1. Introduction
As a crucial social engineering infrastructure, dams must be operated safely to guarantee the needs of a steadily growing national economy are met. Unfortunately, due to the inherent physical limitations of dam materials, dams often have unhealthy structural responses such as dam body cracking and abnormal deformation [
1]. In order to reduce the probability of engineering failures, most dams are equipped with precise health monitoring systems to evaluate their operational behavior and health through real-time measurements of multiple structural and environmental indicators. Among the many monitoring indicators, dam deformation is easy to measure and intuitively reflects the overall structural response state [
2]. In order to improve the effectiveness of management strategies, research focused on accurately predicting dam deformation has increased in recent years. This area of research commonly uses simulations, and the most commonly used forecasting models can be categorized as mathematical statistical models or artificial intelligence models.
Hydrostatic-seasonal-time (HST) can be considered a representative flagship statistical regression model, it quantitatively interprets the influencing factors behind dam deformation based on the assumptions of mechanical theory and, then, performs a linear approximation fitting using the observed data. It was originally proposed by Willm et al. [
3] to forecast deformation of concrete dams and has since been widely implemented. However, there is a strong correlation between dam water level and ambient temperature, which directly influences environmental loads and dam integrity, but the HST model does not consider local air temperature, which will be detrimental to the prediction accuracy under extreme weather conditions. To make up for these shortcomings, Penot et al. [
4] proposed the hydrostatic-seasonal-time-temperature (HSTT) model by correcting the thermal component based on the actual air temperature. Another common approach has been to replace the thermal component with the actual temperature inside dams, which prompted the advent of the hydrostatic-thermal-time (HTT) model. Mata et al. [
5] used a combined principal component analysis (PCA) method to include dam temperature in the model construction and applied the HTT model to explain the observed displacement of a concrete dam more accurately and with a lower residual standard deviation. In addition, there is a certain delay before a dam responds to changes in load, this can be observed in the influence of water level on pore water pressure and temperature on the thermal field of dams. The most popular solution is to add moving averages or gradients of original variables to the model to supplement the delayed information. For example, Popovici et al. [
6] added the moving averages of air temperature for the previous 3, 10, and 30 days and the water level for the previous 3 days as variables to improve the performance of the dam deformation prediction model.
Mathematical statistical models generally output linear relationships between impact factors and target variables. The coefficients are determined by the least squares method using a building process that is simple and easy to understand. However, in practice, the relationship between dam deformation and impact factors is rarely linear and the capacity of the above models to capture nonlinear features and generalize is insufficient. To address this deficit, artificial intelligence algorithms based on machine learning have gradually attracted more attention in dam deformation prediction. The application of artificial intelligence models in dam safety monitoring systems has since become another important research subject, using approaches such as support vector machine (SVM), random forest (RF), and gaussian process (GP). The machine learning algorithm captures the characteristics of observed data through specific algorithm steps and uses the extracted characteristic information to continuously update the model to achieve the best fit. Through various complex processing operations, machine learning algorithms can obtain highly accurate predictive models that meet the management needs of safety monitoring. Mata [
7] introduced a prediction algorithm based on artificial neural networks (ANN) to map the relationship between the load and concrete dam deformation and compared it with the multiple linear regression (MLR) model. The results showed that the ANN model provided a better fit than the traditional statistical model under extreme temperatures. In addition, Kao et al. [
8] showed that the information provided by small static deformations can be enhanced by ANN-based methods. Furthermore, they developed a threshold level method for diagnosing the health of dams, and the impact of different factors on the health of dams was analyzed in detail. Recently, Ranković et al. [
9] constructed an SVM nonlinear autoregressive model with exogenous inputs to predict the nonlinear behavior of a dam’s structure. The safety measures protecting dams can be improved by being able to accurately predict the displacements of dams. Kang et al. [
10] demonstrated the accuracy of a dam deformation prediction model based on the GP method, which added the average air temperature and temperature lag information as input variables to predict the radial displacement of a concrete dam. In subsequent prediction comparisons, their GP model had the smallest error value. More recently, combinations of multiple machine learning algorithms have received increasing attention. Ren et al. [
