A method for reconstructing continuous missing monitoring data of longitudinal displacement of a suspension bridge end

Abstract

The application discloses a kind of suspension bridge beam end longitudinal displacement continuous missing monitoring data reconstruction method, comprising the following steps: S1, the effective data of historical environmental temperature and beam end displacement in monitoring result are preprocessed;S2, using long short-term memory network model, the LSTM regression model between environmental temperature and beam end longitudinal displacement low-frequency component time series is established;S3, based on the frequency band widening model of full convolutional neural network of U-shaped architecture, different frequency band beam end longitudinal displacement data high-frequency component reconstruction is realized gradually in stages;S4, the prediction result of series connection model is corrected using statistical correction method;S5, the performance of entire data reconstruction method on test set is evaluated using performance evaluation index.The application can well make up the data missing defect frequently affected by various reasons in health monitoring system, serve for subsequent data mining, with feasibility, reliability.

Description

TECHNICAL FIELD

[0001] The present application relates to a bridge health monitoring method, in particular to a method for reconstructing continuous missing monitoring data of longitudinal displacement of a suspension bridge end. BACKGROUND

[0002] Structural health monitoring (SHM) data is an important support for the health condition perception, risk warning and management decision-making of long-span bridges. The content of long-span bridge health monitoring generally covers vibration, strain, cable force, displacement, structure temperature and bridge site environmental variables. Among them, the displacement of the beam end is a key factor affecting the health condition of components such as expansion joints, dampers and bearings. Under the long-term effects of environment (temperature and wind) and traffic load, the frequent reciprocating movement of the beam end will produce a large cumulative displacement, which will cause fatigue and wear of the above components, and even affect the bridge structure itself. As the main bridge type of long-span bridges, both cable-stayed bridges and suspension bridges have greater beam end displacement due to the significant flexibility of the latter. The longitudinal displacement monitoring of the beam end of the main girder of a long-span suspension bridge has always been the focus of attention in the field of health monitoring.

[0003] The SHM system generally consists of a sensor subsystem, a data acquisition and transmission subsystem, a data storage and processing subsystem, a structure safety evaluation and early warning subsystem, etc. Any problem in the first three links may lead to data loss or abnormality. It has been found in engineering practice that data loss does indeed occur frequently in SHM systems. The missing monitoring data of the displacement of the beam end of a suspension bridge will reduce the reliability of the performance evaluation conclusion of the beam end components such as expansion joints of the bridge, and even lead to incorrect conclusions. Therefore, the reconstruction of missing beam end displacement data is of great importance to the bridge SHM system.

[0004] SHM data loss mainly includes the following two situations: random loss and continuous loss. The displacement data of the beam end of a suspension bridge is no exception. When the data transmission or storage module of the bridge SHM system fails (the actual situation may not be limited to this), it is easy to have long-term continuous loss of displacement monitoring data in multiple channels. At this time, the reconstruction method commonly used in the current deep learning research, i.e. using the correlation between multiple displacement sensors to realize data reconstruction, cannot be used. When the displacement data of the beam end of other channels cannot be used, other types of monitoring data need to be used, i.e. using the physical correlation between different types of sensors. At this time, the environmental monitoring data with a strong correlation with the longitudinal displacement of the beam end of a suspension bridge and a large number of channels are good basic data. SUMMARY

[0005] The purpose of the present application is to provide a method for reconstructing the longitudinal displacement data of the beam end in the case of continuous loss of displacement data in all channels of the SHM system of a suspension bridge.

[0006] Technical scheme: the suspension bridge end longitudinal displacement continuous missing monitoring data reconstruction method of the application, comprising the following steps:

[0007] S1, the effective data of historical environmental temperature and beam end displacement in the monitoring result are pretreated;

[0008] S2, the LSTM regression model between environmental temperature and beam end longitudinal displacement low-frequency component time series is established by using long short-term memory network model;

[0009] S3, the frequency band widening model based on the full convolutional neural network of U-shaped architecture is used to realize the reconstruction of the high-frequency component of the beam end longitudinal displacement data in different frequency bands in stages;

[0010] S4, the statistical correction method is used to correct the prediction results of the series connection model;

[0011] S5, the performance evaluation index is used to evaluate the performance of the whole data reconstruction method on the test set.

[0012] Further, in step S1, the historical environmental temperature and beam end displacement original data recorded by the health monitoring data system of the large-span suspension bridge are pre-screened and pretreated; the beam end longitudinal displacement spectrum of the suspension bridge is read, and the sampling frequency 2f D is selected, under the premise of retaining frequency domain information, the original data is down-sampled; the sample data obtained after the final pretreatment is divided into training set, validation set and test set according to a certain proportion, and small batch processing method and overlap reservation method are respectively used for model training, model optimization and model evaluation.

