A bridge cluster maintenance decision-making method, system and medium based on a deterioration curve

Abstract

The present disclosure relates to the field of bridge maintenance, and particularly relates to a bridge cluster maintenance decision-making method and system based on degradation curves and a medium. The method comprises: dividing bridge cluster clusters according to bridge inherent attribute data; fitting a reference degradation curve of each type of bridge by using an improved RANSAC algorithm; calculating a current offset of a current technical condition score of a bridge relative to the corresponding curve to obtain a current offset; training a model with the bridge inherent attribute data and the current offset, predicting a future offset of the bridge for the maintenance bridge cluster by using the model, and calculating an offset change; constructing a double-objective function and solving to obtain a plurality of maintenance schemes, screening an optimal maintenance scheme, target 1 being to minimize the weighted current health degree sum of the maintenance bridge cluster under the constraint of the technical condition level priority, and target 2 being to minimize the weighted degradation resistance index sum of the maintenance bridge cluster. The present disclosure improves the refinement degree of the decision-making and is more forward-looking.

Description

Technical Field

[0001] This disclosure relates to the field of bridge maintenance technology, and in particular to a bridge cluster maintenance decision-making method, system, and medium based on degradation curves. Background Technology

[0002] With the large-scale construction and long-term service of transportation infrastructure, the aging process and performance degradation of in-service bridges are becoming increasingly prominent. To ensure the safe operation and service level of the road network, it is necessary to conduct scientific and detailed technical condition assessments of bridge clusters and make maintenance decisions based on these assessments. This will achieve technical effects such as delaying the degradation of bridge structural performance, extending the service life of bridges, and reducing the risk of sudden structural failures.

[0003] Currently, bridge cluster maintenance decision-making systems primarily rely on bridge technical condition assessments for planning. These systems typically generate maintenance decision schemes based on the bridge's current technical condition score or predicted future evolution trends, under given financial constraints, through expert experience-based weighted ranking or multi-objective optimization algorithms.

[0004] For example, the paper "Research and Application of Bridge Degradation Model and Maintenance Decision" published in the journal Highway ([Bu Dejiang, Hu Yerong, Zheng Chen, et al. Research and Application of Bridge Degradation Model and Maintenance Decision[J]. Highway, 2024, 69(1):364-373.]) introduces a network-level highway bridge maintenance management system. The system takes bridge maintenance costs as the core ranking criterion, comprehensively uses the Analytic Hierarchy Process (AHP) and fuzzy evaluation method to evaluate the technical condition of bridges, and on this basis, assists in generating maintenance decisions.

[0005] For example, the paper "Overall Design of Guangzhou Urban Bridge Management Information System" published in the Journal of South China University of Technology (Natural Science Edition) ([Fu Zisha, Li Xinping, Jia Deliang. Overall Design of Guangzhou Urban Bridge Management Information System[J]. Journal of South China University of Technology: Natural Science Edition, 2003, 31(11): 57-60.]) adopts the hierarchical analysis evaluation system, divides the technical status of bridges into five evaluation levels and prioritizes them, and then forms maintenance decisions based on cost constraints.

[0006] For example, in the Chinese patent with publication number CN118710258A entitled "Method, System and Storage Medium for Formulating Long-Term Maintenance Decisions for Bridge Groups", the dual constraints are the lowest total maintenance expenditure cost and the highest total technical condition score of the bridge group, and the overall constraint is that the annual technical condition score of the bridge is not lower than a preset lower limit, and a long-term maintenance plan is output.

[0007] However, the aforementioned decision-making techniques face a series of challenges: First, decision-making methods based on absolute bridge technical condition scores are too coarse-grained and fail to accurately reflect the relative degradation level of a bridge within its class of structures. Specifically, due to inherent differences in design standards, material properties, structural form, and service environment, the degradation patterns of different bridges vary. Judging solely by absolute scores cannot effectively distinguish the degree of deviation of an individual bridge from the "normal degradation trajectory" of its peer group. For example, two bridges with the same score, one with a higher score than other bridges of the same age, indicates that its actual technical condition is better than expected. In this case, relying solely on absolute scores makes it difficult to identify such differences, leading to inaccurate maintenance priority assessments.

[0008] Secondly, existing decision-making methods exhibit significant lag in condition assessment and lack the ability to accurately predict the timing of maintenance. Current decision-making mechanisms are mostly reactive, typically triggering maintenance actions only after bridge defects have become fully apparent or the technical condition score has fallen to a certain preset threshold. This "remedial" decision-making logic fails to effectively combine the bridge's own physical characteristics, service environment, and degradation trajectory to proactively predict its future performance degradation rate, resulting in missed optimal intervention periods for preventative maintenance.

[0009] In summary, existing bridge cluster maintenance decision-making technologies have significant shortcomings in terms of the precision of assessment and the foresight of decision-making. Therefore, there is an urgent need for a bridge cluster maintenance decision-making method and system that combines more precise current status assessment with forward-looking trend prediction. Summary of the Invention

[0010] Therefore, it is necessary to provide a bridge cluster maintenance decision-making method, system, and medium based on degradation curves to address the above problems.

[0011] To solve the above problems, the present disclosure adopts the following technical solution: In a first aspect, this disclosure provides a bridge cluster maintenance decision-making method based on degradation curves, including: Acquire periodic inspection data from multiple bridge clusters, the periodic inspection data including technical condition information; Based on the inherent attribute data of the bridges, the K-means clustering algorithm was used to divide the bridge cluster into multiple categories; For each category, an improved RANSAC algorithm is used to fit the degradation trend curve between bridge age and technical condition score as the benchmark degradation curve for that category of bridges; the sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The current offset of the bridge is obtained by calculating the offset of the bridge's current technical condition score relative to the baseline degradation curve; Using the inherent attribute data of the bridge and the current offset of the bridge as input features, a random forest regression model is trained to predict the future offset of the bridge. The trained random forest regression model is used to predict the future offset of the bridges in the maintenance bridge cluster. The difference between the future offset and the current offset of the bridge cluster under maintenance is used as the change in bridge offset. For the maintenance of bridge clusters, the current health of the bridge is obtained by linear translation of the current offset of the bridge, and the difference between the change in the bridge's offset and the first minimum value of the bridge is calculated as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in offset of all bridges in the bridge's category. A dual objective function is constructed, and multiple maintenance schemes are obtained by solving the dual objective function. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the constraint of technical condition level priority. Objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. Select the optimal maintenance plan.

[0012] In a preferred embodiment, the expression for the baseline degradation curve is: in, Indicate category The bridge in the year Technical condition rating at the time; Indicate category In the year The age of the bridge at that time This indicates the degree to which bridge age has a linear impact on the technical condition of the bridge. This indicates the degree of nonlinear degradation of a bridge's technical condition due to its age.

[0013] In a preferred embodiment, the stratified sampling based on the technical condition information corresponding to the data point is performed based on the score level to which the technical condition score of the data point belongs, wherein the score level is low-level, medium-level, or high-level.

[0014] In a preferred embodiment, the stratified sampling based on the score level to which the technical condition score of the data points belongs specifically includes: For all bridge samples whose technical condition scores belong to the lower strata, data points are sampled at the first sampling rate. The technical condition score of the data points belongs to all bridge samples in the middle layer. In each iteration, a dynamic random sampling method is used to sample all samples with a random probability value in the first probability interval, where the first probability interval is less than the first sampling rate. The technical condition score of the data points belongs to all bridge samples in the high-level hierarchy. The samples are sampled according to the first value, which is equal to the preset minimum total number of samples minus the number of samples in the high-importance hierarchy and then minus the number of samples in the medium-importance hierarchy.

[0015] In a preferred embodiment, in the improved RANSAC algorithm, the interior point determination threshold satisfies: the interior point determination threshold corresponding to the lower stratum > the interior point determination threshold corresponding to the middle stratum > the interior point determination threshold corresponding to the higher stratum.

[0016] In a preferred embodiment, the formula for calculating the total score based on the hierarchical weighted scoring of the data points is as follows: in, For the overall score, Based on the score, For lower-tier reward ratings, For tiered reward scoring, For higher-level reward scores, Scoring is given for curvature bonus.

