameter of the measuring vehicle. i Sensitivity to mass ratio, see Figure 5 .

[0199] Figure 5 It shows that equations (32) and (33) are sensitive to changes in mass ratio. Therefore, when identifying unequal damage, this method needs to determine equations (32) and (33) according to the mass ratio of the test vehicle. Since the forms of equations (32) and (33) are too complex, they are not conducive to engineering applications. This method transforms them into a set of two-variable cubic equations through fitting:

[0200]

[0201] This method provides the following coefficient table after precalculation. In actual measurement, simply interpolate the values ​​in the table based on the mass ratio of the measurement vehicle to determine and construct the system of cubic equations.

[0202] Table 1 Formula (34)X l 2 Coefficient table

[0203]

[0204]

[0205] Table 2 Formula (34)X r 2 Coefficient table

[0206]

[0207] Newton's iteration method can be used to solve the system of cubic equations with two variables.

[0208] 2 / Method Validation

[0209] Case 1: Identification and verification of equal damage to the left and right lower structures

[0210] The following test verifies the identification performance of this method under conditions of equal damage. Three different sets of bridge and vehicle parameters are used to demonstrate that this method is not limited by the bridge and vehicle parameters. The actual damage data is set to: κ = 0.08, α = 1. The case parameter settings and calculation results are shown in the following table:

[0211] Table 3 Identification and verification cases of equal damage to the left and right lower structures

[0212]

[0213]

[0214] The identification results in Table 3 demonstrate that the proposed formula (31), as a general formula for substructure damage, has high accuracy and low error in identifying the stiffness ratio κ. In actual measurements, only the bridge and vehicle frequency ratio is required to be equal to 1, while other bridge and vehicle parameters are not required. This method has high universality.

[0215] Case 2: Identification and verification of unequal damage to the left and right lower structures

[0216] As mentioned earlier, a set of cubic equations for α and κ can be determined based on the mass ratio of the measured vehicles. Taking μ = 0.04 as an example, this method is verified using three different bridge and vehicle pairs, with a bridge-to-vehicle frequency ratio of 1 and a mass ratio μ = 0.04. The following equations can be determined from Tables 1 and 2:

[0217]

[0218] Table 4 Identification and verification cases of unequal damage to the left and right lower structures

[0219]

[0220] This method was validated using three different case studies of bridges and vehicles (see Table 4). The identification results in Table 4 demonstrate that the equations provided by this method have high accuracy, accurately identifying the substructure stiffness ratio and stiffness inequality ratio under conditions of unequal damage to the left and right substructures. This method is simple and unrestricted by bridge and vehicle parameters, making it highly practical.

Claims

1. A method for identifying the degree of degradation of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle, characterized in that: The following steps are involved: 1) Place the inspection vehicle at the upper L end of the bridge and collect the time-varying frequency of the inspection vehicle at the current position Then the detection vehicle is placed at the upper R end of the bridge to collect the time-varying frequency of the detection vehicle at the current position. L end is the left end; R end is the right end; 2) Calculate the damage parameter X based on the time-varying frequency i ; Subscript i=l,r; When i=r, X i represents the damage parameter of the lower R end of the bridge; when i=l, X i represents the damage parameter of the lower L end of the bridge; 3) Based on time-varying frequency Time-varying frequency Determine whether the bridge substructure is damaged to the same extent. If so, proceed to step 4); otherwise, proceed to step 5. 4) Based on the relationship equation between damage parameter and relative stiffness ratio, calculate the damage parameter X i The corresponding relative stiffness ratio; 5) Based on the relationship equation between damage parameter, relative stiffness ratio and stiffness inequality ratio, calculate the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio; When the bridge substructure is damaged to varying degrees, the relationship equations between the damage parameters and the relative stiffness ratio and stiffness inequality ratio are constructed through the following steps: s1) Construct the relationship equations between the damage parameters at the R end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, as well as the relationship equations between the damage parameters at the L end of the lower part of the bridge and the relative stiffness ratio and stiffness inequality ratio, namely: Where μ is the mass ratio of the inspection vehicle to the bridge; β is the natural frequency ratio of the bridge to the vehicle; and the relative stiffness ratio Stiffness inequality K i is the support stiffness; K l K is the support stiffness of the lower structure at the L end, r is the support stiffness of the lower structure at the R end; EI represents the vertical flexural stiffness of the bridge; i = r, l; κ r is the relative stiffness ratio corresponding to the L end; κ l Indicates the relative stiffness ratio corresponding to the R end; L 桥 is the length of the bridge; s2) Fit formula (5)-formula (6) to construct the relationship equation between damage parameters and relative stiffness ratio and stiffness inequality ratio, namely: Where p 00 is a constant; p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 is the fitting coefficient.

2. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: The detection vehicle is equipped with an acceleration sensor; the acceleration sensor is used to collect the acceleration of the vehicle during driving to extract the vehicle frequency.

3. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: When the frequency When , the bridge substructure suffers the same degree of damage; When the frequency The substructure of the bridge was damaged to varying degrees.

4. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: Damage parameter X i As shown below: In the formula, when i=r, X i represents the damage parameter of the lower R end of the bridge; when i=l, X i represents the damage parameter of the lower L end of the bridge; Indicates the natural frequency of the test vehicle; k v 、m v Indicates the stiffness and mass of the test vehicle; when i=r, represents the measured time-varying frequency at the R end of the bridge; when i=l, Represents the measured time-varying frequency at the L end of the bridge.

5. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: When the bridge substructure is damaged to the same extent, the relationship between the damage parameter and the relative stiffness ratio is as follows: Where μ is the mass ratio of the inspection vehicle to the bridge; κ i Represents the relative stiffness ratio.

6. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 5, characterized in that: Calculate the damage parameter X i The corresponding relative stiffness ratio steps include: 1) Fit formula (2) and obtain: 2) Calculate the damage parameter X i The corresponding relative stiffness ratio is: Where, κ i is the relative stiffness ratio.

7. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: Fitting coefficient p 10 、p 01 、p 20 、p 11 、p 02 、p 30 、p 21 、P 12 、P 03 Determined by the mass ratio of the inspection vehicle to the bridge.

8. The method of identifying the degradation degree of vertical stiffness of a bridge substructure using a time-varying frequency detection vehicle according to claim 1 is characterized in that: Calculate the damage parameter X i The corresponding relative stiffness ratio and stiffness inequality ratio methods include Newton's method.

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