Bridge structure early warning method based on mutual verification of displacement, rotation angle and strain

Abstract

A bridge structure early warning method based on displacement, rotation angle, strain mutual verification, calculates bridge overall monitoring index score, sets bridge safety level and coping scheme; the data of the bridge in normal operation is taken as a benchmark, displacement, rotation angle and strain data obtained by real-time monitoring are mutually verified, bridge structure score is calculated, and graded early warning is carried out; the uniform deviation degree and the non-uniform deviation degree of each measuring point compared with the benchmark are calculated, and the deviation degree of each measuring point is comprehensively evaluated, so that the overall state of the bridge structure is evaluated; through the verification of the rotation angle and the displacement, the verification of the strain and the displacement, the more effective monitoring data (displacement data or rotation angle data) is used to calculate the bridge overall monitoring index score, so that the early warning is more accurate; the present application takes the conventional state of the bridge as a benchmark, combines the real-time monitoring data, comprehensively classifies and early warns the bridge, and reflects the safety condition of the bridge structure.

Description

Technical Field

[0001] This invention relates to the field of bridge maintenance technology, specifically to a bridge structure early warning method based on the mutual verification of displacement, rotation angle, and strain. Background Technology

[0002] In recent years, with the rapid development of bridge construction, bridge structures and functions have become increasingly complex, and the scale of projects has grown larger. However, sudden bridge failures have occurred in various countries around the world, leading researchers to believe that research on the health monitoring of bridges during operation is urgently needed. Monitoring the structural condition of bridges can ensure safe operation and prevent accidents; the monitoring information can also provide a basis and guidance for bridge maintenance, repair, and management decisions. However, current methods for monitoring large-scale, multi-degree-of-freedom bridge structures with unknown load excitation only provide structural response information such as displacement, rotation, and strain of individual sections. While this generates massive amounts of monitoring data, it fails to provide accurate and reliable predictions of the overall safety status of the structure or its components. Therefore, extracting parameters that accurately reflect the safety status of bridge structures from the massive amounts of real-time bridge response data and establishing bridge safety prediction models based on this is a critical and urgent problem to be solved.

[0003] In order to comprehensively assess the bridge condition by integrating information from multiple monitoring points, such as displacement, rotation angle, and strain, and thus achieve graded early warning of bridges, a bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain is needed. Summary of the Invention

[0004] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0005] The present invention improves upon the above-mentioned problems. Specifically, the technical problem to be solved by the present invention is to provide a bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain, which has a clear principle and is simple to implement.

[0006] The specific implementation steps of this invention are as follows:

[0007] (1) Select displacement monitoring points, rotation monitoring points, and strain monitoring points;

[0008] (2) Install displacement sensors, rotation sensors and strain sensors at each monitoring point in step 1 on the actual bridge to obtain monitoring data;

[0009] (3) Take 7 days of valid data for each displacement monitoring point and rotation angle monitoring point, and perform data smoothing;

[0010] (4) After processing the statistical data, retrieve the minimum values ​​of displacement and rotation angle from the daily data. The maximum values ​​of displacement and rotation angle in the daily data. Compared with the average of the seven-day data Calculate the average of the daily minimum values. The average of the daily maximum values ,in , Displacement monitoring indicators This is a corner monitoring indicator; Representing the number of days ;

[0011] (5) At regular intervals, compare the rotation angle data and deflection data of each span of the bridge to see if they match. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. By comparing the rotation angle data and deflection data for each span of the bridge, the data from the rotation angle measuring points are used to calculate the corresponding deflection measuring points. That is, the time history curve of deflection at any cross-section of the bridge is obtained from the time history curve of the rotation angle. The average absolute error between the calculated and measured values ​​of all deflection measuring points is then calculated. If the difference is within 15%, the two are considered to be consistent; otherwise, they are considered to be inconsistent. The actual measured value of the deflection measuring point is the data monitored by the displacement sensor.

