A method and system for optimizing the layout of measuring points during bridge construction

Abstract

This invention discloses a method and system for optimizing the layout of monitoring points during bridge construction, belonging to the field of monitoring point layout optimization technology. The system includes: a feature parameter module, a model update module, a performance evaluation module, an optimization trigger module, a candidate monitoring point module, a tracking and screening module, and a scheme determination module. By introducing irreversible evolution constraints and a unidirectional optimization mechanism, this invention ensures that monitoring point layout optimization is only adjusted based on existing schemes, avoiding backtracking and ineffective reconstruction, and ensuring the continuity and stability of monitoring point layout during the construction phase. By evaluating the tracking capability and monitoring performance of each candidate monitoring point scheme, it ensures that the final monitoring point layout scheme meets the preset monitoring requirements at each construction stage, improving the accuracy and reliability of bridge structural health monitoring.

Description

Technical Field

[0001] This invention relates to the field of measuring point layout optimization technology, and in particular to a method and system for optimizing the layout of measuring points during bridge construction. Background Technology

[0002] During bridge construction, the rationality of the monitoring point layout directly affects the effectiveness of structural monitoring and construction safety. Structural health monitoring technology has been widely applied in major engineering projects such as bridges, assessing the bridge's health status by collecting structural response data in real time. However, as construction progresses, the state and dynamic characteristics of the bridge structure change, rendering the original monitoring point layout plan ineffective in continuously and effectively monitoring key structural features. Therefore, how to optimize the monitoring point layout in real time according to the construction progress and structural evolution to ensure the accuracy and effectiveness of monitoring has become a pressing technical challenge in bridge construction.

[0003] Currently, the optimization of bridge monitoring point layout still mainly relies on traditional empirical methods or single static analysis models. These methods often fail to fully consider the dynamic changes and structural complexity during the construction phase, and cannot dynamically adjust the monitoring point layout to adapt to the bridge's evolving condition. In existing technologies, many monitoring point layout schemes are not optimized and updated at different construction stages of the bridge, resulting in significantly reduced monitoring effectiveness, failure to detect potential structural problems in a timely manner, and thus affecting the bridge's safety and construction quality. Summary of the Invention

[0004] The present invention aims to solve the above problems by updating the analysis model based on structural dynamic characteristic parameters and combining the irreversible evolution constraints of the construction stage to optimize and update the layout of measuring points.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for optimizing the layout of measuring points during bridge construction includes:

[0007] During bridge construction, measured structural response data from the previous construction phase are collected, and structural dynamic characteristic parameters are extracted.

[0008] The analysis model of the bridge in the current construction stage is updated using structural dynamic characteristic parameters as input.

[0009] Based on the updated analysis model, the monitoring performance of the existing measuring point layout scheme under the current construction stage is evaluated.

[0010] When the monitoring performance meets the triggering conditions, the measurement point layout optimization and update process is triggered.

[0011] During the optimization and update of the measurement point layout, the following steps are performed:

[0012] Immutable evolution constraints are imposed during the construction phase, treating the bridge construction phase as an irreversible structural state evolution process. Retrospective measurement point reconstruction is prohibited, ensuring that the measurement point layout optimization is only adjusted unidirectionally based on the existing measurement point layout scheme, generating candidate measurement point schemes.

[0013] For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes;

[0014] When the set of feasible solutions is not empty, the final layout of measuring points for the current construction stage is determined from the set of feasible solutions based on the preset optimization criteria.

[0015] As a preferred embodiment of the present invention, the structural dynamic characteristic parameters include: the natural frequency, damping ratio, and modal components corresponding to a predetermined order mode obtained by modal identification of the measured structural response data from the previous construction stage; and the modal participation coefficient and effective modal mass calculated based on the mass matrix of the updated analysis model combined with the modal components and the reference direction vector; wherein the natural frequency is the characteristic frequency of the structure in the corresponding mode; the damping ratio is the equivalent damping parameter of the corresponding mode; the modal components are the modal response values ​​at each measuring point in the corresponding mode; the modal participation coefficient is a scalar coefficient characterizing the degree of participation of the corresponding mode in the reference direction; and the effective modal mass is the equivalent mass parameter corresponding to the modal participation coefficient.

[0016] As a preferred embodiment of the present invention, the updating of the analysis model includes: selecting the natural frequencies and mode shape components of all orders of the structural dynamic characteristic parameters as the target parameters of the analysis model in the current construction stage; performing modal eigenvalue analysis on the mass matrix and stiffness matrix of the analysis model before the update to obtain the calculated natural frequencies and calculated mode shape components corresponding to all orders of the modes, which are used as the calculation target parameters; constructing the objective function for model updating based on the difference between the target parameters and the calculated target parameters; selecting the model parameters to be corrected in the analysis model, performing modal sensitivity analysis based on the target parameters and the model parameters to be corrected to obtain the sensitivity matrix of the target parameters to each model parameter to be corrected; and using the iterative least squares method to successively correct the model parameters to be corrected, updating the calculation target parameters and recalculating the objective function value in each iteration step until the objective function value is less than a preset convergence threshold, thereby obtaining the updated analysis model.

[0017] As a preferred embodiment of the present invention, the evaluation of the monitoring performance includes: based on the updated analysis model, extracting the modal components of the target mode at the existing measurement point locations, constructing a target mode observation matrix corresponding to the existing measurement point layout scheme, and calculating the minimum singular value of the target mode observation matrix, using the minimum singular value as the first monitoring performance index; calculating the modal correlation matrix between the target modes at the existing measurement point locations, wherein the elements of the modal correlation matrix are the normalized inner products between different target modal components, and using the sum of squares of the off-diagonal elements of the modal correlation matrix as the second monitoring performance index.

[0018] As a preferred technical solution of the present invention, the triggering condition is: the first monitoring performance index of any target mode is less than the preset first performance threshold, or the maximum value of the second monitoring performance index of each target mode is greater than the preset second performance threshold.

[0019] As a preferred technical solution of the present invention, the imposition of irreversible evolution constraints during the construction phase includes: before entering the measurement point layout optimization and update process of the current construction phase, determining all measurement point positions in the final measurement point layout scheme of the previous construction phase as an immovable measurement point set, and keeping the spatial positions of the immovable measurement points unchanged in subsequent construction phases; when generating candidate measurement point schemes, only adding measurement point positions based on the immovable measurement point set, or, under the premise of meeting key monitoring requirements, deactivating some immovable measurement points without changing their recorded positions, wherein the key monitoring requirements are that several key measurement point positions that are indispensable to the monitoring impact or have been manually marked as important are pre-specified in the immovable measurement point set, and the key measurement point positions remain in the active state in each construction phase and shall not be deactivated.

[0020] As a preferred technical solution of the present invention, the generation of the candidate measurement point scheme includes: on the updated analysis model, selecting several positions from other discrete structural positions besides the measurement point positions in the immovable measurement point set to form a set of candidate measurement point positions; under the premise of satisfying the irreversible evolution constraint of the construction stage, taking the existing measurement point layout scheme of the current stage as the benchmark, combining the candidate measurement point positions and the measurement point positions currently in the activation state to obtain several temporary measurement point layout schemes; for each temporary measurement point layout scheme, calculating its monitoring performance and comparing it with the monitoring performance of the existing measurement point layout scheme; when the comparison result meets the preset gain threshold and the number of measurement points retained in the immovable measurement point set is not less than the preset lower limit, the temporary measurement point layout scheme is included in the candidate measurement point scheme set.

[0021] As a preferred technical solution of the present invention, the evaluation of the tracking capability includes: based on the updated analysis model and combined with the predetermined construction sequence, performing modal analysis on the bridge structure in the current construction stage and the predetermined subsequent construction stages, solving for the natural frequency, damping ratio, modal component, modal participation coefficient, and effective modal mass of each construction stage, which are used as the predicted values ​​of the structural dynamic characteristics of the construction stage, and arranging them according to the construction sequence to form a predicted evolution sequence of structural dynamic characteristics; under each candidate measurement point scheme, based on the modal component of the target mode at the candidate measurement point location, extracting the predicted components of structural dynamic characteristics related to the candidate measurement point location from the predicted evolution sequence of structural dynamic characteristics, constructing a change vector of structural dynamic characteristic parameters between the current construction stage and each predetermined subsequent construction stage, wherein the change vector of structural dynamic characteristic parameters includes the change in the predicted value of the natural frequency, the change in the predicted value of the damping ratio, and the change in the modal component, and using the modal participation coefficient and effective modal mass of the corresponding mode to weight the change vector of structural dynamic characteristic parameters to obtain the tracking capability index of the candidate measurement point scheme.

[0022] As a preferred technical solution of the present invention, the preset optimization criteria include: in the set of feasible solutions, for each candidate measuring point solution, the corresponding number of sensors, the first monitoring performance index, the second monitoring performance index, and the tracking capability index are statistically analyzed; the number of sensors, the first monitoring performance index, the second monitoring performance index, and the tracking capability index are converted into dimensionless evaluation quantities according to a preset normalization method; a comprehensive evaluation function is constructed based on each dimensionless evaluation quantity and a preset weight coefficient; the comprehensive evaluation function value increases when the number of sensors and the second monitoring performance index decreases, and when the first monitoring performance index and the tracking capability index increase, is used as a constraint relationship; the comprehensive evaluation function value is calculated for each candidate measuring point solution in the set of feasible solutions; and the candidate measuring point solution with the optimal comprehensive evaluation function value is determined as the final measuring point layout solution for the current construction stage.

