Bridge disease marking method based on mathematical model

Abstract

The invention relates to the technical field of bridge health monitoring, and discloses a bridge disease marking method based on a mathematical model. The method comprises the steps of collecting geometric and disease feature information sequences of a bridge disease area; analyzing a fluctuation mode of the disease feature sequence, calculating a disease change index of each fluctuation point, and integrating to obtain an average disease change index; fusing the sequence similarity measurement and the average disease change index, and evaluating a disease activity intensity index; deducing a disease influence coefficient, and generating a marking model parameter adjustment value in combination with a model adaptation coefficient calculated based on geometric features; and taking the adjustment value as an input parameter of the mathematical model of the next adjacent monitoring period to realize closed-loop adaptive optimization of model parameters. According to the method, the disease activity intensity can be dynamically quantified, the marking model parameters are adaptively updated along with the structure state, and the accuracy and long-term reliability of bridge disease marking are improved.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring technology, specifically a method for marking bridge defects based on mathematical models. Background Technology

[0002] Traditional methods for identifying and assessing bridge defects mostly rely on manual inspection records or automated monitoring based on fixed thresholds. These methods typically use the absolute values ​​of defect characteristics or simple statistics as the basis for judgment, and pre-set a static judgment threshold or rule. The mathematical models used are usually set once based on limited historical data or engineering experience, and remain unchanged during long-term service monitoring. Existing technologies have shortcomings when facing the complex and time-varying evolutionary characteristics of bridge defects.

[0003] Static thresholds and fixed rules cannot effectively characterize the dynamic fluctuations and pattern changes in disease development. Disease development is not uniform and linear; its acceleration, deceleration, stabilization, or repeated fluctuations contain important structural state information. Focusing only on instantaneous absolute values ​​ignores these key temporal evolution characteristics, leading to misjudgments or omissions in disease activity and failing to identify abnormal development trends in the early stages. Furthermore, mathematical models using fixed parameters lack self-updating capabilities. As time progresses, environmental effects accumulate, and the structure itself undergoes damage evolution, the model parameters calibrated in the early stages gradually become decoupled from the actual state of the structure, resulting in decreased accuracy of model labeling and preventing the achievement of long-term reliable intelligent assessments that evolve synchronously with the structural state.

[0004] This invention aims to solve two key problems: how to accurately quantify the dynamic activity intensity of diseases from time-series monitoring data, and how to enable the labeled model parameters to be adaptively optimized based on the latest monitoring feedback. Summary of the Invention

[0005] The purpose of this invention is to provide a bridge defect marking method based on a mathematical model to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, this invention provides a bridge defect labeling method based on a mathematical model, the method comprising: Collect geometric and defect characteristics of each bridge defect area at each monitoring time during each monitoring cycle; For each disease characteristic information sequence, the fluctuation pattern in the sequence is analyzed, including the instantaneous change of the fluctuation point, the differential characteristics of the sequence, and the degree of local mean shift, so as to calculate the disease change index of each fluctuation point in each disease characteristic information sequence of each bridge disease area in each monitoring period. By integrating the disease change indicators at each fluctuation point, the average disease change indicators of each bridge disease area at each fluctuation monitoring time in each monitoring cycle are obtained. By integrating the similarity measure of local disease characteristic information sequences and the average disease change index, the intensity index of disease activity in each bridge disease area at each fluctuation monitoring time in each monitoring cycle is evaluated. Based on the disease activity intensity index, the disease impact coefficient of each bridge disease area in each monitoring period was derived; Based on geometric feature information, the model adaptation coefficient of each bridge defect area in each monitoring period is calculated; By combining the disease impact coefficient and the model adaptation coefficient, the adjustment values ​​of the marker model parameters for each bridge disease area in each monitoring period are generated. These adjustment values ​​are then used as the marker model parameter values ​​for each bridge disease area when using the mathematical model to mark the disease in the next adjacent period of each monitoring period, so as to achieve parameter optimization of the bridge disease marking model.

[0007] Preferably, the process of collecting the geometric feature information and the disease feature information includes: The location and shape data at each monitoring time are obtained using the bridge's three-dimensional information model as geometric feature information; Image sensing devices are used to capture crack size and deformation at each monitoring time as characteristic information of the disease.

[0008] Preferably, the process of obtaining the disease change indicators includes: For each bridge defect area in each monitoring period, the extreme value detection method is used to identify all local peak and valley points in the sequence and mark these points as fluctuation points. For each fluctuation point, the absolute difference between the disease characteristic information of the fluctuation point and the disease characteristic information of the previous adjacent monitoring time is calculated as the instantaneous change of the fluctuation point. Based on the first-order difference absolute value sequence of disease characteristic information sequence, the maximum difference value of the entire sequence is extracted as the benchmark difference; For each fluctuation point, the absolute difference between the disease characteristic information of the fluctuation point and the benchmark difference is calculated as the degree of dispersion of the fluctuation point. For each fluctuation point, a data window of fixed length is set with the fluctuation point as the center. The mean of the data before the fluctuation point and the mean of the data after the fluctuation point are calculated respectively. Then, the absolute difference between the two means is calculated as the local mean drift of the fluctuation point. By dividing the product of instantaneous change and local mean drift by the sum of the degree of dispersion and a preset adjustment constant, the defect change index of each fluctuation point in each defect characteristic information sequence of each bridge defect area in each monitoring period is obtained.