[0012] (6) If the rotation angle data and deflection data do not match, compare the strain data and deflection data of each span of the bridge to see if they match. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. If they do not match, then calculate the comprehensive score of the bridge's rotation monitoring index. The comparison of strain and deflection data for each span of the bridge refers to: using data from strain measurement points to calculate the corresponding deflection measurement points, and the average absolute error between the calculated and measured values ​​for all deflection measurement points. If the two are within 15%, they are considered to match; otherwise, they are considered not to match.

[0013] (7) Based on the comprehensive score of monitoring indicators Classify bridges into different early warning levels;

[0014] (8) Comprehensive score based on monitoring indicators Classified early warning systems for bridges. =1 or 2;

[0015] Furthermore, the displacement measuring points, rotation measuring points, and strain measuring points are selected from the bridge supports, 1 / 8, 2 / 8, 3 / 8, 1 / 2, 5 / 8, 6 / 8, and 7 / 8 sections along the longitudinal direction, and from the center of the bottom of the bridge cross section in the transverse direction.

[0016] Furthermore, the valid data refers to statistical values ​​with a 95% guarantee rate;

[0017] Furthermore, the data smoothing process refers to smoothing using the "Smooth" function in Matlab;

[0018] Furthermore, the average of the daily minimum values It is derived from the following formula:

[0019]

[0020] The average of the daily maximum values It is derived from the following formula:

[0021]

[0022] in, , Displacement monitoring indicators This is a corner monitoring indicator; ;

[0023] Furthermore, the specified time interval can be selected as 5-30 minutes; by comparing the angle data and deflection data of each span of the bridge, the data of the corresponding deflection measurement points are calculated using the data from the angle measurement points. That is, the time history curve of deflection at any section of the bridge is obtained from the time history curve of the angle. The average absolute error between the calculated and measured values ​​of all deflection measurement points is... If the two are within 15%, they are considered to match; otherwise, they are considered not to match, as detailed below:

[0024] Assuming the bridge has The span is selected on an axis parallel to the central axis of the bridge under test. Angle sensors were deployed at each measuring point, and angle measuring instruments were selected as the angle sensors. The total measurement time was [time missing]. The total length of the bridge to be measured is Take one end of the bridge as the origin of the coordinate system. Any bridge cross-section The deflection time history curve at point is .

[0025] Assuming the bridge under test is in its first stage... The cross-body was set up An angle measuring instrument can be used to measure this. Rotation time history curves at each measuring point .remember time The rotation angle value at each measuring point is Appropriately select the deflection time history curve of the bridge span. This ensures that it satisfies the support deflection boundary value constraint condition for that span of the bridge:

[0026]

[0027] in, For an appropriately selected set of functions, it is A cardinality of a 3D linear space. The selected function satisfies the support deflection boundary value constraint condition. For example, assuming the coordinates of the two supports of this bridge span are respectively... and For settlement without supports, it can be Take as:

[0028]

[0029] for The time corresponds to the first basis functions The coordinate values. Based on actual measurements. Each corner value can be used to establish A system of equations consisting of:

[0030]

[0031] In the formula, Indicates the first The coordinates of the points where the angle measuring instrument is located; and functions respectively and function groups To each The first derivative; the undetermined parameters at this moment can be easily solved using the least squares method. The optimal solution is obtained, thereby determining the bridge deflection time history curve at that moment;

[0032] The deflection value calculated from the rotation angle is compared with the measured value to calculate the average relative error.

[0033]

[0034] like If the angle data matches the deflection data, then the angle data is considered to match; otherwise, the angle data is considered to match.

[0035] “ " " refers to the displacement data actually measured on the bridge by displacement sensors, which is the deflection data; the subscript "1" indicates that this is the first set of comparisons, that is, the comparison between rotation angle and deflection, and "j" indicates the j-th measuring point;

[0036] “ " " refers to the deflection value indirectly calculated through the data from the angle sensor. Similarly, "1" indicates the first set of comparisons, and "j" indicates the j-th measuring point.

[0037] This represents the total number of measurement points.

