A method, system, and medium for optimal placement and response reconstruction of bridge sensors

Abstract

The present disclosure relates to a bridge sensor optimization layout and response reconstruction method, system and medium, relating to the field of bridges. The method comprises: establishing a finite element model of the bridge; deleting measurement points in the initial sensor layout scheme; calculating load transverse influence lines using the bridge finite element model, reconstructing strain response data of the deleted transverse strain measurement points; reconstructing displacement data of the deleted displacement measurement points and / or acceleration data of the acceleration measurement points based on the relationship between displacement and acceleration; reconstructing strain response data of the deleted longitudinal strain measurement points based on the relationship between strain and displacement, using sensor data of the retained longitudinal strain measurement points and using data of the longitudinal displacement measurement points; constructing the architecture of the BiLSTM neural network model; all sensor data and all reconstructed data are input into the network model, and the network model is used to predict the data of the deleted measurement points. The present disclosure realizes the optimization of the sensor layout while improving the reconstruction accuracy.

Description

Technical Field

[0001] This disclosure relates to the field of digital signal processing technology, and in particular to a method, system, and medium for optimizing the layout and response reconstruction of bridge sensors. Background Technology

[0002] With the rapid development of highways and urban transportation infrastructure, a large number of bridges have gradually entered the middle and late stages of their service life. Under the combined effects of increasing traffic loads and complex environmental factors, their structural safety and service performance face potential safety hazards. Therefore, structural health monitoring of bridges is essential to ensure operational safety and extend their service life. However, how to effectively acquire key structural response information with a limited number of sensors has become a critical problem that urgently needs to be solved in bridge health monitoring.

[0003] Currently, bridge sensor deployment is largely based on engineering experience or relevant code provisions. While this approach is highly feasible, it often suffers from sensor redundancy, insufficient information utilization, and wasted funds, failing to maximize cost-effectiveness. Conversely, arbitrarily reducing the number of sensors may lead to missing critical responses, thus affecting the reliability of the monitoring system. Therefore, conducting research on optimized sensor deployment is crucial to ensuring both system economy and monitoring effectiveness while meeting basic monitoring requirements.

[0004] From a mechanical perspective, the response of bridge structures under traffic loads and environmental influences exhibits significant spatial correlation and physical association characteristics. This allows the response information of some lateral measuring points to be indirectly inferred from other lateral measuring points. This reconfigurability of the response provides a theoretical basis for identifying redundant lateral measuring points and simplifying the sensor count. Therefore, the core research focus is on how to accurately reconstruct all the lateral measuring point information required by the specifications with as few sensors as possible, thereby obtaining sufficient and effective structural response data.

[0005] For example, the paper "Experimental Study on Continuous Bridge-Deflection Estimation through Inclination and Strain" published in the Journal of Bridge Engineering (specifically [Sun L, Li Y, Zhang W. Experimental study on continuous bridge-deflection estimation through inclination and strain[J]. Journal of BridgeEngineering, 2020, 25(5): 04020020.]) constructs a multi-source data fusion framework to monitor data updates to the finite element model, and combines PLSR to solve the equivalent nodal force vectors to achieve extended reconstruction of the response.

[0006] For example, the paper "Full-field displacement and strain reconstruction for beam structures based on the extended inverse finite element method" published in the journal Advances in Structural Engineering (specifically [Zhu H, Du Z, Tang Y. Full-field displacement and strain reconstruction for beam structures based on the extended inverse finite element method[J]. Advances in StructuralEngineering, 2023, 26(13): 2429-2446.]) proposes an extended inverse finite element method for high-precision reconstruction of the full-field displacement and strain field of beam structures from finite strain sensor measurement data.

[0007] For example, the paper "Substructure Sensor Position Optimization and Response Reconstruction" published in the journal Vibration and Shock (specifically [Zhang Xiaohua, Zhou Haiyang, Wu Zhibiao. Substructure Sensor Position Optimization and Response Reconstruction [J]. Vibration and Shock, 2020, 39(6): 257-262.]) reduces the degrees of freedom by dividing the overall structure into several substructures, optimizes the sensor arrangement with the goal of minimizing the reconstruction error, and reconstructs the displacement and strain response of non-lateral measuring points using limited lateral measuring point information.

[0008] For example, the paper "A Time-Domain Dynamic Response Reconstruction Method Based on State Space" published in the journal "Journal of Building Structures" (specifically [Wang Juan, Yang Qingshan. A Time-Domain Dynamic Response Reconstruction Method Based on State Space [J]. Journal of Building Structures, 2016, 37(S1): 460-466.]) proposes a time-domain response reconstruction method that can reconstruct the response at other untested locations using the dynamic response of some lateral measurement points without the need to invert the unknown excitation of the structure.

[0009] For example, Chinese patent CN121118733A proposes a sensor optimization layout method and system for rapid identification of physical field parameters of long tunnels during construction. It establishes a CFD numerical model, corrects the model with measured data, reconstructs the physical field distribution of the entire tunnel with the corrected model, and finally finds the optimal height and position of the sensor layout through deviation analysis, so as to achieve rapid identification of the entire field parameters with a limited number of sensors.

[0010] For example, Chinese patent CN120145773A proposes a "Deformation Monitoring Sensor Optimization Arrangement Method Based on Fisher Information Matrix", which maximizes the amount of information to improve the deformation reconstruction accuracy of the inverse finite element method, thereby achieving efficient sensor arrangement.

[0011] However, the aforementioned methods rely solely on physical characteristics for data reconstruction and sensor deployment optimization, and are computationally complex due to their dependence on physical models. In the context of massive monitoring data and hardware upgrades, the efficiency and adaptability of these methods still need improvement.

[0012] In recent years, with the development of artificial intelligence technology, research on structural response reconstruction and sensor optimization based on neural networks has become a new trend.

[0013] For example, the paper "Anomaly Detection and Reconstruction of Bridge Monitoring Data Based on LSTM Neural Network" published in the Journal of Wuhan University of Technology (Transportation Science and Engineering), specifically [Wu Y, Hou C. Anomaly Detection and Reconstruction of Bridge Monitoring Data Based on LSTM Neural Network [J]. Wuhan Ligong Daxue Xuebao (Jiaotong Kexue YuGongcheng Ban) / Journal of Wuhan University of Technology (TransportationScience and Engineering), 2025, 49(6): 1346-1352.], uses a Long Short-Term Memory (LSTM) neural network to reconstruct and supplement the remaining missing or abnormal data based on a small number of sensors.

[0014] For example, the paper "Research on Reconstruction Method of Missing Bridge Monitoring Data Based on SSA-VMD-GRU Combined Model" published in the journal Vibration and Shock (specifically [Zhou Yu, Zhou Mingyang, Di Shengkui, et al. Research on Reconstruction Method of Missing Bridge Monitoring Data Based on SSA-VMD-GRU Combined Model [J]. Vibration and Shock, 2026, 45(03):115-123.DOI:10.13465 / j.cnki.jvs.2026.03.013.] uses the Sparrow Search Algorithm (SSA) to jointly optimize Variational Mode Decomposition (VMD) and Gated Cyclic Unit (GRU) to realize the reconstruction and supplementation of missing bridge monitoring data.

[0015] For example, Chinese patent CN119004819A proposes "A method for optimizing the arrangement of sensors for high-stability structures of remote sensing satellites based on compressed sensing". Through mathematical reconstruction technology, it achieves the goal of monitoring the entire high-stability structure with the fewest sensors, effectively saving the economic cost of monitoring remote sensing satellite structures.

[0016] However, the aforementioned methods often neglect structural mechanics constraints, and relying solely on data-driven models may lead to insufficient model generalization ability and poor physical interpretability, making them difficult to directly apply to sensor optimization deployment. Therefore, how to deeply integrate deep learning algorithms with the structural mechanics characteristics of bridges has become the key to solving these problems.

[0017] In related research, Chinese patent CN118607295A proposed a "Method for Optimizing the Arrangement of Ultrasonic Array Sensors for Partial Discharge in Transformers." This method establishes a nonlinear ultrasonic propagation model considering temperature, combines it with a Physical Information Neural Network (PINN) for backpropagation, and uses mathematical methods to reconstruct the discharge location, thereby optimizing the sensor arrangement. However, this method is designed for transformer partial discharge monitoring and may not be suitable for sensor deployment on bridge structures.