11] used a fruit fly optimization algorithm to upgrade the SVM and applied it to the hysteresis correction of dam deformation impact factors. Subsequently, Su [
12] proposed an SVM model with a wavelet based kernel function that made full use of the discrete transformation of the wavelet function. Li et al. [
13] used the PCA method to extract the effective information from the dam temperature data as the input for the SVM model, effectively filtering redundant information from the input variables. However, the high-dimensional nonlinear tasks and the characteristic representation of time-varying dam deformation undoubtedly present a huge challenge for traditional shallow learning, meaning that the prediction accuracy of traditional machine learning algorithms is becoming increasingly unable to meet the needs of many engineering management tasks. In recent years, another branch of artificial intelligence technology, deep learning, has been vigorously developed in various industries, these approaches include convolutional neural networks (CNN), which are applied in image processing [
14,
15,
16] and speech recognition [
17,
18,
19], and long short-term memory (LSTM) models, which are applied in time series processing [
20,
21,
22]. Liu et al. [
23] proposed an approach coupling PCA with LSTM to make short-term and long-term predictions of dam observation data. Qu et al. [
24] compared LSTM and SVM prediction algorithms for dam deformation monitoring. Xu et al. [
25] decomposed dam deformation time series into linear and nonlinear parts, then used traditional statistical models to fit the linear part, while LSTM was used to capture the sequence features of the nonlinear part. Deep learning uses a layered structure to embody abstract non-linear relationships and superimposes this structure to improve the expressive ability to map complex relationships. Each layer transfers information to another, with the output of the current layer being used as the input of the next layer, until the final output is obtained. After multiple layers of feature extraction and complex information representation, a sequence feature representation model can be obtained. This layered architecture makes deep learning highly customizable, allowing it to achieve a better prediction accuracy than traditional shallow learning. Furthermore, most studies focus on improving the accuracy of predictive models, but ignore the interpretation and evaluation of input variables, which can be considered using deep learning models.
To better consider the influence of time dimension, this paper coupled an attention mechanism with an LSTM network to develop a dam deformation prediction algorithm. The attention mechanism in the time dimension can preferentially allocate the limited information processing resources in the short term to key data, while the LSTM network can extract long-term change trends from dam deformation time series. This coupled model is able to obtain more accurate dam deformation prediction results while also enriching variable interpretation in the time dimension of the prediction model. During actual monitoring, the physical deformation sensor can be affected by environmental (external) factors or internal factors, which can produce abnormal data due to equipment error. Therefore, the density-based spatial clustering of applications with noise (DBSCAN) density-based clustering algorithm is introduced to eliminate equipment-based abnormal values in real time to ensure that the observed data meet the subsequent modeling accuracy requirements. Then, the relative importance of each input variable is obtained through the variable importance measure data processing method, which not only enriches the information interpretation of the model, but also screens redundant information to reduce the difficulty of modeling. The performance of the proposed model was verified by the real-world concrete gravity dam deformation data. The main contributions of this paper can be summarized as follows:
This paper proposed and tested a DBSCAN method to filter the dam deformation time series data. The method effectively removed the equipment based abnormal values caused by environmental factors or equipment failures, thereby smoothing the random measurement errors in the observed data, which improved prediction accuracy.
The importance of input variables to the dam deformation prediction model was analyzed to interpret and evaluate the model. This resulted in a useful and efficient qualitative measure of dam deformation, which improved prevention and control of abnormal structural responses.
A coupled model was developed to better address the needs of dam deformation prediction. An attention mechanism focuses on the important variables in the short-term time dimension, while the LSTM model captures long-term change characteristics. This algorithm is very suitable for the prediction of dam deformation by accounting for time lag.
The remainder of this paper is organized as follows:
Section 2 describes the detailed process of the established mathematical model of dam deformation and the preprocessing method.
Section 3 introduces the selection of input variables, and the design and operation of the comparative experimental model.
Section 4 elaborates on a case study from which actual monitoring data was collected.
Section 5 explains and analyzes the input variables and evaluates the performance of the proposed coupled method. Finally, conclusions and future research directions are provided in
Section 6.