Bridge damage positioning method of high-resolution modal flexibility structure influence line

Abstract

The invention discloses a bridge damage positioning method based on a high-resolution modal flexibility structure influence line. The method comprises the following steps that at least two sensors are used for collecting displacement responses of a bridge under a moving load to form a displacement matrix U; carrying out FFT (Fast Fourier Transform) on the displacement response, and determining the inherent frequency omega of the bridge; analyzing the displacement matrix U to obtain a principal component matrix G; according to the physical significance of the principal component matrix, high-order power components in principal components of all orders are filtered out, and a high-resolution modal shape # imgabs0 # of all the orders is obtained, and a modal flexibility matrix C is constructed through the inherent frequency omega and the modal shape # imgabs1 #; discretizing the moving process of the unit load into a unit load matrix F; utilizing the modal flexibility matrix C and the unit load matrix F to construct deflection influence lines at a plurality of degrees of freedom; and constructing deflection influence lines of a bridge in a lossless state and a lossy state to obtain a damage index and an identification position. According to the method, the influence line is constructed through modal parameters of the bridge, and accurate damage positioning is obtained through a small number of sensors and simple calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge damage location and identification, and in particular to a bridge damage location method, system, computer equipment and storage medium of a high-resolution modal flexibility structural influence line. Background Art

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

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

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

[0005] The purpose of the present invention is to overcome the shortcomings and deficiencies of the existing methods and to provide a bridge damage location method, system, computer equipment and storage medium with high-resolution modal flexibility structural influence lines. By using a small number of sensors, the deflection influence lines of multiple points can be simultaneously identified through dynamic analysis of the structure, and the deflection influence lines of multiple points can be combined to achieve accurate damage location of the bridge using a small number of sensors.

[0006] A first aspect of the present invention discloses a bridge damage location method using high-resolution modal flexibility construction influence lines, the bridge damage location method comprising the following steps:

[0007] S1. Evenly install z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is subjected to a fast Fourier transform to obtain the natural frequency ω of the bridge structure to be tested.

[0008] S2. Calculate the covariance matrix S of the displacement matrix U:

[0009]

[0010] Where m is the number of sampling points of displacement response data;

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

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

[0013] Where R is the eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, g (1) ,…,g (z) They represent the 1st, …, zth column vectors of the principal component matrix G, also called the 1st, …, zth order principal components of the principal component matrix G;

[0014] S3, using the natural frequency ω as the cutoff frequency, filter out the high-order dynamic components of each order of principal components in the principal component matrix G, and obtain the high-resolution modal vibration shapes of each order The column vector of the principal component matrix, i.e., the principal component, is composed of modal vibration shape and high-order dynamic component information. The frequency corresponding to the high-order dynamic component information is the natural frequency, which is much larger than the frequency corresponding to the modal vibration shape. Therefore, a low-pass filter is selected for filtering.

[0015] S4. Using natural frequency ω and high-resolution mode shapes 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 mode, r = 1, 2, ..., z, ω i is the i-th order natural frequency of the bridge structure to be tested, is the i-th order high-resolution mode shape, () T Represents a transpose operation;

[0018] S5. The deflection influence line refers to the change in the deflection response at a specific position under the action of a unit moving load. Therefore, it is assumed that another unit moving load moves on the bridge to be tested, and the action process of the unit moving load is discretized into multiple unit load vectors. Only the vibration in the vertical direction of the bridge to be tested is considered. Therefore, the bridge to be tested is evenly divided into k vertical degrees of freedom, where k = m. It is assumed that the unit moving load moves from the vertical degree of freedom 1 to the vertical degree of freedom q. The discretization process is expressed as:

[0019]

[0020] Among them, f (1) ,...,f (q) is the discretized unit load vector, DOF qRepresents the vertical degree of freedom q of the bridge structure to be tested, and the vertical degree of freedom DOF corresponding to the zero column vector q+1 , …, DOF k They represent the other vertical degrees of freedom that are not subjected to unit moving load, q = 1, 2, ..., k, () T Represents a transpose operation;

[0021] The discretized unit load vector is constructed into a unit load matrix F, and the deflection response matrix under the unit moving load is calculated, which is expressed as:

[0022]

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

[0024] Where D and F represent the deflection response matrix and unit load matrix respectively, d( 1 )、…、d( q ) represent the 1st, ..., qth column vectors of the deflection response matrix D, and are also represented as the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively.