[0038] Furthermore, comparing the strain and deflection data for each span of the bridge indicates:

[0039] The data from strain gauge points are used to calculate the data from the corresponding deflection gauge points. The average absolute error between the calculated and measured values ​​for all deflection gauge points is... If the two are within 15%, they are considered to match; otherwise, they are considered not to match, as detailed below:

[0040] Using the second integral method of strain, the relationship between structural strain and deformation can be directly established, as shown in the following formula:

[0041]

[0042] In the formula: The vertical deformation at the x-axis coordinate of the structure is positive, with upward being the positive value. The distance of the lower part of the structure from the neutral axis The strain at the point is positive under tension; , They are respectively The angle and deformation at =0, with counterclockwise rotation as positive.

[0043] The deflection value obtained from strain is compared with the measured value to calculate the average relative error.

[0044]

[0045] like If the strain data matches the deflection data, then the strain data is considered to match the deflection data; otherwise, they are considered not to match. This refers to the deflection data actually measured on the bridge using displacement sensors; This refers to the deflection value indirectly calculated using strain sensor data and the second integral of strain. "2" indicates that this is the second set of comparisons, i.e., a comparison between strain data and deflection data. "j" indicates the j-th measurement point. Represents the total number of measuring points;

[0046] Furthermore, the comprehensive score of the monitoring indicators It is calculated using the following formula:

[0047]

[0048] The score represents the non-uniform variation score, referring to the score of the first... The score for non-uniform change of each monitoring indicator is obtained by the following formula:

[0049]

[0050] in, Indicates the first The first monitoring indicator The measurement points and the first The fluctuation and change between individual measuring points can be derived from the following formula:

[0051]

[0052] It refers to the historical average value of the (j+1)th measuring point in the same type of monitoring indicator i;

[0053] For uniformly varying scores, refer to the first... It is derived from the following formula:

[0054]

[0055] in, The evaluation value for each measuring point refers to the value of the first measuring point. The first monitoring indicator The monitoring and evaluation value for each measuring point is obtained from the following formula:

[0056]

[0057] in Indicates the first The first monitoring indicator Current monitoring values ​​at each monitoring point;

[0058] Furthermore, the bridge condition classification refers to scoring the bridge according to monitoring indicators. The bridge monitoring indicators are divided into three levels: green, yellow, and red. The green level refers to the bridge monitoring indicator score. The yellow level refers to the bridge monitoring indicator score: The red level refers to the bridge monitoring indicator score: ;

[0059] Furthermore, the tiered early warning system refers to issuing a yellow alarm when the bridge is at the yellow level and a red alarm when the bridge is at the red level.

[0060] A green alarm indicates that the structure is in a safe and stable state, at which point routine inspections and management can be carried out. When a yellow alarm is displayed, the monitoring unit immediately notifies the maintenance unit to inspect the on-site equipment and records the alarm information, including the location of the alarm, the alarm value, and the normal value. When a red alarm is displayed, the monitoring unit immediately issues a red warning to the maintenance unit. Upon receiving the warning information, the maintenance unit immediately inspects the site, records the alarm information, including the location of the alarm, the alarm value, and the normal value, closes traffic, and carries out bridge repair work.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] First, by monitoring the structural condition of bridges, we can ensure the safe operation of bridges and prevent bridge accidents. At the same time, the monitoring information can provide a basis and guidance for bridge maintenance, repair and management decisions. For large-scale bridge structures with multiple degrees of freedom and unknown load excitation, we can not only obtain structural response information such as displacement, rotation and strain of each structural section, but also obtain accurate and reliable safety status prediction information for the whole structure or components, even with the generation of massive monitoring data.

[0063] Second: Calculate the overall bridge monitoring index score, set the bridge safety level, and formulate response plans; using existing normal operating data of the bridge as a benchmark, cross-validate the displacement, rotation, and strain data obtained from real-time monitoring, calculate the bridge structure score, and conduct graded early warning; by calculating the uniform and non-uniform deviation of each measuring point from the benchmark, the overall state of the bridge structure is assessed by comprehensively considering the deviation of each measuring point; through verification of rotation and displacement, and strain and displacement, more effective monitoring data (displacement data or rotation data) are used to calculate the overall bridge monitoring index score, making the early warning more accurate; this invention uses the normal state of the bridge as a benchmark, combined with real-time monitoring data, to conduct comprehensive graded early warning of the bridge, reflecting the safety status of the bridge structure. The principle of this invention is clear, the implementation is simple, and it has good practical value and economic benefits.

