Bridge displacement prediction method and system based on meteorological data and GRU model

Abstract

The invention discloses a bridge displacement prediction method and system based on meteorological data and a GRU model, and the method comprises the steps: obtaining the previous meteorological data of the position of a bridge and the vertical displacement data of the bridge, and building a data set according to the obtained meteorological data and displacement data; and training the GRU model through the data set, and optimizing hyper-parameters of the GRU model by adopting an optimization algorithm in the training process to obtain an optimal GRU model. Current meteorological data of the position where the bridge is located are obtained, and the vertical displacement of the bridge is predicted through the optimal GRU model. And the method has a wider application range. And the trained GRU model has the advantages of strong non-linear fitting capability and memory time-varying data historical information, and can better capture the long-term dependency relationship in the time series data. In addition, in the training process of the GRU model, an optimization algorithm is used for optimizing hyper-parameters of the GRU model, the performance of the GRU model is improved to the maximum extent, and therefore higher displacement prediction precision can be obtained.

Description

Technical Field

[0001] The invention relates to the technical field of displacement of solids, and in particular to a method and system for predicting bridge displacement based on meteorological data and a GRU model. Background Art

[0002] During the long-term service of bridges, due to the influence of the external environment, their performance in the operation process continues to decline, which affects the safety and stability of the bridge, and even causes the bridge to collapse in extreme cases. Structural health monitoring (SHM) technology is an effective means to monitor bridges in real time, so as to promptly detect potential damage and abnormal conditions of the structure. Vertical displacement is an important parameter for long-term monitoring of the SHM system, and it is also one of the most intuitive and effective indicators for evaluating the overall use status of the bridge. In recent years, some scholars have successfully applied vertical displacement data to bridge safety assessment and damage detection. Therefore, carrying out vertical displacement data monitoring in the SHM system is of great significance for structural safety early warning and health status assessment.

[0003] However, the vertical displacement sensors in the SHM system often suffer from data loss during long-term use due to sensor degradation, unstable power supply, and transmission or storage failure. Data loss, especially long-term continuous data loss, will not only delay emergency response to bridge abnormalities, but also lead to incorrect assessments of structural performance. Therefore, some researchers have tried to recover the lost data to improve the continuity and accuracy of structural response monitoring data. Considering that air temperature (AT) / temperature changes have a significant impact on bridge deformation, related research has mainly focused on using the correlation between temperature sensors and structural response sensors in the SHM system to predict and reconstruct structural response by establishing an input-output model.

[0004] Kromanis, Rolands, and Prakash Kripakaran. "Support vector regression for anomaly detection from measurement histories." Advanced Engineering Informatics 27.4 (2013): 486-495. The support vector regression (SVR) model is proposed to capture the relationship between temperature and structural response, and the strategy of using this model for damage detection is described.

[0005] Zhou, Guang-Dong, et al. "Modeling deformation induced by thermal loading using long-term bridge monitoring data." Journal of Performance of Constructed Facilities 32.3(2018):04018011. A correlation model between thermal load and vertical deformation of long-span arch bridges was proposed based on back propagation neural network.

[0006] Yue, Zixiang, et al. "Mechanics-Guided optimization of an LSTM network for Real-Time modeling of Temperature-Induced deflection of a Cable-Stayed bridge." Engineering Structures 252(2022): 113619. It is proposed to extract temperature features based on mechanical mechanism. Considering that the deep learning model has stronger nonlinear fitting ability, it is proposed to use long short-term memory neural network (LSTM) to predict the deflection caused by temperature change of cable-stayed bridge, which solves the adverse effects of low accuracy and time lag of the prediction model.

[0007] Since the temperature data used in the above study was measured by the bridge SHM system, the temperature data measured by the sensors in the SHM system may also be lost in actual projects. In this case, the accuracy and validity of the temperature data cannot be guaranteed. In response to the problem of temperature data loss in the SHM system, some studies have begun to use the air temperature measured by the meteorological station near the bridge site to replace the temperature data measured by the SHM system, and this method has been proven to be feasible. In addition, with the rapid development of artificial intelligence and big data technologies, the construction and operation of various meteorological sharing data platforms have facilitated the public's query and download of historical meteorological information. Therefore, the data provided by the meteorological sharing platform provides a new idea for reconstructing the structural response of bridges.

[0008] Concrete is one of the most commonly used materials in bridges currently in service. For concrete bridges, in addition to thermal effects, concrete structures have more characteristics in terms of deformation over time than other types of structures due to the inherent shrinkage and creep of concrete. However, when establishing concrete structure response prediction models, most studies tend to ignore the effects of concrete shrinkage and creep on the long-term structural response evolution. Therefore, some researchers have begun to consider incorporating time information into the model input layer to reflect the time-varying effects of long-term use of concrete.

