Optimized arrangement method of sensors for vibration monitoring of T-shaped beam bridge

Abstract

The invention discloses a sensor optimization arrangement method for vibration monitoring of a T-shaped bridge, which comprises the following steps of: firstly, preliminarily drawing up a measuring point group and determining an interested modal order through a finite element model and / or a modal result of the T-shaped bridge obtained by field measurement; then, based on a modal shape matrix of a bridge in a finite element model result, deriving a maximum diagonal element value of a corresponding MAC matrix and a trace of a Fisher information matrix, and increasing and decreasing the degree of freedom of the MAC matrix and the Fisher information matrix through a correction matrix so that the MAC matrix and the Fisher information matrix meet monitoring requirements; comprehensively considering whether the values of the two parameters are in the optimal range or not based on actual measurement and historical data; the measurement point group is the optimal arrangement mode of the vibration sensor if the measurement point group is in the optimal range, and the measurement point group is the optimal arrangement mode of the vibration sensor if the measurement point group is not in the optimal range, the correction matrix acts on the MAC matrix and the Fisher information matrix respectively, the corrected parameter values are compared, and the measurement point group under the optimal parameter value is taken as the optimal arrangement of the vibration sensor.

Description

Technical Field

[0001] The invention belongs to bridge monitoring technology, and in particular relates to a sensor optimization arrangement method for vibration monitoring of a T-beam bridge. Background Art

[0002] Among natural disasters, earthquakes are often sporadic and uncertain, and once they occur, they will cause varying degrees of damage to infrastructure. Bridge structures are important nodes in the highway transportation network in infrastructure, and are also earthquake-prone parts of the road network. The seismic design of bridges is crucial to ensure the smooth flow of lifelines after an earthquake. In addition, with the development of technology and the updating of concepts, vibration monitoring of bridge structures has gradually become one of the important means to ensure the safe and healthy operation of bridge structures.

[0003] In the current field of bridge health monitoring, acceleration sensors, displacement sensors, strain sensors, etc. are often used to monitor the vibration of bridges. For bridges in ordinary areas, the focus is more on health monitoring during daily operation. Sensors suitable for low-frequency vibration, such as displacement sensors or strain sensors, are often used to monitor small deformations or long-term fatigue damage caused by traffic loads. The sensor layout density is relatively low, usually only need to cover the main part of the structure, and the layout redundancy is relatively small; while for bridges in high-intensity areas, the monitoring focus is on evaluating the response of the bridge under earthquake, including the stability of the structure, the degree of damage, and the dynamic characteristics (such as the change of natural frequency and damping ratio). Sensors with higher sensitivity and wider bandwidth are usually used, such as high-precision acceleration sensors. The sensor layout density is relatively high, and the sensor redundancy at key locations is also increased accordingly. The modal information such as the modal vibration shape, natural frequency, and damping ratio of the bridge structure can be obtained through modal analysis; the time-frequency characteristics of the vibration signal can be analyzed through wavelet analysis, which is helpful to identify local damage of the bridge; the bridge deflection can be obtained through mathematical methods to monitor the small deformation of the bridge.

[0004] At present, the layout of bridge vibration monitoring sensors in high-intensity areas mainly adopts a multi-point, high-density layout method. Although this method can obtain more monitoring data, it also has the following problems: 1. The excessive number of sensors leads to increased costs and complex data processing; 2. Data redundancy, the collected data are highly correlated, which increases the difficulty of data processing; 3. It is difficult to optimize the layout. Finding the best sensor layout plan is a complex optimization problem that requires comprehensive consideration of multiple factors.

[0005] The structural form of a T-beam bridge determines that its vibration modes in different parts will be different. The coupling between the rib beam part of the T-beam (i.e. the top of the T) and the bridge deck will cause vibration responses of different frequencies and directions, and these vibration characteristics may vary significantly in different locations. Therefore, the layout of sensors needs to take into account the vibration responses of different parts of the T-beam bridge, especially on components with high stress or critical components, such as piers, beam bottoms and rib beams. Reasonable layout of accelerometers can help accurately capture these local responses, thereby more effectively performing bridge health monitoring and fault diagnosis. Summary of the invention

[0006] Purpose of the invention: In view of the above problems, the present invention provides a method for optimizing the arrangement of sensors for vibration monitoring of a T-beam bridge.