[0023] A bridge construction period measurement point layout optimization system includes:

[0024] Feature parameter module: During bridge construction, the measured structural response data from the previous construction stage are collected, and the structural dynamic characteristic parameters are extracted;

[0025] Model update module: Uses structural dynamic characteristic parameters as input to update the analysis model of the bridge in the current construction stage;

[0026] Performance evaluation module: Based on the updated analysis model, evaluate the monitoring performance of the existing measuring point layout scheme under the current construction stage;

[0027] Optimize trigger module: When the monitoring performance meets the triggering conditions, trigger the measurement point layout optimization and update process;

[0028] Candidate measuring point module: Apply irreversible evolution constraints during the construction phase to generate candidate measuring point schemes;

[0029] Tracking and screening module: For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes;

[0030] Solution determination module: When the set of feasible solutions is not empty, the final layout of measuring points for the current construction stage is determined from the set of feasible solutions based on preset optimization criteria.

[0031] The present invention has the following advantages:

[0032] This invention utilizes measured structural response data from the previous construction phase to dynamically update the bridge analysis model for the current construction phase, making the layout of measuring points more consistent with the actual structural state and avoiding the shortcomings of traditional static analysis models. By evaluating structural dynamic characteristic parameters, it monitors and analyzes the structural changes of the bridge in real time, adjusts the layout of measuring points in a timely manner, and ensures the efficiency and accuracy of the monitoring scheme.

[0033] This invention introduces irreversible evolution constraints and a one-way optimization mechanism, which allows the optimization of the measuring point layout to be adjusted only on the basis of the existing scheme, avoiding backtracking and invalid reconstruction, and ensuring the continuity and stability of the measuring point layout during the construction phase. By evaluating the tracking ability and monitoring performance of each candidate measuring point scheme, it ensures that the final measuring point layout scheme can meet the preset monitoring requirements at each construction phase, thereby improving the accuracy and reliability of bridge structural health monitoring.

[0034] This invention optimizes candidate monitoring point schemes and combines them with a comprehensive evaluation function to minimize the number of sensors and monitoring costs while meeting monitoring requirements, providing a more economical and efficient solution for bridge construction. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only schematic diagrams of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0036] Figure 1 This is a schematic diagram of a bridge construction period measurement point layout optimization system used in an embodiment of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0038] Example 1: A method for optimizing the layout of measuring points during bridge construction, comprising the following steps:

[0039] Step S1: During the bridge construction process, collect the measured structural response data from the previous construction stage and extract the structural dynamic characteristic parameters;

[0040] The structural dynamic characteristic parameters include: the natural frequencies, damping ratios, and modal components corresponding to predetermined orders of modes obtained by modal identification of measured structural response data from the previous construction stage; and the modal participation coefficients and effective modal masses calculated based on the mass matrix of the updated analysis model combined with the modal components and the reference direction vector. The natural frequencies are the characteristic frequencies of the structure in the corresponding modes; the damping ratios are the equivalent damping parameters of the corresponding modes; the modal components are the modal response values ​​at each measuring point in the corresponding modes; the modal participation coefficients are scalar coefficients characterizing the degree of participation of the corresponding modes in the reference direction; and the effective modal mass is the equivalent mass parameter corresponding to the modal participation coefficients.

[0041] In step S1, the previous construction stage refers to the structural state of the bridge after the most recent completion of major procedures before the current construction stage, such as the stable condition corresponding to the completion of the previous segment closure, the completion of the previous span tensioning, or the completion of the previous stage support removal. The structural state in this stage is relatively stable and suitable as the benchmark state for subsequent model updates and measurement point optimization. The measured structural response data of the previous construction stage comes from structural monitoring sensors deployed at existing measurement point locations. The sensor type is configured according to the monitoring purpose, and common scenarios include: accelerometers, used to collect vertical or lateral vibration responses; displacement gauges or deflectometers, used to collect static deflection or slowly varying displacement of key sections; and strain gauges, used to collect the strain response of beam spans or key component sections.

[0042] In typical engineering applications, several measuring points are pre-deployed on the main girder and pier top sections of the bridge. Each measuring point is equipped with one or more accelerometers. The sampling frequency is set to a value that meets the modal identification frequency band requirements, such as 200Hz or 500Hz. The acquisition duration is set to several minutes to tens of minutes, such as 10 minutes or 20 minutes, thereby obtaining a set of measured structural response data matrices composed of time, measuring point number, and response components. The excitation form can be environmental excitation such as vehicle traffic, construction load, wind load, etc., or artificial excitation, such as impact hammer striking or vibration excitation frequency sweeping. In subsequent processing, the measured structural response data undergoes preprocessing operations such as detrending, filtering, and normalization to suppress the influence of noise and drift on the modal identification results.

[0043] Based on the aforementioned measured structural response data, modal identification methods are used to extract the structural dynamic characteristic parameters of the bridge during the previous construction stage. Modal identification methods are applicable to output-only methods that rely solely on the measured response, such as Frequency Domain Decomposition (FDD) and Stochastic Subspace Identification (SSI), and are also applicable to input-output methods that consider input information. Through modal identification, several pairs of representative modes of the overall structural dynamic response are identified within a pre-defined frequency range, forming a set of "predetermined order modes".

[0044] Among them, the predetermined order modes refer to a set of modal orders selected according to engineering needs and monitoring objectives. These typically include first-order to several-order bending and torsional modes that dominate the overall stiffness and dynamic behavior of the structure. For example, for a medium-span continuous beam bridge, the first 4-6 vertical bending modes and 1-2 torsional modes can be selected as the predetermined order mode set for subsequent model updates and measurement point optimization analysis. For large-span or complex bridge types, the number of predetermined order modes can be expanded accordingly based on design frequency band requirements and the actual monitoring frequency range to ensure that the modal range targeted by the measurement point layout optimization matches the engineering requirements.

[0045] For each predetermined mode, the natural frequency, damping ratio, and mode shape components corresponding to that mode are obtained through mode identification. The natural frequency characterizes the structure's natural vibration frequency in that mode, reflecting the combined characteristics of the structure's stiffness and mass; the damping ratio characterizes the energy dissipation capacity of that mode; and the mode shape components describe the relative amplitude distribution of the structure along each measuring point in that mode. In practice, the mode shape components are typically normalized to a unit modal mass or unit modal displacement to ensure a consistent scale for mode shape comparisons between different modes.

[0046] After obtaining the measured modal parameters, the modal participation factor and effective modal mass are further calculated by combining the updated analysis model's mass matrix, modal component, and reference direction vector. The reference direction vector describes the overall response direction of the structure in a given direction of interest, such as the overall displacement direction along the longitudinal or vertical direction of the bridge. It is usually represented as a unit vector or weighted vector consistent with the degrees of freedom of the measurement point. The modal participation factor reflects the degree of participation of each mode in the reference direction; the larger the value, the more significant the contribution to the overall response. The effective modal mass is numerically related to the modal participation factor and is used to quantitatively describe the equivalent mass of the mode in the reference direction. It is often used to assess the contribution of the mode to the overall dynamic response under seismic, wind-induced vibration, or vehicle load conditions.

[0047] Step S2: Update the analysis model of the bridge in the current construction stage using the structural dynamic characteristic parameters as input;

[0048] The updating of the analysis model includes: selecting the natural frequencies and mode shape components of all orders of modes from the structural dynamic characteristic parameters as the target parameters of the analysis model in the current construction stage; performing modal eigenvalue analysis on the mass matrix and stiffness matrix of the analysis model before the update to obtain the calculated natural frequencies and calculated mode shape components corresponding to all orders of modes, which are used as the calculation target parameters; constructing the objective function for model updating based on the difference between the target parameters and the calculated target parameters; selecting the model parameters to be corrected in the analysis model, performing modal sensitivity analysis based on the target parameters and the model parameters to be corrected to obtain the sensitivity matrix of the target parameters to each model parameter to be corrected; and using the iterative least squares method to successively correct the model parameters to be corrected, updating the calculated target parameters and recalculating the objective function value in each iteration step until the objective function value is less than the preset convergence threshold, thus obtaining the updated analysis model.

[0049] In step S2, the analysis model is a numerical model describing the structural dynamic behavior of the bridge during its current construction phase, using the finite element method (FEM). This model maintains a correspondence with the actual bridge structure in terms of structural topology, component arrangement, cross-sectional shape, and boundary conditions. Initial model parameters are set based on design drawings, material testing results, and construction monitoring data. For example, for a continuous beam bridge, the main beam portion of the analysis model is discretized using several Euler-Bernoulli or Timoshenko beam elements, while the piers and cap beams are discretized using beam elements or solid elements. Supports and constraints are set as elastic or rigid constraints according to the designed support method.

