Acceleration acquisition point number optimization method and system for box beam vibration damage detection

Abstract

The invention provides an acceleration acquisition point quantity optimization method and system for vibration damage detection of a box beam, a dual optimization strategy of a damage physical mechanism and modal information entropy is fused, the sensitivity of the damage to modal parameters is quantified, a key area (accounting for 15-20% of the surface area) sensitive to the damage on the surface of the box beam is accurately identified, and the accuracy of the vibration damage detection of the box beam is improved. Acceleration sensors are configured in a key area according to an information amount optimization criterion, so that the use amount of the sensors is remarkably reduced, the micro-damage detection rate is increased to 95% or above, and the positioning error is reduced to be within 0.3 m. According to the method, sensitivity-based damage detection of the box beam can be achieved, the high-precision flaw detection requirement is met, and the method is suitable for large-scale popularization and application. And the number of measuring points and the operation and maintenance burden are obviously reduced.

Description

Technical Field

[0001] This invention relates to the technical field of bridge damage identification, specifically to a method and system for optimizing the number of acceleration acquisition points for vibration damage detection of box girders. Background Technology

[0002] Box girders, as core load-bearing components in bridges, are widely used due to their high torsional stiffness and large load-bearing capacity. However, their closed-section characteristics make internal damage such as cracks in diaphragms and U-ribs, and weld cracks difficult to detect visually. Vibration response-based structural health monitoring technology, which identifies damage by analyzing changes in dynamic characteristics (such as frequency, mode shape, and curvature), has become an effective solution in the engineering field. Among these technologies, accelerometers have become the mainstream data acquisition tool due to their wide frequency response range and convenient installation. In current engineering practice, sensor deployment mainly relies on the engineer's personal experience or a simple principle of uniform distribution, such as deploying acquisition points at equal intervals on the beam surface. This approach results in significant redundancy of measurement points in low-sensitivity areas (such as the middle of the flange) (accounting for over 30%), while high-risk areas such as the web and the ends of stiffening ribs are under-covered. Studies have shown that this type of placement method has a detection rate of less than 40% for minor damage with stiffness loss of less than 5%, and the positioning error exceeds 1.2 meters, making it difficult to meet the requirements of high-precision flaw detection.

[0003] In the field of vibration testing of box girders, existing methods for optimizing the number of sampling points mainly rely on structural dynamics principles to construct mathematical models. The Effective Independence (EFI) method optimizes modal identifiability by maximizing the determinant of the Fisher information matrix: its core is to construct a modal matrix containing the target modal vectors, calculate the effective independence index for each measuring point (this index quantifies the contribution of the measuring point to the linear independence of the modal vectors), and iteratively delete the measuring points with the lowest index values. The remaining set of measuring points ensures that the modal matrix remains in full rank, thereby guaranteeing the accuracy of modal parameter identification. In the field of box girder inspection, this method first identifies key areas through physical sensitivity, and then maximizes the determinant within these areas using EFI, significantly reducing the required number of sensors. Genetic Algorithm (GA) simulates biological evolution to perform a global search: it encodes the measuring point layout scheme as binary chromosomes, uses minimizing the off-diagonal elements of the modal confidence criterion as the fitness objective, and optimizes the population generation by generation through selection, crossover, and mutation operations, ultimately converging to a Pareto optimal solution that satisfies engineering constraints. Audio analysis is based on the physical principle of stress wave propagation: the 20kHz-1MHz high-frequency stress wave released by crack propagation is captured by a sensor array, and the damage location coordinates are calculated using a time-difference positioning equation. Machine learning technology adopts a data-driven strategy: the acceleration time history signal is input into a convolutional neural network, and end-to-end damage identification is achieved through automatic feature extraction and classifier decision-making. Currently, sensor costs account for over 50% of the total investment in large box girder structure monitoring systems. The industry urgently needs an optimization method based on damage mechanisms that can significantly reduce the number of measuring points and maintenance burden while ensuring a micro-damage (≥4% stiffness loss) detection rate of >95%. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method and system for optimizing the number of acceleration acquisition points for vibration damage detection of box beams, which significantly reduces the number of measurement points and maintenance burden while ensuring a micro-damage (≥4% stiffness loss) detection rate of >95%.

