Bridge stress state diagnosis method based on digital twinning and movable sensing

Abstract

The invention belongs to the technical field of bridge engineering, particularly relates to a bridge stress state diagnosis method based on digital twinning and movable sensing, and aims to diagnose the real-time stress state of a bridge with diseases. The method comprises the steps of obtaining existing disease space data of a bridge, implanting disease parameters in a twin model, and generating an initial twin body of the bridge with the disease; a modular monitoring station formed by movable sensing devices is deployed on a bridge, data are transmitted to an edge computing terminal through a Mesh ad hoc network between the devices, and the edge computing terminal executes data preprocessing. In the monitoring period, vehicle load, temperature and humidity, displacement or vibration data are injected into the initial twinborn body of the diseased bridge in real time, an FEM-disease coupling algorithm is established to dynamically correct a structural stiffness matrix, and a digital twinborn body is formed. And establishing a stress state diagnosis index system, comparing the responses of the digital and healthy twins under the same load, calculating the variation amplitude of each diagnosis index, marking a structural health degree map, and judging whether the bridge has an abnormal stress state.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering, and particularly relates to a bridge stress state diagnosis method based on digital twinning and movable sensing. BACKGROUND

[0002] As important traffic infrastructure, the operation safety of a bridge is closely related to the stress state thereof. The existing bridge monitoring system has problems such as high initial investment, long equipment deployment period, poor reusability and the like, which leads to difficulty in quickly responding to real-time monitoring requirements. Meanwhile, the bridge is prone to diseases such as pier deviation, main girder displacement and cracks in the service process due to complex environment, and the traditional bearing capacity evaluation method needs to close the traffic, is low in efficiency, and depends on experience for judgment, so that it is difficult to quantitatively evaluate the dynamic influence of the diseases on the structure stress, and the safety evaluation lacks data support.

[0003] The existing digital twinning technology is mostly based on design drawings to construct an idealized model in the field of bridges, and the stress and displacement responses calculated by the model have deviations from the real structure, especially in the disease development stage, the model cannot accurately reflect the amplification effect of defects on the stress state, and is prone to cause lag in risk warning. Therefore, there is an urgent need for a method that takes into account rapid deployment, data-driven modeling and accurate stress diagnosis to solve the safety monitoring problem of bridges with diseases. SUMMARY

[0004] The present application relates to the technical field of bridge engineering, and particularly relates to a bridge stress state diagnosis method based on digital twinning and movable sensing.

[0005] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: The present application provides a bridge stress state diagnosis method based on digital twinning and movable sensing, comprising: S1: obtaining bridge existing disease spatial data through unmanned aerial vehicle laser scanning or close-range photogrammetry, implanting disease parameters in the twin model, and generating a diseased bridge initial twin; S2: deploying a modular monitoring station composed of movable sensing devices on the bridge, transmitting data from the devices to the edge computing terminal through Mesh ad hoc network, and performing data preprocessing by the edge computing terminal; S3: during the monitoring period, real-time injection of vehicle load, temperature and humidity, displacement or vibration data into the diseased bridge initial twin, dynamic correction of the structure stiffness matrix by establishing a FEM-disease coupling algorithm, simulation of the stress state of the bridge under different working conditions, formation of the digital twin, and realization of the dynamic mapping of the digital twin to the actual bridge; S4: establishing a stress state diagnosis index system, comparing the responses of the digital twin and the healthy twin under the same load, calculating the change amplitude of each diagnosis index, marking the structure health degree atlas, and judging whether the bridge has abnormal stress state.

[0006] In step S1, a bridge structure and a surrounding of a bridge clearance are scanned by a laser scanning device carried by a UAV, a geophysical coordinate system of the bridge is established, and a physical model of the bridge is formed; a bridge component technical condition is marked on the physical model of the bridge according to bridge inspection data, a component inspection list is established, and a same component closest in physical position is selected as a reference component; a component is subdivided into sub-components by comprehensively considering a longitudinal position, a transverse position, a vertical position and a three-dimensional angle of the component; a flight route of the UAV is planned, a close-range camera carried by the UAV is used to shoot a close-up of a disease, a disease feature and a position thereof are extracted, a disease influence area is determined, a stiffness damage factor is defined, and an initial twin of the bridge with the disease is generated.