[0064] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating the implementation of an example of the present invention; Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Please see Figure 1 This invention provides a technical solution: a bridge structure early warning method based on the mutual verification of displacement, rotation angle, and strain, comprising the following steps:

[0068] (1) Select displacement monitoring points, rotation monitoring points, and strain monitoring points;

[0069] (2) Install displacement sensors, rotation sensors and strain sensors at each monitoring point in step 1 on the actual bridge to obtain monitoring data;

[0070] (3) Take 7 days of valid data for each displacement monitoring point and rotation angle monitoring point, and perform data smoothing;

[0071] (4) After processing the statistical data, retrieve the minimum values ​​of displacement and rotation angle from the daily data. The maximum values ​​of displacement and rotation angle in the daily data. Compared with the average of the seven-day data Calculate the average of the daily minimum values. The average of the daily maximum values ,in , Displacement monitoring indicators This is a corner monitoring indicator; Representing the number of days ;

[0072] (5) At regular intervals, compare the rotation angle data and deflection data of each span of the bridge to see if they match. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. By comparing the rotation angle data and deflection data for each span of the bridge, the data from the rotation angle measuring points are used to calculate the corresponding deflection measuring points. That is, the time history curve of deflection at any cross-section of the bridge is obtained from the time history curve of the rotation angle. The average absolute error between the calculated and measured values ​​of all deflection measuring points is then calculated. If the difference is within 15%, the two are considered to be consistent; otherwise, they are considered to be inconsistent. The actual measured value of the deflection measuring point is the data monitored by the displacement sensor.

[0073] (6) If the rotation angle data and deflection data do not match, compare the strain data and deflection data of each span of the bridge to see if they match. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. If they do not match, then calculate the comprehensive score of the bridge's rotation monitoring index. Compare the strain and deflection data for each span of the bridge: use the data from strain measurement points to calculate the corresponding deflection measurement points, and calculate the average absolute error between the calculated and measured values ​​for all deflection measurement points. If the two are within 15%, they are considered to match; otherwise, they are considered not to match.

[0074] (7) Based on the comprehensive score of monitoring indicators Classify bridges into different early warning levels;

[0075] (8) Comprehensive score based on monitoring indicators Implement graded early warning systems for bridges;

[0076] In this embodiment, the displacement measuring points, rotation measuring points, and strain measuring points are selected from the bridge supports, 1 / 8, 2 / 8, 3 / 8, 1 / 2, 5 / 8, 6 / 8, and 7 / 8 sections along the longitudinal direction of the bridge, and from the center of the bottom of the bridge cross section along the transverse direction.

[0077] In this embodiment, valid data refers to statistical values ​​with a 95% guarantee rate;

[0078] In this embodiment, data smoothing refers to using the "Smooth" function in Matlab for smoothing, and the code is given below:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] In this embodiment, the average of the daily minimum values It is derived from the following formula:

[0086]

[0087] Average of daily maximum values It is derived from the following formula:

[0088]

[0089] in, , Displacement monitoring indicators This is a corner monitoring indicator; (The same applies below);

[0090] In this embodiment, a certain time interval can be selected as 5-30 minutes; by comparing the rotation angle data and deflection data of each span of the bridge, the data of the corresponding deflection measurement point is calculated using the data of the rotation angle measurement point. That is, the deflection time history curve of any section on the bridge is obtained from the time history curve of the rotation angle. The average absolute error between the calculated value and the measured value of all deflection measurement points is... If the agreement is within 15%, the two are considered to match; otherwise, they are considered to be inconsistent. Specifically: Assume the bridge has... The span is selected on an axis parallel to the central axis of the bridge under test. An angle measuring instrument was set up at each measuring point, and the total measurement time was [time missing]. The total length of the bridge to be measured is Take one end of the bridge as the origin of the coordinate system. Any bridge cross-section The deflection time history curve at point is .

