Bridge damage location method of high-resolution modal flexibility construction influence line

Abstract

The application discloses a bridge damage positioning method of high-resolution modal flexibility influence line, which comprises the following steps: collecting displacement response of a bridge under a moving load by using at least two sensors to form a displacement matrix U; performing FFT transformation on the displacement response to determine inherent frequency ω of the bridge; performing analysis on the displacement matrix U to obtain a principal component matrix G; filtering high-order dynamic components in each order principal component according to physical meaning of the principal component matrix to obtain each order high-resolution modal vibration mode; constructing a modal flexibility matrix C by using the inherent frequency ω and the modal vibration mode; discretizing a moving process of a unit load into a unit load matrix F; and constructing deflection influence lines at multiple degrees of freedom by using the modal flexibility matrix C and the unit load matrix F; and constructing deflection influence lines of the bridge in a damage-free state and a damaged state to obtain a damage index and identify a position. The method constructs the influence line by using modal parameters of the bridge, and accurately positions the damage by using a small number of sensors and simple calculation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge damage positioning and identification, and particularly relates to a bridge damage positioning method, system, computer device and storage medium of high-resolution modal flexibility constructed influence line. BACKGROUND

[0002] Structural damage detection of a bridge is of great significance and is conducive to timely exclusion of safety hazards. Traditional damage detection methods are mostly limited by the number of sensors and are not suitable for engineering practice.

[0003] Damage detection methods based on deflection influence lines have attracted widespread attention due to their sensitivity to damage and accuracy in damage positioning. Traditional identification methods of deflection influence lines are based on the static characteristics of the structure, and deflection influence lines are separated by decomposing and filtering the original signal, but these methods can only identify the deflection influence line at the position of the sensor. In addition, the damage identification effect of the deflection influence line at a single point is easily affected by noise, damage position and sensor distance, so the traditional method still needs a large number of sensors to accurately locate the damage position when used for damage detection of long-span bridges.

[0004] Therefore, a new method is needed that can combine the advantages of deflection influence lines, accurately and sensitively locate damage, and only need a small number of sensors. SUMMARY

[0005] The present application aims to overcome the shortcomings and deficiencies of the prior art, and provides a bridge damage positioning method, system, computer device and storage medium of high-resolution modal flexibility constructed influence line, which utilizes a small number of sensors, identifies the deflection influence lines of multiple points through dynamic analysis of the structure, and combines the deflection influence lines of multiple points to accurately locate the damage of the bridge using a small number of sensors.

[0006] The first aspect of the present application discloses a bridge damage positioning method of high-resolution modal flexibility constructed influence line, which comprises the following steps:

[0007] S1, evenly installing z sensors on the bridge to be measured, collecting displacement responses through the z sensors when a moving load passes through the bridge to be measured, and constructing a displacement matrix U in the form of a column vector with the displacement response data, and performing fast Fourier transform on the collected displacement responses to obtain the natural frequency ω of the bridge structure to be measured;

[0008] S2, calculating the covariance matrix S of the displacement matrix U:

[0009]

[0010] where m is the number of sampling points of the displacement response data.

[0011] The principal component matrix G of the displacement matrix U is as follows:

[0012] G = UR = g (1) ...g (z)

[0013] where R is an eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, g (1) 、…、g (z) represent the 1st, …, zth column vectors of the principal component matrix G, also known as the 1st, …, zth principal components of the principal component matrix G;

[0014] S3, filtering out the high-order dynamic components of the principal components in the principal component matrix G to obtain high-resolution modal shapes The column vectors of the principal component matrix, i.e., the principal components, are composed of modal shapes and high-order dynamic component information, where the high-order dynamic component information corresponds to a frequency that is much larger than the frequency corresponding to the modal shape, so a low-pass filter is selected for filtering processing;

[0015] S4, using the natural frequency ω and the high-resolution modal shape to construct a high-resolution modal flexibility matrix C, and the calculation formula is as follows:

[0016]

[0017] where i is the modal order, r is the highest order of the selected high-resolution modal, r = 1, 2, …, z, ω i is the i-th natural frequency of the bridge structure to be measured, is the i-th high-resolution modal shape, () T denotes the transpose operation;

[0018] S5, the deflection influence line refers to the deflection response change at a specific location under the action of a unit moving load, so another unit moving load is assumed to move on the bridge to be measured, the action process of the unit moving load is discretized into multiple unit load vectors, and only the vertical vibration of the bridge to be measured is considered, so the bridge to be measured is evenly divided into k vertical degrees of freedom, where k = m, and it is assumed that the unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, and this discretization process is represented as:

[0019]

[0020] where, f (1) ,...,f (q) are the discretized unit load vectors, DOF qq represents vertical degrees of freedom of the bridge structure to be measured, and a zero column vector corresponds to a vertical degree of freedom DOF q+1 ,..., DOF k represent other vertical degrees of freedom not subjected to a unit moving load, q = 1, 2,..., k, respectively T represents a transposition operation;

[0021] The unit load vector after discretization is constructed into a unit load matrix F, and the deflection response matrix under the action of a unit moving load is calculated, and is represented as:

[0022]

[0023] D = CF = d 1 ),..., d q )

[0024] Wherein D and F represent the deflection response matrix and the unit load matrix respectively, d 1 ),..., d q represent the first,..., q column vectors of the deflection response matrix D, and also represent the deflection response vectors at the vertical degrees of freedom 1,..., q respectively.

