Multi-moving load identification method based on displacement influence line
By combining influence line-based methods and nonlinear least squares methods with displacement sensor data, accurate identification of the loads of multiple vehicles on a bridge is achieved, solving the problem of insufficient accuracy in identifying the loads of multiple vehicles in existing technologies, reducing noise interference, and making it suitable for practical engineering.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-10
AI Technical Summary
Existing technologies struggle to accurately identify bridge moving loads caused by multiple vehicles operating simultaneously, and vibration responses are susceptible to data noise interference, resulting in insufficient identification accuracy.
By adopting an influence line-based method, the correspondence between the influence line function and the unknown load displacement response function is calibrated, and displacement sensor data is combined to identify single-vehicle, dual-vehicle, and multi-vehicle loads. The key parameters are then solved using the nonlinear least squares method.
It improves the accuracy and applicability of load identification, reduces noise interference, and is suitable for identifying multiple moving loads in practical engineering.
Smart Images
Figure CN121834097A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the technical field of bridge engineering structure health monitoring and load identification, and particularly relates to a multiple moving load identification method based on influence line, which is especially suitable for dynamic load identification of medium and large span bridges under the condition of vehicle passing. BACKGROUND
[0002] Moving load identification is a key technology in bridge structure health monitoring and evaluation, and its identification accuracy directly affects the safe operation of the bridge. Existing researches are mostly focused on bridge moving load identification under single vehicle working condition, while in actual engineering, bridges usually bear the action of multiple vehicle synchronous moving loads, resulting in more complex structural response. Therefore, the single moving load identification method has obvious limitations in actual application. At the same time, many studies focus on the specific process of vibration response, but this process is easily disturbed by data noise. In contrast, the method based on influence line analyzes the overall characteristics of vibration response time history from the overall perspective, which is less sensitive to load noise and more suitable for multiple moving load identification in actual application. SUMMARY
[0003] The present application aims to provide a multiple moving load identification method based on influence line, which realizes the identification of single vehicle load, double vehicle load and multiple vehicle load by calibrating the corresponding relationship between influence line function and unknown load displacement response function, and can also solve key parameters such as vehicle spacing, thereby improving the identification accuracy.
[0004] To achieve the above technical problems, the technical solution of the present application is as follows:
[0005] A multiple moving load identification method based on influence line, comprising the following steps:
[0006] S1: Displacement sensor layout and data acquisition
[0007] A displacement sensor is laid out on the bridge to be monitored for real-time acquisition of displacement response of the bridge under the action of moving load; the displacement data acquired by the displacement sensor can be stably transmitted to the receiving end;
[0008] S2: Calibration function construction under single known load
[0009] A vehicle with a known load size P passes through the bridge at a constant speed, and the displacement sensor acquires the displacement time history data at the installation position in real time; after time normalization processing of the displacement time history data, function fitting is performed with the moving distance of the moving load on the bridge as the independent variable, and the obtained result is defined as the calibration influence line function , which is used to represent the standardized response of the position of the displacement sensor of the bridge under the action of the known moving load;
[0010] It should be noted that the calibrated influence line function is not a strictly stable function. The influence line is the result of the inversion of the vibration response generated by the known moving load acting on the bridge structure, and its essence is an equivalent representation of the relationship between the structural response and the load position. For the convenience of subsequent data processing and analysis, this paper approximates it as a function.
[0011] Since the calibration process depends on the measured response data, it is sensitive to various factors, including the structural parameters of the bridge itself, the load level of the calibration vehicle, the test environmental conditions, and the arrangement position of the displacement sensor, etc. The above factors may have different degrees of influence on the calibration results of the influence line.