[0007] The component inspection list includes a component with a technical condition score less than 60; the disease feature includes a length and a maximum width of a crack.

[0008] In step S2, the measuring points are divided into multiple application scenarios by comprehensively considering a bridge structure type and a bridge site environmental factor, sensor types and numbers in different application scenarios are designed, a sensor unit with the highest movable sensor score is determined, a modular monitoring station construction scheme is developed and deployed, data is transmitted from the sensor to an edge computing terminal through a Mesh ad hoc network, and the edge computing terminal performs data preprocessing.

[0009] When the sensor unit with the highest movable sensor score is determined, a corresponding scoring and weight system is established; the weight system includes an easy installation degree, a reusable degree, an asset depreciation, a test accuracy and a consumable price of the sensor.

[0010] The data preprocessing performed by the edge computing terminal includes performing an FFT transform and removing noise components with frequencies not in a valid frequency band of the bridge.

[0011] In step S3, a denoised vehicle load spectrum, an environmental temperature and humidity and a vibration frequency parameter are input to the initial twin of the bridge with the disease; a structure stiffness matrix is dynamically corrected through an FEM-disease coupling algorithm; a time-varying influence coefficient is optimized through inversion based on short-term monitoring data, the converged dynamic stiffness matrix is input to the initial twin of the bridge with the disease, a digital twin is formed, and dynamic mapping is realized.

[0012] The short-term monitoring data is one week of monitoring data; the dynamic correction of the structure stiffness matrix is based on an initial stiffness matrix of a healthy structure, the stiffness damage factor and the time-varying influence coefficient.

[0013] In step S4, the cloud twin engine is deployed, and the structural response distribution cloud map is updated regularly; the change range of each diagnostic index of the digital twin and the healthy twin under the same load is calculated; the high-risk, medium-risk and low-risk areas are marked according to the change range, and corresponding early warning is performed; the residual bearing capacity coefficient is calculated, and the change curve and envelope diagram of the residual bearing capacity coefficient with time are drawn, and the priority of the visualized structure reinforcement is determined.

[0014] The time interval of the regular update is 10 minutes; the residual bearing capacity coefficient is the ratio of the residual bearing capacity of the section to the bearing capacity of the healthy state, and is a function of the stiffness damage factor and the time-varying influence coefficient.

[0015] Compared with the prior art, the application has the beneficial effects that: 1. The bridge stress state diagnosis method based on digital twin and movable sensing provided by the embodiment of the application. By combining unmanned aerial vehicle laser scanning and close-range photogrammetry, actual disease parameters are implanted into the initial twin body with diseases generated by the basic model of the bridge digital twin, the quantitative mapping of diseases and stiffness damage is established, and the problem that the traditional digital twin model ignores the actual diseases and has large deviation from the real structure is overcome, thereby laying a precise foundation for subsequent stress analysis. The modular movable monitoring station is adopted, the optimal sensor unit is selected by combining the scoring and weight system, the equipment is reusable and convenient to deploy, and the asset investment and depreciation loss are greatly reduced; the data is preprocessed by Mesh self-organizing network and edge computing to ensure efficient and stable monitoring, and the problems of high cost and poor reusability of the traditional fixed monitoring system are solved.

[0016] 2. The short-term monitoring data is used to inverse optimize the time-varying parameters, and the stiffness matrix of the twin body is dynamically corrected, and only one week of data is required to realize the dynamic mapping of the actual bridge; by comparing the response difference between the digital twin and the healthy twin, and combining the visual analysis of the residual bearing capacity coefficient, the structural health degree is quantified and graded early warning is performed, data support is provided for reinforcement decision-making, the risk lag caused by relying on experience is avoided, and the scientificity and timeliness of bridge safety management are improved. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flowchart of the bridge stress state diagnosis method based on digital twin and movable sensing provided by the embodiment of the application; Figure 2 is a generation flowchart of the digital twin provided by the embodiment of the application; Figure 3 is a mobile monitoring scheme development flowchart provided by the embodiment of the application; Figure 4 is a bridge structure diagnosis and decision-making flowchart provided by the embodiment of the application. DETAILED DESCRIPTION