[0025] If only vertical vibration in a two-dimensional plane is considered, the deflection response vector obtained by multiplying the flexibility matrix by the load vector represents the deflection response of each vertical degree of freedom of the bridge to be measured under the action of the load vector. Therefore, the above formula represents that the unit load vectors f (1) to f (q) are sequentially applied to the bridge to be measured, and the corresponding deflection response vectors are obtained. The deflection influence line refers to the change in deflection response at a specific position under the action of a unit moving load, and therefore the xth row of the deflection response matrix D is the deflection influence line DIL n at the vertical degree of freedom n of the bridge structure to be measured, where x = n, and is represented as

[0026]

[0027] Wherein DIL (n) represents the deflection influence line at the vertical degree of freedom n of the bridge structure to be measured, n = 1, 2,..., k, represent the xth element of the first,..., q column vectors d (1 ),..., d (q of the deflection response matrix D, x = n;

[0028] S6, construct a damage index, repeat the above steps S1 to S5 to obtain the deflection influence line DIL u of the undamaged state and the deflection influence line DIL d, the deflection influence line of the intact state and the deflection influence line of the damaged state of the k vertical degrees of freedom of the bridge structure to be measured are subtracted respectively, and the average value of the deflection influence line difference value of the k vertical degrees of freedom is calculated, and the calculation formula is as follows:

[0029]

[0030] Wherein DILCA is the average value of the deflection influence line difference value, DIL d (n) and DIL u (n) respectively represent the deflection influence line of the vertical degree of freedom n of the bridge to be measured in the damaged state and the intact state;

[0031] S7, using the average value DILCA to identify and locate the damage of the bridge structure to be measured.

[0032] Further, the bridge to be measured is a simply supported beam bridge.

[0033] Further, the sensor is a displacement sensor.

[0034] Further, in step S3, the high-order dynamic component information of each order principal component in the principal component matrix G is filtered out by using a moving average filter to obtain each order high-resolution modal shape For the hth order high-resolution modal shape of the bridge to be measured The calculation formula is as follows:

[0035]

[0036] Wherein W is the moving window length selected by the moving average filter, q s Indicates the sampling frequency of the sensor, Indicates the a-th element of the hth order high-resolution modal shape of the bridge structure to be measured , Indicates the b-th element of the hth order principal component g (h) , h Indicates the hth order natural frequency of the bridge to be measured, h=1, 2, …, z, a=1, 2, …, m, b=1, 2, …, m+W / 2, m is the number of sampling points of displacement response data. The moving average filter is a low-pass filter, and the cutoff frequency can be selected, so the present application selects it to filter out the high-order dynamic component information of the principal component matrix to obtain the modal shape.

[0037] Further, in the step S7, when the curve of the average value DILCA appears a peak value when the structure has damage, it is judged that the bridge structure to be measured has damage, and the position indicated by the peak value is the damage position of the bridge structure to be measured. When the structure has damage, the peak value of the deflection influence line will be offset compared with the deflection influence line of the structure in the damage-free state, and the direction of the offset is consistent with the direction of the damage position, and the difference will appear when the two are subtracted, and the difference between the two reaches the maximum value at the damage position. DILCA utilizes the deflection influence line difference at multiple vertical degrees of freedom, which has a better and more accurate damage identification effect than the influence line difference at a single vertical degree of freedom.

[0038] Further, principal component analysis is matrix operation, and the value range of z is [2, +∞), that is, the number of sensors is at least 2, so that the present application can realize accurate damage identification of the whole bridge by using only two sensors. When the number of rows or columns of the displacement matrix U is less than 2, U is no longer a matrix but a vector, on the other hand, when the number of rows or columns is less than 2, U contains too little information to identify high-resolution modal shapes. Therefore, the matrix operation needs to ensure that the number of rows and columns of the displacement matrix U is greater than or equal to 2, so as to ensure that it has enough dimensions for operation.

[0039] The second aspect of the present application discloses a bridge damage positioning system for high-resolution modal flexibility influence line, which is used for executing the bridge damage positioning method of high-resolution modal flexibility influence line described above, and the bridge damage positioning system comprises:

[0040] A displacement response acquisition module, z sensors are uniformly installed on the bridge to be measured, and when the moving load passes through the bridge to be measured, the displacement responses are collected by the z sensors, and the displacement response data are constructed into a displacement matrix U in the form of a column vector, and the collected displacement responses are subjected to fast Fourier transform to obtain the natural frequency ω of the bridge structure to be measured;

[0041] A matrix calculation module, which calculates the covariance matrix S of the displacement matrix U:

[0042]

[0043] Wherein m is the number of sampling points of the displacement response data;

[0044] The principal component matrix G of the displacement matrix U is calculated as follows:

[0045] G=UR=g (1) ...g (z)

[0046] Wherein R is an eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, and g (1) 、…、g (z)respectively represent the 1st, …, z column vectors of the principal component matrix G, also known as the 1st, …, z order principal components of the principal component matrix G;

[0047] A modal shape model obtaining module filters out high order dynamic components of the order principal components in the principal component matrix G to obtain high resolution modal shapes of the orders

[0048] A modal flexibility matrix constructing module utilizes the natural frequency ω and the high resolution modal shapes to construct a high resolution modal flexibility matrix C, and the calculation formula is as follows:

