Pavement roughness prediction method based on hybrid tern algorithm and bidirectional gating
By introducing the hybrid tern algorithm to optimize the hyperparameters of the BiGRU model, the problem of insufficient accuracy of traditional models in road surface roughness prediction is solved, achieving high-precision road surface roughness prediction and improving the prediction effect of the model.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANTONG UNIV
- Filing Date
- 2026-03-30
- Publication Date
- 2026-06-09
AI Technical Summary
Traditional empirical mechanics or static regression models are difficult to accurately predict the nonlinear upward trend of road surface roughness. The prediction accuracy of the existing BiGRU model depends on the reasonable configuration of hyperparameters, resulting in insufficient prediction accuracy.
The Hybrid Black-and-White Algorithm (HSTOA) is introduced to optimize the hyperparameters of the Bidirectional Gated Recurrent Unit (BiGRU) model. The learning rate, number of neurons, and self-attention mechanism (SA) of the Temporal Convolutional Network (TCN) and BiGRU are optimized through the HSTOA algorithm to improve the accuracy of road surface roughness prediction.
It improves the accuracy of road surface roughness prediction, with a determination coefficient R2 of 0.969 and a root mean square error (RMSE) of only 0.112, which is significantly better than the traditional model, proving that it has high engineering value in dealing with complex road surface degradation indicators.
Smart Images
Figure CN122173784A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of road engineering material performance prediction technology, and in particular to a road surface roughness prediction method based on the hybrid black tern algorithm and bidirectional gating. Background Technology
[0002] In the daily operation and maintenance of roads, pavement roughness (International Roughness Index, IRI) is a core control indicator for assessing pavement service quality, ensuring driving safety, and reducing vehicle operating costs. Therefore, accurately understanding the evolution of pavement roughness is beneficial for road management departments to carry out preventative maintenance in advance, thereby optimizing the allocation of limited maintenance resources, reducing life-cycle costs, and ensuring road operation safety.
[0003] With the increasing service life of road surfaces, the continuous accumulation of dynamic traffic loads, and the intensification of extreme environmental and climate changes, road surface materials age and their structures degrade severely, leading to a complex nonlinear upward trend in road surface roughness. Traditional empirical mechanics or static regression models struggle to accurately predict this. Therefore, this invention introduces a bidirectional gated recurrent unit (BiGRU) model with temporal memory capabilities. This model predicts future road surface roughness by mining contextual information from historical road surface performance data in both forward and reverse directions. However, the prediction accuracy of BiGRU is highly dependent on the appropriate configuration of hyperparameters such as the learning rate and the number of neurons. Summary of the Invention
[0004] The purpose of this invention is to address the problems of existing technologies by proposing a road surface roughness prediction method based on the hybrid sooty tern optimization algorithm and bidirectional gating. The hybrid sooty tern optimization algorithm (HSTOA) is introduced to optimize the hyperparameters of the BiGRU model, ensuring that the prediction model can adaptively lock the globally optimal hyperparameter combination, thereby improving the model's prediction accuracy of road surface roughness.
[0005] This invention is achieved through the following technical solution: a road surface roughness prediction method based on a hybrid tern algorithm and bidirectional gating, comprising the following steps:
[0006] S1: Obtain road performance data from the LTPP database, preprocess it to form a sample dataset, and divide the sample dataset into a training set and a test set;
[0007] S2: The HSTOA algorithm is used to optimize the learning rate and number of neurons of L2 and BiGRU of the temporal convolutional network (TCN) and the key value of self-attention (SA) mechanism to obtain the optimal combination of model hyperparameters.
[0008] S3: Input road surface roughness and related influencing factors data into TCN. TCN extracts local features of the data through dilated convolution and inputs the feature-processed data into the BiGRU layer.
[0009] S4: The BiGRU layer analyzes the contextual information in the sequence through forward GRU and reverse GRU to uncover potential future change features in the data;
[0010] S5: The SA mechanism performs weighted calculations based on the importance of the BiGRU output data and inputs the results into the fully connected layer;
[0011] S6: The fully connected layer performs a nonlinear transformation on the input results to generate the final prediction results; and calculates the evaluation metrics of the HSTOA-BiGRU model and the comparison model, including: root mean square error (RMSE) and coefficient of determination (R²). 2 Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE).