[0050] The structural dynamic characteristic parameters extracted in step S1 include the measured modal parameters from the previous construction stage, where the predetermined order mode set corresponds to several pairs of modes that are representative of the overall dynamic performance of the structure. In step S2, all natural frequencies and mode shape components of the predetermined order modes are selected from the above structural dynamic characteristic parameters as target parameters for the analysis model in the current construction stage. The target parameter values ​​reflect the dynamic response characteristics of the actual structure in the previous construction stage and are used to guide the analysis model to gradually approximate the actual structural state from the initial state.

[0051] Based on the previous analysis model, modal eigenvalue analysis was performed on its mass and stiffness matrices to obtain the calculated natural frequencies and modal components corresponding to the target parameters, which were then used as the calculation target parameters. The mass and stiffness matrices are derived from the superposition of the mass and stiffness of each element in the discrete structural model, and their values ​​are directly related to material parameters, section parameters, connection stiffness, and constraint conditions. Through eigenvalue analysis, a certain deviation was found between the set of modal parameters given by the analysis model and the measured target parameters. This deviation reflects the differences between the initial model and the actual structure in terms of stiffness distribution, mass distribution, or boundary conditions.

[0052] To quantitatively describe the difference between the target parameters and the calculated target parameters, an objective function for model updating is constructed. The objective function characterizes the overall error level between the model's predicted results and the measured modal parameters. In this embodiment, the objective function adopts a weighted combination of frequency error terms and modal shape error terms. Specifically, the relative frequency deviations and modal shape differences of each mode are weighted and summed using weighting coefficients, thus balancing the needs of frequency matching and modal shape matching during model updating. By reasonably setting the weighting factors for each mode, the contribution of different modes to the objective function is adjusted according to the range and importance of modes of engineering interest.

[0053] When selecting parameters to be corrected in the analysis model, the parameters that have a significant impact on the structural dynamic characteristics are chosen, taking into account the bridge's structural form and construction stage. These parameters include, but are not limited to: the equivalent elastic modulus of the main beam and crossbeams, the reduction factor for the section stiffness of components, support stiffness parameters, the hinge stiffness or elastic connection coefficient of connecting components, and the additional mass coefficient of local components. The selection of these parameters achieves effective approximation of the target modal frequencies and vibration modes through the adjustment of a limited number of parameters, avoiding the introduction of a large number of redundant parameters that could lead to instability in the model update process.

[0054] After determining the parameters of the model to be corrected, modal sensitivity analysis is performed based on the target parameters and the parameters of the model to be corrected. Modal sensitivity analysis is used to evaluate the sensitivity of the target parameters to each parameter of the model to be corrected, and the result forms a sensitivity matrix. Each element in the sensitivity matrix represents the partial derivative or approximate rate of change of a certain component of the target parameter (such as a certain natural frequency or mode component) with respect to a certain parameter to be corrected. The structure of the sensitivity matrix reflects the coupling relationship between the parameters and the modal response. Parameters with higher sensitivity have a more significant impact on the objective function and are suitable as priority targets for correction.

[0055] Based on the sensitivity matrix, an iterative least squares method is used to successively correct the parameters of the model to be corrected. The iterative least squares method achieves a gradual reduction in the error between the target parameters and the calculated target parameters by minimizing the L2 norm of the objective function in the parameter space. In each iteration step, a system of linear equations is constructed using the deviation between the sensitivity matrix and the target parameters of the current iteration step. The parameter increment vector is solved and superimposed on the parameter estimates from the previous iteration step to obtain new parameter estimates. Then, based on the updated parameters, the mass matrix and stiffness matrix are reassembled, new modal eigenvalue analysis is performed, the calculated target parameters are updated, and the objective function value is recalculated. Through repeated iterations, the objective function value achieves a monotonically decreasing or stable convergence.

[0056] During implementation, the iterative least squares method is preferably used in conjunction with parameter step size control and iteration count limitation to avoid model instability caused by excessive parameter updates. Step size control introduces a scaling factor into the parameter increment to ensure that the update magnitude is moderate each time; iteration count limitation prevents the model update from getting stuck in an invalid loop by setting a maximum number of iterations. When the objective function value is less than the preset convergence threshold, the model update process is considered to have reached convergence, and the updated analysis model is obtained.

[0057] Step S3: Based on the updated analysis model, evaluate the monitoring performance of the existing measuring point layout scheme under the current construction stage;

[0058] The evaluation of the monitoring performance includes: based on the updated analysis model, extracting the modal components of the target modes at the existing measurement point locations, constructing a target mode observation matrix corresponding to the existing measurement point layout scheme, and calculating the minimum singular value of the target mode observation matrix, using the minimum singular value as the first monitoring performance index; calculating the modal correlation matrix between the target modes at the existing measurement point locations, wherein the elements of the modal correlation matrix are the normalized inner products between different target modal components, and using the sum of squares of the off-diagonal elements of the modal correlation matrix as the second monitoring performance index.

[0059] In step S3, the existing measuring point layout scheme under the current construction stage refers to the set of measuring points that are in an active state when entering this stage. This set inherits from the final measuring point layout scheme of the previous construction stage, and the start / stop status of local measuring points is adjusted as necessary based on the construction conditions of the current construction stage. This existing measuring point layout scheme corresponds spatially to several discrete locations in the discrete model of the bridge structure, such as the mid-span section of the main beam, the 1 / 4 span section, the pier top section, and key connection nodes. These locations are consistent with or have a consistent numbering system of the measuring point locations used to collect measured structural response data in step S1.

[0060] Based on the updated analysis model, the range of target modes is determined. The target modes are consistent with the predetermined order modes described in step S1, and several low-order bending and torsional modes that are representative of the overall dynamic behavior of the structure are selected. For example, in one embodiment, the target mode set includes the first 6 modes of the bridge structure, where modes 1 to 4 are vertical bending modes and modes 5 to 6 are torsional modes. For each target mode, the mode shape components at existing measurement points are calculated in the updated analysis model, forming target mode shape data with measurement points as rows and modes as columns.

[0061] Based on the aforementioned target modal components, a target modal observation matrix corresponding to the existing measurement point layout scheme is constructed. The number of rows in the target modal observation matrix equals the number of measurement points activated in the current stage, and the number of columns equals the number of target modes. The element in the j-th row and i-th column of the matrix corresponds to the modal response value of the i-th target mode at the j-th measurement point location.

[0062] After obtaining the target mode observation matrix, singular value analysis is performed on the matrix to obtain its set of singular values, and the minimum singular value is selected as the first monitoring performance index. The magnitude of the singular value reflects the degree of linear independence between the column vectors of the observation matrix (i.e., the mode shape vectors of each target mode at the measurement points). If the minimum singular value is close to zero, it indicates that at least one target mode is highly similar to other modes in terms of mode shape under the current measurement point arrangement, making it difficult to effectively distinguish the dynamic characteristics of this mode under this measurement point arrangement. If the minimum singular value remains at a high level, it indicates that the response distribution of each target mode at the current measurement point set is significantly different, and the measurement point arrangement has a strong ability to distinguish different modes.

[0063] While calculating the first monitoring performance index, a modal correlation matrix between target modes is further constructed at the existing measurement point locations, serving as the basis for the second monitoring performance index. The rows and columns of the modal correlation matrix correspond to the target mode numbers. The element in the i-th row and k-th column is the normalized inner product between the mode shape vectors of the i-th and k-th target modes at the existing measurement point locations. The normalized inner product is calculated by normalizing the mode shape vectors. The resulting correlation coefficient ranges from 0 to 1; the closer the value is to 1, the more similar the mode shape distributions of the two modes are at the current measurement point; the closer it is to 0, the more significant the difference between them. Diagonal elements correspond to the correlation between modes themselves, with a theoretical value of 1; off-diagonal elements characterize the similarity between different modes. To measure the overall degree of aliasing between different target modes, the off-diagonal elements of the modal correlation matrix are squared and summed to obtain the second monitoring performance index. The larger the value of this indicator, the more pairs of highly similar modes exist under the current measurement point layout scheme, the worse the distinguishability between modes, and the more likely the monitoring data will be aliased and misjudged when performing multimodal identification or modal tracking; the smaller the value of this indicator, the lower the overall modal correlation, and the more significant the differences in the response patterns of different modes of the structure on the current measurement point set.

[0064] Step S4: When the monitoring performance meets the triggering conditions, trigger the measurement point layout optimization and update process;

[0065] The triggering condition is: the first monitoring performance index of any target mode is less than the preset first performance threshold, or the maximum value of the second monitoring performance index of each target mode is greater than the preset second performance threshold.

[0066] In step S4, the trigger condition is used to determine whether the existing monitoring point layout scheme needs to enter the monitoring point layout optimization and update process under the current construction stage. The trigger condition is based on the monitoring performance indicators calculated in step S3. The monitoring performance indicators include a first monitoring performance indicator and a second monitoring performance indicator. The first monitoring performance indicator reflects the linear independence level of the target mode on the existing monitoring point set, and the second monitoring performance indicator reflects the correlation and aliasing degree between target modes on the existing monitoring point set. The trigger condition sets thresholds for these two indicators to form a judgment rule for monitoring performance degradation or excessive mode aliasing.