[0049]

[0050] where i is the modal order, r is the highest order of the selected high resolution modal, r = 1, 2, …, z, ω i is the i-th order natural frequency of the bridge structure to be measured, is the i-th order high resolution modal shape, T represents a transposition operation;

[0051] A deflection influence line calculating module divides the bridge to be measured into k vertical degrees of freedom on average, where k = m, and multiplies the high resolution modal flexibility matrix C by a unit load matrix F of k rows and q columns to obtain a deflection response matrix D of the bridge to be measured when another unit moving load moves from the vertical degree of freedom 1 to the vertical degree of freedom q, q = 1, 2, …, k, and the deflection response matrix D is expressed as:

[0052]

[0053] where D and F respectively represent the deflection response matrix and the unit load matrix, d (1) , …, d (q) respectively represent the 1st, …, q column vectors of the deflection response matrix D, and also represent the deflection response vectors at the vertical degrees of freedom 1, …, q, respectively, T represents a transposition operation;

[0054] The x-th row of the deflection response matrix D is the deflection influence line DIL (n) at the vertical degree of freedom n of the bridge structure to be measured, where x = n, and the deflection influence line DIL

[0055]

[0056] where DIL (n) represents the deflection influence line at the vertical degree of freedom n of the bridge structure to be measured, n = 1, 2, …, k, respectively represent the 1st, …, q column vectors d (1) , …, d (q)the xth element of the vector, x = n;

[0057] The damage index construction module repeatedly calls the above displacement response acquisition module, matrix calculation module, modal shape model acquisition module, modal flexibility matrix construction module, deflection influence line calculation module to obtain the deflection influence line DIL u and the deflection influence line DIL d of the damaged state of the bridge structure to be measured, respectively, and calculates the average value of the deflection influence line difference value of the k vertical degrees of freedom, and the calculation formula is as follows:

[0058]

[0059] Where DILCA is the average value of the deflection influence line difference value, DIL d (n) and DIL u (n) represent the deflection influence line of the vertical degree of freedom n of the damaged state and the undamaged state of the bridge to be measured, respectively.

[0060] The damage identification and positioning module uses the average value DILCA to identify and position the damage of the bridge structure to be measured.

[0061] The third aspect of the present application discloses a computer device, comprising a processor and a memory for storing a processor executable program, when the processor executes the program stored in the memory, the high-resolution modal flexibility construction influence line bridge damage positioning method is realized.

[0062] The fourth aspect of the present application discloses a storage medium, which stores a program, and when the program is executed by a processor, the high-resolution modal flexibility construction influence line bridge damage positioning method is realized.

[0063] The present application has the following advantages and effects relative to the prior art:

[0064] (1) The method proposed in the present application identifies the deflection influence line of the high-resolution modal flexibility obtained by a small number of sensors, and the number of deflection influence lines obtained is determined by the number of sampling points of displacement data, and the influence lines of multiple points other than the sensor position can be obtained at the same time, and the damage identification can be performed in combination with the deflection influence lines at multiple points, which can effectively improve the damage identification accuracy and noise robustness.

[0065] (2) The method proposed in the present application only needs to simply analyze and calculate the displacement response data of the bridge to be measured under the action of the moving load, so as to accurately identify the damage position, and improve the damage identification efficiency.

[0066] (3) The method provided by the application can accurately locate damage of a large-span bridge by using two or more sensors, can effectively reduce cost, and is more suitable for engineering practice. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a flow chart of the method for simultaneously obtaining deflection influence lines at multiple points by using a small number of sensors to locate structure damage in Example 1;

[0068] Figure 2 is a simply supported beam model diagram in the numerical simulation in Example 1;

[0069] Figure 3 is a schematic diagram of the displacement original signal measured in the numerical simulation in Example 1;

[0070] Figure 4 is a frequency spectrum diagram of the displacement signal measured in the numerical simulation in Example 1;

[0071] Figure 5 is a schematic diagram of the deflection influence lines of all single-damage working conditions identified by using the displacement signal of two sensors in the numerical simulation in Example 1;

[0072] Figure 6 is a diagram of the identification results of all single-damage working conditions by using two sensors in the numerical simulation in Example 1;

[0073] Figure 7 is a diagram of the identification results of all double-damage working conditions by using two sensors in the numerical simulation in Example 1;

[0074] Figure 8 is a steel box girder structure diagram in Example 2;

[0075] Figure 9 is a frequency spectrum diagram of the displacement signal measured in the experiment in Example 2;

[0076] Figure 10 is a schematic diagram of the deflection influence lines of all single-damage working conditions and all single-damage working conditions identified by using the displacement signal of two sensors in the experiment in Example 2;

[0077] Figure 11 is a diagram of the identification results of all single-damage working conditions by using two sensors in Example 2;

[0078] Figure 12 is a diagram of the identification results of all double-damage working conditions by using two sensors in Example 2;

[0079] Figure 13 is a structural block diagram of a discipline knowledge graph complex query system based on graph coding in Example 3;

[0080] Figure 14 is a structural block diagram of the computer device in embodiment four. DETAILED DESCRIPTION

[0081] In order to make the objects, technical solutions and advantages of the present application clearer and more apparent, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0082] Embodiment one

[0083] As shown in Figure 1 , it is a flow step diagram of a bridge damage positioning method of a high-resolution modal flexibility construction influence line. The simply supported beam model simulation schematic used in embodiment one is shown in Figure 1 . The length of the simply supported beam model is 20 m, the cross-sectional height is 0.2 m, the width is 0.1 m, and the mass of the moving mass block is 500 kg. The specific implementation process is as follows: Figure 2

[0084] T1, after the simply supported beam model is meshed, the grid is deleted along the beam height direction to simulate the damage, the damage degree is described by the ratio of the crack depth formed by the deleted grid to the cross-sectional height of the simply supported beam model, and the damage position is represented by the relative position. Single damage and double damage are set, and there are 7 damage conditions, as shown in Table 1.

