A decision-making method and system for asphalt pavement maintenance considering multi-dimensional influencing factors

Abstract

The present invention relates to an asphalt pavement maintenance decision-making method and system that considers multi-dimensional influencing factors, and belongs to the field of pavement maintenance technology. The present invention constructs a multi-source data set of asphalt pavement performance, designs an importance analysis method of average weight fusion, and performs feature engineering operations on the data, including feature generation, selection, and conversion, to more accurately characterize the problem domain and improve model efficiency. After encoding and feature dimensionality reduction of some features, the multi-source feature data set is sorted by a variety of statistical and machine learning methods to sort the feature importance, and the feature set that has a significant impact on the prediction of asphalt pavement performance is screened out based on the sorting results. The fusion prediction model based on OOA optimization accurately captures and predicts the changing trend of pavement performance. Taking into account the current performance status and performance prediction trend, the decision on maintenance level and specific maintenance method is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of pavement maintenance, and in particular to an asphalt pavement maintenance decision-making method and system that considers multi-dimensional influencing factors. Background Art

[0002] In order to keep the highway in good condition and prevent its quality from deteriorating, highway maintenance is necessary. In recent years, my country's expressway construction has developed rapidly. With the increase in highway mileage, the workload of maintenance, inspection and management after the completion of the highway has also increased sharply.

[0003] Early research on asphalt pavement performance prediction, both domestically and internationally, was often limited by the amount of available data and often relied on empirical regression analysis, probabilistic statistical models, and other classic prediction methods. With technological advancements and the accumulation of data, researchers have gradually turned to multivariate data analysis using machine learning techniques and neural network methods to achieve more accurate predictions. These explorations and research provide important theoretical foundations and valuable references for this study. However, current research still faces challenges such as incomplete understanding of influencing factors and insufficient prediction accuracy, requiring further in-depth study. Summary of the Invention

[0004] The present invention aims to solve the above technical problems and provide an asphalt pavement maintenance decision-making method and system that considers multi-dimensional influencing factors.

[0005] In order to solve the above technical problems, the technical solution provided by the present invention is:

[0006] A method for asphalt pavement maintenance decision-making considering multi-dimensional influencing factors includes the following steps:

[0007] S1. Asphalt pavement data integration and data quality improvement:

[0008] Collect and integrate the evaluation indicators and multi-source influencing factors that need to be considered in the performance evaluation of asphalt pavement. The evaluation indicators are PCI, RQI, RDI and SRI. The multi-source influencing factors are analyzed and characterized to lay a data foundation for the construction of data-driven performance prediction models and maintenance decisions.

[0009] S2. Importance analysis of factors affecting asphalt pavement performance based on average weighted multi-method fusion:

[0010] The evaluation indicators and multi-source influencing factors of asphalt pavement performance are screened, and the prediction performance is maintained while streamlining the model input. A large amount of feature data is standardized and feature coding is implemented. The importance of the factors affecting asphalt pavement performance is analyzed, and the results are sorted according to importance to find the most predictive feature set.

[0011] S3. Establishment of OOA optimization fusion model for asphalt pavement:

[0012] Establish a predictive OOA optimization fusion model to predict and analyze asphalt pavement performance;

[0013] S4. Establishment of a multi-source maintenance history dataset:

[0014] A multi-source maintenance history dataset was constructed, and a maintenance decision-making method based on the inverse variance weighted improved random forest model was established to improve the accuracy of maintenance decisions.

[0015] S401: Analyzing historical highway data, the PSSI (Structural Strength Index) is consistently above 90, indicating no need for maintenance. Therefore, the pavement indicators selected are PCI, RDI, RQI, and SRI. The collected historical maintenance data and data on unmaintained sections are combined to construct a maintenance method classification dataset, enabling decisions to be made for seven maintenance methods. A maintenance level classification dataset is also constructed, enabling decisions to be made for three maintenance levels.

[0016] S402: Construct a multi-index maintenance method dataset that includes historical data and unmaintained road sections. This dataset incorporates multi-source features including pavement disease data, road basic information data, and traffic load data based on PCI, RDI, RQI, and SRI indicator data to improve the dataset's ability to represent maintenance decision-making issues.

[0017] S5. Decision-making method:

[0018] Construct a multi-source data set of maintenance history, and establish a maintenance decision-making method based on the inverse variance weighted improved random forest model to improve the accuracy of maintenance decisions. Use the prediction results and current situation to select the maintenance decision-making method.

[0019] S501: Construct the OOB data for the trees in the random forest method. The OOB data is an independent validation set for each tree that was not involved in the training. During the training process, each tree is randomly selected from the original training set using replacement sampling as training data. The number of data selected is usually the same as the size of the original training set. Due to the replacement sampling, some data will be repeatedly selected, while others may not be selected. The unselected data constitutes the OOB data of the tree.

[0020] S502: The predictions of the multiple decision trees contained in the random forest are given the same weight to calculate the final prediction result; when using the inverse variance weighting method IVW, a weight is assigned to the prediction of each tree, and the weight of each tree is inversely proportional to its prediction error on the validation set.

[0021] The basic principle of inverse variance weighting is that measurements with high credibility (small errors) should have a greater influence on the integrated results, while measurements with large errors should have a smaller influence. Variance reflects the uncertainty of a measurement and can be considered the degree of data fluctuation. In the task of maintenance decision-making, the decision error rate on the validation set is used as the basis for weight distribution. The weight of each tree is the normalized value of the inverse of the decision error rate. The calculation formula is as follows:

[0022]

[0023] Where n represents the number of decision trees in the random forest algorithm; w i represents the weight of the i-th tree; E i Represents the decision error rate of the i-th tree.

[0024] Each tree votes on the decision result. After inverse variance weighting, the result with the highest vote is taken as the final result of the model to obtain the highway maintenance decision-making method.

[0025] The multi-source influencing factors include climate, traffic flow, road infrastructure information, road damage and maintenance history data.

[0026] The importance of factors affecting asphalt pavement performance was analyzed by using PCA and Pearson analysis methods to achieve feature dimensionality reduction. The importance analysis method based on the fusion of Spearman, Permutation and SHAP average weights was used to rank the importance of multi-source influencing factors of asphalt pavement performance as the basis for subsequent data selection.

[0027] The aforementioned historical inspection data of factors affecting asphalt pavement performance (PCI, PQI, RDI, SRI), basic road information (road age, material, structure), climate data (temperature, precipitation), traffic flow (equivalent, passenger-to-freight ratio, cumulative equivalent), disease data (type, location, area), and maintenance history (time, location, method).

