ALSTNet: Autoencoder fused long- and short-term time-series network for the prediction of tunnel structure-深地科学

ALSTNet: Autoencoder fused long- and short-term time-series network for the prediction of tunnel structure

Abstract

It is crucial to predict future mechanical behaviors for the prevention of structural disasters. Especially for underground construction, the structural mechanical behaviors are affected by multiple internal and external factors due to the complex conditions. Given that the existing models fail to take into account all the factors and accurate prediction of the multiple time series simultaneously is difficult using these models, this study proposed an improved prediction model through the autoencoder fused long- and short-term time-series network driven by the mass number of monitoring data. Then, the proposed model was formalized on multiple time series of strain monitoring data. Also, the discussion analysis with a classical baseline and an ablation experiment was conducted to verify the effectiveness of the prediction model. As the results indicate, the proposed model shows obvious superiority in predicting the future mechanical behaviors of structures. As a case study, the presented model was applied to the Nanjing Dinghuaimen tunnel to predict the stain variation on a different time scale in the future.

Highlights

A novel data-driven model, named autoencoder fused long- and short-term time-series network (ALSTNet), was presented for predicting the structural mechanical behaviors at multiple positions in the field. ALSTNet incorporated the impact of both long- and short-term historical behaviors, as well as the spatial mechanical correlation achieved through encoding the networking that was formed by multivariate time series.
Based on the proposed model, data experiments were conducted using monitoring data recorded by a structural health monitoring system installed in an underwater shield tunnel. The predicted results obtained from ALSTNet were compared with those from several baseline models, including linear regression, support vector regression, multilayer perceptron, long short-term memory, and recurrent neural network. The findings reveal that ALSTNet outperforms the baseline models in terms of prediction accuracy, highlighting its effectiveness and superiority.
As a crucial real-world application, the presented model was used to predict the strain variation at multiple points in the Nanjing Dinghuaimen tunnel for 24 h on end. This application holds immense significance in preventing disasters in practical engineering scenarios and serves as an invaluable reference for similar engineering projects.

1 INTRODUCTION

The continuous expansion of urban areas has led to increasing pressure for efficient transportation, which can be addressed effectively by leveraging underground spaces for public transport systems. Tunnel structures, as typical underground constructions, face complex external loads, environmental challenges, and extreme events like earthquakes, crashes, and blasts (Mahmoodzadeh et al., 2020; Tan, Chen, Wu, et al., 2020; Wang & Ni, 2020). Over time, numerous tunnel projects experience frequent incidents that lead to cost overruns and even jeopardize public safety (Mahmoodzadeh et al., 2021; Tan, Chen, Wang, et al., 2020). With the rapid development of artificial intelligence, structural health monitoring (SHM) is now widely recognized as a reliable technology for maintaining tunnel stability (Spencer et al., 2004; Wong, 2004). SHM systems have evolved from identifying anomalies to predicting and providing early warnings of structural states. Acting upon such warnings is crucial, as addressing damages once they occur can significantly contribute to structural stability (Yuan et al., 2012). Therefore, accurate prediction of tunnel structure mechanical behaviors holds great significance in ensuring the long-term security of operations. This study aimed to achieve accurate prediction of tunnel structure mechanical behaviors by utilizing real-time SHM data. Traditional approaches to prediction of tunnel mechanical behaviors have focused on analytical solutions and numerical simulations (Fahimifar et al., 2010; Sharifzadeh et al., 2013). However, the complex nature of the solution processes and the influence of scaling effects on calculation parameters make direct application of analytical and numerical results challenging in engineering practice (Feng et al., 2019; Sterpi & Gioda, 2009). To address these challenges, several prediction models based on monitoring data have been studied and reported in the literature, including statistical models like Bayes, time-series models like auto regression (AR), and deep learning models like neural networks (Farahani & Penumadu, 2016; Mei et al., 2016; Prakash et al., 2018; Sajedi & Liang, 2020). However, in the field of civil engineering, especially in tunnel engineering, these models have not been extensively explored. Real-time monitoring data recorded from in-service tunnel structures show unique features: (i) existing time series show significant nonstationary and periodical changes corresponding to seasonal variations and (ii) the monitoring data from sensors installed at different points may show similar or opposing evolution trends, which cannot be disregarded in predictive analysis. Analyzing and predicting each sensor separately may lead to information loss, while simultaneous analysis and prediction of all sensors may introduce multicollinearity issues, leading to an unstable solution space. Therefore, it is essential to find a reasonable method to minimize information loss while reducing the number of variables for analysis. By addressing these challenges, this study aims to advance the prediction of tunnel structure mechanical behaviors through the integration of real-time SHM data, which ultimately enhances the long-term security and stability of underground constructions.