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

[0026]

[0027] Among them, DIL (n) Indicates the deflection influence line at the vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, ..., k, denote the first, ..., qth column vectors d of the deflection response matrix D respectively. (1 ),…,d (q ), x=n;

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

[0029]

[0030] Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) They represent the deflection influence lines of the vertical degree of freedom n of the tested bridge in damaged and intact states respectively;

[0031] S7. Use the average value DILCA to identify and locate damage to the bridge structure under test.

[0032] Furthermore, the bridge to be tested is a simply supported beam bridge.

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

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

[0035]

[0036] Where W is the moving window length selected by the moving average filter, q s represents the sampling frequency of the sensor, Represents the h-th high-resolution mode shape of the bridge structure to be tested The ath element of represents the h-th order principal component g (h) The bth element of h represents the h-th order natural frequency of the bridge structure to be tested, h=1,2,…,z, a=1,2,…,m, b=1,2,…,m+W / 2, and m is the number of sampling points of the displacement response data. The moving average filter is a low-pass filter and can select the cutoff frequency. Therefore, the present invention selects it to filter the high-order dynamic component information of the principal component matrix to obtain the modal vibration shape.

[0037] Furthermore, in step S7, when there is damage to the structure, when the curve of the average value DILCA shows a peak, it is judged that there is loss in the bridge structure to be tested, and the position indicated by the peak is the damaged position of the bridge structure to be tested. When the structure is damaged, the peak value of the deflection influence line will be offset compared to the deflection influence line of the structure in the intact state, and the direction of the offset is consistent with the direction of the damage position. Subtracting the two will result in a difference, and the difference between the two reaches a maximum value at the damage position. DILCA simultaneously utilizes the difference in deflection influence lines at multiple vertical degrees of freedom, which has a better and more accurate damage identification effect than the difference in influence lines at a single vertical degree of freedom.

[0038] Furthermore, principal component analysis is a matrix operation, and the value range of z is [2, +∞), that is, the number of sensors is at least 2, so the present invention can realize accurate damage identification of the whole bridge with only 2 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 perform high-resolution modal vibration type identification. Therefore, matrix operations need to ensure that the number of rows and columns of the displacement matrix U are greater than or equal to 2 to ensure that it has sufficient dimensions for operation.

[0039] The second aspect of the present invention discloses a bridge damage location system using high-resolution modal flexibility structure influence lines, which is used to execute the above-mentioned bridge damage location method using high-resolution modal flexibility structure influence lines. The bridge damage location system comprises:

[0040] The displacement response acquisition module evenly installs z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is fast Fourier transformed to obtain the natural frequency ω of the bridge structure to be tested.

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

[0042]

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

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

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

[0046] Where R is the eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, g (1) ,…,g (z)They represent the 1st, …, zth column vectors of the principal component matrix G, also called the 1st, …, zth order principal components of the principal component matrix G;

[0047] The modal vibration model acquisition module uses the natural frequency ω as the cutoff frequency to filter out the high-order dynamic components of each order of principal components in the principal component matrix G, and obtains high-resolution modal vibration shapes of each order.