[0028] The multi-source maintenance history dataset includes pre-maintenance performance, maintenance time, maintenance location, maintenance method and post-maintenance performance. The respective datasets are collected, and after importance analysis, the dataset is reconstructed and maintenance decision training is performed.

[0029] The importance analysis of factors affecting asphalt pavement performance by fusion of average weighted multiple methods in step 2 includes the following steps:

[0030] S201: The Spearman rank correlation coefficient is often used to measure the dependence of two variables. The characteristics and indicators involved often do not meet the requirements of normal distribution. The formula of the Spearman correlation coefficient is shown in formula (1).

[0031]

[0032] Where n is the number of variables; d i is the rank difference between two variables (i = 1, 2, 3...n). The rank of a value is determined by its relative size in a sequence. If there are identical values ​​in the sequence, their rank will be the average of their positions. The difference between the ranks of two different values ​​is called the rank difference.

[0033] S202: Permutation-based feature importance analysis destroys the relationship between the original features and the target variable by randomly permuting the feature values. The feature importance is then evaluated by comparing the performance differences between the original model and the permuted model. The calculation requires training a model. By randomly permuting the data distribution of each feature, the order of the original feature values ​​is disrupted. The model is retrained using the permuted feature values ​​and the true target variable, and the change in model performance is calculated. If the performance of the permuted model decreases significantly, it can be considered that the feature has a greater impact on the model performance, that is, the feature importance is high.

[0034] S203: SHAP is an interpretable model prediction method based on Shapley values ​​in game theory. In machine learning, its role is to quantify the contribution of each feature to illustrate their importance to model prediction. The SHAP method feature importance analysis process is as follows:

[0035] S20301: Initialize data: select a specific data instance and determine its characteristic values;

[0036] S20302: Define model: Define the machine learning model used, such as a linear regression model;

[0037] S20303: Calculate baseline value: The baseline value is the predicted value of the model when no features are involved;

[0038] S20304: Calculate marginal contribution: For each feature, consider all possible feature combinations and calculate the change in predicted value when adding that feature;

[0039] For feature i, its SHAP value is defined as in formula (2).

[0040]

[0041] Where S is the subset of all features except feature i, |S| is the size of S, i.e., the number of features in S, ! represents the factorial, N is the total number of features, and f(S) is the predicted value of the model on the feature subset (S).

[0042] Formula (2) calculates the marginal contribution of feature i under all possible feature subsets and performs weighted summation through the weights in combinatorial mathematics;

[0043] S20305: Assign weights: Assign weights to each feature's marginal contribution according to the definition of Shapley values; weights are assigned based on the number and eigenvalues ​​of features in the combination;

[0044] S204: Use three importance analysis methods to score and rank the factors affecting asphalt pavement performance. Due to differences in the measurement criteria and data characteristics of different methods, the final rankings have some commonalities but also some differences. To avoid the limitations and one-sidedness of using only one method, the Spearman correlation coefficient method, the permutation method, and the SHAP method are integrated. The three importance analysis methods are assigned equal weights and then combined to ensure the validity of the importance weight analysis results of the factors affecting asphalt pavement. The process is as follows:

[0045] S20401: The three methods have different dimensions for the results, so we need to unify the dimensions. For the correlations obtained by the Spearman correlation analysis method, we need to take the absolute value before calculating.

[0046] S20402: Process the weight of each method using formula (3);

[0047]

[0048] Where, F i is the importance weight of the i-th feature after de-dimensioning; I i is the importance weight of the i-th feature before de-dimensioning; n is the number of features;

[0049] S20403: Take the average of the feature importance weights of the three processed methods to obtain the feature importance weights of each fused indicator, re-sort the fused feature importance weights, and use the result as the basis for feature screening.

[0050] The steps of establishing the OOA optimization fusion model for predicting asphalt pavement performance and performing prediction analysis on asphalt pavement performance in step 3 are as follows:

[0051] S301: Matrix modeling is performed according to formula (4);

[0052] S302: Randomly initialize the position of the osprey in the search space according to Publication (5);

[0053]

[0054] x i,j =lb j+r i,j ·(ub j -lb j )(5);

[0055] Where N is the number of ospreys; m is the number of problem variables; X is the osprey position population matrix; X i is the initial position of the i-th osprey, i=1,2...,n; X i,j is the initial position of the i-th osprey in the j-th problem variable, j = 1, 2, ..., m; lb j 、ub j is the lower and upper bounds of the j-th problem variable; r i,j is a random number with a value range of [0,1];

[0056] S303: Calculate the objective function of each osprey, and the evaluation can be expressed as a vector of formula (6);

[0057]

[0058] Where F is the objective function value; F i is the objective function value of the i-th osprey;

[0059] S304: Phase 1 Update:

[0060] The position of each osprey with a higher objective function value in the search space represents the location of the prey fish school; the fish school position of each osprey is expressed using formula (7);

[0061] FP i ={X k |k∈{1,2,...,N}∧F k <F i}∪{X best}(7);

[0062] Where FP i is the set of fish school positions of the i-th osprey; X best It's F i The optimal corresponding X i value;

[0063] When an osprey attacks a fish randomly, it will move toward the fish's location. The new position of the osprey is calculated using equations (8) and (9). If the new position improves the value of the objective function, it replaces the previous position of the osprey.

[0064]

[0065] Where, is the new position of the i-th osprey in the j-th problem variable; SF i,jis the position of the fish selected by the i-th osprey in the j-th problem variable; I i,j The value of is one of {1,2};

[0066] If the osprey improves the value of the objective function in the new position, the new position of the osprey after the update is calculated by formula (10);

[0067]

[0068] Where, is the new position of the i-th osprey; yes The objective function value of

[0069] S305: For each member of the population, use equations (11) and (12) to calculate a new random position as a position suitable for eating fish; if the value of the objective function is improved at this new position, replace the previous position of the corresponding osprey according to equation (13);

[0070]

[0071] An asphalt pavement maintenance system that considers multi-dimensional influencing factors includes:

[0072] Data collection module, used to collect and integrate the evaluation indicators and multi-source influencing factors that need to be considered in the asphalt pavement performance evaluation;

[0073] Data analysis module, used to screen the evaluation indicators and multi-source influencing factors of asphalt pavement performance;

[0074] The asphalt pavement performance prediction module is used to predict and analyze asphalt pavement performance and verify the performance of neural networks and machine learning algorithms in pavement performance prediction tasks, including gray correlation analysis. It introduces the OOA algorithm to optimize the hyperparameters of the machine learning model to address the impact of hyperparameter selection on the performance of the machine learning model. It also establishes a multi-model fusion prediction method based on stacking, leveraging the complementary advantages of multiple models to achieve high-precision prediction of asphalt pavement performance.