Based on stationarity, AR models cannot handle nonstationary time-series data with time-varying model coefficients. Moreover, these models lack the ability to incorporate newly acquired observations for model updates and forward forecasts without reconstruction. On the other hand, Bayes models can overcome these limitations, providing a valuable tool for characterizing uncertainty in time series and quantifying forecast uncertainty. However, they may not be suitable for multivariate time-series prediction as they cannot effectively integrate relationships among different time series, a crucial aspect highlighted in the second feature (Goulet, 2017; Goulet & Koo, 2018). As a result, deep learning models have gained increasing popularity among scholars due to their remarkable abilities in processing nonstationary time-series data and learning from multivariate time series (Mahdevari & Torabi, 2012; Zhu et al., 2020). Among the deep learning models, recurrent neural network (RNN) stands out for its advantageous capability in predicting and extrapolating time-varying processes (Cao et al., 2020). Over the past few years, RNN has witnessed widespread application in various fields, including traffic jam situations, supply chain management, stock prediction, and weather forecasting (Chen et al., 2018). In the field of civil engineering, several scholars have utilized the RNN method to make predictions regarding tunnel settlement and tunnel boring machine (TBM) disturbance (Freitag et al., 2015, 2018; Liu et al., 2020).

With a focus on the current research status and engineering requirements, this study focuses on achieving precise predictions of tunnel structure behavior through an enhanced RNN model driven by real-time monitoring data from SHM system (SHMS). The model seamlessly incorporates core features obtained from encoding extensive monitoring data, encompassing long- and short-term historical behaviors for robust modeling. The flowchart and each component of the proposed prediction model are introduced initially, providing a clear overview of its architecture. Subsequently, data experiments were conducted using monitoring data acquired from the SHMS installed in the Nanjing Dinghuaimen tunnel. The predictive capabilities of the presented model were thoroughly assessed and compared against classical baselines to establish its efficacy. Furthermore, on conducting an ablation study, the outcomes of this analysis confirmed the soundness and effectiveness of the proposed approach and validated the rationale behind the models used in this study. Lastly, the practical relevance of the presented model was demonstrated by applying it to the Nanjing Dinghuaimen tunnel to predict mechanical behaviors across different time scales. This comprehensive investigation aims to advance tunnel engineering by delivering accurate predictions empowered by real-time monitoring data-driven RNN modeling.

2 METHODOLOGY

This section provides an overview of the structure of the proposed model. Section 2 delves into the prediction problem formulation. Given the historical sensor data included within the system, predictive results are obtained through the proposed model. Section 3 introduces the framework of the proposed model, offering a comprehensive understanding of its overall structure. Section 4 focuses on explaining the pivotal role of the autoencoder within the model. This section sheds light on how the autoencoder functions as a critical component, enabling the extraction of essential features from the input data. In Sections 5 and 6, long- and short-term dependencies are introduced into the proposed model. This section elaborates on how these dependencies integrate to enrich the predictive capabilities of the model. Finally, in Section 7, the overall model is explored, offering a more detailed view of its architecture and the synergy of its components.

2.1 Formalization

In the realm of multivariate time-series forecasting, the focus centers around a collection of fully observed time-series signals denoted as $� = {�_{1}, �_{2}, \dots, �_{�}}$ , wherein $�_{�} = {�_{�}^{1}, �_{�}^{2}, \dots, �_{�}^{�}}$ represents the observed signals at time $�$ . Here, $�$ is the total number of sensors. The primary objective involves predicting the value of $�_{� + �}$ , where $�$ denotes the desired horizon ahead of the current time $�$ . The predictive outcome is represented as ${\hat{�}}_{� + �}$ , while the ground-truth counterpart is represented as $�_{� + �} = �_{� + �}$ .