[0013] Further, in step S2, the network structure of the LSTM regression model is as follows: starting from an input layer and ending with a fully connected layer and an output layer; the network core part is m LSTM layers connected in series, each LSTM layer is followed by a dropout layer, and the output of each LSTM layer is randomly set to zero with a probability q; the environmental temperature and beam end longitudinal displacement low-frequency components with a sampling frequency of 2f T are respectively used as the input and output of the LSTM regression model;

[0014] The mean square error is used as the optimization objective function of the LSTM regression model; the optimal LSTM regression model is selected by using the time domain loss function root mean square difference RMSE, and the expression of the mean square error is as follows:

[0015]

[0016] In the formula, D T and These represent the true and predicted value sequences of the low-frequency components of the longitudinal displacement at the beam end, respectively, with the subscript T indicating the time domain; D T (n) D T and The value with index n in the sequence; N represents the length of the time series;

[0017] The formula for calculating the root mean square error (RMSE) of the time-domain loss function is as follows:

[0018]

[0019] In the formula, D T and These represent the true and predicted value sequences of the low-frequency components of the longitudinal displacement at the beam end, respectively, with the subscript T indicating the time domain; D T (n) D T and The value with index n in the sequence; N represents the length of the time series.

[0020] Furthermore, in step S3, three super-resolution models are trained to complete the spectral bandwidth expansion of the longitudinal displacement data at the beam end in three stages, gradually realizing f T to f M1 frequency band, f M1 to f M2 frequency band, f M2 to f D Reconstruction of high-frequency components of beam end displacement data in the frequency band, where f T f represents the spectral bandwidth of the low-frequency component of the longitudinal displacement data at the beam end. D The target bandwidth for reconstructing longitudinal displacement data at the beam end;

[0021] The training and hyperparameter optimization of the super-resolution model in the three stages are carried out independently. Using the preprocessed longitudinal displacement data samples at the beam end in step S1, the sampling frequencies are reduced to 2f. T 2f M1 and 2f M2 Sample longitudinal displacement data at the beam end;

[0022] Before being fed into the super-resolution model at each stage, the input sequence of each stage needs to be upsampled using cubic spline interpolation until the sampling frequency is consistent with the output of the super-resolution model at that stage, while keeping the spectral bandwidth unchanged.

[0023] Further, in step S3, the super-resolution model of each stage adopts a U-shaped architecture, in which the input sequence is first compressed to the shortest length by an encoder and then expanded to the original length by a decoder; the encoding and decoding of the input sequence are respectively implemented by a series of one-dimensional convolution layers and sub-pixel convolution layers, the output of a convolution layer is referred to as a feature map extracted from the input of the layer; in the encoding stage, the length of the feature map is halved layer by layer, while the number of feature channels gradually increases; in the decoding stage, the length of the feature map is doubled layer by layer, while the number of feature channels gradually decreases; in each convolution layer, the number of channels of the convolution kernel automatically keeps consistent with the number of channels of the input feature map, and the number of convolution kernels determines the number of channels of the output feature map; after the convolution operation in each layer, a nonlinear activation function is followed, and a dropout operation is adopted once after every three convolution operations; the super-resolution model training is independently carried out in each stage by using a frequency domain loss function, the prediction effect of the super-resolution model in each stage is evaluated according to the frequency domain index, and the optimal model is determined.

[0024] Further, the prediction effect of the super-resolution model in each stage is evaluated according to the frequency domain index, and the optimal model is determined, and the selected frequency domain loss function and frequency domain index are as follows:

[0025] The frequency domain loss function L F-PCM The super-resolution model training is carried out, and the expression of the frequency domain loss function is:

[0026]

[0027] In the formula, x represents the input sequence, y represents the output sequence, and L represents the frequency domain loss function.

[0028]

[0029]

[0030] In the formula, x represents the input sequence, y represents the output sequence, and L represents the frequency domain loss function. and respectively represent the short-time Fourier transform of and . represents the short-time Fourier transform of . represents a sequence obtained by performing three spline interpolations on the longitudinal displacement sequence of the beam end, the time resolution of which is consistent with D Ts , but the spectral bandwidth is the same as that of the longitudinal displacement sequence of the beam end; represents the residual sequence of D Ts relative to , which essentially represents the high-frequency component reconstructed by the model; represents the residual sequence of relative to ; β represents an amplitude compression coefficient; V and W respectively represent the size of the time and frequency dimensions of the short-time Fourier transform amplitude spectrum; DTs and These represent the model labels and predicted values ​​of the beam end displacement data in each stage of the data reconstruction framework; D F and D Ts and The short-time Fourier transform; D F (v,w) and D F and The values ​​of the short-time Fourier transform amplitude spectrum in the sequence, with time dimension index v and frequency dimension index w;

[0031] The logarithmic spectral distance (LSD) is used to evaluate the prediction performance of the super-resolution model at each stage to determine the optimal model; the logarithmic spectral distance (LSD) is D. T and The logarithmic distance between the short-time Fourier transform amplitude spectra, in dB; the formula for calculating the logarithmic spectral distance (LSD) is as follows:

[0032]

[0033] In the formula, V and W represent the dimensions of the amplitude spectrum and frequency dimension of the short-time Fourier transform, respectively; D Ts and These represent the model labels and predicted values ​​of the beam end displacement data in each stage of the data reconstruction framework; D F and D Ts and The short-time Fourier transform; D F (v,w) and D F and The values ​​of the short-time Fourier transform amplitude spectrum in the sequence, with time dimension index v and frequency dimension index w.