[0009] Oh, Byung Kwan, Hyo Seon Park, and Branko Glisic. "Prediction of long-term strain in concrete structure using convolutional neural networks, air temperature and time stamp of measurements." Automation in Construction 126(2021): 103665. Taking the long-term strain monitoring data of a concrete pedestrian bridge as an example, the temperature data obtained from the local meteorological station was used, and the temperature and time parameters were used as input, and the strain was used as output. A long-term strain prediction model was established based on a convolutional neural network (CNN). However, this study did not consider the impact of changes in historical meteorological information in the process of model establishment. At the same time, the model used failed to reflect the long-term dependence between the data, and there is still room for improvement in the reconstruction accuracy of the structural response. Summary of the invention

[0010] In view of the shortcomings of the prior art, the present invention proposes a bridge displacement prediction method and system based on meteorological data and GRU model, which has a wider application range and higher displacement prediction accuracy. The specific technical solution is as follows:

[0011] In a first aspect, a bridge displacement prediction method based on meteorological data and a GRU model is provided. In a first implementable manner of the first aspect, the method includes:

[0012] Obtain the past meteorological data of the bridge location and the displacement data of the bridge, and construct a data set based on the acquired meteorological data and displacement data;

[0013] The GRU model is trained using the data set, and during the training process, an optimization algorithm is used to optimize the hyperparameters of the GRU model to obtain an optimal GRU model;

[0014] Obtain the current meteorological data at the bridge location and predict the bridge displacement using the optimal GRU model.

[0015] In combination with the first implementable manner of the first aspect, in a second implementable manner of the first aspect, constructing a data set based on meteorological data and displacement data includes:

[0016] Abnormal data in the meteorological data and displacement data are eliminated, and the processed meteorological data and displacement data are subjected to noise reduction, reconstruction and standardization.

[0017] In combination with the first implementable manner of the first aspect, in a third implementable manner of the first aspect, constructing a data set based on meteorological data and displacement data includes:

[0018] Performing correlation analysis on the meteorological data and the displacement data to determine the correlation coefficient between each meteorological factor in the meteorological data and the bridge displacement;

[0019] The data set is constructed by selecting data corresponding to meteorological factors with the correlation coefficient as a reference.

[0020] In combination with the third implementable manner of the first aspect, in a fourth implementable manner of the first aspect, the meteorological factors include air temperature, air pressure, solar radiation intensity and wind speed.

[0021] In combination with the first implementable manner of the first aspect, in a fifth implementable manner of the first aspect, constructing a data set based on meteorological data and displacement data includes:

[0022] Each sample in the data set takes the meteorological data at the current moment and the meteorological data of the historical period as input, and the displacement data at the next moment as output, and all samples form the data set in chronological order.

[0023] In combination with the first implementable manner of the first aspect, in a sixth implementable manner of the first aspect, the GRU model includes an input layer, a GRU layer, a discard layer, a fully connected layer, and an output layer connected in sequence.

[0024] In combination with the first implementable manner of the first aspect, in a seventh implementable manner of the first aspect, optimizing the hyperparameters of the GRU model includes:

[0025] The NGO algorithm is used to optimize the hyperparameters of the GRU model.

[0026] In combination with the fifth implementable manner of the first aspect, in an eighth implementable manner of the first aspect, a weighted root mean square error is used as a fitness function of the NGO algorithm.

[0027] In a second aspect, a bridge displacement prediction system based on meteorological data and a GRU model is provided. In a first implementable manner of the second aspect, the system includes:

[0028] A construction module is configured to obtain past meteorological data of the location of the bridge and displacement data of the bridge, and to construct a data set based on the obtained meteorological data and displacement data;

[0029] A training module, configured to train the GRU model using the data set, and to optimize the hyperparameters of the GRU model using an optimization algorithm during the training process to obtain an optimal GRU model;

[0030] The prediction module is configured to obtain the current meteorological data at the location of the bridge and predict the bridge displacement through the optimal GRU model.

[0031] In combination with the first implementable manner of the second aspect, in a second implementable manner of the second aspect, the training module includes: a parameter optimization unit configured to optimize the hyperparameters of the GRU model using an NGO algorithm.

[0032] Beneficial effects: The bridge displacement prediction method and system based on meteorological data and GRU model of the present invention can use the current meteorological data of the bridge location to predict the location of the bridge through the trained GRU model, without relying on the existing bridge structure health monitoring system, and thus has a wider range of applications. In addition, the GRU model has the advantages of strong nonlinear fitting ability and memory of historical information of time-varying data. The trained GRU model can better capture the long-term dependencies in time series data. During the training process of the GRU model, the hyperparameters of the GRU model are optimized using an optimization algorithm to maximize the performance of the GRU model, thereby obtaining a higher displacement prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific implementation of the present invention, the following will briefly introduce the drawings required for use in the specific implementation. In all the drawings, each element or part is not necessarily drawn according to the actual scale.

[0034] Figure 1 A flow chart of a bridge displacement prediction method based on meteorological data and a GRU model provided in one embodiment of the present invention;

[0035] Figure 2 A system block diagram of a bridge displacement prediction system based on meteorological data and a GRU model provided by an embodiment of the present invention;

[0036] Figure 3 A schematic diagram of the structure of a data set provided by an embodiment of the present invention;

[0037] Figure 4 A schematic diagram of the structure of a GRU model provided by an embodiment of the present invention;

[0038] Figure 5 A schematic diagram of the structure of a gated recurrent unit provided by an embodiment of the present invention;

[0039] Figure 6 is the vertical displacement data collected at a certain point on the bridge;

[0040] Figure 7 To eliminate the vertical displacement data after the abnormal time period;

[0041] Figure 8 are the 10 IMF components obtained by decomposing the vertical displacement data by VMD;

[0042] Fig. 9 is the PE of each IMF component;

[0043] Fig.10 It is the comparison result between the original vertical displacement data and the vertical displacement data after noise reduction and reconstruction;

[0044] Fig.11 To enlarge Fig.10 Data from the first 200 time points;

[0045] Fig.12 is the standardized vertical displacement data;

[0046] Fig.13 The following are the changing curves of temperature, air pressure, solar radiation intensity and wind speed in 2022;