It is important to underscore that for each predictive task, the set ${�_{�}, �_{� - � + 1}, �_{� - � + 2}, \dots, �_{�}}$ exclusively relies on forecast $�_{� + �}$ . In this context, $�_{�}$ represents the short-term daily local dependency of time $� + �$ and $�$ denotes the window size—a parameter whose choice aligns with established practices (Lai et al., 2018; Shih et al., 2019). The choice emerges from the underlying assumption that no meaningful information exists before the specified window.

2.2 The proposed prediction framework

Prior to presenting the model, a fundamental assumption is formulated, namely, that the evolution of structural responses is influenced by both long- and short-term dependencies concurrently. This assumption is pivotal in shaping the foundation of the approach proposed in this study.

The continuous evolution trend of structural response necessitates the utilization of historical structural response data for statistical analysis, thus making it possible to infer the development trend of future responses—a crucial aspect of long-term trend dependency. Simultaneously, the daily patterns shown by structural response are apparent, where the response data at a particular time (t o'clock) of a particular day resemble those of the same time (t o'clock) the day before. This phenomenon represents the short-term daily local dependency.

Combining these essential components, the autoencoder fused long- and short-term time-series network (ALSTNet) was established. ALSTNet operates by initially encoding the long-term dependency using the well-trained autoencoder. Subsequently, the encoded features are fed into the RNN for predictive purposes. Finally, the output from the RNN is combined with the short-term dependency to yield the ultimate prediction results. Figure 2 presents a flowchart as a visual representation of the proposed prediction framework.

In the pretraining stage, historical structural response data are used to instruct the model on the intricacies of the long-term trend dependency. Once the model becomes well acquainted with the historical patterns, it is applied to forecast real-world data, leveraging its learned knowledge to make accurate predictions.

2.3 Autoencoder

Autoencoder, an artificial neural network, excels at acquiring the high-level representation of input data through unsupervised learning. Such representation, known as encoding, typically possesses a much smaller dimension compared with the original input data. The architecture of the autoencoder is depicted in Figure 1a, comprising three types of layers: input layer, hidden layer, and output layer. The dimensions of the input and output layers remain identical.

Details are in the caption following the image — Figure 1
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Architecture of the proposed model. (a) Architecture of autoencoder and (b) architecture of autoencoder fused long- and short-term time-series network (ALSTNet).

The formulation of the autoencoder model is expressed as follows:

�_{�}^{(�)} = � (�_{en}^{(� - 1)} �_{�}^{(� - 1)} + �_{en}^{(� - 1)}),

(1)

{\hat{�}}_{�}^{(� - 1)} = � (�_{de}^{(�)} {\hat{�}}_{�}^{(�)} + �_{de}^{(�)}),

(2)

where

�

denotes the depth of encoder, and

�_{�}^{(0)} = �_{�}

�_{�}^{(�)} = {\hat{�}}_{�}^{(�)}

, and

{\hat{�}}_{�}^{(0)} = {\hat{�}}_{�}

;

�_{�}

represents the original data collected from sensors at time

�

;

�

represents the nonlinear activation function; and

{\hat{�}}_{�}

denotes the reconstruction of

�_{�}

�_{en}^{(�)}

and

�_{en}^{(�)}

are the weight matrix and bias of the rth layer in the encoder, respectively, while

�_{de}^{(�)}

and

�_{de}^{(�)}

denote the weight matrix and bias of the rth layer in the decoder, respectively.

�_{�}^{(�)}

signifies the output of the rth layer of the encoder and

{\hat{�}}_{�}^{(�)}

denotes the input of the rth layer of the encoder.

Equation (1) illustrates the operation of the encoder. The original data are first received by the input layer and subsequently compressed by the hidden layers of the encoder. Each hidden layer takes its predecessor's output as input. The output of the encoder yields the high-level representation of the input data. On the other hand, Equation (2) describes the decoder, which is mirror-symmetric to the structure of the encoder. The output of the encoder serves as the input for the decoder, generating the reconstruction of the original data.

To train an autoencoder, the mean squared error (MSE) is used as the objective function:

� (�_{�}, {\hat{�}}_{�}) = \frac{1}{�} \sum_{� = 1}^{�} {(�_{�}^{�} - {\hat{�}}_{�}^{�})}^{2} .

(3)

After training the autoencoder with the training set, the weights between the input layer and the hidden layer are extracted. These extracted weights enable the compression of original high-dimensional data into a high-level representation. The nonlinear characteristics of the autoencoder ensure that it retains essential information during dimensionality reduction, resulting in highly interpretable data with a clustering effect.