[0067] A preset first performance threshold is used to limit the lower limit of the first monitoring performance index. The preset first performance threshold is set based on the engineering requirements for modal identification accuracy, combined with numerical simulation analysis, actual bridge test results, or empirical data from similar bridges. For example, after comparing the singular value spectra of multiple candidate monitoring point layout schemes, the minimum singular value level that ensures stable identification of the target modality under typical working conditions is used as a reference. A value slightly higher than this reference value is set as the first performance threshold, so that when the first monitoring performance index is lower than the first performance threshold, it is determined that the current monitoring point layout scheme has significant deficiencies in modal observability.

[0068] A preset second performance threshold is used to limit the upper limit of the second monitoring performance index. When the second monitoring performance index is at a low level, it indicates that the mode shape distribution of the target mode differs significantly on the current set of measurement points, and the cross-correlation between different modes is weak, which is beneficial for achieving stable mode identification and mode tracking in the presence of noise. When the second monitoring performance index exceeds a certain value, it indicates that there are one or more groups of modes with highly similar response modes on the measurement points, which can easily lead to mode aliasing and identification errors. The setting of the second performance threshold is based on the empirical upper limit value of the largest off-diagonal element in the modal confidence matrix. That is, when the normalized correlation coefficient between different modes exceeds a certain upper limit, it is judged as severe aliasing. Based on this, the upper limit value of the corresponding sum of squares of off-diagonal elements is derived as the second performance threshold.

[0069] The setting of triggering conditions is coordinated with the construction phase division and monitoring frequency. For example, in the early stages of construction, when the structural stiffness has not yet fully formed, the target modal frequency band varies significantly, and the monitoring performance indicators may fluctuate within a wide range. In this case, a more lenient threshold is used to avoid frequent triggering of adjustments to the measuring point layout. In the middle and later stages of construction, after the mid-span closure and the overall bridge completion, the structural dynamic performance gradually approaches the design state, and the target modal frequencies and mode shapes tend to stabilize. At this time, a more stringent threshold is used to ensure that the measuring point layout scheme has sufficient modal identification and modal tracking capabilities during the long-term monitoring phase.

[0070] When the monitoring performance meets the triggering condition, i.e., the monitoring performance index of the current existing monitoring point layout scheme violates the preset performance threshold constraint, the monitoring point layout optimization and update process is triggered in step S4, and the process proceeds to the irreversible evolution constraint and candidate monitoring point scheme generation stage in the subsequent step S5. In the construction stage where the triggering condition is not met, it indicates that the existing monitoring point layout scheme is within acceptable ranges for both the first and second monitoring performance indicators. In this case, the existing monitoring point layout scheme is kept unchanged to reduce unnecessary construction intervention and sensor layout adjustment workload.

[0071] During the optimization and update of the measurement point layout, the following steps are performed:

[0072] Step S5: Apply irreversible evolution constraints during the construction phase, treating the bridge construction phase as an irreversible structural state evolution process, prohibiting retrospective measurement point reconstruction, and ensuring that the measurement point layout optimization is only adjusted unidirectionally based on the existing measurement point layout scheme to generate candidate measurement point schemes.

[0073] The irreversible evolution constraints applied during the construction phase include: before entering the measurement point layout optimization and update process of the current construction phase, determining all measurement point locations in the final measurement point layout scheme of the previous construction phase as an immovable measurement point set, and keeping the spatial location of the immovable measurement points unchanged in subsequent construction phases; when generating candidate measurement point schemes, only adding measurement point locations based on the immovable measurement point set, or, under the premise of meeting key monitoring requirements, deactivating some immovable measurement points without changing their recorded locations, wherein the key monitoring requirements are that several key measurement point locations that are indispensable to the monitoring impact or have been manually marked as important are pre-specified in the immovable measurement point set, and the key measurement point locations remain in the active state in each construction phase and shall not be deactivated.

[0074] The generation of candidate measurement point schemes includes: on the updated analysis model, selecting several locations from other discrete structural locations besides the measurement point locations in the immovable measurement point set to form a set of candidate measurement point locations; under the premise of satisfying the irreversible evolution constraints of the construction stage, taking the existing measurement point layout scheme of the current stage as the benchmark, combining the candidate measurement point locations and the measurement point locations currently in the activation state to obtain several temporary measurement point layout schemes; for each temporary measurement point layout scheme, calculating its monitoring performance and comparing it with the monitoring performance of the existing measurement point layout scheme; when the comparison result meets the preset gain threshold and the number of measurement points retained in the immovable measurement point set is not less than the preset lower limit, the temporary measurement point layout scheme is included in the candidate measurement point scheme set.

[0075] In step S5, the bridge construction stages are considered as a monotonically evolving sequence of structural states over time, exhibiting irreversible evolutionary characteristics in terms of structural stiffness distribution, mass distribution, and boundary conditions between each construction stage. For example, as the piers are poured, the closure section is completed, and the supports are removed, the structural stiffness gradually forms and tends to stabilize. Completed components and connections are usually not removed or reverted. Therefore, the irreversibility of the construction process must be followed during the optimization of the monitoring point layout to avoid large-scale readjustments of the monitoring point locations already set up in the previous stage during subsequent construction stages, so as not to disrupt the continuity of monitoring data and increase the risk of construction intervention.

[0076] In this embodiment, "backtracking measurement point reconstruction" refers to completely overturning the existing measurement point layout plan in a subsequent construction stage, reselecting measurement point locations and deploying sensors across the entire bridge, resulting in a lack of inheritance relationship between the measurement point location sets of the preceding and following construction stages. While this approach theoretically offers greater search freedom, it introduces the following disadvantages in engineering practice: First, a large number of installed sensors need to be removed and relocated, increasing the workload and cost; second, the spatial location of monitoring data changes abruptly with each construction stage, hindering cross-stage structural state comparison analysis and unified modal parameter identification; and third, frequent changes in measurement point locations may interfere with construction site safety and construction organization. This embodiment explicitly prohibits the aforementioned backtracking measurement point reconstruction by imposing irreversible evolution constraints on construction stages, allowing only unidirectional adjustments based on the existing measurement point layout plan, thereby ensuring the inheritance of measurement point layout and the controllability of the construction process.

[0077] When implementing step S5, before entering the current construction phase's measuring point layout optimization and update process, the set of immovable measuring points is determined based on the final measuring point layout plan of the previous construction phase. The final measuring point layout plan of the previous construction phase includes all measuring point locations and their activation status that were actually used to collect monitoring data at the end of the previous phase. The measuring point locations are identified by node numbers, component numbers, or bridge station mileage coordinates in the discrete model of the bridge structure. All measuring point locations in the plan are included in the immovable measuring point set, indicating that the spatial coordinates of these locations remain unchanged in subsequent construction phases; that is, their installation positions are not shifted or re-laid out, ensuring the spatial comparability of monitoring data across phases.

[0078] Within the set of immovable monitoring points, several key monitoring point locations are pre-designated based on the needs of engineering safety monitoring and construction control. These key monitoring point locations are situated in areas of the structure most sensitive to stress and deformation or with high safety risks, such as the mid-span section of the main span, the pier top section, the connection between the main beam and the main tower, sections near expansion joints, and specific locations of abrupt stiffness changes. Monitoring data is continuously collected at these key monitoring point locations throughout each construction stage to track the stress state and deformation trends of critical sections and provide direct evidence for safety warnings. Based on the above considerations, this embodiment imposes stricter constraints on the key monitoring point locations, requiring them to remain active throughout each construction stage and not be deactivated. This constraint is explicitly stated in the "Key Monitoring Requirements," which in this embodiment refers to the mandatory activation requirement for a subset of monitoring point locations within the immovable monitoring point set. This further tightens the freedom of combining monitoring point activation and deactivation, ensuring that optimization and adjustment of monitoring points do not weaken the monitoring capabilities of key monitoring points.

[0079] When generating candidate measurement point schemes, the set of immovable measurement points forms the basic framework for subsequent measurement point layout optimization. For non-critical measurement point locations within the immovable measurement point set, their start / stop status can be adjusted, provided that critical monitoring requirements and performance requirements are met. This means maintaining the location coordinates and adjusting whether to install or retain sensors based on optimization results. For critical measurement point locations, their installation location and activation status remain unchanged, ensuring continuous provision of measured response data for critical sections throughout each construction phase. Simultaneously, to improve the observability of the target mode and the tracking capability of the structural dynamic characteristics during construction, new measurement point locations need to be introduced outside the set of immovable measurement points.

[0080] Therefore, in the updated analysis model, several locations are selected from the discrete structural locations other than those in the immovable measuring point set to form a candidate measuring point location set. These discrete structural locations originate from the node or component locations in the finite element analysis model. Typically, this involves selecting several node locations where sensors can be deployed at certain intervals within the entire span of the main beam, piers, and key connection points. For example, in one embodiment, the main beam is discretized into 40 analysis nodes, of which the final measuring point layout scheme from the previous construction stage includes 12 measuring point locations. After determining the immovable measuring point set, nodes with a certain distance from the already deployed measuring point locations and located in areas with large modal amplitudes are selected from the remaining 28 nodes to form a candidate measuring point location set. The number of candidate measuring points is set to 10-20 to provide sufficient spatial freedom for optimization without incurring excessive construction costs.