[0017] In a preferred embodiment, the process of performing a linear translation transformation on the current offset of the bridge to obtain the current health of the bridge specifically involves subtracting the minimum value of the current offset of all bridges in the same category from the current offset of the bridge, which equals the current health of the bridge. The formula for the dual objective function is: in, Represents a vector of decision variables. Indicates the bridge number that needs maintenance. Bridge Maintenance decisions, The function representing objective 1 of the NSGA-II algorithm, The function representing objective 2 of the NSGA-II algorithm. Describes the minimum value function. This indicates the total number of bridges requiring maintenance. Bridge Road network importance score, Bridge Current health status Bridge The degradation resistance index; The solution to the function is specifically based on the NSGA-II algorithm to solve the biobjective function.

[0018] In a preferred embodiment, selecting the optimal maintenance plan includes: constructing a benefit evaluation system comprising four indicators, wherein the four indicators are the sum of the current health status of the bridges in the maintenance bridge cluster. The sum of the degradation resistance indices of bridges in the maintenance of bridge clusters Maintenance intensity and the total density of maintenance funds The combined weighting method based on subjective and objective values ​​is used to calculate the combined weighting weight of each indicator. Based on the four indicators and their corresponding combined weighting weights, the benefit evaluation score of each maintenance plan is calculated. The optimal maintenance plan is determined based on the benefit evaluation score. The maintenance intensity and the total density of maintenance funds The calculation formula is: in, The total number of bridges in the bridge cluster is for maintenance. The total cost of maintaining the bridge complex, The total value of the road network importance coefficient for the maintenance of bridge clusters.

[0019] Secondly, this disclosure provides a bridge cluster maintenance decision-making method system based on degradation curves, including: The acquisition module is used to acquire periodic inspection data of multiple bridge clusters, the periodic inspection data including technical condition information; The clustering module is used to divide the bridge cluster into multiple categories based on the inherent attribute data of the bridges using the K-means clustering algorithm. The curve generation module is used to fit a degradation trend curve between bridge age and technical condition score for each category using an improved RANSAC algorithm as the benchmark degradation curve for that category of bridges. The sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The first calculation module calculates the current offset of the bridge by measuring the current technical condition score of the bridge relative to the baseline degradation curve. The training module is used to train a random forest regression model using the inherent attribute data of the bridge and the current offset of the bridge as input features. The random forest regression model is used to predict the future offset of the bridge. The prediction module is used to predict the future offset of the bridges in the maintenance bridge cluster using the trained random forest regression model. The second calculation module is used to calculate the difference between the future offset and the current offset of the bridge cluster under maintenance as the change in bridge offset. The processing and calculation module is used to perform a linear translation transformation on the current offset of the bridge for the maintenance bridge cluster to obtain the current health of the bridge, and to calculate the difference between the change in the bridge offset and the first minimum value of the bridge as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in the offset of all bridges in the bridge category. The scheme generation module is used to construct and solve a dual objective function to obtain multiple maintenance schemes. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the priority constraint of technical condition level, and objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. The filtering module is used to select the optimal maintenance plan.

[0020] Thirdly, this disclosure provides a computer-readable storage medium comprising instructions, characterized in that, when the instructions are executed on a computer, the computer causes the computer to perform the steps of a bridge cluster maintenance decision-making method based on degradation curves as described in the first aspect.

[0021] The aforementioned bridge cluster maintenance decision-making method, system, and medium based on degradation curves first cluster bridges according to their inherent attribute data, constructing benchmark degradation curves for bridges of the same category, and calculating the current offset based on these benchmark curves. Then, using the bridges' inherent attribute data and current offsets as input, the method predicts the future offsets of the bridges and calculates the change in offset. This proactively predicts the future technical condition trends of the bridges before the deviation significantly increases. Finally, based on the bridges' current health and degradation resistance index, a dual-objective function is constructed and multiple maintenance schemes are solved, selecting the optimal bridge cluster maintenance scheme. Compared to existing technologies, this disclosure accurately identifies the degree of deviation of individual bridges from their respective groups, improves the precision of maintenance decisions based on benchmark degradation curves, and makes maintenance decisions more forward-looking by predicting future offsets and deriving maintenance decisions accordingly. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating a method in one embodiment of the present disclosure; Figure 2 This is a diagram of the K-means clustering elbow rule in one embodiment of this disclosure; Figure 3This is a comparison diagram of the fitting of the benchmark degradation curve of the bridge cluster in one embodiment of this disclosure; Figure 4 This is a schematic diagram of the system structure in one embodiment of the present disclosure. Detailed Implementation

[0023] The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0024] See Figure 1 This embodiment provides a bridge cluster maintenance decision-making method based on degradation curves, the method comprising: Acquire periodic inspection data from multiple bridge clusters, the periodic inspection data including technical condition information; Based on the inherent attribute data of the bridges, the K-means clustering algorithm was used to divide the bridge cluster into multiple categories; For each category, an improved RANSAC algorithm is used to fit the degradation trend curve between bridge age and technical condition score as the baseline degradation curve for that category of bridges; the sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method of the improved RANSAC algorithm is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The current offset of the bridge is obtained by calculating the offset of the bridge's current technical condition score relative to the baseline degradation curve; Using the inherent attribute data of the bridge and the current offset of the bridge as input features, a random forest regression model is trained, which is used to predict the future offset of the bridge. The trained random forest regression model is used to predict the future offset of the bridges in the maintenance bridge cluster. The difference between the future offset and the current offset of the bridge cluster under maintenance is used as the change in bridge offset. For the maintenance of bridge clusters, the current health of the bridge is obtained by linear translation of the current offset of the bridge, and the difference between the change in the bridge's offset and the first minimum value of the bridge is calculated as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in offset of all bridges in the bridge's category. A dual objective function is constructed, and multiple maintenance schemes are obtained by solving the dual objective function. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the constraint of technical condition level priority. Objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. Select the optimal maintenance plan.

[0025] In this embodiment, the technical condition information includes the technical condition level, technical condition score, and technical condition assessment date.

[0026] In this embodiment, obtaining periodic inspection data from multiple bridge clusters involves: acquiring periodic inspection data from multiple bridge clusters and generating a bridge feature dataset. The bridge feature dataset includes bridge codes, construction years, bridge dynamic information data, and inherent bridge attribute data. The bridge dynamic information data includes technical condition level information. Furthermore, the bridge dynamic information data also includes maintenance record information.

[0027] In this embodiment, the current offset of the bridge is the difference between the current actual technical condition score of the bridge and the corresponding technical condition score on the benchmark degradation curve of the bridge.

[0028] Understandably, the future offset is the amount corresponding to the current offset, which is essentially the offset of the bridge's future technical condition score relative to the baseline degradation curve. However, the random forest regression model does not only predict the bridge's future technical condition score first and then calculate the corresponding offset, but also directly predicts the future offset based on the current offset.

[0029] The method is described in detail below, including: Step 1: Acquire and preprocess periodic inspection data from multiple bridge clusters. Periodic inspection data is collected from multiple target bridge clusters, including but not limited to: bridge code, construction year, technical condition assessment date and level, geometric parameters, mechanical parameters, durability indicators, and external environmental characteristics. The collected periodic inspection data is preprocessed to generate a bridge inherent attribute dataset and a bridge feature dataset. Preprocessing typically includes data cleaning. The bridge feature dataset includes the bridge code, construction year, bridge dynamic information data, and all data from the bridge inherent attribute dataset. The bridge dynamic information data includes technical condition assessment information, which includes the technical condition assessment date, technical condition level, and technical condition score.

[0030] The bridge's inherent attribute dataset includes the bridge code, year of construction, geometric parameters, and mechanical parameters.

[0031] Furthermore, the bridge dynamic information data also includes maintenance record information. This maintenance record information includes: maintenance date and maintenance items.

[0032] Step 1.1, Data Acquisition. Regular inspection data from multiple target bridge clusters is collected, primarily from two sources: on-site measurements and historical archives. On-site measurement data is acquired using intelligent inspection equipment. For example, drones are used to obtain high-definition images of the superstructure, 3D laser scanners are used to acquire bridge point cloud data, and bridge inspection vehicles equipped with high-precision sensors perform on-site inspections and parameter extraction of core load-bearing components such as supports, main beams, and piers. Historical archive data is obtained through digitized archiving and information extraction of bridge design drawings, construction records, and maintenance records, supplementing the bridge's life-cycle state evolution trajectory. This multi-source inspection data is automatically identified and analyzed by the system, combined with manual verification, and then uniformly entered into a standardized bridge inspection database.