[0047] Fig.14 It is the fitness convergence curve of the NGO-GRU model under Condition 1 to 4;

[0048] Fig.15 The predicted result of vertical displacement at a certain point of the bridge under Condition 1 to 4;

[0049] Fig.16 The scatter plot is of the predicted value and true value of vertical displacement of the GRU model on the test set under Condition 1 to 4;

[0050] Fig.17 To enlarge Fig.15 The prediction results of the model under various input conditions on the test set;

[0051] Fig.18 is the residual of the GRU model on the test set under Condition 1 and Condition 2;

[0052] Fig.19 It is the prediction result of the vertical displacement extreme value of the GRU model under Condition 2 to 4;

[0053] Fig. 20 It is the RMSE of different models on the test set under Condition 1 to 4. DETAILED DESCRIPTION

[0054] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0055] like Figure 1 The flowchart of the bridge displacement prediction method based on meteorological data and GRU model is shown, and the prediction method includes:

[0056] Step 1: Obtain the previous meteorological data of the location of the bridge and the displacement data of the bridge, and construct a data set based on the obtained meteorological data and displacement data;

[0057] Step 2: training the GRU model using the data set, and optimizing the hyperparameters of the GRU model using an optimization algorithm during the training process to obtain an optimal GRU model;

[0058] Step 3: Obtain the current meteorological data at the location of the bridge and predict the bridge displacement using the optimal GRU model.

[0059] Specifically, first, the meteorological data corresponding to each time period in the past range of the location of the bridge can be obtained through a platform that provides meteorological data services. Meteorological data can include meteorological data of meteorological factors that affect the structural response of the bridge, such as temperature, air pressure, solar radiation intensity, and wind speed. At the same time, the vertical displacement data corresponding to the bridge at the corresponding time point can be collected through the SHM system. The meteorological data and displacement data corresponding to each time point obtained are used as samples to construct a data set for GRU model training.

[0060] Then, the GRU model can be trained using the data set, and the root mean square error (RMSE) is used as an evaluation index to evaluate the prediction effect of the trained GRU model on the vertical displacement of the bridge. During the training process, existing optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, can be used to optimize the hyperparameters of the GRU model to obtain the optimal GRU model.

[0061] Finally, the current meteorological data at the location of the bridge can be obtained, and the vertical displacement of the bridge can be predicted through the optimal GRU model obtained through training. In this way, the location of the bridge can be predicted using only the meteorological data at the location of the bridge, without relying on the existing bridge structure health monitoring system, so it has a wider range of applications. Moreover, the trained GRU model has the advantages of strong nonlinear fitting ability and memory of historical information of time-varying data, and can better capture the long-term dependencies in time series data. During the training process of the GRU model, the optimization algorithm is also used to optimize the hyperparameters of the GRU model, which maximizes the performance of the GRU model, so that higher displacement prediction accuracy can be obtained.

[0062] In this embodiment, optionally, a data set is constructed based on meteorological data and displacement data, including:

[0063] Abnormal data in the meteorological data and displacement data are eliminated, and the processed meteorological data and displacement data are subjected to noise reduction, reconstruction and standardization.

[0064] Specifically, considering that the bridge SHM monitoring data presents a certain change pattern in the long term, when the collected vertical displacement data is too large, too small or other abnormal conditions appear, the data in this time period needs to be eliminated. In order to ensure the continuity of the subsequent data set construction, the time period for eliminating data is carried out in days. Abnormal data elimination is mainly for the vertical displacement data collected by the bridge SHM system. The reason is that the meteorological data recorded by the meteorological data platform is more complete and accurate than the bridge monitoring data, and generally no abnormal values ​​will appear during the measurement period.

[0065] It should be understood that data noise is inevitable in the data measurement process, and its existence will cover the key information of the data itself. In order to obtain effective data and train an excellent deep learning model, the data can be denoised and reconstructed. Currently commonly used denoising methods include wavelet denoising, empirical mode decomposition (EMD) and variational mode decomposition (VMD). Since VMD has stronger robustness to sampling and noise, and can effectively avoid modal aliasing, this embodiment uses variational mode decomposition for denoising and reconstruction.

[0066] The principle of variational mode decomposition is to obtain several intrinsic mode functions (IMF) with a certain bandwidth by iteratively searching for the optimal solution of the variational mode, so as to achieve effective separation of each component. Before performing VMD, it is necessary to predetermine the value of the modal number K, which determines the accuracy of each component after decomposition. Too large a K value will lead to over-decomposition, while too small a value will lead to under-decomposition. The observation of the center frequency method is an intuitive method that can effectively find the optimal K value. In addition, in order to more intuitively identify the noise in the data, the permutation entropy (PE) algorithm is used to describe each component. The PE algorithm can be used to detect the randomness of a time series, and its value range is 0 to 1. The smaller the value, the more regular the time series. In this embodiment, the threshold of PE can be set to 0 to 0.6.

[0067] In order to eliminate the errors caused by differences in data size, characteristics and distribution, and to accelerate the convergence speed of gradient descent during network training, all data need to be standardized and the numerical values ​​mapped to the range of 0 to 1. The calculation formula is as follows:

[0068]

[0069] Among them, x, x std are the denoised and reconstructed data and the standardized data, respectively. max 、xmin are the minimum and maximum values ​​in the data sequence after denoising and reconstruction.