[0018] In summary, while current sensor optimization deployment and response reconstruction for bridges have achieved some degree of optimization of lateral measuring point layout and response reconstruction based on sensor data, they generally fail to effectively integrate the physical characteristics of the bridge structure with the spatiotemporal correlation between monitoring data. This is either because the accuracy of reconstruction needs to be improved, or because too many sensors are still used, making it difficult to achieve an optimal sensor deployment and reconstruction scheme that balances economy and monitoring effectiveness.

[0019] Therefore, it is necessary to design an optimized deployment and response reconstruction method, system, and medium for bridge sensors to achieve high-accuracy data reconstruction with a small number of sensors, thereby reducing the cost of bridge construction without affecting bridge monitoring. Summary of the Invention

[0020] Therefore, it is necessary to provide a method, system, and medium for optimizing the deployment and response reconstruction of bridge sensors to address the above-mentioned problems.

[0021] To solve the above problems, the present disclosure adopts the following technical solution: In a first aspect, this disclosure provides a method for optimizing the deployment and response reconstruction of bridge sensors, comprising the following steps: Based on the bridge's structural form, determine the initial sensor deployment plan; Establish a finite element model of the bridge; Deleting measurement points in the initial sensor deployment scheme: If the difference in bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of strain response values ​​is higher than a preset correlation threshold, then one of the strain measurement points is deleted; if the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold, then the displacement measurement point or the acceleration measurement point is deleted. Acquire sensor data from all retained measurement points; The lateral influence line of the load is calculated using the finite element model. Based on the load lateral influence line, and using the sensor data of the retained lateral strain measurement points, the strain response data of the deleted lateral strain measurement points are reconstructed. Based on the relationship between displacement and acceleration, the displacement data of the deleted displacement measurement points is reconstructed using the sensor data of the retained displacement measurement points, and / or the acceleration data of the deleted acceleration measurement points is reconstructed using the sensor data of the retained acceleration measurement points. Based on the relationship between strain and displacement, the strain response data of the deleted longitudinal strain measurement points are reconstructed using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The architecture for constructing a BiLSTM neural network model; All the sensor data and reconstructed data are used as input to a BiLSTM neural network model, which is then used to predict the data for the deleted measurement points.

[0022] In a preferred embodiment, all the sensing data and all the reconstructed data are used as input to a BiLSTM neural network model. The data used by the BiLSTM neural network model to predict the deleted measurement points specifically includes: The retained transverse strain measurement point sensor data and the reconstructed strain response data of the deleted transverse strain measurement point are used as input to the BiLSTM neural network model, and the BiLSTM neural network model is used to predict the data of the deleted transverse strain measurement point. The data used to reconstruct the strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model, and the reconstructed strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model. The BiLSTM neural network model is then used to predict the data of the deleted longitudinal strain measurement points. Sensor data from retained displacement measurement points and reconstructed displacement data from the deleted displacement measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict data from the deleted displacement measurement points; and / or, sensor data from retained acceleration measurement points and reconstructed acceleration data from the deleted acceleration measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict data from the deleted acceleration measurement points.

[0023] In a preferred embodiment, the calculation formula for the strain response data of the reconstructed and deleted transverse strain measurement points includes: in, This indicates the number of the strain gauge point that was deleted from the beam. Indicates the strain gauge points that were removed from the beam. Response weights are assigned; Indicates the strain gauge points that were removed from the beam. Location; express The lateral influence line value at that location; This indicates the number of the strain measurement points retained on the beam. , This indicates the total number of strain gauge points retained on the beam; Indicates the remaining strain measurement points on the beam. Location, express The lateral influence line value at that location; This indicates the total number of strain measurement points retained on the beam that participated in the reconstruction. This indicates the number of the strain measurement points retained on the beam that participated in the reconstruction. Indicates time, This indicates the strain measurement points retained on the beam that participated in the reconstruction. In time The measured response data, This indicates the strain measurement points retained on the beam that participated in the reconstruction. The response is assigned weights. This represents the equivalent vertical action obtained by inverting measured response data; Indicates the strain gauge points that were removed from the beam. In time The refactoring response.

[0024] In a preferred embodiment, when the distance between a displacement measuring point and an acceleration measuring point in the same direction is less than a preset threshold, the acceleration measuring point is deleted; the calculation formula for the strain response data of the reconstructed and deleted longitudinal strain measuring points is: in, Represents modal coordinates, Indicates time, Indicates intermediate variables. This indicates the total number of longitudinal displacement measurement points that are retained and participate in the reconstruction. , This indicates the sequential number of the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The longitudinal displacement measuring points that were retained and participated in the reconstruction were in time. Internally collected response data, This represents the total number of longitudinal strain measurement points that are retained and participate in the reconstruction. , Indicates the first The longitudinal strain measurement points that were retained and participated in the reconstruction were in time. Internally collected sensor data, This indicates the first longitudinal strain measurement point that was retained and participated in the reconstruction at time... Internally collected sensor data, Indicates the first The longitudinal strain measurement points that were retained and participated in the reconstruction were in time. Internally collected sensor data, Indicates the first The mode shape vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The mode shape vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The mode vectors corresponding to the longitudinal strain measurement points that are retained and participate in the reconstruction. Indicates the first The mode shape vectors corresponding to the retained and reconstructed longitudinal strain measurement points are all , and the dimension of each mode shape vector is . , This represents the mode shape vector of the deleted longitudinal strain measurement point; This represents the strain response data of the deleted longitudinal strain measurement points after reconstruction.

[0025] In a preferred embodiment, the relationship between displacement and acceleration includes: in, Indicates the time number, Indicates time The previous moment, Indicates time The next moment, Indicates displacement. Indicates time Displacement at that point Indicates time Displacement at that point Indicates time Displacement at; Indicates time Acceleration at that point; This indicates the time interval.

[0026] In a preferred embodiment, determining the initial sensor deployment scheme based on the bridge structure specifically involves determining the initial sensor deployment scheme based on the bridge structure and relevant standards for bridge health monitoring.

[0027] In a preferred embodiment, the initial sensor deployment scheme includes the deployment of transverse strain measurement points, longitudinal strain measurement points, transverse acceleration measurement points, longitudinal acceleration measurement points, transverse displacement measurement points, and longitudinal displacement measurement points.

[0028] In a preferred embodiment, the step of constructing the architecture of the BiLSTM neural network model includes: The data input layer for constructing a BiLSTM neural network model architecture; BiLSTM temporal feature extraction module for constructing BiLSTM neural network model architecture; A collaborative reconstruction mechanism for constructing BiLSTM neural network model architecture.

[0029] Secondly, this disclosure provides a system for optimizing the deployment and reconstructing the response of bridge sensors, comprising: The initial scheme determination module is used to determine the initial sensor deployment scheme based on the bridge structure. The finite element model creation module is used to create finite element models of bridges. The measurement point deletion module is used to delete measurement points in the initial sensor deployment scheme. Specifically, it is used to delete one of the strain measurement points when the difference in the bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of the strain response values ​​is higher than a preset correlation threshold; and it is used to delete the displacement measurement point or the acceleration measurement point when the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold. The acquisition module is used to acquire sensor data from all retained measurement points; The first reconstruction module is used to calculate the lateral influence line of the load using the finite element model; and to reconstruct the strain response data of the deleted lateral strain measurement points based on the lateral influence line of the load and the sensor data of the retained lateral strain measurement points. The second reconstruction module is used to reconstruct the displacement data of the deleted displacement measurement points based on the relationship between displacement and acceleration, using the sensor data of the retained displacement measurement points, and / or to reconstruct the acceleration data of the deleted acceleration measurement points using the sensor data of the retained acceleration measurement points. The third reconstruction module is used to reconstruct the strain response data of the deleted longitudinal strain measurement points based on the relationship between strain and displacement, using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The model building module is used to construct the architecture of BiLSTM neural network models; The model prediction module inputs all the sensor data and all the reconstructed data into the BiLSTM neural network model, and uses the BiLSTM neural network model to predict the data of the deleted measurement points.

[0030] Thirdly, this disclosure provides a storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the optimized layout and response reconstruction method for bridge sensors described in the first aspect.