[0034] Further, in step S4, the structure of the cascaded model is as follows: the LSTM regression model obtained in step S2 and the first-stage super-resolution model, second-stage super-resolution model, and third-stage super-resolution model obtained in step S3 are sequentially connected in series; by connecting the optimized LSTM regression model from steps S2 and S3 with the three super-resolution models in series, the longitudinal displacement data of the beam end initially reconstructed using the temperature samples in the training set is obtained. The true value of the beam end displacement data in the training set is represented by... express;

[0035] Will and The data is divided into d segments based on the number of days in the training set; after removing the daily trend term from each segment, the daily trend is calculated from... and The daily standard deviation of each data segment is divided into segments. and σ i , i = 1, 2, ..., d;

[0036] Establish using the least squares method and σ i The regression relationship between them yields the corrected standard deviation. As shown in the following formula:

[0037]

[0038] and σ i The regression relationship between them was obtained from the training set samples; the effect of correcting the validation set data was assessed, and the variance correction equation with the smallest root mean square error (RMSE) was selected; finally, the selected optimal variance correction equation was applied to the test set; when applying it to the validation and test sets, the initially reconstructed beam end displacement data was segmented by day, and then the daily standard deviation of each segment was calculated. Correction to Complete the statistical correction of the data.

[0039] Furthermore, in step S5, the root mean square error (RMSE), logarithmic spectral distance (LSD), and cumulative displacement relative error (RECD) are used as evaluation indicators for the entire recovery method: RMSE is used to evaluate the error between the reconstructed data and the true data value in the time domain, LSD is used to evaluate the error between the reconstructed data and the true data value in the frequency domain, and RECD is used to evaluate the feasibility of using the reconstructed data to evaluate the fatigue life of longitudinal displacement expansion joints in practical engineering applications.

[0040] The formula for calculating the root mean square error (RMSE) is as follows:

[0041]

[0042] In the formula, D Ta and These represent the true value sequence and the final predicted value sequence of the longitudinal displacement sequence at the beam end in the entire reconstruction method, respectively, with the subscript T indicating the time domain; D Ta (n) D represents Ta and The value with index n in the sequence; N represents the length of the time series;

[0043] The formula for calculating the logarithmic spectral distance (LSD) is as follows:

[0044]

[0045] In the formula, D Fa and These represent the short-time Fourier transforms of the label sequence and the final predicted sequence of the beam end displacement data in the entire reconstruction method, respectively; V and W represent the dimensions of the short-time Fourier transform amplitude spectrum and the time and frequency dimensions, respectively; D Fa (v,w) and D Fa and The values ​​of the short-time Fourier transform amplitude spectrum in the sequence, with time dimension index v and frequency dimension index w;

[0046] The formula for calculating the cumulative relative displacement error (RECD) is as follows:

[0047]

[0048] In the formula, D Ta and These represent the label value and predicted value of the final beam end displacement data achieved using the entire reconstruction method, respectively; N represents the length of the time series; D Ta (n) D represents Ta and The value of index n in the sequence; D Ta (n+1) D represents Ta and The value with index n+1 in the sequence.

[0049] Compared with the prior art, the significant advantages of this invention are as follows:

[0050] 1. While preserving sufficient frequency domain information, appropriately downsampling the original data can significantly reduce the amount of sample data, thereby reducing the training burden on the model and improving training efficiency.

[0051] 2. Existing one-step bandwidth widening operations are difficult to achieve a large spectrum bandwidth expansion ratio. The step-by-step super-resolution (bandwidth widening) strategy in this invention can decompose the high expansion ratio problem into multiple small expansion ratio problems. Due to the accumulation of errors caused by the cascaded operation of multiple models, a statistical correction strategy can be used to correct the standard deviation of the results of the cascaded models.

[0052] 3. When reconstructing the high-frequency part of the beam end displacement, the defined loss function can effectively alleviate the "amplitude anomaly" and "phase anomaly" phenomena that may occur in the data reconstruction results, which is of great significance for improving the accuracy and stability of the super-resolution (bandwidth extension) model.

[0053] 4. When the longitudinal displacement data of the beam end in all channels of the health monitoring system is unavailable, that is, when the correlation between the longitudinal displacement data sensors at the beam end cannot be utilized, a solution is provided for the problem of reconstructing the longitudinal displacement data at the beam end. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1(a) is a common arrangement of bridge end displacement and temperature sensors,

[0055] Figure 1(b) is a top view of Figure 1(a), where GED is a bridge end displacement sensor and AT is a temperature sensor;

[0056] Figure 2 is a spectrum of the bridge end longitudinal displacement;

[0057] Figure 3 is a long short-term memory neural network regression model structure;

[0058] Figure 4 is a long short-term memory neural network layer structure;

[0059] Figure 5 is a step-by-step super flowchart;

[0060] Figure 6 is a U-shaped architecture full convolution model structure. DETAILED DESCRIPTION

[0061] The present application will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present application and are not used to limit the scope of the present application. After reading the present application, those skilled in the art can make various modifications to the present application, and such modifications fall within the scope defined by the appended claims.