[0070] Taking the vertical displacement data collected by a sensor at a certain location on a bridge from January 1, 2022 to March 31, 2024 as an example, the above method is used to preprocess the data. Figure 6 It can be seen that the original vertical displacement data is abnormal in three consecutive time periods, so the data in this time period needs to be removed. After removing the abnormal time period, the vertical displacement data changes more regularly over time and can better highlight the data characteristics. Figure 7 shown.

[0071] Based on the data after removing abnormal data, the optimal modal number K value is determined to be 10 by observing the center frequency method, and the IMF components obtained by decomposing the VMD algorithm are as follows: Figure 8 In addition, the PE value of each IMF component is calculated as follows Fig. 9 As shown in the figure. From the calculation results, it can be seen that the PE of IMF5-10 is smaller than that of other components, and within the threshold range, it can be regarded as an effective component; the PE of IMF1-4 is larger than that of other components, and can be determined as a noise-dominated component. Therefore, the first four components are discarded, and IMF5-10 is selected for reconstruction. The reconstructed data is shown in Fig.10 shown. Fig.11 Further magnified Fig.10 The curve corresponding to the first 200 data points in the figure shows that the curve after noise reduction and reconstruction is smoother and can better highlight the important features of the data. Finally, the noise-reduced and reconstructed data is standardized, and the data obtained is as follows Fig.12 It is worth noting that for vertical displacement data, after denoising and reconstruction, not only can the noise in the data be eliminated, but also the impact of vehicle load can be reduced. This is beneficial to the establishment of a correlation model between meteorological factors and vertical displacement.

[0072] In this embodiment, optionally, a data set is constructed based on meteorological data and displacement data, including:

[0073] Performing correlation analysis on the meteorological data and the displacement data to determine the correlation coefficient between each meteorological factor in the meteorological data and the bridge displacement;

[0074] The data set is constructed by selecting data corresponding to the meteorological factors with the correlation coefficient as a reference.

[0075] Specifically, after preprocessing the acquired meteorological data and displacement data, the Pearson correlation coefficient algorithm can be used to calculate the correlation coefficient between each meteorological factor and the vertical displacement of the bridge. According to the correlation coefficient corresponding to each meteorological factor, the monitoring data corresponding to each meteorological factor that is strongly correlated with the vertical displacement of the bridge is selected as a sample to construct the data set.

[0076] Specifically, based on the meteorological data and displacement data obtained after preprocessing, the Pearson correlation coefficient algorithm was used to calculate the Pearson correlation coefficients of temperature, air pressure, solar radiation intensity, wind speed and vertical displacement in 2022. The calculation results are as follows: Fig.13 As shown in the figure, AT represents air temperature, AP represents air pressure, SRI represents solar radiation intensity, WS represents wind speed, and VD represents vertical displacement.

[0077] The calculation results show that the correlation coefficients between temperature, air pressure, solar radiation intensity and wind speed and vertical displacement are 0.9387, -0.8057, 0.2787 and 0.3333 respectively. Among them, there is a strong correlation between temperature and vertical displacement, which confirms that the influence of temperature on structural performance is more significant than other meteorological factors. In addition, in addition to temperature, air pressure also has a significant effect on vertical displacement.

[0078] However, it can be seen from the correlation coefficient between solar radiation intensity and wind speed and vertical displacement that the linear correlation between the two is not obvious, but this does not mean that there is no regularity between solar radiation intensity or wind speed and vertical displacement. Because the Pearson correlation coefficient is only used to measure the linear correlation between two variables, and the change in vertical displacement is usually related to historical meteorological information, this is also the limitation of the Pearson correlation coefficient. Therefore, in this application, the Pearson correlation coefficient is only used as a reference coefficient to measure the correlation of data. In view of this, the monitoring data corresponding to air pressure, solar radiation intensity and wind speed should also be added to construct a data set to improve the accuracy of the model.

[0079] The transient response of bridges is often related to historical meteorological changes. Therefore, in order for the model to fully capture this relationship and improve its interpretability and accuracy, it is necessary to construct the input data for the historical observation period. The schematic diagram of the data set is shown in the figure. Figure 3 shown.

[0080] The input of each set of samples in the data set consists of the data at the current moment and the data of the historical period, and the output is the vertical displacement at the next moment. The interval of sample construction is one data point, and the data set is constructed in chronological order to introduce the time information of collecting meteorological data and displacement data.

[0081] In this embodiment, optionally, the GRU model includes an input layer, a GRU layer, a discard layer, a fully connected layer and an output layer that are connected in sequence.

[0082] Specifically, if Figure 4As shown in the figure, the GRU model includes an input layer, a GRU layer, a dropout layer, a fully connected layer, and an output layer. Among them, the GRU layer is the core of the entire neural network architecture. The purpose of adding a Dropout layer after the GRU layer is to drop some neurons with random probability during the model training process, thereby preventing the model from being too dependent on local features and improving the generalization ability of the model.

[0083] The GRU layer is composed of multiple gated recurrent units, such as Figure 5 Compared with the RNN module, the core idea of ​​the gated recurrent unit is to introduce a gating mechanism, including a reset gate and an update gate. The reset gate gives a way to combine the previous memory and the new input information, while the update gate is used to selectively forget or retain the historical hidden state. The input information is the current input X t and the hidden state H at the previous moment t-1 , the output information is H~ t and H t , reset gate R t and update gate Z t The calculation formula is as follows:

[0084] R t =σ(X t W xr +H t-1 W hr +b r );

[0085] Z t =σ(X t W xz +H t-1 W hz +b z );

[0086] Where σ is the sigmoid activation function; W xr , W xz , W hr and W hz are the corresponding weight parameter matrices; b r and b z are the corresponding bias vectors respectively.