[0007] Technical solution: A sensor optimization arrangement method for T-beam bridge vibration monitoring, comprising the following steps:

[0008] S1. Preliminarily formulate a measurement point group and determine the modal order of interest based on the modal results of the T-type bridge obtained by finite element model and / or field measurement;

[0009] S2. Based on the modal vibration matrix of the bridge in the finite element model results, the maximum diagonal element value of the corresponding MAC matrix and the trace of the Fisher information matrix are derived, and the degrees of freedom of the MAC matrix and the Fisher information matrix are increased or decreased through the correction matrix to meet the monitoring requirements;

[0010] S3. Based on the actual measurement and historical data, comprehensively consider whether the values ​​of the above two parameters are within the optimal range;

[0011] S4. If it is within the optimal range, then the measurement point group is the optimal arrangement of the best vibration sensor. If it is not within the optimal range, the correction matrix is ​​applied to the MAC matrix and the Fisher information matrix respectively, and the parameter values ​​after each correction are compared. The measurement point group under the optimal parameter value is taken as the optimal arrangement of the vibration sensor.

[0012] Furthermore, step S1 first obtains the modal vibration shape, modal frequency and damping ratio of the beam bridge under the environmental vibration test by deploying several vibration measuring points on the beam bridge, and then compares the modal parameter results in the finite element analysis of the beam bridge with the results under the environmental measurement, and takes the first n-order modes with similar results as the monitoring objects of interest.

[0013] After determining the first n modes, the degrees of freedom of the measuring point group are preliminarily determined based on experience and finite element analysis results, and the values ​​of the off-diagonal elements of the MAC matrix and the trace of the Fisher information matrix under this degree of freedom are determined; subsequently, the structural degrees of freedom are changed by adding or reducing the measuring point group, so that the values ​​of the off-diagonal elements of the MAC matrix are as small as possible and the trace of the Fisher information matrix is ​​as large as possible.

[0014] Furthermore, the method firstly characterizes the spatial angle characteristics between the bridge vibration mode vectors through the MAC matrix, and the expression of the element in the i-th row and j-th column is as follows:

[0015]

[0016] In the formula, Φ i and Φ j is the vibration mode vector of the i-th mode and the j-th mode. The off-diagonal elements in the MAC matrix reflect the angle between the corresponding two mode vibration mode vectors, and its value is between 0 and 1. The smaller the off-diagonal elements of the MAC matrix, the better the independence of the vibration modes of each order calculation, and the better the sensor configuration effect. On the contrary, it means that the correlation of the vibration modes of each order calculation is greater, and the sensor configuration effect is worse.

[0017] Preferably, the values ​​of the non-diagonal elements of the MAC matrix do not exceed 0.25.

[0018] In order to further improve the rationality of sensor arrangement, the method adopts MAC matrix control method to obtain the optimal arrangement of sensors, and introduces Fisher information matrix for control;

[0019] For the modal test of the structure, when the input excitation can fully excite the mode of the structure, the Fisher information matrix is ​​expressed as follows:

[0020]

[0021] In the formula, is a static Gaussian white noise, which is generally a constant value for a specific measurement process, so the Fisher information matrix is ​​simplified to the following form:

[0022] Q=Φ T Φ

[0023] Where Φ is the vibration mode vector of a certain order mode. In actual situations, the arrangement of sensors can be optimized by the size of the trace of the Fisher information matrix. The larger the trace of the Fisher information matrix, the better the arrangement method of the sensors, and vice versa.

[0024] Furthermore, the degree of freedom of the MAC matrix diagonal element value and the Fisher information matrix is ​​increased by modifying the matrix, including:

[0025] Assume that the modal order of the structure to be concerned is n, the first selected measurement degree of freedom is m, the total number of degrees of freedom of the structure is M, and the remaining number of degrees of freedom of the structure is q is a generalized coordinate, and the corresponding modal vector matrix is ​​expressed as follows:

[0026] φ m×n =[φ 1 (q 11 ,q 21 ,...,q m1 ) m×1 ,φ 2 (q 12 ,q 22 ,...,q m2 ) m×1 ,...,φ n (q 1n ,q 2n ,...,q mn ) m×1 ] m×n

[0027]

[0028]

[0029]

[0030]

[0031] Correction matrix The first k items of Right now:

[0032]

