Mixed multi-column wall type pier damper distribution position positioning method and positioning system

Abstract

The invention relates to the technical field of bridge structure simulation, in particular to a hybrid multi-column wall type bridge pier damper distribution position positioning method which comprises the following steps: step 1, loading a three-dimensional model of a hybrid multi-column wall type bridge pier, and dividing the three-dimensional model into a plurality of stress units; 2, the damper arrangement position of a single multi-column wall type pier with the same structure as the mixed multi-column wall type pier is obtained, and an initial position set of dampers is generated; and 3, carrying out stress characteristic analysis on the damper arrangement position of the single multi-column wall type pier to generate damper arrangement characteristics. According to the technical scheme, the inapplicability of traditional empirical arrangement on the mixed material pier is effectively overcome, intelligent optimization positioning of the damper position from empirical dependence to hybrid structure dynamic response and performance target based is achieved, and the damping efficiency and engineering economy of the damper in the complex mixed pier are improved.

Description

Technical Field

[0001] This application relates to the field of bridge structure simulation technology, and more specifically, to a method for locating the distribution of dampers in a hybrid multi-column pier. Background Technology

[0002] Wall-mounted piers are a common type of pier in modern bridge engineering. Their structural materials are mainly divided into traditional reinforced concrete (RC) and ultra-high performance concrete (UHPC), which has seen rapid development in recent years. UHPC, with its superior compressive strength, toughness, and durability, is often used in key load-bearing parts of piers or as an outer cladding layer, forming a hybrid material (RC-UHPC) wall-mounted pier with the RC core. This hybrid structure aims to combine the economic advantages of RC with the high performance of UHPC, thereby improving the overall seismic resistance and service life of the pier.

[0003] In bridge seismic design, dampers, as an important passive energy dissipation and vibration reduction device, are widely used in bridge pier structures. Their core function is to actively absorb and dissipate the energy input from earthquakes through their hysteretic or viscous energy dissipation characteristics, thereby significantly reducing the stress, deformation, and damage to key parts of the pier (such as the pier base, pier top, and connection nodes), and improving the overall seismic performance of the bridge. Currently, in engineering practice, the placement of dampers is usually determined based on experience, simplified models, or seismic analysis results for piers made of a single material (mainly RC), often adopting relatively fixed patterns (such as concentrated placement at the pier base or uniform distribution along the pier height), lacking refined consideration of the complex dynamic response of the structure.

[0004] Existing damper placement strategies are primarily developed for homogeneous reinforced concrete (RC) piers. Their applicability faces significant challenges when applied to multi-column piers made of hybrid materials (RC-UHPC). Due to the significant differences in material properties (such as elastic modulus, strength, and damping characteristics) between UHPC and RC, the dynamic response mode, plastic hinge formation mechanism, internal force distribution, and energy dissipation path of hybrid piers are fundamentally different from those of pure RC piers. Existing "fixed position" or "empirical position" placement methods based on RC piers fail to fully consider the enhancing effect of the high-performance region of UHPC on structural stiffness and energy dissipation capacity, as well as the complex stress state and potential weak points at the interface between the two materials. This results in limited applicability of damper placement in hybrid piers, potentially failing to fully realize their optimal energy dissipation efficiency, and even hindering the utilization of UHPC material advantages or triggering localized adverse effects due to improper placement, making it difficult to achieve the expected overall seismic performance improvement goal of hybrid piers. Summary of the Invention

[0005] The summary section of this application is intended to provide a brief overview of the concepts, which will be described in detail in the detailed description section below. This summary section is not intended to identify key or essential features of the claimed technical solutions, nor is it intended to limit the scope of the claimed technical solutions.

[0006] Some embodiments of this application propose a method for locating the distribution of dampers in hybrid multi-column piers to address the technical problems mentioned in the background section above.

[0007] As a first aspect of this application, some embodiments of this application provide a method for locating the distribution of dampers in a hybrid multi-column pier, comprising the following steps: Step 1: Load the 3D model of the hybrid multi-column pier and divide the 3D model into several stress elements; Step 2: Obtain the damper arrangement positions of a single multi-column pier that is identical to the hybrid multi-column pier structure, and generate the initial position set of the dampers; Step 3: Perform stress characteristic analysis on the damper arrangement location of a single multi-column wall-type bridge pier to generate damper arrangement characteristics; Step 4: Based on the damper arrangement features, extract several similar damper arrangement positions from the 3D model and add them to the initial position set; Step 5: Load all damper placement positions from the initial position set onto the 3D model, set up dampers at the damper placement positions, and simulate the displacement information of the 3D model when subjected to random earthquake information. Step 6: Construct the damper setting equation, with the objective condition that the displacement information of each force unit does not exceed the maximum threshold, and gradually reduce the number of dampers until the optimal damper position allocation scheme is obtained.

[0008] The technical solution provided in this application constructs a three-dimensional model of a hybrid multi-column pier and divides it into force-bearing elements. Combining existing layout experience (initial location set) and force characteristic analysis (layout characteristics) of single-material piers, it expands to potential damper force-bearing elements applicable to the characteristics of hybrid materials. Subsequently, it uses seismic motion simulation to model the displacement response of the pier under random earthquake loading, and iteratively optimizes the damper setting equations based on the core objective of controlling the displacement of key components to within limits. This optimization process, while ensuring the overall structural seismic safety (meeting displacement threshold requirements), systematically and gradually reduces the number of dampers, ultimately selecting the allocation scheme with the fewest damper configurations and optimal locations. This method effectively overcomes the inapplicability of traditional empirical layouts on hybrid material piers, realizing intelligent optimization of damper placement from experience-dependent to based on the dynamic response and performance objectives of the hybrid structure, thus improving the damping efficiency and engineering economy of dampers in complex hybrid piers.