[0009] Preferably, the extreme value detection method adopts the sliding window gradient analysis method, wherein for each data point in the sequence, the gradient change rate between it and the adjacent points in the window is calculated, and when the gradient direction is reversed, it is identified as an extreme value point.

[0010] Preferably, the process of obtaining the average disease change index includes: For each bridge defect area, in each defect feature information sequence in each monitoring period, verify whether the monitoring time where the defect point is located also has a defect feature information sequence in all other types of defects. If so, define the monitoring time as the defect monitoring time. For each fluctuation monitoring time, the arithmetic mean of the disease change index of the fluctuation points of all types of disease characteristic information sequences at the fluctuation monitoring time is calculated, and it is used as the average disease change index of each bridge disease area at each fluctuation monitoring time in each monitoring cycle.

[0011] Preferably, the process of obtaining the disease activity intensity index includes: For each fluctuation monitoring time in each monitoring cycle, clustering technology is used to group the average disease change index of all bridge disease areas into multiple clusters; The cluster to which the average defect change index of each bridge defect area belongs is used as the reference cluster for the bridge defect area. For each bridge defect area, at each fluctuation monitoring time in each monitoring cycle, extract the data window sequence centered on the fluctuation monitoring time as a local window sequence; For each bridge defect area at each fluctuation monitoring time in each monitoring cycle, the average Euclidean distance between the local window sequence of each defect feature information and the local window sequence of the same defect feature information of other bridge defect areas in the reference cluster is calculated as the sequence deviation of the defect feature information. The average of the sequence deviations of all disease characteristic information is taken as the overall sequence deviation at the time of fluctuation monitoring; By dividing the product of the average disease change index and the number of elements in the reference cluster by the sum of the overall sequence deviation and a preset adjustment factor, the disease activity intensity index of each bridge disease area at each fluctuation monitoring time in each monitoring cycle is obtained.

[0012] Preferably, the process of obtaining the disease impact coefficient includes: The intensity index of disease activity in each bridge disease area at all fluctuating monitoring times in each monitoring cycle is input into the threshold segmentation algorithm to obtain the optimal segmentation threshold. Based on the optimal segmentation threshold, the fluctuation monitoring time is divided into high-activity time and low-activity time; For each bridge defect area in each monitoring cycle, the absolute difference between the average value of the defect activity intensity index during all high-activity periods and the average value of the defect activity intensity index during all low-activity periods is calculated as the activity difference degree. The proportion of low-activity moments to the total number of monitoring moments in the monitoring period is calculated as the low-activity duration proportion. Calculate the product of the average value of the disease activity intensity index during all high-activity periods and the activity difference, and divide the product by the proportion of low-activity duration to obtain the disease impact coefficient of each bridge disease area in each monitoring period.

[0013] Preferably, the process of obtaining the model fitness coefficient includes: For each bridge defect area in each monitoring cycle, the mean of the location data and morphological data at each monitoring time is calculated as the initial geometric feature at that monitoring time; For each bridge defect area, identify all high-activity moments within the monitoring period; Calculate the sum of changes in initial geometric features between adjacent high-activity moments, including changes in position and changes in shape; Calculate the sum of time intervals between adjacent periods of high activity; Dividing the sum of the changes by the sum of the time intervals yields the model adaptation coefficients for each bridge defect area in each monitoring period.

[0014] Preferably, the process of obtaining the adjustment values ​​of the marker model parameters includes: The disease impact coefficient and the model fitness coefficient were normalized respectively. Calculate the sum of the normalized disease impact coefficient and the normalized model fitness coefficient; Multiplying the sum of the above by the initial preset value of the marker model parameters yields the adjusted value of the marker model parameters for each bridge defect area in each monitoring period.

[0015] Preferably, applying the adjusted values ​​of the marker model parameters to the mathematical model for the next monitoring cycle involves: In the initialization phase of the next monitoring cycle, the parameter settings of the mathematical model are updated using the parameter adjustment values ​​of the current cycle's marker model. During the monitoring cycle, the updated mathematical model is used to dynamically mark and predict the trends of bridge defects.

[0016] Compared with the prior art, the beneficial effects of the present invention are: By analyzing the fluctuation patterns of disease characteristic time series, multi-dimensional indicators, including instantaneous changes, differential characteristics, and local mean shifts, are calculated and further integrated with local sequence similarity measures to ultimately assess the intensity of disease activity. This approach departs from the conventional method of directly relying on absolute data values, enabling the extraction of comprehensive quantitative indicators characterizing the level of disease evolution activity from the morphology, trends, and historical comparisons of data sequences. It can more sensitively capture subtle abnormal changes and nonlinear characteristics in the disease development process; even if some characteristic values ​​have not exceeded preset thresholds, abnormal fluctuation patterns can be effectively identified, thereby improving the accuracy of disease evolution characterization and the potential for early warning.