[0031] The above-mentioned method, system, and medium for optimizing the layout and response reconstruction of bridge sensors present an optimized sensor layout scheme that reduces redundant measuring points and optimizes the bridge sensor layout. Based on this optimized sensor layout scheme, a response reconstruction scheme is designed to cover all key response information with as few sensors as possible. Specifically, physical methods (based on the lateral influence line of the load, the relationship between displacement and acceleration, or the relationship between strain and displacement) are used to initially reconstruct the data of the deleted measuring points. The sensor data of the retained measuring points and the data of the initial reconstruction are both input into a BiLSTM neural network model, which is given physical constraints. This invention embeds physical constraints in the optimization layout process, and can provide highly accurate data reconstruction results for all optimized measuring points, reducing the equipment investment cost of bridges and improving the effectiveness of bridge monitoring. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating a method in one embodiment of the present disclosure; Figure 2 This is a sensor layout diagram for a 4×30m continuous beam bridge section; Figure 3 for Figure 2 The sensor layout method at the mid-span section of the corresponding T-beam structure; Figure 4 for Figure 2 The corresponding sensor layout method at the mid-span section of the box girder structure; Figure 5 This is a finite element model of a bridge. Figure 6 for Figure 2 A schematic diagram of the result after step 1; Figure 7 for Figure 3 A schematic diagram of the result after step 1; Figure 8 for Figure 4 A schematic diagram of the result after step 1; Figure 9 A time history comparison diagram of finite element simulation monitoring data and strain data reconstructed based on transverse influence line theory for transverse strain measurement point P2; Figure 10This is a scatter plot of the monitoring data from the finite element simulation of the transverse strain measurement point P2 and the strain data reconstructed based on the transverse influence line theory. Figure 11 A schematic diagram showing the retention and deletion of longitudinal measuring points on the central main beam; Figure 12 A time history comparison diagram of finite element simulation monitoring data and strain data reconstructed by a pure data-driven method for longitudinal acceleration measuring point A1; Figure 13 A scatter plot of strain data reconstructed from finite element simulation monitoring data and pure data-driven methods for longitudinal acceleration measurement point A1; Figure 14 A time history comparison diagram of the finite element simulation monitoring data and the strain data reconstructed by the pure data-driven method for the transverse strain measuring point P2; Figure 15 A scatter plot of strain data reconstructed by finite element simulation monitoring data and pure data-driven method for transverse strain measurement point P2; Figure 16 A time history comparison diagram of finite element simulation monitoring data and strain data reconstructed by a pure data-driven method for longitudinal acceleration measuring point A1; Figure 17 A scatter plot of strain data reconstructed from finite element simulation monitoring data and pure data-driven methods for longitudinal acceleration measurement point A1; Figure 18 A time history comparison chart of finite element simulation monitoring data and reconstructed data obtained based on a physics-guided BiLSTM neural network model for transverse strain measurement point P2; Figure 19 The scatter plot shows the monitoring data from the finite element simulation of the transverse strain measuring point P2 and the reconstructed data obtained from the physical-guided BiLSTM neural network model. Figure 20 A time history comparison chart of finite element simulation monitoring data and reconstructed data obtained based on a physical-guided BiLSTM neural network model for longitudinal acceleration measurement point A1; Figure 21 The scatter plot shows the finite element simulation monitoring data of longitudinal acceleration measurement point A1 and the reconstructed data obtained based on the physical-guided BiLSTM neural network model. Figure 22 This is a system architecture diagram of a method in one embodiment of the present disclosure. Detailed Implementation

[0033] The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0034] See Figure 1This embodiment provides a method for optimizing the deployment and response reconstruction of bridge sensors, the method comprising: Based on the bridge's structural form, determine the initial sensor deployment plan; Establish a finite element model of the bridge; Deleting measurement points in the initial sensor deployment scheme: If the difference in bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of strain response values ​​is higher than a preset correlation threshold, then one of the strain measurement points is deleted; if the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold, then the displacement measurement point or the acceleration measurement point is deleted. Acquire sensor data from all retained measurement points; The lateral influence line of the load is calculated using the finite element model. Based on the load lateral influence line, and using the sensor data of the retained lateral strain measurement points, the strain response data of the deleted lateral strain measurement points are reconstructed. Based on the relationship between displacement and acceleration, the displacement data of the deleted displacement measurement points are reconstructed using sensor data from the retained displacement measurement points; and / or, the acceleration data of the deleted acceleration measurement points are reconstructed using sensor data from the retained acceleration measurement points; Based on the relationship between strain and displacement, the strain response data of the deleted longitudinal strain measurement points are reconstructed using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The architecture for constructing a BiLSTM neural network model; All the sensor data and reconstructed data are used as input to a BiLSTM neural network model, which is then used to predict the data for the deleted measurement points.

[0035] It should be understood that the above method does not imply that all steps must be performed in this order. Those skilled in the art can modify or change the execution order of the above steps based on this disclosure. For example, the step of acquiring the sensor data of all retained measuring points may include multiple steps (including the step of acquiring the sensor data of retained lateral strain measuring points, the step of acquiring the sensor data of retained lateral displacement measuring points, and the step of acquiring the sensor data of retained lateral acceleration measuring points), and in the following steps, the sensor data of the required portion of retained measuring points may be acquired according to real-time needs.

[0036] This method is not limited to any type of bridge; it can be for long-span or medium-span bridges. For ease of explanation, the following description uses medium-span bridges as an example. Further details of the method are provided below.

[0037] The following section will focus on the optimization deployment methods.

[0038] The optimized deployment method includes: determining the initial sensor deployment scheme (for bridges with pre-deployed sensors) based on the bridge structure; establishing a finite element model of the bridge (with pre-deployed sensors); and performing redundancy analysis based on the finite element model and the initial sensor deployment scheme to infer the measurement points that can be deleted.

[0039] In this embodiment, only one sensor is set at each measuring point, meaning each sensor corresponds to one measuring point, and each measuring point corresponds to only one sensor. Measuring points that are not deleted are retained. The initial sensor deployment plan includes strain measurement points, displacement measurement points, and acceleration measurement points.

[0040] As you can understand, in this article, "lateral" refers to the transverse direction of the bridge, which is perpendicular to the axis of the main beam; "along the bridge direction" refers to the longitudinal direction, also known as the vertical direction, which is along the axis of the main beam of the bridge. Measurement points include transverse and longitudinal measurement points. Specifically, strain measurement points include transverse and longitudinal strain measurement points, acceleration measurement points include transverse and longitudinal acceleration measurement points, and displacement measurement points include transverse and longitudinal displacement measurement points. In other words, the initial sensor deployment plan includes the layout of transverse strain measurement points, longitudinal strain measurement points, transverse acceleration measurement points, longitudinal acceleration measurement points, transverse displacement measurement points, and longitudinal displacement measurement points.

[0041] For bridges with pre-installed sensors, the initial sensor deployment plan should be determined based on the bridge's structural form and relevant standards for bridge health monitoring. Specifically, the selection of sensor types and their placement in health monitoring systems for (small and medium span) bridges should be in accordance with current relevant standards.

[0042] The bridge structure can be classified according to its stress distribution, including beam bridges, arch bridges, rigid frame bridges, suspension bridges, cable-stayed bridges, and composite system bridges. As an example, relevant standards for bridge health monitoring include the "Technical Specification for Health Monitoring of Highway Bridges" (2026 edition), the "Design Standard for Safety Monitoring System of Small and Medium Span Bridges (2024)," and the "Technical Specification for Selection and Deployment of Bridge Health Monitoring Sensors" (T / CCES 15-2020).

[0043] Based on relevant specifications and the bridge's structural form, a preliminary sensor deployment plan was developed. Specifically, for displacement and dynamic response monitoring, one longitudinal displacement sensor and one longitudinal acceleration sensor were deployed at the mid-span section of the main beam in each span to monitor the bridge's longitudinal deformation characteristics and dynamic properties. For strain monitoring, one strain sensor was deployed at the bottom of each main beam at the mid-span section of each span to obtain the principal tensile strain response under positive bending moment. To further cover the critical strain control sections recommended by relevant specifications, the 1 / 4 and 3 / 4 spans of the main span were selected as supplementary monitoring sections, and strain sensors were added to the bottom of each main beam at these corresponding sections to enhance the structure's ability to identify stress distribution patterns and bending moment change mechanisms. (See also...) Figures 2 to 4 , Figure 2 This is a sensor layout diagram for a 4×30m continuous beam bridge section. Figure 3 for Figure 2 The corresponding sensor layout method at the mid-span section of the T-beam structure. Figure 4 for Figure 2 The corresponding sensor layout method at the mid-span section of the box girder structure. Figure 2 "Strain monitoring" refers to strain measurement points used to monitor strain response, "displacement monitoring" refers to displacement measurement points used to monitor displacement, and "vibration acceleration monitoring" refers to acceleration measurement points used to detect acceleration.