2.4 Long-term time-series trend dependency

The continuity of the evolution trend in structural response is a key characteristic, wherein the existing response evolution effectively reflects the development process, direction, and trend of the evolution. By leveraging the analogy or extension of the available evolution sequence data, the future structural response can be accurately predicted.

RNN serves as an essential tool for processing sequence data, diverging from the conventional feedforward neural network. Its fundamental design principle revolves around infusing the neural network with memory capabilities, akin to the memory mechanism observed in the human brain. Consequently, the trained RNN model becomes proficient in predicting the value of the next time stamp, drawing insights from several previously encountered states.

In the context of RNN, a recurrent function

�

is defined to calculate the hidden state

ℎ_{�} \in �^{�}

for each time stamp

�

, given the input

�_{�} \in �^{�}

for RNN at the specific time. The hidden state of recurrent units in RNN at time

�

can be formulated as

ℎ_{�} = \tanh (� �_{�} + � ℎ_{� - 1} + �_{ℎ}),

(4)

where

� \in �^{� \times �}

represents the weight matrix from the input series to the hidden layer;

�

denotes the dimension size of the hidden state in RNN;

� \in �^{� \times �}

signifies the weight matrix between hidden layers; and

�_{ℎ} \in �^{�}

represents the bias vector in the hidden layer. Additionally, the output at time t is expressed as

�_{�} = softmax (� ℎ_{�} + �_{�}),

(5)

where

� \in �^{� \times �}

represents the weight matrix from the hidden layer to the output layer and

�_{�}

stands for the bias vector in the output layer. It should be noted that all the parameters in RNN are shared across the network. The optimal design of RNN allows it to effectively memorize historical information, thus enabling it to cap relatively long-term dependencies.

2.5 Short-term daily local dependency

The response of the tunnel structure is predominantly influenced by temperature, water level, and live loads—key factors with daily patterns. As a result of these patterns, the structural response of the tunnel also shows a clear daily pattern. Specifically, the structural responses at a particular time (t o'clock) of a particular day closely resemble those observed at the same time (t o'clock) the day before.

However, capturing this type of dependency poses challenges for RNN due to the excessively long length of one period and subsequent optimization complexities. In order to predict the structural responses accurately at t o'clock for the particular day, a classical approach involves leveraging the records from historical days at t o'clock. This strategy has been proven to be effective in the past, and accordingly, the short-term daily local dependency is incorporated into the proposed prediction model. By considering such dependency, this study aims to enhance the precision of the prediction.

2.6 ALSTNet

This section presents the proposed prediction framework, ALSTNet, which integrates the three components introduced earlier. The architecture of ALSTNet is demonstrated in Figure 2b. Initially, the original data within the prediction window are encoded using a well-trained autoencoder. The resulting features corresponding to each time stamp are then fed into an RNN model. Subsequently, the hidden states from the last step of the RNN model are decoded by the same well-trained autoencoder. The final prediction is generated by combining the observed signals from the day before the target predicting time stamp with the output of the decoder. Assuming that time $� + �$ is the target predicting time stamp, more details will be explored on how the framework generates the prediction ${\hat{�}}_{� + �}$ in the following section.

As defined in Section 2, the prediction of

�_{� + �}

relies solely on

{�_{�}, �_{� - � + 1}, �_{� - � + 2}, \dots, �_{�}}

. In the first step, the original data from time

� - � + 1

to time

�

are encoded by the well-trained autoencoder to obtain the feature vector corresponding to each time stamp. Consequently, the inputs for the RNN model become

{�_{� - � + 1}, �_{� - � + 2}, \dots, �_{�}}

, where

�_{�} \in �^{�}

. By applying the recurrent function

�

, the hidden states in the RNN from time

� - � + 1

to time

�

are calculated, generating

{ℎ_{� - � + 1}, ℎ_{� - � + 2}, \dots, ℎ_{�}}

. Here,

�_{�}

represents the short-term daily local dependency of time

� + �

, and

ℎ_{�}

is integrated with

�_{�}

to generate the prediction

{\hat{�}}_{� + �}

, formulated as follows:

{\hat{�}}_{� + �} = �_{2} ((Decoder (�_{1} ℎ_{�} + �_{1})) + �_{�}) + �_{2},

(6)

where

�_{1} \in �^{� \times �}, �_{2} \in �^{� \times �}, �_{1} \in �^{�}

, and

�_{2} \in �^{�}

�_{1}

is used to adjust the dimension of

ℎ_{�}

to meet the requirement of the decoder.