[0017] After each monitoring cycle, the disease influence coefficient is derived based on the disease activity intensity index calculated within that cycle. This coefficient, combined with the model adaptation coefficient reflecting the morphology of the diseased area, generates adjustment values ​​for the marker model parameters used in the next monitoring cycle. This establishes a periodic, data-feedback-based closed-loop parameter adjustment process. This breaks the limitation of fixed parameters in traditional models, enabling the mathematical model used for disease marking to self-correct and optimize based on the latest structural state and disease development characteristics. Model parameters are no longer statically set but dynamically evolve as the monitoring cycle progresses, thus achieving adaptive tracking of the time-varying characteristics of the bridge structure by the marking model, ensuring the continuous reliability and accuracy of the marking results during long-term monitoring. Attached Figure Description

[0018] Figure 1 This is a schematic diagram illustrating the working principle of the bridge defect marking method based on mathematical models described in this invention. Figure 2 A flowchart illustrating the process of obtaining disease change indicators; Figure 3 A flowchart illustrating the process of obtaining disease activity intensity indicators; Figure 4 A time-series analysis diagram of the intensity of bridge damage activities; Figure 5 A parameter correlation analysis diagram for a bridge defect labeling model. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Please see Figure 1This invention provides a bridge defect labeling method based on a mathematical model. The method includes: collecting geometric feature information and defect feature information of each bridge defect area at each monitoring time in each monitoring cycle; for each defect feature information sequence, analyzing the fluctuation pattern in the sequence, including the instantaneous change of fluctuation points, the differential features of the sequence, and the degree of local mean shift, thereby calculating the defect change index of each fluctuation point in each defect feature information sequence of each bridge defect area in each monitoring cycle; integrating the defect change indices of each fluctuation point to obtain the average defect change index of each bridge defect area at each fluctuation monitoring time in each monitoring cycle; and fusing the local defect feature information sequences. Similarity measurement and average disease change index are used to assess the disease activity intensity index of each bridge disease area at each fluctuating monitoring time in each monitoring cycle. Based on the disease activity intensity index, the disease influence coefficient of each bridge disease area in each monitoring cycle is derived. Based on geometric feature information, the model fitness coefficient of each bridge disease area in each monitoring cycle is calculated. Combining the disease influence coefficient and the model fitness coefficient, the adjustment value of the labeling model parameter of each bridge disease area in each monitoring cycle is generated. This adjustment value is used as the labeling model parameter value when the mathematical model is used to label the disease in the next adjacent cycle of each monitoring cycle, so as to achieve parameter optimization of the bridge disease labeling model.

[0021] Example 1: The process of collecting geometric feature information and disease feature information includes: obtaining the location data and morphological data of each monitoring moment through the three-dimensional information model of the bridge as geometric feature information; and capturing the crack size and deformation degree of each monitoring moment using an image sensing device as disease feature information.

[0022] In practice, the acquisition of geometric and defect information is achieved through an integrated monitoring system. This system collaborates with the bridge's 3D information model and image sensing devices to acquire data. The bridge's 3D information model, as a digital twin of the bridge, stores precise 3D geometric and spatial relationship data of the bridge components. At each preset monitoring moment, the system automatically extracts the 3D spatial coordinates, boundary contour point cloud data, and surface curvature change information of the designated defect area from the bridge's 3D information model. These data are defined as location data and morphological data, collectively constituting geometric feature information. The image sensing devices are typically high-resolution industrial cameras or 3D scanners, which are fixedly deployed at observation points that can fully cover the defect area. At the same monitoring moment, the image sensing devices trigger image capture, obtaining high-definition digital images or point clouds of the defect area. Subsequently, computer vision algorithms automatically identify crack morphology and spalling areas in the images, and quantify and calculate the estimated length, width, and depth of cracks, as well as the estimated area and volume of the concrete spalling area. These quantification results are defined as crack size and deformation degree, collectively constituting defect feature information.

[0023] In some embodiments, the data acquisition operations of the bridge's 3D information model and the image sensing device are synchronized by a unified timing controller to ensure that the geometric feature information and the defect feature information acquired at each monitoring moment are strictly aligned on the time axis. In specific implementations, location data is obtained by querying the global coordinate system coordinates of the polygons or mesh vertices of the defect area in the bridge's 3D information model, while morphological data acquisition involves calculating the normal vector distribution of the triangular facets on the defect area's surface, as well as the area's volume or surface area. It can be understood that crack size capture relies on the 2D images acquired by the image sensing device, converting the measured pixel length and width in the image into actual millimeter or centimeter units using a pre-calibrated pixel-to-physical size conversion coefficient; deformation degree capture requires comparing images from consecutive monitoring moments and quantifying the deformation amount by calculating the displacement field of surface features using digital image correlation algorithms.

[0024] Optionally, the bridge's 3D information model will be updated periodically or event-driven based on the actual condition of the bridge. For example, after reinforcement and maintenance, the bridge's 3D information model needs to be updated accordingly to reflect the new geometric state, thereby ensuring the accuracy of geometric feature information collected in subsequent cycles. Specific implementation methods for the bridge's 3D information model include establishing a digital mechanism that updates synchronously with the bridge entity. Periodic updates follow a preset time interval plan, such as quarterly or annual comprehensive geometric data re-collection and reconstruction of the model to incorporate long-term deformation accumulation under environmental loads. Event-driven updates are triggered by bridge condition change events, such as immediately acquiring new point cloud data of the affected area through 3D laser scanning or photogrammetry after structural reinforcement and maintenance, component replacement, or major damage repair projects are detected. This data is then registered and fused with the original model to dynamically correct the position coordinates and morphological contours in the model, ensuring that the geometric feature information always remains consistent with the actual physical state of the bridge. The image sensing device is equipped with an environmental adaptability module, such as an automatic dimming filter and a protective cover, to cope with changes in day and night lighting, rain, fog, and other outdoor environmental interferences, ensuring that the captured defect feature information is clear and stable. In practice, all the raw data collected and the processed feature information are entered into a dedicated database. Each data record contains the bridge number, the disease area identifier, the monitoring period, the monitoring time, the geometric feature information field, and the disease feature information field, forming a complete time series dataset.