[0012] Furthermore, the S1 process is implemented through the following steps: preprocessing the data obtained from the database to form a dataset, the preprocessing including removing missing values and handling outliers, and randomly dividing the dataset into a training set and a test set in an 8:2 ratio.
[0013] Furthermore, the S2 process is implemented through the following steps: The HSTOA algorithm deeply integrates the Sooty tern optimization algorithm (STOA), which focuses on global breadth exploration, with the whale optimization algorithm (WOA), which focuses on local depth exploration, and achieves an effective balance between global exploration and local development by dividing the population into twin populations;
[0014] The parameters for the HSTOA algorithm are set as follows: (STOA algorithm settings) The range is [0.01, 2], the Tent chaotic mapping parameter is 0.5, and the Cauchy perturbation parameter is [0.5, 0]; in the WOA algorithm parameters, the shrinking encirclement mechanism parameter is [2, 0], and the spiral shrinking constant b=1; the deep temporal network algorithm is initialized, and the total population is divided into two parts: one part is allocated to the STOA subpopulation, with a size of The other portion was allocated to the WOA subpopulation, with a size of [missing information]. And satisfy ;
[0015] The STOA algorithm initializes the population by randomly generating individual positions, and its position initialization expression is as follows:
[0016]
[0017] In the formula: The chaotic values generated by the Tent mapping; the chaotic sequence generated by the Tent mapping is then mapped to the search space to obtain the initial position:
[0018]
[0019] In the formula: For the first The individual in the first Initial actual values in each dimension; For the first The minimum allowed value of the parameter to be optimized in each dimension; For the first The maximum allowed value of the parameter to be optimized in each dimension;
[0020] To improve the smoothness of the transition between the early exploration phase and the later convergence phase of the algorithm, a cosine annealing strategy is introduced to dynamically calculate the nonlinear control parameters. And calculate the individual's collision avoidance safe position. Its mathematical expression is:
[0021]
[0022]
[0023] In the formula, This indicates the position one should be in without colliding with other terns. Indicates the first The individual in the first The current position vector at the next iteration, adjust The control constant for the basic size, The maximum number of iterations set for the algorithm. This represents the current iteration number of the algorithm.
[0024] Calculate the step size of an individual as it approaches the current global optimum. And derive the comprehensive exploration gap vector:
[0025]
[0026]
[0027] In the formula, Let be the step size vector by which an individual moves toward its current globally optimal position. Indicates as of the date The location of the global optimal solution in the next iteration. The range of values is Uniformly distributed random numbers between This is a comprehensive exploration gap vector that integrates collision avoidance behavior and aggregation behavior;
[0028] Set the spiral radius With random angle Calculate the unique three-dimensional spiral coordinate coefficients of the Black-tailed Tern. , and To prevent getting trapped in local extrema, random perturbations are introduced using the Cauchy distribution, thus completing the final position update.
[0029]
[0030]
[0031]
[0032]
[0033]
[0034] In the formula, This represents the radius of each spiral. express Variables between; and This is a constant that defines its spiral shape, and in this invention, it is set to 1. It is the base of the natural logarithm; These are random numbers distributed according to the standard Cauchy distribution. For an individual, after the location is updated, their new location in the next generation;
[0035] When constructing the population, the WOA algorithm first calculates the convergence factor, which decreases linearly with the number of iterations. Determine the coefficient vector and :
[0036]
[0037]
[0038]
[0039] In the formula: The convergence factor of the WOA algorithm increases with the number of iterations. The increase in decreases linearly from 2 to 0; and This is the decision coefficient vector, used to control the stride and weights of the humpback whale's contraction and exploration. and The numbers are uniformly distributed random numbers;
[0040] When random number At this time, humpback whales will either tighten their encirclement or swim around to explore;
[0041] like Individuals execute a shrinking encirclement strategy to approach the global optimum:
[0042]
[0043] like Individuals execute a random walk strategy, randomly selecting a reference individual from the population. Update:
[0044]
[0045] In the formula: This represents the location of a reference individual randomly selected from the current population during the random walk exploration phase.