[0009] Furthermore, step 1 includes the following steps: Step 11: Load the 3D model of the hybrid multi-column wall pier, set the RC structure as the normal area, and set the UHPC as the high-strength area; Step 12: Define the minimum partitioning regions of the RC structure and the UHPC structure; Step 13: Divide the ordinary region into several force-bearing elements according to the minimum division region of the RC structure; Step 14: Divide the high-strength region into several stress-bearing elements according to the minimum division region of the UHPC structure.

[0010] This application defines differentiated minimum segmentation regions based on material properties (RC and UHPC) when segmenting stress-bearing elements. By defining the RC structure as a "normal region" and setting its minimum segmentation size, and defining the UHPC structure as a "high-strength region" and setting its (usually smaller) minimum segmentation size, a refined mesh generation based on material properties is achieved. This method effectively overcomes the limitations of traditional uniform mesh generation on hybrid material piers, significantly improves the accuracy of stress / deformation analysis in key regions (especially the UHPC region and its interface with RC), ensures that the structural response simulation results (such as the displacement information in step 5) upon which subsequent damper position optimization depends more realistically reflect the actual mechanical behavior of the hybrid materials, and avoids unnecessary computational resource consumption caused by over-refining the RC region mesh.

[0011] Furthermore, step 2 includes the following steps: Step 21: Obtain the design specifications for a single multi-column pier and extract several damper placement locations from the design specifications; Step 22: Obtain several actual design cases of single multi-column wall-type bridge piers, and extract all damper placement positions from the actual design cases; Step 23: Collect all damper placement positions from Step 21 and Step 22 to generate an initial position set.

[0012] This application integrates both theoretical specifications and engineering practice when generating the initial damper location set. By not only extracting theoretically recommended placement locations from the design specifications of single-material bridge piers, but also extensively collecting damper locations used in actual engineering cases of similar bridge piers, the initial location set constructed by this method highly condenses typical and mature placement schemes in the industry. This dual-source data fusion strategy of "specifications + cases" significantly improves the comprehensiveness, representativeness, and engineering credibility of the initial location set, providing a high-quality and highly relevant starting point for subsequent intelligent location expansion (step 4) and optimization screening (step 6) based on the characteristics of mixed materials. It effectively avoids the limitations or impracticality of schemes that may result from relying solely on theoretical specifications, greatly improving the reliability and engineering practical value of the entire damper positioning optimization process.

[0013] Furthermore, step 3 includes the following steps: Step 31: Extract the damper arrangement position of a single multi-column wall-type bridge pier and obtain the design features of the damper arrangement position; Step 32: Obtain the tension-compression characteristics at the damper placement location; Step 33: Generate a similarity plane by using the similarity of design features as the horizontal axis and the similarity of tension-compression features as the vertical axis. Generate a selection region in the similarity plane and use the selection region as the damper arrangement feature.

[0014] This application, in analyzing damper arrangement characteristics, distills the complex structural stress response into design features (spatial location) and tension-compression features (mechanical behavior in key directions). By constructing a similarity plane with the similarity of these two features as coordinate axes, and defining selected regions as comprehensive "damper arrangement features," this method achieves efficient and intuitive representation and quantification of complex mechanical laws. This strategy of dual-dimensional feature extraction and planar representation significantly reduces the complexity of traditional multi-parameter, high-dimensional stress analysis, while accurately capturing and refining the core mechanical laws affecting damper effectiveness (such as force transmission paths and energy dissipation mechanisms in key directions).

[0015] Furthermore, the design feature is the distance from the center of the damper to the support column along the direction of the damper's force. The tension-compression characteristic refers to the structural pressure and tension that the damper needs to bear within the same diffusion range at both ends of the damper.

[0016] This application innovatively distills the complex structural stress response into two core quantitative dimensions when analyzing damper arrangement characteristics. By constructing a similarity plane with the similarity of these two features as coordinate axes, and defining the selected region as the comprehensive "damper arrangement feature," this method achieves efficient and intuitive characterization and quantification of complex mechanical laws. This strategy of dual-dimensional feature extraction and planar representation significantly reduces the complexity of traditional multi-parameter, high-dimensional stress analysis, while accurately capturing and refining the core mechanical laws affecting damper effectiveness.

[0017] Step 4 includes the following steps: Step 41: Load the 3D model and map each force element in the 3D model to a similarity plane; Step 42: Determine whether the position of the force unit mapped to the similarity plane is located in the selected area. If it is located in the selected area, the force unit is arranged as a similar damper position. If it is not located in the selected area, the force unit is not a similar damper position. Step 43: Add all similar damper placement locations to the initial location set.