[0012] S3: Single unknown moving load identification:
[0013] When a vehicle with an unknown load size F passes through the bridge at a constant speed, the displacement response of the displacement sensor is obtained and fitted into a function d(x); through the corresponding relationship between d(x) and the calibration function , a solution model of the unknown load F is established, and the identification of the single unknown moving load is realized accordingly;
[0014] ,
[0015] then: ,
[0016] ;
[0017] where L represents the length of the bridge, and in the mathematical sense represents the integral of the corresponding function from 0 to L, and in practical application represents the displacement influence line coverage area of the corresponding moving load on the bridge;
[0018] S4: Double moving load parameter identification:
[0019] When two groups of vehicles with unknown load sizes F1 and F2 pass through the bridge at a constant speed, and their relative distance H remains unchanged but cannot be predicted, the displacement response is also obtained by the displacement sensor and fitted to obtain the corresponding displacement function; combined with the superposition response relationship when two moving loads act, a multi-parameter equation containing F1, F2 and H is established;
[0020] ,
[0021] Further solve the unknown loads F1 and F2 by using the application influence area:
[0022] ,
[0023] ,
[0024] ,
[0025] Since the functions are linearly independent, the nonlinear least squares method is used to solve F1, F2 and H together;
[0026] S5: Multiple moving load extension identification:
[0027] When m vehicle loads, each maintaining a constant relative distance, are simultaneously moving at a uniform speed on a bridge, the superposition response relationship under the action of these m moving loads is used to establish a system containing F1, F2, ..., F... m and h1, h2, ..., h m-1 A system of multi-parameter equations, where h1, h2, ..., h m-1 They represent the first The distance between the load of vehicle m and the loads of the remaining m-1 vehicles;
[0028] ,
[0029] ,
[0030] ,
[0031] ...
[0032] ,
[0033] ,
[0034] ...
[0035] h m-2 , L+ h m-1 ],
[0036] There are 2m-1 linearly independent function formulas and 2m-1 parameters to be determined. The nonlinear least squares method is used to determine the unknown vehicle loads F1, F2, ..., F... mDistances h1, h2, ..., h between the loads of vehicles and adjacent vehicles m-1 Perform a joint solution.
[0037] Furthermore, step S1 also includes a step in which the processor digitizes, filters, and performs validity processing on the displacement data collected by the displacement sensor.
[0038] Furthermore, in step S2, when normalizing the displacement data, a smoothing process is also performed.
[0039] Furthermore, in step S2, the known calibration function of the loaded vehicle is constructed and repeated tests are conducted multiple times to obtain stable and consistent displacement response data. During the multiple tests, the driving speed of the known loaded vehicle must be kept consistent to ensure the consistency of the time scale of the calibration function φ(x).
[0040] Furthermore, the speed of the moving load vehicle in steps S3 and S4 must remain constant, but the constant speed for different tests can be different.
[0041] Furthermore, the vehicle wheelbase l should not exceed 1 / 40 of the bridge span.
[0042] Furthermore, in step S1, there are multiple displacement sensors, which are installed at different locations on the bridge structure.
[0043] Furthermore, in the calibration function construction process described in S2, the same data processing and function fitting are performed on the displacement time history data collected by multiple displacement sensors, and the calibration influence line functions are respectively... , where i=1,2,…,n, and n is the number of displacement sensors.
[0044] Furthermore, in the process of identifying unknown loads in S3, S4, and S5, the same data processing and function fitting are performed on the displacement time history data under unknown loads collected by multiple displacement sensors. Load identification and spacing are performed using the data from each displacement sensor, and the average value is taken as the final identification result.
[0045] Furthermore, the number of displacement sensors is three, which are evenly distributed along the length of the bridge.
[0046] Compared with other existing studies, the present invention has the following advantages:
[0047] (1) Using the influence surface method for load identification can effectively reduce noise interference and improve identification accuracy.
[0048] (2) It can identify situations where multiple loads move simultaneously, has a wider range of applications, and can meet the needs of actual engineering conditions. Attached Figure Description
[0049] Figure 1 A schematic diagram of the model is shown when a single load moves.
[0050] Figure 2 This is a theoretical diagram of the displacement influence line when a single load moves.
[0051] Figure 3 This is a graph showing the bridge displacement curves monitored by three displacement sensors during a single load movement process.
[0052] Figure 4 The displacement curve is a result of processing the bridge displacement data monitored by three displacement sensors when a single load moves.
[0053] Figure 5 A schematic diagram of a bridge model is shown when two loads are shifting.
[0054] Figure 6 This is a theoretical diagram of the displacement influence lines when two loads move.
[0055] Figure 7 This is a graph showing the actual displacement monitored by three displacement sensors during the two load movements.
[0056] Figure 8 This is a displacement curve graph showing the processed actual displacement data monitored by three displacement sensors during two load movements.