[0018] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0019] The embodiment of the present application provides a bridge stress state diagnosis method based on digital twinning and movable sensing, for example, as shown in Figure 1 The method comprises the following steps: S1: obtaining bridge existing disease space data through unmanned aerial vehicle laser scanning or close-range photogrammetry, implanting disease parameters in the twin model, and generating an initial twin body of the bridge with diseases.

[0020] In combination with Figure 1 and Figure 2 , in step S1, a laser scanning device is carried by a drone to perform laser scanning on the bridge structure and the surrounding of the architectural limit, for example, the scanning range should cover the working obstacle avoidance interval of the drone, to establish a geophysical coordinate system of the bridge and form a bridge physical model; according to the bridge inspection data, the technical condition of the bridge component is marked on the bridge physical model, a component inspection list is established, and the same type of component closest in physical position is selected as a reference component; the inspection component is subdivided into sub-components by comprehensively considering the longitudinal position, transverse position, vertical position and three-dimensional angle of the component; the flight route of the unmanned aerial vehicle is planned, the unmanned aerial vehicle carries a close-range camera to shoot a close-up of the disease, the disease characteristics and its position are extracted, the disease influence area is determined, the stiffness damage factor is defined, and the initial twin body of the bridge with diseases is generated.

[0021] The component inspection list includes components with a technical condition score less than 60. The disease characteristics include the length and maximum width of the crack.

[0022] For example, L / 4~3L / 4 of the box-shaped main beam is taken as an example to divide the analysis unit, and the length of the analysis unit may be 1 / 2~1 times the width of the main beam; taking the transverse crack as the first statistical item, the longitudinal position, crack length , crack width , whether there is a vertical crack within ±1 / 2 stirrup spacing and the length , width of the vertical crack are analyzed one by one; the crack influence area is further calculated, the length , width , and height of the initial value can be calculated according to formula (1); (1) wherein, The effective height of a component (such as a main beam) is usually the distance from the neutral axis of the cross section to the tension or compression edge. This refers to the flange width of a component (such as a main beam). This refers to the width of the web of a structural member (such as a main beam).

[0023] The stiffness damage factor D is defined based on the type of damage. First, the first... Stiffness of the relative cross-section neutral axis of the affected area and the stiffness of the original cross section Then, the stiffness damage factor of the analysis unit is calculated according to formula (2); (2) S2: Deploy modular monitoring stations consisting of mobile sensing devices on the bridge. The devices transmit data to the edge computing terminal through a Mesh self-organizing network, and the edge computing terminal performs data preprocessing.

[0024] Reference Figure 3 In step S2, taking into account the bridge structure type and bridge site environmental factors, the measuring points are divided into multiple application scenarios, and the sensor categories and quantities under different application scenarios are designed; the sensor unit with the highest mobile sensing score is determined, and a modular monitoring station construction plan is formulated and deployed; the sensors transmit data to the edge computing terminal through the ZigBee Mesh network, and the edge computing terminal performs data preprocessing.

[0025] For example, taking into account the bridge structure type, site environment, materials, test type, and test accessibility, the test points were divided into... 1. Application scenarios, and design sensor categories for different application scenarios. quantity .

[0026] When determining the sensor unit with the highest mobile sensing score, a corresponding scoring and weighting system is established. The weighting system includes the sensor's ease of installation, reusability, asset depreciation, testing accuracy, and consumable price.

[0027] One possible approach is to create a list of different types of sensor devices and then pair each sensor with the others. In application scenarios The scores are assigned based on factors such as ease of installation, reusability, asset depreciation, testing accuracy, and consumable prices. One by one, the sensors In application scenarios The importance of factors such as ease of installation, reusability, asset depreciation, testing accuracy, and consumable prices should be weighted. .