[0033] Step 1.2, Data Extraction and Preprocessing. Extract periodic inspection data of all target bridges from the bridge inspection database. Key fields include, but are not limited to: bridge code, construction year, technical condition assessment date, technical condition level, maintenance records (usually only the most recent maintenance records are retrieved), total length, total span length, maximum single-span span, bridge deck clear width, structural type, material type, pier type, design load level, seismic resistance level, and track technical level.

[0034] The collected data is numerically transformed according to the inherent attributes of the bridge and engineering specifications to construct a bridge feature dataset. This feature dataset includes all data from the bridge feature dataset, including bridge code, construction year, bridge dynamic information data, and the bridge inherent attribute dataset; the bridge dynamic information data includes the technical condition assessment date and technical condition level. This bridge feature dataset includes, but is not limited to, the following dimensions: bridge age (technical condition assessment date - construction year), technical condition level, technical condition score, logarithmic transformation value of total length (taken as log10 to reduce errors caused by large numerical ranges), span ratio (total span length / maximum single span), bridge deck clear width, load factor (numericalized according to design load level), seismic fortification factor (numericalized according to bridge seismic resistance level), pier structure factor (numericalized according to bridge seismic resistance level), span configuration factor (numericalized according to span type), and service level factor (numericalized according to the technical level of the line where the bridge is located), etc.

[0035] Data cleaning was performed on the aforementioned bridge feature dataset. Based on historical maintenance records, data related to bridge samples that had not undergone maintenance intervention were filtered out to ensure the data reflects the natural degradation process. In other words, the final bridge feature dataset contains data from bridges that have undergone maintenance intervention. Data cleaning also included: employing statistical analysis methods (such as box plots or 3D modeling). σ (Principle) Identify and remove outlier data that deviates from the normal distribution, and finally obtain a regular feature set for subsequent clustering and modeling analysis.

[0036] The inherent properties of a bridge that do not change with the increase of its service life are extracted from the bridge feature dataset. These properties mainly include, but are not limited to, the logarithmic transformation value of the total length, the span ratio, the net width of the bridge deck, the load factor, the seismic design factor, the pier type structure factor, the span configuration factor, and the service level factor, which are used to construct the inherent property feature set of the bridge.

[0037] This embodiment extracts periodic inspection data of small and medium span prestressed concrete beam bridges in a certain area for four consecutive years (2021-2024), obtains data information of more than 1,000 target bridges, and obtains their bridge feature dataset and bridge inherent attribute dataset.

[0038] It is particularly important to note that the technical condition score in this embodiment is based on the bridge technical condition classification boundaries in the "Highway Bridge Technical Condition Assessment Standard" (JTG / TH21—2011), mapping the technical condition level to a specific numerical value. By default, the technical condition score of a bridge with an age of 0 years and a technical condition level of Class 1 is 100. The scores of other bridges are taken as the median of the upper and lower limits of the technical condition classification, that is: the median score of Class 1 bridges is 97.5, the median score of Class 2 bridges is 87.5, the median score of Class 3 bridges is 70, the median score of Class 4 bridges is 50, and the median score of Class 5 bridges is 20.

[0039] Step 2, Feature Clustering. Based on the inherent attribute data of the bridges in the bridge feature dataset and information about bridge degradation behavior, the K-means clustering algorithm is used to divide the bridge cluster into multiple categories; The bridge cluster was divided into multiple categories using the K-means clustering algorithm. Bridges in the same category have similar inherent physical properties.

[0040] The inherent properties of a bridge are those that do not change over time. Specifically, inherent physical properties refer to the structural parameters that are determined when the bridge is built and do not change significantly over time. These parameters determine the basic mechanical behavior and load-bearing potential of the bridge.

[0041] First, the bridge feature dataset generated in step 1 is deduplicated by bridge code to ensure that each bridge has a unique identifier. In some embodiments, the bridge feature dataset obtained in step 1 does not contain duplicate bridge codes.

[0042] We selected inherent bridge properties that do not change over time as clustering features, using the bridge property dataset as the clustering feature to avoid interference from time-dependent factors. The elbow rule was employed to determine the optimal number of clusters. The K-means algorithm was used to cluster the bridges, grouping bridges with similar physical properties into the same category. The formula for determining the optimal number of clusters using the elbow rule and the objective function of the K-means clustering algorithm are as follows: in, This represents the total number of clusters, which is the optimal number of clusters mentioned above. Indicates the sequential numbering of the cluster. Indicates the first Clusters, Indicates the number of the data point in the cluster. Indicates the first Data points, Indicates the first The center of each cluster, This represents the square of the Euclidean distance. This represents the within-group sum of squared errors function. This represents the minimum value function.

[0043] Figure 2 The elbow rule curve diagram in this embodiment is shown. Figure 2 The x-axis represents the number of clusters, and the y-axis represents the inertia value. Based on this curve, select... As the optimal number of clusters, the corresponding inertia value is 7942. It can be seen that the bridge cluster is divided into 5 categories using the K-means clustering algorithm, denoted as category 1 to 5. The bridges in each category have similar inherent physical properties and degradation behavior.

[0044] Step 3: Fitting the baseline degradation curve.

[0045] For each category, an improved RANSAC algorithm is used to fit a degradation trend curve between bridge age and technical condition score as the baseline degradation curve for that category of bridges. The improved RANSAC algorithm employs stratified sampling based on the technical condition level and / or technical condition score corresponding to each data point (i.e., based on the importance of the data point to the bridge degradation study). The improved RANSAC algorithm's scoring method involves stratified weighted scoring based on the technical condition level and / or technical condition score corresponding to each data point (i.e., based on the importance of the data point to the bridge degradation study). The importance of the data point to the bridge degradation study can be determined based on the corresponding technical condition level and / or technical condition score.

[0046] Understandably, the data points refer to the data points used for curve fitting, i.e., the data points are coordinate points (bridge age, technical condition score).

[0047] For each cluster of bridges, an improved RANSAC algorithm was used. Through a stratified sampling mechanism and a stratified weighted scoring method, a degradation trend curve between the bridge's age and its technical condition score was fitted. This curve was then used as the baseline degradation curve for that bridge category. It can be understood that the baseline degradation curve is the degradation curve mentioned in the name. A total of five baseline degradation curves were obtained.

[0048] Step 3.1: Fit the baseline degradation curve for each bridge cluster category based on the improved RANSAC algorithm.

[0049] The core idea of ​​the RANSAC algorithm is to select the optimal model parameters through random sampling and consistency checks. The specific implementation process is as follows: First, initialize the algorithm parameters, including initializing the minimum number of sampling points. Maximum number of iterations and interior point determination threshold Randomly selected Fit the initial curve to 1 sample point As a candidate model, the remaining sample points are substituted into the candidate model, and the residuals are calculated. If the residual is less than a threshold, it is considered an interior point; otherwise, it is discarded. The total number of interior points in the current model is counted. ,Will Compared with the historical best model Comparing the interior points, if If it's larger, then update. For the current model, record the set of interior points and dynamically adjust the remaining number of iterations; repeat the above process until the number of iterations is exhausted, and finally output the model with the most interior points as the best fitting result.

[0050] To address the scarcity and uneven distribution of low-scoring points in bridge inspection data, this embodiment employs an improved RANSAC algorithm to fit a degradation trend curve between the bridge age and technical condition score of bridge clusters within the same category (cluster category), serving as the benchmark degradation curve for that type of bridge. This curve uses a semi-empirical nonlinear degradation model, with the following basic form: in, For category The bridge in the year Technical condition rating at the time; For category The bridge in the year Bridge age at that time; , , is the nonlinear degradation coefficient, where , and All are greater than 0. This represents the initial technical condition score of a newly constructed bridge (bridge age 0). This represents the degree of linear degradation of a bridge's technical condition due to its age. The bridge age represents the degree of nonlinear degradation of the bridge's technical condition, and together they determine the rate at which the bridge's technical condition deteriorates with increasing bridge age.