[0091] Assuming the bridge under test is in its first stage... The cross-body was set up A rotation measuring instrument can be used to measure this. Rotation time history curves at each measuring point .remember time The rotation angle value at each measuring point is Appropriately select the deflection time history curve of the bridge span. This ensures that it satisfies the support deflection boundary value constraint condition for that span of the bridge:

[0092]

[0093] in, For an appropriately selected set of functions, it is A cardinality of a 3D linear space. The selected function satisfies the support deflection boundary value constraint condition. For example, assuming the coordinates of the two supports of this bridge span are respectively... and For settlement without supports, it can be Take as:

[0094]

[0095] for The time corresponds to the first basis functions The coordinate values. Based on actual measurements. Each corner value can be used to establish A system of equations consisting of:

[0096]

[0097] In the formula, Indicates the first The coordinates of the points where the angle measuring instrument is located; and functions respectively and function groups To each The first derivative; the undetermined parameters at this moment can be easily solved using the least squares method. The optimal solution is obtained, thereby determining the bridge deflection time history curve at that moment.

[0098] The deflection value calculated from the rotation angle is compared with the measured value to calculate the average relative error.

[0099]

[0100] like If the angle data matches the deflection data, then the angle data is considered to match; otherwise, the angle data is considered to match.

[0101] In this embodiment, comparing the strain data and deflection data for each span of the bridge refers to:

[0102] The data from strain gauge points are used to calculate the data from the corresponding deflection gauge points. The average absolute error between the calculated and measured values ​​for all deflection gauge points is... If the two are within 15%, they are considered to match; otherwise, they are considered not to match, as detailed below:

[0103] Using the second integral method of strain, the relationship between structural strain and deformation can be directly established, as shown in the following formula:

[0104]

[0105] In the formula: The vertical deformation at the x-axis coordinate of the structure is positive, with upward being the positive value. The distance of the lower part of the structure from the neutral axis The strain at the point is positive under tension; , They are respectively The angle and deformation at =0, with counterclockwise rotation as positive.

[0106] The deflection value obtained from strain is compared with the measured value, and the relative error is calculated by averaging.

[0107]

[0108] like If the strain data matches the deflection data, then the strain data is considered to match the deflection data; otherwise, they are considered not to match.

[0109] In this embodiment, the comprehensive score of the monitoring indicators It is calculated using the following formula:

[0110]

[0111] The score represents the non-uniform variation score, referring to the score of the first... The score for non-uniform change of each monitoring indicator is obtained by the following formula:

[0112]

[0113] in, Indicates the first The first monitoring indicator The measurement points and the first The fluctuation and change between individual measuring points can be derived from the following formula:

[0114]

[0115] For uniformly varying scores, refer to the first... It is derived from the following formula:

[0116]

[0117] in, The evaluation value for each measuring point refers to the value of the first measuring point. The first monitoring indicator The monitoring and evaluation value for each measuring point is obtained from the following formula:

[0118]

[0119] in Indicates the first The first monitoring indicator Current monitoring values ​​at each monitoring point;

[0120] In this embodiment, the bridge condition classification refers to scoring the bridge according to monitoring indicators. The bridge monitoring indicators are divided into three levels: green, yellow, and red. The green level refers to the bridge monitoring indicator score. The yellow level refers to the bridge monitoring indicator score: The red level refers to the bridge monitoring indicator score: ;

[0121] In this embodiment, the graded alarm means that a yellow alarm is triggered when the bridge is in the yellow state, and a red alarm is triggered when the bridge is in the red state.