[0048] Modal flexibility matrix construction module using natural frequencies ω and high-resolution mode shapes 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 mode, r = 1, 2, ..., z, ω i is the i-th order natural frequency of the bridge structure to be tested, is the i-th order high-resolution mode shape, () T Represents a transpose operation;

[0051] The deflection influence line calculation module divides the bridge to be tested into k vertical degrees of freedom on average, where k = m. The high-resolution modal flexibility matrix C is right-multiplied by the unit load matrix F with k rows and q columns to obtain the deflection response matrix D of the bridge to be tested when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k, expressed as:

[0052]

[0053] Where D and F represent the deflection response matrix and unit load matrix respectively, d (1) ,…,d (q) They represent the 1st, ..., qth column vectors of the deflection response matrix D, and are also represented as the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Represents a transpose operation;

[0054] The xth row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure to be tested. (n) , where x = n, expressed as

[0055]

[0056] Among them, DIL (n) Indicates the deflection influence line at the vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, ..., k, denote the first, ..., qth column vectors d of the deflection response matrix D respectively. (1) ,…,d (q)The xth element of , x = n;

[0057] The damage index construction module repeatedly calls the above displacement response acquisition module, matrix calculation module, modal vibration model acquisition module, modal flexibility matrix construction module, and deflection influence line calculation module for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state. u and the deflection influence line DIL of the damaged state d , respectively, the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested are subtracted, and then the average value of the difference of the deflection influence line of the k vertical degrees of freedom is calculated. The calculation formula is as follows:

[0058]

[0059] Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) They represent the deflection influence lines of the vertical degree of freedom n of the tested bridge in damaged and intact states respectively;

[0060] The damage identification and location module uses the average value DILCA to identify and locate damage to the bridge structure under test.

[0061] A third aspect of the present invention discloses a computer device, comprising a processor and a memory for storing a program executable by the processor, wherein when the processor executes the program stored in the memory, the above-mentioned bridge damage location method based on high-resolution modal flexibility structural influence lines is implemented.

[0062] A fourth aspect of the present invention discloses a storage medium storing a program, which, when executed by a processor, implements the above-mentioned bridge damage location method based on high-resolution modal flexibility structural influence lines.

[0063] Compared with the prior art, the present invention has the following advantages and effects:

[0064] (1) The method proposed in the present invention uses the high-resolution modal flexibility obtained by a small number of sensors to identify the deflection influence lines. The number of deflection influence lines obtained is determined by the number of sampling points of the displacement data. The influence lines of multiple points not limited to the sensor position can be obtained simultaneously, and the deflection influence lines at multiple points can be combined for damage identification, which can effectively improve the damage identification accuracy and noise robustness.

[0065] (2) The method proposed in the present invention can accurately identify the damage location by simply analyzing and calculating the displacement response data of the bridge to be tested under the action of the moving load, thereby improving the efficiency of damage identification.

[0066] (3) The method proposed in the present invention only requires two or more sensors to accurately locate damage on a long-span bridge, which can effectively reduce costs and is more suitable for actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flowchart of the method for locating structural damage by using a small number of sensors to simultaneously obtain deflection influence lines at multiple points proposed in the first embodiment;

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

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

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

[0071] Figure 5 is a schematic diagram of the deflection influence lines of all single damage conditions identified by the displacement signals of two sensors in the numerical simulation in the first embodiment;

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

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

[0074] Figure 8 It is the structural diagram of the experimental steel box girder in Example 2;

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

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

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

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

[0079] Fig.13 It is a structural block diagram of the subject knowledge graph complex query system based on graph coding in Example 3;

[0080] Fig.14 It is a structural block diagram of the computer device in the fourth embodiment. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the technical solution in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0082] Embodiment 1

[0083] like Figure 1 As shown, Figure 1 Schematic diagram of the process steps of a bridge damage location method using high-resolution modal flexibility structure influence lines. Figure 2 As shown. The length of the simply supported beam model is 20m, the cross-sectional height is 0.2m, the width is 0.1m, and the mass of the moving mass block is 500kg. The specific implementation process is as follows:

[0084] T1. After meshing the simple beam model, the mesh is deleted along the beam height direction to simulate damage. The degree of damage is described by the ratio of the crack depth formed by deleting the mesh to the cross-sectional height of the simply supported beam model. The damage position is expressed as a relative position. Two damage forms, single damage and double damage, are set, with a total of 7 damage conditions, as shown in Table 1.