For model training, the root mean square error ( RMSE) is adopted as the objective function, expressed as

� (�_{� + �}, {\hat{�}}_{� + �}) = \sqrt{\frac{1}{�} \sum_{� = 1}^{�} {(�_{� + �}^{�} - {\hat{�}}_{� + �}^{�})}^{2}} .

(7)

To assess the effectiveness of the proposed model, four evaluation metrics were used: RMSE, mean absolute error (MAE), mean absolute percentage error (MAPE), and Pearson correlation coefficient (PCC).

RMSE quantifies the deviation between the prediction value and the true value and is computed as follows:

RMSE = \sqrt{\frac{1}{�} \frac{1}{length (�_{test})} \sum_{� = 1}^{�} \sum_{� \in �_{test}} {(�_{�}^{�} - {\hat{�}}_{�}^{�})}^{2}} .

(8)

MAE represents the mean of the absolute error between the prediction value and the true value, offering a comprehensive view of the prediction value errors, and is calculated as

MAE = \frac{1}{�} \frac{1}{length (�_{test})} \sum_{� = 1}^{�} \sum_{� \in �_{test}} | �_{�}^{�} - {\hat{�}}_{�}^{�} | .

(9)

MAPE, another commonly used indicator for assessing forecast accuracy, reflects the mean of the absolute percentage error between the prediction value and the true value, and is formulated as

MAPE = \frac{1}{�} \frac{1}{length (�_{test})} \sum_{� = 1}^{�} \sum_{� \in �_{test}} | \frac{�_{�}^{�} - {\hat{�}}_{�}^{�}}{�_{�}^{�}} | .

(10)

PCC quantifies the linear correlation between two variables, where its magnitude varies from −1 to 1. A value of 1 denotes a total positive linear correlation; 0 indicates no linear correlation; and −1 signifies a total negative linear correlation. The calculation is as follows:

\begin{array}{ccl} � � � & = & \frac{1}{�} \sum_{� = 1}^{�} \\ \frac{\sum_{� \in �_{test}} (�_{�}^{�} - � � � � (�^{�})) ({\hat{�}}_{�}^{�} - � � � � ({\hat{�}}^{�}))}{\sqrt{\sum_{� \in �_{test}} {(�_{�}^{�} - � � � � (�^{�}))}^{2} {({\hat{�}}_{�}^{�} - � � � � ({\hat{�}}^{�}))}^{2}}}, \end{array}

(11)

where

�

, as defined in Section 2, represents the number of sensors;

�_{test}

denotes the set of time stamps for testing;

�_{�}^{�}

signifies the ground truth of the ith sensor at time

�

; and

{\hat{�}}_{�}^{�}

represents the prediction for the ith sensor at time

�

. Additionally,

�^{�}

and

{\hat{�}}^{�}

denote the ground truth and prediction for the

�

th sensor in

�_{test}

, respectively.

3 EXPERIMENT

A prediction framework was developed for the Nanjing Yangtze River tunnel, using the aforementioned methodology. Data experiments were conducted to evaluate the effectiveness of ALSTNet. Additionally, a carefully designed ablation study was performed to explore the impact of two important parameters on ALSTNet's performance.

3.1 Baseline

To showcase the superiority of the proposed method, it was compared with several classic predictive models, which serve as the baseline models.

Linear regression (LR): The model examines the relationship between the dependent variable and independent variables. It assumes a linear correlation between the independent variables and the dependent variable, following a multivariate linear equation. The parameters of the model are obtained by minimizing the loss function.

Support vector regression (SVR): As a supervised learning algorithm, SVR utilizes kernel functions to solve nonlinear problems with high dimensionality. It shows rapid convergence and efficiency by detecting correlations between output and input data.

Multilayer perceptron (MLP): MLP is a type of artificial neural network that may contain multiple hidden layers between the input and output layers. The simplest MLP consists of only one hidden layer, and the input of the next layer is the output of the previous layer. Due to the inclusion of hidden layers, MLP possesses the ability to fit complex functions effectively.

Recurrent neural network (RNN): This has been introduced in Section 5.