[0051] The improved RANSAC algorithm used in this embodiment has the following improvements compared to the traditional RANSAC (Random Sample Consensus) algorithm: (1) Based on the importance of data points to bridge degradation research, stratified sampling and in-point determination are performed. It can be understood that in this embodiment, the analysis of bridge degradation is based on maintenance decision-making, and the importance of bridge degradation research is equivalent to the importance of its role in maintenance decision analysis.

[0052] The technical condition scores of data points are classified into three levels: low, medium, and high. Bridges classified as technical condition category 4 and 5 receive low scores, those classified as category 3 receive medium scores, and those classified as category 1 and 2 receive high scores. In this embodiment, the technical condition score level of the data points corresponding to bridges of technical condition category 4 and 5 is designated as the low level, the technical condition score level of the data points corresponding to bridges of technical condition category 3 is designated as the medium level, and the technical condition score level of the data points corresponding to bridges of technical condition category 1 and 2 is designated as the high level.

[0053] In other words, based on the technical condition level / technical condition score, the importance of data points in the technical solution of this disclosure is tiered. Data points with higher technical condition scores (importance for bridge degradation research) are less important than those with lower scores. Therefore, this disclosure tiers data point importance according to the technical condition level, dividing the data point importance into three tiers: Tier 1 (high importance or low tier), Tier 2 (medium importance or medium tier), and Tier 3 (low importance or high tier). Each tier is assigned a differentiated sampling and interior point determination mechanism. Specifically, the data point importance tiers are divided into high, medium, and low importance tiers, and the score tiers are divided into low, medium, and high tiers. The technical condition score of a data point belongs to the low, medium, or high score tier. The technical condition scores for the first level are all lower than those for the second level, and the technical condition scores for the second level are all lower than those for the third level.

[0054] The traditional RANSAC algorithm constructs a hypothetical model by randomly selecting a fixed number of samples from the entire dataset. Under this mechanism, data points with high importance (e.g., representing only about 3% of the total data) have an extremely low probability of being selected, making them easily discarded during model fitting. Therefore, this embodiment employs a stratified sampling strategy to improve upon this approach, assigning differentiated sampling rates to data points based on their importance.

[0055] Understandably, the sampling operation has a preset minimum total number of samples. In this embodiment, a high-probability fixed sampling method is adopted for the high-importance level. All bridge samples in the high-importance level (all bridge samples whose technical condition scores for data points belong to the low stratum) are sampled at a first sampling rate, specifically, at a fixed proportion of 90%. For all bridge samples in the medium-importance level (all bridge samples whose technical condition scores for data points belong to the medium stratum), a dynamic random sampling method is adopted. In each iteration, samples are taken at a second sampling rate, specifically from the first probability interval (e.g., the interval of 60% to 80%). A sampling rate is randomly generated within the range of [a certain level], and samples are taken from intermediate points accordingly. For the low importance level (all bridge samples whose technical condition scores belong to the high level), an on-demand supplementary sampling method is adopted. After determining the sampling quantity for the high importance and medium importance levels, the remaining required samples are supplemented from the low importance level according to the preset minimum total sampling number requirement. That is, the sampling quantity for data points in the low importance level (i.e., the first value) is: the preset minimum total sampling number minus the sampling quantity for the high importance level minus the sampling quantity for the medium importance level. Here, it is required that each level has sampling, and the sampling quantity for each level is not 0. The first sampling rate is greater than the second sampling rate, that is, the first sampling rate is greater than the first probability interval. Preferably, the sampling quantity for the low importance level does not exceed the sampling quantity for the medium importance level.

[0056] Traditional RANSAC algorithms use a globally uniform threshold for inlier determination, which leads to data points with low technical status scores but containing crucial information (i.e., low-scoring points) being easily misclassified as outliers and removed. To address this limitation, the improved RANSAC algorithm in this embodiment implements a differentiated threshold strategy based on the scoring region division. It raises the inlier determination threshold for high-importance data points, minimizing the removal of such data points, and further lowers the inlier determination threshold for low-importance data points, removing more of them. In other words, it uses a more inclusive determination standard for data points carrying important information, effectively avoiding the misremoval of critical data. In the improved RANSAC algorithm, the inlier determination threshold satisfies the following condition: the inlier determination threshold corresponding to the lower stratum is greater than the inlier determination threshold corresponding to the middle stratum, and the inlier determination threshold corresponding to the middle stratum is greater than the inlier determination threshold corresponding to the higher stratum. The formula for calculating the inlier determination threshold is as follows: in, This represents the inlier threshold corresponding to the lower stratum, i.e., the inlier threshold for the middle stratum. This represents the threshold for determining interior points in the intermediate importance tier (i.e., the tier of moderate importance). This represents the threshold for determining interior points in data at higher tiers (i.e., lower importance tiers). This represents the basic threshold, the value of which is calculated by an algorithm based on data fluctuations. This indicates a lower multiple of 2.5. This indicates a middle multiple, with a value of 1.5; This represents the multiple of a high score, with a value of 0.9.

[0057] (2) Assign reward weights based on the importance of data points and construct a hierarchical weighted scoring mechanism. The traditional RANSAC algorithm uses the total number of inliers as the scoring basis, which has the drawback of easily selecting models that have a large number of inliers but sacrifice key low-scoring points. To address this problem, this embodiment proposes a hierarchical weighted scoring mechanism to select the optimal model (i.e., select the degradation trend curve with the highest score as the benchmark degradation curve for this type of bridge). The total score formula is as follows: in, For the overall score, Based on the score, The reward score is assigned to the lower tier, which is the score for the higher importance level. This is a tiered reward system, meaning a score at the medium importance level. The higher the importance level, the higher the reward score, which is the score for a lower importance level. Scoring is given for curvature bonus.

[0058] In this embodiment, the total score formula is as follows: in, This represents the total number of points. This represents the number of interior points in the lower-level region (i.e., the higher-importance level). This represents the number of interior points in the intermediate-level region (i.e., the intermediate-importance level). This represents the number of interior points in the high-level region (i.e., the low-importance level). Bonus points are awarded for low retention rates, i.e., bonus points are awarded for high retention rates at higher importance levels. This is a retention rate bonus, specifically a retention rate bonus for the medium importance level. These are the coefficients of the quadratic term (fitting parameters).

[0059] Based on the completion of hierarchical sampling and model assumptions, the improved RANSAC algorithm generates candidate models through multiple iterations (2000 iterations in this implementation case), that is, it generates candidate degradation trend curves. Based on the above hierarchical weighted scoring mechanism, each candidate model is comprehensively evaluated, and finally the candidate model with the highest score is selected as the benchmark degradation curve of the data cluster.

[0060] The baseline degradation curves for the five types of bridge clusters fitted in this embodiment can be found in [reference needed]. Figure 3 The baseline degradation curves for the five cluster categories are expressed as follows: The specific values ​​of the nonlinear degradation coefficients are shown in Table 1.

[0061] Table 1 Nonlinear Degradation Coefficient Table

[0062] Step 4, Individual Bridge Degradation Rate (Offset Change) Prediction: Calculate the current offset of each bridge in the bridge feature dataset. The current offset of a bridge is the difference between its current actual technical condition score and the corresponding technical condition score on the benchmark degradation curve. Using the bridge's inherent attribute data and its current offset as input features, train a random forest regression model to predict future offsets. Use the trained random forest regression model to predict the future offsets of bridges in the maintenance bridge cluster (i.e., the bridge cluster for which maintenance decisions are to be made). Calculate the difference between the future offset and the current offset of the same bridge; this difference is the offset change, which can also be used as the bridge's degradation rate.

[0063] Understandably, the above steps also include: acquiring the inherent attribute data and technical condition information of the bridges in the maintenance bridge cluster; determining the category of the bridges in the maintenance bridge cluster based on the inherent attribute data of the bridges in the maintenance bridge cluster; calculating the current offset of the bridges based on their current technical condition scores; and inputting the inherent attribute data of the bridges in the maintenance bridge cluster and the corresponding current offsets of the bridges into the trained random forest regression model.

[0064] Understandably, the above-mentioned acquisition of the inherent attribute data and technical condition information of bridges in the maintenance bridge cluster specifically refers to the acquisition of the inherent attribute data and dynamic information data of bridges in the maintenance bridge cluster.