[0085] Table 1. Numerical simulation damage condition table

[0086]

[0087]

[0088] T2, collect the displacement response of the simply supported beam model under the undamaged condition, use the moving mass block as the moving load, pass through the simply supported beam model at a speed of 0.5 m / s, use the 7 sensors evenly placed on the simply supported beam model to collect the displacement response during the whole process, as shown in Figure 3 , the displacement data contains 4000 sampling points. And do the fast Fourier transform of the displacement response, get the natural frequency ω of the simply supported beam model, the first order natural frequency of the simply supported beam model is 1.123 Hz, the second order natural frequency is 4.468 Hz, as shown in Figure 4 .

[0089] T3, the above displacement response data is combined into a displacement matrix U in the form of a column vector, the covariance matrix S of the displacement matrix U is calculated, the formula is as follows:​

[0090]

[0091] The principal component matrix G is calculated as follows:

[0092] G = UR = g (1) ...g (7)

[0093] Where R is the eigenvector matrix obtained by decomposing the covariance matrix S, and g (1) ...g (7) These represent the 1st, ..., 7th columns of the principal component matrix G, also known as the 1st, ..., 7th order principal components.

[0094] T4. Using the natural frequency ω as the cutoff frequency, a moving average filter is used to remove the higher-order dynamic components of each principal component in the principal component matrix G, thus obtaining the high-resolution mode shapes of each order of the simply supported beam model. For the h-th high-resolution mode shape of the simply supported beam model The calculation formula is as follows:

[0095]

[0096] Where W is the length of the moving window selected for the moving average filter, q s Indicates the sensor's sampling frequency. This represents the h-th high-resolution mode shape of a simply supported beam model. The a-th element, G represents the h-th principal component. (h) The b-th element, ω h Let h represent the h-th natural frequency of the simply supported beam model, h = 1, 2, ..., 7, a = 1, 2, ..., 4000, b = 1, 2, ..., 4000 + W / 2.

[0097] T5. Considering that higher-order modes are often difficult to excite in actual engineering, the first two-order modes are used to identify the deflection influence line of the simply supported beam model under non-destructive working conditions.

[0098] The natural frequency ω and the high-resolution mode shape The high-resolution modal compliance matrix C is constructed as follows:

[0099]

[0100] Where ω i Let i be the i-th natural frequency of the simply supported beam model. This represents the i-th high-resolution mode shape of a simply supported beam model;

[0101] Since the moving mass is moved from one end to the other end of the simply supported beam model, the unit load matrix F after discretization of the process is a unit diagonal matrix, and the deflection influence line of the simply supported beam model is calculated by using the high-resolution modal flexibility matrix C, and the calculation formula is as follows:

[0102]

[0103] D = CF = d( 1 )...d( 4000 )

[0104]

[0105] Where D and F represent the deflection response matrix and the unit load matrix respectively, DIL (n) represents the deflection influence line of the vertical degree of freedom n of the simply supported beam model, n = 1, 2, …, 4000, d( 1 ), …, d( 4000 ) represent the 1st, …, 4000th column vectors of the deflection response matrix D respectively, and also represent the deflection response vectors at the vertical degrees of freedom 1, …, 4000 respectively, represent the 1st, …, 4000th column vectors d( 1 )...d( 4000 ) of the deflection response matrix D, and the xth element of the 1st, …, 4000th column vectors d( 1 )...d( 4000 ) respectively, where x = n;

[0106] T6, delete the grid of the simply supported beam model to manufacture the loss condition, and repeat the above steps T2 to T5 to obtain the deflection influence line of the simply supported beam model under the loss condition, and the mid-span deflection influence line of the single loss condition is shown in Figure 5 When the simply supported beam model is damaged, the corresponding deflection influence line will be downwardly offset compared with the deflection influence line under the non-damage state of the simply supported beam model, and the offset amplitude will increase with the increase of the damage degree, and at the same time, the peak value of the deflection influence line will be offset towards the damage position.

[0107] T7, the deflection influence lines of the 4000 vertical degrees of freedom of the non-damage condition and the loss condition of the simply supported beam model are corresponded one by one, and the difference is calculated, and then the average value of the deflection influence lines of each vertical degree of freedom is calculated, and the formula is as follows:

[0108]

[0109] Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) represent the deflection influence lines of the vertical degree of freedom n of the simply supported beam model under the loss condition and the non-damage condition respectively.

[0110] The average value DILCA is used as an injury index to locate the damage of the simply supported beam model.