[0018] In this application, when expanding the damper's load-bearing units, the physical load-bearing units in the 3D pier model are mapped to the mechanical feature space (similarity plane) defined in step 3. By rigorously determining whether the projection point of each load-bearing unit in the feature space falls within the "selection area" representing the effective arrangement pattern, this method achieves intelligent screening based on the similarity of core mechanical features. This "physical location -> feature space mapping -> area matching" mechanism can accurately and efficiently identify potential damper installation points from complex hybrid structure models that have similar key mechanical behaviors (design features and tension-compression characteristics) to historical successful experiences (single-material piers).

[0019] Furthermore, step 5 includes the following steps: Step 51: Simulate the spatial propagation effect of seismic waves by time lag to generate time lag information of the impact of seismic waves on each stress unit; Step 52: Load all damper placement positions in the initial position set onto the 3D model, set dampers at the damper placement positions, and model the 3D model to generate motion equations based on the time lag information. Step 53: Solve the equations of motion to generate displacement information for each stress element under seismic waves.

[0020] This application innovatively introduces a time lag effect to simulate the spatial propagation process of seismic waves in bridge pier structures when simulating seismic response. By calculating and applying the time lag information of each stress unit affected by seismic waves, the motion equation constructed by this method realistically reproduces the asynchronous nature of the forces on different parts of the bridge pier under non-uniform seismic input. This dynamic modeling mechanism effectively overcomes the shortcomings of traditional uniform excitation models in capturing traveling wave effects and differences in local dynamic responses, significantly improving the physical realism and accuracy of the simulation results of structural response (especially displacement information). This scheme can accurately characterize the complex dynamic imbalance state and internal force redistribution of hybrid bridge piers (especially key areas such as the interface between RC and UHPC materials and multi-column connections) caused by wave propagation under seismic loading, providing a highly reliable dynamic response data foundation that reflects the actual wave characteristics for subsequent damper optimization based on displacement threshold (step 6).

[0021] Step 6 includes the following steps: Step 61: Obtain all damper locations, select the dampers to be reduced based on the particle swarm optimization algorithm, and generate a new damper loading scheme; The loss function of the particle swarm optimization algorithm is related to the number of dampers and the displacement information of the force-bearing elements. Step 62: According to the damper loading scheme, adjust the damping parameters of the damper placement positions in the equation of motion to the corresponding damping parameters in sequence to update the equation of motion; Step 63: Resolve the motion equations to generate displacement information of each stress element under seismic waves, and determine whether the displacement information of each stress element does not exceed the maximum threshold based on the vibration information of each stress element.

[0022] In the technical solution provided in this application, the constructed motion equations only need to adjust the damping parameters to simulate whether the corresponding force-bearing unit has installed a damper. Thus, at a low cost, various damper installation schemes can be simulated. In this way, the particle swarm optimization algorithm can be used to continuously reduce the number of dampers and quickly select the required damper arrangement scheme.

[0023] Furthermore, the equations of motion are: ; Where M represents the total mass of the pier, i represents the stiffness coefficient of the i-th load-bearing element, and c i This represents the damping coefficient of the i-th force-bearing element, where i represents the index of the force-bearing element. Indicates the horizontal velocity at the center point. Indicates the horizontal displacement of the center point. Indicates the horizontal acceleration at the center point. This represents the seismic displacement input of the i-th stress element. This represents the seismic velocity input for the i-th stress-bearing unit.

[0024] As a second aspect of this application, this application provides a hybrid multi-column pier damper distribution positioning system, comprising: Data entry device for entering structural information of hybrid multi-column piers; The simulation test device uses the aforementioned method for locating the distribution of dampers in hybrid multi-column piers to generate the optimal damper location allocation scheme.

[0025] This application has the following beneficial effects: By differentiating material properties to segment the stress-bearing elements and applying the time lag effect to simulate the spatial propagation of seismic waves, a model reflecting the dynamic response of structures under non-uniform excitation was established. This model accurately captures the complex dynamic behavior and displacement response of key areas (such as material interfaces and connection points), providing a reliable data foundation for optimization.

[0026] An initial location set was constructed by combining design specifications and historical cases. Similarity plane definition layout features were constructed using design features and tension-compression features. Potential high-potential locations with similar mechanical properties in mixed bridge piers were identified through feature space mapping. The initial candidate set was systematically expanded and screened.

[0027] Based on the particle swarm optimization algorithm and a dual-objective loss function (minimizing the number of dampers and satisfying displacement threshold constraints), this method efficiently evaluates the performance of different schemes by adjusting only the damping parameters, selecting the arrangement scheme with the fewest dampers and the optimal location, which significantly reduces engineering costs. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of a hybrid multi-column wall bridge pier.

[0029] Figure 2 A flowchart illustrating the method for locating the distribution of dampers in hybrid multi-column bridge piers. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments. The same reference numerals in the accompanying drawings represent the same components. It should be noted that the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the described embodiments of this application without creative effort are within the scope of protection of this application.

[0031] Compared to the embodiments shown in the accompanying drawings, feasible embodiments within the scope of this application may have fewer components, other components not shown in the drawings, different components, differently arranged components, or components with different connections, etc. Furthermore, two or more components in the drawings may be implemented in a single component, or a single component shown in the drawings may be implemented as multiple separate components.

[0032] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” and similar terms used in this specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not necessarily indicate a quantity limitation. Terms such as “upper” and “lower” are used only to indicate relative positional relationships, and these relative positional relationships may change accordingly when the absolute position of the described object changes.