[0057] Specific Implementation Cases
[0058] This invention specifically emphasizes a load identification method for bridges, regardless of the specific form of the bridge. Therefore, to facilitate understanding of the method, the simplest single-span simply supported beam is used as an example to illustrate the method in detail.
[0059] The multi-moving load identification method based on displacement influence lines described in this invention includes the following steps:
[0060] S1: First, a displacement sensor is installed at 1 / 4, 1 / 2 and 3 / 4 of the position under the simply supported beam bridge. The three displacement sensors are used to record the dynamic displacement response of the bridge when vehicles pass.
[0061] S2: A vehicle with a known load P passes over the bridge at a constant speed v, and n displacement sensors acquire displacement time history data corresponding to their positions.
[0062] Since the raw data collected by the displacement sensor uses time as the independent variable, directly solving for the coverage area of the bridge vibration displacement response using time as the independent variable will result in variations with vehicle speed. Therefore, in data processing, the time variable needs to be normalized to eliminate the influence of speed differences on the load identification results, and the displacement response data needs to be converted into a function with the vehicle travel distance as the independent variable.
[0063] The displacement data collected by the i-th displacement sensor is time-normalized and smoothed to obtain the calibration influence line function. , is used to characterize the standardized response of the position I of the i-th displacement sensor of the bridge under a known moving load.
[0064] It should be noted that the calibrated influence line function It is not a stability function in the strict sense. This influence line is the result of inversion of the vibration response of the bridge structure caused by a known moving load, and its essence is an equivalent representation of the relationship between the structural response and the load position. For the convenience of subsequent data processing and analysis, this paper approximates it as a function.
[0065] Since the calibration process relies on measured response data... It exhibits strong sensitivity to various factors, including the bridge's structural parameters, the load level of the calibration vehicle, test environmental conditions, and the placement of the displacement sensors. These factors can all influence the calibration results of the influence lines to varying degrees. Due to the different positions of the displacement sensors, three different displacement sensor locations can yield three different calibration influence line functions. , respectively defined as , , .
[0066] S3: Combination Figure 1 and Figure 2 When a single unknown load F1 moves at a constant speed on a simply supported bridge, the displacement response at position I of the i-th displacement sensor on the bridge is obtained and fitted into a function d. i (x); through d i (x) and the calibration function The correspondence between them is established to build a solution model for the unknown load F1, and based on this, the identification of a single unknown moving load is realized.
[0067] ,
[0068] ,
[0069] ;
[0070] The unknown load F1 is:
[0071] ,
[0072] Where L represents the length of the bridge, This represents the load identified after processing data collected by the i-th displacement sensor at bridge location I. This represents the average identified load obtained after processing data collected from n displacement sensors. and In mathematical terms, it represents the integral of the corresponding function over the interval from 0 to L, while in practical applications, it represents the area covered by the displacement influence line of the corresponding moving load on the bridge.
[0073] In this embodiment, the bridge displacement data measured by the three displacement sensors are shown below. Figure 3 As shown. Taking the data collected by the displacement sensor at the 1 / 4 position as an example, the displacement function fitted by it and the calibration function have the following correspondence.
[0074] ,
[0075] After standardization, the influence of different speeds on the size of the affected area can be eliminated. (See...) Figure 4 As shown in the figure. The result of the displacement sensor at the 1 / 4 position recognizing the load F is shown in the following formula.
[0076] ,
[0077] Similarly, the unknown loads F identified using the bridge displacement data detected by the other two displacement sensors are as follows:
[0078] ,
[0079] ,
[0080] The unknown load F1 is taken as the load F identified by the three displacement sensors. 11 F 12 F 13 The average value, that is: .
[0081] S4: Combination Figure 5 and Figure 6 For two vehicles with unknown loads simultaneously crossing a bridge at a constant speed, let their loads be F1 and F2, and the distance between them be H, which is constant but unknown beforehand. The superimposed displacement response measured by the i-th displacement sensor is fitted as D. i (x). The actual displacement monitoring data at the location of the i-th displacement sensor can be established using the following formula:
[0082] ,
[0083] Further integration of the above response yields the following relationship:
[0084] ,
[0085] ,
[0086] ,
[0087] Since the functions involved in these equations are linearly independent, the nonlinear least squares method can be used to solve F simultaneously. 1j F 2j and vehicle spacing H i This method can achieve accurate identification of dual-vehicle moving loads without requiring vehicle synchronization information or prior spacing.
