A prestress monitoring method and system for a high-pier large-span PC continuous rigid frame bridge

Abstract

The present application relates to the technical field of bridge prestress monitoring, in particular to a high-pier large-span PC continuous rigid frame bridge prestress monitoring method and system, the method comprising the following steps: obtaining the external cable force value and the key section internal prestress of the high-pier large-span PC continuous rigid frame bridge; establishing a finite element model of the bridge, inputting the external cable force value as a known load into the finite element model to solve the bridge bending moment distribution, and then calculating the internal prestress, and correcting the calculation result based on the key section internal prestress, temperature and humidity, concrete age and anchoring distance; using the corrected internal prestress to inverse the internal prestress of the whole bridge and calculate the prestress loss rate, and issuing a warning when the prestress loss rate exceeds the prestress loss threshold. The present application only needs to measure the external beam cable force and a small amount of key section internal prestress of the high-pier large-span PC continuous rigid frame bridge, and can obtain the internal prestress of the whole bridge, has high accuracy, strong applicability, and reduces the damage to the bridge structure and the detection cost.

Description

Technical Field

[0001] This invention relates to the field of bridge prestress monitoring technology, and in particular to a prestress monitoring method and system for high-pier, long-span PC continuous rigid frame bridges. Background Technology

[0002] High-pier, long-span prestressed concrete (PC) continuous rigid frame bridges are widely used in highway and railway bridge construction due to their strong span capacity and good overall performance. The prestressed tendons within the structure are the core load-bearing components of these bridges, controlling cracking and limiting mid-span deflection. The effective prestress level within these tendons directly determines the bridge's load-bearing capacity and long-term service performance. Therefore, long-term, continuous, and reliable monitoring of the effective prestress within high-pier, long-span PC continuous rigid frame bridges is crucial for ensuring bridge construction quality and operational safety.

[0003] Currently, there are still some shortcomings in the prestress monitoring of long-span PC continuous rigid frame bridges. On the one hand, the prestressing tendons inside the concrete are embedded, and traditional methods rely on sensors such as fiber optic gratings (FBGs) embedded in the tendons. However, these sensors are expensive, and their survival rate is greatly affected by construction conditions. On the other hand, external prestressing tendons have been increasingly used in the construction and reinforcement of bridges in recent years due to their accessibility, re-tensioning capability, and ease of replacement. Non-destructive testing methods such as magnetic flux sensors can achieve long-term accurate monitoring of the tendon force. However, existing technologies generally treat the external tendon force monitoring data separately from the internal prestress state, only qualitatively judging the prestress loss trend by comparing finite element analysis results. In other words, the structural information carried by the external tendons is not fully explored, while the monitoring of internal prestress still heavily relies on discrete and expensive point sensors, making it difficult to obtain complete information on the prestress field of the entire bridge in an economical and efficient manner. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and system for monitoring the prestress of high-pier, long-span PC continuous rigid frame bridges.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge. The method includes the following steps: acquiring the original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge, and preprocessing them to obtain the external cable force values ​​and the internal prestress of the key sections; establishing a finite element model of the bridge, and inputting the external cable force values ​​as known loads into the finite element model to solve for the bridge bending moment distribution; calculating the internal prestress of the high-pier, long-span PC continuous rigid frame bridge based on the bridge bending moment distribution, and correcting the calculation results based on the internal prestress of the key sections, temperature and humidity, concrete age, and anchorage distance; using the corrected internal prestress to invert the overall internal prestress of the bridge and calculate the prestress loss rate, and issuing an early warning when the prestress loss rate exceeds the prestress loss threshold. This invention only requires measuring the external cable force and a small amount of internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge to obtain the overall internal prestress of the bridge, achieving high accuracy, strong applicability, and reducing damage to the bridge structure and detection costs.

[0006] Optionally, the step of obtaining the original external cable force values ​​and the original internal prestress of key sections of a high-pier, long-span PC continuous rigid frame bridge and performing preprocessing to obtain the external cable force values ​​and the internal prestress of key sections includes the following steps: The original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge were collected. The collected data is filtered and denoised, outlier identification and removal is performed, missing value filling is performed, and resampling is performed to obtain the external cable force value and the internal prestress of the key section.

[0007] Optionally, the step of obtaining the original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge and performing preprocessing to obtain the external cable force values ​​and the internal prestress of key sections further includes: A temperature and humidity-strength correction formula is established, and the external strength value is corrected using the temperature and humidity-strength correction formula.

[0008] Optionally, establishing a finite element model of the bridge and inputting the external cable force values ​​as known loads into the finite element model to solve for the bending moment distribution of the bridge includes the following steps: A finite element model containing geometric information of the internal and external bundles was established based on the design drawings of the high-pier, long-span PC continuous rigid frame bridge. The external cable force values ​​are then input into the finite element model as known loads, and the bending moment distribution of the high-pier, long-span PC continuous rigid frame bridge is obtained by solving the overall structural equilibrium equations.