[0081] Under the premise of satisfying the irreversible evolution constraint during the construction phase, and based on the existing measuring point layout scheme of the current phase, several temporary measuring point layout schemes are constructed by combining the activation and deactivation of candidate measuring point locations and currently activated measuring point locations. The basic idea of ​​the activation and deactivation combination is to use the existing activated measuring points as the initial scheme, and without changing the coordinates of immovable measuring point locations, generate a set of candidate layout schemes that differ from the original scheme in both quantity and location by activating some candidate measuring point locations and deactivating some non-critical immovable measuring point locations. To avoid an excessive number of combinations, the number of newly added and deactivated measuring points in each optimization is usually limited in practice. For example, the number of newly added measuring points is set to no more than a certain number, and the number of deactivated measuring points is set to no more than a certain number, thereby controlling the computational complexity and construction adjustment workload while ensuring search diversity.

[0082] For each temporary monitoring point layout scheme, its first and second monitoring performance indicators are calculated based on the monitoring performance evaluation method in step S3, and compared with the monitoring performance indicators of the existing monitoring point layout schemes in the current stage. The comparison results are determined using a preset gain threshold. In this embodiment, the preset gain threshold is used to describe the minimum improvement in monitoring performance that the temporary monitoring point layout scheme needs to achieve compared to the existing scheme. It is usually calculated by weighting the increase in the first monitoring performance indicator and the decrease in the second monitoring performance indicator. For example, the preset gain threshold is set to a positive value. When the combined effect of the improvement in the first monitoring performance indicator and the decrease in the second monitoring performance indicator of the temporary scheme causes the overall performance gain to exceed the threshold, the temporary scheme is determined to be superior to the existing scheme in terms of monitoring performance.

[0083] In addition to monitoring performance gains, it is also necessary to ensure that the number of immovable monitoring points retained in the temporary scheme is not less than a preset lower limit. The preset lower limit is set based on the monitoring tasks and safety control requirements of the construction phase, reflecting the minimum monitoring capability of the overall immovable monitoring point set. For example, if the final scheme in the previous construction phase uses 12 monitoring points, the preset lower limit can be set to 8-10 to ensure that the temporary monitoring point layout scheme does not weaken the basic coverage capability of the existing monitoring system by excessively disabling immovable monitoring points during the optimization process. Only when the temporary monitoring point layout scheme simultaneously meets the above constraints in terms of both monitoring performance gains and the number of immovable monitoring points retained will the temporary scheme be included in the candidate monitoring point scheme set.

[0084] Step S6: For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes.

[0085] The evaluation of the tracking capability includes: based on the updated analysis model and combined with the predetermined construction sequence, performing modal analysis on the bridge structure in the current construction stage and the predetermined subsequent construction stages, solving for the natural frequency, damping ratio, modal component, modal participation coefficient, and effective modal mass of each construction stage, which are used as the predicted values ​​of the structural dynamic characteristics of that construction stage, and arranging them according to the construction sequence to form a predicted evolution sequence of structural dynamic characteristics; under each candidate measurement point scheme, based on the modal component of the target mode at the candidate measurement point location, extracting the predicted components of structural dynamic characteristics related to the candidate measurement point location from the predicted evolution sequence of structural dynamic characteristics, constructing a change vector of structural dynamic characteristic parameters between the current construction stage and each predetermined subsequent construction stage, the change vector of structural dynamic characteristic parameters including the change in the predicted value of the natural frequency, the change in the predicted value of the damping ratio, and the change in the modal component, and using the modal participation coefficient and effective modal mass of the corresponding mode to weight the change vector of structural dynamic characteristic parameters to obtain the tracking capability index of the candidate measurement point scheme.

[0086] In step S6, the "predicted evolution path of structural dynamic characteristics" refers to the overall change process of the structural dynamic characteristic parameters at each construction stage as the bridge structure progresses along the predetermined construction sequence from the current construction stage. This evolution process reflects the comprehensive influence of the gradual changes in structural stiffness, mass distribution, and boundary conditions during construction on dynamic characteristic quantities such as natural frequency, damping ratio, modal components, modal participation coefficient, and effective modal mass.

[0087] In this embodiment, "tracking capability" refers to the ability to observe and characterize the predicted evolution path of the structural dynamic characteristics using the locations of the measuring points covered by a given candidate measuring point layout scheme. Specifically, the tracking capability index quantitatively measures the sensitivity and identification accuracy of the candidate measuring point scheme to changes in structural dynamic characteristics under multiple construction stages and multimodal joint considerations. When the tracking capability index of a candidate measuring point scheme is high, it indicates that the modal parameter change information obtained through the measuring point layout scheme during the entire construction process comprehensively and accurately reflects the evolution trend of structural stiffness and mass, facilitating subsequent construction health monitoring, condition assessment, and damage identification.

[0088] To evaluate the tracking capability of each candidate monitoring point scheme, modal analysis was first performed on the current construction stage and the planned subsequent construction stages based on the updated analysis model and the predetermined construction sequence. The predetermined construction sequence was defined according to the construction organization design and the arrangement of key processes.

[0089] Arranging the predicted structural dynamic characteristics of each construction stage according to the construction sequence yields the predicted evolution sequence of structural dynamic characteristics. This sequence is a multidimensional parameter trajectory arranged in chronological order, where each stage corresponds to a set of dynamic characteristic quantities for a predetermined order mode. For a given mode, as the construction stages progress, its predicted natural frequency typically shows a gradual increase or slight fluctuation with stiffness formation and span changes; the predicted damping ratio reflects the change in the structure's energy dissipation capacity; the modal components demonstrate the spatial distribution evolution of the modal shapes at different stages; and the modal participation coefficient and effective modal mass reflect the change in the contribution of that mode to the overall response.

[0090] Under each candidate measurement point scheme, based on the measurement point locations included in that scheme, and the modal vibration components of the target mode at the candidate measurement point locations, the predicted components of the structural dynamic characteristics related to the candidate measurement point locations are extracted from the predicted evolution sequence of structural dynamic characteristics. This process is equivalent to retaining only the modal vibration components corresponding to the candidate measurement point locations in the predicted modal vibrations of each construction stage, and combining them with the target mode set corresponding to that measurement point scheme to form a subsequence ordered by construction stage and with the response of the target mode at the candidate measurement point as its element.

[0091] When analyzing the changes in structural dynamic characteristics between the current construction phase and each planned subsequent construction phase, this change process is quantified by constructing a vector of structural dynamic characteristic parameter changes. For each target mode, a set of parameter differences is constructed from the current phase to a certain subsequent phase, including the change in the predicted natural frequency, the change in the predicted damping ratio, and the change in the mode shape components at candidate measurement points. The change in natural frequency reflects the change in the overall stiffness and mass combination characteristics of the mode, the change in damping ratio reflects the change in the energy dissipation characteristics of the mode, and the change in mode shape components reflects the change in the spatial response mode of the mode at candidate measurement points. Arranging these parameter changes in a predetermined order to form a vector of structural dynamic characteristic parameter changes yields a vectorized representation sufficient to describe the evolution of dynamic characteristics from the current phase to subsequent phases.

[0092] To reflect the varying importance of different modes to the overall structural response, modal participation coefficient (MOD) and effective modal mass (EMM) are introduced as weighting factors when constructing the tracking capability index. In this embodiment, by weighting the structural dynamic characteristic parameter variation vector using MOD and EM, the parameter variations of modes that contribute significantly to the overall response are given higher weight in the tracking capability index, thereby constructing a comprehensive tracking capability evaluation metric that takes into account the differences in the importance of multiple modes.

[0093] In practical implementation, the tracking capability index is synthesized by weighted changes in different construction stages, different target modes, and different parameter components to obtain a scalar for evaluating the overall tracking capability of candidate measuring point schemes. The higher the value of this scalar, the stronger the comprehensive sensitivity to the evolution of structural dynamic characteristics during the construction stage under the current candidate measuring point layout scheme. That is, parameter changes in each stage and important mode are fully captured and distinguished through the measuring point response. When the value of this scalar is low, it indicates that there are areas where parameter changes are not effectively observed in some construction stages or some important modes, and the candidate measuring point scheme is insufficient in long-term tracking of structural state.

[0094] A preset capability threshold is used to determine whether the tracking capability of candidate measuring point schemes meets engineering requirements. The preset capability threshold is determined based on the following information: First, tracking capability indicators are calculated using numerical simulation under different measuring point layout schemes, and the indicator values ​​corresponding to known layout schemes with good tracking performance are used as references; second, based on experience from long-term monitoring projects in similar bridge engineering, the minimum tracking capability level that ensures stable identification of key modal frequencies and mode shape changes is selected; third, considering the quantitative requirements for structural state identification accuracy during key construction stages of this bridge project, indicators such as frequency deviation and mode shape correlation thresholds are converted into the lower limit of the tracking capability index. In actual engineering, to balance safety and economy, the preset capability threshold is set slightly higher than the empirical lower limit.

[0095] Step S7: When the set of feasible solutions is not empty, determine the final layout scheme of measuring points for the current construction stage from the set of feasible solutions based on the preset optimization criteria.