[0028] All sensors of the sensor category that meet the needs of the test Arranged from the sensor list, called sensor units A sensor unit, calculate the movable sensor score of each sensor unit according to formula (3).

[0029] (3) After calculation, the sensor unit with the highest movable sensor score is determined as the modular monitoring station, and a modular monitoring station construction scheme is formulated according to the use function of the sensor, the installation and removal requirements, the collection requirements, etc. The sensor transmits data to the edge computing terminal through ZigBee Mesh network automatic topology.

[0030] The data preprocessing performed by the edge computing terminal includes performing FFT transformation and eliminating noise components whose frequencies are not in the effective frequency band of the bridge. Through FFT transformation, i.e. fast Fourier transform, the original signal collected by the sensor can be converted from time domain to frequency domain, so that the frequency components in the signal can be accurately identified. Since the specific effective frequency band of the bridge structure when subjected to stress vibration is related to the stiffness, mass and other characteristics of the bridge itself, and the noise signal frequencies of environmental interference such as wind noise and non-related vibration are usually outside the effective frequency band, therefore, eliminating these noise components can significantly improve the signal-to-noise ratio of the monitoring data.

[0031] The clean data after processing can more truly reflect the actual stress response (such as vibration, displacement, etc.) of the bridge, providing reliable input for subsequent injection of digital twin for stiffness matrix correction, time-varying parameter inversion and other steps, ensuring the dynamic mapping accuracy of the twin to the actual state of the bridge, and ultimately improving the accuracy of the stress state diagnosis.

[0032] S3: During the monitoring period, real-time injection of vehicle load, temperature and humidity, displacement or vibration data into the initial twin of the bridge with diseases, establishing a FEM-disease coupling algorithm to dynamically correct the structure stiffness matrix, simulating the stress state of the bridge under different working conditions, forming a digital twin, and realizing dynamic mapping of the digital twin to the actual bridge.

[0033] In step S3, the denoised vehicle load spectrum, environmental temperature and humidity, and vibration frequency parameters are input into the initial twin of the bridge with diseases; the structure stiffness matrix is dynamically corrected through the FEM-disease coupling algorithm; the time-varying influence coefficient is optimized based on the short-term monitoring data, and the converged dynamic stiffness matrix is input into the initial twin of the bridge with diseases to form a digital twin and realize dynamic mapping.

[0034] For example, the dynamic correction formula of the structure stiffness matrix is as formula (4): (4) In the formula: The initial stiffness matrix of the healthy structure is derived from the as-built 3D model of the bridge. The first calculated according to equation (2) Stiffness damage factor of the affected area; For the first The time-varying influence coefficient of each disease-affected area at time t.

[0035] As one possible approach, short-term monitoring data is collected over one week. Dynamic correction of the structural stiffness matrix is ​​based on the initial stiffness matrix of the healthy structure, the stiffness damage factor, and the time-varying influence coefficient.

[0036] For example, the influence coefficient of time-varying data based on short-term (one-week) monitoring data. Inverse optimization involves first constructing the objective function as shown in equation (5), then solving it using gradient descent according to equation (6), and iterating until convergence.

[0037] (5) (6) in, This refers to the structural response data obtained from the kth actual monitoring. Based on the current time-varying coefficients The k-th structural response data obtained from twin simulation. Let be the value of the i-th time-varying influence coefficient in the j-th iteration, used for gradient descent optimization. The "learning rate" of gradient descent controls the step size for each iteration; for example, it is set to 0.01.

[0038] The converged dynamic stiffness matrix is ​​input into the digital twin to achieve dynamic mapping of the digital twin to the actual bridge structure.

[0039] Step S3 involves injecting real-time monitored vehicle load, environmental parameters, and structural response data into the initial digital twin of the bridge with defects. The stiffness matrix is ​​then dynamically corrected using the FEM-disease coupling algorithm, enabling the digital twin model to keep pace with the actual state of the bridge in real time. This overcomes the limitation of traditional static models in reflecting the time-varying characteristics of the structure. By correcting the stiffness matrix and integrating the stiffness damage factor with the real-time time-varying influence coefficient, the dynamic impact of defects on structural stiffness under different working conditions is quantified. This solves the problem of the disconnect between defects and stress state in traditional analysis, making the simulation results more closely match the actual stress conditions of the bridge.