[0062] The reconstruction method of continuous missing bridge end longitudinal displacement data in the suspension bridge health monitoring system of the present application comprises the following steps:

[0063] Step one, pre-process the data.

[0064] Generally, in the health monitoring system of a long-span suspension bridge, monitoring devices such as temperature sensors, bridge end displacement sensors, etc. as shown in Figure 1(a) , 1(b) are arranged. In order to reconstruct the continuous missing bridge end longitudinal displacement, it is necessary to base on effective historical monitoring data. First, the recorded historical environmental temperature and bridge end displacement original data are pre-screened and pre-processed. On the one hand, the day sequence number with relatively complete data is screened out; on the other hand, a small amount of outliers in the data are identified and replaced through some outlier detection algorithms, and a small amount of discrete missing values in the data are interpolated through some simple interpolation algorithms. In addition, the bridge end longitudinal displacement spectrum as shown in Figure 2 is read from the measured suspension bridge, and a suitable sampling frequency 2f DThe original data is down-sampled under the premise of retaining sufficient frequency domain information. The sample data obtained after the final preprocessing is divided into a training set, a validation set and a test set in a certain proportion (such as 8:1:1), and a small batch processing method and an overlap reservation method are used for training, optimization and evaluation of all deep learning models involved.

[0065] In the training, optimization and evaluation stages, the required sample data is fed into the deep learning models involved in each step using the small batch processing method. The input / output of each iteration calculation is a group of equal-length short sequences (referred to as 1 batch), which contains a number of short sequences referred to as batch size. This series of short sequences is obtained by dividing the original sample sequence with a sliding window at a certain translation rate. The smaller the translation rate of the sliding window, the more short sequences are divided. The number of iterations required for the model to complete a round of training is the total number of short sequences divided by the batch size and rounded. When calculating the training error of each iteration, a group of sequences in each batch is merged by the overlap reservation method, and the group of short sequences output by the deep learning model is restored to the original length and order before calculation. Among them, the overlap reservation method refers to taking the average of multiple prediction results of the overlapping part as the final prediction result.

[0066] Step two, reconstruct the low-frequency component of the longitudinal displacement of the beam end.

[0067] A long short-term memory neural network (LSTM network) regression model is established as shown in Figure 3 The temperature and beam end displacement data preprocessed in step one are down-sampled at a sampling frequency of 2f T to obtain the low-frequency components (trend items) of the ambient temperature and the longitudinal displacement of the beam end, which are used as the input and output of the LSTM regression model, respectively. The LSTM regression model is trained using the training set to obtain the LSTM regression model parameters, and then the mean square error is used as the loss function to optimize the hyperparameters using the validation set.

[0068] The entire LSTM regression model starts with an input layer and ends with a fully connected layer and an output layer. The core part of the network is m LSTM layers connected in series, and m is one of the model's optimized hyperparameters. Each LSTM layer is followed by a dropout layer, i.e., the output of each LSTM layer is randomly set to zero with a probability q (set to 0.2 in this embodiment). During the training phase, part of the hidden layer output is randomly discarded through the dropout operation.

[0069] The input layer divides the LSTM regression model input into several time series composed of T time steps and outputs them as the input of the first LSTM layer, which is passed back in turn. The internal information flow of the LSTM layer is as follows Figure 4The output of the previous network layer is taken as the input of the current layer, and each input contains N time steps, and the data X t of each time step is input into an LSTM unit respectively. The state of each unit is composed of a hidden state H t and a memory cell state C t . The cell state contains the data feature information obtained from the previous time step and only flows within the current layer. The hidden state continues to be taken as the output of the current layer and enters the next network layer. The LSTM unit uses three gates, i.e., a forget gate F t , an input gate I t and an output gate O t to control the flow of information.

[0070] The control of the data flow by the vector / matrix Hadamard product. The forget gate F t acts on the cell state C t-1 passed from the previous time step to control the information level of the previous time step transmitted to the current time step. The candidate cell state represents the candidate information to be added to the cell state C t of the current time step. The input gate It acts on to control the degree of the current input used to update C t . The output gate Ot acts on Ct to determine the output of the current time step. Specifically, the relevant calculations in each unit are as follows:

[0071] Forget gate: F t = σ (W X,F X t + W H,F H t-1 + b F ) (1)

[0072] Input gate: I t = σ (W X,I X t + W H,I H t-1 + b I ) (2)

[0073] Output gate: O t = σ (W X,O X t + W H,O H t-1 + b O ) (3)

[0074] Candidate cell state:

[0075] Cell state:

[0076] Hidden state: H t = O t tanh(C t ) (6)

[0077] In the formula, σ represents a sigmoid activation function, which serves as a gate activation function, meaning that the value of the three gates ranges from (0, 1); tanh represents a hyperbolic tangent function, which serves as a state activation function, and the value thereof ranges from (-1, 1); W X,F , W X,I , W X,O , and W X,C represent input weights of a forget gate, an input gate, an output gate, and a candidate cell state; W H,F , W H,I , W H,O , and W H,C represent update weights of the forget gate, the input gate, the output gate, and the candidate cell state; b F , b I , b O , and b C represent bias parameters of the forget gate, the input gate, the output gate, and the candidate cell state. The above weights and bias parameters are model parameters learned by the LSTM layer, and the weights in each LSTM unit are the same.