[0044] The establishment of the finite element model of the bridge refers to the creation of a finite element model of the actual bridge based on the bridge design drawings and using numerical simulation methods. The finite element model is as follows: Figure 5 As shown.

[0045] Based on this finite element model, and combining the load lateral influence line (hereinafter referred to as the lateral influence line) and the physical correlation (kinematic relationship and modal superposition principle) between acceleration, strain and displacement along the bridge direction, the feasibility of reducing the number of measuring points in the initial layout scheme is described in detail below.

[0046] If the difference in bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation between the strain response (strain response value) of the two strain measurement points is higher than a preset correlation threshold, then either strain measurement point will be deleted.

[0047] If the distance between a displacement measuring point (used for deploying displacement sensors) and a measurement point (used for monitoring acceleration sensors) in the same direction (both horizontal or both vertical) is less than a preset threshold (usually almost overlapping), then the displacement measuring point or the acceleration measuring point is deleted.

[0048] Analysis of the bridge reveals that at the mid-span section of each span, the main girder components form a cohesive stress system under load. The strain responses at the bottom of the beams exhibit significant correlation in the transverse direction (e.g., transverse Pearson correlation coefficients are all > 0.7), rather than being independent. Therefore, at the mid-span section of each span, retaining only two representative strain measurement points at the bottom of the beams (i.e., the middle beam and one side beam) is sufficient to effectively characterize the transverse strain distribution at that section. The remaining strain measurement points are omitted because response reconstruction based on transverse influence lines is feasible.

[0049] Considering the bridge structure is mirror-symmetrical about the central pier, the second span's 1 / 4 and the third span's 3 / 4, as well as the second span's 3 / 4 and the third span's 1 / 4, form symmetrical sections. Their bending moment and strain responses exhibit high consistency in amplitude and trend, resulting in significant information redundancy. Therefore, only the bottom strain sensors need to be installed at the 3 / 4 spans of the second and third spans, eliminating the need for measuring points at other symmetrical locations. Response reconstruction is achieved through modal superposition. For asymmetrical bridges, given the similar bending moment amplitudes (i.e., bending moments) and strong correlation between the responses (strain response values) at the 1 / 4 and 3 / 4 span sections within the same span, a simplified layout strategy retaining only one side of the measuring points can be adopted. The target response can be obtained through displacement monitoring combined with strain reconstruction.

[0050] Furthermore, displacement and acceleration satisfy a definite kinematic relationship, that is, acceleration is the second derivative of displacement with respect to time, and the two have a deterministic mapping relationship in theory. Therefore, when displacement sensors and acceleration sensors are deployed at the same location (which can be considered the same location since the distance is less than a preset threshold), the acceleration response can be obtained by differentiating the displacement signal or by reconstructing the response based on modal superposition, thereby realizing the replacement or reduction (i.e., deletion) of acceleration measurement points.

[0051] Based on the above reduction strategies, the initial sensor deployment plan is optimized by reducing the number of measurement points. This process results in a distinction between retained and deleted measurement points. For example... Figures 6 to 8 As shown, Figures 6 to 8 In the diagram, retained measurement points are marked in red, and deleted measurement points are marked in black. Figures 6 to 8 One-to-one correspondence Figures 2 to 4 P1 to P8 represent the numbers of the (lateral) strain measurement points.

[0052] The response reconstruction method based on the above optimized layout is described in detail below, using the finite element model and other methods. It is understandable that both the theoretical analysis of the optimized layout and response reconstruction method, and the actual deployment of sensors on a bridge according to this optimized layout, are applicable to all steps of this response reconstruction. The measurement points of the corresponding sensors actually deployed on the constructed bridge are the retained measurement points. Alternatively, a BiLSTM neural network model, called the first model, can be obtained based on the sensor data from the finite element model and all reconstructed data. In the actual bridge, the first model can be directly used without reconstruction.

[0053] The response reconstruction method includes: reconstructing data using purely physical methods; and predicting and reconstructing the (detection) data of the measurement points using a physically guided BiLSTM neural network model. Specifically, it includes: Step 1: Calculate the transverse influence line of the load based on the finite element model, obtain the sensor data of the retained transverse strain measurement points, and reconstruct the strain response data of the deleted transverse strain measurement points based on the transverse influence line of the load and the sensor data (i.e. strain data) of the retained transverse strain measurement points.

[0054] Specifically, a mapping relationship between responses at different lateral positions is established based on the load lateral influence line, thereby enabling lateral inference and reconstruction of the strain response of deleted lateral strain measurement points.

[0055] The lateral load influence line refers to a discrete lateral influence line vector obtained by progressively moving a unit load laterally along the bridge deck using a finite element model. The lateral load influence line characterizes the response distribution relationship between the main girder components in the lateral position. Based on this lateral load influence line, the strain distribution coefficients between the main girders can be further calculated.

[0056] The lateral inference and reconstruction of the strain response of the deleted lateral strain measurement points refers to reconstructing the strain data of the deleted lateral strain measurement points based on the lateral influence line of the load, using the strain data of the retained middle beam and the retained edge beam. Specifically, for Figure 7 Using the data from the retained transverse strain measurement points P3 and P5, the strain responses of the deleted transverse strain measurement points P1, P2, and P4 are reconstructed; for Figure 8 Using the data from the retained measuring points (retained transverse strain measuring points) P7 and P8, the strain response of the deleted measuring point (deleted transverse strain measuring point) P6 is reconstructed.

[0057] Specifically, the aforementioned Figure 7 and Figure 8The strain data at transverse strain measuring points P1 to P8 were obtained by applying a random seismic wave excitation generated by MATLAB with a duration of 80 seconds, a mean of 0, a standard deviation of 0.02 g (where g represents gravitational acceleration), and a time step of 0.01 seconds to the finite element model, and then performing dynamic time history analysis to obtain the true response (directly calculated from the finite element model).

[0058] By progressively moving a unit load laterally along the bridge deck in a finite element model, discrete lateral influence line vectors are obtained. These vectors are then normalized, and the response weighting at the removed strain gauge points on the crossbeam is calculated. Considering that under ideal elastic conditions, the response of each lateral strain measurement point at the same moment can be regarded as being driven by a uniform equivalent vertical force, the difference mainly lies in the lateral weighting. If strain sensors are installed at some lateral locations and measured responses are obtained... Then, the equivalent generalized load time history can be inverted by horizontally allocating weights. Finally, for the strain measurement points removed from the beam, the response... A preliminary physical reconstruction can be performed by assigning weights laterally. Based on the lateral influence line, the deleted lateral strain measurement points (strain measurement points deleted on the beam) are physically reconstructed by assigning weights laterally, as shown in the following formula: in, This indicates the number of the strain gauge point that was deleted from the beam. Indicates the strain gauge points that were removed from the beam. Response weights are assigned; Indicates the strain gauge points that were removed from the beam. Location; express The lateral influence line value at that location; This indicates the number of the strain measurement points retained on the beam. , This indicates the total number of strain gauge points retained on the beam; Indicates the remaining strain measurement points on the beam. Location, express The lateral influence line value at that location; This indicates the total number of strain measurement points retained on the beam that participated in the reconstruction. This indicates the number of the strain measurement points retained on the beam that participated in the reconstruction. Indicates time, This indicates the strain measurement points retained on the beam that participated in the reconstruction. In time The measured response data, This indicates the strain measurement points retained on the beam that participated in the reconstruction. The response is assigned weights. This represents the equivalent vertical action obtained by inverting measured response data; Indicates the strain gauge points that were removed from the beam. In time The refactoring response.

[0059] After reconstructing the lateral influence line of the load, to verify the feasibility of lateral inference, the strain response of the reconstructed strain measurement points (after deleting the lateral strain measurement points) is compared with the actual response directly calculated by the finite element model. To quantitatively evaluate the reconstruction effect, a coefficient of determination (COP) is introduced. The root mean square error (RMSE) and relative prediction deviation (RPD) are used as evaluation indicators. A value closer to 1 indicates a better reconstruction effect, and a larger RPD value indicates higher prediction accuracy. Specific evaluation results are shown in Table 1.