[0009] Optionally, in the finite element model, the concrete constitutive model adopts a time-varying elastic modulus model that takes into account shrinkage and creep.

[0010] Optionally, the step of calculating the internal prestress of the high-pier, long-span PC continuous rigid frame bridge based on the bridge bending moment distribution, and correcting the calculation results based on the internal prestress of the key sections, temperature and humidity, concrete age, and anchorage distance, includes the following steps: Based on the bending moment distribution inversion, the internal prestress of the high-pier long-span PC continuous rigid frame bridge is obtained, and the internal prestress inversion value is obtained. An error correction model is constructed based on the inverted values ​​of the in-body prestress, the in-body prestress of the key section, temperature and humidity, concrete age and anchorage distance; The error correction model is used to correct the inverted value of the in vivo prestress to obtain the effective value of the in vivo prestress.

[0011] Optionally, an iterative inversion algorithm with physical constraints is used to calculate the effective prestress within the body of a high-pier, long-span PC continuous rigid frame bridge, thereby obtaining the inverted value of the prestress within the body.

[0012] Optionally, the physical constraints include monotonicity constraints, smoothness constraints, and boundary constraints, and the physical constraints are transformed into penalty terms in the objective function of the iterative inversion algorithm using a penalty function method. The monotonic constraint is that from the anchorage end to the mid-span, in the section without the turning block, the prestress in the body gradually decreases; The smoothness constraint is that the average change in prestress between adjacent sections does not exceed a preset change threshold. The boundary constraint is that the prestress within the anchorage end body should be within the range specified according to the design tension value.

[0013] Optionally, the step of constructing an error correction model based on the inverted prestress values, the prestress in the key section, temperature and humidity, concrete age, and anchorage distance includes the following steps: The inverted values ​​of the in-body prestress at the key section are selected and the prestress inversion error is calculated. At the same time, the temperature difference at the key section relative to the reference temperature and the humidity difference relative to the reference humidity are calculated. A dataset is constructed using the in-body prestress inversion values ​​at key sections, the prestress inversion error, the temperature difference, the humidity difference, the concrete age, and the anchorage distance; The prestress inversion value, temperature difference, humidity difference, concrete age, and anchorage distance are used as model inputs, and the prestress inversion error is used as model output. An error correction model is constructed using a support vector regression model and the dataset.

[0014] Secondly, the present invention provides a prestress monitoring system for a high-pier, long-span PC continuous rigid frame bridge. The prestress monitoring system for a high-pier, long-span PC continuous rigid frame bridge includes: a data input device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor, cause the processor to implement the prestress monitoring method for a high-pier, long-span PC continuous rigid frame bridge provided by the present invention.

[0015] In summary, the present invention has at least the following beneficial effects: 1. This invention only requires measuring the cable force of the external tendons and the internal prestress of a small number of key sections. It can obtain the continuous distribution of internal prestress of a high-pier, long-span PC continuous rigid frame bridge through inversion. It does not require a large number of high-cost sensors to be pre-embedded throughout the entire bridge, and reduces the damage to the bridge structure and monitoring costs.

[0016] 2. This invention uses the time-varying elastic modulus of concrete shrinkage and creep, which can reflect the time evolution law of long-term prestress loss, making this invention applicable to both the initial construction stage and long-term monitoring during operation of high-pier, long-span PC continuous rigid frame bridges.

[0017] 3. In obtaining the prestress in the body, this invention adopts an iterative inversion algorithm with physical constraints to overcome the ill-conditioned inversion problem of pure mechanical model. Then, by using the support vector regression model and finite FBG measured data, the inversion results are corrected globally to improve the accuracy of the inversion results.

[0018] 4. A system adapted to the method is provided, which not only improves the practicality of the method but also facilitates its promotion. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating a prestress monitoring method for a high-pier, long-span PC continuous rigid frame bridge according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the frame of a prestressed monitoring system for a high-pier, long-span PC continuous rigid frame bridge according to an embodiment of the present invention. Detailed Implementation

[0021] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0022] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0023] It should be noted in advance that, in one alternative embodiment, except for independent descriptions, the same symbols or letters appearing in all formulas have the same meaning.

[0024] In one optional embodiment, please refer to Figure 1 This invention provides a method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge, the method comprising the following steps: S1. Obtain the original external cable force values ​​and the original internal prestress of the key sections of the high-pier, long-span PC continuous rigid frame bridge, and perform preprocessing to obtain the external cable force values ​​and the internal prestress of the key sections.

[0025] Step S1 specifically includes the following steps: S11. Collect the original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge.

[0026] Specifically, in this embodiment, a magnetic flux sensor (sampling frequency 100Hz) pre-installed on the high-pier, long-span PC (Prestressed Concrete) continuous rigid frame bridge is used to collect the original external cable force values. During installation, the magnetic flux sensor is fitted onto the free section of the cable and fixed with clamps to ensure tight coupling with the cable. For monitoring internal prestress, fiber Bragg grating (FBG) sensors (sampling frequency 50Hz) are pre-embedded outside the prestressing ducts at key sections such as the main beam pier top root section, the main span mid-span section, the main span 1 / 4 section, the high pier control section, and the side span maximum positive bending moment section to collect the original internal prestress at these key sections.