[0075] The visualization interaction module is used to build a resource integration database based on the fusion data and maintenance detection information, so that users can interact with the resource integration database through a three-dimensional visualization window.

[0076] After adopting the above method, the present invention has the following advantages:

[0077] This paper constructs a multi-source dataset of asphalt pavement performance and designs an importance analysis method using average weight fusion. To address the issues of insufficient correlation analysis between multi-source data on pavement influencing factors and incomplete consideration of influencing factors, the paper extracts fine-grained features such as monthly and seasonal characteristics of rainfall, temperature, and traffic flow data, and incorporates features from historical maintenance data and disease data to construct a multi-source dataset of asphalt pavement performance influencing factors. The multi-source influencing factors are ranked by importance, and the characteristic factors with the greatest impact on asphalt pavement performance prediction are selected based on the ranking results.

[0078] This asphalt pavement performance prediction method, which uses an OOA optimization fusion model, addresses the issue of insufficient accuracy in pavement performance prediction models. Considering that different models are suitable for predicting different performance indicators (PCI, RQI, RDI, and SRI), a stacking method is used to combine the prediction advantages of RF, XGBoost, and CatBoost models. OOA is then used for parameter optimization to make the model more suitable for pavement performance prediction tasks based on multi-source feature datasets. This method solves the overfitting problem that can result from biased data learning by a single model, achieving high-precision prediction of asphalt pavement performance.

[0079] A multi-source data maintenance decision-making method based on random forests modified with inverse variance weights was proposed. To address the low accuracy of existing asphalt pavement maintenance decision-making methods, a multi-source dataset of maintenance history was constructed. This dataset provides a stronger representation of maintenance decision-making than traditional decision-making methods that only consider performance indicators (PCI, RQI, RDI, and SRI), thereby improving the accuracy of maintenance decisions. Furthermore, a multi-source data maintenance decision-making method based on random forests modified with inverse variance weights was designed, which not only enables decisions on maintenance levels but also on specific maintenance methods.

[0080] The above summary is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments and features described above, further aspects, embodiments and features of the present invention will be readily apparent by reference to the accompanying drawings and the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0082] Figure 1 It is a technical flow chart of the present invention;

[0083] Figure 2is an analysis chart of a multi-source data set of asphalt pavement performance according to the present invention;

[0084] Figure 3 This is a representative area 1 annual temperature change map of the present invention;

[0085] Figure 4 It is a maintenance benefit diagram of the preventive maintenance of the present invention;

[0086] Figure 5 It is a maintenance benefit diagram of the repair and maintenance of the present invention;

[0087] Figure 6 is a flow chart of the present invention;

[0088] Figure 7 It is a comparison chart of the IVW-RF maintenance decision results of the present invention. DETAILED DESCRIPTION

[0089] Specific embodiments of the present invention will now be mentioned in detail. Although the present invention is described in conjunction with these specific embodiments, it should be appreciated that the present invention is not intended to be limited to these specific embodiments. On the contrary, these embodiments are intended to cover substitutions, changes or equivalent embodiments that may be included in the spirit and scope of the invention defined by the claims. In the following description, a large amount of specific details are set forth to provide a comprehensive understanding of the present invention. The present invention can be implemented without some or all of these specific details. In other cases, in order not to make the present invention unnecessarily obscure, well-known process operations are not described in detail.

[0090] When used in conjunction with "including," "methods comprising," or similar language in this specification and the appended claims, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0091] The present invention will be described in further detail below in conjunction with the full text.

[0092] Combined with attachment Figure 1-Figure 7This invention performs feature engineering on data, including feature generation, selection, and transformation, to more accurately represent the problem domain and improve model efficiency. After encoding and dimensionality reduction of some features, the multi-source feature dataset is ranked by importance using various statistical and machine learning methods. Feature sets with significant impact on asphalt pavement performance prediction are screened based on the ranking results. A fusion prediction model based on OOA optimization is designed to accurately capture and predict changing trends in pavement performance. A multi-source data maintenance decision-making method using an inverse variance weighted modified random forest is proposed, which comprehensively considers current performance status and performance prediction trends to determine maintenance levels and specific maintenance methods. In its implementation, the PQI comprehensively considers multiple key technical conditions, including pavement damage, pavement smoothness, rutting, vehicle bouncing, wear, skid resistance, and structural strength. Each sub-indicator corresponds to a specific performance characteristic of the highway. After scientific weighting and normalization, these sub-indicators form a scale from 0 to 100 that reflects the technical condition of the pavement.

[0093] The proposed model is suitable for predicting different performance indicators (PCI, RQI, RDI, and SRI). By combining the predictive strengths of RF, XGBoost, and CatBoost models through a stacking approach and using OOA for parameter optimization, the model is more adaptable to pavement performance prediction tasks based on multi-source feature datasets. This overcomes the overfitting problem that can result from biased data learning in a single model, achieving high-precision prediction of asphalt pavement performance.

[0094] To address the low accuracy of existing asphalt pavement maintenance decision-making methods, a multi-source maintenance history dataset was constructed. This dataset has a stronger ability to represent maintenance decision-making problems than traditional decision-making methods that only consider performance indicator data such as PCI, RQI, RDI, and SRI, thereby improving the accuracy of maintenance decisions.

[0095] The PQI should be calculated according to formula 15:

[0096] PQI=w PCI PCI+w RQI RQI+w RDI RDI+w PBI PBI+w PWI PWI+w SRI SRI+w PSSI PSSI (15);

[0097] Where w PCI 、w RQI 、w RDI 、w PBI 、w PWI 、w SRI 、w PSSI is the weight of each indicator in PQI.

[0098] PCI=100-a0DR a1 (16); where DR is the damage rate of the highway pavement; in asphalt pavement, the coefficient a0 is recorded as 15.00 and the coefficient a1 is recorded as 0.412;

[0099] In Equations 17 and 18, the unit of IRI measurement value is m / km; the coefficient a0 is 0.026 for first-class highways and expressways, and 0.0185 for other levels of highways; the coefficient a1 is 0.65 for first-class highways and expressways, and 0.85 for other levels of highways; Z S Z is the absolute vertical movement distance of the vehicle body; u is the absolute vertical movement distance of the tire; L is the distance traveled by the vehicle.