[0033] Hybrid multi-column wall-end piers are a modern bridge pier structure characterized by the combined use of concrete materials with different properties to optimize structural performance and economic efficiency. A typical hybrid pier usually consists of multiple (usually 2-4) relatively slender wall-end columns connected as a whole by a foundation and a cap beam. In critical load-bearing areas (such as the pier base, the connection between the column top and the cap beam, or areas expected to have plastic hinges), ultra-high performance concrete (UHPC) is used to provide extremely high strength, toughness, and durability; while in non-critical or secondary load-bearing areas, conventional reinforced concrete (RC) is used to control costs. Figure 1 As shown, Figure 1 The actual structure of the hybrid multi-column pier is shown in the figure.

[0034] Generally, the structure of hybrid multi-column piers varies depending on the design requirements. The design of hybrid multi-column piers is typically based on the actual needs of the project. After completing the design of the hybrid multi-column pier, dampers need to be installed on the pier. The core function of the damper is to significantly improve the seismic performance of the pier. When strong dynamic loads such as earthquakes act on the bridge, the damper actively absorbs and dissipates the large amount of kinetic energy input into the pier structure by the earthquake through its internal efficient energy dissipation mechanisms (such as fluid friction, material yielding, or viscoelastic hysteresis). This energy dissipation process effectively suppresses the vibration amplitude (displacement response) and acceleration response of key parts of the pier (especially the interface between UHPC and RC materials, the expected area of ​​plastic hinges, and the connection between the column base and column top), thereby significantly reducing the stress level borne by the structural components (concrete and steel reinforcement), delaying or preventing crack propagation and structural damage accumulation, ensuring the overall safety and functionality of the pier under seismic loading, and helping to meet stringent seismic fortification requirements.

[0035] The number of dampers should not be increased excessively. Too many dampers not only significantly increase construction costs and maintenance burdens but may also cause localized stress concentrations at connection points, potentially leading to additional structural damage. Furthermore, their marginal damping benefits decrease significantly with increasing quantity. Therefore, when installing dampers on hybrid multi-column piers, systematic optimization is essential. Key considerations include: the structural dynamic characteristics of the pier (e.g., natural frequency, mode shape), expected seismic motion characteristics, identification of critical energy-dissipating areas (especially vulnerable areas such as the high-strength UHPC zone, the interface between RC and UHPC materials, plastic hinge zones, and the top / bottom connection of the columns), selection of damper type and parameters, precise matching of installation location and orientation, and clear performance control targets (e.g., displacement threshold). Ultimately, the goal is to find a configuration scheme that minimizes the number of dampers, optimizes their location, and achieves the best economic efficiency while ensuring seismic safety. Based on this, this application provides a method for locating the distribution of dampers on hybrid multi-column piers. This method can reasonably generate a damper arrangement scheme and accurately locate the dampers while meeting bridge vibration reduction requirements.

[0036] A method for locating the distribution of dampers in a hybrid multi-column bridge pier includes the following steps: Step 1: Load the 3D model of the hybrid multi-column pier and divide the 3D model into several stress elements.

[0037] Step 1 includes the following steps: Step 11: Load the 3D model of the hybrid multi-column pier, set the RC structure as the normal area, and set the UHPC as the high-strength area.

[0038] The 3D model is a digital model that accurately reflects the geometry, dimensions, and material distribution of a hybrid multi-column pier through computer-aided design. Based on the pier design drawings, all structural parts of the model composed of ordinary reinforced concrete (RC) (such as the pier body, abutment, and non-node areas of the cap beam) are precisely selected manually or based on material property scripts using the geometry selection tool, and uniformly assigned and marked as "ordinary areas"; at the same time, key structural parts composed of ultra-high performance concrete (UHPC) (such as the plastic hinge area at the bottom of the pier, the core area of ​​the column top node, and the local reinforced section) are selected and uniformly assigned and marked as "high-strength areas".

[0039] Step 12: Define the minimum partition region of the RC structure and the minimum partition region of the UHPC structure.

[0040] When performing vibration analysis on bridge piers, to reduce computational complexity, the continuous structure needs to be discretized into a finite number of support points (i.e., element nodes), with each support point representing the mechanical behavior of its surrounding area. Due to significant differences in material properties and stress characteristics between RC (reinforced concrete) and UHPC (ultra-high-performance concrete) structures, the density of support points (i.e., the minimum segmentation size) should also differ: for the ordinary region (RC), due to its lower material strength and relatively gentle stress distribution, a larger minimum segmentation size (e.g., 0.5m) can be set. 3 With sparser support points, the accuracy of critical overall deformation is ensured while significantly saving computational resources. For high-strength regions (UHPC), their ultra-high strength and stiffness easily lead to high local stress concentration (especially in plastic hinge regions and material interfaces), and it is necessary to accurately capture their complex damage evolution process. Therefore, a significantly smaller minimum segmentation region size (e.g., 0.2m) must be set. 3 This approach uses high-density support points to meticulously characterize the local high-gradient stress field and microcrack behavior, ensuring the reliability of response analysis in critical areas. This strategy of differentiated support point density based on material properties is the core principle for balancing computational efficiency and simulation accuracy.

[0041] Step 13: Divide the ordinary region into several force-bearing elements according to the minimum division region of the RC structure; Step 14: Divide the high-strength region into several stress-bearing elements according to the minimum division region of the UHPC structure.