[0046] When random number At that time, a logarithmic spiral bubble-blowing attack is launched;
[0047] Calculate the distance between an individual and the optimal solution. Generate random numbers Position updates are performed using the logarithmic spiral equation:
[0048]
[0049]
[0050] In the formula: This represents the absolute straight-line distance between the individual and the global optimal solution. To control the logarithmic constant of the logarithmic spiral shape, this invention sets it to 1; The random number determines the specific form of the spiral approach to the optimal solution.
[0051] Furthermore, the S3 process is implemented through the following steps: the TCN algorithm can exponentially increase the amount of road performance data by expanding the convolutional structure, and it can effectively solve the overfitting problem caused by the recursive structure of BiGRU during training through residual connections; the expression of the TCN algorithm is shown in equation (19):
[0052]
[0053] In the formula: This represents the output of the dilated convolution operation; The size of the convolution kernel; These are the weights of the convolution kernel; For time steps The input signal.
[0054] Furthermore, the S4 process is implemented through the following steps: GRU, as an improved model of LSTM, merges the input gate and forget gate of LSTM into an update gate, and combines the reset gate and candidate hidden vectors to generate the state vector of the next time step, thereby reducing the complexity of the LSTM model; compared with the traditional GRU algorithm, BiGRU can capture potential future change features in the data by simultaneously integrating forward and backward GRU modules; the expression of BiGRU is shown in equations (20) to (22);
[0055]
[0056]
[0057]
[0058] In the formula: and These represent the forward and backward outputs of the BiGRU, respectively. This represents the input at the current moment; This is the output of the entire BiGRU model; This indicates a splicing operation.
[0059] Furthermore, the S5 process is implemented through the following steps: The gradient update decay of the BiGRU model during training is large, which causes the first input features to be diluted by the subsequent input features, and the features at the beginning of the sequence cannot be fully utilized, causing the gradient vanishing problem. This paper introduces the SA mechanism to update the model weights, so that the model selectively focuses on important information and ignores irrelevant information; the expression of the SA mechanism is shown in equations (23) to (26):
[0060]
[0061]
[0062]
[0063]
[0064] In the formula: , and These represent the query, key, and numerical matrix, respectively. Represents the input matrix; , and They represent , and The corresponding weight matrix; express , and Dimensions.
[0065] Further, the S6 process is implemented through the following steps: inputting the test set into the HSTOA-BiGRU model for road surface roughness prediction, and calculating the evaluation metrics of the HSTOA-BiGRU model and the comparison models. The comparison models include: Artificial Neural Network (ANN), Thunder Gradient Boosting Machine (GBM), Random Forest (RF), Long Short-Term Memory (LSTM), and Bayesian Neural Network (BNN). The evaluation metrics include:
[0066]
[0067]
[0068]
[0069]
[0070] In the formula: Indicates the number of samples; Indicates the actual value; Indicates the predicted value; This represents the average value.
[0071] Beneficial effects:
[0072] (1) The HSTOA-BiGRU model proposed in this invention has a determination coefficient of (R0). 2The R² value is 0.969, while the root mean square error (RMSE) is only 0.112. Compared to the traditional machine learning models ANN (0.840) and RF (0.862) which do not consider temporal dependencies, this model has a significantly higher R² value. 2 The accuracy was significantly improved by 15.3% and 12.4% respectively, as shown in Table 1. This demonstrates that traditional static models have a clear upper limit when dealing with the decay index caused by the long-term cumulative effects of environmental and traffic loads, such as IRI. Compared with the classic LSTM model's accuracy of 0.870, the accuracy of our model improved by 0.099. This indicates that although a single recurrent neural network can capture temporal information, its feature extraction capability is still limited when facing the complex spatial coupling of multidimensional meteorological and traffic features. Compared with the cutting-edge BNN model with uncertainty quantification capabilities, our model improved the prediction accuracy by 0.041. Furthermore, the extremely low RMSE further confirms the model's high engineering application value.