[0025] Example 2: See Figure 2The process of obtaining disease change indicators includes: for each disease characteristic information sequence of each bridge disease area in each monitoring period, using the extreme value detection method to identify all local peaks and valleys in the sequence, and marking these points as fluctuation points; for each fluctuation point, calculating the absolute difference between the disease characteristic information of the fluctuation point and the disease characteristic information of the previous adjacent monitoring time, as the instantaneous change of the fluctuation point; based on the first-order difference absolute value sequence of the disease characteristic information sequence, extracting the maximum difference value of the entire sequence as the benchmark difference; for each fluctuation point, calculating the disease at the fluctuation point. The absolute difference between the feature information and the baseline difference is used as the dispersion of the fluctuation point. For each fluctuation point, a data window of fixed length is set with the fluctuation point as the center. The mean of the data before the fluctuation point and the mean of the data after the fluctuation point are calculated separately. Then, the absolute difference between the two means is calculated as the local mean drift of the fluctuation point. By dividing the product of the instantaneous change and the local mean drift by the sum of the dispersion and a preset adjustment constant, the disease change index of each fluctuation point in each disease feature information sequence of each bridge disease area in each monitoring period is obtained. The extreme value detection method adopts the sliding window gradient analysis method, in which for each data point in the sequence, the gradient change rate between its adjacent points in the window is calculated. When the gradient direction reverses, it is identified as an extreme value point.

[0026] In practice, the acquisition of disease change indicators is based on the time series of disease characteristic information of bridge disease areas in each monitoring period. Here, the crack width sequence is used as an example. For a specified bridge disease area in a monitoring period, the crack width sequence records the width measurement values ​​of the area at multiple equally spaced monitoring times. An extreme value detection method is used to identify all local peak points and local valley points in the crack width sequence; these points are marked as fluctuation points. The extreme value detection method employs a sliding window gradient analysis method, where the length of the sliding window is set to cover five consecutive monitoring time data points. For each data point in the sequence, the difference in crack width between it and the previous and next data points within the sliding window is calculated and converted into a gradient rate of change. When the gradient rate of change changes from positive to negative, the point is identified as a local peak point; when the gradient rate of change changes from negative to positive, the point is identified as a local valley point.

[0027] In some embodiments, for each identified fluctuation point, the absolute difference between the crack width value of the fluctuation point and the crack width value at the previous adjacent monitoring time is calculated. This absolute difference is defined as the instantaneous change of the fluctuation point. Based on the first-order difference absolute value sequence of the disease feature information sequence, the maximum difference value of the entire sequence is extracted as the benchmark difference. The first-order difference absolute value sequence of the crack width sequence is obtained by calculating the absolute value of the difference between the crack widths at adjacent monitoring times. The maximum value of this difference sequence is found by traversing it. For each fluctuation point, the absolute difference between the crack width value of the fluctuation point and the benchmark difference is calculated. This absolute difference is defined as the dispersion of the fluctuation point.

[0028] Optionally, for each fluctuation point, a fixed-length data window is set centered on the fluctuation point, covering the data from two monitoring times before and after the fluctuation point. The mean values ​​of the data before and after the fluctuation point within the data window are calculated separately, and then the absolute difference between these two means is defined as the local mean drift of the fluctuation point. The disease change index at the fluctuation point is calculated through a mathematical formula that integrates instantaneous change, dispersion, and local mean drift. The formula for calculating the disease change index is:

[0029] in: Indicators representing changes in disease. Represents the instantaneous change at the fluctuation point. This represents the local mean shift at the point of fluctuation. This represents the degree of dispersion of the fluctuation points. This represents a preset adjustment constant, which is introduced to prevent numerical instability caused by a denominator that is zero or too small.

[0030] In practice, the above calculation process is applied in parallel to other defect feature information sequences of the same bridge defect area within the same monitoring period, such as crack length sequences and spalling area sequences. For each defect feature information sequence, the fluctuation point identification and defect change index calculation process is executed independently, thereby obtaining the defect change index of each fluctuation point in each defect feature information sequence of each bridge defect area in each monitoring period. It can be understood that the sliding window gradient analysis method accurately locates extreme points by analyzing the reversal of local gradient directions. This method can effectively filter out spurious fluctuations caused by minor undulations or noise in the sequence.

[0031] Example 3: See Figure 3The process of obtaining the average disease change index includes: for each fluctuation point in each disease characteristic information sequence of each bridge disease area in each monitoring period, verifying whether the monitoring time where the fluctuation point is located also has fluctuation points in all other types of disease characteristic information sequences. If so, the monitoring time is defined as the fluctuation monitoring time. For each fluctuation monitoring time, calculate the arithmetic mean of the disease change index of the fluctuation points of all types of disease characteristic information sequences at the fluctuation monitoring time, and use it as the average disease change index of each bridge disease area at each fluctuation monitoring time in each monitoring period. The process of obtaining the disease activity intensity index includes: for each fluctuation monitoring time in each monitoring cycle, using clustering technology to group the average disease change index of all bridge disease areas into multiple clusters; the cluster to which the average disease change index of each bridge disease area belongs is used as the reference cluster of the bridge disease area; for each disease feature information of each bridge disease area at each fluctuation monitoring time in each monitoring cycle, a data window sequence centered on the fluctuation monitoring time is extracted as a local window sequence; for each bridge disease area at each fluctuation monitoring time in each monitoring cycle, the average Euclidean distance between the local window sequence of each disease feature information and the local window sequences of the same disease feature information of other bridge disease areas in the reference cluster is calculated as the sequence deviation of the disease feature information; the average of the sequence deviations of all disease feature information is used as the overall sequence deviation of the fluctuation monitoring time; by dividing the product of the average disease change index and the number of elements in the reference cluster by the sum of the overall sequence deviation and a preset adjustment factor, the disease activity intensity index of each bridge disease area at each fluctuation monitoring time in each monitoring cycle is obtained.