[0088] Similarly, the load F1, load F2, and vehicle spacing H are taken as the average values of the load and spacing identified by the three displacement sensors, respectively. That is:
[0089] ,
[0090] ,
[0091] ,
[0092] For details on displacement identification and data processing results, please refer to... Figure 7 and Figure 8 .
[0093] S5: When three or more vehicles are on a bridge simultaneously, as long as the vehicle speeds remain relatively stable, the response can be further extended into a linear superposition of multiple loads based on influence line theory. Through a fitting and solving process similar to the previous steps, the magnitudes of multiple moving loads and the relative positions between vehicles can be jointly identified, enabling the method to be extended to multi-vehicle operating conditions.
[0094] Specifically, this embodiment takes the installation of a displacement sensor on a bridge as an example to illustrate the identification process of three or more loads.
[0095] Assuming that m vehicle loads, each maintaining a constant relative distance, are simultaneously traveling at a uniform speed on a bridge, the superposition response relationship under the action of these m moving loads is established, including F1, F2, ..., F... mand h1, h2, ..., h m-1 A system of multi-parameter equations, where h1, h2, ..., h m-1 They represent the first The distance between the load of vehicle m and the loads of the remaining m-1 vehicles.
[0096] ,
[0097] ,
[0098] ,
[0099] ...
[0100] ,
[0101] ,
[0102] ...
[0103] h m-2 , L+ h m-1 ];
[0104] There are 2m-1 linearly independent function formulas and 2m-1 parameters to be determined. The nonlinear least squares method is used to determine the unknown vehicle loads F1, F2, ..., F... m The distances h1, h2 between the loads of the vehicles and the adjacent vehicles are... h m-1 Perform a joint solution.
[0105] It is worth mentioning that the placement of displacement sensors can be flexibly chosen, as long as they can accurately reflect the displacement response when a moving load passes by. There is no limit to the number of displacement sensors; even a single sensor can be used to identify various load parameters F and vehicle spacing H. If multiple sensors are deployed, the average value of the parameter identification results from each sensor can be taken. Using multiple displacement sensors enhances the stability, reliability, and accuracy of the identification results.
[0106] When two or more unknown loads are identified, the speed of the moving load vehicle must be kept constant, but the constant speed can be different for different tests.
[0107] According to some embodiments of the present invention, when the data measured by each displacement sensor is processed and fitted into a function, the calibration function for each position is... The monitoring data functions d(x) and D(x) have a one-to-one correspondence.
[0108] According to some embodiments of the present invention, regarding the influence of vehicle wheelbase on bridge displacement response, although the theoretical model simplifies the vehicle load to a concentrated load, the resulting error is controllable. Taking a simply supported beam and a two-axle vehicle as an example, at the mid-span position, the maximum error between the actual vehicle displacement and the equivalent concentrated force displacement satisfies the following formula.
[0109]
[0110] When the allowable error is 5%, the vehicle wheelbase l should not exceed 1 / 40 of the bridge span to ensure the reliability of the load identification results.
[0111] The number of moving loads can typically be determined based on the initial response data collected by displacement sensors. When a single vehicle passes the location of a displacement sensor, its response signal will show a significant peak; when multiple vehicles pass the bridge sequentially, the structural response signal will show multiple significant peaks. Therefore, the number of moving loads can be determined by identifying and statistically analyzing the number of significant peaks in the initial response data.
[0112] This load identification method has a fundamental premise: it assumes that the vehicle load travels at a constant speed on the bridge, meaning it assumes that the vehicle does not overtake or engage in other abnormal driving behaviors while crossing the bridge. If the vehicle load changes speed, leading to overtaking or other abnormal driving conditions, this method is no longer applicable.
[0113] The goal is simply to accurately reflect the displacement response as the moving load passes by. There is no limit to the number of displacement sensors; a single sensor can solve for each load parameter F and each vehicle distance parameter H. Using multiple displacement sensors further improves the stability and accuracy of the identification results.
[0114] It should be noted that, for those skilled in the art, it is obvious that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
[0115] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.