[0100] Among them, in formula 19.

[0101] RD is the rutting depth, in mm; rutting depth parameter RD a Use 10.0; rutting depth parameter RD b Use 40.0; model parameter a0 is 1.0; model parameter a1 is 3.0.

[0102] In formula 20, SFC is the lateral force coefficient; SRI is min As the calibration parameter, 35.0 is used; a0 and a1 are model coefficients, which are 28.6 and -0.105 respectively.

[0103] like Figure 2 As shown, data integration was performed on multiple sources, including climate, traffic flow, road infrastructure, road damage, and maintenance history data. The pavement performance of a specific RC highway was analyzed, and multi-source influencing factors were analyzed and features constructed. This provided data preparation for feature importance analysis, asphalt pavement performance prediction model development, and maintenance decision-making. Basic road information, including material quality, thickness, and road age, directly impacts the pavement's performance degradation process. For example, greater pavement thickness can, to a certain extent, slow the rate of pavement damage and extend its service life. Therefore, basic road information plays a crucial role in evaluating degradation.

[0104] Traffic flow is also a significant factor influencing pavement degradation. High traffic volume on a road section imposes significant loads on the pavement, exacerbating fatigue and deformation. The frequency and weight of heavy vehicles passing through it, in particular, further influence the rate of pavement degradation.

[0105] Furthermore, climatic conditions can significantly impact pavement degradation. For example, temperature can cause pavement materials to shrink and expand, exacerbating cracks and wear. Precipitation and snow accumulation can also worsen road conditions, negatively impacting pavement performance.

[0106] At the same time, during the life of a road, various types and degrees of road damage will appear. Typical road damage includes potholes, patches, and cracks. These damages have a negative impact on the performance of the road, accelerating its degradation and shortening its overall lifespan.

[0107] The complexity and diversity of influencing factors complicate data collection and organization. Irrational selection of influencing factors can negatively impact prediction results. The data collected in this paper includes highway scheduled inspection data, road infrastructure data, climate data, traffic flow data, disease data, and maintenance data. Furthermore, some data that is difficult to directly apply requires feature construction.

[0108] Take a certain RC highway as an example:

[0109] 1. Road basic information data processing

[0110] The basic road data of a certain RC highway is mainly divided into two sections, with road ages of 23 years and 20 years respectively. The corresponding start and end pile numbers are shown in Table 1.

[0111] Table 1 Highway section age information

[0112]

[0113]

[0114] The material information of a certain RC highway pavement structure is shown in Table 2 below

[0115] Table 2 Material information of a RC highway pavement structure

[0116]

[0117] As can be seen from Table 2, Section 1 (excluding the bridge section) and Section 2 (excluding the bridge section) used the same surface and middle and lower layer materials, including a 4 cm AK-16 asphalt concrete overlay, a 5 cm AC-20 asphalt concrete middle layer, and a 6 cm AC-25 asphalt concrete lower layer. The base materials of the two were different. Section 1 used 20 and 30 (33) cm lime fly ash stabilized soil, while Section 2 used 20 cm of the same material.

[0118] 2. Climate data processing

[0119] Climate data obtained along a specific RC Expressway primarily includes temperature and precipitation data. Considering that climate data for adjacent sections is generally consistent, climate data from five counties along the highway were used as a proxy. Official meteorological data for each region was used, and temperature and precipitation data for each region were processed and integrated separately.

[0120] 3. Climate data processing

[0121] Climate data obtained along a specific RC Expressway primarily includes temperature and precipitation data. Considering that climate data for adjacent sections is generally consistent, climate data from five counties along the highway were used as a proxy. Official meteorological data for each region was used, and temperature and precipitation data for each region were processed and integrated separately.

[0122] like Figure 3 As shown in Figure 2, temperature data has a strong periodicity. During feature construction, representative data can be used instead of all data to reduce data redundancy and facilitate model learning. Furthermore, pavement performance is significantly affected by temperature fluctuations, especially during periods of high temperatures and freeze-thaw cycles. Seasonal data can better capture these cyclical changes.

[0123] Based on the characteristics of the data, the time points within a year are divided into four different categories, rather than simply dividing them according to the traditional four seasons of spring, summer, autumn and winter. The K-means algorithm is used to cluster the climate data into four seasons.

[0124] 1) Initialization: Randomly select k samples from the data as the initial cluster centers.

[0125] 2) Cluster assignment: Calculate the Euclidean distance between each data sample and each cluster center, and assign each sample to the closest cluster center. The Euclidean distance formula 21 is as follows.

[0126]

[0127] Where x i is the i-th data point in the dataset, c j is the jth cluster center, D is the dimension or number of features of the data, Represents the data point x i The value in the dth dimension, Represents the cluster center c j The value in the dth dimension.

[0128] (3) Center Update: Based on the newly formed clusters, recalculate the center of each cluster, generally taking the average of all cluster points. The cluster center update formula, Formula 22, is as follows.

[0129]

[0130] Where c j ′ is the new cluster center of the jth cluster, S j is the set of data points assigned to the jth cluster, |S j | is the set S j The size is the number of data points, x i is the data point assigned to the jth cluster.

[0131] Temperatures vary significantly between seasons, reflecting the characteristics of high-temperature cycles and freeze-thaw cycles. Temperatures also vary between regions, which can be used as a feature in asphalt pavement performance prediction models.

[0132] Seasonal characteristics are shown in Table 3.

[0133] Table 3 Seasonal characteristics

[0134]

[0135]

[0136] Table 4 shows the seasonal characteristics of the clustered temperature data. Season 2 has the lowest average temperature, with minimums often below 0°C. Season 1 has moderate temperatures, with maximums often between 13°C and 22°C and minimums between 4°C and 10°C. Season 4 has maximums around 25°C and minimums around 15°C. Season 3 is traditionally summer, with maximums consistently exceeding 30°C. The seasonal characteristics of each region are shown in Table 3.