[0111] T8, the number of sensors is reduced to 2, and the above steps T1 to T7 are repeated, wherein the damage location effect of each single damage working condition using 2 sensors is as shown in Figure 6 The DILCA curve appears a peak at 0.4, i.e. the damage location of the single damage working condition, and the effect of the double damage working condition is as shown in Figure 7 The DILCA curve appears peaks at 0.4 and 0.7, i.e. the two damage locations of the double damage working condition, and there is a smooth transition between the two peaks. In addition, whether it is a single damage working condition or a double damage working condition, the peak value of the DILCA curve increases with the increase of the damage degree. Therefore, the present application can accurately locate the damage location using only 2 sensors in the first embodiment.

[0112] Embodiment II

[0113] A simply supported beam experimental model is built. A hollow steel box beam is used as the bridge body, as shown in Figure 8 The length of the simply supported beam experimental model is 6m, the cross-sectional height is 0.1m, the width is 0.2m, and the thickness is 3mm, and a small car with a mass of 10.55kg is used as a moving load. The specific implementation process is as follows:

[0114] P1, during the experiment, the damage is simulated by cutting the bottom of the simply supported beam experimental model, the damage degree is described by the crack depth of the cutting, and the damage location is represented by the relative position. Two damage conditions, single damage and double damage, are set, and a total of 5 damage working conditions are set, as shown in Table 2.

[0115] Table 2. Experimental damage working condition table

[0116] Damage Case Number Damage Level (Damage Location 0.68) Damage Level (Damage Location 0.38) 1 3 mm - 2 5 mm - 3 7 mm - 4 7 mm 4 mm 5 7 mm 7 mm

[0117] P2, a DC motor is used to drag the small car to pass through the simply supported beam experimental model at a speed of 0.5m / s, and 5 sensors evenly placed on the beam are used to collect the displacement response during the whole process. The displacement data contains 6000 sampling points.

[0118] P3, referring to step T2 in embodiment 1, the natural frequency ω is obtained, the first order natural frequency of the simply supported beam experimental model is 10.01Hz, and the second order natural frequency is 33.51Hz, as shown in Figure 9 .

[0119] P4, referring to steps T3 to T4 in embodiment 1, the high-resolution modal shape of each order of the simply supported beam experimental model is obtained

[0120] P5, refer to step T5 in example 1, to obtain the deflection influence line of the intact condition of the simply supported beam test model.

[0121] P6, reduce the number of sensors to 2, repeat the above steps P2 to P5 to obtain the deflection influence line of the intact condition of the simply supported beam test model using 2 sensors.

[0122] P7, cut the bottom of the simply supported beam test model to create damage, repeat the above steps P1 to P6 to obtain the deflection influence line of the damaged condition of the simply supported beam test model using 5 sensors and 2 sensors respectively, wherein the mid-span deflection influence line of the single damage condition of the simply supported beam test model using 2 sensors is shown in Figure 10 As shown in the results of example one, when the simply supported beam test model is damaged, the corresponding deflection influence line will shift downward compared to the deflection influence line of the intact condition of the simply supported beam test model, and the magnitude of the shift will increase with the increase of the damage degree, and the peak value of the deflection influence line will shift towards the direction of the damage position.

[0123] P8, using the deflection influence lines of the intact and damaged conditions of the simply supported beam test model obtained by 5 sensors, refer to step T7 in example 1 to obtain the average value DILCA of the deflection influence line difference of the simply supported beam test model using 5 sensors, and use the average value DILCA as the damage indicator to locate the damage of the simply supported beam test model.

[0124] P9, using the deflection influence lines of the intact and damaged conditions of the simply supported beam test model obtained by 2 sensors, refer to step T7 in example 1 to obtain the average value DILCA of the deflection influence line difference of the simply supported beam test model using 2 sensors, and use the average value DILCA to locate the damage of the simply supported beam test model, the damage locating effect of the single damage condition using 2 sensors is shown in Figure 11 As shown in the results of example one, when the simply supported beam test model is damaged, the corresponding deflection influence line will shift downward compared to the deflection influence line of the intact condition of the simply supported beam test model, and the magnitude of the shift will increase with the increase of the damage degree, and the peak value of the deflection influence line will shift towards the direction of the damage position. Figure 12 As shown in the results of example one, when the simply supported beam test model is damaged, the corresponding deflection influence line will shift downward compared to the deflection influence line of the intact condition of the simply supported beam test model, and the magnitude of the shift will increase with the increase of the damage degree, and the peak value of the deflection influence line will shift towards the direction of the damage position.

[0125] Example three

[0126] As shown in the results of example one, when the simply supported beam test model is damaged, the corresponding deflection influence line will shift downward compared to the deflection influence line of the intact condition of the simply supported beam test model, and the magnitude of the shift will increase with the increase of the damage degree, and the peak value of the deflection influence line will shift towards the direction of the damage position. Figure 13As shown, the embodiment provides a high-resolution modal flexibility configuration influence line bridge damage positioning system, which comprises a displacement response acquisition module 1301, a matrix calculation module 1302, a modal vibration mode model acquisition module 1303, a modal flexibility matrix construction module 1304, a deflection influence line calculation module 1305, a damage index construction module 1306 and a damage identification and positioning module 1307, and the specific functions of each module are as follows:

[0127] The displacement response acquisition module 1301 uniformly installs z sensors on the bridge to be measured, collects displacement responses through the z sensors when the moving load passes through the bridge to be measured, constructs a displacement matrix U in the form of a column vector with the displacement response data, and performs fast Fourier transform on the collected displacement responses to obtain the natural frequency ω of the bridge structure to be measured.