Claims
1. A method for identifying multiple moving loads based on displacement influence lines, characterized in that, Includes the following steps: S1: Displacement sensor deployment and data acquisition: A displacement sensor is installed on the bridge to be monitored to collect the displacement response of the bridge under moving load in real time; the displacement data collected by the displacement sensor can be stably transmitted to the receiving end. S2: Construction of calibration function under a single known load: A vehicle with a known load of P is driven across a bridge at a constant speed, and a displacement sensor acquires the displacement time history data at its installation location in real time. After time normalization, the displacement time history data is fitted with a function using the moving distance of the moving load on the bridge as the independent variable, and the result is defined as the calibration influence line function. This is used to characterize the standardized response of the bridge's displacement sensor location under a known moving load; S3: Identification of a Single Unknown Moving Load: When a vehicle with an unknown load of F crosses a bridge at a constant speed, the displacement response at the location of the bridge's displacement sensor is acquired and fitted into a function d(x); d(x) is then compared with a calibration function. The correspondence between them is established to build a solution model for the unknown load F, and based on this, the identification of a single unknown moving load is realized. ; Then we have: ; ; Where L represents the length of the bridge, and In mathematical terms, it represents the integral of the corresponding function over the distance from 0 to L, while in practical applications it represents the area covered by the displacement influence line of the corresponding moving load on the bridge. S4: Dual Moving Load Parameter Identification: When two vehicles with unknown loads F1 and F2 pass over a bridge at a constant speed, and their relative distance H remains constant but is unpredictable, displacement sensors are used to obtain the displacement response and fit the corresponding displacement function. Combining the superposition response relationship when the two moving loads are applied, a multi-parameter equation system containing F1, F2 and H is established. , Further, the influence surface is used to solve for the unknown loads F1 and F2: , , , Since the functions are linearly independent, the nonlinear least squares method is used to solve F1, F2 and H together; S5: Multi-moving load extension identification: When m vehicle loads, each maintaining a constant relative distance, are simultaneously moving at a uniform speed on a bridge, the superposition response relationship under the action of these m moving loads is used to establish a system containing F1, F2, ..., F... m and h1, h2, ..., h m-1 A system of multi-parameter equations, where h1, h2, ..., h m-1 They represent the first The distance between the load of vehicle m and the loads of the remaining m-1 vehicles; …… , , …… , h m-2 , L+ h m-1 ], There are 2m-1 linearly independent function formulas and 2m-1 parameters to be determined. The nonlinear least squares method is used to determine the unknown vehicle loads F1, F2, ..., F... m Distances h1, h2, ..., h between the loads of vehicles and adjacent vehicles m-1 Perform a joint solution.
2. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, Step S1 also includes the step of digitizing, filtering and validity processing of the displacement data collected by the displacement sensor by the processor.
3. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, In step S2, when normalizing the displacement data, a smoothing process is also performed.
4. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, In step S2, the calibration function of the known load vehicle is constructed and repeated tests are conducted multiple times to obtain stable and consistent displacement response data. During the multiple tests, the driving speed of the known load vehicle must be kept consistent to ensure the consistency of the time scale of the calibration function φ(x).
5. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, The speed of the moving load vehicle in steps S3 and S4 must be kept constant, but the constant speed for different tests can be different.
6. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, The wheelbase of the vehicle should not exceed 1 / 40 of the bridge span.
7. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, In step S1, there are multiple displacement sensors, which are installed at different locations on the bridge structure.
8. The method for identifying multiple moving loads based on displacement influence lines according to claim 7, characterized in that, In the calibration function construction process described in S2, the same data processing and function fitting are performed on the displacement time history data collected by multiple displacement sensors, and the calibration influence line functions are respectively... , where i=1,2,…,n, and n is the number of displacement sensors.
9. The method for identifying multiple moving loads based on displacement influence lines according to claim 1, characterized in that, In the process of identifying unknown loads in S3, S4, and S5, the displacement time history data under unknown loads collected by multiple displacement sensors are subjected to the same data processing and function fitting. Load identification and spacing are performed using the data from each displacement sensor, and the average value is taken as the final identification result.
10. The method for identifying multiple moving loads based on displacement influence lines according to claim 7, characterized in that, The displacement sensors are three in number and are evenly distributed along the length of the bridge.