[0033] The element values ​​of the MAC matrix are:

[0034]

[0035] The modified MAC matrix and Fisher information matrix are:

[0036]

[0037]

[0038] Theoretically, it is necessary to compare the modified MAC matrix off-diagonal element values ​​and the Fisher information matrix trace under different k values. During the operation, in order to simplify the calculation, the percentage of weakening of the largest off-diagonal element of the MAC matrix by the modified matrix is ​​ΔM, and the percentage of increasing the Fisher information matrix trace is ΔF. The correction effect of the modified matrix on the two can be recorded as ΔMF, that is:

[0039] ΔMF=αΔM+(1-α)ΔF

[0040] Where α is the weight coefficient, and its value range is 0 to 1. The value of α can be changed according to different requirements to obtain the desired optimal arrangement of sensors.

[0041] Furthermore, the method includes an optimized arrangement of sensors suitable for vibration monitoring of T-beam bridges in high-intensity earthquake zones.

[0042] Beneficial effects: The present invention optimizes the arrangement of the detection positions of beam bridge sensors based on the modal confidence matrix and the Fisher information matrix, achieves the minimum detection positions and the best monitoring effect in combination with the correction matrix, and establishes the data correlation between sensors, avoiding the increase in costs and the complexity of data processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the process of the method of the present invention;

[0044] Figure 2 This is the overall finite element model diagram of the T-beam bridge;

[0045] Figure 3 shows the first six vibration modes of the beam bridge structure. Figure 3(a)-Figure 3(f) They are the vibration mode diagrams of order 1 to 6 respectively;

[0046] Figure 4 Schematic diagram of the preferred measurement point arrangement in the embodiment. DETAILED DESCRIPTION

[0047] To explain the technical solution provided by the present invention in detail, further introduction is given below in conjunction with the accompanying drawings.

[0048] For bridge monitoring tasks in high-intensity areas, in addition to meeting the measurement point layout principles for bridges in general areas, a large number of acceleration sensors will also be arranged at key nodes of the bridge structure, such as mid-span, supports, piers, main beam connections, key sections, etc. Compared with bridges in general areas, the sensor layout is more dense, which increases the hardware cost and subsequent data analysis cost. Based on this, the present invention provides a sensor optimization layout method for T-beam bridge vibration monitoring, which is a modal confidence (MAC) matrix and Fisher information matrix (FIM) optimization layout method suitable for T-beam bridge vibration monitoring in high-intensity earthquake areas.

[0049] In order to realize the sensor optimization layout method for vibration monitoring of T-beam bridges in high-intensity earthquake zones, it is necessary to arrange as many vibration measurement points as possible on a reasonable basis, and obtain the modal vibration shape, modal frequency and damping ratio of the beam bridge under environmental vibration test. Then, the modal parameter results in the finite element analysis of the beam bridge are compared with the results under environmental measurement, and the first n-order modes with similar results are taken as key monitoring objects.

[0050] After determining the first n-order modes to be monitored, the degrees of freedom of the measuring point group are preliminarily determined based on experience and finite element analysis results, and the values ​​of the non-diagonal elements of the MAC matrix and the trace of the Fisher information matrix under this degree of freedom are determined; subsequently, the structural degrees of freedom are changed by adding or reducing the measuring point group, and the MAC matrix and the Fisher information matrix also change accordingly.

[0051] According to the MAC matrix and FIM optimization layout method, the value of the non-diagonal element of the MAC matrix is ​​required to be as small as possible, ideally equal to 0, and the maximum value is generally recommended to be 0.25; at the same time, for the Fisher information matrix, the trace of the matrix is ​​required to be as large as possible. There is a measurement point group, under the arrangement of this measurement point group, the value of the non-diagonal element of the MAC matrix is ​​small, and the trace of the Fisher information matrix is ​​also large. At this time, the measurement point group is the optimal arrangement method for vibration measurement points.