[0042] After dividing the 3D model into several force-bearing elements, the entire 3D model can be simplified into a model composed of force-bearing elements. By analyzing each force-bearing element and whether it will produce a displacement exceeding the limit under the corresponding tensile and compressive forces, it can be determined whether the bridge pier meets the requirements.

[0043] Step 2: Obtain the damper arrangement positions of a single multi-column pier that is identical to the hybrid multi-column pier structure, and generate the initial position set of the dampers.

[0044] Furthermore, step 2 includes the following steps: Step 21: Obtain the design specifications for a single multi-column pier and extract several damper placement locations from the design specifications.

[0045] The structures of single-column multi-walled bridge piers and hybrid multi-column multi-walled bridge piers are the same. However, single-column multi-walled bridge piers are entirely constructed of reinforced concrete (RC), resulting in lower bearing capacity. Therefore, the design quantity and location of dampers differ from those of hybrid multi-column multi-walled bridge piers in practice. Nevertheless, because their structures are similar, the placement of dampers in single-column multi-walled bridge piers is of significant reference value. For example, the "Code for Seismic Design of Highway Bridges" specifies the location and number of dampers. The choice of design code can be adjusted according to the actual situation. Step 21 essentially involves finding potential locations for dampers from established single-column multi-walled bridge pier design schemes.

[0046] Step 22: Obtain several actual design cases of single multi-column wall-type bridge piers, and extract all damper placement positions from the actual design cases.

[0047] Several design cases refer to relevant actual cases where bridge construction and acceptance have been completed, from which the location of the damper is extracted.

[0048] Step 23: Collect all damper placement positions from Step 21 and Step 22 to generate an initial position set.

[0049] Thus, through steps 21 and 22, all theoretically and compliantly possible locations for placing dampers can be identified. These locations are also among the most likely places to place dampers in hybrid multi-column pier bridges.

[0050] Step 3: Perform stress characteristic analysis on the damper arrangement location of a single multi-column wall-type bridge pier to generate damper arrangement characteristics.

[0051] In step 2, all theoretically and practically possible damper locations were obtained. However, due to the structural differences between single multi-column piers and hybrid multi-column piers, some locations where dampers could be placed may have been missed. Therefore, it is necessary to further extract possible locations for damper placement based on the stress characteristics.

[0052] Furthermore, step 3 includes the following steps: Step 31: Extract the damper arrangement position of a single multi-column wall-type bridge pier and obtain the design features of the damper arrangement position; The design feature is the distance from the center of the damper to the support column along the direction of the force applied to the damper.

[0053] Design features refer to the core geometric parameters of the damper installation location, specifically defined as the vertical distance (d) from the center point of the damper (usually the midpoint of the line connecting the two connection points) along its preset main force direction (such as the direction of the damper piston rod axis) to the surface of the nearest supporting column (wall-type pier) structure (outer edge of concrete).

[0054] This distance reflects the lever arm length of the damper relative to the main load-bearing component, directly affecting its energy dissipation efficiency. In the three-dimensional model of a single multi-column pier, the geometric center coordinates of the target damper are located, its preset principal force direction vector is determined, and the vertical distance from the center point along the force direction vector to the outer surface of the nearest pier is calculated (this can be achieved through geometric projection and intersection algorithms). This distance value (d) is the design characteristic value of the damper's placement position.

[0055] Step 32: Obtain the tension-compression characteristics at the damper placement location; The tension-compression characteristic refers to the structural pressure and tension that the damper needs to bear within the same diffusion range at both ends of the damper.

[0056] The tension-compression characteristic refers to the load-bearing capacity index of the local structure at the damper installation location against tensile and compressive loads. Specifically, it is defined as follows: taking the connection points at both ends of the damper as the center, delineate a standardized geometric diffusion range in the structural entity (e.g., a spherical region with a radius of 1.5 times the size of the connector centered on the connection point, or a cubic region with a side length equal to the maximum size of the connector plate), and calculate the maximum allowable structural compressive force and maximum allowable structural tensile force that the structure within this diffusion range can withstand in the damper's preset principal force direction (tension / compression direction).

[0057] This characteristic reflects the material strength and structural resistance of the local area at the installation point, and is a key parameter for evaluating whether the damper can effectively transmit large-tonnage cyclic loads. In the three-dimensional finite element model of a single multi-column pier, the coordinates of the connection points at both ends of the target damper are located, and the diffusion range geometry is generated according to preset rules. Based on material properties (RC or UHPC) and local structure (reinforcement ratio, connector strength), the ultimate pressure value resisting crushing and the ultimate tensile force value resisting peeling / cracking in the direction of damper force are obtained through local static analysis or standard formula calculations. These two values ​​together constitute the tensile-compression characteristic vector at this location.

[0058] Step 33: Generate a similarity plane by using the similarity of design features as the horizontal axis and the similarity of tension-compression features as the vertical axis. Generate a selection region in the similarity plane and use the selection region as the damper arrangement feature.

[0059] Specifically, a two-dimensional feature space is constructed with design feature similarity (Δd) as the abscissa and tension-compression feature similarity (Δσ) as the ordinate. Here, design feature similarity (Δd) is defined as the normalized result of the absolute difference between the design feature values ​​at corresponding positions of the target pier and a single pier; tension-compression feature similarity is defined as the normalized result of the Euclidean distance between the tension-compression feature vectors at corresponding positions of the target pier and a single pier.