[0073] Table 1 Comparison Results of the Models
[0074]
[0075] (2) To address the problem of low optimization accuracy in traditional optimization algorithms, the HSTOA algorithm is used to optimize the L2 of TCN, the learning rate and number of neurons of BiGRU, and the key value of SA mechanism. For the limitations of the original STOA algorithm in dealing with high-dimensional complex function optimization, such as insufficient population diversity and low local development accuracy, Tent chaotic mapping is introduced to initialize the population, and cosine annealing strategy is used to dynamically control key parameters and improve the position update mechanism in the attack phase. Attached Figure Description
[0076] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.
[0077] Figure 2 This is a graph showing the comparison between the actual and predicted values of the HSTOA-BiGRU model of this invention. Detailed Implementation
[0078] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0079] The pavement data used in this invention are all from the LTPP database. LTPP is a national macro-level research program that conducts extensive and long-term monitoring and analysis of pavement performance throughout the United States and Canada. This database encompasses an extremely rich system of road characteristics, including traffic loads, pavement structure, climatic conditions, material properties, construction events, and historical performance monitoring indicators, providing strong data support for targeted research on pavement degradation mechanisms. Based on the above dataset, this invention constructs an HSTOA-BiGRU pavement roughness prediction model, providing technical support for optimizing the allocation of limited maintenance resources, reducing life-cycle costs, and ensuring road operational safety.
[0080] like Figure 1 As shown, a road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating includes the following steps:
[0081] S1: Obtain road performance data from the LTPP database, preprocess it to form a sample dataset, and divide the sample dataset into a training set and a test set;
[0082] The S1 process is implemented through the following steps: preprocessing the data obtained from the database to form a dataset, the preprocessing includes removing missing values and handling outliers, and randomly dividing the dataset into a training set and a test set in a ratio of 8:2.
[0083] S2: The HSTOA algorithm is used to optimize the learning rate and number of neurons of L2 and BiGRU of the temporal convolutional network (TCN) and the key value of self-attention (SA) mechanism to obtain the optimal combination of model hyperparameters.
[0084] The S2 process is implemented through the following steps: The HSTOA algorithm deeply integrates the Sooty tern optimization algorithm (STOA), which focuses on global breadth exploration, and the whale optimization algorithm (WOA), which focuses on local depth exploration, to achieve an effective balance between global exploration and local development by dividing the population into twin populations.
[0085] The parameters for the HSTOA algorithm are set as follows: (STOA algorithm settings) The range is [0.01, 2], the Tent chaotic mapping parameter is 0.5, and the Cauchy perturbation parameter is [0.5, 0]; in the WOA algorithm parameters, the shrinking encirclement mechanism parameter is [2, 0], and the spiral shrinking constant b=1; the deep temporal network algorithm is initialized, and the total population is divided into two parts: one part is allocated to the STOA subpopulation (size is...). Another portion was allocated to the WOA subpopulation (size: ), and satisfy ;
[0086] The STOA algorithm initializes the population by randomly generating individual positions, and its position initialization expression is as follows:
[0087]
[0088] In the formula: The chaotic values generated by the Tent mapping. The initial position is obtained by mapping the chaotic sequence generated by the Tent mapping onto the search space.
[0089]
[0090] In the formula: For the first The individual in the first Initial actual values in each dimension; For the first The minimum allowed value of the parameter to be optimized in each dimension; For the first The maximum allowed value of the parameter to be optimized in each dimension;
[0091] To improve the smoothness of the transition between the early exploration phase and the later convergence phase of the algorithm, a cosine annealing strategy is introduced to dynamically calculate the nonlinear control parameters. And calculate the individual's collision avoidance safe position. Its mathematical expression is:
[0092]
[0093]
[0094] In the formula, This indicates the position one should be in without colliding with other terns. Indicates the first The individual in the first The current position vector at the next iteration, adjust The control constant for the basic size, The maximum number of iterations set for the algorithm. This represents the current iteration number of the algorithm.
[0095] Calculate the step size of an individual as it approaches the current global optimum. And derive the comprehensive exploration gap vector:
[0096]
[0097]
[0098] In the formula, Let be the step size vector by which an individual moves toward its current globally optimal position. Indicates as of the date The location of the global optimal solution in the next iteration. The range of values is Uniformly distributed random numbers between This is a comprehensive exploration gap vector that integrates collision avoidance behavior and aggregation behavior;
[0099] Set the spiral radius With random angle Calculate the unique three-dimensional spiral coordinate coefficients of the Black-tailed Tern. , and To prevent getting trapped in local extrema, random perturbations are introduced using the Cauchy distribution, thus completing the final position update.