[0087] Candidate hidden state at time t As shown in the following formula, finally according to the candidate hidden state H~ t and the hidden state H at the previous moment t-1 Get the hidden state at time t, the specific calculation formula is as follows:

[0088]

[0089] Among them, tanh is the hyperbolic tangent activation function, ⊙ is the Hadamard product; W xh and W hh are the corresponding weight parameter matrices, b h is the corresponding bias vector.

[0090] It should be understood that the above-mentioned weight parameter matrix and bias vector can be updated during the back-propagation process of model training, and all gated recurrent units share the same set of weight parameter matrix and bias vector.

[0091] It should be noted that the above-mentioned weight parameter matrix and bias vector can be updated during the back-propagation process of model training, and all GRU modules share the same set of weight parameter matrix and bias vector.

[0092] The hyperparameters of the GRU model mainly include: initial learning rate, learning rate decay strategy, number of GRU layers, batch size, number of hidden units, Dropout ratio and historical observation time. Considering that a learning rate that is too low will make the model learn too slowly, and a learning rate that is too high will make it difficult for the model to converge, a learning rate decay strategy is adopted during training. By using the LearningRateScheduler regulator, the model reduces the learning rate by 5% every 4 iterations. At the same time, considering the input data size and time calculation cost, a single GRU layer is sufficient to train the model and maintain good accuracy, so the number of GRU layers can be fixed to one layer. The number of training steps epoch is set to 300, and the optimizer uses the Adam optimizer.

[0093] In this embodiment, optionally, the hyperparameters of the GRU model are optimized, including:

[0094] The NGO algorithm is used to optimize the hyperparameters of the GRU model.

[0095] Specifically, the prediction accuracy and stability of the GRU neural network are affected by the training hyperparameters. In order to improve the generalization ability of the neural network, it is necessary to find a set of suitable hyperparameters for model training. There are many classic optimization algorithms, such as genetic algorithm (GA), particle swarm optimization algorithm (PSO), etc. Although GA has good global search ability, its local search ability is poor. Compared with other optimization algorithms, its search efficiency is low and it is easy to fall into premature convergence.

[0096] PSO is relatively simple in parameter setting and easy to implement, but it is overly dependent on the inertia factor value. When the inertia factor value is large, PSO has strong global optimization ability but weak local optimization ability; conversely, when the inertia factor value is small, the global optimization ability is weak but the local optimization ability is strong.

[0097] Compared with the above-mentioned classic optimization algorithms, the NGO algorithm has good global and local search capabilities. It has higher search efficiency and better optimization results, and is suitable for processing regression problems with large amounts of data. Therefore, in this embodiment, the Northern Goshawk Optimization Algorithm (NGO algorithm) can be used to optimize the hyperparameters of the GRU model. In the hyperparameter optimization stage, the data set used to train the GRU model can be further subdivided into a training data set and a validation data set, and the initial population size of the NGO algorithm is set to 5, and the maximum number of iterations is set to 5. The following table gives the search intervals for the hyperparameters to be optimized for the GRU neural network:

[0098] Hyperparameter Name Hyperparameter search interval Initial learning rate [0.001,0.1] Batch size [10,128] Number of hidden units [32,256] Dropout ratio 0.1,0.2,0.3,0.4and0.5 Historical observation time 3,6,9,12,18and24

[0099] Table 1 Search interval of hyperparameters to be optimized for GRU neural network

[0100] The NGO algorithm simulates the behavior of the northern goshawk during hunting, which is divided into two stages: the first stage is the prey recognition and attack stage, and the second stage is the pursuit and escape stage.

[0101] In the prey identification and attack stage, the northern goshawk will conduct a global search of the search space, randomly select prey and attack. The mathematical expression is:

[0102] P i =X k ;

[0103]

[0104] i=1,2,…,M; k=1,2,…,i-1,i+1,…,M.

[0105] Among them, X i is the position of the i-th northern goshawk, i.e., the hyperparameter of the GRU model, F i is the fitness function value corresponding to the i-th northern goshawk, P i The location of the prey selected by the i-th northern goshawk, F Pi is the fitness function value corresponding to the prey position selected by the i-th northern goshawk, x i , j is the position of the i-th northern goshawk in the j-dimension, p i , j is the position of the prey in the jth dimension, is the new position of the jth dimension of the i-th northern goshawk, r is a random number in the range [0,1], I takes the value of 1 or 2, They are respectively the global new position and fitness value of the i-th northern goshawk after the update in the first stage.

[0106] During the pursuit and escape phase, the northern goshawk will chase the escaping prey. The simulation of this behavior can improve the local search ability of the optimization algorithm. Assuming that this hunting occurs within the attack range of radius R, the mathematical expression is as follows:

[0107]

[0108] in, is the j-th dimension position of the i-th northern goshawk after the second stage update, t is the current iteration number, T is the maximum iteration number, They are respectively the global new position and fitness value of the i-th northern goshawk after the second stage update.

[0109] In this embodiment, optionally, a weighted root mean square error is used as the fitness function of the NGO algorithm. Specifically, in order to improve the generalization ability of the model, the weighted root mean square error can be selected as the fitness function of the NGO algorithm, and the weights of the training error and the verification error are set to 0.4 and 0.6 respectively. The fitness function is specifically:

[0110] f(θ)=0.4×RMSE train +0.6×RMSE valid ;

[0111] Among them, RMSE train 、RMSE valid are the root mean square errors of the training set and validation set used in the hyperparameter optimization phase, respectively.