Long short-term memory (LSTM): LSTM is an improvement over RNN, specifically designed to address long-term dependency issues such as gradient explosion and gradient vanishing. It utilizes cell states and gates to handle various memory unit operations.

Gated recurrent unit (GRU): GRU is a variant derived from LSTM. It combines the forget gate and the input gate into a single update gate and integrates the cell state and the hidden state. As a result, GRU is simpler than standard LSTM but shows similar effectiveness.

It is worth noting that LR and SVR are usually used for univariate time-series prediction. However, in the actual code, a multioutput regressor in Sklearn is used to enable their use for multivariate time-series prediction. This adjustment makes it possible to include them in the comparison with the other models.

3.2 Data set and model setup

This study highlights the practical application of the proposed model by conducting a case study on the Nanjing Yangtze River tunnel. This tunnel serves as a representative example of an underwater shield tunnel and is equipped with a sophisticated SHMS for real-time monitoring. The SHMS has been in operation since July 2016, and it relies on fiber optical sensors as the primary instruments for field monitoring. To ensure comprehensive monitoring coverage, 10 monitoring sections were strategically chosen for sensor installation. Within each monitoring section, 20 stress sensors, four water pressure sensors, and two temperature sensors were preembedded in segments to capture relevant data.

This study specifically focuses on the monitoring data from 28 stress sensors located at various segments within the tunnel. These sensors continuously measure the resistance caused by external loads acting on the tunnel structure. The monitoring data are recorded at hourly intervals, generating a total of 1632 stress records. Each record contains stress values corresponding to all selected sensors. These observations are divided into training, validation, and testing data, with a ratio of 0.7, 0.1, and 0.2, respectively. Normalization is performed using MaxMin normalization, scaling the data to [0,1].

For the autoencoder used in this study, the parameter $�$ is set to 1. The dimension sizes for the input layer, hidden layer, and output layer in the autoencoder are 28, 10, and 28, respectively. To introduce nonlinearity, the sigmoid function is adopted as the activation function for both the encoder and the decoder. The autoencoder is trained on the training data using the Adam optimizer with a learning rate of 0.002 and a batch size of 16. The best autoencoder model is saved based on minimal error observed on the validation data. This model is then used to compress 28 values observed every hour into a 10-dimensional feature vector for the proposed prediction method.

In the proposed prediction method, the batch size is set to 16 and the window $�$ is set to 24 because the information in the 1-day trend is enough for future prediction. This parameter will also be studied later. The $�$ is varied in ${4,8,12}$ , with each value corresponding to one experiment. In every experiment, the hidden state size in RNN (8, 12, 16, 20) and the learning rates of the Adam optimizer (0.0005, 0.0008, 0.0010) vary for determining the optimal settings. Also, the best prediction model is saved when the error is minimal on validation data.

All methods are implemented using Python 3.5.2, with deep learning methods implemented using TensorFlow 1.12. The experiments are conducted on a computer equipped with an Intel i7-7700 CPU, 4 cores, and 16 GB RAM.

3.3 Experiment result

Table 1 presents a comprehensive evaluation of all methods across various test sets and metrics. The horizon $�$ is set as ${4,8,12}$ , representing different prediction timeframes, where larger horizons imply more challenging prediction tasks. The best results for each horizon are highlighted in boldface, highlighting the superior performance of the proposed prediction framework, ALSTNet.

Table 1. Summary of results (in RMSE, MAE, MAPE, and PCC) of all methods when the window size is 24.

Methods	RMSE	MAE	MAPE (%)	PCC	RMSE	MAE	MAPE (%)	PCC	RMSE	MAE	MAPE (%)	PCC
Methods		q = 4				q = 8				q = 12
LR	2.251	1.752	1.424	0.834	2.588	2.038	1.662	0.800	3.353	2.604	2.098	0.747
SVR	2.013	1.544	1.229	0.883	2.285	1.726	1.345	0.858	2.414	1.793	1.368	0.853
MLP	2.864	2.242	1.779	0.841	3.283	2.555	1.969	0.822	3.642	2.740	2.064	0.684
RNN	2.239	1.769	1.475	0.849	2.454	1.892	1.537	0.831	2.688	2.051	1.599	0.819
GRU	2.119	1.654	1.385	0.871	2.337	1.766	1.458	0.838	2.539	1.945	1.585	0.817
LSTM	2.604	2.011	1.857	0.859	2.715	2.135	1.813	0.816	2.859	2.202	1.795	0.787
ALSTNet	1.707	1.334	1.101	0.910	1.963	1.480	1.157	0.889	2.224	1.684	1.321	0.867

Note: The bolded values represent the best experimental results of all models.