[0027] S12. The collected data is filtered and denoised, outlier identification and removal is performed, missing value filling is performed, and resampling is performed to obtain the external cable force value and the internal prestress of the key section.

[0028] Specifically, in this embodiment, wavelet thresholding denoising is first used to filter the original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge to suppress high-frequency noise. Then, a further method is employed. Outliers were identified and removed based on criteria. Data exceeding the mean ± 3 standard deviations were identified and removed. Lagrange interpolation was used to fill in missing values ​​to ensure data continuity. To address the inconsistency in sampling frequencies between the original external cable force values ​​and the original internal prestress of key sections, cubic spline interpolation was used to resample the external cable force data and internal prestress data, uniformly adjusting them to a synchronous sampling frequency of 20Hz. Finally, the external cable force values ​​and internal prestress of key sections were obtained, providing reliable data support for the subsequent acquisition of the internal prestress of the entire bridge.

[0029] S13. Establish a temperature and humidity-strength correction formula, and use the temperature and humidity-strength correction formula to correct the external strength value.

[0030] Specifically, in this embodiment, the external prestressing tendons are typically arranged outside the box girder (outside the web, below the bottom plate, or inside the box). Although some are protected by sleeves, they are essentially in direct contact with the external environment. The linear expansion coefficient of steel is approximately... When the temperature rises, the steel strand elongates. With the distance between the anchor points at both ends remaining constant, the cable force decreases. Conversely, when the temperature decreases, the cable force increases. In other words, temperature has a direct and immediate effect on the external cable force value. Furthermore, the linear expansion coefficient and elastic modulus of steel are not sensitive to humidity; their changes do not directly lead to changes in the length or stiffness of the steel strand. However, for external cable monitoring using magnetic flux sensors, high humidity environments (such as relative humidity > 80%) may cause slight drift in the sensor's magnetic properties, thus affecting the measurement accuracy of the external cable force value.

[0031] To separate the additional forces caused by thermal expansion and contraction due to temperature, restore the true level of effective prestress, and improve the accuracy of external cable force values, this embodiment establishes a temperature and humidity-cable force correction formula. This formula is then used to correct the external cable force values ​​for subsequent inversion of internal prestress. The temperature and humidity-cable force correction formula satisfies the following relationship: in, The external cable force value at time t after correction, in kN; Let be the external cable force value at time t; The temperature influence coefficient represents the drift in cable force measurement caused by a unit temperature change, and is typically taken as... ; The temperature at time t is measured by a temperature sensor and is expressed in °C. The reference temperature is usually the temperature at which the sensor was installed and calibrated. The humidity effect coefficient represents the drift in cable force measurement caused by a unit change in relative humidity. It can be determined through controlled variable experiments in the laboratory (independent variables are temperature and humidity, dependent variable is...). and To calibrate, generally take directly. However, it is necessary to ensure that the magnetic flux sensor is well packaged. The humidity at time t is measured by a humidity sensor and is expressed in "%RH". The baseline relative humidity is 60%RH.

[0032] In addition, it should be noted that the measured value of the internal prestress (the original internal prestress of the key section) is obtained by the FBG sensor. This type of sensor has a built-in temperature self-compensation mechanism (dual grating differential method) at the hardware level. Its output value is the effective prestress after deducting the influence of temperature. Moreover, the internal prestress is embedded in the concrete, and the influence of humidity on it is negligible. Therefore, there is no need to correct the internal prestress of the key section for temperature and humidity.

[0033] S2. Establish a finite element model of the bridge, and input the external cable force values ​​as known loads into the finite element model to solve for the bending moment distribution of the bridge.

[0034] Step S2 specifically includes the following steps: S21. Based on the design drawings of the high-pier, long-span PC continuous rigid frame bridge, establish a finite element model containing the geometric information of the internal and external bundles.

[0035] Specifically, in this embodiment, Midas Civil is used to construct the finite element model of a high-pier, long-span PC continuous rigid frame bridge. First, the geometric modeling and material definition of the high-pier, long-span PC continuous rigid frame bridge are completed. In Midas Civil, "kN" and "meter (m)" are used as the basic units. Based on the concrete strength grade and prestressed steel specifications given in the design drawings of the high-pier, long-span PC continuous rigid frame bridge, material parameters are defined. The elastic modulus, Poisson's ratio, and coefficient of linear expansion of the concrete can be directly obtained from existing prestressed concrete bridge and culvert design specifications. For material parameters that differ slightly from existing specifications in actual engineering, custom settings can be used. For the variable cross-section box girder of the main beam, only the geometric dimensions of the two control sections at the supports and mid-span need to be input during modeling. Then, the variable cross-section group function of Midas Civil automatically generates the geometric properties of all sections within the entire beam height variation section, with the beam height variation section gradually changing according to a 1.8-order parabola. The bridge piers are modeled as beam units based on the pier cross-section and pier height dimensions in the design drawings. The main pier and the main beam are rigidly connected at the top of the pier by sharing a node, while the side piers and the main beam are connected by setting support boundary conditions according to the drawings.