[0065] For a given bridge, the difference between the bridge's current actual technical condition score and the corresponding technical condition score on the benchmark degradation curve is defined as the "current offset". The offset is used to characterize the degree of nonlinear deviation of the bridge's technical condition score from the standard degradation trajectory (benchmark degradation curve), thereby quantifying the deviation of the bridge's condition from the average degradation level of similar bridges.

[0066] The current offset of a bridge is the difference between two technical condition scores, specifically: the difference between the bridge's current actual technical condition score and the corresponding technical condition score on the benchmark degradation curve. For example, if a bridge's current actual technical condition score is 75, and its inherent attribute data indicates its cluster category is Category 2, then the corresponding benchmark degradation curve can be determined. Based on the bridge's current age and the benchmark degradation curve, the technical condition score corresponding to the current bridge on the benchmark degradation curve is determined, for example, to be 78, which can be called the benchmark technical condition score. The current offset would then be -3 points.

[0067] The specific formula for calculating the current offset is as follows: in, Number the bridges. For bridges The current offset, For bridges The current actual technical status score, For bridges The bridge's age, i.e., its current age. For bridges The baseline degradation curve of the cluster category at bridge age The corresponding value at that location.

[0068] A positive value indicates that the current technical condition of the bridge is better than the average level of similar bridges; A negative value indicates that the current technical condition of the bridge is inferior to the average level of similar bridges.

[0069] Using the bridge's inherent attribute data (bridge inherent attribute feature set) and the bridge's current offset as input features, a random forest regression model is trained and evaluated. This model is used to predict future offsets, meaning the output includes future offsets.

[0070] The difference between the future offset and the current offset of the same bridge represents the degradation rate of a specific bridge during the prediction period. This value is usually negative, and the larger its absolute value, the faster the bridge will degrade during the prediction period.

[0071] In some embodiments, the trained random forest regression model is used to calculate the difference between the future offset and the current offset, that is, the output of the random forest regression model includes this difference.

[0072] The difference (i.e. the amount of offset change) is the amount of offset change of the bridge.

[0073] The trained and validated random forest regression model is applied to bridges requiring maintenance. By inputting the inherent attribute data of the bridges requiring maintenance and their current year's offset into the trained and validated random forest regression model, the predicted bridge structure can be output. The future offset, that is, in Offset after the year Since the prediction period is fixed, the difference between the future offset and the current offset can be calculated to equivalently represent the bridge. offset change ,Right now: in, This value assesses the overall degradation trend of a specific bridge during the forecast period; it is generally negative. The larger the value, the faster the bridge will degrade during the forecast period, indicating a risk of accelerated degradation.

[0074] As an example and not a limitation, the random forest prediction model consists of 200 decision trees, with the following key parameters set: maximum depth 15, minimum number of split samples 2, minimum number of leaf node samples 1, and maximum number of features "sqrt" (square root).

[0075] All valid samples used to train the random forest regression model were randomly divided into a training set and a test set in an 8:2 ratio. The training set was used to fit the model and learn the mapping relationship between features and future biases. The test set was used to evaluate the model's generalization ability by calculating the coefficient of determination. Mean absolute error Root mean square error Three indicators are used to evaluate the performance of the prediction results.

[0076] Coefficient of determination The calculation formula is: in, This indicates the bridge number in the test set. This represents the total number of bridges in the test set. For bridges Actual value of the technical condition score. For bridges Predicted technical condition score The average of the actual values ​​of the technical condition scores for the bridges in the test set. This represents the number of samples.

[0077] Mean Absolute Error The calculation formula is: Root mean square error The calculation formula is: This embodiment collects regular inspection data for four consecutive years (2021-2024), and therefore mainly predicts the future offset of the bridge three years later, thereby assessing the change in offset. It should be noted that the prediction period can be dynamically adjusted according to actual data conditions and maintenance decision-making needs. When more historical data is accumulated, the prediction period can be extended accordingly to ensure the scientific nature and adaptability of long-term maintenance planning.

[0078] In this embodiment, the model on the test set The value reached 0.727868, proving that it has good predictive ability. The specific evaluation index values ​​are shown in Table 2 below.

[0079] Table 2 Evaluation Indicators

[0080] Step 5, Maintenance Decision Generation. For the bridge cluster under maintenance, a linear translation transformation is performed on the current offset to obtain the current health status of the bridge. For the bridge cluster under maintenance, a linear translation transformation is performed on the change in bridge offset to obtain the bridge degradation resistance index. The bridge health status represents the current health level of the bridge compared to similar bridges, while the bridge degradation resistance index represents the degradation rate of the bridge during the prediction period. These two constitute the dual core quantitative indicators for decision-making, and a bridge network importance coefficient is introduced for weighted correction. Using the weighted indicators as input, a dual objective function is constructed. Solving the dual objective function yields multiple maintenance schemes. Objective 1 is to minimize the weighted sum of the current health status of the bridge cluster under the priority constraint of technical condition level, and Objective 2 is to minimize the weighted sum of the degradation resistance indices of the bridge cluster under maintenance.

[0081] The degradation resistance index is the difference between the change in offset and a first minimum value, where the first minimum value is the minimum change in offset of all bridges in the bridge's category.

[0082] Step 5.1, Quantify the evaluation index. To adapt to the conventional requirement of non-negativity of input variables in multi-objective optimization models and to ensure that each objective function is optimized under a uniform numerical scale, a linear translation transformation is performed on the current offset and offset change of the bridge.

[0083] Specifically, the current offset of the bridge Perform a translation transformation to obtain the bridge. Current health This index is a non-negative scale; the larger the value, the healthier the bridge's current condition relative to the average level of similar bridges. Therefore, when formulating maintenance plans, the principle of "prioritizing those with lower health scores" should be followed. That is, under the premise of the same technical condition level, maintenance interventions should be prioritized for bridges with lower health scores. The current health score of the bridge is the degradation resistance index, and the specific formula is as follows: in, Bridge The minimum current offset of bridges in the category (all bridges).

[0084] Bridge offset change during the prediction period Perform a translation transformation to obtain the bridge. Degeneration resistance index ,Should The degradation resistance index (CRI) is a non-negative scale; a larger value indicates a slower rate of bridge degradation during the predicted period. Therefore, when developing maintenance plans, the principle of "prioritizing bridges with lower degradation resistance index values" should be followed, meaning maintenance interventions should be prioritized for bridges with lower CRI values. The specific formula is as follows: in, Bridge The minimum future offset of bridges in the category (of all bridges).

[0085] In this embodiment, the core status indicators are weighted and adjusted according to the importance of bridges in the road network. The importance of a bridge in the road network is mainly determined by three key factors: its route technical grade (quantified according to the route grade of the bridge), its administrative grade (quantified according to the administrative grade of the bridge), and its traffic flow (quantified according to the traffic flow grade of the bridge). By standardizing the scores of each factor and then weighting and summing them, the road network importance score of the bridge is obtained. Bridge network importance score The calculation formula is as follows: in, This indicates the route rating score. This indicates the administrative rank score. This indicates the traffic flow score. This represents the weighting coefficient of the line grade index. This represents the weighting coefficient of the administrative rank indicator. This represents the weighting coefficient of the traffic flow indicator, specifically... , , The values ​​are 0.3, 0.3, and 0.4 respectively.

[0086] Step 5.2, Construction and solution of the dual objective function.

[0087] Within the framework of practical engineering constraints (such as resource allocation), a dual objective function is constructed. Objective 1 is to minimize the total weighted sum of the current health of the bridge cluster under the constraint of technical condition level priority, and Objective 2 is to minimize the total weighted sum of the degradation resistance indices of the bridges under maintenance.

[0088] Regarding the "priority constraint of technical condition level," it is understandable that the optimal solution must be found under the premise of conforming to the priority ranking rules, with lower technical condition levels taking priority. In other words, the technical condition level of the bridge is the core guiding principle, mandating priority treatment of bridges in poor technical condition (i.e., high risk), using this as a prerequisite for resource allocation. In this embodiment, the order of maintenance is: first, Class IV and Class V bridges; then Class III bridges; then Class II bridges; and finally Class I bridges.