[0032] In practice, the process of obtaining the average disease change index begins with the integrated analysis of the identified fluctuation points in each disease characteristic information sequence of each bridge disease area in each monitoring period. For a specific bridge disease area within a given monitoring period, its disease characteristic information includes crack width sequence, crack length sequence, and spalling area sequence. Each sequence independently completes the identification of fluctuation points and calculates the disease change index for each fluctuation point. The process verifies whether a fluctuation point in the crack width sequence also exists in the crack length sequence and spalling area sequence at that monitoring time. If the same monitoring time is identified as a fluctuation point in all other types of disease characteristic information sequences, then this monitoring time is defined as the fluctuation monitoring time. For each identified fluctuation monitoring time, the disease change indexes of the fluctuation points in the crack width sequence, crack length sequence, and spalling area sequence are extracted at that fluctuation monitoring time. The arithmetic mean of these three disease change indices is calculated, and this arithmetic mean is defined as the average disease change index for each bridge disease area at each fluctuation monitoring time in each monitoring period.

[0033] In some embodiments, the assessment process for the intensity index of bridge disease activity then proceeds. For all fluctuating monitoring times in the current monitoring period, clustering techniques are used to group the average disease change index calculated for all bridge disease areas at that fluctuating monitoring time. The clustering technique employs the K-means algorithm to divide the set of average disease change index values ​​into multiple clusters. The cluster to which the average disease change index value of a specified bridge disease area belongs is used as the reference cluster for that specified bridge disease area. For the disease characteristic information of this specified bridge disease area at the current fluctuating monitoring time in the current monitoring period, taking the current fluctuating monitoring time as the center, two monitoring times are taken before and after, and a crack width subsequence containing data from five consecutive monitoring times is extracted. This subsequence is defined as the local window sequence of crack width characteristics. The same method is applied to the crack length sequence and the spalling area sequence to generate their respective local window sequences.

[0034] Optionally, the Euclidean distance between the local window sequence of crack width in this specified bridge defect area and the local window sequences of crack width in all other bridge defect areas within its reference cluster at the same time window is calculated. The average of all calculated Euclidean distances is defined as the sequence deviation of the crack width feature. The same calculation is repeated for the crack length feature and the spalling area feature to obtain the sequence deviations of the crack length feature and the spalling area feature, respectively. The sequence deviations of the crack width feature, the crack length feature, and the spalling area feature are added together and divided by three. The resulting value is defined as the overall sequence deviation at the current fluctuation monitoring time. It can be understood that the defect activity intensity index is calculated by combining the average defect change index, the reference cluster size, and the overall sequence deviation using a mathematical relationship. The formula is:

[0035] in: Indicators representing the intensity of disease activity. This represents the average change in disease incidence. Represents the number of elements in the reference cluster. Represents the overall sequence deviation. This represents a preset adjustment factor.

[0036] In practice, the above calculation process is performed independently for each fluctuation monitoring moment and each bridge defect area, thereby obtaining the defect activity intensity index of each bridge defect area at each fluctuation monitoring moment in each monitoring cycle. It can be understood that by forming reference clusters through clustering, the calculation of sequence bias is performed within a group of bridge defect areas with similar defect development patterns, enhancing the rationality of the comparison. The number of clusters in the K-means clustering algorithm is predetermined based on the historical data distribution using the silhouette coefficient method.

[0037] Example 4: The process of obtaining the disease impact coefficient includes: inputting the disease activity intensity index of each bridge disease area at all fluctuating monitoring times in each monitoring cycle into the threshold segmentation algorithm to obtain the optimal segmentation threshold; dividing the fluctuating monitoring times into high activity times and low activity times according to the optimal segmentation threshold; for each bridge disease area in each monitoring cycle, calculating the absolute difference between the average value of the disease activity intensity index at all high activity times and the average value of the disease activity intensity index at all low activity times as the activity difference degree; calculating the proportion of the number of low activity times to the total number of monitoring times in the monitoring cycle as the low activity duration proportion; calculating the product of the average value of the disease activity intensity index at all high activity times and the activity difference degree, and dividing the product by the low activity duration proportion to obtain the disease impact coefficient of each bridge disease area in each monitoring cycle. The process of obtaining the model fitness coefficient includes: for each bridge defect area in each monitoring period, calculating the mean of the location data and morphological data at each monitoring time as the initial geometric features of the monitoring time; for each bridge defect area, determining all high-activity times within the monitoring period; calculating the sum of the changes in the initial geometric features between adjacent high-activity times, including changes in location and morphology; calculating the sum of the time intervals between adjacent high-activity times; and dividing the sum of the changes by the sum of the time intervals to obtain the model fitness coefficient of each bridge defect area in each monitoring period.

