A multi-source and multi-scale intelligent hierarchical early warning method and system for bridges
By establishing a finite element model and analyzing influencing factors and dividing risk levels, the problems of deflection and cracks under continuous rigid frame bridges are solved, ensuring the safety and durability of the bridge, and providing timely reinforcement measures.
Patent Information
- Application Number
- CN202210868232.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-07-22
- Publication Date
- 2025-07-11
- Estimated Expiration
- 2042-07-22
AI Technical Summary
During the long-term service of continuous rigid frame bridges, due to the increase in the middle and lower deflection of the span, the bridge has poor linear shapes during the operation period, affecting driving safety and durability, and it is difficult for the existing technology to effectively predict and early warning.
The multi-source, multi-scale intelligent hierarchical early warning method and system of bridges is adopted. By establishing a finite element model, the impact of multiple influencing factors on the deflection and cracks under the bridge is analyzed, the risk assessment levels are divided, and the corresponding response measures are determined based on the actual factor values.
A hierarchical warning of the deflection and cracks under continuous rigid frame bridges is achieved, ensuring the safety and durability of the bridge structure during service period, and providing timely reinforcement measures.
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Figure CN115114832B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of bridge management and maintenance, and in particular to a multi-source and multi-scale intelligent hierarchical early warning method and system for bridges. Background Art
[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.
[0003] A continuous rigid frame bridge is a continuous beam bridge with pier-beam consolidation. It usually adopts a prestressed concrete structure, has more than two main piers, and adopts a pier-beam consolidation system. Prestressed concrete continuous rigid frame bridges are widely used in bridge engineering due to their advantages of high structural rigidity, good driving smoothness, and low cost.
[0004] However, during the long-term service of continuous rigid frame bridges, as the service life increases, the mid-span of the continuous rigid frame continues to deflect, which will cause poor linearity during the operation period of the bridge and cause discomfort to passengers, and even endanger driving safety. That is, after the bridge is opened to traffic, various loads cause the beam to bend, resulting in a downward displacement of the mid-span, namely deflection. The serious deflection problem in the mid-span of the continuous rigid frame bridge will affect the safety and durability of the bridge structure, limiting the further application of the continuous rigid frame bridge in engineering. Therefore, the risk assessment and early warning research on the deflection prediction of continuous rigid frame bridges is of great significance to ensure the safety and durability of the bridge structure during service. Summary of the invention
[0005] In order to address the deficiencies of the above-mentioned prior art, the present invention provides a multi-source and multi-scale intelligent graded early warning method and system for bridges, which can realize graded early warning of deflection and cracks of continuous rigid frame bridges, select corresponding countermeasures according to the levels of deflection and cracks of continuous rigid frame bridges, and ensure the safety and durability of bridge structures during service.
[0006] In a first aspect, the present disclosure provides a multi-source and multi-scale intelligent hierarchical early warning method for bridges:
[0007] A multi-source and multi-scale intelligent hierarchical early warning method for bridges, comprising:
[0008] Establish the finite element model of the bridge and the mid-span model with the largest deflection of the bridge based on the actual design data of the bridge;
[0009] Based on the finite element model of the bridge, the influence of various influencing factors on the deflection of the bridge is analyzed, the internal forces of the bridge under different deflection degrees are obtained, and the deflection threshold of the mid-span of the bridge is determined;
[0010] Based on the mid-span model with the largest deflection of the bridge, combined with different deflection degrees and the internal forces of the bridge under different deflection degrees, the crack conditions of the bridge under different deflection degrees are analyzed;
[0011] Based on the bridge crack condition, divide the deflection threshold of the mid-span of the bridge to obtain the risk assessment level;
[0012] Construct the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks. According to the actual values of various different influencing factors, determine the actual deflection and crack conditions of the bridge, and then determine the corresponding risk assessment level.
[0013] A further technical solution is to establish an initial finite element model of the steel bridge based on the MIDAS large finite element software according to the structural geometric dimensions, component cross-sections and positions, and material properties in the design data.
[0014] A further technical solution is that the influencing factors include loading age, environmental relative humidity, prestress loss rate, crack stiffness reduction rate, and overweight rate.
[0015] A further technical solution is that the loading age and environmental relative humidity are inversely proportional to the bridge deflection, and the prestress loss rate, crack stiffness reduction rate, and overweight rate are directly proportional to the bridge deflection.
[0016] A further technical solution is that the determination of the mid-span deflection threshold of the bridge refers to obtaining the mid-span deflection threshold of the bridge by combining the deflection-span ratio specified in the code requirements.