[0128] The matrix calculation module 1302 calculates the covariance matrix S of the displacement matrix U:

[0129]

[0130] Wherein m is the number of sampling points of the displacement response data;

[0131] The principal component matrix G of the displacement matrix U is calculated as follows:

[0132] G = UR = g (1) …g (z)

[0133] Wherein R is an eigenvector matrix obtained by matrix decomposition on the covariance matrix S, z is the number of sensors, g (1) 、…、g (z) Respectively represent the 1st, …, zth column vectors of the principal component matrix G, also known as the 1st, …, zth principal components of the principal component matrix G;

[0134] The modal vibration mode model acquisition module 1303 filters out the high-order dynamic components of each order principal component in the principal component matrix G with the natural frequency ω as the cutoff frequency to obtain each order high-resolution modal vibration mode

[0135] The modal flexibility matrix construction module 1304 constructs a high-resolution modal flexibility matrix C using the natural frequency ω and the high-resolution modal vibration mode The calculation formula is as follows:

[0136]

[0137] Wherein i is the modal order, r is the highest order of the selected high-resolution modal, r = 1, 2, …, z, ω ithe i-th natural frequency of the bridge structure to be tested, the i-th high-resolution modal shape, T denotes a transposition operation;

[0138] The deflection influence line calculation module 1305 divides the bridge structure to be tested into k vertical degrees of freedom, where k = m, and multiplies the high-resolution modal flexibility matrix C by a unit load matrix F of k rows and q columns to obtain a deflection response matrix D of the bridge structure to be tested when a unit displacement load moves from vertical degree of freedom 1 to vertical degree of freedom q, q = 1, 2, …, k, which is expressed as:

[0139]

[0140] where D and F represent the deflection response matrix and the unit load matrix, respectively, d (1) , …, d (q) represent the 1st, …, qth column vectors of the deflection response matrix D, respectively, and also represent the deflection response vectors at vertical degrees of freedom 1, …, q, respectively, T denotes a transposition operation;

[0141] The xth row of the deflection response matrix D is the deflection influence line DIL (n) at vertical degree of freedom n of the bridge structure to be tested, where x = n, and is expressed as

[0142]

[0143] where DIL (n) represents the deflection influence line at vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, …, k, represent the xth elements of the 1st, …, qth column vectors d (1) , …, d (q) of the deflection response matrix D, respectively, where x = n;

[0144] The damage index construction module 1306 repeatedly calls the above-mentioned displacement response acquisition module, matrix calculation module, modal shape model acquisition module, modal flexibility matrix construction module, and deflection influence line calculation module to obtain the deflection influence line DIL u of the undamaged state and the deflection influence line DIL d of the damaged state of the bridge structure to be tested, respectively, and then calculates the average value of the deflection influence line difference values of the k vertical degrees of freedom by subtracting the deflection influence line of the undamaged state from the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested, and the calculation formula is as follows:

[0145]

[0146] wherein DILCA is the average value of the deflection influence line difference value, DIL d (n) and DIL u (n) respectively represent the deflection influence line of the vertical degree of freedom n of the bridge to be measured in the damaged state and the undamaged state;

[0147] The damage identification and positioning module 1307 identifies and positions the damage of the bridge structure to be measured by using the average value DILCA.

[0148] The specific implementation of each module in this embodiment can be referred to the above-mentioned embodiment 1, which will not be repeated here; it should be noted that the device provided in this embodiment is only used as an example to divide the above-mentioned functional modules, in actual application, the above-mentioned functions can be distributed by different functional modules to complete all or part of the functions described above, that is, the internal structure is divided into different functional modules to complete all or part of the functions described above.

[0149] Embodiment four

[0150] The embodiment provides a computer device, which can be a computer, such as Figure 14 As shown in the figure, the processor 1402, the memory, the input device 1403, the display 1404 and the network interface 1405 connected by the system bus 1401, the processor is used to provide calculation and control ability, the memory includes a non-volatile storage medium 1406 and an internal memory 1407, the non-volatile storage medium 1406 stores an operating system, a computer program and a database, the internal memory 1407 provides an environment for the running of the operating system and the computer program in the non-volatile storage medium, when the processor 1402 executes the computer program stored in the memory, the implementation of the above-mentioned embodiment 1 is realized. The bridge damage positioning method of the high-resolution modal flexibility construction influence line proposed in the above-mentioned embodiment 1 includes the following steps:

[0151] T1, evenly install z sensors on the bridge to be measured, collect displacement responses through the z sensors when the moving load passes through the bridge to be measured, and construct a displacement matrix U in the form of a column vector with the displacement response data, and perform fast Fourier transform on the collected displacement responses to obtain the natural frequency ω of the bridge structure to be measured;

[0152] T2, calculate the covariance matrix S of the displacement matrix U and the principal component matrix of the displacement matrix U;

[0153] T3, taking the natural frequency ω as the cutoff frequency, filtering out the high-order dynamic components of each order principal component in the principal component matrix G, to obtain each order high-resolution modal shape

[0154] T4, using the natural frequency ω and the high-resolution modal shape constructing a high-resolution modal flexibility matrix C;