[0112] To further evaluate the predictive ability of the GRU model optimized by the NGO algorithm, the training dataset and the validation dataset in the optimization phase can be merged into one dataset again, and the GRU model can be retrained using the optimal hyperparameters.

[0113] During the training process, the root mean square error (RMSE) can be used as an evaluation indicator. The specific calculation formula is as follows:

[0114]

[0115] Where N is the number of samples in the test set, f j ,y j are the predicted value and true value of the jth sample in the test set, respectively.

[0116] The smaller the RMSE value, the smaller the deviation between the model's prediction result and the true value, and the more accurate the prediction result. RMSE can intuitively reflect the absolute error of the model, but it is not suitable for evaluating relative error. Therefore, the ratio of the RMSE variation range (RRVS) in the cut data set (training set or test set) can also be introduced to evaluate the relative error size of the model. The specific calculation formula is as follows:

[0117]

[0118] Among them, D max , D min are the maximum and minimum values ​​of vertical displacement in the cutting data set, respectively.

[0119] To illustrate the technical effect of the prediction method provided in this embodiment, the data from January 1, 2022 to March 31, 2023 in the above-constructed dataset is used to construct a training set, and the data from April 1, 2023 to March 31, 2024 is used to construct a test set. In order to optimize the hyperparameters in the GRU model, the training set is further subdivided into a training data set and a validation data set in the hyperparameter optimization stage. The time period of the training data set is from January 1, 2022 to December 31, 2022, which contains sufficient information on the full range of variability. The time period of the validation data set is from January 1, 2023 to March 31, 2023.

[0120] In order to find the combination of influencing factors with the highest vertical displacement prediction accuracy, referring to the correlation between various meteorological factors and vertical displacement, four working conditions with different data types are proposed as the input of the NGO-GRU model, as shown in Table 2:

[0121] Condition Input information 1 Temperature 2 Temperature; time information 3 Temperature; time information; air pressure 4 Temperature; time information; air pressure; solar radiation intensity; wind speed

[0122] Table 2 Input of NGO-GRU model in Condition 1 to 4

[0123] Considering that air temperature is the main meteorological factor that causes the vertical displacement of the bridge, air temperature is included in the input layer of the model in all four input conditions. Condition 1 only uses the historical air temperature in the meteorological data as the input of the model and serves as a comparison model for subsequent input conditions. Considering that concrete shrinks and creeps, which is a slow process that changes over time, Condition 2 adds the time information corresponding to the air temperature measurement to the input layer of the model, so the input information includes two variables: air temperature and time information.

[0124] Condition 3 takes into account the strong correlation between air pressure and vertical displacement, and adds air pressure as the input of the NGO-GRU model based on Condition 2. Condition 4 comprehensively considers five factors, namely temperature, air pressure, solar radiation intensity, wind speed and time information, as the input of the NGO-GRU model to verify whether the continued addition of other meteorological factors will further improve the prediction accuracy of the model.

[0125] Based on the above-constructed data set, the GRU models of the above four different input conditions are trained respectively, and finally the fitness convergence curves under Condition 1 to 4 are obtained as shown in the figure below: Fig.14 As shown. Fig.14 It can be seen that the fitness functions of the NGO-GRU models under Condition 1 to 4 have converged, indicating that 5 iterations are sufficient for the NGO algorithm to find the optimal hyperparameters of the GRU model. In the NGO solution process, since the optimal position moves slowly, reflecting the direction of the entire group, the position of the goshawk gradually converges into a "straight line" with the "elite reverse learning strategy", which effectively improves the convergence speed and accuracy. In particular, Condition 1 to 4 all reached the minimum fitness in the second iteration, and obtained the optimization results that met the accuracy, which further illustrates the stability of the NGO algorithm.

[0126] Fig.15 The following are the prediction results of different input conditions Condition 1 to 4 on the training set and the test set. It can be seen from the prediction results that the four different input conditions can predict the fluctuation trend of the overall vertical displacement well, whether in the training set or the test set. In particular, the prediction effect of the test set that was not used for model training can more intuitively reflect the model's ability to reconstruct long-term vertical displacement. In addition, from the prediction results of Condition 1, only using air temperature as the input of the model can accurately predict the change trend of the overall vertical displacement of the bridge, which verifies that air temperature is the main controlling factor of the vertical displacement of concrete bridges. However, comparing the prediction results under the four different input conditions, Condition 2 to 4 have a better reconstruction effect on the vertical displacement than Condition 1. Fig.16 From top to bottom in the figure are the scatter plots of the predicted and true values ​​of the vertical displacement on the test set for the four different inputs of Condition 1 to 4. If the vertical displacement prediction is accurate, the scatter points should be concentrated near the linear function with a slope of 1.0. It can also be seen from Figure 16 that the model under all working conditions predicts the vertical displacement accurately, and the scatter points tend to the linear function, but the scatter plot under Condition 1 has a drift phenomenon.