The proposed ALSTNet outperforms all baselines across all settings. Specifically, ALSTNet demonstrates remarkable superiority over the two strong baselines, SVR and GRU, by margins of 15.2% and 19.4% in the RMSE metric for a horizon of 4. Similarly, for horizons of 8 and 12, ALSTNet outperforms SVR and GRU by 14.1% and 16.0%, as well as 7.87% and 12.4%, respectively, in the RMSE metric. Moreover, in the other three metrics, the proposed framework consistently outperforms all baselines, showcasing its effectiveness in accurately forecasting structural responses.

To further illustrate the effectiveness of the proposed method, Figure 3 visually compares the performance of SVR, GRU, and ALSTNet on the testing data with a horizon set as 8. The plot shows the ground truth curve and the predicted values by SVR, GRU, and ALSTNet over the set of time stamps for testing. The blue curve represents the true data, while the red curve denotes the system-forecasted signals.

Figure 3 clearly demonstrates that SVR and GRU can only capture the overall general trend of the structural response evolution process while neglecting the finer variations within a day. Their performance is limited to handling long-term trends. In contrast, the prediction results of the proposed ALSTNet model align closely with the true data. This model effectively captures both the long-term trend and the short-term ups and downs within a day, showcasing its ability to predict the structural response hourly with remarkable accuracy. This level of precision is crucial in real-world applications, where traditional forecasting models often fall short.

3.4 Ablation study

To assess the effectiveness of the framework design, a meticulous ablation study was conducted by selectively using partial components from the original framework. These components are categorized as follows:

1.
$DAILY$ : This component relies solely on forecasting results from $�_{�}$ .
2.
RNN: Here, only the RNN is used for long-term trend forecasting.
3.
RNN+DAILY: These components combine the long-term trend forecasting result from RNN with the short-term daily dependency $�_{�}$ .
4.
AE+RNN: This category involves the use of an autoencoder to obtain essential base features, which are then fed into the RNN for long-term trend forecasting.

To ensure fair comparisons and eliminate performance gains induced by model complexity, the hidden dimensions of these models are tuned to match those of the complete proposed framework. The window size $�$ is set to 24 for consistency. Figure 4 illustrates the test results obtained from these different components.

Several noteworthy observations arise from these results:

1.
Neither DAILY nor RNN alone performs satisfactorily in prediction. However, the integration of these two components, as seen in RNN+DAILY, results in a significant performance improvement. This highlights the efficiency of combining long-term trends with short-term daily dependencies.
2.
Adopting an autoencoder to reduce the dimensionality of high-dimensional data and using the encoded features as input for the RNN (AE+RNN) also leads to performance improvement compared to using only RNN for forecasting.
3.
Despite these variations, the best prediction results for each horizon are consistently achieved with the full ALSTNet framework.

These findings highlight the superiority of the proposed ALSTNet over individual components and its ability to effectively capture both long-term trends and short-term daily dependencies, making it a robust and versatile solution for accurate structural response forecasting.

3.5 Parameter analysis

The window size $�$ and horizon $�$ are critical parameters that significantly influence the performance of the proposed framework. Experiments were conducted to analyze their effects on the predictive capabilities of the model.

For the variable window size $�$ , the values within the range of ${6,12,18,24,30,36,42,48}$ were tested, while the horizon $�$ was set to 4. Figure 5 presents the results in terms of RMSE, MAE, MAPE, and PCC. From the observations, it can be found that as $�$ increases from small values, such as 6, the prediction performance steadily improves. This is because smaller values of $�$ provide limited useful information for the prediction model to make accurate forecasts. However, as $�$ reaches 24, the model achieves its optimal performance, indicating that this window size strikes a balance between capturing enough useful information for accurate predictions and avoiding unnecessary complexity. As $� exceeds$ 24, the performance starts to decline, as larger values introduce redundant information into the model, leading to increased complexity and longer training processes that negatively affect performance. Therefore, for the proposed framework, $� = 24$ is the recommended setting.