[0085] Table 1. Numerical simulation damage conditions

[0086]

[0087]

[0088] T2. Collect the displacement response of the simply supported beam model under non-destructive working conditions. Use the mobile mass block as the mobile load and pass it uniformly on the simply supported beam model at a speed of 0.5m / s. Use 7 sensors evenly placed on the simply supported beam model to collect the displacement response of the whole process, such as Figure 3 As shown, the displacement data contains 4000 sampling points. The displacement response is transformed by fast Fourier transform to obtain the natural frequency ω of the simply supported beam model. The first-order natural frequency of the simply supported beam model is 1.123Hz, and the second-order natural frequency is 4.468Hz, as shown in Figure 4 shown.

[0089] T3. The above displacement response data are combined into a displacement matrix U in the form of a column vector, and 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) ... (7)

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

[0094] T4. Taking the natural frequency ω as the cutoff frequency, the moving average filter is used to filter out the high-order dynamic components of each order of the principal component in the principal component matrix G to obtain the high-resolution modal vibration 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 moving window length selected by the moving average filter, q s represents the sampling frequency of the sensor, Represents the h-th high-resolution mode shape of the simply supported beam model The ath element of represents the h-th order principal component g (h) The bth element of h represents the hth 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 high-order modes in actual engineering are often difficult to excite, the first two modes are used to identify the deflection influence line of the non-destructive working condition of the simply supported beam model.

[0098] The natural frequency ω and high-resolution mode shape Construct the high-resolution modal flexibility matrix C, the formula is as follows:

[0099]

[0100] where ω i is the i-th natural frequency of the simply supported beam model, represents the i-th high-resolution mode shape of the simply supported beam model;

[0101] Since the moving mass block moves from one end of the simply supported beam model to the other end, the discretized unit load moment F of this process is a unit diagonal matrix. The deflection influence line of the simply supported beam model is calculated using the high-resolution modal flexibility matrix C. 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 unit load matrix respectively, DIL (n) Represents the deflection influence line at 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, and also represent the deflection response vectors at the 1st, ..., 4000th vertical degrees of freedom, respectively. denote the 1st, ..., 4000th column vectors d( 1 )...d( 4000 ), where x=n;

[0106] T6. Delete the mesh of the simply supported beam model to create a lossy condition, and repeat the above steps T2 to T5 to obtain the deflection influence line of the lossy condition of the simply supported beam model. The mid-span deflection influence line of the single loss condition is as follows: Figure 5 As shown in the figure, when the simply supported beam model is damaged, the corresponding deflection influence line will shift downward compared to the deflection influence line of the simply supported beam model in the intact state, and the amplitude of the shift will increase with the increase of the damage degree. At the same time, the peak value of the deflection influence line will shift toward the direction of the damage location.

[0107] T7. The influence lines of the non-destructive working condition of the simply supported beam model and the 4000 vertical degrees of freedom of the lossy working condition are matched one by one, and the difference is made. Then the difference of the deflection influence line of each vertical degree of freedom is calculated as the average value. 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) They represent the deflection influence lines of the vertical degree of freedom n of the simply supported beam model with lossy conditions and without lossy conditions respectively.

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

[0111] T8. Reduce the number of sensors to 2 and repeat the above steps T1 to T7. The damage location effect of each single damage condition using 2 sensors is as follows: Figure 6 As shown in the figure, the DILCA curve has a peak at 0.4, which is the damage position of the single damage condition. The effect of the double damage condition is as follows: Figure 7 As shown in FIG. 1 , the DILCA curve has peaks at both 0.4 and 0.7, that is, peaks appear at two damage locations in the double damage condition, and there is a smooth transition between the two peaks. In addition, regardless of the single damage condition or the double damage condition, the peak of the DILCA curve increases with the increase in the degree of damage. Therefore, the present invention can accurately locate the damage location using only two sensors in Example 1.