[0038] In practice, the process of obtaining the disease impact coefficient is based on the set of disease activity intensity indicators for each fluctuating monitoring time in a specified bridge disease area within a monitoring period. This set of indicators contains multiple values ​​arranged chronologically. The set of indicators is then input into a threshold segmentation algorithm, which employs Otsu's method. This algorithm iterates through all thresholds, dividing the set into two groups, and calculates the inter-group variance. The threshold with the largest inter-group variance is selected as the optimal segmentation threshold. Based on this optimal threshold, the disease activity intensity indicator for each fluctuating monitoring time is compared with the threshold. Fluctuating monitoring times with an indicator greater than the optimal threshold are classified as high-activity times, while those with an indicator less than or equal to the threshold are classified as low-activity times.

[0039] In some embodiments, for the monitoring period data after segmentation, the average value of the disease activity intensity index for all high-activity moments is calculated, and the average value of the disease activity intensity index for all low-activity moments is also calculated. The absolute difference between these two average values ​​is defined as the activity variability. The proportion of low-activity moments to the total number of fluctuating monitoring moments within the monitoring period is calculated; this proportion is defined as the low-activity duration proportion. The disease impact coefficient is calculated using a mathematical formula that integrates the average disease activity intensity index for high-activity moments, the activity variability, and the low-activity duration proportion. The formula for calculating the disease impact coefficient is:

[0040] in: Represents the disease impact coefficient. This represents the average value of the disease activity intensity index across all periods of high activity. Represents the degree of difference in activities. This represents the proportion of low activity duration.

[0041] Optionally, the process for obtaining the model fitness coefficient and the calculation of the disease influence coefficient use the same high-activity time segmentation results. For the same bridge disease area within the same monitoring period, location data and morphological data for each monitoring time are extracted from the geometric feature information. Location data can be a three-dimensional coordinate point, and morphological data can be an area value. The coordinate mean of all collected location data at each monitoring time is calculated as the location mean for that monitoring time. Simultaneously, the arithmetic mean of all collected morphological data at each monitoring time is calculated as the morphological mean for that monitoring time. The location mean and morphological mean together constitute the initial geometric features for that monitoring time. All monitoring times marked as high-activity times within the monitoring period are identified and arranged in chronological order.

[0042] In practical implementation, the sum of changes in initial geometric features between adjacent high-activity moments is calculated. For example, the three-dimensional Euclidean distance of the mean position between the first and second high-activity moments is calculated as the positional change, and the absolute difference of the mean morphological features between the first and second high-activity moments is calculated as the morphological change. The positional and morphological changes between all pairs of adjacent high-activity moments are summed to obtain the total positional and total morphological changes. The sum of the total positional and total morphological changes is then obtained. The sum of time intervals between adjacent high-activity moments is also calculated, with time intervals in hours or days. The model fitness coefficient is obtained by dividing the sum of changes by the sum of time intervals, using the following formula:

[0043] in: The model fitness coefficient represents the model's performance. Represents the sum of changes. This represents the sum of time intervals. This can be understood by referring to Table 1, which shows the breakdown of high-activity periods within a monitoring cycle.

[0044] Table 1: Classification of Activity Levels at Fluctuation Monitoring Times within a Certain Monitoring Period

[0045] It is understandable that the disease impact coefficient The numerator reflects the intensity and differentiation of the disease during its active phase, while the denominator reflects the relative length of the inactive phase, thus quantifying the overall impact potential of the disease within that cycle. Model fitness coefficient This characterizes the average rate of change of the geometric features of the diseased area over time under high activity conditions.

[0046] See Figure 4 This is a time-series analysis chart of bridge disease activity intensity, a core tool in the disease impact coefficient calculation stage. It displays the comparison between disease activity intensity and the optimal segmentation threshold at different monitoring times. Intensity indices at times t_5, t_14, t_23, t_31, and t_40 are significantly higher than the threshold (8.83), representing periods of high disease activity; intensity indices at times t_9, t_18, t_27, and t_35 are lower than the threshold, representing periods of relatively calm disease activity. The intensity indices exhibit an alternating "peak-trough" fluctuation pattern, indicating a clear periodic change in disease activity. This chart is used to divide disease activity periods, quickly identifying high / low activity times through the optimal segmentation threshold, providing fundamental data support for subsequent calculations of the disease impact coefficient and assessment of disease risk.

[0047] Example 5: The process of obtaining the labeled model parameter adjustment values ​​includes: normalizing the disease influence coefficient and the model fitness coefficient respectively; calculating the sum of the normalized disease influence coefficient and the normalized model fitness coefficient; multiplying the above sum by the initial preset value of the labeled model parameters to obtain the labeled model parameter adjustment values ​​for each bridge disease area in each monitoring cycle. Applying the labeled model parameter adjustment values ​​to the mathematical model of the next monitoring cycle involves: in the initialization stage of the next monitoring cycle, updating the parameter settings of the mathematical model using the labeled model parameter adjustment values ​​of the current cycle; during the execution of the monitoring cycle, using the updated mathematical model to perform dynamic labeling and trend prediction of bridge diseases.