In the case of variable horizon $�$ , experiments were conducted with $�$ ranging from {2,4,6,8,10,12,14,16,18,20,22,24}, while the window size $�$ was set at 24. Figure 6 illustrates the results in terms of RMSE, MAE, MAPE, and PCC. As can be seen from the figure, the performance declines as the horizon $�$ increases, particularly when $�$ surpasses 12, where the performance declines more significantly. This is due to the fact that as the time scale increases, future strain values become more similar to their respective closing time values, and the long-term history of strain reflects the future strain mechanism less effectively. Consequently, the model's performance deteriorates with increasing horizon, as the predictive task becomes more challenging.

4 APPLICATION

As a promising application, ALSTNet was used in the monitoring of the Nanjing Yangtze River tunnel to predict the structural responses recorded by multiple sensors.

To monitor and manage the tunnel in a scientific and effective manner, ALSTNet was utilized to predict the strain of the tunnel for the next 24 h. To achieve this, historical strain responses recorded by all gauges were used to train an autoencoder, making it possible to extract essential features from the strain data.

The prediction process was conducted as follows: At each time step $�$ , the strain responses from time $� - 23$ up to the current time $�$ and the daily dependency for time $� + 1$ are used as inputs for ALSTNet. This setup enables to predict the strain responses at time $� + 1$ for all gauges accurately. Subsequently, the prediction results for time $� + 1$ , combined with the strain responses from time $� - 22$ to time $�$ and the daily dependency for time $� + 2$ , are used to predict the strain responses for time $� + 2$ . With this iterative process continuing, the strain responses for the future 24 h can be predicted in a sequential manner.

As an illustration, Figure 7 shows the predicted strain variation for the next 24 h for two of the gauges in the tunnel. The ALSTNet model effectively predicts the strain responses, making it possible to anticipate the structural behavior over the specified time period with considerable accuracy.

5 CONCLUSION

To address the critical need to prevent infrastructure disasters and ensure stability, this study introduced an enhanced prediction model to proactively detect abnormal variations in structural mechanical behaviors. The proposed model considered various internal and external factors that influence the future mechanical behaviors of structures and addressed the challenge of simultaneous prediction for multivariate time series. The key findings and conclusions drawn from this study are summarized as follows:

1.
A novel data-driven model, named ALSTNet, was presented for predicting the structural mechanical behaviors at multiple positions in the field. ALSTNet incorporates the impact of both long- and short-term historical behaviors, as well as the spatial mechanical correlation achieved through encoding the networking formed by multivariate time series.
2.
Based on the proposed model, data experiments were conducted using monitoring data recorded by an SHMS installed in an underwater shield tunnel. The predicted results obtained from ALSTNet were compared with those from several baseline models, including LR, SVR, MLP, LSTM, and RNN. The findings reveal that ALSTNet outperforms the baseline models in terms of prediction accuracy, highlighting its effectiveness and superiority.
3.
To validate the robustness of the presented model, an ablation study and parameter analysis were conducted. The ablation study demonstrated that all components of ALSTNet significantly contribute to its excellent predictive performance. The parameter analysis revealed a strong correlation between the short-term mechanical behavior of the tunnel structure and its historical behavior over the past 24 h. Additionally, the prediction accuracy decreases with an increase in the prediction horizon, emphasizing the importance of appropriate time scales for accurate predictions.
4.
As a crucial real-world application, the proposed model was used to predict the strain variation at multiple points in the Nanjing Dinghuaimen tunnel for 24 h on end. This application holds immense significance in preventing disasters in practical engineering scenarios and serves as an invaluable reference for similar engineering projects.

ACKNOWLEDGMENTS

We thank the reviewers for providing valuable feedback on this research work. The successful completion of this study was supported by the National Key R&D Program of China No. 2018YFB2101003, the National Natural Science Foundation of China under Grant No. 51991395, U1806226, 51778033, 51822802, 71901011, U1811463, 51991391, and the Science and Technology Major Project of Beijing under Grant No. Z191100002519012.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.

Biography

Dr. Xuyan Tan obtained her BSc degree in Safety Engineering from Shandong University of Science and Technology, China, in 2016, and her PhD in Geotechnical Engineering from the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, China, in 2021. Currently, she is a research assistant professor at the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Her research interests include (1) intelligent monitoring for the spatio-temporal mechanical behaviors of underground engineering and (2) the application of deep learning technology in the analysis of structural mechanical response, anomaly diagnosis, and early warning in the field.