[0112] Embodiment 2

[0113] Build a simply supported beam experimental model. Use a hollow steel box beam as the bridge body, such as Figure 8 As shown, the simply supported beam experimental model is 6m long, 0.1m high, 0.2m wide, 3mm thick, and a 10.55kg trolley is used as a moving load. The specific implementation process is as follows:

[0114] P1. During the experiment, the damage was simulated by cutting the bottom of the simply supported beam test model. The degree of damage was described by the depth of the cut crack, and the damage position was expressed by the relative position. Two damage conditions, single damage and double damage, were set, with a total of 5 damage conditions, as shown in Table 2.

[0115] Table 2. Experimental damage conditions

[0116] Damage condition number Damage degree (damage location 0.68) Damage degree (damage location 0.38) 1 3mm - 2 5mm - 3 7mm - 4 7mm 4mm 5 7mm 7mm

[0117] P2. Use a DC motor to drag the cart to pass uniformly on the simply supported beam experimental model at a speed of 0.5 m / s. Use five sensors evenly placed on the beam to collect the displacement response of the entire process. The displacement data contains 6000 sampling points.

[0118] P3. Referring to step T2 in Example 1, the natural frequency ω is obtained. The first-order natural frequency of the simply supported beam experimental model is 10.01 Hz, and the second-order natural frequency is 33.51 Hz. Fig. 9 shown.

[0119] P4. Referring to step T3 to step T4 in Example 1, obtain the high-resolution modal vibration shapes of each order of the simply supported beam experimental model.

[0120] P5. Referring to step T5 in Example 1, the deflection influence line of the non-destructive working condition of the simply supported beam experimental model is obtained.

[0121] P6. Reduce the number of sensors to 2, repeat the above steps P2 to P5, and obtain the deflection influence line of the non-destructive working 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, and repeat the above steps P1 to P6 to obtain the deflection influence lines of the damaged working conditions of the simply supported beam test model using 5 sensors and 2 sensors, respectively. The mid-span deflection influence line of the single damaged working condition of the simply supported beam test model using 2 sensors is as follows: Fig.10 As shown, the results are the same as those in Example 1. When damage occurs to the simply supported beam experimental model, the corresponding deflection influence line will shift downward compared to the deflection influence line of the simply supported beam experimental model in the intact state, and the amplitude of the shift will increase with the increase of the degree of damage. At the same time, the peak value of the deflection influence line will shift toward the direction of the damage location.

[0123] P8. The deflection influence lines of the non-destructive working condition and the destructive working condition of the simply supported beam experimental model are obtained by using 5 sensors. Referring to step T7 in Example 1, the average value DILCA of the deflection influence line difference of the simply supported beam experimental model using 5 sensors is obtained, and the average value DILCA is used as the damage indicator to locate the damage of the simply supported beam experimental model.

[0124] P9. Using the deflection influence lines of the non-destructive working condition and the damage working condition of the simply supported beam test model obtained using the two 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 the two sensors, and perform damage location on the simply supported beam test model. The damage location effect of each single damage working condition using the two sensors is as follows: Fig.11 As shown in the figure, the DILCA curve has a peak at 0.68, which is the damage position of the single damage condition. The effect of the double damage condition is as follows: Fig.12 As shown, the DILCA curve has peaks at 0.38 and 0.68, that is, peaks appear at two damage locations in the double damage condition, and there is a smooth transition between the two peaks. In addition, whether it is a single damage condition or a double damage condition, the peak of the DILCA curve increases with the increase of the damage degree. Therefore, the present invention can accurately locate the damage location using only two sensors in Example 2.

[0125] Embodiment 3

[0126] like Fig.13As shown, this embodiment provides a bridge damage location system with high-resolution modal flexibility structural influence line, and the bridge damage location system with high-resolution modal flexibility structural influence line includes: a displacement response acquisition module 1301, a matrix calculation module 1302, a modal vibration shape 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 location module 1307. The specific functions of each module are as follows:

[0127] The displacement response acquisition module 1301 evenly installs z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is fast Fourier transformed to obtain the natural frequency ω of the bridge structure to be tested.