[0122] A green status indicates that the structure is in a safe and stable state, at which point routine inspections and management can be carried out. When a yellow alarm is displayed, the monitoring unit immediately notifies the maintenance unit to inspect the on-site equipment and records the alarm information, including the location of the alarm, the alarm value, and the normal value. When a red alarm is displayed, the monitoring unit immediately issues a red warning to the maintenance unit. Upon receiving the warning information, the maintenance unit immediately inspects the site, records the alarm information, including the location of the alarm, the alarm value, and the normal value, and takes measures such as closing traffic and carrying out bridge repair work if necessary.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A bridge structure early warning method based on the mutual verification of displacement, rotation angle, and strain, the method comprising the following steps: Step 1: Select displacement monitoring points, rotation monitoring points, and strain monitoring points; Step 2: Install displacement sensors, rotation sensors, and strain sensors on the actual bridge according to the monitoring points in Step 1, and acquire monitoring data. Step 3: Take 7 days of valid data for each displacement monitoring point and rotation angle monitoring point, and perform data smoothing. Step 4: After processing the statistical data, retrieve the minimum values ​​of displacement and rotation angle from the daily data. The maximum values ​​of displacement and rotation angle in the daily data. Compared with the average of the seven-day data Calculate the average of the daily minimum values. The average of the daily maximum values ,in , Displacement monitoring indicators This is a corner monitoring indicator; Representing the number of days ; Step 5: At regular time intervals, compare the rotation angle data and deflection data of each span of the bridge to see if they match. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. By comparing the rotation angle data and deflection data for each span of the bridge, the data from the rotation angle measuring points are used to calculate the corresponding deflection measuring points. That is, the time history curve of deflection at any cross-section of the bridge is obtained from the time history curve of the rotation angle. The average absolute error between the calculated and measured values ​​of all deflection measuring points is then calculated. If the difference is within 15%, the two are considered to be consistent; otherwise, they are considered to be inconsistent. The actual measured value of the deflection measuring point is the data monitored by the displacement sensor. Step 6: If the rotation angle data and deflection data do not match, compare the strain data and deflection data for each span of the bridge. If they match, calculate the comprehensive score of the bridge's deflection monitoring index. If they do not match, then calculate the comprehensive score of the bridge's rotation monitoring index. The comparison of strain and deflection data for each span of the bridge refers to: using data from strain measurement points to calculate the corresponding deflection measurement points, and the average absolute error between the calculated and measured values ​​for all deflection measurement points. If the two are within 15%, they are considered to match; otherwise, they are considered not to match. Step 7: Based on the comprehensive score of the monitoring indicators Classify bridges into different early warning levels; Step 8: Based on the comprehensive score of the monitoring indicators Classified early warning systems for bridges. =1 or 2.

2. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 1, characterized in that: The displacement monitoring points, rotation monitoring points, and strain monitoring points are selected along the longitudinal direction of the bridge at the bridge support, and at sections 1 / 8, 2 / 8, 3 / 8, 1 / 2, 5 / 8, 6 / 8, and 7 / 8. In the transverse direction, the points are selected at the center of the bottom of the bridge cross section.

3. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 1, characterized in that: The valid data refers to statistical values ​​with a guarantee rate of over 95%.

4. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 2, characterized in that: The data smoothing process refers to the smoothing process performed using the "Smooth" function in Matlab. ； ； ； ； ； 。 5. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 4, characterized in that: The average of the daily minimum values It is derived from the following formula: ； The average of the daily maximum values It is derived from the following formula: ； in, , Displacement monitoring indicators This is a corner monitoring indicator; .

6. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 5, characterized in that: The specified time interval is 5-30 minutes; the rotation angle data and deflection data of each span of the bridge are compared as follows: Assuming the bridge has The span is selected on an axis parallel to the central axis of the bridge under test. Angle sensors were deployed at each measuring point, and angle measuring instruments were selected as the angle sensors. The total measurement time was [time missing]. The total length of the bridge to be measured is Take one end of the bridge as the origin of the coordinate system. Any bridge cross-section The deflection time history curve at point is ; Assuming the bridge under test is in its first stage... The cross-body was set up An angle measuring instrument can be used to measure this. Rotation time history curves at each measuring point ;remember time The rotation angle value at each measuring point is Appropriately select the deflection time history curve of the bridge span. This ensures that it satisfies the support deflection boundary value constraint condition for that span of the bridge: ； in, For an appropriately selected set of functions, it is A cardinality of a 3D linear space; To select a function that satisfies the support deflection boundary value constraint, assume that the coordinates of the two supports of this bridge span are as follows: and For settlement without supports, Take as: ； for The time corresponds to the first basis functions The coordinate values ​​are based on actual measurements. Each corner value is used to establish... A system of equations consisting of: ； In the formula, Indicates the first The coordinates of the points where the angle measuring instrument is located; and functions respectively and function groups To each The first derivative; the undetermined parameters at this moment can be easily solved using the least squares method. The optimal solution is obtained, thereby determining the bridge deflection time history curve at that moment; The deflection value calculated from the rotation angle is compared with the measured value to calculate the average relative error. ; ； like If the angle data matches the deflection data, then the angle data is considered to match; otherwise, the angle data is considered to match. " " " refers to the displacement data actually measured on the bridge by displacement sensors, which is deflection data; the subscript "1" indicates that this is the first set of comparisons, that is, the comparison between rotation angle and deflection, and "j" indicates the j-th measuring point; " " " refers to the deflection value indirectly calculated through the data from the angle sensor. Similarly, "1" indicates the first set of comparisons, and "j" indicates the j-th measuring point. This represents the total number of measurement points.

7. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 6, characterized in that: The strain and deflection data for each span of the bridge are compared as follows: Using the second integral method of strain, the relationship between structural strain and deformation is directly established, as shown in the following formula: ； In the formula: The vertical deformation at the x-axis coordinate of the structure is positive, with upward being the positive value. The distance of the lower part of the structure from the neutral axis The strain at the point is positive under tension; , They are respectively The angle and deformation at =0, with counterclockwise rotation as positive; The deflection value obtained from strain is compared with the measured value to calculate the average relative error. ; ； like If the strain data matches the deflection data, then the strain data is considered to match; otherwise, the strain data is considered to match. This refers to the deflection data actually measured on the bridge using displacement sensors; This refers to the deflection value indirectly calculated using strain sensor data and the second integral method of strain. "2" indicates that this is the second set of comparisons, i.e., a comparison between strain data and deflection data, and "j" indicates the j-th measurement point. This represents the total number of measurement points.

8. The bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 7, characterized in that: The comprehensive score of the monitoring indicators It is calculated using the following formula: ； The score represents the non-uniform variation score, referring to the score of the first... The scores for non-uniform changes in each monitoring indicator The total number of measuring points is represented by the following formula: ； in, Indicates the first The first monitoring indicator The measurement points and the first The fluctuation and change between individual measuring points can be derived from the following formula: ； It refers to the historical average value of the (j+1)th measuring point in the same type of monitoring indicator i; For uniformly varying scores, refer to the first... The total number of monitoring points corresponding to this type of monitoring indicator is calculated using the following formula: ； in, The evaluation value for each measuring point refers to the value of the first measuring point. The first monitoring indicator The monitoring and evaluation value for each measuring point is obtained from the following formula: ； in Indicates the first The first monitoring indicator The current monitoring value of each measuring point.

9. A bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 8, characterized in that: The early warning level of the bridge refers to the score given to the bridge based on monitoring indicators. The bridge monitoring indicators are divided into three levels: green, yellow, and red. The green level refers to the bridge monitoring indicator score. The yellow level refers to the bridge monitoring indicator score: The red level refers to the bridge monitoring indicator score: .

10. A bridge structure early warning method based on mutual verification of displacement, rotation angle, and strain according to claim 9, characterized in that: The tiered early warning system refers to issuing a yellow alarm when the bridge is at the yellow level and a red alarm when the bridge is at the red level. A green alarm indicates that the structure is in a safe and stable state, at which point routine inspections and management can be carried out. When a yellow alarm is displayed, the monitoring unit immediately notifies the maintenance unit to inspect the on-site equipment and records the alarm information, including the location of the alarm, the alarm value, and the normal value. When a red alarm is displayed, the monitoring unit immediately issues a red warning to the maintenance unit. Upon receiving the warning information, the maintenance unit immediately inspects the site, records the alarm information, including the location of the alarm, the alarm value, and the normal value, closes traffic, and carries out bridge repair work.

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