[0089] The biobjective function is solved using the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm. The randomly generated population size is... The initial population is calculated, and the value of each individual in the initial population on all objective functions is calculated. Then, a fast non-dominated sort is performed on the initial population to divide the population into different non-dominated levels. The specific objective functions are as follows: in, Represents a vector of decision variables. Indicates the bridge number that needs maintenance. Bridge Maintenance decisions ( (Value can be 0 or 1) The function represents the first objective of the NSGA-II algorithm, where the first objective is objective 1. The function representing the second objective of the NSGA-II algorithm, where the second objective is objective 2. Describes the minimum value function. This indicates the total number of bridges requiring maintenance. Bridge Road network importance score, Bridge Current health status Bridge The degradation resistance index; For each individual within a non-dominated hierarchy, calculate their crowding distance using the following formula: In the formula, The individual's ID number is greater than 1 and less than 1. Positive integers; This indicates the ID of the last individual in the non-dominated hierarchy (i.e., the total number of individuals in this hierarchy). Represents an individual Crowding distance, This represents the crowding distance for individual 1. Represents an individual Crowding distance, This represents the [number]th [item] after sorting by objective function value. Index of each solution, This represents the [number]th [item] after sorting by objective function value. Index of each solution, This represents the maximum value of the first objective. This represents the minimum value of the first objective. This represents the maximum value of the second objective. This represents the minimum value of the second objective. This indicates the order after sorting by the first objective function. The function value of the solution on the first objective. This indicates the order after sorting by the first objective function. The function value of the solution on the first objective. This indicates the order after sorting by the second objective function. The function value of the solution on the second objective. This indicates the order after sorting by the second objective function. The function value of the solution on the second objective.

[0090] Based on the non-dominated ranking rank and crowding distance in the NSGA-II algorithm, an elite retention strategy is implemented from the merged population to select the best performers. The best individuals are selected as the parents for the next generation. Then, offspring are generated through tournament selection, single-point crossover, and polynomial mutation, with a constraint repair mechanism introduced to ensure that new individuals strictly meet engineering constraints. The algorithm's iteration is controlled by convergence conditions; when the maximum number of iterations is reached... The algorithm stops and outputs the final Pareto optimal solution set when the change in the Pareto front (i.e., the Pareto optimal boundary) between two consecutive generations is less than the corresponding threshold. The specific convergence conditions are as follows: in, This represents the current iteration number; Maximum number of iterations (500); For the first At that time, the mean or center point of the objective function of the solution set with a non-dominated level of 1 (i.e., the Pareto optimal frontier); For the first The state of the previous generation's Pareto optimal frontier; This is the convergence threshold.

[0091] In this embodiment, data from 110 bridges were collected. These 110 bridges belong to a bridge cluster, and the sample covers two categories of bridges with scores of 87.5 and 97.5. The total cost of comprehensive maintenance for these 110 bridges was calculated to be 1.7122 million yuan, with an actual budget constraint of 1 million yuan. Based on this budget constraint, the algorithm output 12 Pareto optimal solutions, as shown in Table 3.

[0092] Table 3 Example of Maintenance Details

[0093] Step 6: Construct a benefit evaluation system comprising four indicators, which represent the sum of the current health status of the bridges in the maintenance bridge cluster. The sum of the degradation resistance indices of bridges in the maintenance of bridge clusters Maintenance intensity and the total density of maintenance funds The combined weighting method based on subjective and objective values ​​(AHP-CRITIC combined weighting method) is used to calculate the combined weighting weight of each indicator. Based on the four indicators and their corresponding combined weighting weights, the benefit evaluation score of each maintenance plan is calculated, and the optimal maintenance plan is determined according to the benefit evaluation score.

[0094] Specifically, this step involves the evaluation, optimization, and iteration of maintenance scheme benefits. A benefit evaluation index system is constructed, encompassing four dimensions: the total health of the maintained bridges, the total degradation resistance index of the maintained bridges, the total maintenance intensity, and the total maintenance funding density. The weights of each index are calculated using the AHP-CRITIC combined weighting method, thereby conducting a comprehensive benefit evaluation of each candidate scheme and selecting the optimal scheme based on the evaluation values. Actual implementation data of the bridge maintenance scheme is recorded, and the comparison and analysis between the implementation results and expected goals drives the optimization and adjustment of the next round of maintenance decisions.

[0095] Specifically, a benefit evaluation index system is constructed, encompassing four dimensions: total maintenance health, total maintenance degradation resistance index, total maintenance intensity, and total maintenance capital density. Among these, the total maintenance health... This refers to the value of Target 1 in Table 3 above, reflecting the overall health status of the bridge under maintenance; the sum of maintenance degradation resistance indices. This refers to the value of Target 2 in Table 3 above, which characterizes the bridge's ability to resist performance degradation and delay the development of defects; maintenance intensity Defined as the ratio of maintenance workload to road network importance, it measures the amount of maintenance work required per unit of road network importance; total maintenance funding density. Defined as the ratio of maintenance cost to road network importance, this measure indicates the maintenance funds required per unit of road network importance. All four indicators are inverse indicators; the smaller the indicator value, the better the overall benefit of the maintenance plan. Based on this four-dimensional indicator system, the AHP-CRITIC combined weighting method is used to determine the weights of each indicator. The weight of the Analytic Hierarchy Process (AHP), reflecting expert experience, is primary, with a weight coefficient of 0.7. The weight of the CRITIC method (objective weighting method), reflecting data objectivity, is secondary, with a weight coefficient of 0.3. Based on this, a comprehensive benefit evaluation is conducted on each candidate maintenance plan, and the optimal plan is selected according to the evaluation value. The AHP-CRITIC combined weighting formula and... , The specific formula is as follows: in, The weights calculated using the AHP-CRITIC combined weighting method are referred to as combined weighted weights. These are the subjectively assigned weights obtained based on the Analytic Hierarchy Process (AHP), i.e., the subjective assignment method. These are the objective weights obtained based on the CRITIC weighting method, with 0.7 and 0.3 being weight coefficients. To maintain the total number of bridges, The total cost of bridge maintenance, The total value of the importance coefficient for the maintenance of the bridge and road network.

[0096] AHP-CRITIC portfolio weighting The specific calculation method is as follows: First, the indicators are calculated using the Analytic Hierarchy Process (AHP). , , , Subjective weighting Consult experts and construct a judgment matrix. Calculate the geometric mean of each row of the judgment matrix. The weights are then normalized. The specific formula is as follows: in, This indicates the row number of the judgment matrix. Indicates the column number of the judgment matrix. Indicates the first The first indicator and the first The importance comparison values ​​of each indicator This indicates the order of the judgment matrix (total number of indicators). Indicates the first The geometric mean of the row elements. Indicates the first The subjective weight of each indicator, Indicates a temporary index variable. Indicates the first Row geometric mean.

[0097] Calculate the consistency index and consistency ratio It is generally believed that when When the value is less than 0.1, the judgment matrix has satisfactory consistency; otherwise, the judgment matrix needs to be adjusted until the consistency requirement is met. The specific formula is as follows: in, To determine the largest eigenvalue of a matrix, To determine the matrix With weight vector The product of the product, the resulting vector is the first... Item is denoted as , This refers to the item number in the result vector, which is equivalent to the row number in the judgment matrix. To determine the order of a matrix, For the first The weight of each indicator.

[0098] in, It is a random consistency index, and its value is related to the order of the judgment matrix, which can be obtained by looking up a table. The values ​​are shown in Table 4: Table 4 Value table

[0099] Secondly, the index is calculated using the CRITIC weighting method. , , , Objective weighting Constructing the indicator feature matrix The results are then processed using Min-Max inverse standardization (max-min inverse standardization), and the standard deviation, correlation coefficient matrix, conflict index, and information content of each indicator are calculated sequentially to obtain the objective weight of each indicator. The specific calculation formula is as follows: in, Indicates the indicator number, Indicates the indicator number, The ordinal number of the object (within the range of 1 to 1). (integers) Indicates the total number of objects. Indicates the total number of indicators. Indicates the first The standard deviation of each indicator Indicates the first The object in the first The standardized value for each indicator Indicates the first The average of the indicators, Indicates the first The object in the first The standardized value for each indicator Indicates the first The average of the indicators, Indicators and The correlation coefficient, , For temporary index variables, Indicates the first The conflict of several indicators For the first The amount of information in each indicator The CRITIC weighting method is used to calculate the first... The objective weight of each indicator, For the first The amount of information in each indicator.

[0100] Finally, through the formula Calculation indicators , , , Combined weighting weights .