[0036] Further, prestressing simulation is performed. The simulation of the prestressing system is divided into two parts: internal prestressing tendons and external prestressing tendons. For internal prestressing tendons, since they are embedded inside the concrete box girder through ducts during the construction stage and have a bond with the concrete, the prestressing tendon simulation function built into the software is used for modeling. The specific modeling process is based on existing technology and will not be described in detail here. After modeling, Midas Civil can automatically calculate the prestressing loss caused by friction between the prestressed steel bars and the duct wall (the duct friction coefficient and the influence coefficient of local deviation per meter on friction can be taken according to the existing prestressed concrete bridge and culvert design specifications), the prestressing loss caused by anchor deformation and steel bar retraction, and the prestressing loss caused by concrete elastic compression. At the same time, the program can automatically consider the stress relaxation loss of the prestressed steel bars and the shrinkage and creep loss of the concrete in subsequent stages, and automatically superimpose the prestressing losses of each stage (including friction loss, anchor deformation loss, concrete elastic compression loss, stress relaxation loss, and shrinkage and creep loss) to ensure the accuracy of the total loss calculation.

[0037] The simulation method for externally prestressed tendons in the finite element model differs fundamentally from that for internally prestressed tendons. Force transfer between the externally prestressed tendons and the main beam only occurs at the anchorage points and turning blocks; there is no bond between the externally prestressed tendons and the main beam at other locations. Therefore, the equivalent load method used for internally prestressed tendons cannot be used for simulation. There are two main methods for finite element calculation of external prestressing: one is to add external prestressing in the form of equivalent loads, and the other is to establish separate external tendon elements in the finite element model. Considering that this embodiment requires subsequent inversion of internal prestressing through external cable force values, it is necessary to accurately reflect the mechanical relationship between the external tendon force and the main beam force. Therefore, separate external tendon elements are established in the finite element model. Specifically, nodes are set at the anchorage points and turning block locations of the external tendons, and these nodes are connected using truss elements to establish an independent external tendon element system. The external tendon elements are connected to the main beam nodes at the anchorage points and turning blocks through multi-point constraints, transferring the cable force of the external tendons to the main beam in the form of nodal forces. Subsequently, the external cable force values ​​collected in real time by the magnetic flux sensor need to be applied as external loads to the truss elements, and the internal forces of the external prestressing elements are the external cable force values. When the tension of the external prestressing tendons changes, this change will act on the main beam through the anchor points and steering blocks, thereby changing the bending moment distribution of the entire bridge. This modeling method for external prestressed tendons can better consider the secondary effects of external prestressed tendons, that is, the influence of changes in the lever arm caused by the position of the steering blocks and the deformation of the main beam on the internal forces of the structure when the external cable force values ​​change.

[0038] Furthermore, boundary conditions need to be set. During the construction of the finite element model, the boundary conditions must be set strictly according to the design drawings and actual support layout of the high-pier, long-span PC continuous rigid frame bridge. For high-pier, long-span PC continuous rigid frame bridges, the main piers and main beams are fixed at the pier tops and can be directly connected using shared nodes; supports are set at the tops of the side piers, and the corresponding degrees of freedom are constrained according to the support type, typically constraining vertical displacement and some horizontal displacement, while releasing rotational degrees of freedom. In addition, the pile-soil interaction effect must be considered. Based on the soil layer parameters in the geological survey report, the "m" method is used to equate the constraint effect of the soil around the piles on the pile foundation to soil springs distributed along the pier height, and corresponding elastic supports are applied to each node of the pier body.

[0039] Furthermore, to accurately simulate the impact of concrete shrinkage and creep and the time-varying elastic modulus on the long-term performance of bridge structures, the concrete constitutive model in the finite element model adopts a time-varying elastic modulus model that considers shrinkage and creep. This model describes the growth law of the elastic modulus with age, realizing the definition of time-dependent characteristics, namely: in, The elastic modulus of concrete at an age t (in days), expressed in MPa. The elastic modulus of concrete under standard curing conditions for 28 days; 'b' and 'b' are empirical parameters, dimensionless, and related to concrete strength grade, cement type, and curing conditions. For example, for C50 concrete, b=0.5.

[0040] Finally, the defined time-varying elastic modulus model is associated with the corresponding concrete material, so that the shrinkage and creep effects of concrete and the increase of elastic modulus over time can be automatically considered in the construction stage analysis and long-term operation analysis.