[0078] In the embodiment, the reconstructed beam end displacement trend term (i.e., a low-frequency component) adopts a time-domain loss function, i.e., a root mean square error as an optimization objective function for model training. Based on the mean square error, the following formula is used for calculation:

[0079]

[0080] In the formula, N represents a sequence length; D T and (the subscript T represents a time domain) represent a real value (also referred to as a label value) sequence and a predicted value sequence of a low-frequency component sequence of a beam end longitudinal displacement respectively, D T (n) and D represent values of the n-th in the D T and D sequences respectively.

[0081] Hyperparameter optimization refers to a human-set parameter that needs to be determined by comparing errors of models with different hyperparameter combinations on a validation set. The hyperparameters that need to be optimized include: a number of hidden units in the LSTM network, a number of network layers, a length of a divided sequence window, a sliding translation rate of the divided sequence window, an initial learning rate, and a learning rate reduction scheme.

[0082] A time-domain metric, Root Mean Square Error (RMSE), is used to evaluate the predictive performance of the regression model and determine the optimal regression model. RMSE represents the standard deviation of the prediction error, and its unit is consistent with the evaluation object. A smaller RMSE indicates a better regression model. The formula for calculating RMSE is as follows:

[0083]

[0084] In the formula, D T and (Subscript T indicates time domain) represent the true value (also called label value) sequence and the predicted value sequence of the low-frequency component sequence of the longitudinal displacement at the beam end, respectively; D T (n) D T and The value with index n in the sequence; N represents the length of the time series.

[0085] Step 3: Reconstruct the high-frequency components of the longitudinal displacement at the beam end.

[0086] according to Figure 5 As shown, the spectral bandwidth of the low-frequency component of the longitudinal displacement data at the beam end obtained in step two is f. T The target bandwidth for reconstructing the longitudinal displacement data at the beam end is f. D Therefore, it is necessary to establish a corresponding deep learning model to supplement f. T to f D The information in the frequency band refers to the high-frequency components of the beam-end displacement that need to be reconstructed. Three super-resolution (bandwidth extension) models are trained to perform three stages of spectral bandwidth extension of the longitudinal displacement data at the beam end (first stage: f...). T →f M1 Second stage: f M1 →f M2 Third stage: f M2 →f D ), gradually realize f T to f M1 frequency band, f M1 to f M2 frequency band, f M2 to f D The reconstruction of the high-frequency components of the beam end displacement data in the frequency band is performed as follows.

[0087] Three super-resolution (bandwidth extension) models were established to perform three stages of spectrum bandwidth extension tasks, with training and hyperparameter optimization of the three models conducted independently. The inputs and outputs of the three super-resolution (bandwidth extension) models were directly derived from measured longitudinal displacement data at the beam ends. Specifically, the preprocessed longitudinal displacement data samples at the beam ends (sampling frequency 2f) from step one were used. D), the beam-end longitudinal displacement data samples with sampling frequency of 2f T , 2f M1 and 2f M2 are obtained by downsampling. Further, the input and output of the super-resolution (bandwidth extension) model in the first stage are the beam-end longitudinal displacement sequences with sampling frequency of 2f T and 2f M1 respectively. Similarly, the input and output of the super-resolution (bandwidth extension) model in the second and third stages can be known. For convenience of description, the input and output of each super-resolution (bandwidth extension) model are relatively called low-resolution and high-resolution beam-end longitudinal displacement sequences respectively. To ensure the consistency of the length of the input and output of the super-resolution (bandwidth extension) model in each stage, the input sequence of the super-resolution (bandwidth extension) model in each stage (i.e. the beam-end longitudinal displacement data samples after downsampling) needs to be upsampled to the sampling frequency consistent with the output of the super-resolution (bandwidth extension) model in the stage by using cubic spline interpolation before being fed into the super-resolution (bandwidth extension) model in the stage, and the spectral bandwidth remains unchanged.

[0088] In the model test or actual application, the models in each stage are connected in series. The output of the model in the previous stage is used as the input of the model in the next stage, and the input of the model in the first stage is the low-frequency component (with sampling frequency of 2f T ) of the beam-end longitudinal displacement data predicted by temperature in step two. The interpolation / upsampling operation of the input of the model before being fed into the model is also needed.