[0060] Table 1 Evaluation table of reconstruction effect in step 1

[0061] Because the established finite element model is symmetrically arranged in the transverse direction, the transverse influence lines and strain distribution coefficients of the loads at the corresponding sections of transverse measuring points P2 and P4 are completely identical, resulting in the same strain response and reconstruction results at the two transverse strain measuring points. From the perspective of quantitative evaluation indicators, the transverse strain measuring points... The values ​​are all similar to those of measuring point P2 (approximately 0.75). Although this level of accuracy is not ideal, considering the trend reconstruction effect of measuring point P2, it can be considered that the strain measuring points in the middle of the span are substitutable at the information level, thus supporting the feasibility of their deletion in the actual monitoring scheme.

[0062] Figure 9 and Figure 10 The strain data reconstructed from transverse strain measuring point P2 based on transverse influence line theory (referred to as reconstructed strain or transverse influence line reconstructed data) and the finite element simulation monitoring data of transverse strain measuring point P2 (corresponding to...) were compared. Figure 9 (Numerical simulation monitoring data). It can be seen that the reconstructed data is basically consistent with the monitoring data in terms of overall trend, and can recover the strain response characteristics of the deleted measuring points relatively well. However, there is a certain deviation between the reconstructed data and the monitoring data, and the coefficient of determination... =0.7467, indicating that only trend-level reconstruction can be achieved, and the reconstruction accuracy is not ideal.

[0063] Step 2: Obtain sensor data from the retained displacement measurement points and acceleration measurement points. Based on the sensor data and the relationship between displacement and acceleration, reconstruct the displacement data of the deleted lateral displacement measurement points and the acceleration data of the deleted lateral acceleration measurement points. Typically, after optimization, lateral acceleration measurement points are deleted. Therefore, the sensor data from the retained lateral displacement measurement points is obtained, and the acceleration data from the deleted lateral acceleration measurement points is reconstructed based on this data.

[0064] Based on the kinematic relationship between displacement and acceleration, acceleration can be obtained from the second derivative of displacement with respect to time, as shown in the following formula:

[0065] In the formula, The number representing a moment, i.e., the number of a specific time point. Indicates time The previous moment, Indicates time The next moment, Indicates displacement. Indicates time Displacement at that point Indicates time Displacement at that point Indicates time Displacement at; For time Acceleration at that point; This is used as a time interval.

[0066] Step 3: Obtain the sensor data of all retained longitudinal measuring points; based on the relationship between displacement and acceleration, reconstruct the displacement data of the deleted longitudinal displacement measuring points and / or reconstruct the acceleration data of the deleted longitudinal acceleration measuring points; based on the relationship between strain and displacement, reconstruct the strain response data of the deleted longitudinal strain measuring points.

[0067] Considering that displacement, acceleration, and retained strain measurement points are mainly located on the central main girder, this embodiment selects the central main girder as the representative object for reconstruction analysis along the bridge direction. Since the calculation methods for the response along the bridge direction are consistent between T-beams and box girders, a beam model is uniformly adopted for processing. The retention and deletion of measurement points (longitudinal measurement points) on the central main girder are as follows: Figure 11As shown, red represents retained measurement points, black represents deleted measurement points, hollow circles represent strain monitoring, solid circles represent vibration acceleration monitoring, pentagrams represent position monitoring, S1~S8 represent longitudinal strain measurement points, A1~A4 represent longitudinal acceleration measurement points, and D1~D4 represent longitudinal displacement measurement points. Specifically, S1, S3, S4, S6, S7, and S8 represent retained longitudinal strain measurement points, D1~D4 represent retained longitudinal displacement measurement points, and A1~A4 represent deleted longitudinal acceleration measurement points.

[0068] Along the bridge direction, physical reconstruction of acceleration and strain response is carried out based on known displacement measurement data.

[0069] Specifically, in Figure 11 In the arrangement of measuring points shown, the time history data of the corresponding longitudinal acceleration measuring points A1 to A4 can be reconstructed based on the time history data of the longitudinal displacement measuring points D1 to D4. See step 2 for details.

[0070] Considering that displacement and strain share a unified modal coordinate system, a mapping relationship between the two types of responses can be established. Modal coordinates are calculated using the retained displacement and strain measurement point data and mode shapes after optimization, and the response of the deleted strain measurement points is reconstructed based on the modal superposition principle. The calculation formula is as follows: Considering that displacement and strain share a unified modal coordinate system, a mapping relationship between the two types of responses can be established. Modal coordinates are calculated using the retained displacement and strain measurement point data and mode shapes after optimization, and the response of the deleted longitudinal strain measurement points is reconstructed based on the modal superposition principle. Under the premise that "when the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold, the acceleration measurement point is deleted," the formula for reconstructing the longitudinal strain is as follows:

[0071]

[0072] In the formula, Modal coordinates; These are merely intermediate variables and can be understood as having no specific meaning. This indicates the total number of longitudinal displacement measurement points that are retained and participate in the reconstruction. , This indicates the sequential number of the longitudinal displacement measurement points that are retained and participate in the reconstruction. For the first The longitudinal displacement measuring points that were retained and participated in the reconstruction were in time. Internally collected response data, To retain the total number of longitudinal strain measurement points that participate in the reconstruction, , For the first One longitudinal strain measurement point (strain measurement point) was retained and participated in the reconstruction. In time Internally acquired response data (sensor data), based on The meaning is self-evident. and The meaning of . For the first The mode vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction are based on The meaning is known and The meaning, Indicates the first The mode shape vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The mode vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction; For strain measurement points The corresponding mode shape vector, based on The meaning is known and The meaning, Indicates the first The mode vectors corresponding to the longitudinal strain measurement points that are retained and participate in the reconstruction. Indicates the first The mode shape vectors corresponding to the retained and reconstructed longitudinal strain measurement points are all , and the dimension of each mode shape vector is . To ensure matrix invertibility during modal coordinate solution, the order of the modes involved in reconstruction is taken to be equal to the total number of measurement points, i.e., the dimension of each mode vector is equal to the total number of measurement points. . The mode shape vector of the deleted longitudinal strain measurement point; The physical reconstruction response of the deleted longitudinal strain measurement point (the reconstructed strain response data of the deleted longitudinal strain measurement point).

[0073] Specifically, for Figure 11 The measured points shown are used as inputs, retaining the response data of measured points D2, S3, S4, S6, and S7. By solving the modal coordinates and combining them with the corresponding modal shape functions, the strain time histories of the deleted measured points S2 and S5 are reconstructed. The response calculation formula for the reconstructed deleted longitudinal strain measured points is as follows:

[0074]

[0075] in, This represents the mode shape vector corresponding to the longitudinal displacement measurement point D2 that is retained and participates in the reconstruction. This represents the mode shape vector corresponding to the longitudinal strain measurement point S3 that is retained and participates in the reconstruction. This represents the mode shape vector corresponding to the longitudinal strain measurement point S4 that is retained and participates in the reconstruction. This represents the mode shape vector corresponding to the longitudinal strain measurement point S6 that is retained and participates in the reconstruction. This represents the mode shape vector corresponding to the longitudinal strain measurement point S7 that is retained and participates in the reconstruction. express, This represents the retained longitudinal strain measurement point S3 sensor data. This indicates the retained longitudinal strain measurement point S4 sensor data. This indicates the retained longitudinal strain measurement point S6 sensor data. This indicates the retained longitudinal strain measurement point S7 sensor data. This represents the strain response data (mode vector) of the deleted longitudinal strain measurement point S2. This indicates the strain response data of the deleted longitudinal strain measurement point S5. This represents the physical reconstruction response of the deleted longitudinal strain measurement point S2. This represents the physical reconstruction response of the deleted longitudinal strain measurement point S5.

[0076] The displacement and strain data of the above measuring points were obtained by applying a random seismic wave generated by MATLAB with a duration of 80 seconds, a mean of 0, a standard deviation of 0.02 g, and a time step of 0.01 seconds to the finite element model and conducting dynamic time history analysis.

[0077] To verify the feasibility of reconstruction along the bridge direction, the reconstruction results were compared and analyzed with the actual responses directly calculated by the finite element model. The reconstruction results and error indices for each measuring point are shown in Table 2. Since the finite element model is ideally symmetrically arranged in terms of geometry and boundary conditions, the calculation results for some symmetrical measuring points (such as measuring points A1 and A4, and A2 and A3) are completely consistent. As shown in Table 2, the acceleration measuring points (A1 / A4, A2 / A3) reconstructed based on the displacement-acceleration kinematic relationship... The accuracy reached 0.9571 and 0.9792 respectively, which is relatively high.