[0155] T5, dividing the bridge to be measured into k vertical degrees of freedom, where k = m, multiplying the high-resolution modal flexibility matrix C by a unit load matrix F of k rows and q columns to obtain a deflection response matrix D of the bridge to be measured when a unit displacement load moves from vertical degree of freedom 1 to vertical degree of freedom q, q = 1, 2, …, k, the xth row of the deflection response matrix D being the deflection influence line DIL at vertical degree of freedom n of the bridge structure to be measured (n) , where x = n;

[0156] T6, constructing a damage index, repeating the steps T1 to T5 to obtain the deflection influence line DIL in the undamaged state and the deflection influence line DIL in the damaged state of the bridge structure to be measured, respectively u d , respectively, subtracting the deflection influence line in the undamaged state from the deflection influence line in the damaged state at the k vertical degrees of freedom of the bridge structure to be measured, and calculating the average of the deflection influence line difference values of the k vertical degrees of freedom;

[0157] T7, using the average DILCA to identify and locate damage in the bridge structure to be measured.

[0158] Example Five

[0159] The embodiment provides a storage medium, which is a computer readable storage medium, and stores a computer program, the computer program being executed by a processor to implement a bridge damage positioning method of high-resolution modal flexibility constructed influence line according to the above-mentioned embodiment 1, and the method comprises the following steps:

[0160] T1, evenly installing z sensors on the bridge to be measured, collecting displacement responses through the z sensors when a moving load passes through the bridge to be measured, and constructing a displacement matrix U in the form of a column vector from the displacement response data, and performing fast Fourier transform on the collected displacement responses to obtain the natural frequency ω of the bridge structure to be measured;

[0161] T2, calculating the covariance matrix S of the displacement matrix U and the principal component matrix of the displacement matrix U;

[0162] T3, filtering out high-order dynamic components of each order principal component in the principal component matrix G by taking the natural frequency ω as a cutoff frequency to obtain each order high-resolution modal shape

[0163] T4, constructing a high-resolution modal flexibility matrix C using the natural frequency ω and the high-resolution modal shape

[0164] ​​T5, divide the bridge to be measured into k vertical degrees of freedom, wherein k=m, multiply the high-resolution modal flexibility matrix C by a unit load matrix F of k rows and q columns to obtain a deflection response matrix D of the bridge to be measured when a unit displacement load moves from vertical degree of freedom 1 to vertical degree of freedom q, q=1, 2, …, k, the xth row of the deflection response matrix D is the deflection influence line DIL at vertical degree of freedom n of the bridge structure to be measured (n ), wherein x=n;

[0165] T6, construct a damage index, repeat steps T1 to T5 to obtain the deflection influence line DIL of the undamaged state and the deflection influence line DIL of the damaged state of the bridge structure to be measured respectively u d , respectively, subtract the deflection influence line of the undamaged state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be measured, and then calculate the average value of the deflection influence line difference of the k vertical degrees of freedom;

[0166] T7, use the average value DILCA to identify and locate the damage of the bridge structure to be measured.

[0167] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited by the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application are equivalent replacement methods and are included in the protection scope of the present application.​

Claims

1. A method for locating bridge damage using high-resolution modal compliance structure influence lines, characterized in that, The bridge damage location method includes the following steps: S1. Install z sensors evenly on the bridge to be tested, where z is a positive integer greater than or equal to 2. When the moving load passes over the bridge to be tested, collect the displacement response through the z sensors and construct the displacement matrix U in the form of column vectors. Perform a fast Fourier transform on the collected displacement response to obtain the natural frequency ω of the bridge structure to be tested. S2. Calculate the covariance matrix S of the displacement matrix U: Where m is the number of sampling points for the displacement response data; The principal component matrix G of the displacement matrix U is calculated as follows: G=UR=g (1) …g (z) Where R is the eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, and g (1) ... g (z) These represent the 1st, ..., zth column vectors of the principal component matrix G, also known as the 1st, ..., zth order principal components of the principal component matrix G; S3. Using the natural frequency ω as the cutoff frequency, filter out the higher-order dynamic components of each principal component in the principal component matrix G to obtain the high-resolution mode shapes of each order. S4. Utilizing natural frequency ω and high-resolution mode shapes The high-resolution modal compliance matrix C is constructed using the following formula: Where i is the modal order, r is the highest order of the selected high-resolution mode, and r = 1, 2, ..., z, ω i Let be the i-th natural frequency of the bridge structure under test. For the i-th high-resolution mode shape, () T Indicates the transpose operation; S5. Divide the bridge under test into k vertical degrees of freedom, where k = m. Multiply the high-resolution modal compliance matrix C by the k-row, q-column unit load matrix F to obtain the deflection response matrix D of the bridge under test when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, q = 1, 2, ..., k, expressed as: Where D and F represent the deflection response matrix and the unit load matrix, respectively, and d (1) 、…、d (q) Let represent the 1st, ..., qth column vectors of the deflection response matrix D, and also the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Indicates the transpose operation; The x-th row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure under test. n ), where x = n, denoted as DIL (n) This represents the deflection influence line at point n in the vertical degree of freedom of the bridge structure under test, where n = 1, 2, ..., k. Let d represent the 1st, ..., qth column vectors of the deflection response matrix D, respectively. (1) 、…、d (q) The x-th element, x = n; S6. Construct damage index: Repeat steps S1 to S5 above to obtain the deflection influence line (DIL) of the undamaged state and the damaged state of the bridge structure under test. u And the deflection influence line DIL in the damaged state d The deflection influence lines of the undamaged state and the deflection influence lines of the damaged state at k vertical degrees of freedom of the bridge structure under test are subtracted respectively. Then, the average value of the difference of the deflection influence lines of k vertical degrees of freedom is calculated. The calculation formula is as follows: Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) The deflection influence lines represent the vertical degrees of freedom n of the bridge under test in the damaged and undamaged states, respectively. S7. Use the average value DILCA to identify and locate damage to the bridge structure under test.