[0127] Fig.17 Further magnified Fig.15The prediction results of vertical displacement of the test set of the model under the four input conditions from August 10 to 19, 2023 and February 10 to 19, 2024. It can be seen that all input conditions can accurately predict the fluctuation trend of vertical displacement. However, the predicted value of Condition 1 does not fluctuate around the true value, there is a large deviation between the predicted curve and the true curve, and the vertical displacement predicted by the model is generally greater than the true vertical displacement, which cannot accurately predict the long-term vertical displacement of the concrete bridge. Condition 2 considers the measurement time information corresponding to the temperature on the basis of Condition 1, which significantly improves the prediction accuracy of the vertical displacement and makes the vertical displacement prediction curve closer to the true value. Conditions 3 to 4 add other meteorological factors on the basis of considering the temperature and time information, which can also accurately predict the long-term vertical displacement of concrete bridges.

[0128] To further illustrate the importance of adding time information to the model input layer, Fig.18 The residual size of the model on the test set under Condition 1 and Condition 2 is shown. The residual is calculated by subtracting the true value from the predicted value. From the residual result of Condition 1, it can be seen that the residual distribution is extremely uneven, and the residual values ​​are greater than zero in a large number of time periods.

[0129] In addition, the residual of Condition 1 shows an increasing trend over time. This is because the time-varying effect of concrete in long-term use is not considered, which leads to an overall deviation in the vertical displacement prediction curve under Condition 1. In contrast, Condition 2 further adds the time information of the temperature measurement on the basis of considering the temperature to construct the input set of the model. From the residual results, it can be seen that the residual distribution of Condition 2 is more uniform than that of Condition 1, and it can better learn the characteristics of concrete bridges changing over time during long-term use.

[0130] In order to find the best meteorological data combination for predicting the vertical displacement of concrete bridges, in Condition 3, the model input layer adds air pressure as input on the basis of considering temperature and time information. From the results of RMSE, the data set constructed after adding air pressure can further improve the prediction accuracy of the model. Condition 4 uses five variables, namely temperature, time information, air pressure, solar radiation intensity and wind speed, to construct the data set of the model, and it is found that the prediction accuracy of vertical displacement is improved again. It can be seen that although the Pearson correlation coefficient between solar radiation intensity and wind speed and vertical displacement is small and the linear law is not obvious, they still show a positive effect in predicting vertical displacement.

[0131] Therefore, among the models with four different input conditions, Condition 4 can more accurately predict the long-term vertical displacement of concrete bridges. In addition, it can be seen from the RRVS results that the relative errors of the model training set and test set under Conditions 1 to 4 are all below 6%. Among them, Condition 4 has the smallest relative errors in the training set and test set, which are 1.96% and 2.78% respectively, and its reconstruction accuracy of vertical displacement is the highest. Therefore, under the premise of being able to obtain air temperature, time information, air pressure, solar radiation intensity and wind speed, the accuracy of predicting the long-term vertical displacement of concrete bridges is the highest when these five factors are comprehensively considered as model inputs.

[0132]

[0133] Table 3 Error evaluation index size of the model under four input conditions on the training set and test set

[0134] In order to further test the prediction accuracy of the NGO-GRU model for the extreme values ​​of vertical displacement under Conditions 2 to 4, the maximum and minimum values ​​of the actual values ​​of vertical displacement in the test set in August 2023 and February 2024 and the predicted values ​​of vertical displacement under Conditions 2 to 4 were extracted, and the correlation scatter plot between them was drawn as shown in the figure. Fig.19 shown.

[0135] from Fig.19 It can be seen that, whether in August or February, the predicted value and the true value scatter points under Condition 4 are closer to the linear regression equation. The RMSE values ​​of the extreme values ​​under Conditions 2 to 4 in the above two time periods were further calculated and shown in the figure. Obviously, the RMSE value under Condition 4 is the smallest, which is 0.4102 and 0.5072 respectively. Therefore, from the perspective of safety assessment, Condition 4 is the most effective in predicting vertical displacement compared with other working conditions. In summary, taking temperature, time information, air pressure, solar radiation intensity and wind speed as the input of the NGO-GRU model, the accuracy is the highest whether it is the waveform prediction of long-term vertical displacement or the extreme value prediction.

[0136] In order to verify the advancement of the NGO algorithm and the superiority of the GRU regression model, the GA algorithm and the PSO algorithm were selected as comparison algorithms, and the RNN and LSTM neural networks were selected as comparison models. Four models, GA-GRU, PSO-GRU, NGO-RNN, and NGO-LSTM, were constructed and compared with the NGO-GRU model. It should be noted that the training conditions of the above four models are the same as those of the NGO-GRU. Taking the prediction of vertical displacement under Condition 1 to 4 as an example, Fig. 20The RMSE values ​​of different models on the test set under various input conditions are given.

[0137] From the prediction results, it can be seen that the prediction accuracy of the NGO-GRU model under four different input conditions is better than that of other models. From the algorithm level, the performance of the NGO-optimized GRU model is improved by 2.02% to 23.58% compared with the GA- and PSO-optimized GRU models. The NGO algorithm can make full use of the characteristics of the solution function and find and use the optimal parameters in the solution space as much as possible, thereby increasing the possibility of finding a new local optimal solution, enhancing the convergence accuracy near the local optimal solution and the ability to use the local optimal solution.

[0138] From the perspective of regression models, the performance of the GRU model optimized by the NGO algorithm is 28.77% to 46.17% higher than that of the RNN model and 6.35% to 44.30% higher than that of the LSTM model. The prediction results show that the GRU can effectively handle the long-term dependency of data by introducing a gating mechanism, and the accuracy of predicting vertical displacement is higher than that of the RNN model. Moreover, the prediction accuracy of the NGO-GRU model is higher than that of the LSTM model.