[0100]
[0101]
[0102]
[0103]
[0104]
[0105] In the formula, This represents the radius of each spiral. express Variables between; and This is a constant that defines its spiral shape, and in this invention, it is set to 1. It is the base of the natural logarithm; These are random numbers distributed according to the standard Cauchy distribution. For an individual, after the location is updated, their new location in the next generation;
[0106] When constructing the population, the WOA algorithm first calculates the convergence factor, which decreases linearly with the number of iterations. Determine the coefficient vector and :
[0107]
[0108]
[0109]
[0110] In the formula: The convergence factor of the WOA algorithm increases with the number of iterations. The increase in decreases linearly from 2 to 0; and This is the decision coefficient vector, used to control the stride and weights of the humpback whale's contraction and exploration. and The numbers are uniformly distributed random numbers;
[0111] When random number At this time, humpback whales will either tighten their encirclement or swim around to explore;
[0112] like Individuals execute a shrinking encirclement strategy to approach the global optimum:
[0113]
[0114] like Individuals execute a random walk strategy, randomly selecting a reference individual from the population. Update:
[0115]
[0116] In the formula: This represents the location of a reference individual randomly selected from the current population during the random walk exploration phase.
[0117] When random number At that time, a logarithmic spiral bubble-blowing attack is launched;
[0118] Calculate the distance between an individual and the optimal solution. Generate random numbers Position updates are performed using the logarithmic spiral equation:
[0119]
[0120]
[0121] In the formula: This represents the absolute straight-line distance between the individual and the global optimal solution. To control the logarithmic constant of the logarithmic spiral shape, this invention sets it to 1; The random number determines the specific form of the spiral approach to the optimal solution.
[0122] S3: Input road surface roughness and related influencing factors data into TCN. TCN extracts local features of the data through dilated convolution and inputs the feature-processed data into the BiGRU layer.
[0123] The S3 process is implemented through the following steps: The TCN algorithm can exponentially increase the amount of road performance data by expanding the convolutional structure, and it can effectively solve the overfitting problem caused by the recursive structure of BiGRU during training through residual connections; the expression of the TCN algorithm is shown in equation (19):
[0124]
[0125] In the formula: This represents the output of the dilated convolution operation; The size of the convolution kernel; These are the weights of the convolution kernel; For time steps The input signal.
[0126] S4: The BiGRU layer analyzes the contextual information in the sequence through forward GRU and reverse GRU to uncover potential future change features in the data;
[0127] The S4 process is implemented through the following steps: GRU, as an improved model of LSTM, merges the input gate and forget gate of LSTM into an update gate, and combines the reset gate and candidate hidden vectors to generate the state vector of the next time step, thereby reducing the complexity of the LSTM model; compared with the traditional GRU algorithm, BiGRU can capture potential future change features in the data by simultaneously integrating forward and backward GRU modules; the expression of BiGRU is shown in equations (20) to (22);
[0128]
[0129]
[0130]
[0131] In the formula: and These represent the forward and backward outputs of the BiGRU, respectively. This represents the input at the current moment; This is the output of the entire BiGRU model; This indicates a splicing operation.
[0132] S5: The SA mechanism performs weighted calculations based on the importance of the BiGRU output data and inputs the results into the fully connected layer;
[0133] The S5 process is implemented through the following steps: The gradient update decay of the BiGRU model during training is large, which causes the first input features to be diluted by the subsequent input features, and the features at the beginning of the sequence cannot be fully utilized, causing the gradient vanishing problem. This paper introduces the SA mechanism to update the model weights, so that the model selectively focuses on important information and ignores irrelevant information; the expression of the SA mechanism is shown in equations (23) to (26):
[0134]
[0135]
[0136]
[0137]
[0138] In the formula: , and These represent the query, key, and numerical matrix, respectively. Represents the input matrix; , and They represent , and The corresponding weight matrix; express , and Dimensions.