[0078] Table 2 Evaluation table of longitudinal measurement point reconstruction effect in step 3

[0079] Table 2 shows the longitudinal measurement points. The values ​​all remained above 0.79, verifying the preliminary reconstruction method of the bridge-direction response based on the mechanical relationship between displacement-strain-acceleration. The deletion of measurement points along the bridge direction is substitutable at the information level, thus supporting its feasibility for deletion in actual monitoring schemes.

[0080] Figure 12 and Figure 13Taking measurement point A2 as an example, the data reconstructed based on the mechanical relationship between displacement and acceleration is visualized (corresponding to...). Figure 12 The reconstruction acceleration, corresponding to Figure 13 A time history comparison between the reconstructed data and the finite element simulation monitoring data; and the strain measurement points (S2, S5) reconstructed based on the modal superposition method. The values ​​are only 0.8058 and 0.7984. This indicates that for weakly correlated tasks with clear mechanical analytical relationships (displacement derived from acceleration), pure physics methods can achieve good results; however, for strain reconstruction that relies on modal coordinate transformation at multiple measurement points, pure physics methods are limited by modal truncation and model simplification, resulting in limited accuracy.

[0081] Step 4, Construct a physically guided BiLSTM neural network model architecture: Construct a bidirectional long short-term memory (BiLSTM) network to correct and compensate for all reconstruction results in order to improve the accuracy and robustness of response estimation.

[0082] The physical reconstruction response calculated in steps 1 to 3, along with the measurement point data retained after optimized deployment, are input into the network. Physical prior information guides model training, reducing reliance on large-scale samples while preserving the nonlinear expressive power of the neural network, thus achieving a dual improvement in physical interpretability and reconstruction accuracy. In this mechanism, physical priors provide constraints on the overall trend of data changes, while the data drives the neural network model to capture high-frequency details and nonlinear residuals. These two aspects form a hierarchical and complementary collaborative reconstruction mechanism, enabling high-precision response reconstruction for deleted measurement points.

[0083] In one specific embodiment, this step includes: Step 4.1, construct the data input layer of the BiLSTM neural network model architecture: fuse the strain response data of the deleted transverse strain measurement points obtained in Step 1, the reconstructed data obtained in Step 2, the strain response data of the deleted longitudinal strain measurement points obtained in Step 3, and the measured response data (i.e., measured data) of the retained measurement points to form a joint input dataset; Step 4.2: Construct the BiLSTM temporal feature extraction module of the BiLSTM neural network model architecture. The BiLSTM temporal feature extraction module includes a forward LSTM layer and a backward LSTM layer. The forward and backward dependency features of the time series are extracted by the forward LSTM layer and the backward LSTM layer respectively. The hidden states of the two are concatenated to output the complete temporal dynamic features. Step 4.3: Construct a collaborative reconstruction mechanism for the BiLSTM neural network model architecture. The collaborative reconstruction mechanism is a combination of physical prior information-guided training and neural network feature extraction used to reconstruct the data of the deleted measurement points. The input of the BiLSTM neural network model serves as physical prior information to provide data change trends and guide the training process of the BiLSTM neural network model. Specifically: the physical prior information in steps 1 to 3 provides overall change trends to guide the training process, and the BiLSTM neural network model characterizes high-frequency details and nonlinear residuals. The two form a hierarchical and complementary collaborative reconstruction mechanism. While retaining nonlinear expressive power, the model ensures that the reconstruction results conform to the laws of structural mechanics. Step 4.4: Use the BiLSTM neural network model to reconstruct the response of the measurement points to be deleted with high precision, and output the final reconstruction result, thus completing the prediction of the data of the deleted measurement points.

[0084] By comparing the errors between the reconstructed values ​​and the measured values ​​of the deleted measuring points, the substitutability of the deleted measuring points using the optimized layout method can be verified through deletion and verification. Simultaneously, it is also demonstrated that this method can be used to predict data from deleted measuring points on bridges that have already been constructed.

[0085] In one embodiment, the BiLSTM neural network model is structurally composed of forward LSTM units and backward LSTM units. Both the forward and backward LSTM units internally include a forget gate, an input gate, an output gate, and a tanh activation function (tanh layer), achieving selective retention and updating of long-term temporal information through a gating mechanism. Specifically, the forget gate controls the degree of information retention in the cell state of the previous time step; the input gate and the tanh layer collaboratively determine the method of writing new information, where the input gate is used to filter important information, and the tanh layer is used to generate candidate state vectors; the output gate is used to calculate the hidden state output at the current time step based on the current cell state. The forward LSTM unit processes the input sequence sequentially from front to back, accumulating historical response information time-by-time to generate a forward hidden state sequence, as shown in the following formula:

[0086] in, Represents the time of the forward LSTM unit The output, Indicates time The input vector represents , This represents the computation function of the forward LSTM unit.

[0087] The inverse LSTM unit processes the same sequence in reverse chronological order, capturing evolutionary dependencies in future time periods and generating a backward hidden state sequence, as shown in the following formula:

[0088] in, Represents the time of the inverse LSTM unit The output, Represents the time of the inverse LSTM unit The output, This represents the computation function of the inverse LSTM unit.

[0089] Subsequently, at each time step, the network concatenates the features from the forward and backward outputs and outputs the reconstructed value at that time step through a fully connected layer. The formula is as follows:

[0090] in, Indicates time The reconstructed value, Indicates the weights of the output layer. This indicates the bias of the output layer.

[0091] This bidirectional gating structure enables the neural network model to simultaneously perceive the current input, historical state, and future context at each decision moment, thereby extracting global dynamic features within the complete time window. This makes it more suitable for reconstruction tasks with significant time dependence and phase characteristics, such as bridge vibration response. During the training and validation phases of the neural network model, all samples are divided into training and validation sets in an 8:2 ratio.

[0092] The data for predicting the deletion of measurement points specifically includes: The sensor data of the retained transverse strain measurement points and the strain response data of the deleted transverse strain measurement points reconstructed (based on the transverse influence line of the load) are used as inputs to the BiLSTM neural network model, and the BiLSTM neural network model is used to predict the data of the deleted transverse strain measurement points. The data used to reconstruct the strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model, and the reconstructed strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model. The BiLSTM neural network model is then used to predict the data of the deleted longitudinal strain measurement points. Sensor data from retained displacement measurement points and reconstructed displacement data from the deleted displacement measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict data from the deleted displacement measurement points; and / or, sensor data from retained acceleration measurement points and reconstructed acceleration data from the deleted acceleration measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict data from the deleted acceleration measurement points.

[0093] To compare with this disclosure, this disclosure constructs a BiLSTM reconstruction model, which employs a purely data-driven method for bridge response reconstruction. The input layer of this model only contains the measured response data (sensor data) of the retained measurement points, without embedding any prior physical information based on mechanical relationships. It relies entirely on a data-driven approach to learn the spatiotemporal mapping relationship between measurement points. Using the data from measurement points P3 and P5 as input, the strain response data of measurement points P1, P2, and P4 are reconstructed; using the data from measurement points P7 and P8 as input, the strain response data of measurement point P6 is reconstructed; using the measured data from measurement points D2, S3, S4, S6, and S7 as input, the strain response data of measurement points S2 and S5 are reconstructed; and using the measured data from measurement points D1 and D2 as input, the acceleration data of measurement points A1 and A2 are reconstructed. The reconstruction results for each measurement point are shown in Table 3. Figure 14 and Figure 15 A comparison between the reconstructed data of measuring point P2 and the numerical simulation monitoring data is presented. Figure 16 and Figure 17 A comparison between the reconstructed data and the numerical simulation monitoring data of measuring point A1 is presented.

[0094] Table 3 Evaluation of the effect of the pure data-driven method on bridge response reconstruction

[0095] Depend on Figures 14-17 As shown in Table 3, the BiLSTM model using a purely data-driven approach performs excellently in the transverse strain reconstruction task (measurement points P1, P2 / P4, and P6). All reached above 0.9867, which is higher than that of purely physical methods. The value was approximately 0.75, representing an improvement of about 31.5%. In the strain reconstruction task along the bridge (measuring points S2 and S5), The results reached 0.9948 and 0.9933 respectively, which is better than that of purely physical methods. The performance improved by approximately 24% (≈0.80). This validates that for strongly correlated tasks (such as mappings between similar responses, especially between symmetrical measurement points), the purely data-driven BiLSTM model can effectively learn the intrinsic relationships between measurement points. However, in the acceleration reconstruction task along the bridge direction, the performance of the purely data-driven BiLSTM model significantly deteriorated. (Measurement points A1 / A4 and A2 / A3...) R 2The values ​​are only 0.6885 and 0.8558, significantly lower than the 0.9571 and 0.9792 of the pure physics method. This is because the mechanical relationship between acceleration and displacement is a strongly analytical constraint, and the pure data-driven model struggles to autonomously discover this differential relationship from limited displacement inputs, leading to a significant deterioration in reconstruction accuracy. These results demonstrate that the pure data-driven method excels in scenarios with strong correlation and high redundancy, but performs poorly in scenarios with weak correlation and strong physical constraints; conversely, the pure physics method is more reliable in scenarios with weak correlation.