[0139] In summary, compared with GA-GRU, PSO-GRU, NGO-RNN and NGO-LSTM models, it is determined that the NGO-GRU model has the highest accuracy in vertical displacement prediction. And under the optimal meteorological factor combination of temperature, time information, air pressure, solar radiation intensity and wind speed, the GRU model optimized by the NGO algorithm can achieve higher bridge vertical displacement prediction accuracy.

[0140] like Figure 2 The system block diagram of the bridge displacement prediction system based on meteorological data and GRU model shown in FIG. 1 includes:

[0141] A construction module is configured to obtain past meteorological data of the location of the bridge and displacement data of the bridge, and to construct a data set based on the obtained meteorological data and displacement data;

[0142] A training module, configured to train the GRU model using the data set, and to optimize the hyperparameters of the GRU model using an optimization algorithm during the training process to obtain an optimal GRU model;

[0143] The prediction module is configured to obtain the current meteorological data at the location of the bridge and predict the bridge displacement through the optimal GRU model.

[0144] Specifically, the prediction system includes a construction module, a training module and a prediction module. Among them, the construction module can obtain the meteorological data corresponding to each time point in the past period of time at the location of the bridge through a platform that provides meteorological data services. Meteorological data can include meteorological data of meteorological factors such as temperature, air pressure, solar radiation intensity and wind speed that will affect the structural response of the bridge. At the same time, the vertical displacement data corresponding to the bridge at the corresponding time point can be collected through the SHM system. The meteorological data and displacement data corresponding to each time point obtained are used as samples to construct a data set for GRU model training.

[0145] The training module can train the GRU model through the data set, and use the root mean square error (RMSE) as the evaluation index to evaluate the prediction effect of the trained GRU model on the vertical displacement of the bridge. During the training process, existing optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, can be used to optimize the hyperparameters of the GRU model to obtain the optimal GRU model. The prediction module can obtain the current meteorological data at the location of the bridge, and predict the vertical displacement of the bridge through the optimal GRU model obtained through training.

[0146] In this embodiment, optionally, the training module includes:

[0147] The parameter optimization unit is configured to optimize the hyperparameters of the GRU model using the NGO algorithm.

[0148] Specifically, the training module includes a parameter optimization unit, which can use the NGO algorithm to optimize the hyperparameters of the GRU model. Compared with the above-mentioned classic optimization algorithm, the NGO algorithm has good global and local search capabilities. It has higher search efficiency and better optimization results, and is suitable for processing regression problems with large amounts of data.

[0149] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A bridge displacement prediction method based on meteorological data and GRU model, characterized in that: include: Obtain the past meteorological data of the bridge location and the displacement data of the bridge, and construct a data set based on the acquired meteorological data and displacement data; The GRU model is trained using the data set, and during the training process, an optimization algorithm is used to optimize the hyperparameters of the GRU model to obtain an optimal GRU model; Obtain the current meteorological data at the bridge location and predict the bridge displacement using the optimal GRU model.

2. The bridge displacement prediction method based on meteorological data and GRU model according to claim 1 is characterized in that: The dataset is constructed based on meteorological data and displacement data, including: Abnormal data in the meteorological data and displacement data are eliminated, and the processed meteorological data and displacement data are subjected to noise reduction, reconstruction and standardization.

3. The bridge displacement prediction method based on meteorological data and GRU model according to claim 1 is characterized in that: The dataset is constructed based on meteorological data and displacement data, including: Performing correlation analysis on the meteorological data and the displacement data to determine the correlation coefficient between each meteorological factor in the meteorological data and the bridge displacement; The data set is constructed by selecting data corresponding to meteorological factors with the correlation coefficient as a reference.

4. The bridge displacement prediction method based on meteorological data and GRU model according to claim 3 is characterized in that: The meteorological factors include air temperature, air pressure, solar radiation intensity and wind speed.

5. The bridge displacement prediction method based on meteorological data and GRU model according to claim 1 is characterized in that: The dataset is constructed based on meteorological data and displacement data, including: Each sample in the data set takes the meteorological data at the current moment and the meteorological data of the historical period as input, and the displacement data at the next moment as output, and all samples form the data set in chronological order.

6. The bridge displacement prediction method based on meteorological data and GRU model according to claim 1 is characterized in that: The GRU model includes an input layer, a GRU layer, a discard layer, a fully connected layer and an output layer which are connected in sequence.

7. The bridge displacement prediction method based on meteorological data and GRU model according to claim 1 is characterized in that: The hyperparameters of the GRU model are optimized, including: The NGO algorithm is used to optimize the hyperparameters of the GRU model.

8. The bridge displacement prediction method based on meteorological data and GRU model according to claim 5 is characterized in that: The weighted root mean square error is used as the fitness function of the NGO algorithm.

9. A bridge displacement prediction system based on meteorological data and GRU model, characterized in that: include: A construction module is configured to obtain past meteorological data of the location of the bridge and displacement data of the bridge, and to construct a data set based on the obtained meteorological data and displacement data; A training module, configured to train the GRU model using the data set, and to optimize the hyperparameters of the GRU model using an optimization algorithm during the training process to obtain an optimal GRU model; The prediction module is configured to obtain the current meteorological data at the location of the bridge and predict the bridge displacement through the optimal GRU model.

10. The bridge displacement prediction system based on meteorological data and GRU model according to claim 9 is characterized in that: The training module includes: The parameter optimization unit is configured to optimize the hyperparameters of the GRU model using the NGO algorithm.

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