[0041] After completing the geometric modeling, material definition, prestress simulation, boundary setting, and time-dependent characteristic definition of the high-pier, long-span PC continuous rigid frame bridge, thus completing the initial construction of the finite element model, it is necessary to calibrate the key parameters (duct friction coefficient and deviation coefficient) of the finite element model through static load tests. Specifically, under known loading conditions, the measured results of deflection and strain response of key sections are obtained using laser displacement sensors and FBG sensors, respectively. At the same time, the simulated results of deflection and strain response of key sections are obtained using the initially constructed finite element model. The measured results are compared with the simulated results, and the duct friction coefficient and deviation coefficient are continuously adjusted using sensitivity analysis methods until the error between the simulated results and the measured results is within 5%. This yields the calibrated finite element model, which is used as the final finite element model for subsequent in-cell prestress inversion.

[0042] S22. The external cable force value is input into the finite element model as a known load, and the bending moment distribution of the high-pier, long-span PC continuous rigid frame bridge is obtained by solving the overall structural equilibrium equation.

[0043] Specifically, in this embodiment, it is assumed that the structural response is linear and the deformation is small (under normal operating conditions, the applied cable load is relatively small compared to the structural design bearing capacity, and the structural deformation is within the elastic range, so the effects of geometric nonlinearity and material nonlinearity can be ignored; therefore, solving the bending moment distribution based on the linear assumption is sufficiently accurate). Thus, the components of the cable force in the x, y, and z directions can be determined according to the geometric arrangement of the external prestressing tendons (such as horizontal cables and inclined cables). The external cable force values ​​are then input as known loads into the finite element model constructed in step S21. The nodal displacements of each node on the high-pier, long-span PC continuous rigid frame bridge are obtained by solving the overall structural equilibrium equations. The total bending moment of each section is then calculated using the nodal displacements to obtain the bending moment distribution of the high-pier, long-span PC continuous rigid frame bridge. The solution to the bending moment distribution is automatically completed by Midas Civil; therefore, the detailed calculation process will not be described here. The overall structural equilibrium equations satisfy the following relationship: in, For the overall stiffness matrix, Let be the nodal displacement vector. It is the load vector (including dead load, live load, cable force of external prestressed tendons, etc.).

[0044] S3. Calculate the internal prestress of the high-pier, long-span PC continuous rigid frame bridge based on the bending moment distribution of the bridge, and correct the calculation results based on the internal prestress of the key section, temperature and humidity, concrete age and anchorage distance.

[0045] Step S3 specifically includes the following steps: S31. Based on the bending moment distribution, the internal prestress of the high-pier, long-span PC continuous rigid frame bridge is inverted to obtain the internal prestress inversion value.

[0046] Specifically, in this embodiment, to monitor the long-term prestress loss of the high-pier, long-span PC continuous rigid frame bridge over time, and considering that live load bending moment (bending moment contributed by variable loads such as vehicles and pedestrians) is difficult to quantify and instantaneous, it is not considered. Therefore, the total bending moment at each section includes dead load bending moment (bending moment contributed by the structure's self-weight, secondary dead load, etc.), external bending moment (bending moment contributed by external prestressing tendons), and internal bending moment (bending moment contributed by internal prestressing tendons), which can be specifically expressed as follows: in, Let be the internal bending moment at position k, used to represent the actual internal bending moment at position k. K is the number of selected sections; The total bending moment at location k (the coordinate along the longitudinal axis of the bridge, usually with the support at one end of the bridge as the origin and pointing to the other end of the bridge) is expressed in kN·m. The dead load bending moment generated at position k is obtained through finite element model calculation; w is the total number of external prestressing tendons. Let be the external cable force value of the i-th external prestressed tendon at position k; The eccentricity of the i-th external prestressed tendon at position k relative to the neutral axis of the cross section is expressed in meters and can be obtained from the design drawings. The external bending moment at position k is represented by n; n is the total number of internal prestressing tendons. Let be the tension of the j-th internal prestressed tendon at position k, which is the unknown quantity to be inverted; The eccentricity of the j-th internal prestressed tendon at position k relative to the neutral axis of the cross section can be obtained from the design drawings.

[0047] but, The tension is unknown, and there are many cross-sections and multiple prestressing tendons within the structure, resulting in numerous equations (one for each cross-section), each a linear combination of unknown tension forces. Therefore, this embodiment employs an iterative inversion algorithm to solve for the tension of the prestressing tendons within the structure. Specifically, the iterative least squares method is used. However, considering that a simple iterative least squares method might yield unreasonable results—for example, the tension of a certain prestressing tendon becoming negative (i.e., under tension), or the prestressing from the anchorage end to mid-span fluctuating wildly—physical constraints are introduced during the solution process to obtain the inversion value of the tension of the prestressing tendons within the structure. These physical constraints include monotonicity constraints, smoothness constraints, and boundary constraints, which are transformed into penalty terms in the objective function of the iterative inversion algorithm using a penalty function method. After obtaining the inversion value of the tension of the prestressing tendons within the structure, the tension is converted into prestressing force according to the following formula to obtain the effective prestressing force of the prestressing tendons within the structure of the high-pier, long-span PC continuous rigid frame bridge, which is then used as the inversion value of the prestressing force within the structure of the high-pier, long-span PC continuous rigid frame bridge.