[0005] The embodiments of this application are implemented as follows: This application provides a method for optimizing the number of acceleration acquisition points in vibration damage detection of box girders, characterized by the following steps: Step S1: Select appropriate test points on the box girder, determine the test parameters required for the experiment, and establish a test model; Step S2: Set circular or rectangular damage elements in the vulnerable areas of the middle of the web, the flange weld and the end of the stiffening rib, and simulate the degree of damage by stiffness reduction. Step S3: Use the algorithm to traverse m damage conditions, perform damage condition modal analysis, synthesize the node comprehensive sensitivity, and drive the identification of key areas. Step S4, calculate the node comprehensive sensitivity S obtained in the previous steps. j Sensitivity cloud maps are generated by mapping onto the surface of the box girder, thereby filtering out the dataset of highly sensitive nodes; Step S5: Perform spatial clustering on the dataset to obtain k key sensitive regions. Construct a candidate measurement point set within the sensitive regions and iteratively optimize the measurement points to output the final measurement point coordinate set.

[0006] In some optional implementations, the suitable test points mentioned in step S1 include a pre-set rectangular damage area in the middle of the plate and a wake-up damage area set at the flange weld. The test points meet the requirements of an equidistant network to ensure the accuracy of displacement calculation.

[0007] In some optional implementations, the test parameters in step S1 include the box girder's geometry, material properties, and boundary conditions. The geometry is the cross-sectional width B, height H, and plate thickness t, and the material properties are the elastic modulus E and density ρ.

[0008] In some optional implementations, the expression for the damage stiffness in step S2 is:

[0009] In the formula: α is the original stiffness of the element; α is the stiffness reduction factor. Calculate the first N modal parameters under both the undamaged and damaged states, where N ≥ 10, including natural frequencies. fi 0, mode vector Φ i ,0 and modal curvature κi ,0;; The expression for modal curvature is:

[0010] In the formula: ▽ is the operator.

[0011] In some optional implementations, the damage condition modal analysis described in step S3 includes the following steps: Step S 31 Frequency sensitivity:

[0012] In the formula: f i,0 f represents the i-th natural frequency in the lossless state. i,j Represents the i-th natural frequency under the j-th damage condition; Step S 32 Mode shape sensitivity:

[0013] Where: Φ i,0Φ represents the i-th order mode shape vector in the lossless state. i,j This represents the mode shape vector corresponding to the damage. MAC is a modal confidence criterion, and its calculation formula is as follows:

[0014] MAC characterizes the correlation between two mode vectors. The closer the MAC value is to 1, the higher the mode consistency. Step S 33 Curvature sensitivity:

[0015] In the formula: κ i,0 κ represents the lossless modal curvature. i,j Represents the modal curvature after damage, where |·| is the Euclidean norm, used to measure the magnitude of the difference in curvature vectors.

[0016] In some optional implementations, the node comprehensive sensitivity described in step S3 is driven by a weighted synthesis of the three formulas from the preceding steps to identify key regions, as follows:

[0017] In the formula: w i Let be the proportion of the mass participation rate of the i-th modal, satisfying ∑ wi =1; β1, β2, β3 are weighting coefficients.

[0018] In some optional implementations, the screening criteria for highly sensitive nodes in step S4 are as follows:

[0019] In the formula: S th μ is the sensitivity threshold. S σ is the mean of sensitivity. S Standard deviation; The critical area proportion is controlled at 15%~20% of the box girder surface area, thereby selecting the highly sensitive node dataset Ω. high ={j | S j >S th}

[0020] In some optional implementations, the measurement point optimization in step S5 includes the following steps: p candidate points are randomly generated on the surface of the key sensitive area according to the principle of uniform distribution. The measurement points are then simplified using the effective independence method to construct the target mode matrix:

[0021] In the formula, M≤N represents the order of the sensitive mode; The effective independent index of measuring point q is calculated using the following formula:

[0022] In the formula: Ψ q To remove the mode matrix after point q; Repeatedly iterate and delete EFI q The minimum value corresponds to the measurement point, until the number of remaining measurement points equals the preset target value K. target ; Output the final set of coordinates of the measured points based on the calculated measured point values: S opt ={coordinate1, …, coordinates} Ktarget}

[0023] In some optional implementations, the geometric dimensions of the refined finite element model of the test model box girder satisfy the following formula:

[0024] In the formula: L is the span of the box girder, in meters.