[0096] The BiLSTM neural network model disclosed herein is a physics-guided BiLSTM architecture. This physics-guided BiLSTM neural network architecture refers to embedding physical prior information into the model input layer to achieve high-precision response reconstruction. Specifically, the network input includes preliminary reconstructed values ​​of deleted measurement points obtained based on physical relationships (lateral influence lines, displacement-strain-acceleration mapping relationships). In this architecture, physical priors provide constraints on the overall trend of change for the model, ensuring the physical rationality of the reconstruction results; while the data-driven model is responsible for characterizing high-frequency details and nonlinear residuals. The two form a hierarchical, complementary, and collaborative reconstruction mechanism, thereby effectively improving reconstruction accuracy and result stability.

[0097] In the lateral reconstruction task, the preliminary reconstructed strain values ​​of the deleted lateral measuring points P1, P2, and P4 obtained based on the lateral influence line are used together with the actual sensing data of the retained lateral measuring points P3 and P5 as network inputs to perform further high-precision reconstruction of the deleted lateral measuring points P1, P2, and P4. Subsequently, using the same strategy, the preliminary reconstructed value of the deleted lateral measuring point P6 and the actual strain data of the retained lateral measuring points P7 and P8 are used as inputs to achieve fine reconstruction of the detection data of measuring point P6.

[0098] In the bridge-direction reconstruction task, combining the physical relationship between displacement, strain, and acceleration, the preliminary reconstructed strain values ​​of deleted measuring points S2 and S5 obtained based on the modal superposition method are input into the network along with the measured response data of retained measuring points D2, S3, S4, S6, and S7 to achieve corrective prediction of the deleted strain measuring points. Simultaneously, using the measured data of retained longitudinal displacement measuring points D1 and D2 and the preliminary reconstructed values ​​of acceleration measuring points, the acceleration responses of deleted longitudinal acceleration measuring points A1 and A2 are reconstructed, further improving the reconstruction accuracy of the acceleration response.

[0099] The final reconstruction results for each measuring point are shown in Table 4. Figure 18 and Figure 19 This is a comparison chart of the finite element simulation monitoring data of measurement point P2 and the reconstructed data obtained from the physics-guided BiLSTM neural network model. Figure 20 and Figure 21This is a comparison chart of finite element simulation monitoring data and reconstructed data obtained from a physics-guided BiLSTM neural network model at measurement point A1. Figures 18-21 As shown in Table 4, after reconstruction of the BiLSTM neural network model guided by physics, the measurement points at each point... All values ​​were improved to above 0.97, demonstrating high overall accuracy. Under the physics-guided BiLSTM neural network model, the transverse strain measurement points... The efficiency reached 0.9986, an improvement of approximately 33% compared to the purely physical method (≈0.75), and also better than the purely data-driven BiLSTM model. The coefficient of performance (C=0.9867) increased slightly, but the RPD increased from 8.67 to 24.97, indicating a significant improvement in the model's predictive ability. Strain measurement points along the bridge direction... The efficiency reached 0.9993, an improvement of approximately 24% compared to purely physical methods (≈0.80), and also compared to purely data-driven BiLSTM models. =0.9933) A slight increase, and RPD jumped from approximately 13 to 44.56, significantly improving prediction capability. Acceleration measurement points along the bridge direction Reaching 0.9742, compared to pure BiLSTM ( =0.6885) is a 41.5% improvement, compared to the pure physical method ( =0.9571) slightly increased by 1.8%, successfully overcoming the failure of pure data-driven tasks in weakly correlated tasks and exceeding the upper limit of pure physical accuracy.

[0100] Table 4 Evaluation of the Reconstruction Effect of the BiLSTM Neural Network Model Guided by Physics

[0101] The above results demonstrate that the physics-guided BiLSTM neural network model achieves optimal reconstruction performance across all measurement points by balancing the structural mechanical properties of the bridge with the spatiotemporal correlation of monitoring data, thus surpassing both purely physics-based and purely data-driven methods. Particularly in weakly correlated tasks (displacement reconstructing acceleration), physics guidance avoids the accuracy collapse inherent in purely data-driven methods; in strongly correlated tasks, it further reduces the residual error of purely data-driven methods. This fully proves the effectiveness of the synergistic reconstruction strategy combining physics priors and data-driven approaches.

[0102] See Figure 22 This embodiment provides a system for optimizing the deployment and reconstructing the response of bridge sensors, including: The initial scheme determination module is used to determine the initial sensor deployment scheme based on the bridge structure. The finite element model creation module is used to create finite element models of bridges. The measurement point deletion module is used to delete measurement points in the initial sensor deployment scheme. Specifically, it is used to delete one of the strain measurement points when the difference in the bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of the strain response values ​​is higher than a preset correlation threshold; and it is used to delete the displacement measurement point or the acceleration measurement point when the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold. The acquisition module is used to acquire sensor data from all retained measurement points; The first reconstruction module is used to calculate the lateral influence line of the load using the finite element model (established by the finite element model building module); and reconstruct the strain response data of the deleted lateral strain measuring points based on the lateral influence line of the load and the sensor data of the retained lateral strain measuring points. The second reconstruction module is used to reconstruct the displacement data of the deleted displacement measurement points based on the relationship between displacement and acceleration, using the sensor data of the retained displacement measurement points, and / or to reconstruct the acceleration data of the deleted acceleration measurement points using the sensor data of the retained acceleration measurement points. The third reconstruction module is used to reconstruct the strain response data of the deleted longitudinal strain measurement points based on the relationship between strain and displacement, using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The model building module is used to construct the architecture of BiLSTM neural network models; The model prediction module inputs all the sensor data and all the reconstructed data into the BiLSTM neural network model, and uses the BiLSTM neural network model to predict the data of the deleted measurement points.

[0103] In this embodiment, the initial scheme determination module is specifically used to determine the initial sensor deployment scheme based on the bridge structure and relevant specifications for bridge health monitoring.

[0104] In specific implementation, the optimized deployment and response reconstruction system for bridge sensors can be implemented by referring to the optimized deployment and response reconstruction method of bridge sensors in any of the above embodiments. The specific implementation steps will not be repeated.

[0105] An electronic device can be implemented according to the method of this disclosure. The electronic device includes: a memory; one or more processors; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing an optimized deployment and response reconfiguration method for a bridge sensor according to any of the above embodiments.

[0106] This disclosure also provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for optimizing the layout and reconstructing the response of a bridge sensor.

[0107] The advantages of the optimized deployment and response reconstruction method, system, and medium for bridge sensors disclosed herein are as follows: An optimized sensor deployment scheme was designed to reduce redundant measuring points and optimize the bridge sensor layout. Based on this optimized sensor deployment scheme, a response reconstruction scheme was designed to cover all key response information with as few sensors as possible. Specifically, physical methods are used to initially reconstruct the data of deleted measuring points. The sensor data of the retained measuring points and the initially reconstructed data are both input into a BiLSTM neural network model, which is given physical constraints. This invention embeds physical constraints in the optimized deployment process, which can provide highly accurate data reconstruction results for all optimized measuring points, reducing the equipment investment cost of bridges and improving the effectiveness of bridge monitoring.

[0108] Specifically: This disclosure optimizes the deployment of bridge sensors, reduces redundant measuring points, and lowers engineering costs. By introducing collaborative modeling of structural physical characteristics and the spatiotemporal correlation of response, key measuring points are retained while redundant measuring points are removed. This achieves coverage of all key response information with as few sensors as possible, improving the rationality and relevance of the deployment scheme.

[0109] The measuring points reserved in this disclosure can accurately reflect the stress and deformation characteristics of the structure, avoiding the blind spots and over-configuration problems caused by empirical or standardized layout, thereby reducing equipment investment and operation and maintenance costs, and improving the overall economic benefits and promotion value of the monitoring system.