[0137] Extreme temperatures can also affect pavement performance. When temperatures are high, the pavement becomes more sensitive to vehicle pressure, potentially leading to deformation or rutting. High temperatures also accelerate the aging process of asphalt pavements, reducing their durability. When temperatures are low, especially below freezing, the pavement material shrinks and becomes more brittle. This can lead to the formation and aggravation of cracks. Freeze-thaw cycles can also damage the pavement structure, causing potholes and other damage. Therefore, the number of days with the highest and lowest temperatures (maximum temperatures greater than 35°C) and lowest temperatures (minimum temperatures less than 0°C) each year is counted as factors influencing pavement performance prediction. The data characteristics are shown in Table 4.

[0138] Table 4 Extreme temperature characteristics of various areas on a certain RC highway

[0139]

[0140]

[0141] Rainfall data feature construction,

[0142] The cumulative rainfall data for each region are shown in Table 5. These data reflect the climate characteristics and precipitation distribution of each region and can be used as factors affecting pavement performance degradation.

[0143] Table 5 Cumulative rainfall characteristics of each area on a certain RC highway

[0144] Rainfall in the past year Rainfall in the past two years Rainfall in the past three years Rainfall in the past four years Area 1 638.39 1699.92 2472.27 3245.48 Area 2 788.31 2026.74 3014.6 3963.48 Area 3 777.93 2015.97 3050.31 4076.38 Area 4 616.85 1676.46 2498.67 3351.98 Area 5 458.24 1340.27 1921.15 2563.99

[0145] Traffic flow data processing,

[0146] Taking the section from K0+000 to K4+960 as an example, the data are shown in Table 6.

[0147] Table 6 Traffic flow data sample display of a section from K0+000 to K4+960 on a certain RC highway

[0148]

[0149]

[0150] Due to varying raw data sources and formats, data and technical indicators for various vehicle types are not fully consistent. To ensure data availability, we extracted equivalent data that reflects the overall characteristics of traffic volume. Furthermore, passenger cars and trucks have different impacts on the road surface, so we extracted data on the freight-to-passenger ratio that reflects the specific distribution of traffic volume.

[0151] As can be seen from the table, traffic volumes vary significantly across different road sections and at different times. Fine-grained monthly data, including monthly equivalents and passenger-to-freight ratios, can be used as important features for predicting asphalt pavement performance. Furthermore, when integrating data and constructing features, the cumulative equivalents from the past four years, which have a significant impact on pavement performance, are selected to represent the cumulative effect of traffic flow. This also serves to represent the impact of traffic flow on the pavement at an annual granularity.

[0152] Disease data processing,

[0153] Road surface damage reflects a decline in pavement performance, and further damage will impact the road's service life. The road surface damage rate (DR) reflects 11 types of damage on the road surface. The distribution and statistics of various damage types are obtained by analyzing raw data from road inspection vehicles. When integrating the damage data, seven key indicators were initially selected: longitudinal cracks, transverse cracks, strip repairs, block cracks, block repairs, potholes, and cracks.

[0154] Ensuring data quality is a critical step in predicting asphalt pavement performance. Temporal and spatial scale alignment involves integrating and aligning different types of collected data to a unified spatial location and time scale for accurate analysis and prediction. Using the 100-meter markers on the highway, all data is aligned to this reference system.

[0155] The road infrastructure data, including surface materials and the thickness of the road surface and base layers, is a property of the road itself and does not change over time. This data is aligned to the 100-meter stakes using location information. For climate and traffic flow data, representative historical data and features are selected and then aligned to the 100-meter stakes using location information. Defect data and maintenance history data are spatially aligned in a manner consistent with pavement performance indicators.

[0156] For climate data, we divided the data into regions and matched the start and end stakes of the road sections within each region according to the actual location. We also matched the data according to the 100-meter stakes. For traffic flow data and maintenance history data, we aligned the data according to the start and end stakes of each monitored road section. The disease data counted the cumulative disease distribution on each 100-meter road section. We selected some representative samples of the integrated data for display. The results are shown in Table 7-14.

[0157] Table 7 Characteristics of representative samples of seasonal temperature data for a certain RC highway (unit: °C)

[0158]

[0159] Table 8 Characteristics of representative samples of monthly rainfall on a certain RC highway (unit: mm)

[0160]

[0161]

[0162] Table 9 Characteristics of representative samples of cumulative rainfall on a certain RC highway (unit: mm)

[0163] Starting pile number Rainfall in the past year Rainfall in the past two years Rainfall in the past three years Rainfall in the past four years K0+400 638.39 1699.92 2472.27 3245.48 K17+300 788.31 2026.74 3014.6 3963.48 K46+900 616.85 1676.46 2498.67 3351.98 K42+200 777.93 2015.97 3050.31 4076.38 K50+700 458.24 1340.27 1921.15 2563.99 ...

[0164] Table 10 Characteristics of representative samples of RC highway disease data (unit: m 2 )

[0165] direction Starting pile number longitudinal cracks Horizontal cracks Strip repair Blocky cracks Block repair potholes cracks Upward K11+300 0.00 0.22 0.00 0.00 0.06 0.00 0.00 Upward K14+700 0.19 0.00 0.00 0.32 0.56 0.35 0.00 Downward K38+400 0.20 0.50 0.00 0.00 0.00 0.20 0.00 Downward K45+200 0.13 0.00 0.53 0.00 0.54 0.00 0.60 Downward K79+800 0.00 0.00 0.00 0.52 0.40 0 0 ...

[0166] Table 11 Characteristics of a representative sample of the monthly freight-passenger ratio of a certain RC highway

[0167]

[0168]

[0169] Table 12 Characteristics of a representative sample of RC high-speed monthly vehicle equivalent (unit: 10,000)

[0170] Starting pile number January February March April May June July August September October November December K0+000 81 174 163 149 184 181 192 195 189 135 117 258 K20+200 99 245 260 252 305 284 292 209 307 194 166 293 K33+400 131 58 212 73 261 262 284 98 95 68 98 162 K54+700 83 178 228 203 215 201 200 189 190 128 97 153 K61+800 140 277 291 268 286 179 130 190 269 188 166 186 ...

[0171] Table 13 Characteristics of representative samples of a certain RC high-speed cumulative equivalent

[0172] Starting pile number Cumulative equivalent in the past year Cumulative equivalent in the past two years Cumulative equivalent in the past three years Cumulative equivalent in the past four years K0+000 20198024 36265656 51065598 67574548 K20+200 29054842 62415879 70668447 81098687 K33+400 18035862 44687498 56386688 72006133 K54+700 20641427 57279625 74093665 94735145 K61+800 25692382 55866798 71773158 90217703 ...