[0048] In practice, the process of obtaining the labeled model parameter adjustment value is based on the calculated disease impact coefficient and model fitness coefficient. For a specified monitoring period and a specified bridge disease area, the calculation of the labeled model parameter adjustment value first requires normalization of the disease impact coefficient and model fitness coefficient. The normalization process uses the min-max normalization method. This requires obtaining the set of disease impact coefficients for all bridge disease areas within the current monitoring period, identifying the maximum and minimum values ​​in this set, and then subtracting the minimum value from the disease impact coefficient for each bridge disease area and dividing by the difference between the maximum and minimum values ​​to obtain the normalized disease impact coefficient. The same min-max normalization method is then used to process the set of model fitness coefficients to obtain the normalized model fitness coefficients. The normalized disease impact coefficient and the normalized model fitness coefficient are then added together to obtain a new composite parameter value. The labeled model parameter adjustment value is obtained by multiplying this composite parameter value by the initial preset value of the labeled model parameters. The formula for calculating the labeled model parameter adjustment value is as follows:

[0049] in: This represents the adjusted values ​​of the labeled model parameters. This represents the initial preset values ​​for the marker model parameters. This represents the normalized disease impact coefficient. This represents the normalized model fitness coefficient.

[0050] In some embodiments, applying the adjusted marker model parameters to the mathematical model for the next monitoring cycle involves two phases. During the initialization phase of the next monitoring cycle, the system reads the adjusted marker model parameters calculated for the current bridge defect area in the current monitoring cycle. These adjusted parameters are then used to directly update the parameter settings in the mathematical model corresponding to this defect area, replacing the original parameter values. During the execution of the monitoring cycle, the mathematical model uses the updated parameter values ​​for dynamic marker marking and trend prediction of bridge defects. Dynamic marker marking includes automatic classification and severity assessment of newly acquired defect characteristics, while trend prediction includes extrapolating the development rate and future state of defects based on time-series data.

[0051] Optional, initial preset values ​​for the marker model parameters. These are baseline parameters set when the system is first deployed or reset. They can be a scalar coefficient that controls the sensitivity of the model, or a weight vector of a specific computational layer within the model. Min-max normalization ensures that the disease impact coefficient and model fitness coefficient with different dimensions or numerical ranges can be mapped to similar numerical intervals, usually [0,1], making the summation of the two mathematically reasonable and comparable.

[0052] In practical implementation, the model parameter adjustment values ​​are marked. The calculation and updating are performed periodically. At the end of each monitoring cycle, new labeling model parameter adjustment values ​​are generated for each bridge distress area based on the data of that cycle, and applied to the mathematical model at the beginning of the next monitoring cycle. After obtaining the updated parameters, the mathematical model's internal processing logic, such as the feature extraction threshold, the classification decision boundary, or the coefficients of the prediction function, will be adjusted accordingly, so that its labeling behavior can adaptively reflect the activity impact and geometric change characteristics of bridge distress in the previous monitoring cycle.

[0053] See Figure 5 This is a parameter correlation analysis diagram of a bridge defect labeling model, a core tool in the parameter optimization stage of the labeling model. It is used to show the changes and correlations between the defect impact coefficient and the model fitness coefficient in different monitoring periods. In period 2, both the defect impact coefficient (approximately 1.5) and the model fitness coefficient (approximately 1.5) reach their peaks, indicating that defects are active and geometric features change rapidly during this period, making it a high-risk time. In period 3, the model fitness coefficient drops to its lowest point (approximately 0.05), but the defect impact coefficient remains around 1.0, indicating that the defect impact has not weakened but the changes in geometric features have slowed down. Both exhibit synchronous fluctuations of alternating peaks and troughs (except in period 3), reflecting the correlation between defect impact and changes in geometric features. This is used for the dynamic adjustment of the labeling model parameters. Through the correlation analysis between the two, the parameter adjustment values ​​for different periods are determined, achieving precise optimization of the bridge defect labeling model.

[0054] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0055] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for marking bridge defects based on a mathematical model, characterized in that, The method performs the following operations sequentially: Collect geometric and defect characteristics of each bridge defect area at each monitoring time during each monitoring cycle; For each disease characteristic information sequence, the fluctuation pattern in the sequence is analyzed, including the instantaneous change of the fluctuation point, the differential characteristics of the sequence, and the degree of local mean shift, so as to calculate the disease change index of each fluctuation point in each disease characteristic information sequence of each bridge disease area in each monitoring period. By integrating the disease change indicators at each fluctuation point, the average disease change indicators of each bridge disease area at each fluctuation monitoring time in each monitoring cycle are obtained. By integrating the similarity measure of local disease characteristic information sequences and the average disease change index, the intensity index of disease activity in each bridge disease area at each fluctuation monitoring time in each monitoring cycle is evaluated. Based on the disease activity intensity index, the disease impact coefficient of each bridge disease area in each monitoring period was derived; Based on geometric feature information, the model adaptation coefficient of each bridge defect area in each monitoring period is calculated; By combining the disease impact coefficient and the model adaptation coefficient, the adjustment values ​​of the marker model parameters for each bridge disease area in each monitoring period are generated. These adjustment values ​​are then used as the marker model parameter values ​​for each bridge disease area when using the mathematical model to mark the disease in the next adjacent period of each monitoring period, so as to achieve parameter optimization of the bridge disease marking model.

2. The bridge defect marking method based on mathematical models as described in claim 1, characterized in that, The process of collecting the geometric feature information and disease feature information includes: The location and shape data at each monitoring time are obtained using the bridge's three-dimensional information model as geometric feature information; Image sensing devices are used to capture crack size and deformation at each monitoring time as characteristic information of the disease.