[0017] A further technical solution is to input the internal forces suffered by the bridge under different deflection degrees into the mid-span model with the largest bridge deflection, and obtain the bridge crack conditions under different deflection degrees based on the mid-span model with the largest bridge deflection.
[0018] A further technical solution is that the risk assessment level is as follows: setting it as a yellow warning when it reaches 60% and below of the deflection threshold, and taking no measures; setting it as an orange warning when it reaches 60% - 80% of the deflection threshold, and taking appropriate reinforcement measures; setting it as a red warning when it reaches more than 80% of the deflection threshold, and must take reinforcement measures as soon as possible.
[0019] In the second aspect, the present disclosure provides a multi-source and multi-scale intelligent grading warning system for bridges, including:
[0020] A model building module for establishing a bridge finite element model and a mid-span model with the largest bridge deflection according to the actual design data of the bridge;
[0021] A risk assessment level division module for analyzing the influence of various different influencing factors on the bridge deflection based on the bridge finite element model to obtain the internal forces suffered by the bridge under different deflection degrees, and at the same time determining the mid-span deflection threshold of the bridge; based on the mid-span model with the largest bridge deflection, combining different deflection degrees and the internal forces suffered by the bridge under different deflection degrees, analyzing the bridge crack conditions under different deflection degrees; based on the bridge crack conditions, dividing the mid-span deflection threshold of the bridge to obtain the risk assessment level;
[0022] A data processing module for constructing the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks.
[0023] A risk assessment module for determining the actual deflection and crack conditions of the bridge based on the actual values of various different influencing factors, and further determining the corresponding risk assessment level.
[0024] In a third aspect, the present disclosure also provides an electronic device, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps of the method described in the first aspect are completed.
[0025] In a fourth aspect, the present disclosure also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the method described in the first aspect are completed.
[0026] The above one or more technical solutions have the following beneficial effects:
[0027] 1. The present disclosure proposes a multi-source and multi-scale intelligent grading early warning method and system for bridges. By analyzing the overall bridge, bridge deflection, and local cracks of the bridge, the relationships between multiple different influencing factors of the bridge and the bridge deflection and crack conditions are obtained, and the bridge deflection threshold is divided based on the crack conditions to obtain the risk assessment level. The risk assessment of the bridge can be realized according to the actual influencing factor values of the bridge, which is convenient for the staff to take corresponding countermeasures.
[0028] 2. The present disclosure proposes a multi-source and multi-scale intelligent grading early warning method and system for bridges. By analyzing the cracks, a reasonable threshold for the actual deflection of the continuous rigid frame bridge is obtained, and the grading early warning of the deflection and cracks of the continuous rigid frame bridge is realized. Corresponding countermeasures are selected according to the grades of the deflection and cracks of the continuous rigid frame bridge to ensure the safety and durability of the bridge structure during the service period. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.
[0030] Figure 1 It is the overall framework diagram of the multi-source and multi-scale intelligent grading early warning method for bridges described in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0031] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.
[0032] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0033] Embodiment 1
[0034] This embodiment provides a multi-source and multi-scale intelligent grading warning method for bridges:
[0035] As Figure 1 shown, a multi-source and multi-scale intelligent grading warning method for bridges includes:
[0036] Step 1: Establish a finite element model of the bridge and a mid-span model with the maximum deflection of the bridge according to the actual design data of the bridge.
[0037] Step 2: Based on the finite element model of the bridge, analyze the influence of various different influencing factors on the downward deflection of the bridge, obtain the internal forces suffered by the bridge under different downward deflection degrees, and at the same time determine the mid-span deflection threshold of the bridge.
[0038] Step 3: Based on the mid-span model with the maximum deflection of the bridge, combine different downward deflection degrees and the internal forces suffered by the bridge under different downward deflection degrees, and analyze the crack conditions of the bridge under different downward deflection degrees.
[0039] Step 4: Based on the crack conditions of the bridge, divide the mid-span deflection threshold of the bridge to obtain the risk assessment level.
[0040] Step 5: Construct the corresponding relationships between various different influencing factors and the changes in the bridge deflection and cracks, and determine the actual deflection and crack conditions of the bridge according to the actual values of various different influencing factors, and then determine the corresponding risk assessment level.
[0041] In this embodiment, in Step 1, first analyze the overall bridge, and establish a finite element model of the bridge and a mid-span model with the maximum deflection of the bridge according to the actual design data of the bridge.