[0096] The preset optimization criteria include: in the feasible scheme set, for each candidate measuring point scheme, the corresponding number of sensors, first monitoring performance index, second monitoring performance index, and tracking capability index are statistically analyzed; the number of sensors, first monitoring performance index, second monitoring performance index, and tracking capability index are converted into dimensionless evaluation quantities according to a preset normalization method; a comprehensive evaluation function is constructed based on each dimensionless evaluation quantity and a preset weight coefficient; the comprehensive evaluation function value increases when the number of sensors and second monitoring performance index decreases and the first monitoring performance index and tracking capability index increase, as a constraint relationship; the comprehensive evaluation function value is calculated for each candidate measuring point scheme in the feasible scheme set; and the candidate measuring point scheme with the optimal comprehensive evaluation function value is determined as the final measuring point layout scheme for the current construction stage.

[0097] In step S7, the "preset optimization criterion" refers to a unified evaluation rule given for each candidate monitoring point scheme in the feasible scheme set, after comprehensively considering factors such as deployment cost, monitoring performance, and tracking capability. The preset optimization criterion is not limited to a single indicator but simultaneously considers the following four types of evaluation quantities: the number of sensors, the first monitoring performance indicator, the second monitoring performance indicator, and the tracking capability indicator. Specifically, the number of sensors reflects the implementation cost and system complexity of the monitoring point deployment scheme; the first monitoring performance indicator reflects the independence level of the target mode in the monitoring point space; the second monitoring performance indicator reflects the degree of mode aliasing; and the tracking capability indicator reflects the observability of the evolution of structural dynamic characteristics across construction stages. By dimensionlessly combining and weighting the above four types of evaluation quantities, the preset optimization criterion transforms the multi-indicator decision problem into an optimization problem of a single comprehensive evaluation function.

[0098] When evaluating each candidate monitoring point scheme in the feasible scheme set, the number of sensors corresponding to that scheme is first counted. The number of sensors refers to the total number of monitoring points that are active and used to collect monitoring data in the current construction phase, including the active monitoring point locations in the set of immovable monitoring points and the active monitoring point locations in the candidate monitoring point locations. The number of sensors is directly related to the construction and installation workload, subsequent maintenance costs, and data processing load. Therefore, in the comprehensive evaluation, schemes with fewer sensors have an advantage in terms of cost.

[0099] Subsequently, combining the monitoring performance evaluation results in step S3 and the tracking capability calculation results in step S6, the corresponding first monitoring performance index, second monitoring performance index, and tracking capability index are extracted for each candidate monitoring point scheme. The first and second monitoring performance indices are consistent with the definitions of existing schemes, representing the minimum singular value of the target modal observation matrix and the sum of squares of the off-diagonal elements of the modal correlation matrix under the candidate scheme, respectively. The tracking capability index is obtained by synthesizing the structural dynamic characteristic parameter change vector under the weighting of modal participation coefficient and effective modal mass, representing the comprehensive ability of the scheme to track the evolution of structural dynamic characteristics across construction stages.

[0100] Because the four types of evaluation quantities differ in physical dimensions, numerical range, and scale of change, to avoid any one evaluation quantity from having an excessively large numerical scale and thus holding too high a weight in the overall evaluation, a pre-defined normalization method is needed to convert them into dimensionless evaluation quantities. The normalization method is determined based on engineering practices and indicator attributes. For example, for indicators where "smaller values ​​are better" (such as the number of sensors and the second monitoring performance indicator), a linear normalization method based on the maximum and minimum values ​​is used to map the value range to a dimensionless quantity within the 0-1 interval. Inverse processing is then used to ensure that larger normalization results indicate better performance. For indicators where "larger values ​​are better" (such as the first monitoring performance indicator and the tracking capability indicator), a normalization method with a consistent direction is used, mapping larger original values ​​to larger dimensionless evaluation quantities. Through normalization, four dimensionless evaluation quantities within a unified numerical range and with consistent directions are formed for subsequent weighted summation.

[0101] Based on the normalized dimensionless evaluation quantities, a comprehensive evaluation function is constructed using preset weighting coefficients. These weighting coefficients characterize the relative importance of each evaluation quantity in the overall decision-making process and are set according to the project's monitoring objectives, cost constraints, and safety requirements. For example, in projects emphasizing long-term monitoring economy and maintenance convenience, the weight of the number of sensors is set slightly higher; in projects emphasizing the accuracy of key modal identification and dynamic risk control during construction, the weights of the first monitoring performance indicator and the tracking capability indicator are set relatively high; and in structures where modal aliasing is prominent, the weight of the second monitoring performance indicator is appropriately increased. The weighting coefficients satisfy the constraints of non-negativity and a sum of 1, ensuring that the comprehensive evaluation function reflects the balance of each evaluation dimension in the overall decision-making process.

[0102] The construction of the comprehensive evaluation function follows the basic constraint that "the value of the comprehensive evaluation function increases when the number of sensors and the second monitoring performance index decrease, and when the first monitoring performance index and the tracking capability index increase." This constraint reflects the optimization direction of this embodiment: on the one hand, improving the quality of structural dynamic parameter monitoring and cross-stage tracking capability; on the other hand, controlling the scale of sensor deployment and the degree of modal aliasing. Specifically, when the number of sensors corresponding to a certain scheme decreases while other evaluation quantities remain unchanged, the value of the comprehensive evaluation function increases; when the first monitoring performance index or the tracking capability index increases while other conditions remain unchanged, the value of the comprehensive evaluation function increases; and when the second monitoring performance index decreases, the value of the comprehensive evaluation function increases. This monotonicity requirement is used as a constraint in the design of the comprehensive evaluation function to exclude weighting methods that violate engineering common sense and ensure that the comprehensive evaluation results are consistent with intuitive engineering understanding.

[0103] Example 2: A system for optimizing the layout of measuring points during bridge construction (see [link]). Figure 1 As shown, it includes the following modules:

[0104] Feature parameter module: During bridge construction, the measured structural response data from the previous construction stage are collected, and the structural dynamic characteristic parameters are extracted;

[0105] Model update module: Uses structural dynamic characteristic parameters as input to update the analysis model of the bridge in the current construction stage;

[0106] Performance evaluation module: Based on the updated analysis model, evaluate the monitoring performance of the existing measuring point layout scheme under the current construction stage;

[0107] Optimize trigger module: When the monitoring performance meets the triggering conditions, trigger the measurement point layout optimization and update process;

[0108] Candidate measuring point module: Apply irreversible evolution constraints during the construction phase to generate candidate measuring point schemes;

[0109] Tracking and screening module: For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes;

[0110] Solution determination module: When the set of feasible solutions is not empty, the final layout of measuring points for the current construction stage is determined from the set of feasible solutions based on preset optimization criteria.

[0111] Example 3: A method and system for optimizing the layout of measuring points during bridge construction. This example uses a three-span continuous beam bridge as an example to illustrate the specific implementation process of the method and system for optimizing the layout of measuring points during bridge construction.

[0112] I. Project Object and Initial Analysis Model;

[0113] This embodiment selects a three-span continuous prestressed concrete box girder bridge as the engineering object. Based on the design drawings and construction conditions, the superstructure of the bridge is simplified into a multi-element cantilever simply supported beam finite element model. The main beam is divided into elements, and nodes are set at positions such as mid-span, quarter-span, and near the supports as potential measurement points for subsequent testing.

[0114] Before construction, an initial finite element (bridge) analysis model is established based on the bridge design parameters (section dimensions, material parameters, prestressing arrangement, support constraints, etc.) to obtain the initial mass matrix and stiffness matrix. This initial model serves as the basis for subsequent model updates and measurement point layout optimization during the construction phase.

[0115] II. Measured response acquisition and dynamic characteristic identification during the construction phase;

[0116] During bridge construction, structural dynamic tests are conducted after each construction stage (such as the completion of pier construction, the pouring of several cantilever segments, before closure, and after closure) is completed. The tests use environmental or artificial excitation methods to induce vibrations in the bridge structure, and the structural acceleration response time history is collected at the locations of acceleration sensors deployed in the previous construction stage.

[0117] Specifically, after a certain construction phase k is completed:

[0118] The data acquisition system is activated to synchronously sample each measuring point channel, obtaining several sets of measured acceleration response data. The measured data undergoes denoising, filtering, and truncation. Random Subspace Identification (SSI) or Frequency Domain Decomposition (FDD) methods are used to perform modal identification on the processed response data, obtaining the target modes of a predetermined order: natural frequencies; damping ratios; and mode shape components at each measured measuring point. These natural frequencies, damping ratios, and mode shape components constitute the measured target modal parameters from the previous construction stage, providing input for subsequent analysis model updates and monitoring performance evaluation.

[0119] III. Update of the analysis model based on QR decomposition;

[0120] This illustration shows the process of establishing and correcting the digital model in this embodiment. To ensure that the analysis model reflects the actual dynamic characteristics of the bridge during the current construction phase, this embodiment employs an iterative least squares model update method based on QR decomposition to correct the analysis model.