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

[0129]

[0130] Where m is the number of sampling points of 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] Where R is the eigenvector matrix obtained by matrix decomposition of the covariance matrix S, z is the number of sensors, g (1) ,…,g (z) They represent the 1st, …, zth column vectors of the principal component matrix G, also called the 1st, …, zth order principal components of the principal component matrix G;

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

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

[0136]

[0137] Where i is the modal order, r is the highest order of the selected high-resolution mode, r = 1, 2, ..., z, ω iis the i-th order natural frequency of the bridge structure to be tested, is the i-th order high-resolution mode shape, () T Represents a transpose operation;

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

[0139]

[0140] Where D and F represent the deflection response matrix and unit load matrix respectively, d (1) ,…,d (q) They represent the 1st, ..., qth column vectors of the deflection response matrix D, and are also represented as the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Represents a transpose operation;

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

[0142]

[0143] Among them, DIL (n) Indicates the deflection influence line at the vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, ..., k, denote the first, ..., qth column vectors d of the deflection response matrix D respectively. (1) ,…,d (q) The xth element of , x = n;

[0144] The damage index construction module 1306 repeatedly calls the displacement response acquisition module, matrix calculation module, modal vibration model acquisition module, modal flexibility matrix construction module, and deflection influence line calculation module for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state. u and the deflection influence line DIL of the damaged state d , respectively, the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested are subtracted, and then the average value of the difference of the deflection influence line of the k vertical degrees of freedom is calculated. The calculation formula is as follows:

[0145]

[0146] Where DILCA is the average value of the deflection influence line difference, DIL d (n) and DIL u (n) They represent the deflection influence lines of the vertical degree of freedom n of the tested bridge in damaged and intact states respectively;

[0147] The damage identification and location module 1307 uses the average value DILCA to identify and locate damage to the bridge structure to be tested.

[0148] The specific implementation of each module in this embodiment can refer to the above-mentioned embodiment 1, which will not be described one by one here; it should be noted that the device provided in this embodiment is only illustrated by the division of the above-mentioned functional modules. In actual applications, the above-mentioned functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0149] Embodiment 4

[0150] This embodiment provides a computer device, which may be a computer, such as Fig.14 As shown, a processor 1402, a memory, an input device 1403, a display 1404 and a network interface 1405 connected via a system bus 1401 are provided. The processor is used to provide computing and control capabilities. 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 operation 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 bridge damage location method for realizing a high-resolution modal flexibility structural influence line proposed in the above embodiment 1 includes the following steps:

[0151] T1. Evenly install z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is fast Fourier transformed to obtain the natural frequency ω of the bridge structure to be tested.

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

[0153] T3, using the natural frequency ω as the cutoff frequency, filter out the high-order dynamic components of each order of principal components in the principal component matrix G, and obtain high-resolution modal vibration shapes of each order

[0154] T4. Using natural frequency ω and high-resolution mode shapes Construct a high-resolution modal flexibility matrix C;

[0155] T5. Divide the bridge to be tested into k vertical degrees of freedom on average, where k = m. Multiply the high-resolution modal flexibility matrix C by the unit load matrix F with k rows and q columns on the right to obtain the deflection response matrix D of the bridge to be tested when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k. The xth row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure to be tested. (n) , where x = n;

[0156] T6, structural damage index, repeat the above steps T1 to T5 for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state u and the deflection influence line DIL of the damaged state d , respectively make the difference between the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested, and then calculate the average value of the difference of the deflection influence line of the k vertical degrees of freedom;

[0157] T7. Use the average value DILCA to identify and locate damage to the bridge structure under test.

[0158] Embodiment 5

[0159] This embodiment provides a storage medium, which is a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, a bridge damage location method of a high-resolution modal flexibility structural influence line of the above embodiment 1 is implemented, including the following steps:

[0160] T1. Evenly install z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is fast Fourier transformed to obtain the natural frequency ω of the bridge structure to be tested.