[0048] in, This is the inversion value of the tension of the prestressed tendons within the body, in units of "N"; The internal prestress of the internal prestressed tendon is expressed in N / mm². 2 ”; The nominal cross-sectional area of ​​the prestressed tendons within the body, expressed in mm. 2 ”; The anchor efficiency coefficient is dimensionless and ranges from 0.95 to 0.98.

[0049] More specifically, the iterative least squares method is used to... The solution process is as follows: 1. Settings To initialize with 80% of the designed tension value .

[0050] 2. Based on what has already been obtained Calculate the bending moment inside the body and record the result as... , is used to represent the inferred internal bending moment at position k.

[0051] 3. Substituting into the objective function, we calculate the objective function value J. The objective function satisfies the following relationship: in, To infer the bending moment vector within the body, ; This represents the actual bending moment vector within the body. ; This is the regularization parameter, and its empirical value is 0.01 to 0.1; These are physical constraint terms.

[0052] In the physical constraints, due to the same prestressed tendon within the body... and Generally, these constraints are fixed; therefore, tensile force is used here to represent the smoothness constraint. Thus, in this embodiment, tensile force is used instead of internal prestress to represent each physical constraint term, simplifying calculations and improving monitoring efficiency. Specifically, the monotonicity constraint means that from the anchorage end to mid-span, in the section without turning blocks, the internal prestress gradually decreases, i.e. The smoothness constraint is that the average change in prestress between adjacent sections does not exceed a preset change threshold. Due to the same prestressed tendon in the body and Generally, it is fixed, therefore tension is used here to represent the smoothness constraint, i.e. , Let J be the tension of the j-th internal prestressed tendon at position k+1. The length of the j-th internal prestressed tendon from position k to position k+1 is expressed in meters. The value range is 5~15kN / m; the boundary constraint is that the prestress in the anchorage end should be within the range specified according to the design tension value, i.e. , This is the lower limit of the tensile force. , Let K be the design tension value of the j-th internal prestressed tendon at position k. This is the upper limit of the tensile force. Therefore, the final physical constraint terms can be set as follows: in, , and These are referential symbols designed to facilitate writing. , , ; This indicates taking the positive value.

[0053] 4. Continuously adjust using the Gauss-Newton method. The maximum number of iterations is set to 500 steps, and the calculation is repeated for each adjustment. Continue until the maximum number of iterations is reached or 5 consecutive adjustments are made. The calculated objective function value satisfies , For the (r+1)th adjustment The calculated objective function value, For the r-th adjustment Calculate the objective function value and output it at this point. This is used as the inversion value of the tension of the prestressed tendons in the body.

[0054] Furthermore, to further improve the reliability of the finite element model, this embodiment also includes an adaptive closed-loop verification and model update process. Specifically, fiber optic grating sensors are used to collect the tension values ​​of the prestressed tendons at key interfaces within the body. After preprocessing, the difference between these values ​​and the corresponding inversion values ​​is calculated as the tension inversion error of the key section. If the tension inversion error exceeds five percent of the design tension value, the parameters of the finite element model are triggered for correction. Specifically, sensitivity analysis is used to continuously update the duct friction coefficient and deviation coefficient until the tension inversion error is less than five percent of the design tension value.

[0055] S32. Construct an error correction model based on the inverted prestress values, the prestress in the key section, temperature and humidity, concrete age, and anchorage distance.

[0056] Step S32 specifically includes the following steps: S321. Screen the inverted values ​​of the in-body prestress at the key section and calculate the prestress inversion error. At the same time, calculate the temperature difference between the temperature at the key section and the reference temperature, and the humidity difference between the humidity at the reference humidity and the reference humidity.

[0057] Specifically, in this embodiment, after converting the inversion value of the tension of the prestressed tendons into the inversion value of the prestress, the inversion value of the prestress at the key section is selected, and then the prestress inversion error is calculated. The prestress inversion error is the difference between the inversion value of the prestress at the key section and the prestress at the key section. Simultaneously, the temperature difference at the key section relative to the reference temperature and the humidity difference relative to the reference humidity are calculated. The reference temperature and reference humidity need to be determined comprehensively based on factors such as the climate conditions of the bridge location, the concrete mix proportion, and the construction environment.

[0058] S322. Construct a dataset using the in-body prestress inversion values ​​at key sections, the prestress inversion error, the temperature difference, the humidity difference, the concrete age, and the anchorage distance.

[0059] Specifically, in this embodiment, for any critical section, the inverted prestress values ​​at the same time, the prestress within the critical section, the temperature difference, the humidity difference, the concrete age, and the anchorage distance are collected as a set of data, and multiple sets of such data are used to construct a dataset. The anchorage distance refers to the longitudinal distance from the critical section to the nearest anchorage point. In other optional embodiments, the inverted prestress values, prestress, temperature difference, humidity difference, concrete age, and anchorage distance at some non-critical sections can also be collected to expand the dataset, thereby improving the comprehensiveness and reliability of the dataset.