2. The bridge damage localization method based on the high-resolution modal compliance structure influence line according to claim 1, characterized in that, The bridge to be tested is a simply supported beam bridge.

3. The bridge damage localization method based on the high-resolution modal compliance structure influence line according to claim 1, characterized in that, The sensor is a displacement sensor.

4. The bridge damage localization method based on the high-resolution modal compliance structure influence line according to claim 1, characterized in that, In step S3, a moving average filter is used to filter out the higher-order dynamic component information of each principal component in the principal component matrix G, thereby obtaining the high-resolution mode shapes of each order. For the h-th high-resolution mode shape of the bridge under test The calculation formula is as follows: Where W is the length of the moving window selected for the moving average filter, and q s Indicates the sensor's sampling frequency. This represents the h-th high-resolution mode shape of the bridge structure under test. The a-th element, G represents the h-th principal component. (h) The b-th element, ω h Let h represent the h-th natural frequency of the bridge structure under test, h = 1, 2, ..., z, a = 1, 2, ..., m, b = 1, 2, ..., m + W / 2, where m is the number of sampling points for the displacement response data.

5. The bridge damage localization method based on the high-resolution modal compliance structure influence line according to claim 1, characterized in that, In step S7, when there is damage to the structure, when the curve of the average value DILCA shows a peak, it is determined that the bridge structure under test has a loss, and the location indicated by the peak is the location of the damage to the bridge structure under test.

6. A bridge damage localization system using high-resolution modal compliance structural influence lines, for executing the bridge damage localization method using high-resolution modal compliance structural influence lines as described in any one of claims 1 to 5, characterized in that, The bridge damage location system includes: The displacement response acquisition module uniformly installs z sensors on the bridge under test. When the moving load passes over the bridge, the displacement response is collected through the z sensors. The displacement response data is then used to construct a displacement matrix U in the form of a column vector. The collected displacement response is then subjected to a fast Fourier transform to obtain the natural frequency ω of the bridge structure under test. The matrix calculation module calculates the covariance matrix S of the displacement matrix U: Where m is the number of sampling points for the displacement response data; The principal component matrix G of the displacement matrix U is calculated as follows: G=UR=g (1) …g (z) Where R is the eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, and g (1) ... g (z) These represent the 1st, ..., zth column vectors of the principal component matrix G, also known as the 1st, ..., zth order principal components of the principal component matrix G; The modal model acquisition module uses the natural frequency ω as the cutoff frequency to filter out the higher-order dynamic components of each principal component in the principal component matrix G, thereby obtaining high-resolution modal shapes of each order. Modal compliance matrix construction module, utilizing natural frequencies ω and high-resolution mode shapes The high-resolution modal compliance matrix C is constructed using the following formula: Where i is the modal order, r is the highest order of the selected high-resolution mode, and r = 1, 2, ..., z, ω i Let be the i-th natural frequency of the bridge structure under test. For the i-th high-resolution mode shape, () T Indicates the transpose operation; The deflection influence line calculation module divides the bridge under test into k vertical degrees of freedom, where k = m. It then multiplies the high-resolution modal compliance matrix C by a k-row, q-column unit load matrix F to obtain the deflection response matrix D of the bridge under test when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k. This is expressed as: Where D and F represent the deflection response matrix and the unit load matrix, respectively, and d (1) 、…、d (q) Let represent the 1st, ..., qth column vectors of the deflection response matrix D, and also the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Indicates the transpose operation; The x-th row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure under test. (n) Where x = n, it is represented as DIL (n) This represents the deflection influence line at point n in the vertical degree of freedom of the bridge structure under test, where n = 1, 2, ..., k. Let d represent the 1st, ..., qth column vectors of the deflection response matrix D, respectively. (1) 、…、d (q) The x-th element, x = n; The damage index construction module repeatedly calls the displacement response acquisition module, matrix calculation module, modal mode model acquisition module, modal compliance matrix construction module, and deflection influence line calculation module to obtain the deflection influence line (DIL) of the undamaged state from the displacement responses of the bridge structure under test in both the undamaged and damaged states. u And the deflection influence line DIL in the damaged state d The deflection influence lines of the undamaged state and the deflection influence lines of the damaged state at k vertical degrees of freedom of the bridge structure under test are subtracted respectively. Then, the average value of the difference of the deflection influence lines of k vertical degrees of freedom is calculated. The calculation formula is as follows: Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) The deflection influence lines represent the vertical degrees of freedom n of the bridge under test in the damaged and undamaged states, respectively. The damage identification and localization module uses the average value DILCA to identify and locate damage to the bridge structure under test.

7. A computer device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the bridge damage localization method according to any one of claims 1-5, which uses the high-resolution modal compliance construction influence line.

8. A storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the bridge damage localization method according to any one of claims 1-5, which uses high-resolution modal compliance construction influence lines.

Images