[0089] The deep learning-based super-resolution (bandwidth extension) models in each stage in this step adopt Figure 6The U-shaped architecture. The U-shaped architecture is a kind of fully convolutional neural network concept based on autoencoder, whose most prominent features are its bottleneck structure and the skip connection between the encoder and the decoder. In the U-shaped architecture model, the input sequence is first compressed to the shortest length by the encoder, and then expanded to the original length by the decoder. The encoding and decoding of the input sequence are realized by a series of one-dimensional convolutional layers and sub-pixel convolutional layers, respectively. The output of a convolutional layer is called a feature map extracted from the input of the layer. In the encoding stage, the length of the feature map is halved layer by layer (except for the first convolutional layer), while the number of feature channels gradually increases (64→64→64→128→128→128→256→256→256). The decoding stage is the opposite. The convolution operation represents the process of calculating the sliding dot product between the input sequence (or feature map) and the convolution kernel sequence. The convolution kernel has two dimensions of length and channel number, and its internal weights are the parameters learned by the model. The length of the convolution kernel represents its receptive field, which is one of the hyperparameters of the model. In each convolutional layer, the number of channels of the convolution kernel automatically matches the number of channels of the input feature map, and the number of convolution kernels determines the number of channels of the output feature map (i.e., each convolution kernel generates one channel of the output feature map). One-dimensional sub-pixel convolution has an additional sub-pixel shuffle operation compared to one-dimensional convolution, which is used to increase the size of the input features. The skip connection refers to the direct connection of the feature maps on the mirror layers in the encoder and the decoder in the feature channel dimension. In addition, a nonlinear activation function follows each convolution operation in each layer except the output layer. To alleviate the overfitting phenomenon, a dropout operation is performed once every three layers. That is, the elements in the convolution output of a certain layer of the U-shaped architecture are randomly set to zero after activation with a probability q.

[0090] The embodiment adopts a frequency domain loss function The loss function is expressed as:

[0091]

[0092] In the formula,

[0093]

[0094]

[0095]

[0096] In the formula, and represent the short-time Fourier transform of and respectively; represents the short-time Fourier transform of ​denotes the sequence obtained by cubic spline interpolation of the longitudinal displacement sequence at the beam end (low frequency), whose time resolution is consistent with D Ts , but the spectral bandwidth is the same as that of the longitudinal displacement sequence at the beam end (low frequency); denotes the residual sequence of D Ts relative to D , which essentially represents the high-frequency component reconstructed by the model; denotes the residual sequence of D relative to D ; β denotes the amplitude compression coefficient; V and W denote the size of the time and frequency dimensions of the short-time Fourier transform amplitude spectrum, respectively; v and w denote the sequence number of the time and frequency dimensions of the short-time Fourier transform amplitude spectrum, respectively; D Ts and denote the model label and predicted value of the beam end displacement data in each stage of the data reconstruction framework, respectively; D F and denote the short-time Fourier transform of D Ts and , respectively; D F (v,w) and denote the value of the short-time Fourier transform amplitude spectrum in the sequence D F and , whose time dimension sequence number is v and whose frequency dimension sequence number is w.

[0097] The hyperparameters to be optimized in the U-shaped architecture deep convolutional model used in this step include: sequence window length division, sequence window sliding translation rate, amplitude compression coefficient, convolution kernel length, initial learning rate, learning rate reduction scheme.

[0098] The frequency domain index: log spectral distance (LSD) is used to evaluate the prediction effect of each stage of the super-resolution (bandwidth expansion) model to determine the optimal model. LSD describes the logarithmic distance between the short-time Fourier transform amplitude spectra of D T and , and the closer the value is to zero, the more similar the two spectra are. The calculation formula of LSD is as follows:

[0099]

[0100] In the formula, D F and denote the short-time Fourier transform of the model label and predicted value of the beam end displacement data in each stage of the reconstruction framework, respectively; V and W denote the size of the time and frequency dimensions of the short-time Fourier transform amplitude spectrum, respectively; D F (v,w) and denote the value of the short-time Fourier transform amplitude spectrum in the sequence D F and The values ​​of the short-time Fourier transform amplitude spectrum in the sequence, with time dimension index v and frequency dimension index w.

[0101] Step four: Use statistical correction strategies to correct the output of the cascaded model.

[0102] The optimized LSTM regression model from step two is concatenated with the three optimized super-resolution (bandwidth broadening) models from step three. The output of the LSTM regression model in step two is the low-frequency component of the beam end displacement data obtained using temperature prediction (sampling frequency 2f). T The interpolation process maintains the sequence length equal to the output of the first stage in step three. The low-frequency components of the interpolated beam end displacement data are used as input to the super-resolution (bandwidth broadening) model in the first stage of step three. Furthermore, the three super-resolution (bandwidth broadening) models in step three need to be concatenated, meaning the output of the previous stage is used as the input to the next stage. The interpolation operation before feeding each stage's super-resolution (bandwidth broadening) model is also necessary. By concatenating the optimized LSTM regression models from steps two and three with the three super-resolution (bandwidth broadening) models, the longitudinal displacement data of the beam end, initially reconstructed using the temperature samples in the training set, is obtained. Represented accordingly. The true values ​​of the beam end displacement data in the training set are represented by... Indicate. Will and The data is divided into d segments based on the number of days in the training set. After removing the daily trend term from each segment, the daily trend is calculated separately. and The daily standard deviation of each data segment is divided into segments. and σ i (i = 1, 2, ..., d). Establish using the least squares method. and σ i The regression relationship p between them, i.e. Furthermore, the corrected standard deviation can be obtained. As shown in the following formula:

[0103]

[0104] p is obtained from the training set samples. By comparing the effects of correcting the validation set data using linear, quadratic, and exponential functions, the variance correction equation with the smallest root mean square error (RMSE) is selected. Finally, the selected optimal variance correction equation is applied to the test set. When applying it to both the validation and test sets, the initially reconstructed beam end displacement data needs to be segmented by day, and then the daily standard deviation of each segment needs to be calculated. Correction to This allows for the statistical correction of the data.