[0040] In addition, by inverting and optimizing time-varying parameters based on a week of short-term monitoring data, the digital twin model can be quickly converged, which greatly improves the construction efficiency of the digital twin and meets the timeliness requirements of bridge real-time monitoring.

[0041] S4: Establish a stress state diagnostic index system, compare the response of the digital twin and the healthy twin under the same load, calculate the change range of each diagnostic index, mark the structural health spectrum, and determine whether the bridge has an abnormal stress state.

[0042] Reference Figure 4 In step S4, a cloud twin engine is deployed to periodically update the structural response distribution cloud map.

[0043] As one possible implementation, the update interval is 10 minutes.

[0044] Calculate the variation range of various diagnostic indicators between the digital twin and the healthy twin under the same load. Mark high-risk, medium-risk, and low-risk areas based on the variation range and issue corresponding early warnings; calculate the remaining carrying capacity coefficient, plot its variation curve and envelope diagram over time, and visualize the priority of architecture hardening.

[0045] Among them, the residual bearing capacity coefficient Remaining bearing capacity of the cross section With health status carrying capacity The ratio is the stiffness damage factor. and time-varying influence coefficient function , It can be calculated based on the principles of structural mechanics. Taking bending moment bearing capacity as an example, .

[0046] For example, the responses of diseased twins and healthy twins under the same load are analyzed and calculated one by one, and the changes in each diagnostic indicator are calculated. ;in For twins with disease in time The response For healthy twins in time The response.

[0047] Will Locations with responses exceeding 1.2, 1.1, and 1.0 times those of a healthy twin model are marked as high-risk, medium-risk, and low-risk areas, respectively, and are given red, orange, and yellow alerts. The user interface uses a WebGL compressed model for lightweight rendering and supports viewing key structural responses such as stress at the upper and lower edges of cross-sections.

[0048] draw Over time The change curves are analyzed to identify characteristic points. Further investigation is conducted to determine the effects of vehicle load spectra, environmental temperature and humidity at those characteristic points, and to analyze the causes of anomalies. The remaining bearing capacity coefficients of each analysis unit of the bridge structure are plotted. Within the monitoring period, regarding time the envelope plot is color mapped by the size of the remaining load carrying capacity coefficient the envelope plot is color mapped by the size of the remaining load carrying capacity coefficient the smallest reinforcement priority is the highest.

[0049] In summary, the embodiment of the application establishes a bridge physical model by a UAV carrying a laser scanning device, and plans a flight path carrying a close-range camera in combination with bridge maintenance data, improves the disease scanning efficiency of the UAV close-range camera, and improves the quality of the bridge disease twin body; and a disease parameter-rigidity damage factor mapping model is established, the influence of bridge diseases on structural stress is quantified, and the actual structure mapping is more accurate. A modular monitoring station considering factors such as easy installation, reusability, test accuracy, and economy is proposed, and a modular monitoring station scheme development method with a movable sensing score as an index, the bridge monitoring cost is greatly reduced, and the wide application of the method is possible.

[0050] Moreover, only one week of monitoring data is required to invert the time-varying influence coefficient drive the twin body to correct the disease model, greatly improving the efficiency of the disease twin body; through the simulation results of the bridge twin body in the monitoring period, the remaining load carrying capacity coefficient of the component is quantified, the user end visualizes the reinforcement priority of the component through lightweight rendering, reduces the user threshold, and has good usability, solves the three major pain points of high industry cost, poor timeliness, and high user technical threshold, and provides a new method for infrastructure intelligent management and monitoring.