[0042] Finite element analysis is an effective numerical analysis method in structural mechanics analysis and is often applied in technical fields such as hydraulic engineering, civil engineering, bridges, machinery, electrical machinery, mechanics, physics, etc. In the prior art, there are various software programs developed based on finite element analysis algorithms, namely finite element analysis software. Common general finite element software includes Midas, Abaqus, LMS-Samtech, Algor, Femap / NX Nastran, Hypermesh, COMSOL Multiphysics, FEPG, etc. In this embodiment, according to the design data, construction data, etc. of the actual project of the bridge, the MIDAS finite element software is used to construct a finite element model of the bridge. The design data and construction data mainly include the shape, material, size, construction stage, construction steps, environmental factors, etc. of the bridge. Specifically, based on the MIDAS large-scale finite element software, a finite element model of the bridge is established according to the structural geometric dimensions, component cross-sections and positions, and material properties in the design data. The specific process is as follows: First, all the nodes of the finite element model are established with the steel bridge structure node coordinates; then, all the elements of the finite element model are established according to the design cross-sections, material parameters, and their positions; finally, couplings and constraints are applied to the nodes according to the constraint conditions to obtain the finite element model of the bridge.
[0043] Similarly, in this embodiment, according to the design data, construction data, etc. of the actual project of the bridge, the ABAQUS finite element software is used to construct a mid-span model with the largest deflection of the bridge.
[0044] The finite element model of the bridge is used to analyze the overall force and displacement deformation of the bridge, while the mid-span model with the largest deflection of the bridge is used to analyze the local crack conditions at the mid-span of the bridge.
[0045] The problem of bridge cracks will seriously endanger the durability and bearing capacity of road bridges, and the degree of harm of cracks of different degrees is also different. To a lesser extent, it can interfere with the comfort of drivers when driving, and to a greater extent, it can directly endanger the safety of vehicles and personnel. That is to say, cracks have a greater impact on the overall stiffness and usability safety of the bridge. Conducting an overall analysis of the bridge combined with the crack analysis at the maximum deflection at the mid-span can better grasp the performance of the bridge.
[0046] In step 2, based on the constructed finite element model of the bridge, the influences of various different influencing factors on the deflection of the bridge are analyzed to obtain the internal forces suffered by the bridge under different deflection degrees, and at the same time, the deflection threshold of the mid-span of the bridge is determined.
[0047] Specifically, based on the established MIDAS bridge finite element model, the effects of various common influencing factors on bridge deflection are analyzed. First, according to the research status of continuous rigid frame bridges and combined with the actual engineering situation of continuous rigid frame bridges, various influencing factors that affect bridge deflection are determined. These influencing factors are screened, with the less influential factors removed and the more influential factors retained, and finally the more influential factors are determined. The selection of the above-mentioned various influencing factors that affect bridge deflection is determined according to the specific actual situation of the project. Similarly, for the screening of these influencing factors, technicians can also make their own judgments according to the specific actual situation of the project, either removing certain influencing factors or not, and this embodiment does not make any limitations here. In this embodiment, the finally determined more influential factors include loading age, environmental relative humidity, prestress loss rate, crack stiffness reduction rate, and overweight rate.
[0048] After determining the influencing factors, the effects of various different influencing factors on bridge deflection are analyzed. Based on this bridge finite element model, the values of the above-mentioned influencing factors are adjusted, such as adjusting the number of days of loading age, the percentage of environmental relative humidity, the percentage of prestress loss, the percentage of stiffness reduction, and the overweight rate. By changing the values of the influencing factors, various working conditions are adjusted, and the deflection change law of the bridge under different working conditions is observed. The internal forces borne by the bridge under different deflection degrees are obtained through MIDAS finite element software.
[0049] Among them, the higher the environmental relative humidity, the smaller the deflection; the longer the loading age, the smaller the deflection; the higher the prestress loss rate, the greater the deflection; the higher the crack stiffness reduction rate, the greater the deflection; the higher the overweight rate, the greater the deflection. That is, the loading age and environmental relative humidity are inversely proportional to the bridge deflection, while the prestress loss rate, crack stiffness reduction rate, and overweight rate are directly proportional to the bridge deflection.
[0050] In addition, determining the mid-span deflection threshold of the bridge means obtaining the mid-span deflection threshold of the studied continuous rigid frame bridge by combining the deflection-span ratio specified in the code requirements. Among them, the specified deflection-span ratio refers to the deflection-span ratio specified in the "Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362-2018), and the deflection-span ratio should not exceed 1 / 600.