[0105] Step five, the performance of the whole data reconstruction method on the test set is evaluated by using the performance evaluation index.

[0106] The root mean square error (RMSE), the log-spectral distance (LSD) and the relative error of cumulative displacement (RECD) are used as evaluation indexes to evaluate the effect of the whole reconstruction method applied to the test set. The RMSE is used to evaluate the error between the reconstructed data and the true value of the data in the time domain, the LSD is used to evaluate the error between the reconstructed data and the true value of the data in the frequency domain, and the RECD is used to evaluate the feasibility of using the reconstructed data to evaluate the fatigue life of the longitudinal displacement expansion joint in actual engineering applications. For different bridges, the ranges of the three evaluation indexes are different. For the same suspension bridge, the smaller the three evaluation indexes, the higher the accuracy of the longitudinal displacement data reconstructed by the method. The calculation formula of the RECD is as follows:

[0107]

[0108] In the formula, D Ta and respectively represent the label value and the predicted value of the final beam end displacement data realized by using the whole reconstruction method; N represents the length of the time series; D Ta (n) and D Ta (n+1) respectively represent the values of D Ta (n) and D Ta (n+1) in the sequence. ​​​​

Claims

1. A method for reconstructing missing longitudinal displacement monitoring data of a suspension bridge end, characterized in that, The steps include the following: S1, preprocessing the effective data of historical ambient temperature and beam end displacement in the monitoring results; S2, using a long short-term memory network model to establish an LSTM regression model between the ambient temperature and the low-frequency component time series of the beam end longitudinal displacement; S3, based on the frequency band widening model of the U-shaped architecture full convolutional neural network, the reconstruction of the high-frequency component of the beam end longitudinal displacement data in different frequency bands is gradually realized in stages; S4, the statistical correction method is used to correct the prediction results of the series model; S5, the performance evaluation index is used to evaluate the performance of the entire data reconstruction method on the test set; In step S3, the spectral bandwidth expansion of the three stages of the beam end longitudinal displacement data is completed by training three super-resolution models respectively, and the beam end longitudinal displacement data is gradually reconstructed f T to f M1 the frequency band, f M1 to f M2 the frequency band, f M2 to f D the frequency band of the beam end displacement data high frequency component reconstruction, wherein, f T is the spectral bandwidth of the low frequency component of the beam end longitudinal displacement data, f D is the target bandwidth of the beam end longitudinal displacement data reconstruction; The training and hyperparameter optimization of the three-stage super-resolution model are independently carried out, and by using the beam end longitudinal displacement data samples preprocessed in step S1, beam end longitudinal displacement data samples with sampling frequencies of 2 f T , 2 f M1 , and 2 f M2 are obtained by down-sampling. Before feeding the input sequence of each stage super-resolution model into the super-resolution model of the stage, it needs to be up-sampled to the same sampling frequency as the output of the super-resolution model of the stage by using cubic spline interpolation, and the spectral bandwidth remains unchanged; Each stage of the super-resolution model adopts a U-shaped architecture, in which the input sequence is first compressed to the shortest length by the encoder, and then expanded to the original length by the decoder; the encoding and decoding of the input sequence are realized by a series of one-dimensional convolution layers and sub-pixel convolution layers, respectively; the output of a convolution layer is called a feature map extracted from the input of the layer; in the encoding stage, the length of the feature map is halved layer by layer, while the number of feature channels gradually increases; in the decoding stage, the length of the feature map is doubled layer by layer, while the number of feature channels gradually decreases; in each convolution layer, the number of convolution kernels automatically matches the number of input feature channels, and the number of convolution kernels determines the number of output feature channels; except for the output layer, a non-linear activation function follows each convolution operation in each layer, and a dropout operation is performed once after every three convolution operations; the frequency domain loss function is used to independently train the super-resolution model at each stage, and the prediction effect of the super-resolution model at each stage is evaluated according to the frequency domain index to determine the optimal model; The selected frequency domain loss function and frequency domain index are as follows: Using a frequency domain loss function Carrying out the super-resolution model training, and the expression of the frequency domain loss function is: In the formula, wherein, and respectively represent and short-time Fourier transforms; represents a short-time Fourier transform; represents a sequence obtained by cubic spline interpolation of the sequence of longitudinal displacements of the beam end, whose time resolution is consistent with but the spectral bandwidth remains the same as that of the sequence of longitudinal displacements of the beam end; represents a residual sequence with respect to , which essentially represents the high-frequency components reconstructed by the model; represents a residual sequence with respect to ; β represents the amplitude compression coefficient; V and W respectively represent the size of the time and frequency dimensions of the short-time Fourier transform amplitude spectrum; and respectively represent the model label and the predicted value of the beam end displacement data in each stage of the data reconstruction framework; and respectively represent and short-time Fourier transforms; and respectively represent and the values of the short-time Fourier transform amplitude spectrum in the sequence with the time dimension sequence number v and the frequency dimension sequence number w ; The log spectral distance (LSD) is used to evaluate the prediction effect of the super-resolution model at each stage to determine the optimal model. and The log spectral distance (LSD) is the log distance between the short-time Fourier transform amplitude spectrum, with units of dB; the calculation formula of the log spectral distance (LSD) is as follows: wherein V and W denote the size of the time and frequency dimension of the short-time Fourier transform magnitude spectrum, respectively; and denote the model label and predicted value of the girder end displacement data in each stage of the data reconstruction framework, respectively; and denote and the short-time Fourier transform of and denote and the value of the time dimension index v and the frequency dimension index w of the short-time Fourier transform magnitude spectrum in the sequence 2. The method of claim 1, wherein the method further comprises: In step S1, the collected large-span suspension bridge health monitoring data system records the historical environmental temperature and beam end displacement original data for pre-screening and preprocessing; the beam end longitudinal displacement spectrum of the suspension bridge is read, and the sampling frequency 2 f D The original data is down-sampled under the premise of preserving the frequency domain information; The sample data obtained after the final preprocessing is divided into training set, validation set and test set in proportion, and the small batch processing method and the overlap reservation method are used for model training, model optimization and model evaluation, respectively.