[0139] S6: The fully connected layer performs a nonlinear transformation on the input results to generate the final prediction results. The calculation results are as follows: Figure 2 As shown; and calculate the evaluation indicators of the HSTOA-BiGRU model and the comparison model, including: root mean square error (RMSE), coefficient of determination (R²), etc. 2 Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE);
[0140] The S6 process is implemented through the following steps: The test set is input into the HSTOA-BiGRU model for road surface roughness prediction, and evaluation metrics are calculated for the HSTOA-BiGRU model and the comparison models. The comparison models include: Artificial Neural Network (ANN), Thunder Gradient Boosting Machine (GBM), Random Forest (RF), Long Short-Term Memory (LSTM), and Bayesian Neural Network (BNN). The evaluation metrics include:
[0141]
[0142]
[0143]
[0144]
[0145] In the formula: Indicates the number of samples; Indicates the actual value; Indicates the predicted value; This represents the average value.
[0146] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A road surface roughness prediction method based on hybrid tern algorithm and bidirectional gating, characterized in that: Includes the following steps: S1: Obtain road performance data from the LTPP database, preprocess it to form a sample dataset, and divide the sample dataset into a training set and a test set; S2: The HSTOA algorithm is used to optimize the learning rate and number of neurons of L2 and BiGRU in the temporal convolutional network, as well as the key value of the self-attention mechanism, to obtain the optimal combination of model hyperparameters; S3: Input road surface roughness and related influencing factors data into TCN. TCN extracts local features of the data through dilated convolution and inputs the feature-processed data into the BiGRU layer. S4: The BiGRU layer analyzes the contextual information in the sequence through forward GRU and reverse GRU to uncover potential future change features in the data; S5: The SA mechanism performs weighted calculations based on the importance of the BiGRU output data and inputs the results into the fully connected layer; S6: The fully connected layer performs a nonlinear transformation on the input results to generate the final prediction results; The evaluation metrics for the HSTOA-BiGRU model and the comparison model were calculated, including: root mean square error (RMSE) and coefficient of determination (R²). 2 Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE).
2. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 1, characterized in that: The S1 process is implemented through the following steps: preprocessing the data obtained from the database to form a dataset, the preprocessing includes removing missing values and handling outliers, and randomly dividing the dataset into a training set and a test set in a ratio of 8:
2.
3. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 2, characterized in that: The S2 process is implemented through the following steps: The HSTOA algorithm deeply integrates the tern optimization algorithm, which focuses on global breadth exploration, with the whale optimization algorithm, which focuses on local depth mining, and achieves an effective balance between global exploration and local development by dividing the twin populations. The parameters for the HSTOA algorithm are set as follows: (STOA algorithm settings) The range is [0.01, 2], the Tent chaotic mapping parameter is 0.5, and the Cauchy perturbation parameter is [0.5, 0]; in the WOA algorithm parameters, the shrinking encirclement mechanism parameter is [2, 0], and the spiral shrinking constant b=1; the deep temporal network algorithm is initialized, and the total population is divided into two parts: one part is allocated to the STOA subpopulation, with a size of The other portion was allocated to the WOA subpopulation, with a size of [missing information]. And satisfy ; The STOA algorithm initializes the population by randomly generating individual positions, and its position initialization expression is as follows: In the formula: The chaotic values generated by the Tent mapping; the chaotic sequence generated by the Tent mapping is then mapped to the search space to obtain the initial position: In the formula: For the first The individual in the first Initial actual values in each dimension; For the first The minimum allowed value of the parameter to be optimized in each dimension; For the first The maximum allowed value of the parameter to be optimized in each dimension; To improve the smoothness of the transition between the early exploration phase and the later convergence phase of the algorithm, a cosine annealing strategy is introduced to dynamically calculate the nonlinear control parameters. And calculate the individual's collision avoidance safe position. Its mathematical expression is: In the formula, This indicates the position one should be in without colliding with other terns. Indicates the first The individual in the first The current position vector at the next iteration, adjust The control constant for the basic size, The maximum number of iterations set for the algorithm. This represents the current iteration number of the algorithm. Calculate the step size of an individual as it approaches the current global optimum. And derive the comprehensive exploration gap vector: In the formula, Let be the step size vector by which an individual moves toward its current globally optimal