[0060] All stress elements are plotted as scattered points according to the (Δd, Δσ) coordinates. A closed region (such as an ellipse or polygon) with high density and low difference is delineated by a preset threshold boundary (e.g., Δd ≤ 0.2 and Δσ ≤ 0.3). The points in this region represent candidate points whose design features and mechanical performance are highly matched with the reference position of a single pier. This closed region is defined as the selected region.

[0061] Step 4: Based on the damper arrangement features, extract several similar damper arrangement positions from the 3D model and add them to the initial position set.

[0062] Step 4 includes the following steps: Step 41: Load the 3D model and map each force element in the 3D model to a similarity plane; Step 42: Determine whether the position of the force unit mapped to the similarity plane is located in the selected area. If it is located in the selected area, the force unit is set as a similar damper arrangement position. If it is not located in the selected area, the force unit is not a similar damper arrangement position.

[0063] Step 43: Add all similar damper placement locations to the initial location set.

[0064] The process involves scanning all load-bearing elements. For each element, the vertical distance from its center point to the outer surface of the nearest support column along the damper's force direction is measured (design feature). The maximum tensile and compressive forces that the structural concrete can withstand within a specific diffusion range centered on this point are evaluated (tensile-compression feature). Next, these two feature values ​​are quantitatively compared with the corresponding features of a single pier reference location, calculating the percentage score for location proximity and the percentage score for bearing capacity matching. These two scores are then plotted as coordinate points on a pre-established "similarity plane" (horizontal axis for location proximity score, vertical axis for bearing capacity matching score). The system automatically detects whether the coordinate point falls within a pre-defined "selected area" on the plane. If the point is within this area, the candidate location is determined to have similar mechanical behavior to the reference location and is retained as an effective damper placement point. If the point is outside the area, it is determined to be a dissimilar location and is excluded. Finally, a set of all similar locations that pass the judgment is output to guide the optimal placement of dampers.

[0065] Step 5: Load all damper placement positions from the initial position set onto the 3D model, set up dampers at the damper placement positions, and simulate the displacement information of the 3D model when subjected to random earthquake information.

[0066] Step 5 includes the following steps: Step 51: Simulate the spatial propagation effect of seismic waves by time lag to generate time lag information of the impact of seismic waves on each stress unit; Step 51 specifically includes the following steps: Step 511: Predefine a basic dataset, which includes the total mass M of the piers and the stiffness k of the load-bearing elements. i Damping of the force-bearing unit c i Coordinates of the stress element (x) i y i ), reference point coordinates (x) ref y ref Seismic wave propagation direction θ, apparent wave velocity V app Reference point earthquake acceleration time history The reference point defines the baseline location where seismic waves arrive. When calculating time lag information, all other points are calculated based on the reference point.

[0067] Step 512: Calculate the time lag information of seismic waves ; ; Step 513: Calculate the seismic input time history of the stress element; ; ; ; This represents the acceleration time history of the i-th force-bearing element. This represents the velocity-time history of the i-th force-bearing element. The displacement time history of the i-th stress element, where t represents the index of the time node.

[0068] In this scheme, the force-bearing element will be treated as a point mass, that is, the center point of the force-bearing element will be used to analyze the point, so as to reduce the dimensionality of the calculation.

[0069] The parameters related to the seismic waves in step 51 are: V app , θ, (x ref y ref ), , , , Most of these parameters are directly defined data, while the time history information is calculated. Among them, the time history of seismic acceleration at the reference point includes the intensity information of the seismic waves (amplitude during the earthquake).

[0070] Step 52: Load all damper placement positions in the initial position set onto the 3D model, set dampers at the damper placement positions, and generate motion equations by modeling the 3D model based on the time lag information.

[0071] The equation of motion is: ; Where M represents the total mass of the pier, i represents the stiffness coefficient of the i-th load-bearing element, and c i This represents the damping coefficient of the i-th force-bearing element, where i represents the index of the force-bearing element. Indicates the horizontal velocity at the center point. Indicates the horizontal displacement of the center point. Indicates the horizontal acceleration at the center point. This represents the seismic displacement time history of the i-th stress element. This represents the seismic velocity time history of the i-th load-bearing element. The center point refers to the center point of the upper crossbeam in the pier, and n represents the total number of load-bearing elements.

[0072] Step 53: Solve the equations of motion to generate displacement information for each stress element under seismic waves.

[0073] Step 53 includes the following steps: Step 531: Construct the state-space equations based on the equations of motion and acceleration time histories; ; ; n represents the total number of force-bearing elements; yes A matrix that describes the internal dynamic relationships of a system: ; ; ; ; ; yes A matrix describing how seismic acceleration input affects the system. , , , These are the intermediate parameter matrices of A; ; It is a matrix of all zeros. Each pair of rows corresponds to one stress unit.

[0074] Step 532: Solve the state-space equations using the fourth-order Runge-Kutta method to generate the time history of the state variables X; N represents the total number of time points in solving the time history of the state variable X; Step 533: Calculate the relative displacement of each force element based on the state variable time history X. ; ; This indicates the horizontal displacement of the center point.

[0075] Step 6: Construct the damper setting equation, with the objective condition that the displacement information of each force unit does not exceed the maximum threshold, and gradually reduce the number of dampers until the optimal damper position allocation scheme is obtained.