[0060] S323. Using the prestress inversion value, the temperature difference, the humidity difference, the concrete age, and the anchorage distance as model inputs, and the prestress inversion error as model output, an error correction model is constructed using a support vector regression model and the dataset.

[0061] Specifically, in this embodiment, the dataset constructed in step S322 is divided into a training set and a validation set in a 7:3 ratio to complete the training and validation of the Support Vector Regression (SVR) model, resulting in an error correction model. The error correction model uses the prestress inversion value of the key section, temperature difference, humidity difference, concrete age, and anchorage distance as inputs, and the prestress inversion error as the model output. When training the SVR model, the loss function used is an ε-insensitive loss function. The parameter ε needs to be determined based on the design effective prestress, typically ranging from one percent to three percent of the design effective prestress.

[0062] S33. The error correction model is used to correct the inverted value of the in vivo prestress to obtain the effective value of the in vivo prestress.

[0063] Specifically, in this embodiment, the real-time prestress inversion value of the key section, temperature difference, humidity difference, concrete age and anchorage distance are input into the error correction model to obtain the prestress inversion error of the prestress in the key section. The prestress inversion value of the key section is added to the corresponding prestress inversion error to correct the in-body prestress inversion value and obtain the corresponding effective value of the in-body prestress.

[0064] S4. Use the corrected in-body prestress to invert the in-body prestress of the entire bridge and calculate the prestress loss rate. Issue an early warning when the prestress loss rate exceeds the prestress loss threshold.

[0065] Specifically, in this embodiment, a piecewise linear interpolation method is used to reconstruct the prestress distribution of the entire bridge. First, based on the anchorage locations of the prestressing tendons and the locations of key sections, the entire bridge is divided into several continuous segments. Then, within each segment, assuming that the prestress changes linearly along the longitudinal direction of the bridge, the prestress value at any location within the segment is calculated using a linear interpolation formula based on the correction values ​​at both ends of the segment. Finally, the interpolation results of the prestress in each segment are spliced ​​together to obtain the continuously distributed prestress field of the entire bridge. In other optional embodiments, if the nonlinear characteristics of the prestress along the bridge are to be considered, the theoretical prestress distribution can be extracted from the finite element model first, the ratio of the measured value to the theoretical value of the prestress at each key section can be calculated, and this ratio can be recorded as a correction coefficient. Then, piecewise linear interpolation is performed on this ratio to obtain the ratio coefficient distribution of the entire bridge. Finally, based on the theoretical prestress distribution and the ratio coefficient distribution, the product of the theoretical value of the prestress at each section and the ratio coefficient can be calculated to obtain the continuously distributed prestress field of the entire bridge.

[0066] Furthermore, based on the obtained in-body prestress field, the prestress loss rate of each section is calculated, and the prestress loss rate satisfies the following relationship: in, The prestress loss rate of the cross section, For the design of the cross section, effective prestress, The modified in-body prestress is the cross-section.

[0067] Furthermore, the prestress loss threshold is set at 15%, when When the level is greater than or equal to 15%, an audible and visual warning will be issued via a buzzer and LED lights.

[0068] It should be noted that in some cases, the actions described in the specification can be performed in different orders and still achieve the desired results. In this embodiment, the order of steps is given only to make the embodiment clearer and easier to explain, and not to limit it.

[0069] In one optional embodiment, please refer to Figure 2 To improve the practicality of this method and facilitate its promotion, the present invention also provides a prestress monitoring system for high-pier, long-span PC continuous rigid frame bridges. The prestress monitoring system for high-pier, long-span PC continuous rigid frame bridges includes: a data input device 1, a data output device 2, a processor 3, and a storage device 4. The storage device 4 includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor 3, cause the processor 3 to perform the contents described in steps S1 to S4.

[0070] In summary, this invention has at least the following beneficial effects: This invention only requires measuring the cable force of the external tendons and a small amount of prestress in key sections to obtain the continuous distribution of prestress in the body of a high-pier, long-span PC continuous rigid frame bridge through inversion, eliminating the need for extensive pre-embedding of high-cost sensors throughout the entire bridge and reducing damage to the bridge structure and monitoring costs; this invention utilizes the time-varying elastic modulus of concrete shrinkage and creep, which can reflect the time evolution of long-term prestress loss, making it suitable for both the initial construction phase and long-term operational monitoring of high-pier, long-span PC continuous rigid frame bridges; this invention adopts... An iterative inversion algorithm with physical constraints was introduced to overcome the ill-conditioned inversion problem of pure mechanical models. Then, a support vector regression model was used to perform global error correction on the inversion results with finite FBG measured data, which improved the accuracy of the inversion results. By comparing the measured values ​​of local prestress in the body with the inverted values, when the error exceeds the limit, the coefficients in the finite element model are automatically corrected and the inversion is restarted until convergence, forming an intelligent closed loop of "monitoring-inversion-verification-update", which improves the adaptability of the scheme to different bridges. A system adapted to the method is provided, which not only improves the practicality of the method, but also facilitates its promotion.