[0052] Further, combined with Figure 1 , the steps of the method of the present invention include:

[0053] S1. Preliminarily formulate a measurement point group and determine the modal order of interest based on the modal results of the T-type bridge obtained by finite element model and / or field measurement;

[0054] S2. Based on the modal vibration matrix of the bridge in the finite element model results, the maximum diagonal element value of the corresponding MAC matrix and the trace of the Fisher information matrix are derived, and the degrees of freedom of the MAC matrix and the Fisher information matrix are increased or decreased through the correction matrix to meet the monitoring requirements;

[0055] S3. Based on the actual measurement and historical data, comprehensively consider whether the values ​​of the above two parameters are within the optimal range;

[0056] S4. If it is within the optimal range, then the measurement point group is the optimal arrangement of the best vibration sensor. If it is not within the optimal range, the correction matrix is ​​applied to the MAC matrix and the Fisher information matrix respectively, and the parameter values ​​after each correction are compared. The measurement point group under the optimal parameter value is taken as the optimal arrangement of the vibration sensor.

[0057] We modeled a T-beam bridge in a high-intensity area in Xuzhou and performed modal analysis. The finite element model is as follows Figure 2 As shown in Figure 2, the first six modal vibration shapes of the structure are the focus of attention in an earthquake. Figure 3(a)-Figure 3(f) The first six modal vibration shapes of the T-beam bridge are given.

[0058] Ideally, each natural frequency of the structure corresponds to a modal vibration mode, and the modal vibration mode vectors of different frequencies are mutually orthogonal. In actual situations, affected by the measurement point layout, instrument accuracy, environmental noise, etc., the measured modal vibration mode vectors of different frequencies cannot maintain their orthogonality well, and may even cause the angle vector between the modal vibration mode vectors to be too small, resulting in the loss of some important modes. Therefore, the selection of a suitable measurement point group can ensure that some important modes are not lost as much as possible and to a large extent guarantee the orthogonality of the modal vibration mode. According to existing research, the modal confidence (MAC) matrix can be used to reflect the spatial angle characteristics between different vibration mode vectors, and the expression of its i-th row and j-th column element is as follows:

[0059]

[0060] In the formula, Φ i and Φ j are the vibration mode vectors of the i-th mode and the j-th mode. The off-diagonal elements in the MAC matrix reflect the angle between the corresponding two modal vibration mode vectors, and their values ​​are between 0 and 1. The smaller the off-diagonal elements of the MAC matrix, the better the independence of the vibration modes of each order calculation, and the better the sensor configuration effect. Conversely, it means that the greater the correlation of the vibration modes of each order calculation, the worse the sensor configuration effect. Therefore, the arrangement of the measuring point group should make the value of the off-diagonal element of the MAC matrix tend to 0. In actual situations, its maximum value is generally 0.25. In order to further improve the rationality of the sensor layout, the present invention introduces the Fisher information matrix for control on the basis of adopting the MAC matrix control method to obtain the optimal arrangement of the sensor. For the modal test of the structure, when the input excitation can fully excite the mode of the structure, the Fisher information matrix can be expressed as follows:

[0061]

[0062] In the formula, is a static Gaussian white noise, which is generally a constant value for a specific measurement process, so the Fisher information matrix can be simplified into the following form:

[0063] Q=Φ T Φ (3)

[0064] Where Φ is the vibration mode vector of a certain order mode. In actual situations, the arrangement of sensors can be optimized by the size of the trace of the Fisher information matrix. The larger the trace of the Fisher information matrix, the better the arrangement method of the sensors, and vice versa.

[0065] In the actual measurement point group selection process, the values ​​of the MAC matrix diagonal elements and the Fisher information matrix trace of the first selected measurement points are difficult to meet the requirements. Therefore, it is necessary to increase or decrease the degrees of freedom of the above two matrices, that is, to introduce a correction matrix to re-examine whether the indicators of the corrected matrix meet the relevant requirements. Assume that the structural modal order to be concerned is n, the first selected measurement degree of freedom is m, the total number of degrees of freedom of the structure is M, and the remaining number of structural degrees of freedom is q is a generalized coordinate, then the corresponding modal vector matrix can be expressed as follows:

[0066] φ m×n =[φ 1 (q 11 ,q 21 ,...,q m1 ) m×1 ,φ 2 (q 12 ,q 22 ,...,q m2 ) m×1 ,...,φ n (q 1n ,q 2n ,...,q mn ) m×1 ] m×n (4)

[0067]

[0068] Correction matrix The first k items of Right now:

[0069]

[0070] From equations (1) and (4), we can get that the element value of the MAC matrix is:

[0071]

[0072] The modified MAC matrix and Fisher information matrix are:

[0073]

[0074]