[0173] Table 14 Sample characteristics of historical maintenance data of a certain RC highway

[0174]

[0175]

[0176] In summary, the evaluation indicators and multi-source influencing factors that need to be considered in asphalt pavement performance evaluation are presented. Data integration was performed on multiple sources, including climate, traffic flow, road infrastructure, road damage, and maintenance history data. The pavement performance of a specific RC highway was analyzed, and multi-source influencing factors were analyzed and characterized. This provided data for feature importance analysis, asphalt pavement performance prediction model development, and maintenance decision-making.

[0177] Prior to feature dimensionality reduction and importance analysis of multi-source feature influencing factors, non-numerical features were first encoded and then data normalized to prevent the impact of data format and numerical value on the analysis results. Three feature importance analysis methods were used for average weight fusion to screen for key characteristic factors of pavement performance evaluation indicators and eliminate collinearity factors, paving the way for subsequent pavement performance evaluation indicator prediction.

[0178] Data on factors influencing pavement performance from multiple sources and domains is standardized and feature encoded. Feature dimensionality reduction is then achieved using various techniques, including PCA and Pearson analysis. An importance analysis method based on a fusion of Spearman, Permutation, and SHAP average weights is proposed to rank the multi-source influencing factors of asphalt pavement performance. Based on the ranking results, the most influential characteristic factors for asphalt pavement performance prediction are selected.

[0179] Leveraging these key influencing factors and considering the historical performance of various road condition indicators, an asphalt pavement performance prediction model was developed. The performance of gray relational analysis, neural networks, and machine learning algorithms in the pavement performance prediction task was verified. To address the impact of hyperparameter selection on machine learning model performance, an OOA algorithm was introduced to optimize the hyperparameters of the machine learning model. A multi-model fusion prediction method based on stacking was developed, leveraging the complementary strengths of multiple models to achieve high-precision predictions of asphalt pavement performance.

[0180] A single grey prediction model, deep learning models such as TabNet and LSTM-FCNN, and machine learning models such as Random Forest, XGBoost, and CatBoost were developed to predict asphalt pavement performance. The introduction of the Out-of-the-Box (OOA) optimization algorithm significantly improved the model hyperparameter selection process, outperforming the Bayesian optimization algorithm. Finally, a multi-model stacking method was used to complement each other and more comprehensively capture the changing patterns of pavement performance. Experimental comparisons confirmed the superiority and reliability of the proposed model in predicting asphalt pavement performance.

[0181] Performance analysis based on the maintenance method dataset. All models achieved higher accuracy on the maintenance level classification dataset than on the maintenance method classification dataset. This is analyzed in conjunction with the confusion matrix presented in Table 15. This is because the data distribution in the maintenance level classification dataset is more even, making it easier for the models to make correct predictions.

[0182] Table 15 Confusion matrix of IVW-RF maintenance method decision

[0183] No.1 No.2 No.3 No.4 No.5 No.6 No.7 precision recall F1-score No.1 1 0 2 4 0 1 0 0.5 0.12 0.2 No.2 0 4 6 1 0 3 0 0.44 0.29 0.35 No.3 0 1 148 15 1 22 10 0.56 0.75 0.64 No.4 0 3 19 505 0 14 0 0.87 0.93 0.9 No.5 0 0 13 2 1 12 2 0.14 0.03 0.05 No.6 0 1 41 39 3 71 8 0.49 0.44 0.46 No.7 1 0 36 15 2 22 9 0.31 0.11 0.16

[0184] No.1 to No.7 represent synchronous fiber wearing layer, ultra-thin wearing layer, micro-surfacing, no maintenance, milling upper middle surface layer resurfacing, milling upper surface layer resurfacing and milling full layer resurfacing respectively.

[0185] The confusion matrix in Table 20 shows the decision results using IVW-Random Forest, where each row represents the true category and each column represents the predicted category. The values ​​on the diagonal indicate the number of correct decisions, meaning that the actual solution is the same as the decision solution. Precision refers to the proportion of true positive examples among the positive examples identified by the classifier. Recall refers to the proportion of samples correctly identified as positive by the classifier among all positive examples. The F1-score is the harmonic mean of precision and recall.

[0186] Analysis of the confusion matrix in Table 20 shows that the accuracy of the No Maintenance category is very high, with a precision of 0.87, a recall of 0.93, and an F1-score of 0.90. This category performs best among all categories, with a high degree of consistency between the predictions and the actual results. Micro-surfacing also has high accuracy, with a precision of 0.56, a recall of 0.75, and an F1-score of 0.64, indicating a relatively high degree of consistency between the predictions and the actual results. However, the decision-making performance for the Milling and Resurfacing method was poor, with low scores across multiple indicators, indicating that the model's predictions for these categories are poor and the probability of correct judgments is low.

[0187] In addition, the number of samples of synchronous fiber wear layer and ultra-thin wear layer is small, and many samples are misclassified into other categories because the number of samples of these two categories in the dataset is not enough for the model to learn enough features for accurate decision-making.

[0188] (2) Effect analysis based on maintenance level dataset

[0189] The data distribution of the maintenance level dataset is relatively even, and the data of various decision results are relatively balanced. Table 16 shows the performance of IVW-RF on this dataset.

[0190] Table 16 Confusion matrix for IVW-RF maintenance level decision

[0191] Repair and maintenance No maintenance Preventive maintenance precision recall F1-score Repair and maintenance 154 54 70 0.75 0.55 0.64 No maintenance 8 532 1 0.87 0.98 0.92 Preventive maintenance 44 24 151 0.68 0.69 0.68

[0192] First, for the no-maintenance class, the model performed best, achieving the highest precision of 0.87, recall of 0.98, and F1-score of 0.92. This means that the model is very accurate and reliable in identifying cases where no maintenance is required. Almost all no-maintenance instances were correctly identified, with only 9 of the 541 samples being misclassified as other labels. There were also very few instances misclassified as no-maintenance.

[0193] For the preventive maintenance class, precision was slightly lower at 0.68, with recall and F1-score at 0.69 and 0.68, respectively. This indicates that the model balanced the error when predicting preventive maintenance, but performance was slightly lower than when predicting no maintenance. 151 instances were correctly classified, while 44 were misclassified as restorative maintenance and 24 as no maintenance.