[0101] Record actual implementation data of bridge maintenance plans, including maintenance costs, construction period, and changes in technical condition after maintenance. Incorporate the actual implementation results as new sample data into the regular inspection database. Based on a comparative analysis of the implementation results and expected goals, conduct deviation cause analysis, and then adjust the indicator weights and model parameters to drive the next round of decision optimization. This forms a closed-loop optimization mechanism of "monitoring—decision-implementation—feedback," enabling continuous iteration and dynamic improvement of bridge maintenance decisions.

[0102] In this embodiment, the Analytic Hierarchy Process (AHP) is first used to determine the subjective weights of each bridge maintenance indicator. A judgment matrix is ​​then constructed using bridge health, degradation resistance index, maintenance intensity, and funding density as evaluation indicators. The largest eigenvalue was obtained through calculation. =4.0017, Consistency Index =0.0006, random consistency index =0.90, consistency ratio =0.0006 < 0.1, passing the consistency test, thus obtaining the AHP weights. .

[0103] The CRITIC weighting method is then used to calculate the objective weights. A feature matrix is ​​then constructed. Based on the normalized standard feature matrix, the standard deviations of each indicator are 0.3807, 0.3370, 0.3096, and 0.3067, respectively. The calculated conflict rates of each indicator are 4.2454, 2.6856, 3.0187, and 2.5537, respectively, and the information content is 1.6160, 0.9050, 0.9347, and 0.7832, respectively. The resulting CRITIC weights are then used to determine the CRITIC values. .

[0104] Finally, the weights obtained from the analytic hierarchy process (AHP) and the CRITIC weighting method are weighted and fused to obtain the index. , , , Combined weighting weights Based on this weight, the comprehensive score of each scheme is calculated, and the scheme with the higher score is better. The calculation results are shown in Table 5. Therefore, Scheme 1 is selected as the preferred scheme for bridge maintenance.

[0105] Table 5 Maintenance Decision File Information Table

[0106] Compared with existing methods, this disclosure reduces emergency repair incidents by 58.3%, significantly increases the timely maintenance rate from 35% to 82% (a relative increase of 134%), and optimizes the cost-benefit ratio from 6.9% to 5.5%, resulting in a comprehensive improvement in overall maintenance efficiency.

[0107] See Figure 4 This embodiment provides a bridge cluster maintenance decision-making system based on degradation curves. The system includes: The acquisition module is used to acquire periodic inspection data of multiple bridge clusters, the periodic inspection data including technical condition information; The clustering module is used to divide the bridge cluster into multiple categories based on the inherent attribute data of the bridges using the K-means clustering algorithm. The curve generation module is used to fit a degradation trend curve between bridge age and technical condition score for each category using an improved RANSAC algorithm as the benchmark degradation curve for that category of bridges. The sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The first calculation module calculates the current offset of the bridge by measuring the current technical condition score of the bridge relative to the baseline degradation curve. The training module is used to train a random forest regression model using the inherent attribute data of the bridge and the current offset of the bridge as input features. The random forest regression model is used to predict the future offset of the bridge. The prediction module is used to predict the future offset of the bridges in the maintenance bridge cluster using the trained random forest regression model. The second calculation module is used to calculate the difference between the future offset and the current offset of the bridge cluster under maintenance as the change in bridge offset. The processing and calculation module is used to perform a linear translation transformation on the current offset of the bridge for the maintenance bridge cluster to obtain the current health of the bridge, and to calculate the difference between the change in the bridge offset and the first minimum value of the bridge as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in the offset of all bridges in the bridge category. The scheme generation module is used to construct and solve a dual objective function to obtain multiple maintenance schemes. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the priority constraint of technical condition level, and objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. The filtering module is used to select the optimal maintenance plan.

[0108] In this embodiment, the curve generation module is specifically used to sample data points for all bridge samples whose technical condition scores belong to the low stratum using a first sampling rate; to sample all bridge samples whose technical condition scores belong to the middle stratum using a dynamic random sampling method in each iteration, sampling all samples with a random probability value in a first probability interval, where the first probability interval is less than the first sampling rate; and to sample all bridge samples whose technical condition scores belong to the high stratum using a first value, where the first value is equal to a preset minimum total number of samples minus the number of samples in the high importance stratum and then minus the number of samples in the medium importance stratum.

[0109] In this embodiment, the scheme generation module is specifically used to construct a benefit evaluation system including four indicators, which are the sum of the current health status of the bridges in the bridge maintenance cluster. The sum of the degradation resistance indices of bridges in the maintenance of bridge clusters Maintenance intensity and the total density of maintenance funds The combined weighting method based on subjective and objective values ​​is used to calculate the combined weighting weight of each indicator. Based on the four indicators and their corresponding combined weighting weights, the benefit evaluation score of each maintenance plan is calculated, and the optimal maintenance plan is determined according to the benefit evaluation score.

[0110] In this embodiment, the system further includes an acquisition and preprocessing module, used to acquire the inherent attribute data and technical condition information of the bridges in the maintenance bridge cluster; determine the category of the bridges in the maintenance bridge cluster based on the inherent attribute data of the bridges in the maintenance bridge cluster; calculate the current offset of the bridges based on the current technical condition score of the bridges in the maintenance bridge cluster; and input the inherent attribute data of the bridges in the maintenance bridge cluster and the corresponding current offset of the bridges into the trained random forest regression model.

[0111] In specific implementation, the bridge cluster maintenance decision system can refer to the bridge cluster maintenance decision method in any of the above embodiments to realize a specific embodiment of bridge cluster maintenance decision-making. The specific implementation steps will not be repeated.

[0112] An electronic device can be implemented according to the method of this disclosure, the electronic device comprising: a memory; one or more processors; one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for executing a bridge cluster maintenance decision method based on degradation curves according to any of the above embodiments.

[0113] This disclosure also provides a computer-readable storage medium including instructions that, when executed on a computer, cause the computer to perform the steps of the bridge cluster maintenance decision-making method based on degradation curves as described in any of the above embodiments.

[0114] A bridge cluster maintenance decision-making method, system, and medium based on degradation curves are disclosed. First, bridges are clustered based on their inherent attribute data to construct benchmark degradation curves for bridges of the same category. The current offset is calculated based on these benchmark curves. Then, using the bridges' inherent attribute data and current offsets as input, the future offsets of the bridges are predicted, and the change in offset is calculated. This proactively predicts the future technical condition trend of the bridges before the deviation significantly increases. Finally, a dual-objective function is constructed based on the bridges' current health and degradation resistance index, and multiple maintenance schemes are solved to select the optimal bridge cluster maintenance scheme. Compared to existing technologies, this disclosure, by calculating the current offset based on benchmark degradation curves, accurately identifies the degree of deviation of individual bridges from their corresponding groups, accurately reflecting the relative degradation level of bridges within the same type of structure, thus providing a more accurate assessment of the bridge's condition. Furthermore, this disclosure improves the precision of maintenance decisions based on benchmark degradation curves, making maintenance decisions more forward-looking by predicting future offsets and deriving maintenance decisions accordingly.

[0115] Maintaining bridges based on decisions obtained from this disclosure can not only ensure the safety of the current road network operation, but also extend the service life of bridges through predictive maintenance, thereby improving the durability and overall benefits of the bridges throughout their entire life cycle.

[0116] Specifically: (1) By constructing a benchmark degradation curve for similar bridges as a dynamic reference system, a refined assessment and horizontal comparability of technical condition are achieved. Existing technologies mostly rely on absolute scores for decision-making, making it difficult to distinguish the deviation of the actual state caused by inherent differences in design standards, material properties, and other attributes behind the same score. This invention establishes a "normal degradation trajectory" for similar bridges through cluster analysis and curve fitting, and introduces "current offset" as a new assessment index. Compared with traditional methods that only focus on "how many points a bridge has received," this invention can accurately identify the degree of deviation of an individual bridge from its similar group in terms of actual state, effectively solving the assessment blind spot of "different quality for the same score," and providing a more scientific and refined basis for prioritizing maintenance.