[0075] Theoretically, it is necessary to compare the modified MAC matrix off-diagonal element values ​​and the Fisher information matrix trace under different k values. During the operation, in order to simplify the calculation, the percentage of weakening of the largest off-diagonal element of the MAC matrix by the modified matrix is ​​ΔM, and the percentage of increasing the Fisher information matrix trace is ΔF. The correction effect of the modified matrix on the two can be recorded as ΔMF, that is:

[0076] ΔMF=αΔM+(1-α)ΔF (10)

[0077] In the formula, α is the weight coefficient, and its value range is 0 to 1. The value of α can be changed according to different requirements to obtain the desired optimal arrangement of sensors.

[0078] From the above modal analysis results, it can be seen that the vibration peaks of the bridge are basically located at the mid-span, 1 / 4 span and one side support of the structure. Based on the analysis results and experience, the initial selected measuring points are as follows: Figure 4 As shown in the figure, there are 66 measuring points on each beam, totaling 264 measuring points. The measuring points are arranged as follows: 1 on the bottom plate of the support, 2 on the web, and 3 on the flange. This arrangement method is also used near the mid-span and 1 / 4 span.

[0079] For other measuring points, their layout abbreviations and layout descriptions are shown in Table 1 below.

[0080] Table 1. Abbreviations and descriptions of measurement point group layout

[0081]

[0082] The weakening effects of different measurement point group arrangements on the non-diagonal elements of the MAC matrix are shown in Tables 3 to 10. The first row and second column of the percentage data in the table represent the weakening percentage of the matrix element MAC12, and the other data are similar. Table 11 lists the percentage increase of the Fisher information matrix of each measurement point group.

[0083] Table 2. Weakening effect of measuring point group I (55_1up_w)

[0084]

[0085] Table 3. Weakening effect of measurement point group II (55_1down_w)

[0086]

[0087] Table 4. Weakening effect of measurement point group III (55_2side_f)

[0088]

[0089] Table 5. Weakening effect of point group IV (44_1mid_f)

[0090]

[0091] Table 6. Weakening effect of measurement point group V (33_1f_1w)

[0092]

[0093] Table 7. Weakening effect of measurement point group VI (21_1f_1w_1s)

[0094]

[0095] Table 8. Weakening effect of measurement point group VII (15_1f_1w)

[0096]

[0097]

[0098] Table 9. Weakening effect of measurement point group VIII (9_1f_1w_1s)

[0099]

[0100] Table 10. Effect of increasing the trace of the Fisher information matrix

[0101]

[0102] Substituting the data in Tables 2 to 10 into formula (11), the values ​​of the correction effect ΔMF of each measuring point group are obtained and listed in Table 12. According to actual needs, α is taken as 0.9.

[0103] Table 11. ΔMF values ​​for each measurement point group

[0104]

[0105]

[0106] According to the data in the table above, it can be concluded that the sensor layout effects of this type of T-beam bridge are ranked from best to worst as follows: 9_1f_1w_1s>15_1f_1w>21_1f_1w_1s>55_1up_w>65 (initial layout)>55_1down_w>55_2side_f>44_1mid_f>33_1f_1w. According to actual usage, combined with factors such as layout cost, the 9_1f_1w_1s layout method is preferred to obtain relatively complete structural vibration shape data as much as possible on the basis of low control cost, and obtain better vibration measurement results.

[0107] The method of the present invention can comprehensively consider the rationality of the layout cost and the structural vibration mode data, and the calculation method is convenient and fast, and can provide a reference for the layout of vibration sensors for T-type bridges without experimental conditions.

Claims

1. A sensor optimization arrangement method for T-beam bridge vibration monitoring, characterized in that the steps include: S1. Preliminarily formulate a measurement point group and determine the modal order of interest based on the modal results of the T-type bridge obtained by finite element model and / or field measurement; S2. Based on the modal vibration matrix of the bridge in the finite element model results, the maximum diagonal element value of the corresponding MAC matrix and the trace of the Fisher information matrix are derived, and the degrees of freedom of the MAC matrix and the Fisher information matrix are increased or decreased through the correction matrix to meet the monitoring requirements; S3. Based on the actual measurement and historical data, comprehensively consider whether the values ​​of the above two parameters are within the optimal range; S4. If it is within the optimal range, the measuring point group is the layout position of the vibration sensor. If it is not within the optimal range, the correction matrix is ​​applied to the MAC matrix and the Fisher information matrix respectively, and the parameter values ​​after each correction are compared. The measuring point group under the optimal parameter value is taken as the optimal layout of the vibration sensor.

2. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to claim 1 is characterized in that: Step S1 firstly obtains the modal vibration shape, modal frequency and damping ratio of the beam bridge under the environmental vibration test by deploying several vibration measuring points on the beam bridge, and then compares the modal parameter results in the finite element analysis of the beam bridge with the results under the environmental measurement, and takes the first n-order modes with similar results as the monitoring objects of interest.

3. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to claim 2 is characterized in that: After determining the first n modes, the degrees of freedom of the measuring point group are preliminarily determined based on experience and finite element analysis results, and the values ​​of the off-diagonal elements of the MAC matrix and the trace of the Fisher information matrix under this degree of freedom are determined; subsequently, the structural degrees of freedom are changed by adding or reducing the measuring point group so that the values ​​of the off-diagonal elements of the MAC matrix are as small as possible and the trace of the Fisher information matrix is ​​as large as possible.

4. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to claim 1 is characterized in that: The method firstly characterizes the spatial angle characteristics between the bridge vibration shape vectors through the MAC matrix, and the expression of the element in the i-th row and j-th column is as follows: In the formula, Φ i and Φ j is the vibration mode vector of the i-th mode and the j-th mode. The off-diagonal elements in the MAC matrix reflect the angle between the corresponding two mode vibration mode vectors, and its value is between 0 and 1. The smaller the off-diagonal elements of the MAC matrix, the better the independence of the vibration modes of each order calculation, and the better the sensor configuration effect. On the contrary, it means that the correlation of the vibration modes of each order calculation is greater, and the sensor configuration effect is worse. In order to further improve the rationality of sensor arrangement, the method adopts MAC matrix control method to obtain the optimal arrangement of sensors, and introduces Fisher information matrix for control; For the modal test of the structure, when the input excitation can fully excite the mode of the structure, the Fisher information matrix is ​​expressed as follows: In the formula, is a static Gaussian white noise, which is generally a constant value for a specific measurement process, so the Fisher information matrix is ​​simplified to the following form: Q=Φ T F Where Φ is the vibration mode vector of a certain order mode. In actual situations, the arrangement of sensors can be optimized by the size of the trace of the Fisher information matrix. The larger the trace of the Fisher information matrix, the better the arrangement method of the sensors, and vice versa.

5. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to claim 4 is characterized in that: The processing of increasing the degree of freedom of the diagonal element value of the MAC matrix and the Fisher information matrix by modifying the matrix includes: Assume that the modal order of the structure to be concerned is n, the first selected measurement degree of freedom is m, the total number of degrees of freedom of the structure is M, and the remaining number of degrees of freedom of the structure is q is a generalized coordinate, and the corresponding modal vector matrix is ​​expressed as follows: φ m×n =[φ1(q 11 ,q 21 ,...,q m1 ) m×1 ,φ2(q 12 ,q 22 ,...,q m2 ) m×1 ,...,φ n (q 1n ,q 2n ,...,q mn ) m×1 ] m×n Correction matrix The first k items of Right now: Therefore, the element values ​​of the MAC matrix are: The modified MAC matrix and Fisher information matrix are: Theoretically, it is necessary to compare the modified MAC matrix off-diagonal element values ​​and the Fisher information matrix trace under different k values. To simplify the calculation, the percentage of weakening of the largest off-diagonal element of the MAC matrix by the modified matrix is ​​ΔM, and the percentage of increasing the Fisher information matrix trace is ΔF. The modification effect of the modified matrix on the two is ΔMF, that is, ΔMF=αΔM+(1-α)ΔF Where α is the weight coefficient, and its value range is 0 to 1. The value of α can be changed according to different requirements to obtain the desired optimal arrangement of sensors.

6. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to any one of claim 3, characterized in that: The values ​​of the off-diagonal elements of the MAC matrix do not exceed 0.

25.

7. The sensor optimization arrangement method for T-beam bridge vibration monitoring according to any one of claim 1, characterized in that: The method includes an optimized arrangement of sensors suitable for vibration monitoring of T-beam bridges in high-intensity earthquake zones.

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