[0194] The precision for the repair and maintenance class is 0.75, higher than the preventive maintenance class but lower than the no maintenance class. However, its recall is low at 0.55, and its F1-score is moderate at 0.64. This indicates that the model is relatively good at identifying instances requiring repair and maintenance, but a significant proportion of instances are still misclassified.

[0195] (3) Effect analysis based on multi-index maintenance method dataset

[0196] On some road sections, accurate decisions cannot be made solely based on performance indicators. Therefore, more features are needed to assist in decision-making. Because the data is derived from real historical data from a specific RC highway, data collection is limited. The multi-source feature dataset only contains repair and maintenance data. Table 17 shows the performance of IVW-RF on the maintenance method decision dataset containing multi-source features.

[0197] The prediction of "no maintenance" was very accurate, with the highest precision of 0.96 and recall of 0.98. The F1-score also reached a maximum of 0.97, demonstrating that the classification model accurately identified this category. The recall value of the "milled top layer resurfacing" category was high at 0.86, indicating that the model was effective in detecting this category. However, its precision was low at 0.77, indicating that there was a certain degree of error in predicting this category. Some data points in the other three categories were misclassified as "milled top layer resurfacing", especially the misclassification of "milled top layer resurfacing" from "milled full layer resurfacing" was particularly common, with 26 misclassifications.

[0198] Table 17 Confusion matrix of maintenance method decision under IVW-RF multi-source characteristics

[0199]

[0200] Combining the experimental results across the three datasets reveals that, due to the data being collected from real historical data, the datasets are somewhat imperfect. This incomplete data prevents us from fully characterizing the model's decision-making capabilities in various scenarios. However, considering the performance across the three datasets allows us to analyze the IVW-RF model's performance and potential challenges with data-based maintenance decision-making approaches.

[0201] The IVW-RF model performed well compared to other models, outperforming them across multiple datasets. Analysis of the decision-making results showed that data with smaller sample sizes had lower accuracy, while the no-maintenance category had the highest accuracy. This is because no-maintenance cases have more distinct characteristics and the data volume is sufficient for the model to discover these characteristics.

[0202] In other categories, significant improvements were achieved when using a maintenance grade dataset with better sample balance, which shows that the IVW-RF model has certain potential in maintenance decision-making and may achieve better performance on highly balanced datasets.

[0203] If certain categories share very similar features, the model may have difficulty distinguishing them. For example, features for milling full-layer resurfacing and milling upper-layer resurfacing may overlap significantly, leading to model confusion. By adding more multi-source features that can aid in maintenance decision-making, we can help distinguish similar categories and improve the accuracy of model decisions.

[0204] Preventive maintenance is a maintenance measure implemented before minor pavement wear or damage begins. Its core concept is to slow the development and degradation of pavement damage through early intervention. Regular inspection and assessment of the pavement, even without significant functional loss, allows for the early identification of potential problems and the implementation of maintenance measures. Preventive maintenance typically includes crack filling and encapsulation, fog sealing, thin overlays, pavement sweeping, and drainage system repairs. These measures are relatively low-cost, minimally disruptive to traffic, and effectively protect the pavement structure, extending its service life and reducing the need for future major repairs.

[0205] Unlike preventive maintenance, restorative maintenance focuses more on significant damage and functional degradation that has already occurred. It is a remedial measure implemented when pavement problems have progressed to the point where they affect traffic safety and driving comfort. The goal of restorative maintenance is to restore the pavement's structural integrity and serviceability. This typically involves clearing, filling, reinforcing, or rebuilding damaged areas. This includes localized deep repairs, extensive milling and resurfacing, and structural reinforcement. While this work is costly and has a significant impact on traffic, it can prevent further damage and slow the overall decline of the pavement structure.

Claims

1. A decision-making method for asphalt pavement maintenance considering multi-dimensional influencing factors, characterized by: The following steps are involved: S1. Asphalt pavement data integration and data quality improvement: Collect and integrate the evaluation indicators and multi-source influencing factors that need to be considered in the performance evaluation of asphalt pavement, analyze and construct the characteristics of the multi-source influencing factors, and lay a data foundation for the construction of data-driven performance prediction models and maintenance decisions. S2. Importance analysis of factors affecting asphalt pavement performance based on average weighted multi-method fusion: The evaluation indicators and multi-source influencing factors of asphalt pavement performance are screened, and the prediction performance is maintained while streamlining the model input. A large amount of feature data is standardized and feature coding is implemented. The importance of the factors affecting asphalt pavement performance is analyzed, and the results are sorted according to importance to find the most predictive feature set. S3. Establishment of OOA optimization fusion model for asphalt pavement: Establish a predictive OOA optimization fusion model to predict and analyze asphalt pavement performance; S4. Establishment of a multi-source maintenance history dataset: A multi-source maintenance history dataset was constructed, and a maintenance decision-making method based on the inverse variance weighted improved random forest model was established to improve the accuracy of maintenance decisions. S401: Analysis of historical highway data shows that the PSSI (Structural Strength Index) is always above 90, indicating that no maintenance is required based on the structural strength index. Therefore, the pavement indicators selected are PCI, RDI, RQI, and SRI. After merging the collected maintenance history data and the data of unmaintained road sections, a maintenance method classification dataset was constructed to make decisions on seven maintenance methods; a maintenance level classification dataset was constructed to make decisions on three maintenance levels; S402: Construct a multi-index maintenance method dataset that includes historical data and unmaintained road sections. This dataset incorporates multi-source features including pavement disease data, road basic information data, and traffic load data based on PCI, RDI, RQI, and SRI indicator data to improve the dataset's ability to represent maintenance decision-making issues. S5. Pavement maintenance decision-making method: Construct a multi-source maintenance history dataset and establish a maintenance decision-making method based on the inverse variance weighted improved random forest model to improve the accuracy of maintenance decisions. Use the prediction results and current situation to select the maintenance decision-making method. S501: Construct the OOB data of the trees in the random forest method. The OOB data is an independent validation set for each tree that does not participate in training. During the training process, each tree will use random data with replacement sampling from the original training set as training data when it is established. The number of data selected is usually the same as the size of the original training set. Due to the replacement sampling, some data will be repeatedly selected, while others may not be selected. The data that is not selected constitutes the OOB data of this tree. S502: The predictions of the multiple decision trees contained in the random forest are given the same weight to calculate the final prediction result; when using the inverse variance weighting method IVW, a weight is assigned to the prediction of each tree, and the weight of each tree is inversely proportional to its prediction error on the validation set.

2. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The multi-source influencing factors include climate, traffic flow, road infrastructure information, road damage and maintenance history data.

3. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The importance of factors affecting asphalt pavement performance was analyzed by using PCA and Pearson analysis methods to achieve feature dimensionality reduction. The importance analysis method based on the fusion of Spearman, Permutation and SHAP average weights was used to rank the importance of multi-source influencing factors of asphalt pavement performance as the basis for subsequent data selection.

4. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The factors affecting asphalt pavement performance include historical inspection data, road infrastructure information, climate data, traffic flow, disease data, and maintenance history.

5. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 4 is characterized by: Historical inspection data include PCI, PQI, RDI, and SRI; basic road information includes road age, material, and structure; climate data includes temperature and precipitation; traffic flow includes equivalent volume, passenger-to-freight ratio, and cumulative equivalent volume; defect data includes type, location, and area; and maintenance history includes time, location, and method.

6. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The multi-source maintenance history dataset includes pre-maintenance performance, maintenance time, maintenance location, maintenance method and post-maintenance performance. The respective datasets are collected, and after importance analysis, the dataset is reconstructed and maintenance decision training is performed.

7. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The importance analysis of factors affecting asphalt pavement performance by fusion of average weighted multiple methods in S2 includes the following steps: S201: The Spearman rank correlation coefficient is often used to measure the dependence of two variables. The characteristics and indicators involved often do not meet the requirements of normal distribution. The formula of the Spearman correlation coefficient is shown in formula (1). Where n is the number of variables; d i is the rank difference between two variables (i = 1, 2, 3...n). The rank of a value is determined by its relative size in a sequence. If there are identical values ​​in the sequence, their rank will be the average of their positions. The difference between the ranks of two different values ​​is called the rank difference. S202: Permutation-based feature importance analysis destroys the relationship between the original features and the target variable by randomly permuting the feature values. The feature importance is then evaluated by comparing the performance differences between the original model and the permuted model. The calculation requires training a model. By randomly permuting the data distribution of each feature, the order of the original feature values ​​is disrupted. The model is retrained using the permuted feature values ​​and the true target variable, and the change in model performance is calculated. If the performance of the permuted model decreases significantly, it can be considered that the feature has a greater impact on the model performance, that is, the feature importance is high. S203: SHAP is an interpretable model prediction method based on Shapley values ​​in game theory. In machine learning, its role is to quantify the contribution of each feature to illustrate their importance to model prediction. The SHAP method feature importance analysis process is as follows: S20301: Initialize data: select a specific data instance and determine its characteristic values; S20302: Define model: Define the machine learning model used, such as a linear regression model; S20303: Calculate baseline value: The baseline value is the predicted value of the model when no features are involved; S20304: Calculate marginal contribution: For each feature, consider all possible feature combinations and calculate the change in predicted value when adding that feature; For feature i, its SHAP value is defined as formula (2); Where S is the subset of all features except feature i, |S| is the size of S, i.e., the number of features in S, ! represents the factorial, N is the total number of features, and f(S) is the predicted value of the model on the feature subset (S). Formula (2) calculates the marginal contribution of feature i under all possible feature subsets and performs weighted summation through the weights in combinatorial mathematics; S20305: Assign weights: Assign weights to each feature's marginal contribution according to the definition of Shapley values; weights are assigned based on the number and eigenvalues ​​of features in the combination; S204: Use three importance analysis methods to score and rank the factors affecting asphalt pavement performance. Due to differences in the measurement criteria and data characteristics of different methods, the final rankings have some commonalities but also some differences. To avoid the limitations and one-sidedness of using only one method, the Spearman correlation coefficient method, the permutation method, and the SHAP method are integrated. The three importance analysis methods are assigned equal weights and then combined to ensure the validity of the importance weight analysis results of the factors affecting asphalt pavement. The process is as follows: S20401: The three methods have different dimensions for the results, so we need to unify the dimensions. For the correlations obtained by the Spearman correlation analysis method, we need to take the absolute value before calculating. S20402: Process the weight of each method using formula (3); Where, F i is the importance weight of the i-th feature after de-dimensioning; I i is the importance weight of the i-th feature before de-dimensioning; n is the number of features; S20403: Take the average of the feature importance weights of the three processed methods to obtain the feature importance weights of each fused indicator, re-sort the fused feature importance weights, and use the result as the basis for feature screening.

8. The asphalt pavement maintenance decision-making method considering multi-dimensional influencing factors according to claim 1 is characterized by: The steps of establishing the OOA optimization fusion model for predicting asphalt pavement performance in S3 and performing prediction analysis on asphalt pavement performance are as follows: S301: Matrix modeling is performed according to formula (4); S302: Randomly initialize the position of the osprey in the search space according to Publication (5); x i,j =lb j +r i,j ·(ub j -lb j )(5); Where N is the number of ospreys; m is the number of problem variables; X is the osprey position population matrix; X i is the initial position of the i-th osprey, i=1,2...,n; X i,j is the initial position of the i-th osprey in the j-th problem variable, j = 1, 2, ..., m; lb j 、ub j is the lower and upper bounds of the j-th problem variable; r i,j is a random number with a value range of [0,1]; S303: Calculate the objective function of each osprey, and the evaluation can be expressed as a vector of formula (6); Where F is the objective function value; F i is the objective function value of the i-th osprey; S304: Phase 1 Update: The position of each osprey with a higher objective function value in the search space represents the location of the prey fish school; the fish school position of each osprey is expressed using formula (7); FP i ={X k |k∈{1,2,...,N}∧F k <F i }∪{X best } (7); Where FP i is the set of fish school positions of the i-th osprey; X best It's F i The optimal corresponding X i value; When an osprey attacks a fish randomly, it will move toward the fish's location. The new position of the osprey is calculated using equations (8) and (9). If the new position improves the value of the objective function, it replaces the previous position of the osprey. Where, is the new position of the i-th osprey in the j-th problem variable; SF i,j is the position of the fish selected by the i-th osprey in the j-th problem variable; I i,j The value of is one of {1,2}; If the osprey improves the value of the objective function in the new position, the new position of the osprey after the update is calculated by formula (10); Where, is the new position of the i-th osprey; F i P1 yes The objective function value of S305: For each member of the population, use equations (11) and (12) to calculate a new random position as a position suitable for eating fish; if the value of the objective function is improved at this new position, replace the previous position of the corresponding osprey according to equation (13);

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