[0121] The specific steps are as follows:

[0122] From the modal identification results of the previous construction stage, the natural frequencies and mode shape components of several target modes are selected to form a target parameter vector. The target modes include the main span vertical bending mode, the side span bending mode, and some torsional modes to cover the main working modes.

[0123] Modal eigenvalue analysis is performed on the unupdated analysis model in the current construction phase to obtain the calculated natural frequencies and modal components of the corresponding modes, which constitute the target parameter vector for calculation.

[0124] The objective function is updated by constructing a model based on the difference between the target parameters and the calculated target parameters. The objective function adopts the form of weighted squared error to measure the degree of deviation between the model and the measured dynamic characteristics.

[0125] Several model parameters to be corrected are selected in the risk model, including the equivalent stiffness of the key section, the support stiffness, and the connection stiffness. The sensitivity matrix of the target parameter to each model parameter to be corrected is calculated using modal sensitivity analysis theory.

[0126] In each iteration step, a linearized least squares problem is established, with the sensitivity matrix and the current target parameter deviation as inputs. The iterative least squares solution is achieved using QR decomposition: the sensitivity matrix is ​​decomposed into an orthogonal matrix Q and an upper triangular matrix R; the increment of the model parameters to be corrected is solved in the least squares sense using the back substitution method; the parameters to be corrected in the analysis model are updated, and modal analysis is performed again to obtain new calculated target parameters and target function values.

[0127] Repeat the above steps until the objective function value is less than the preset convergence threshold to obtain the updated analysis model for the current construction stage that matches the measured dynamic characteristics.

[0128] IV. Performance evaluation of existing measurement points based on EI method and MAC index;

[0129] After obtaining the updated analysis model for the current construction phase, this embodiment evaluates the monitoring performance of the existing measuring point layout scheme from the previous construction phase to determine whether a measuring point layout optimization update process needs to be triggered. This evaluation employs a combination of the EI (Effective Independence) method and the MAC (Modal Confidence Index).

[0130] Based on the updated analysis model, the modal components of the target mode are extracted at the existing measurement points, and the target mode observation matrix is ​​constructed.

[0131] The first monitoring performance indicator – observability evaluation based on the EI method:

[0132] The EI method is used to evaluate the information content of the observation matrix. Its core idea is to construct an information matrix using the observation matrix, perform eigenvalue decomposition or singular value decomposition on the information matrix, and evaluate the independent contribution of each measuring point to the modal information. In engineering implementation, to simplify the indicators, this embodiment denotes the minimum singular value of the target modal observation matrix as the first monitoring performance indicator. The larger the minimum singular value, the better the observation matrix conditions and the higher the overall observability of the target mode.

[0133] The second monitoring performance indicator – Modal correlation evaluation based on MAC:

[0134] At the existing measurement points, the mode shape vectors of different target modes are calculated using the updated analysis model. The mode correlation matrix is ​​constructed by defining the MAC mode confidence level, and its elements are the normalized inner products between different target mode shapes.

[0135] In this embodiment, the sum of squares of the off-diagonal elements of the modal correlation matrix is ​​used as the second monitoring performance index to measure the degree of coupling between different modes. The smaller this index is, the more obvious the difference in response between different modes at the existing measurement points, and the easier it is to distinguish them in experiments.

[0136] Triggering conditions:

[0137] When the first monitoring performance index of any target mode is lower than the preset first performance threshold, or the maximum value of the second monitoring performance index is higher than the preset second performance threshold, the monitoring performance of the current existing measurement point layout scheme is considered insufficient, triggering the measurement point layout optimization and update process.

[0138] V. Inheritance and constraints of measuring points under the constraints of irreversible evolution during the construction phase;

[0139] Considering the irreversible evolution of the structural state during bridge construction according to the construction sequence, this embodiment introduces irreversible evolution constraints during the measurement point layout optimization and update process:

[0140] Before entering the current construction phase's measurement point layout optimization and update process, all measurement point locations in the final measurement point layout scheme of the previous construction phase are determined as an immovable measurement point set. In subsequent construction phases, the spatial positions of each measurement point in this immovable measurement point set remain unchanged; their positions cannot be adjusted or deleted through a complete relocation scheme. Within the immovable measurement point set, several measurement point locations that are crucial to structural safety or manually marked as key monitoring areas are pre-designated as critical measurement points. These critical measurement points remain active throughout the entire construction phase and must not be deactivated. These constraints ensure that the measurement point layout optimization evolves unidirectionally based on the existing measurement point scheme, avoiding frequent and large-scale changes to sensor positions during construction.

[0141] VI. Generation of Candidate Measurement Point Schemes Based on SM Method

[0142] Under the constraint of irreversible evolution during the construction phase, this embodiment adopts the sequential measurement point layout method (SM method) to generate candidate measurement point schemes.

[0143] Construction of the candidate measurement point location set: In the updated analysis model nodes, locations in the immovable measurement point set are removed, and the remaining discrete locations are used to form the candidate measurement point location set. Candidate locations may include nodes near the mid-span, theoretical high-strain zones, and structurally weak points.

[0144] Enable / disable the combination of generating temporary measuring point layout schemes:

[0145] Based on the existing measurement point layout scheme at the current stage, and under the premise of satisfying the irreversible evolution constraint and the requirement that key measurement points are always in use, the SM method is used to combine the candidate measurement point locations and the currently used measurement point locations: one or more measurement points are added to the candidate measurement point locations one by one to obtain a "point addition" type temporary scheme; under the premise of not violating the key measurement point constraint and the total number of immovable measurement points not being lower than the preset lower limit, some non-key measurement points are deactivated to obtain a "point reduction" type temporary scheme; for each set of temporary measurement point layout schemes generated, the first monitoring performance index and the second monitoring performance index are calculated based on the updated analysis model.

[0146] Preliminary screening based on performance gain threshold: The monitoring performance of each temporary measurement point layout scheme is compared with the performance of the existing scheme. When the improvement of the first monitoring performance index is not lower than the preset gain threshold, the second monitoring performance index is not higher than the corresponding index of the existing scheme, and the number of measurement points retained in the set of immovable measurement points is not lower than the preset lower limit, the temporary scheme is included in the candidate measurement point scheme set.

[0147] In a typical implementation process, the initial scheme is insufficient in terms of target modal observability and modal distinguishability. As the SM method iteratively generates and filters different enable / disable combinations, the monitoring performance of the measurement point layout scheme gradually improves, eventually converging to several sets of candidate measurement point schemes, providing a basis for subsequent tracking capability evaluation and comprehensive optimization.

[0148] VII. Evaluation of the ability to track the evolution of structural dynamic characteristics based on the KEM concept;

[0149] To ensure that the monitoring point layout scheme not only has good monitoring performance in the current construction phase, but also effectively reflects the evolution trend of structural dynamic characteristics in subsequent construction phases, this embodiment introduces an evaluation of structural dynamic characteristic tracking capability based on the KEM modal kinetic energy method at the candidate monitoring point scheme level. The process is as follows:

[0150] Construction of the structural dynamic characteristic prediction evolution sequence: Based on the updated analysis model and combined with the predetermined construction sequence given in the construction organization design, finite element models are constructed sequentially for the current construction stage and several predetermined subsequent construction stages. Modal analysis is performed to obtain the following for each stage: predicted natural frequencies; predicted damping ratios; modal components at each node; and modal participation coefficients and effective modal masses calculated based on the mass matrix, modal components, and reference direction vectors. These parameters are arranged according to the construction stage sequence to form the structural dynamic characteristic prediction evolution sequence.

[0151] Construction of Structural Dynamic Characteristic Parameter Variation Vector: For each candidate measurement point scheme, the modal components corresponding to the measurement point location of that scheme are extracted from the predicted evolution sequence and compared with the structural dynamic characteristics of the current construction stage to construct a structural dynamic characteristic parameter variation vector between construction stages. This variation vector includes the changes in the predicted natural frequencies, the changes in the predicted damping ratios, and the changes in the modal components.

[0152] The tracking capability index calculation introduces KEM weights: Drawing on the idea of ​​the KEM modal kinetic energy method, this embodiment uses the modal participation coefficient and effective modal quality of the corresponding mode to weight the change vector for parameter changes of different modes and different measurement point locations. Modes with larger kinetic energy contributions and higher effective modal quality have a greater weight in the impact of parameter changes on the overall tracking capability.

[0153] Formation of feasible solution set: Candidate measurement point solutions with tracking capability indicators below the preset capability threshold are eliminated, and only solutions with tracking capability indicators reaching the preset capability threshold are retained to form a feasible solution set.

[0154] 8. Comprehensive evaluation of multiple indicators and determination of the final measurement point layout plan;

[0155] After obtaining the set of feasible solutions, in order to select among multiple candidate solutions, this embodiment uses a multi-index comprehensive evaluation method to rank the solutions and determine the final measurement point layout scheme. The specific steps are as follows:

[0156] Indicator statistics and normalization;

[0157] For each feasible solution in the set of feasible solutions, the following indicators are statistically analyzed: number of sensors; first monitoring performance indicator (minimum singular value based on EI method); second monitoring performance indicator (sum of squared modal correlations based on MAC); and structural dynamic characteristic tracking capability indicator. These indicators are then normalized into dimensionless evaluation quantities according to predetermined rules, allowing for comparison on a uniform scale.