[0117] (2) By introducing a deviation prediction mechanism based on the individual bridge degradation rate (change in offset), a shift from "passive response" to "proactive prevention" in decision-making is achieved. Existing decisions are mostly "post-event remediation" models, typically taking action only after defects appear or thresholds are triggered, thus missing the best opportunity for preventative maintenance. This disclosure uses the inherent physical characteristics of the bridge and its current offset to make a forward-looking prediction of its future offset. This not only predicts the future technical condition of the bridge but also issues early warnings before the deviation significantly increases, shifting the timing of maintenance intervention from "treating existing problems" to "preventing future problems," greatly reducing the passivity of maintenance and significantly improving the foresight and scientific nature of maintenance decisions.

[0118] (3) By integrating deviation analysis throughout the entire process of prediction and decision-making, the synergistic improvement of the short-term and long-term benefits of bridge cluster maintenance is achieved. Existing methods often struggle to balance the resource allocation conflicts between short-term emergency maintenance and long-term performance maintenance. This disclosure identifies potentially risky bridges by analyzing "current deviations" to identify "future deviations," unifying refined assessment and forward-looking prediction within the deviation analysis framework. The maintenance decision-making scheme generated on this basis can not only ensure the current operational safety of the road network but also extend the service life of bridges through predictive maintenance, effectively improving the durability and comprehensive benefits of the bridge structure throughout its entire life cycle.

[0119] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0120] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the protection scope of this disclosure. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A bridge cluster maintenance decision-making method based on degradation curves, characterized in that, include: Acquire periodic inspection data from multiple bridge clusters, the periodic inspection data including technical condition information; Based on the inherent attribute data of the bridges, the K-means clustering algorithm was used to divide the bridge cluster into multiple categories; For each category, an improved RANSAC algorithm is used to fit the degradation trend curve between bridge age and technical condition score as the benchmark degradation curve for that category of bridges; the sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The current offset of the bridge is obtained by calculating the offset of the bridge's current technical condition score relative to the baseline degradation curve; Using the inherent attribute data of the bridge and the current offset of the bridge as input features, a random forest regression model is trained to predict the future offset of the bridge. The trained random forest regression model is used to predict the future offset of the bridges in the maintenance bridge cluster. The difference between the future offset and the current offset of the bridge cluster under maintenance is used as the change in bridge offset. For the maintenance of bridge clusters, the current health of the bridge is obtained by linear translation of the current offset of the bridge, and the difference between the change in the bridge's offset and the first minimum value of the bridge is calculated as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in offset of all bridges in the bridge's category. A dual objective function is constructed, and multiple maintenance schemes are obtained by solving the dual objective function. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the constraint of technical condition level priority. Objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. Select the optimal maintenance plan.

2. The bridge cluster maintenance decision-making method based on degradation curves according to claim 1, characterized in that, The expression for the baseline degradation curve is: in, Indicate category The bridge in the year Technical condition rating at the time; Indicate category In the year The age of the bridge at that time This indicates the degree to which bridge age has a linear impact on the technical condition of the bridge. This indicates the degree of nonlinear degradation of a bridge's technical condition due to its age.

3. The bridge cluster maintenance decision-making method based on degradation curves according to claim 1, characterized in that, The stratified sampling based on the technical condition information corresponding to the data points specifically involves: performing stratified sampling based on the score level to which the technical condition score of the data points belongs, wherein the score level is low-level, medium-level, or high-level.

4. The bridge cluster maintenance decision-making method based on degradation curves according to claim 3, characterized in that, The stratified sampling based on the score level to which the data points belong according to their technical condition specifically includes: For all bridge samples whose technical condition scores belong to the lower strata, data points are sampled at the first sampling rate. The technical condition score of the data points belongs to all bridge samples in the middle layer. In each iteration, a dynamic random sampling method is used to sample all samples with a random probability value in the first probability interval, where the first probability interval is less than the first sampling rate. The technical condition score of the data points belongs to all bridge samples in the high-level hierarchy. The samples are sampled according to the first value, which is equal to the preset minimum total number of samples minus the number of samples in the high-importance hierarchy and then minus the number of samples in the medium-importance hierarchy.

5. The bridge cluster maintenance decision-making method based on degradation curves according to claim 3, characterized in that, In the improved RANSAC algorithm, the interior point determination threshold satisfies the following: the interior point determination threshold corresponding to the lower stratum > the interior point determination threshold corresponding to the middle stratum > the interior point determination threshold corresponding to the higher stratum.

6. The bridge cluster maintenance decision-making method based on degradation curves according to claim 3, characterized in that, The formula for calculating the total score based on the hierarchical weighted scoring of the data points is as follows: in, For the overall score, Based on the score, For lower-tier reward ratings, For tiered reward scoring, For higher-level reward scores, Scoring is given for curvature bonus.

7. The bridge cluster maintenance decision-making method based on degradation curves according to claim 1, characterized in that, The method of obtaining the current health status of a bridge by performing a linear translation transformation on the current offset of the bridge is as follows: the current offset of the bridge minus the minimum value of the current offset of all bridges in the same category equals the current health status of the bridge. The formula for the dual objective function is: in, Represents a vector of decision variables. Indicates the bridge number that needs maintenance. Bridge Maintenance decisions, The function representing objective 1 of the NSGA-II algorithm, The function representing objective 2 of the NSGA-II algorithm. Describes the minimum value function. This indicates the total number of bridges requiring maintenance. Bridge Road network importance score, Bridge Current health status Bridge The degradation resistance index; The solution to the function is specifically based on the NSGA-II algorithm to solve the biobjective function.

8. The bridge cluster maintenance decision-making method based on degradation curves according to claim 1, characterized in that, The selection of the optimal maintenance plan includes: constructing a benefit evaluation system comprising four indicators, which represent the sum of the current health status of the bridges in the maintenance bridge cluster. The sum of the degradation resistance indices of bridges in the maintenance of bridge clusters Maintenance intensity and the total density of maintenance funds The combined weighting method based on subjective and objective values ​​is used to calculate the combined weighting weight of each indicator. Based on the four indicators and their corresponding combined weighting weights, the benefit evaluation score of each maintenance plan is calculated. The optimal maintenance plan is determined based on the benefit evaluation score. The maintenance intensity and the total density of maintenance funds The calculation formula is: in, The total number of bridges in the bridge cluster is for maintenance. The total cost of maintaining the bridge complex, The total value of the road network importance coefficient for the maintenance of bridge clusters.

9. A bridge cluster maintenance decision-making system based on degradation curves, characterized in that, include: The acquisition module is used to acquire periodic inspection data of multiple bridge clusters, the periodic inspection data including technical condition information; The clustering module is used to divide the bridge cluster into multiple categories based on the inherent attribute data of the bridges using the K-means clustering algorithm. The curve generation module is used to fit a degradation trend curve between bridge age and technical condition score for each category using an improved RANSAC algorithm as the benchmark degradation curve for that category of bridges. The sampling method of the improved RANSAC algorithm is to perform stratified sampling based on the technical condition information corresponding to the data points, and the scoring method is to perform stratified weighted scoring based on the technical condition information corresponding to the data points. The first calculation module calculates the current offset of the bridge by measuring the current technical condition score of the bridge relative to the baseline degradation curve. The training module is used to train a random forest regression model using the inherent attribute data of the bridge and the current offset of the bridge as input features. The random forest regression model is used to predict the future offset of the bridge. The prediction module is used to predict the future offset of the bridges in the maintenance bridge cluster using the trained random forest regression model. The second calculation module is used to calculate the difference between the future offset and the current offset of the bridge cluster under maintenance as the change in bridge offset. The processing and calculation module is used to perform a linear translation transformation on the current offset of the bridge for the maintenance bridge cluster to obtain the current health of the bridge, and to calculate the difference between the change in the bridge offset and the first minimum value of the bridge as the degradation resistance index of the bridge. The first minimum value is the minimum value of the change in the offset of all bridges in the bridge category. The scheme generation module is used to construct and solve a dual objective function to obtain multiple maintenance schemes. Objective 1 is to minimize the weighted sum of the current health of the bridge cluster under the priority constraint of technical condition level, and objective 2 is to minimize the weighted sum of the degradation resistance index of the bridge cluster. The filtering module is used to select the optimal maintenance plan.

10. A computer-readable storage medium comprising instructions, characterized in that, When the instructions are executed on a computer, the computer performs the steps of a bridge cluster maintenance decision-making method based on degradation curves as described in any one of claims 1-8.

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