[0025] A system for optimizing the number of acceleration acquisition points in vibration damage detection of box girders, characterized in that it includes: The modeling module selects appropriate test points on the box girder, determines the test parameters required for the experiment, and establishes the test model. The damage simulation module sets circular or rectangular damage elements in vulnerable areas and simulates the degree of damage by reducing stiffness. The data filtering module performs damage condition modal analysis, synthesizes the comprehensive sensitivity of nodes, and generates a sensitivity cloud map to filter out high-sensitivity node datasets. The data optimization module performs spatial clustering on the dataset to obtain k key sensitive regions, constructs a candidate measurement point set, iterates repeatedly to optimize the measurement points, and outputs the final measurement point coordinate set.

[0026] The beneficial effects of this application are as follows: This application provides a method and system for optimizing the number of acceleration acquisition points for vibration damage detection of box girders. It integrates a dual optimization strategy of damage physics mechanism and modal information entropy. By quantifying the sensitivity of damage to modal parameters, it achieves precise control of acquisition points in key areas such as diaphragm cracks. It only requires 40% of the number of sensors of traditional methods to increase the micro-damage detection rate to over 95%. While improving the accuracy of micro-damage identification, it can also significantly reduce the detection cost. The sensitivity-based candidate region screening mechanism effectively enhances the anti-interference ability and meets the application needs of complex environments in engineering sites. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating the optimization process for the number of acceleration sampling points in an embodiment of this application. Figure 2 This is a simplified model diagram of a box girder according to an embodiment of this application; Figure 3 This is a comprehensive sensitivity cloud diagram of the box girder nodes in an embodiment of this application; Figure 4 This is a diagram showing the effective independent method EFI iterative optimization results of this application embodiment; Figure 5 This is a comparative analysis chart of operation and maintenance costs for embodiments of this application; Figure 6 This is a laboratory testing diagram from an embodiment of this application. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0030] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0031] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0032] The features and performance of this application will be further described in detail below with reference to the embodiments.

[0033] This invention provides a method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders. This method quantifies the sensitivity of damage to modal parameters, accurately identifies key areas (accounting for 15% to 20% of the surface area) on the box girder surface that are sensitive to damage, and applies information optimization criteria to configure acceleration sensors in key areas. This significantly reduces the number of sensors used while increasing the micro-damage detection rate to over 95% and reducing the positioning error to within 0.3 meters.

[0034] This method is implemented through the following technical solution: 1. Scope and target audience of this method: Vulnerable areas of box girder structures include the middle of the web, flange welds, and ends of stiffening ribs. For micro-damage detection with stiffness loss greater than 4%, such as web cracks and weld failures; For monitoring large structures such as bridges, it can be adapted to box girders of different sizes.

[0035] 2. The implementation process of the method is as follows (see Figure 1 ): 1. Arrangement of test points and selection of test parameters 1.1 Select appropriate test points on the box girder. A rectangular damage zone is pre-defined in the center of the plate, and a warning damage zone is established at the flange welds. Adhere to the requirements of the equidistant network to ensure the accuracy of displacement calculations.

[0036] 1.2 Determine the test parameters required for the experiment and establish the test model. This includes the geometric dimensions of the box girder (section width B, height H, plate thickness t), material properties (elastic modulus E, density ρ), and boundary conditions. Use engineering software (such as Abaqus and Ansys) to establish a refined finite element model.

[0037] 2. Damage simulation and modal function extraction 2.1 Establish a refined finite element model of the box girder, whose geometric dimensions satisfy the following formula:

[0038] In the formula: L is the span of the box girder (unit: m).