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

[0162] T3, using the natural frequency ω as the cutoff frequency, filter out the high-order dynamic components of each order of principal components in the principal component matrix G, and obtain high-resolution modal vibration shapes of each order

[0163] T4. Using natural frequency ω and high-resolution mode shapes Construct a high-resolution modal flexibility matrix C;

[0164] T5. Divide the bridge to be tested into k vertical degrees of freedom on average, where k = m. Multiply the high-resolution modal flexibility matrix C by the unit load matrix F with k rows and q columns on the right to obtain the deflection response matrix D of the bridge to be tested when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k. The xth row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure to be tested. (n ), where x = n;

[0165] T6, structural damage index, repeat the above steps T1 to T5 for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state u and the deflection influence line DIL of the damaged state d , respectively make the difference between the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested, and then calculate the average value of the difference of the deflection influence line of the k vertical degrees of freedom;

[0166] T7. Use the average value DILCA to identify and locate damage to the bridge structure under test.

[0167] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A bridge damage location method based on high-resolution modal flexibility structure influence line, characterized in that: The bridge damage location method comprises the following steps: S1. Evenly install z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is subjected to a fast Fourier transform 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 of 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, g (1) ,…,g (z) They represent the 1st, …, zth column vectors of the principal component matrix G, also called 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 high-order dynamic components of each order of principal components in the principal component matrix G, and obtain the high-resolution modal vibration shapes of each order S4. Using natural frequency ω and high-resolution mode shapes Construct a high-resolution modal flexibility matrix C, and the calculation formula is as follows: Where i is the modal order, r is the highest order of the selected high-resolution mode, r = 1, 2, ..., z, ω i is the i-th order natural frequency of the bridge structure to be tested, is the i-th order high-resolution mode shape, () T Represents a transpose operation; S5. Divide the bridge to be tested into k vertical degrees of freedom on average, where k = m. Multiply the high-resolution modal flexibility matrix C by the unit load matrix F with k rows and q columns on the right to obtain the deflection response matrix D of the bridge to be tested when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k, expressed as: Where D and F represent the deflection response matrix and unit load matrix respectively, d (1) ,…,d (q) They represent the 1st, ..., qth column vectors of the deflection response matrix D, and are also represented as the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Represents a transpose operation; The xth row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure to be tested. (n) , where x = n, expressed as Among them, DIL (n) Indicates the deflection influence line at the vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, ..., k, denote the first, ..., qth column vectors d of the deflection response matrix D respectively. (1) ,…,d (q) The xth element of , x = n; S6, construct damage index, repeat the above steps S1 to S5 for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state u and the deflection influence line DIL of the damaged state d , respectively, the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested are subtracted, and then the average value of the difference of the deflection influence line of the 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) They represent the deflection influence lines of the vertical degree of freedom n of the tested bridge in damaged and intact states respectively; S7. Use the average value DILCA to identify and locate damage to the bridge structure under test.

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

3. The bridge damage location method based on high-resolution modal flexibility structure influence line according to claim 1 is characterized in that: The sensor is a displacement sensor.

4. The bridge damage location method based on high-resolution modal flexibility structure influence line according to claim 1 is characterized in that: In step S3, a moving average filter is used to filter out the high-order dynamic component information of each order of principal components in the principal component matrix G to obtain high-resolution modal vibration shapes of each order. For the h-th high-resolution mode shape of the bridge to be tested The calculation formula is as follows: Where W is the moving window length selected by the moving average filter, q s represents the sampling frequency of the sensor, Represents the h-th high-resolution mode shape of the bridge structure to be tested The ath element of represents the h-th order principal component g (h) The bth element of h represents the h-th order natural frequency of the bridge structure to be tested, h=1,2,…,z, a=1,2,…,m, b=1,2,…,m+W / 2, m is the number of sampling points of the displacement response data.

5. The bridge damage location method based on high-resolution modal flexibility structure influence line according to claim 1 is characterized in that: In step S7, when there is damage to the structure, when a peak appears in the curve of the average value DILCA, it is determined that there is loss in the bridge structure to be measured, and the position indicated by the peak is the damage position of the bridge structure to be measured.