[0158] Based on the project's requirements for monitoring accuracy, modal distinguishability, construction economy, and long-term tracking capability, weight coefficients for each dimensionless evaluation quantity are pre-set, and a comprehensive evaluation function is constructed. It is stipulated that: when the number of sensors decreases, the value of the comprehensive evaluation function increases; when the second monitoring performance index decreases (modal coupling weakens), the value of the comprehensive evaluation function increases; and when the first monitoring performance index and the tracking capability index increase, the value of the comprehensive evaluation function increases.

[0159] Calculate the comprehensive evaluation function value for each candidate scheme in the feasible scheme set, and determine the candidate scheme with the largest comprehensive evaluation function value as the final measuring point layout scheme for the current construction stage.

[0160] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the layout of measuring points during bridge construction, characterized in that, include: During bridge construction, measured structural response data from the previous construction phase are collected, and structural dynamic characteristic parameters are extracted. The analysis model of the bridge in the current construction stage is updated using structural dynamic characteristic parameters as input. Based on the updated analysis model, the monitoring performance of the existing measuring point layout scheme under the current construction stage is evaluated. When the monitoring performance meets the triggering conditions, the measurement point layout optimization and update process is triggered. During the optimization and update of the measurement point layout, the following steps are performed: Immutable evolution constraints are imposed during the construction phase, treating the bridge construction phase as an irreversible structural state evolution process. Retrospective measurement point reconstruction is prohibited, ensuring that the measurement point layout optimization is only adjusted unidirectionally based on the existing measurement point layout scheme, generating candidate measurement point schemes. The irreversible evolution constraints applied during the construction phase include: before entering the measurement point layout optimization and update process of the current construction phase, determining all measurement point locations in the final measurement point layout scheme of the previous construction phase as an immovable measurement point set, and keeping the spatial location of the immovable measurement points unchanged in subsequent construction phases; when generating candidate measurement point schemes, only adding measurement point locations based on the immovable measurement point set, or, under the premise of meeting key monitoring requirements, deactivating some immovable measurement points without changing their recorded locations, wherein the key monitoring requirements are that several key measurement point locations that are indispensable to the monitoring impact or have been manually marked as important are pre-specified in the immovable measurement point set, and the key measurement point locations remain in the active state in each construction phase and shall not be deactivated; The generation of candidate measurement point schemes includes: on the updated analysis model, selecting several locations from other discrete structural locations besides the measurement point locations in the immovable measurement point set to form a set of candidate measurement point locations; under the premise of satisfying the irreversible evolution constraints of the construction stage, taking the existing measurement point layout scheme of the current stage as the benchmark, combining the candidate measurement point locations and the measurement point locations currently in the activation state to obtain several temporary measurement point layout schemes; for each temporary measurement point layout scheme, calculating its monitoring performance and comparing it with the monitoring performance of the existing measurement point layout scheme; when the comparison result meets the preset gain threshold and the number of measurement points retained in the immovable measurement point set is not less than the preset lower limit, the temporary measurement point layout scheme is included in the candidate measurement point scheme set; For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes; When the set of feasible solutions is not empty, the final layout of measuring points for the current construction stage is determined from the set of feasible solutions based on the preset optimization criteria.

2. The method for optimizing the layout of measuring points during bridge construction according to claim 1, characterized in that, The structural dynamic characteristic parameters include: the natural frequencies, damping ratios, and modal components corresponding to predetermined orders of modes obtained by modal identification of measured structural response data from the previous construction stage; and the modal participation coefficients and effective modal masses calculated based on the mass matrix of the updated analysis model combined with the modal components and the reference direction vector. The natural frequencies are the characteristic frequencies of the structure in the corresponding modes; the damping ratios are the equivalent damping parameters of the corresponding modes; the modal components are the modal response values ​​at each measuring point in the corresponding modes; the modal participation coefficients are scalar coefficients characterizing the degree of participation of the corresponding modes in the reference direction; and the effective modal mass is the equivalent mass parameter corresponding to the modal participation coefficients.

3. The method for optimizing the layout of measuring points during bridge construction according to claim 2, characterized in that, The updating of the analysis model includes: selecting the natural frequencies and mode shape components of all orders of modes from the structural dynamic characteristic parameters as the target parameters of the analysis model in the current construction stage; performing modal eigenvalue analysis on the mass matrix and stiffness matrix of the analysis model before the update to obtain the calculated natural frequencies and calculated mode shape components corresponding to all orders of modes, which are used as the calculation target parameters; constructing the objective function for model updating based on the difference between the target parameters and the calculated target parameters; selecting the model parameters to be corrected in the analysis model, performing modal sensitivity analysis based on the target parameters and the model parameters to be corrected to obtain the sensitivity matrix of the target parameters to each model parameter to be corrected; and using the iterative least squares method to successively correct the model parameters to be corrected, updating the calculated target parameters and recalculating the objective function value in each iteration step until the objective function value is less than the preset convergence threshold, thus obtaining the updated analysis model.

4. The method for optimizing the layout of measuring points during bridge construction according to claim 2, characterized in that, The evaluation of the monitoring performance includes: based on the updated analysis model, extracting the modal components of the target modes at the existing measurement point locations, constructing a target mode observation matrix corresponding to the existing measurement point layout scheme, and calculating the minimum singular value of the target mode observation matrix, using the minimum singular value as the first monitoring performance index; calculating the modal correlation matrix between the target modes at the existing measurement point locations, wherein the elements of the modal correlation matrix are the normalized inner products between different target modal components, and using the sum of squares of the off-diagonal elements of the modal correlation matrix as the second monitoring performance index.

5. The method for optimizing the layout of measuring points during bridge construction according to claim 4, characterized in that, The triggering condition is: the first monitoring performance index of any target mode is less than the preset first performance threshold, or the maximum value of the second monitoring performance index of each target mode is greater than the preset second performance threshold.

6. The method for optimizing the layout of measuring points during bridge construction according to claim 4, characterized in that, The evaluation of the tracking capability includes: based on the updated analysis model and combined with the predetermined construction sequence, performing modal analysis on the bridge structure in the current construction stage and the predetermined subsequent construction stages, solving for the natural frequency, damping ratio, modal component, modal participation coefficient, and effective modal mass of each construction stage, which are used as the predicted values ​​of the structural dynamic characteristics of that construction stage, and arranging them according to the construction sequence to form a predicted evolution sequence of structural dynamic characteristics; under each candidate measurement point scheme, based on the modal component of the target mode at the candidate measurement point location, extracting the predicted components of structural dynamic characteristics related to the candidate measurement point location from the predicted evolution sequence of structural dynamic characteristics, constructing a change vector of structural dynamic characteristic parameters between the current construction stage and each predetermined subsequent construction stage, the change vector of structural dynamic characteristic parameters including the change in the predicted value of the natural frequency, the change in the predicted value of the damping ratio, and the change in the modal component, and using the modal participation coefficient and effective modal mass of the corresponding mode to weight the change vector of structural dynamic characteristic parameters to obtain the tracking capability index of the candidate measurement point scheme.

7. The method for optimizing the layout of measuring points during bridge construction according to claim 6, characterized in that, The preset optimization criteria include: in the feasible scheme set, for each candidate measuring point scheme, the corresponding number of sensors, first monitoring performance index, second monitoring performance index, and tracking capability index are statistically analyzed; the number of sensors, first monitoring performance index, second monitoring performance index, and tracking capability index are converted into dimensionless evaluation quantities according to a preset normalization method; a comprehensive evaluation function is constructed based on each dimensionless evaluation quantity and a preset weight coefficient; the comprehensive evaluation function value increases when the number of sensors and second monitoring performance index decreases and the first monitoring performance index and tracking capability index increase, as a constraint relationship; the comprehensive evaluation function value is calculated for each candidate measuring point scheme in the feasible scheme set; and the candidate measuring point scheme with the optimal comprehensive evaluation function value is determined as the final measuring point layout scheme for the current construction stage.

8. A system for optimizing the layout of measuring points during bridge construction, characterized in that, The system employs a bridge construction period measurement point layout optimization method as described in any one of claims 1 to 7, including: Feature parameter module: During bridge construction, the measured structural response data from the previous construction stage are collected, and the structural dynamic characteristic parameters are extracted; Model update module: Uses structural dynamic characteristic parameters as input to update the analysis model of the bridge in the current construction stage; Performance evaluation module: Based on the updated analysis model, evaluate the monitoring performance of the existing measuring point layout scheme under the current construction stage; Optimize trigger module: When the monitoring performance meets the triggering conditions, trigger the measurement point layout optimization and update process; Candidate measuring point module: Apply irreversible evolution constraints during the construction phase to generate candidate measuring point schemes; Tracking and screening module: For each candidate measurement point scheme, evaluate its ability to track the predicted evolution path of the structural dynamic characteristics of the bridge from the current stage to the predetermined subsequent construction stage; retain candidate schemes whose tracking ability reaches the preset capability threshold to form a set of feasible schemes; Solution determination module: When the set of feasible solutions is not empty, the final layout of measuring points for the current construction stage is determined from the set of feasible solutions based on preset optimization criteria.

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