[0071] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge, characterized in that, Includes the following steps: The original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge were obtained and pre-processed to obtain the external cable force values ​​and the internal prestress of key sections. A finite element model of the bridge is established, and the external cable force values ​​are input into the finite element model as known loads to solve for the bridge bending moment distribution. The internal prestress of the high-pier, long-span PC continuous rigid frame bridge is calculated based on the bending moment distribution of the bridge, and the calculation results are corrected based on the internal prestress of the key section, temperature and humidity, concrete age and anchorage distance. The modified in-body prestress is used to invert the in-body prestress of the entire bridge and calculate the prestress loss rate. An early warning is issued when the prestress loss rate exceeds the prestress loss threshold.

2. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 1, characterized in that, The process of obtaining the original external cable force values ​​and the original internal prestress of key sections of a high-pier, long-span PC continuous rigid frame bridge, and performing preprocessing to obtain the external cable force values ​​and internal prestress of key sections, includes the following steps: The original external cable force values ​​and the original internal prestress of key sections of the high-pier, long-span PC continuous rigid frame bridge were collected. The collected data is filtered and denoised, outlier identification and removal is performed, missing value filling is performed, and resampling is performed to obtain the external cable force value and the internal prestress of the key section.

3. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 2, characterized in that, The process of obtaining the original external cable force values ​​and the original internal prestress of key sections of a high-pier, long-span PC continuous rigid frame bridge and performing preprocessing to obtain the external cable force values ​​and the internal prestress of key sections also includes: A temperature and humidity-strength correction formula is established, and the external strength value is corrected using the temperature and humidity-strength correction formula.

4. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 1, characterized in that, The process of establishing a finite element model of the bridge and inputting the external cable force values ​​as known loads into the finite element model to solve for the bending moment distribution of the bridge includes the following steps: A finite element model containing geometric information of the internal and external bundles was established based on the design drawings of the high-pier, long-span PC continuous rigid frame bridge. The external cable force values ​​are then input into the finite element model as known loads, and the bending moment distribution of the high-pier, long-span PC continuous rigid frame bridge is obtained by solving the overall structural equilibrium equations.

5. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 1, characterized in that: In the finite element model, the concrete constitutive model adopts a time-varying elastic modulus model that considers shrinkage and creep.

6. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 1, characterized in that, The process of calculating the internal prestress of a high-pier, long-span PC continuous rigid frame bridge based on the bridge bending moment distribution, and correcting the calculation results based on the internal prestress of the key sections, temperature and humidity, concrete age, and anchorage distance, includes the following steps: Based on the bending moment distribution inversion, the internal prestress of the high-pier long-span PC continuous rigid frame bridge is obtained, and the internal prestress inversion value is obtained. An error correction model is constructed based on the inverted values ​​of the in-body prestress, the in-body prestress of the key section, temperature and humidity, concrete age and anchorage distance; The error correction model is used to correct the inverted value of the in vivo prestress to obtain the effective value of the in vivo prestress.

7. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 6, characterized in that: The effective prestress within the body of a high-pier, long-span PC continuous rigid frame bridge is calculated using an iterative inversion algorithm with physical constraints, and the inversion value of the prestress within the body is obtained.

8. The method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 7, characterized in that: The physical constraints include monotonicity constraints, smoothness constraints, and boundary constraints, and the physical constraints are transformed into penalty terms in the objective function of the iterative inversion algorithm using the penalty function method. The monotonic constraint is that from the anchorage end to the mid-span, in the section without the turning block, the prestress in the body gradually decreases; The smoothness constraint is that the average change in prestress between adjacent sections does not exceed a preset change threshold. The boundary constraint is that the prestress within the anchorage end body should be within the range specified according to the design tension value.

9. A method for monitoring the prestress of a high-pier, long-span PC continuous rigid frame bridge according to claim 6, characterized in that, The step of constructing an error correction model based on the inverted prestress values, the prestress in the key section, temperature and humidity, concrete age, and anchorage distance includes the following steps: The inverted values ​​of the in-body prestress at the key section are selected and the prestress inversion error is calculated. At the same time, the temperature difference at the key section relative to the reference temperature and the humidity difference relative to the reference humidity are calculated. A dataset is constructed using the in-body prestress inversion values ​​at key sections, the prestress inversion error, the temperature difference, the humidity difference, the concrete age, and the anchorage distance; The prestress inversion value, temperature difference, humidity difference, concrete age, and anchorage distance are used as model inputs, and the prestress inversion error is used as model output. An error correction model is constructed using a support vector regression model and the dataset.

10. A prestressing monitoring system for a high-pier, long-span PC continuous rigid frame bridge, characterized in that, The prestress monitoring system for a high-pier, long-span PC continuous rigid frame bridge includes: a data input device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor, cause the processor to implement the prestress monitoring method for a high-pier, long-span PC continuous rigid frame bridge as described in any one of claims 1-9.

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