6. The bridge damage location method based on high-resolution modal flexibility structural influence line according to claim 1 is characterized in that: The value range of z is [2,+∞).

7. A bridge damage location system using high-resolution modal flexibility structural influence lines, used to implement the bridge damage location method using high-resolution modal flexibility structural influence lines as described in any one of claims 1 to 6, characterized in that: The bridge damage location system comprises: The displacement response acquisition module evenly installs z sensors on the bridge to be tested. When the moving load passes through the bridge to be tested, the displacement response is collected by the z sensors, and the displacement response data is used to construct a displacement matrix U in the form of a column vector. The collected displacement response is fast Fourier transformed to obtain the natural frequency ω of the bridge structure to be tested. Matrix calculation module, calculates the covariance matrix S of the displacement matrix U: Where m is the number of sampling points of 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, g (1) ,…,g (z) They represent the 1st, …, zth column vectors of the principal component matrix G, also called the 1st, …, zth order principal components of the principal component matrix G; The modal vibration model acquisition module uses the natural frequency ω as the cutoff frequency to filter out the high-order dynamic components of each order of principal components in the principal component matrix G, and obtains high-resolution modal vibration shapes of each order. Modal flexibility matrix construction module using natural frequencies ω and high-resolution mode shapes Construct a high-resolution modal flexibility matrix C, and the calculation formula is as follows: Where i is the modal order, r is the highest order of the selected high-resolution mode, r = 1, 2, ..., z, ω i is the i-th order natural frequency of the bridge structure to be tested, is the i-th order high-resolution mode shape, () T Represents a transpose operation; The deflection influence line calculation module divides the bridge to be tested into k vertical degrees of freedom on average, where k = m. The high-resolution modal flexibility matrix C is right-multiplied by the unit load matrix F with k rows and q columns to obtain the deflection response matrix D of the bridge to be tested when another unit moving load moves from vertical degree of freedom 1 to vertical degree of freedom q, where q = 1, 2, ..., k, expressed as: Where D and F represent the deflection response matrix and unit load matrix respectively, d (1) ,…,d (q) They represent the 1st, ..., qth column vectors of the deflection response matrix D, and are also represented as the deflection response vectors at the vertical degrees of freedom 1, ..., q, respectively. T Represents a transpose operation; The xth row of the deflection response matrix D is the deflection influence line DIL at the vertical degree of freedom n of the bridge structure to be tested. (n) , where x = n, expressed as Among them, DIL (n) Indicates the deflection influence line at the vertical degree of freedom n of the bridge structure to be tested, n = 1, 2, ..., k, denote the first, ..., qth column vectors d of the deflection response matrix D respectively. (1) ,…,d (q) The xth element of , x = n; The damage index construction module repeatedly calls the above displacement response acquisition module, matrix calculation module, modal vibration model acquisition module, modal flexibility matrix construction module, and deflection influence line calculation module for the displacement response of the intact state and the damaged state of the bridge structure to be tested to obtain the deflection influence line DIL of the intact state. u and the deflection influence line DIL of the damaged state d , respectively, the deflection influence line of the intact state and the deflection influence line of the damaged state at the k vertical degrees of freedom of the bridge structure to be tested are subtracted, and then the average value of the difference of the deflection influence line of the 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) They represent the deflection influence lines of the vertical degree of freedom n of the tested bridge in damaged and intact states respectively; The damage identification and location module uses the average value DILCA to identify and locate damage to the bridge structure under test.

8. A computer device comprising a processor and a memory for storing a program executable by the processor, characterized in that: When the processor executes the program stored in the memory, the bridge damage location method of the high-resolution modal flexibility structural influence line described in any one of claims 1-6 is implemented.

9. A storage medium storing a program, characterized in that: When the program is executed by a processor, the bridge damage location method of high-resolution modal flexibility structural influence line according to any one of claims 1 to 6 is implemented.

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