3. The method of claim 1, wherein the method further comprises: In step S2, the network structure of the LSTM regression model is as follows: starting with an input layer and ending with a fully connected layer and an output layer; the core part of the network is m LSTM layers connected in series, each followed by a dropout layer, and the output of each LSTM layer is randomly set to zero with a probability q; The sampling frequency is 2 f T The ambient temperature and the low-frequency component of the longitudinal displacement of the beam end are respectively taken as the input and output of the LSTM regression model. The mean square error As the optimization objective function of the LSTM regression model; adopt the time domain loss function root mean square error RMSE to select the optimal LSTM regression model, the mean square error The expression is as follows: In the formula, and respectively represent the real value sequence and the predicted value sequence of the low-frequency component sequence of the longitudinal displacement of the beam end, and the subscript T represents the time domain; , respectively represent the values of the sequence with the sequence number and in the sequence; n N represents the length of the time sequence;​ The calculation formula of the time domain loss function root mean square error RMSE is as follows: wherein and denote the real value sequence and the predicted value sequence of the low frequency component of the longitudinal displacement of the beam end, respectively, and the index T denotes the time domain; , denote the value of the sequence and at the index n ; N denotes the length of the time sequence.

4. The method of claim 1, wherein the method further comprises: In step S4, the structure of the series connection model is as follows: the LSTM regression model obtained in step S2 and the first-stage super-resolution model, the second-stage super-resolution model, and the third-stage super-resolution model obtained in step S3 are connected in series; after the LSTM regression model and the three super-resolution models are connected in series, the beam end longitudinal displacement data preliminarily reconstructed by using the temperature samples in the training set is obtained, which is represented by ; the true value of the beam end displacement data in the training set is represented by . ​ Let and be divided into d segments respectively by day, d denotes the number of days contained in the training set samples; after removing the daily trend term in each segment of data, the daily standard deviation of each segment of data divided from and is calculated respectively and , i = 1, 2, …, d ; A regression relationship between the standard deviation and the number of samples is established using the least square method to obtain a corrected standard deviation as shown in the following equation: and The regression equation between the two is obtained by the training set samples; the effect of the modified validation set data is selected to select the variance correction equation with the minimum root mean square error RMSE; finally, the selected optimal variance correction equation is applied to the test set; when applied to the validation set and the test set, the preliminary reconstructed beam end displacement data is segmented by day, and then the daily standard deviation of each segment of data is corrected to , and the statistical correction of the data is completed.

5. The method of claim 1, wherein the method further comprises: In step S5, the root mean square error RMSE, the logarithmic spectral distance LSD and the cumulative displacement relative error RECD are used as evaluation indexes of the entire recovery method: RMSE is used to evaluate the error between the reconstructed data and the true value of the data in the time domain, LSD is used to evaluate the error between the reconstructed data and the true value of the data in the frequency domain, and RECD is used to evaluate the feasibility of using the reconstructed data to evaluate the longitudinal displacement expansion joint fatigue life in actual engineering applications; ​ The calculation formula of the root mean square error RMSE is as follows: wherein and denote the real value sequence and the final predicted value sequence of the longitudinal displacement sequence of the beam end in the entire reconstruction method, respectively, and the subscript T denotes the time domain; , denote and the value in the sequence with the serial number n ; N denotes the length of the time sequence; The calculation formula of the logarithmic spectral distance LSD is as follows: wherein and denote the short-time Fourier transform of the sequence of labels and the final prediction sequence, respectively, of the beam end displacement data throughout the reconstruction method; V and W denote the size of the time and frequency dimension, respectively, of the short-time Fourier transform magnitude spectrum; and denote the and values of the short-time Fourier transform magnitude spectrum in the sequence at time v and frequency index w , respectively. The calculation formula of the cumulative displacement relative error RECD is as follows: wherein, and denote the label and predicted values of the final beam end displacement data achieved by the entire reconstruction method, respectively; N denotes the length of the time series; , denote and the value at position n in the sequence; , denote and the value at position n + 1 in the sequence.

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