[0076] Step 6 includes the following steps: Step 61: Obtain all damper locations, select the dampers to be reduced based on the particle swarm optimization algorithm, and generate a new damper loading scheme; where the loss function of the particle swarm optimization algorithm is related to the number of dampers and the displacement information of the force-bearing elements.

[0077] Particle swarm optimization is an objective optimization algorithm that continuously generates solutions to approximate the optimal solution given the known optimization objective.

[0078] Step 62: According to the damper loading scheme, adjust the damping parameters of the damper placement positions in the equation of motion to the corresponding damping parameters in sequence to update the equation of motion; In step 61, the particle swarm optimization algorithm randomly selects several solutions, each of which needs to be solved using the motion equations from step 5. Therefore, in step 62, the corresponding motion equations are loaded, which means adjusting the damping information at the corresponding positions.

[0079] For example, in Scheme 1, a damper is added to the force-bearing element at position (11, 12), so the damping coefficient of that force-bearing element needs to be adjusted to match the damping coefficient of the damper. In this way, the damping coefficient of all possible schemes can be adjusted.

[0080] Step 63: Resolve the motion equations to generate displacement information of each stress element under seismic waves, and determine whether the displacement information of each stress element does not exceed the maximum threshold based on the vibration information of each stress element.

[0081] After loading all possible damper arrangement schemes in step 62, the scheme in step 5 can be used to simulate and calculate the relative displacement of each force unit. Based on the relative displacement of each force unit, it can be determined whether the scheme meets the requirements. In this way, the input damper arrangement schemes can be continuously evaluated to obtain the damper arrangement scheme with the lowest cost and the best quality.

[0082] Example 2: Example 1 illustrates how to obtain the optimal damper arrangement. The idea behind Example 1 is to identify all possible locations for dampers, then subtract from these locations to find a damper arrangement that meets engineering requirements while minimizing cost.

[0083] The key to Example 1 is that although the identified damper placement locations are all redundant, each one is a relatively classic damper placement location. No additional location optimization is required; it is only necessary to consider whether to place the damper at that location.

[0084] Example 2, based on Example 1, provides a specific implementation of the particle swarm optimization algorithm, which can accurately provide the required damper arrangement scheme: Furthermore, step 61 includes the following steps: Step 611: Obtain all damper placement locations and number all damper placement locations; Step 612: Determine whether to place dampers at all damper placement locations to generate a feasible solution matrix; The feasible solution matrix has Z rows, and the element of each row is C(k, Z), where k represents the row index, Z represents the total number of damper placement positions, and C represents the combination number calculation symbol. The k-th row of the feasible solution matrix represents the number of schemes for selecting k positions to place dampers from all the damper placement positions.

[0085] Step 613: Generate H particles in the feasible solution matrix, with particle index h, and set the fitness function f(x) h Set the termination condition for the iteration; f(x) h =q1+q2; where q1 represents the displacement influencing element, which is positively correlated with the sum of the relative displacements of all force-bearing units in the scheme corresponding to the particle, and q2 represents the cost influencing factor, which is positively correlated with the number of positions for screening dampers.

[0086] Thus, guided by the fitness function set in this application, the particles will try to optimize simultaneously in two directions: reducing the displacement of the entire bridge pier during an earthquake and reducing the number of dampers.

[0087] Step 614: For each particle, update the particle velocity and update the particle position based on the global optimal solution and the individual optimal position of each particle; Step 615: After the termination condition is met, output the globally optimal position as the corresponding solution.

[0088] The key in step 61 is to use the particle swarm optimization algorithm to select a suitable solution from the feasible solution matrix. Given that the feasible solution matrix and fitness function have already been constructed, how to perform particle iteration is a current technique.

[0089] The feasible solution matrix is ​​a two-dimensional matrix, but the number of feasible solutions in each row of the feasible solution matrix is ​​not the same. For example, taking 10 damper placement positions as an example, the number of feasible solutions in each row of the calculated 10-row feasible solution matrix is ​​1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1; Each particle has two dimensions (horizontal displacement and vertical displacement). Because the number of feasible solutions varies for each row, the position of a particle is measured as a percentage of that row.

[0090] For example, if particle A is in the 5th position in row 2, its position is (2, 0.5). When particle A's vertical velocity is 1 and its horizontal velocity is 0 in the next iteration, it needs to move from row 2 to row 3. The corresponding position of particle A then becomes (3, 0.5). Multiplying 0.5 by 45 gives 22.5, which, after rounding down, becomes 22. Thus, particle A's position becomes row 3, the 22nd feasible solution.

[0091] This scheme presents the method for constructing the feasible solution matrix and the method for updating particle positions. Therefore, the required damper allocation scheme can be quickly solved using only the fitness function.

[0092] Example 3: A hybrid multi-column wall bridge pier damper distribution location positioning system, comprising: a data input device for inputting structural information of the hybrid multi-column wall bridge pier; and a simulation testing device for generating the optimal damper position allocation scheme using the aforementioned hybrid multi-column wall bridge pier damper distribution location positioning method.