3. The bridge defect marking method based on mathematical models as described in claim 1, characterized in that, The process of obtaining the disease change indicators includes: For each bridge defect area in each monitoring period, the extreme value detection method is used to identify all local peak and valley points in the sequence and mark these points as fluctuation points. For each fluctuation point, the absolute difference between the disease characteristic information of the fluctuation point and the disease characteristic information of the previous adjacent monitoring time is calculated as the instantaneous change of the fluctuation point. Based on the first-order difference absolute value sequence of disease characteristic information sequence, the maximum difference value of the entire sequence is extracted as the benchmark difference; For each fluctuation point, the absolute difference between the disease characteristic information of the fluctuation point and the benchmark difference is calculated as the degree of dispersion of the fluctuation point. For each fluctuation point, a data window of fixed length is set with the fluctuation point as the center. The mean of the data before the fluctuation point and the mean of the data after the fluctuation point are calculated respectively. Then, the absolute difference between the two means is calculated as the local mean drift of the fluctuation point. By dividing the product of instantaneous change and local mean drift by the sum of the degree of dispersion and a preset adjustment constant, the defect change index of each fluctuation point in each defect characteristic information sequence of each bridge defect area in each monitoring period is obtained.

4. The bridge defect marking method based on mathematical models as described in claim 3, characterized in that, The extreme value detection method adopts the sliding window gradient analysis method, in which for each data point in the sequence, the gradient change rate between it and the adjacent points in the window is calculated, and when the gradient direction is reversed, it is identified as an extreme value point.

5. The bridge defect marking method based on mathematical models as described in claim 1, characterized in that, The process of obtaining the average disease change index includes: For each bridge defect area, in each defect feature information sequence in each monitoring period, verify whether the monitoring time where the defect point is located also has a defect feature information sequence in all other types of defects. If so, define the monitoring time as the defect monitoring time. For each fluctuation monitoring time, the arithmetic mean of the disease change index of the fluctuation points of all types of disease characteristic information sequences at the fluctuation monitoring time is calculated, and it is used as the average disease change index of each bridge disease area at each fluctuation monitoring time in each monitoring cycle.

6. The bridge defect marking method based on mathematical models as described in claim 1, characterized in that, The process of obtaining the disease activity intensity index includes: For each fluctuation monitoring time in each monitoring cycle, clustering technology is used to group the average disease change index of all bridge disease areas into multiple clusters; The cluster to which the average defect change index of each bridge defect area belongs is used as the reference cluster for the bridge defect area. For each bridge defect area, at each fluctuation monitoring time in each monitoring cycle, extract the data window sequence centered on the fluctuation monitoring time as a local window sequence; For each bridge defect area at each fluctuation monitoring time in each monitoring cycle, the average Euclidean distance between the local window sequence of each defect feature information and the local window sequence of the same defect feature information of other bridge defect areas in the reference cluster is calculated as the sequence deviation of the defect feature information. The average of the sequence deviations of all disease characteristic information is taken as the overall sequence deviation at the time of fluctuation monitoring; By dividing the product of the average disease change index and the number of elements in the reference cluster by the sum of the overall sequence deviation and a preset adjustment factor, the disease activity intensity index of each bridge disease area at each fluctuation monitoring time in each monitoring cycle is obtained.

7. The bridge defect marking method based on mathematical model as described in claim 1, characterized in that, The process of obtaining the disease impact coefficient includes: The intensity index of disease activity in each bridge disease area at all fluctuating monitoring times in each monitoring cycle is input into the threshold segmentation algorithm to obtain the optimal segmentation threshold. Based on the optimal segmentation threshold, the fluctuation monitoring time is divided into high-activity time and low-activity time; For each bridge defect area in each monitoring cycle, the absolute difference between the average value of the defect activity intensity index during all high-activity periods and the average value of the defect activity intensity index during all low-activity periods is calculated as the activity difference degree. The proportion of low-activity moments to the total number of monitoring moments in the monitoring period is calculated as the low-activity duration proportion. Calculate the product of the average value of the disease activity intensity index during all high-activity periods and the activity difference, and divide the product by the proportion of low-activity duration to obtain the disease impact coefficient of each bridge disease area in each monitoring period.

8. The bridge defect marking method based on mathematical model as described in claim 2, characterized in that, The process of obtaining the model fitness coefficient includes: For each bridge defect area in each monitoring cycle, the mean of the location data and morphological data at each monitoring time is calculated as the initial geometric feature at that monitoring time; For each bridge defect area, identify all high-activity moments within the monitoring period; Calculate the sum of changes in initial geometric features between adjacent high-activity moments, including changes in position and changes in shape; Calculate the sum of time intervals between adjacent periods of high activity; Dividing the sum of the changes by the sum of the time intervals yields the model adaptation coefficients for each bridge defect area in each monitoring period.

9. The bridge defect marking method based on mathematical model as described in claim 1, characterized in that, The process of obtaining the adjusted values ​​of the marker model parameters includes: The disease impact coefficient and the model fitness coefficient were normalized respectively. Calculate the sum of the normalized disease impact coefficient and the normalized model fitness coefficient; Multiplying the sum of the above by the initial preset value of the marker model parameters yields the adjusted value of the marker model parameters for each bridge defect area in each monitoring period.

10. The bridge defect marking method based on mathematical model as described in claim 1, characterized in that, The application of the adjusted values ​​of the marked model parameters to the mathematical model for the next monitoring cycle involves: In the initialization phase of the next monitoring cycle, the parameter settings of the mathematical model are updated using the parameter adjustment values ​​of the current cycle's marker model. During the monitoring cycle, the updated mathematical model is used to dynamically mark and predict the trends of bridge defects.

Images