[0039] 2.2 Define the damage library. Circular / rectangular damage elements are set in vulnerable areas (mid-web, flange welds, and stiffener ends), and the degree of damage is simulated by stiffness reduction. Damage elements are set in the mid-web, flange welds, and stiffener ends. The damage stiffness expression is:

[0040] In the formula: α represents the original stiffness of the element; α is the stiffness reduction factor.

[0041] Calculate the first N modal parameters under both the undamaged and damaged states, where N ≥ 10, including natural frequencies. fi 0, mode vector Φ i ,0 and modal curvature κi ,0;; The expression for modal curvature is:

[0042] In the formula: ▽ is the operator.

[0043] 3. Modal Sensitive Quantization 3.1 Damage Condition Modal Analysis. An algorithm is used to traverse m damage conditions (different positions j, different α) in the damage database.

[0044] The node sensitivity metrics are defined as follows: (1) Frequency sensitivity:

[0045] In the formula: f i,0 f represents the i-th natural frequency (reference value) in the lossless state. i,j This represents the i-th natural frequency under the j-th damage condition; this formula quantifies the degree of natural frequency shift caused by damage, reflecting the overall stiffness change of the structure.

[0046] (2) Mode sensitivity:

[0047] Where: Φ i,0 Φ represents the i-th order mode shape vector in the lossless state. i,j This represents the mode shape vector (displacement distribution) corresponding to the damage; this formula characterizes the degree of variation in mode shape caused by damage and is sensitive to local defects (such as weld cracks).

[0048] MAC is a modal confidence criterion, and its calculation formula is as follows:

[0049] MAC characterizes the correlation between two mode vectors. The closer the MAC value is to 1, the higher the mode consistency.

[0050] (3) Curvature sensitivity:

[0051] In the formula: κ i,0 κ represents the lossless modal curvature. i,jThe modal curvature after damage is represented by |·|, which is the Euclidean norm used to measure the magnitude of the difference in curvature vectors. This formula represents the curvature abrupt change caused by capturing local damage (such as web cracks), since curvature is directly related to bending moment.

[0052] 3.2 The overall sensitivity of the synthesized nodes is driven by a weighted synthesis of the three formulas from the previous steps, which in turn drives the identification of key regions. The formulas are as follows:

[0053] In the formula: wi is the proportion of the mass participation rate of the i-th mode, which satisfies ∑wi=1; β1, β2, β3 are weighting coefficients (default β1=0.3, β2=0.4, β3=0.3, and can be calibrated through subsequent experiments).

[0054] 4. Identification of key sensitive areas 4.1 Generate a sensitivity cloud map. Map the nodal sensitivity Sj obtained in the previous steps onto the surface of the box girder to generate a sensitivity cloud map.

[0055] The criteria for selecting key sensitive nodes are:

[0056] In the formula: S th μ is the sensitivity threshold. S σ is the mean of sensitivity. S The standard deviation is denoted as .

[0057] The critical area proportion is controlled at 15%~20% of the box girder surface area, thereby selecting the highly sensitive node dataset Ω. high ={j | S j >S th Spatial clustering of the dataset yields k key sensitive regions, and measurement point optimization is performed within these key regions.

[0058] 5. Optimization of measuring points in sensitive areas 5.1 Construct a candidate measurement point set within the sensitive area and iterate repeatedly. Randomly generate p candidate points on the surface of the key sensitive area according to the principle of uniform distribution. Refine the measurement points using the effective independence method and construct the target mode matrix:

[0059] In the formula, M≤N represents the order of the sensitive mode.

[0060] The effective independent index of measuring point q is calculated using the following formula:

[0061] In the formula: Ψ q This is the modality matrix after removing point q.

[0062] Repeatedly iterate and delete EFI q The minimum value corresponds to the measurement point, until the number of remaining measurement points equals the preset target value K. target .