position. Indicates as of the date The location of the global optimal solution in the next iteration. The range of values is Uniformly distributed random numbers between This is a comprehensive exploration gap vector that integrates collision avoidance behavior and aggregation behavior; Set the spiral radius With random angle Calculate the unique three-dimensional spiral coordinate coefficients of the Black-tailed Tern. , and To prevent getting trapped in local extrema, random perturbations are introduced using the Cauchy distribution, thus completing the final position update. In the formula, This represents the radius of each spiral. express Variables between; and These are constants that define its spiral shape, all set to 1. It is the base of the natural logarithm; These are random numbers distributed according to the standard Cauchy distribution. For an individual, after the location is updated, their new location in the next generation; When constructing the population, the WOA algorithm first calculates the convergence factor, which decreases linearly with the number of iterations. Determine the coefficient vector and : In the formula: The convergence factor of the WOA algorithm increases with the number of iterations. The increase in decreases linearly from 2 to 0; and This is the decision coefficient vector, used to control the stride and weights of the humpback whale's contraction and exploration. and The numbers are uniformly distributed random numbers; When random number At this time, humpback whales will either tighten their encirclement or swim around to explore; like Individuals execute a shrinking encirclement strategy to approach the global optimum: like Individuals execute a random walk strategy, randomly selecting a reference individual from the population. Update: In the formula: This represents the location of a reference individual randomly selected from the current population during the random walk exploration phase. When random number At that time, a logarithmic spiral bubble-blowing attack is launched; Calculate the distance between an individual and the optimal solution. Generate random numbers Position updates are performed using the logarithmic spiral equation: In the formula: This represents the absolute straight-line distance between the individual and the global optimal solution. To control the shape of the logarithmic spiral, the logarithmic constant is set to 1; The random number determines the specific form of the spiral approach to the optimal solution.
4. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 3, characterized in that: The S3 process is implemented through the following steps: The TCN algorithm can sense road performance data exponentially by expanding the convolutional structure, and it can solve the overfitting problem caused by the recursive structure of BiGRU during the training process through residual connections. The expression for the TCN algorithm is shown in equation (19): In the formula: This represents the output of the dilated convolution operation; The size of the convolution kernel; These are the weights of the convolution kernel; For time steps The input signal.
5. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 4, characterized in that: The S4 process is implemented through the following steps: GRU, as an improved model of LSTM, merges the input gate and forget gate of LSTM into an update gate, and combines a reset gate and candidate hidden vectors to generate the state vector for the next time step, reducing the complexity of the LSTM model; BiGRU, by simultaneously integrating forward and backward GRU modules, can capture potential future change features in the data; Bi The expressions for GRU are shown in equations (20) to (22); In the formula: and These represent the forward and backward outputs of the BiGRU, respectively. This represents the input at the current moment; This is the output of the entire BiGRU model; This indicates a splicing operation.
6. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 5, characterized in that: The S5 process is implemented through the following steps: The gradient update decay of the BiGRU model during training is large, which causes the first input features to be diluted by the subsequent input features. The features at the beginning of the sequence cannot be fully utilized, which leads to the gradient vanishing problem. The SA mechanism is introduced to update the model weights, so that the model selectively focuses on important information and ignores irrelevant information. The expression of the SA mechanism is shown in equations (23) to (26): In the formula: , and These represent the query, key, and numerical matrix, respectively. Represents the input matrix; , and They represent , and The corresponding weight matrix; express , and Dimensions.
7. The road surface roughness prediction method based on the hybrid tern algorithm and bidirectional gating as described in claim 6, characterized in that: The S6 process is implemented through the following steps: The test set is input into the HSTOA-BiGRU model for road surface roughness prediction, and evaluation metrics are calculated for the HSTOA-BiGRU model and the comparison models. The comparison models include: artificial neural networks, Thunder gradient boosters, random forests, long short-term memory networks, and Bayesian neural networks. The evaluation metrics include: In the formula: Indicates the number of samples; Indicates the actual value; Indicates the predicted value; This represents the average value.