[0093] The above are merely preferred embodiments of this application and are not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for locating the distribution of dampers in a hybrid multi-column bridge pier, characterized in that, Includes the following steps: Step 1: Load the 3D model of the hybrid multi-column pier and divide the 3D model into several stress elements; Step 2: Obtain the damper arrangement positions of a single multi-column pier that is identical to the hybrid multi-column pier structure, and generate the initial position set of the dampers; Step 3: Perform stress characteristic analysis on the damper arrangement location of a single multi-column wall-type bridge pier to generate damper arrangement characteristics; Step 4: Based on the damper arrangement features, extract several similar damper arrangement positions from the 3D model and add them to the initial position set; Step 5: Load all damper placement positions from the initial position set onto the 3D model, set up dampers at the damper placement positions, and simulate the displacement information of the 3D model when subjected to random earthquake information. Step 6: Construct the damper setting equation, with the objective condition that the displacement information of each force unit does not exceed the maximum threshold, and gradually reduce the number of dampers until the optimal damper position allocation scheme is obtained.

2. The method for locating the distribution of hybrid multi-column wall-type bridge pier dampers according to claim 1, characterized in that, Step 1 includes the following steps: Step 11: Load the 3D model of the hybrid multi-column wall pier, set the RC structure as the normal area, and set the UHPC as the high-strength area; Step 12: Define the minimum partitioning regions of the RC structure and the UHPC structure; Step 13: Divide the ordinary region into several force-bearing elements according to the minimum division region of the RC structure; Step 14: Divide the high-strength region into several stress-bearing elements according to the minimum division region of the UHPC structure.

3. The method for locating the distribution of hybrid multi-column wall-type bridge pier dampers according to claim 1, characterized in that, Step 2 includes the following steps: Step 21: Obtain the design specifications for a single multi-column pier and extract several damper placement locations from the design specifications; Step 22: Obtain several actual design cases of single multi-column wall-type bridge piers, and extract all damper placement positions from the actual design cases; Step 23: Collect all damper placement positions from Step 21 and Step 22 to generate an initial position set.

4. The method for locating the distribution of dampers in a hybrid multi-column pier according to claim 1, characterized in that, Step 3 includes the following steps: Step 31: Extract the damper arrangement position of a single multi-column wall-type pier and obtain the design features of the damper arrangement position; Step 32: Obtain the tension-compression characteristics at the damper placement location; Step 33: Generate a similarity plane by using the similarity of design features as the horizontal axis and the similarity of tension-compression features as the vertical axis. Generate a selection region in the similarity plane and use the selection region as the damper arrangement feature.

5. The method for locating the distribution position of hybrid multi-column wall-type bridge pier dampers according to claim 4, characterized in that, The design feature is the distance from the center of the damper to the support column along the direction of the damper's force. The tension-compression characteristic refers to the structural pressure and tension that the damper needs to bear within the same diffusion range at both ends of the damper.

6. The method for locating the distribution of dampers in a hybrid multi-column pier according to claim 1, characterized in that, Step 4 includes the following steps: Step 41: Load the 3D model and map each force element in the 3D model to a similarity plane; Step 42: Determine whether the position of the force unit mapped to the similarity plane is located in the selected area. If it is located in the selected area, the force unit is arranged as a similar damper position. If it is not located in the selected area, the force unit is not a similar damper position. Step 43: Add all similar damper placement locations to the initial location set.

7. The method for locating the distribution position of hybrid multi-column wall-type bridge pier dampers according to claim 1, characterized in that, Step 5 includes the following steps: Step 51: Simulate the spatial propagation effect of seismic waves by time lag to generate time lag information of the impact of seismic waves on each stress unit; Step 52: Load all damper placement positions in the initial position set onto the 3D model, set dampers at the damper placement positions, and model the 3D model to generate motion equations based on the time lag information. Step 53: Solve the equations of motion to generate displacement information for each stress element under seismic waves.

8. The method for locating the distribution position of hybrid multi-column wall-type bridge pier dampers according to claim 7, characterized in that, Step 6 includes the following steps: Step 61: Obtain all damper locations, select the dampers to be reduced based on the particle swarm optimization algorithm, and generate a new damper loading scheme; The loss function of the particle swarm optimization algorithm is related to the number of dampers and the displacement information of the force-bearing elements. Step 62: According to the damper loading scheme, adjust the damping parameters of the damper placement positions in the equation of motion to the corresponding damping parameters in sequence to update the equation of motion; Step 63: Resolve the motion equations to generate displacement information of each stress element under seismic waves, and determine whether the displacement information of each stress element does not exceed the maximum threshold based on the vibration information of each stress element.

9. The method for locating the distribution position of the hybrid multi-column wall-type bridge pier damper according to claim 7, characterized in that, The equation of motion is: ； Where M represents the total mass of the pier, i represents the stiffness coefficient of the i-th load-bearing element, and c i This represents the damping coefficient of the i-th force-bearing element, where i represents the index of the force-bearing element. Indicates the horizontal velocity at the center point. Indicates the horizontal displacement of the center point. Indicates the horizontal acceleration at the center point. This represents the seismic displacement input of the i-th stress element. This represents the seismic velocity input for the i-th stress-bearing unit, where t represents the index of the time point, n represents the total number of stress-bearing units, and k represents the total number of stress-bearing units. i This represents the stiffness of the i-th stress-bearing element.

10. A hybrid multi-column wall bridge pier damper distribution positioning system, characterized in that, include: Data entry device for entering structural information of hybrid multi-column piers; The simulation testing device uses the method described in any one of claims 1 to 9 to generate the optimal damper position allocation scheme.

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