[0063] 5.2 Output the final coordinate set of the measured points based on the calculated measured point values: S opt ={coordinate1, …, coordinates} Ktarget}

[0064] Example 1 The proposed method for optimizing acceleration acquisition points in box girder vibration damage detection, through a dual optimization strategy integrating damage physics mechanisms and modal entropy information, improves the accuracy of micro-damage identification while significantly reducing detection costs. (See attached diagram) Figure 2 To illustrate the finite element model and candidate region distribution of the box girder (web crack case), the model dimensions are 12m long * 2.5m wide, with a plate thickness of 14mm. A rectangular damage zone (0.4m × 0.8m, stiffness reduction factor α = 0.85) is established, and a reactivation damage zone (inner diameter 8mm, outer diameter 40mm, α = 0.75) is established at the flange weld. Referring to modal analysis theory, the comprehensive sensitivity index is calculated using the following formula:

[0065] In the formula: Δf / f is the relative rate of change of frequency; MAC is the modal confidence criterion; Let be the Euclidean norm of the modal curvature variation.

[0066] Damage sensitivity analysis yielded a comprehensive sensitivity threshold δ1 = 0.18 and a strain energy density threshold δ2 = 35 kJ / m³. The red area in the figure represents the candidate region Ω that satisfies the dual threshold conditions. candidate Its area accounts for only 28.7% of the structure's surface area.

[0067] The sensitivity quantification formula of this invention is as follows:

[0068] The node sensitivity distribution calculated using the above formula (see...) Figure 3 The middle part of the web exhibits a highly sensitive area (S). j With a focal length >0.75, the area accounts for 18.3%, and compared with the traditional uniform point distribution, the focusing intensity of the sensitive area is improved by 3.2 times. This method reduces the total number of sensors by 40.6% by combining the improved Effective Independent Point (EFI) method to screen measurement points.

[0069] like Figure 4As shown, according to the acceleration acquisition point number optimization method provided by the present invention, the measurement points in the key sensitive area are iteratively optimized by the improved Effective Independence Method (EFI). Only 14 sensors are needed to achieve a modal information retention rate of up to 92.7%, which exceeds the engineering benchmark requirement of 90%, and achieves the optimal balance between engineering accuracy and hardware cost.

[0070] like Figure 5 As shown, compared with the traditional uniform distribution scheme, the embodiment provided by the present invention achieves a 60% reduction in hardware procurement costs through a high-sensitivity area focusing distribution strategy, from RMB 36,000 to RMB 14,000; a sharp reduction in data processing energy consumption of 44%, from 28W to 15.7W; and a 62% reduction in annual maintenance costs, from RMB 11,200 to RMB 4,300.

[0071] The sensitivity-based candidate region screening mechanism provided by this invention effectively enhances anti-interference capabilities and meets the application requirements of complex engineering environments. The optimized sensor placement scheme provided by this method yields damage detection results that highly match real-world laboratory experiments (see...). Figure 6 The method's engineering reliability was verified, and at the same time, the scheme significantly reduced the cost of the detection system (hardware cost was reduced by 37.5%). Thus, this method, which balances performance and economic benefits, has important application value for large-scale structural health monitoring projects.

Claims

1. A method for optimizing the number of acceleration acquisition points in vibration damage detection of box girders, characterized in that, Includes the following steps: Step S1: Select appropriate test points on the box girder, determine the test parameters required for the experiment, and establish a test model; Step S2: Set circular or rectangular damage elements in the vulnerable areas of the middle of the web, the flange weld and the end of the stiffening rib, and simulate the degree of damage by stiffness reduction. Step S3: Use the algorithm to traverse m damage conditions, perform damage condition modal analysis, synthesize the node comprehensive sensitivity, and drive the identification of key areas. Step S4, calculate the node comprehensive sensitivity S obtained in the previous steps. j Sensitivity cloud maps are generated by mapping onto the surface of the box girder, thereby filtering out the dataset of highly sensitive nodes; Step S5: Perform spatial clustering on the dataset to obtain k key sensitive regions. Construct a candidate measurement point set within the sensitive regions and iteratively optimize the measurement points to output the final measurement point coordinate set.

2. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 1, characterized in that, The appropriate test points mentioned in step S1 include a pre-set rectangular damage area in the middle of the plate and a wake-up damage area set at the flange weld. The test points meet the requirements of an equidistant network to ensure the accuracy of displacement calculation.

3. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 2, characterized in that, The test parameters mentioned in step S1 include the geometric dimensions, material properties, and boundary conditions of the box girder. The geometric dimensions are the cross-sectional width B, height H, and plate thickness t. The material properties are the elastic modulus E and density ρ.

4. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 3, characterized in that, The expression for damage stiffness mentioned in step S2 is: In the formula: α is the original stiffness of the element; α is the stiffness reduction factor. Calculate the first N modal parameters under both the undamaged and damaged states, where N ≥ 10, including natural frequencies. fi 0, mode vector Φ i ,0 and modal curvature κi ,0;; The expression for modal curvature is: In the formula: ▽ is the operator.

5. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 4, characterized in that, The damage condition modal analysis described in step S3 includes the following steps: Step S 31 Frequency sensitivity: In the formula: f i,0 f represents the i-th natural frequency in the lossless state. i,j Represents the i-th natural frequency under the j-th damage condition; Step S 32 Mode shape sensitivity: Where: Φ i,0 Φ represents the i-th order mode shape vector in the lossless state. i,j This represents the mode shape vector corresponding to the damage. MAC is a modal confidence criterion, and its calculation formula is as follows: MAC characterizes the correlation between two mode vectors. The closer the MAC value is to 1, the higher the mode consistency. Step S 33 Curvature sensitivity: In the formula: κ i,0 κ represents the lossless modal curvature. i,j Represents the modal curvature after damage, where |·| is the Euclidean norm, used to measure the magnitude of the difference in curvature vectors.

6. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 5, characterized in that, The node comprehensive sensitivity mentioned in step S3 is driven by the weighted synthesis of the three formulas from the previous steps to identify key regions. The formulas are as follows: In the formula: w i Let be the proportion of the mass participation rate of the i-th modal, satisfying ∑ wi =1; β1, β2, β3 are weighting coefficients.

7. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 6, characterized in that, The screening criteria for highly sensitive nodes mentioned in step S4 are as follows: In the formula: S th μ is the sensitivity threshold. S σ is the mean of sensitivity. S Standard deviation; The critical area proportion is controlled at 15%~20% of the box girder surface area, thereby selecting the highly sensitive node dataset Ω. high ={j | S j >S th } 8. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 7, characterized in that, Step S5, the measurement point optimization, includes the following steps: p candidate points are randomly generated on the surface of the key sensitive area according to the principle of uniform distribution. The measurement points are then simplified using the effective independence method to construct the target mode matrix: In the formula, M≤N represents the order of the sensitive mode; The effective independent index of measuring point q is calculated using the following formula: In the formula: Ψ q To remove the mode matrix after point q; Repeatedly iterate and delete EFI q The minimum value corresponds to the measurement point, until the number of remaining measurement points equals the preset target value K. target ; Output the final set of coordinates of the measured points based on the calculated measured point values: S opt ={coordinate1, …, coordinates} Ktarget } 9. The method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders according to claim 2 or 8, characterized in that, The refined finite element model of the test model box girder has geometric dimensions that satisfy the following formula: In the formula: L is the span of the box girder, in meters.

10. A system employing the method for optimizing the number of acceleration acquisition points for vibration damage detection of box girders as described in claim 2 or 8, characterized in that, include: The modeling module selects appropriate test points on the box girder, determines the test parameters required for the experiment, and establishes the test model. The damage simulation module sets circular or rectangular damage elements in vulnerable areas and simulates the degree of damage by reducing stiffness. The data filtering module performs damage condition modal analysis, synthesizes the comprehensive sensitivity of nodes, and generates a sensitivity cloud map to filter out high-sensitivity node datasets. The data optimization module performs spatial clustering on the dataset to obtain k key sensitive regions, constructs a candidate measurement point set, iterates repeatedly to optimize the measurement points, and outputs the final measurement point coordinate set.

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