[0051] In step 3, based on the mid-span model with the maximum bridge deflection, combined with different deflection degrees and the internal forces borne by the bridge under different deflection degrees, the crack conditions of the bridge under different deflection degrees are analyzed.
[0052] Input the internal forces on the bridge under different degrees of downward deflection obtained in Step 2 above into the mid-span model of the bridge with the largest deflection constructed by the ABAQUS finite element analysis software. The mid-span model of the bridge with the largest deflection simulates the crack condition of the bridge. By adjusting the loading age days, relative environmental humidity percentage, prestress loss percentage, stiffness reduction percentage, and overweight rate to vary within a certain numerical range, determine the bridge deflection and crack conditions corresponding to different working conditions. In fact, the larger the downward deflection value of the continuous rigid frame bridge, the more and wider the cracks, and the more serious the crack condition.
[0053] In Step 4, based on the crack condition of the bridge, divide the deflection threshold of the mid-span of the bridge to obtain the risk assessment level. Through Steps 2 and 3, respectively obtain the corresponding deflection threshold of the mid-span of the bridge and the crack condition under different working conditions. According to the crack condition under different working conditions, divide the deflection threshold of the mid-span of the bridge to obtain the risk assessment level.
[0054] The analysis of the crack condition can be determined according to the specific actual working conditions. For example, divide the crack condition into harmless, minor, and serious according to the width of the crack. According to the crack condition, divide the deflection threshold of the mid-span of the bridge to achieve the division of the risk assessment level. In this embodiment, when it reaches 60% and below of the deflection threshold, it is set as a yellow warning. At this time, the deflection and cracks can be ignored and no measures are taken; when it reaches 60% - 80% of the deflection threshold, it is set as an orange warning, and appropriate reinforcement measures should be taken; when it reaches more than 80% of the deflection threshold, it is set as a red warning, and reinforcement measures must be taken as soon as possible.
[0055] In Step 5, construct the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks. According to the actual values of various different influencing factors, determine the actual deflection and crack conditions of the bridge, and then determine the corresponding risk assessment level.
[0056] Specifically, through the numerical values of various different influencing factors obtained in the above steps and the bridge deflection and crack conditions under this numerical value, construct a database corresponding to the internal force - deflection - crack. Use Python for data processing to construct the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks. On this basis, according to the actual multiple or single influencing factor numerical values of this bridge, the current actual deflection and crack conditions of this bridge can be determined. Combining with the determined deflection threshold, the risk assessment level of this bridge can be further determined, and whether to take reinforcement measures is selected according to the risk assessment level.
[0057] In the above solution of this embodiment, through the analysis of cracks, obtain a reasonable threshold for the deflection of the actual continuous rigid frame bridge, realize the hierarchical warning of the downward deflection and cracks of the continuous rigid frame bridge, and select corresponding countermeasures according to the levels of the downward deflection and cracks of the continuous rigid frame bridge to ensure the safety and durability of the bridge structure during the service period.
[0058] Example 2
[0059] This embodiment provides a multi-source and multi-scale intelligent grading early warning system for bridges, including:
[0060] A model building module, configured to establish a finite element model of the bridge and a mid-span model with the largest deflection of the bridge according to the actual design data of the bridge;
[0061] A risk assessment level division module, configured to analyze the influence of various different influencing factors on the deflection of the bridge based on the finite element model of the bridge, obtain the internal forces suffered by the bridge under different deflection degrees, and determine the deflection threshold of the mid-span of the bridge at the same time; based on the mid-span model with the largest deflection of the bridge, combined with different deflection degrees and the internal forces suffered by the bridge under different deflection degrees, analyze the crack conditions of the bridge under different deflection degrees; based on the crack conditions of the bridge, divide the deflection threshold of the mid-span of the bridge to obtain the risk assessment level;
[0062] A data processing module, configured to establish the corresponding relationships between various different influencing factors and the deflection and crack changes of the bridge;
[0063] A risk assessment module, configured to determine the actual deflection and crack conditions of the bridge according to the actual values of various different influencing factors, and then determine the corresponding risk assessment level.
[0064] Example 3
[0065] This embodiment provides an electronic device, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps in the above-mentioned multi-source and multi-scale intelligent grading early warning method for bridges are completed.
[0066] Example 4
[0067] This embodiment also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by the processor, the steps in the above-mentioned multi-source and multi-scale intelligent grading early warning method for bridges are completed.
[0068] The steps involved in the above Examples 2 to 4 correspond to those in Method Example 1. For specific implementation manners, reference may be made to the relevant description part of Example 1. The term "computer-readable storage medium" should be understood to include a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.