[0110] This disclosure incorporates physical constraints into the reconstruction process: reconstructions are performed based on the lateral influence line of the load, the relationship between displacement and acceleration, and the relationship between strain and displacement. The reconstruction results are then used to physically guide a BiLSTM neural network model, resulting in high accuracy and stability for the reconstruction using the BiLSTM neural network model. This means that accurate data predictions can be made for all measurement points deleted in the optimized layout. This disclosure improves reconstruction accuracy, thereby enhancing monitoring effectiveness and improving engineering feasibility.

[0111] This disclosure not only reduces the investment cost of bridge equipment while improving the effectiveness of bridge monitoring, but also has strong applicability, simple calculation, and convenient operation, making it highly valuable for promotion.

[0112] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0113] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0114] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the protection scope of this disclosure. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for optimizing the deployment and reconstructing the response of bridge sensors, characterized in that, Includes the following steps: Based on the bridge's structural form, determine the initial sensor deployment plan; Establish a finite element model of the bridge; Deleting measurement points in the initial sensor deployment scheme: If the difference in bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of strain response values ​​is higher than a preset correlation threshold, then one of the strain measurement points is deleted; if the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold, then the displacement measurement point or the acceleration measurement point is deleted. Acquire sensor data from all retained measurement points; The lateral influence line of the load is calculated using the finite element model. Based on the load lateral influence line, and using the sensor data of the retained lateral strain measurement points, the strain response data of the deleted lateral strain measurement points are reconstructed. Based on the relationship between displacement and acceleration, the displacement data of the deleted displacement measurement points is reconstructed using the sensor data of the retained displacement measurement points, and / or the acceleration data of the deleted acceleration measurement points is reconstructed using the sensor data of the retained acceleration measurement points. Based on the relationship between strain and displacement, the strain response data of the deleted longitudinal strain measurement points are reconstructed using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The architecture for constructing a BiLSTM neural network model; All the sensor data and reconstructed data are used as input to a BiLSTM neural network model, which is then used to predict the data for the deleted measurement points.

2. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, All the aforementioned sensing data and all the reconstructed data are used as input to the BiLSTM neural network model. The data used by the BiLSTM neural network model to predict the deleted measurement points specifically includes: The retained transverse strain measurement point sensor data and the reconstructed strain response data of the deleted transverse strain measurement point are used as input to the BiLSTM neural network model, and the BiLSTM neural network model is used to predict the data of the deleted transverse strain measurement point. The data used to reconstruct the strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model, and the reconstructed strain response data of the deleted longitudinal strain measurement points are used as input to the BiLSTM neural network model. The BiLSTM neural network model is then used to predict the data of the deleted longitudinal strain measurement points. Sensor data from retained displacement measurement points and reconstructed displacement data from the deleted displacement measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict the data of the deleted displacement measurement points; and / or, sensor data from retained acceleration measurement points and reconstructed acceleration data from the deleted acceleration measurement points are used as inputs to a BiLSTM neural network model, which is then used to predict the data of the deleted acceleration measurement points.

3. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, When the distance between a displacement measuring point and an acceleration measuring point in the same direction is less than a preset threshold, the acceleration measuring point is deleted. The calculation formula for the strain response data of the reconstructed and deleted transverse strain measurement points includes: in, This indicates the number of the strain gauge point that was deleted from the beam. Indicates the strain gauge points that were removed from the beam. Response weights are assigned; Indicates the strain gauge points that were removed from the beam. Location; express The lateral influence line value at that location; This indicates the number of the strain measurement points retained on the beam. , This indicates the total number of strain gauge points retained on the beam; Indicates the remaining strain measurement points on the beam. Location, express The lateral influence line value at that location; This indicates the total number of strain measurement points retained on the beam that participated in the reconstruction. This indicates the number of the strain measurement points retained on the beam that participated in the reconstruction. Indicates time, This indicates the strain measurement points retained on the beam that participated in the reconstruction. In time The measured response data, This indicates the strain measurement points retained on the beam that participated in the reconstruction. The response is assigned weights. This represents the equivalent vertical action obtained by inverting measured response data; Indicates the strain gauge points that were removed from the beam. In time The refactoring response.

4. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, The formula for calculating the strain response data of the longitudinal strain measurement points deleted during reconstruction is as follows: in, Represents modal coordinates, Indicates time, Indicates intermediate variables. This indicates the total number of longitudinal displacement measurement points that are retained and participate in the reconstruction. , This indicates the sequential number of the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The longitudinal displacement measuring points that were retained and participated in the reconstruction were in time. Internally collected response data, This represents the total number of longitudinal strain measurement points that are retained and participate in the reconstruction. , Indicates the first The longitudinal strain measurement points that were retained and participated in the reconstruction were in time. Internally collected sensor data, This indicates the first longitudinal strain measurement point that was retained and participated in the reconstruction at time... Internally collected sensor data, Indicates the first The longitudinal strain measurement points that were retained and participated in the reconstruction were in time. Internally collected sensor data, Indicates the first The mode shape vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The mode shape vectors corresponding to the longitudinal displacement measurement points that are retained and participate in the reconstruction. Indicates the first The mode vectors corresponding to the longitudinal strain measurement points that are retained and participate in the reconstruction. Indicates the first The mode shape vectors corresponding to the retained and reconstructed longitudinal strain measurement points are all , and the dimension of each mode shape vector is . , This represents the mode shape vector of the deleted longitudinal strain measurement point; This represents the strain response data of the deleted longitudinal strain measurement points after reconstruction.

5. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, The relationship between displacement and acceleration includes: in, Indicates the time number, Indicates time The previous moment, Indicates time The next moment, Indicates displacement. Indicates time Displacement at that point Indicates time Displacement at that point Indicates time Displacement at; Indicates time Acceleration at that point; This indicates the time interval.

6. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, The initial sensor deployment plan, determined based on the bridge structure, is specifically based on the bridge structure and relevant standards for bridge health monitoring.

7. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, The initial sensor deployment scheme includes the deployment of transverse strain measurement points, longitudinal strain measurement points, transverse acceleration measurement points, longitudinal acceleration measurement points, transverse displacement measurement points, and longitudinal displacement measurement points.

8. The method for optimizing the layout and reconstructing the response of bridge sensors according to claim 1, characterized in that, The steps for constructing the architecture of the BiLSTM neural network model include: The data input layer for constructing a BiLSTM neural network model architecture; BiLSTM temporal feature extraction module for constructing BiLSTM neural network model architecture; A collaborative reconstruction mechanism for constructing BiLSTM neural network model architecture.

9. A system for optimizing the deployment and reconstructing the response of bridge sensors, characterized in that, include: The initial scheme determination module is used to determine the initial sensor deployment scheme based on the bridge structure. The finite element model creation module is used to create finite element models of bridges. The measurement point deletion module is used to delete measurement points in the initial sensor deployment scheme. Specifically, it is used to delete one of the strain measurement points when the difference in the bending moment amplitude between two strain measurement points is lower than a preset difference threshold and the correlation of the strain response values ​​is higher than a preset correlation threshold; and it is used to delete the displacement measurement point or the acceleration measurement point when the distance between a displacement measurement point and an acceleration measurement point in the same direction is less than a preset threshold. The acquisition module is used to acquire sensor data from all retained measurement points; The first reconstruction module is used to calculate the lateral influence line of the load using the finite element model. Based on the load lateral influence line, and using the sensor data of the retained lateral strain measurement points, the strain response data of the deleted lateral strain measurement points are reconstructed. The second reconstruction module is used to reconstruct the displacement data of the deleted displacement measurement points based on the relationship between displacement and acceleration, using the sensor data of the retained displacement measurement points, and / or to reconstruct the acceleration data of the deleted acceleration measurement points using the sensor data of the retained acceleration measurement points. The third reconstruction module is used to reconstruct the strain response data of the deleted longitudinal strain measurement points based on the relationship between strain and displacement, using the sensor data of the retained longitudinal strain measurement points, the displacement data of the reconstructed longitudinal displacement measurement points, and / or the sensor data of the retained longitudinal displacement measurement points. The model building module is used to construct the architecture of BiLSTM neural network models; The model prediction module inputs all the sensor data and all the reconstructed data into the BiLSTM neural network model, and uses the BiLSTM neural network model to predict the data of the deleted measurement points.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for optimizing the layout and response reconstruction of bridge sensors as described in any one of claims 1-7.

Images