[0051] In the description of the present specification, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0052] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A bridge stress state diagnosis method based on digital twinning and movable sensing, characterized in that, The method comprises the following steps: S1: Obtain the spatial data of the existing diseases of the bridge by unmanned aerial vehicle laser scanning or close-range photogrammetry, implant the disease parameters in the twin model, and generate the initial twin body of the bridge with diseases; S2: Deploy a modular monitoring station composed of mobile sensing devices on the bridge, transmit data between devices through Mesh ad hoc network to the edge computing terminal, and perform data preprocessing by the edge computing terminal; S3: During the monitoring period, real-time injection of vehicle load, temperature and humidity, displacement or vibration data into the initial twin body of the bridge with diseases, establishment of FEM-disease coupling algorithm to dynamically correct the structure stiffness matrix, simulation of the stress state of the bridge under different working conditions, formation of the digital twin body, and realization of the dynamic mapping of the digital twin body to the actual bridge; S4: Establish a stress state diagnosis index system, compare the responses of the digital twin body and the healthy twin body under the same load, calculate the change amplitude of each diagnosis index, mark the structure health degree atlas, and judge whether the bridge has abnormal stress state.

2. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 1, characterized in that, In step S1, the unmanned aerial vehicle is equipped with a laser scanning device to scan the bridge structure and the surrounding building limit, establish a geophysical coordinate system of the bridge, and form a physical model of the bridge; according to the bridge inspection data, mark the technical condition of the bridge component on the physical model, establish a component inspection list, and select the same type of component closest to the physical position as the reference component; Considering the longitudinal position, transverse position, vertical position and three-dimensional angle of the component, the inspection component is subdivided into sub-components; the flight route of the unmanned aerial vehicle is planned, the unmanned aerial vehicle is equipped with a close-range camera to shoot the disease close-up, the disease characteristics and position are extracted, the disease influence area is determined, the stiffness damage factor is defined, and the initial twin body of the bridge with diseases is generated.

3. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 2, characterized in that, The component inspection list includes components with a technical condition score less than 60; the disease characteristics include the length and maximum width of the crack.

4. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 1, characterized in that, In step S2, considering the bridge structure type and bridge site environmental factors, the measuring points are divided into multiple application scenarios, and the sensor types and quantities in different application scenarios are designed; The sensor unit with the highest mobile sensing score is determined, the modular monitoring station construction scheme is developed and deployed; the sensor transmits data to the edge computing terminal through Mesh ad hoc network, and the edge computing terminal performs data preprocessing.

5. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 4, characterized in that, When determining the sensor unit with the highest mobile sensing score, a corresponding scoring and weighting system is established; the content of the weighting system includes the ease of installation, reusability, asset depreciation, test accuracy and consumable price of the sensor.

6. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 4, characterized in that, The data preprocessing performed by the edge computing terminal includes performing FFT transformation and removing noise components with frequencies not in the effective frequency band of the bridge.

7. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 1, characterized in that, In step S3, the denoised vehicle load spectrum, environmental temperature and humidity, and vibration frequency parameters are input into the initial twin body of the bridge with diseases; the structure stiffness matrix is dynamically corrected by the FEM-disease coupling algorithm; the time-varying influence coefficient is optimized based on the short-term monitoring data, the converged dynamic stiffness matrix is input into the initial twin body of the bridge with diseases, the digital twin body is formed, and the dynamic mapping is realized.

8. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 7, characterized in that, The short-term monitoring data is one-week monitoring data; and the dynamic correction of the structural stiffness matrix is based on an initial stiffness matrix of a healthy structure, a stiffness damage factor and a time-varying influence coefficient.

9. The bridge stress state diagnosis method based on digital twin and movable sensing of claim 4, wherein, In step S4, a cloud twin engine is deployed to periodically update a structural response distribution cloud map; to calculate the change range of each diagnostic index of the digital twin and the healthy twin under the same load; to mark high-risk, medium-risk and low-risk areas according to the change range and to perform corresponding early warning; A residual bearing capacity coefficient is calculated, and a change curve and an envelope diagram thereof with time are drawn to visualize the reinforcement priority of the structure.

10. The bridge stress state diagnosis method based on digital twin and movable sensing according to claim 9, characterized in that, The time interval of the periodic update is 10 minutes; the residual bearing capacity coefficient is the ratio of the residual bearing capacity of the section to the bearing capacity in the healthy state, and is a function of the stiffness damage factor and the time-varying influence coefficient.

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