[0069] Those skilled in the art should understand that the various modules or steps of the present invention described above can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.
[0070] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
[0071] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.
Claims
1. A multi-source and multi-scale intelligent hierarchical early warning method for bridges, characterized in that, Including: Establish a finite element model of the bridge and a mid-span model with the maximum bridge deflection according to the actual design data of the bridge; Based on the finite element model of the bridge, analyze the influence of various different influencing factors on the bridge deflection, obtain the internal forces suffered by the bridge under different deflection degrees, and at the same time determine the mid-span deflection threshold of the bridge; Based on the mid-span model with the maximum bridge deflection, combine different deflection degrees and the internal forces suffered by the bridge under different deflection degrees, and analyze the bridge crack conditions under different deflection degrees; Based on the bridge crack conditions, divide the mid-span deflection threshold of the bridge to obtain the risk assessment level; Construct the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks, and determine the actual deflection and crack conditions of the bridge according to the actual values of various different influencing factors, and then determine the corresponding risk assessment level.
2. The multi-source and multi-scale intelligent hierarchical early warning method for bridges according to claim 1, characterized in that Based on the MIDAS large finite element software, establish an initial finite element model of the steel bridge according to the structural geometric dimensions, component cross-sections and positions, and material properties in the design data.
3. The multi-source and multi-scale intelligent hierarchical early warning method for bridges according to claim 1, characterized in that, The influencing factors include loading age, environmental relative humidity, prestress loss rate, crack stiffness reduction rate, and overweight rate.
4. The multi-source and multi-scale intelligent grading early warning method for bridges according to claim 3, characterized in that, The loading age and environmental relative humidity are inversely proportional to the bridge deflection, and the prestress loss rate, crack stiffness reduction rate, and overweight rate are directly proportional to the bridge deflection.
5. The multi-source and multi-scale intelligent hierarchical early warning method for bridges according to claim 1, characterized in that, The determination of the mid-span deflection threshold of the bridge means obtaining the mid-span deflection threshold of the bridge in combination with the deflection-span ratio specified in the code requirements.
6. The multi-source and multi-scale intelligent hierarchical early warning method for a bridge according to claim 1, characterized in that Based on the mid-span model with the maximum bridge deflection, combining different deflection degrees and the internal forces suffered by the bridge under different deflection degrees, analyzing the bridge crack conditions under different deflection degrees means: Input the internal forces suffered by the bridge under different deflection degrees into the mid-span model with the maximum bridge deflection, and obtain the bridge crack conditions under different deflection degrees based on the mid-span model with the maximum bridge deflection.
7. A multi-source and multi-scale intelligent grading early warning method for bridges according to claim 1, characterized in that, The risk assessment levels are as follows: setting it as a yellow warning when reaching 60% and below of the deflection threshold, and taking no measures; setting it as an orange warning when reaching 60% - 80% of the deflection threshold, and taking appropriate reinforcement measures; setting it as a red warning when reaching more than 80% of the deflection threshold, and must take reinforcement measures as soon as possible.
8. A multi-source and multi-scale intelligent hierarchical early warning system for bridges, characterized in that, Including: A model building module for establishing a finite element model of the bridge and a mid-span model with the maximum bridge deflection according to the actual design data of the bridge; A risk assessment level division module for analyzing the influence of various different influencing factors on the bridge deflection based on the finite element model of the bridge, obtaining the internal forces suffered by the bridge under different deflection degrees, and at the same time determining the mid-span deflection threshold of the bridge; based on the mid-span model with the maximum bridge deflection, combining different deflection degrees and the internal forces suffered by the bridge under different deflection degrees, analyzing the bridge crack conditions under different deflection degrees; based on the bridge crack conditions, dividing the mid-span deflection threshold of the bridge to obtain the risk assessment level; A data processing module for constructing the corresponding relationships between various different influencing factors and the changes in bridge deflection and cracks; A risk assessment module for determining the actual deflection and crack conditions of the bridge according to the actual values of various different influencing factors, and then determining the corresponding risk assessment level.
9. An electronic device, characterized in that: It includes a memory, a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of a multi-source multi-scale intelligent hierarchical early warning method for bridges as described in any one of claims 1-7 are completed.
10. A computer-readable storage medium, characterized in that: For storing computer instructions, when the computer instructions are executed by the processor, the steps of a multi-source multi-scale intelligent hierarchical early warning method for bridges as described in any one of claims 1-7 are completed.
Citation Information
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